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piscal/dataassim/math/optimization/d_odr.f
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poprhythm d40505e161 Initial commit
2016-02-03 18:52:05 +00:00

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*DMPREC
DOUBLE PRECISION FUNCTION DMPREC()
C***BEGIN PROLOGUE DPREC
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE DETERMINE MACHINE PRECISION FOR TARGET MACHINE AND COMPILER
C ASSUMING FLOATING-POINT NUMBERS ARE REPRESENTED IN THE
C T-DIGIT, BASE-B FORM
C SIGN (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
C WHERE 0 .LE. X(I) .LT. B FOR I=1,...,T, AND
C 0 .LT. X(1).
C TO ALTER THIS FUNCTION FOR A PARTICULAR TARGET MACHINE,
C EITHER
C ACTIVATE THE DESIRED SET OF DATA STATEMENTS BY
C REMOVING THE C FROM COLUMN 1
C OR
C SET B, TD AND TS USING I1MACH BY ACTIVATING
C THE DECLARATION STATEMENTS FOR I1MACH
C AND THE STATEMENTS PRECEEDING THE FIRST
C EXECUTABLE STATEMENT BELOW.
C***END PROLOGUE DPREC
C...LOCAL SCALARS
DOUBLE PRECISION
+ B
INTEGER
+ TD,TS
C...EXTERNAL FUNCTIONS
C INTEGER
C + I1MACH
C EXTERNAL
C + I1MACH
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C DOUBLE PRECISION B
C THE BASE OF THE TARGET MACHINE.
C (MAY BE DEFINED USING I1MACH(10).)
C INTEGER TD
C THE NUMBER OF BASE-B DIGITS IN DOUBLE PRECISION.
C (MAY BE DEFINED USING I1MACH(14).)
C INTEGER TS
C THE NUMBER OF BASE-B DIGITS IN SINGLE PRECISION.
C (MAY BE DEFINED USING I1MACH(11).)
C MACHINE CONSTANTS FOR COMPUTERS FOLLOWING IEEE ARITHMETIC STANDARD
C (E.G., MOTOROLA 68000 BASED MACHINES SUCH AS SUN AND SPARC
C WORKSTATIONS, AND AT&T PC 7300; AND 8087 BASED MICROS SUCH AS THE
C IBM PC AND THE AT&T 6300).
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 53 /
C MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM.
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 60 /
C MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM
C THE BURROUGHS 6700/7700 SYSTEMS
C DATA B / 8 /
C DATA TS / 13 /
C DATA TD / 26 /
C MACHINE CONSTANTS FOR THE CDC 6000/7000 (FTN5 COMPILER)
C THE CYBER 170/180 SERIES UNDER NOS
C DATA B / 2 /
C DATA TS / 48 /
C DATA TD / 96 /
C MACHINE CONSTANTS FOR THE CDC 6000/7000 (FTN COMPILER)
C THE CYBER 170/180 SERIES UNDER NOS/VE
C THE CYBER 200 SERIES
C DATA B / 2 /
C DATA TS / 47 /
C DATA TD / 94 /
C MACHINE CONSTANTS FOR THE CRAY
C DATA B / 2 /
C DATA TS / 47 /
C DATA TD / 94 /
C MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C MACHINE CONSTANTS FOR THE HARRIS COMPUTER
C DATA B / 2 /
C DATA TS / 23 /
C DATA TD / 38 /
C MACHINE CONSTANTS FOR THE HONEYWELL DPS 8/70
C THE HONEYWELL 600/6000 SERIES
C DATA B / 2 /
C DATA TS / 27 /
C DATA TD / 63 /
C MACHINE CONSTANTS FOR THE HP 2100
C (3 WORD DOUBLE PRECISION OPTION WITH FTN4)
C DATA B / 2 /
C DATA TS / 23 /
C DATA TD / 39 /
C MACHINE CONSTANTS FOR THE HP 2100
C (4 WORD DOUBLE PRECISION OPTION WITH FTN4)
C DATA B / 2 /
C DATA TS / 23 /
C DATA TD / 55 /
C MACHINE CONSTANTS FOR THE IBM 360/370 SERIES
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C MACHINE CONSTANTS FOR THE IBM PC
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 53 /
C MACHINE CONSTANTS FOR THE INTERDATA (PERKIN ELMER) 7/32
C INTERDATA (PERKIN ELMER) 8/32
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR).
C DATA B / 2 /
C DATA TS / 27 /
C DATA TD / 54 /
C MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR).
C DATA B / 2 /
C DATA TS / 27 /
C DATA TD / 62 /
C MACHINE CONSTANTS FOR THE PDP-11 SYSTEM
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 56 /
C MACHINE CONSTANTS FOR THE PERKIN-ELMER 3230
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C MACHINE CONSTANTS FOR THE PRIME 850 AND PRIME 4050
C DATA B / 2 /
C DATA TS / 23 /
C DATA TD / 47 /
C MACHINE CONSTANTS FOR THE SEL SYSTEMS 85/86
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C MACHINE CONSTANTS FOR SUN AND SPARC WORKSTATIONS
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 53 /
C MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES
C DATA B / 2 /
C DATA TS / 27 /
C DATA TD / 60 /
C MACHINE CONSTANTS FOR THE VAX-11 WITH FORTRAN IV-PLUS COMPILER
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 56 /
C MACHINE CONSTANTS FOR THE VAX/VMS SYSTEM WITHOUT G_FLOATING
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 56 /
C MACHINE CONSTANTS FOR THE VAX/VMS SYSTEM WITH G_FLOATING
C DATA B / 2 /
C DATA TS / 24 /
C DATA TD / 53 /
C MACHINE CONSTANTS FOR THE XEROX SIGMA 5/7/9
C DATA B / 16 /
C DATA TS / 6 /
C DATA TD / 14 /
C***FIRST EXECUTABLE STATEMENT DMPREC
C B = I1MACH(10)
C TS = I1MACH(11)
C TD = I1MACH(14)
DMPREC = B ** (1-TD)
RETURN
END
*DASUM
DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX)
C***BEGIN PROLOGUE DASUM
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A3A
C***KEYWORDS ADD,BLAS,DOUBLE PRECISION,LINEAR ALGEBRA,MAGNITUDE,SUM,
C VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE SUM OF MAGNITUDES OF D.P. VECTOR COMPONENTS
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C --OUTPUT--
C DASUM DOUBLE PRECISION RESULT (ZERO IF N .LE. 0)
C RETURNS SUM OF MAGNITUDES OF DOUBLE PRECISION DX.
C DASUM = SUM FROM 0 TO N-1 OF DABS(DX(1+I*INCX))
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DASUM
C...SCALAR ARGUMENTS
INTEGER
+ INCX,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*)
C...LOCAL SCALARS
INTEGER
+ I,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS,MOD
C***FIRST EXECUTABLE STATEMENT DASUM
DASUM = 0.D0
IF(N.LE.0)RETURN
IF(INCX.EQ.1)GOTO 20
C CODE FOR INCREMENTS NOT EQUAL TO 1.
NS = N*INCX
DO 10 I=1,NS,INCX
DASUM = DASUM + DABS(DX(I))
10 CONTINUE
RETURN
C CODE FOR INCREMENTS EQUAL TO 1.
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 6.
20 M = MOD(N,6)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DASUM = DASUM + DABS(DX(I))
30 CONTINUE
IF( N .LT. 6 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,6
DASUM = DASUM + DABS(DX(I)) + DABS(DX(I+1)) + DABS(DX(I+2))
1 + DABS(DX(I+3)) + DABS(DX(I+4)) + DABS(DX(I+5))
50 CONTINUE
RETURN
END
*DAXPY
SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE DAXPY
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A7
C***KEYWORDS BLAS,DOUBLE PRECISION,LINEAR ALGEBRA,TRIAD,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE D.P COMPUTATION Y = A*X + Y
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DA DOUBLE PRECISION SCALAR MULTIPLIER
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C DY DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCY STORAGE SPACING BETWEEN ELEMENTS OF DY
C --OUTPUT--
C DY DOUBLE PRECISION RESULT (UNCHANGED IF N .LE. 0)
C OVERWRITE DOUBLE PRECISION DY WITH DOUBLE PRECISION DA*DX + DY.
C FOR I = 0 TO N-1, REPLACE DY(LY+I*INCY) WITH DA*DX(LX+I*INCX) +
C DY(LY+I*INCY), WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N
C AND LY IS DEFINED IN A SIMILAR WAY USING INCY.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DAXPY
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ DA
INTEGER
+ INCX,INCY,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*),DY(*)
C...LOCAL SCALARS
INTEGER
+ I,IX,IY,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DAXPY
IF(N.LE.0.OR.DA.EQ.0.D0) RETURN
IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
5 CONTINUE
C CODE FOR NONEQUAL OR NONPOSITIVE INCREMENTS.
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DY(IY) = DY(IY) + DA*DX(IX)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 4.
20 M = MOD(N,4)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DY(I) = DY(I) + DA*DX(I)
30 CONTINUE
IF( N .LT. 4 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,4
DY(I) = DY(I) + DA*DX(I)
DY(I + 1) = DY(I + 1) + DA*DX(I + 1)
DY(I + 2) = DY(I + 2) + DA*DX(I + 2)
DY(I + 3) = DY(I + 3) + DA*DX(I + 3)
50 CONTINUE
RETURN
C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
60 CONTINUE
NS = N*INCX
DO 70 I=1,NS,INCX
DY(I) = DA*DX(I) + DY(I)
70 CONTINUE
RETURN
END
*DCHEX
SUBROUTINE DCHEX(R,LDR,P,K,L,Z,LDZ,NZ,C,S,JOB)
C***BEGIN PROLOGUE DCHEX
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D7B
C***KEYWORDS CHOLESKY DECOMPOSITION,DOUBLE PRECISION,EXCHANGE,
C LINEAR ALGEBRA,LINPACK,MATRIX,POSITIVE DEFINITE
C***AUTHOR STEWART, G. W., (U. OF MARYLAND)
C***PURPOSE UPDATES THE CHOLESKY FACTORIZATION A=TRANS(R)*R OF A
C POSITIVE DEFINITE MATRIX A OF ORDER P UNDER DIAGONAL
C PERMUTATIONS OF THE FORM TRANS(E)*A*E WHERE E IS A
C PERMUTATION MATRIX.
C***DESCRIPTION
C DCHEX UPDATES THE CHOLESKY FACTORIZATION
C A = TRANS(R)*R
C OF A POSITIVE DEFINITE MATRIX A OF ORDER P UNDER DIAGONAL
C PERMUTATIONS OF THE FORM
C TRANS(E)*A*E
C WHERE E IS A PERMUTATION MATRIX. SPECIFICALLY, GIVEN
C AN UPPER TRIANGULAR MATRIX R AND A PERMUTATION MATRIX
C E (WHICH IS SPECIFIED BY K, L, AND JOB), DCHEX DETERMINES
C AN ORTHOGONAL MATRIX U SUCH THAT
C U*R*E = RR,
C WHERE RR IS UPPER TRIANGULAR. AT THE USERS OPTION, THE
C TRANSFORMATION U WILL BE MULTIPLIED INTO THE ARRAY Z.
C IF A = TRANS(X)*X, SO THAT R IS THE TRIANGULAR PART OF THE
C QR FACTORIZATION OF X, THEN RR IS THE TRIANGULAR PART OF THE
C QR FACTORIZATION OF X*E, I.E. X WITH ITS COLUMNS PERMUTED.
C FOR A LESS TERSE DESCRIPTION OF WHAT DCHEX DOES AND HOW
C IT MAY BE APPLIED, SEE THE LINPACK GUIDE.
C THE MATRIX Q IS DETERMINED AS THE PRODUCT U(L-K)*...*U(1)
C OF PLANE ROTATIONS OF THE FORM
C ( C(I) S(I) )
C ( ) ,
C ( -S(I) C(I) )
C WHERE C(I) IS DOUBLE PRECISION. THE ROWS THESE ROTATIONS OPERATE
C ON ARE DESCRIBED BELOW.
C THERE ARE TWO TYPES OF PERMUTATIONS, WHICH ARE DETERMINED
C BY THE VALUE OF JOB.
C 1. RIGHT CIRCULAR SHIFT (JOB = 1).
C THE COLUMNS ARE REARRANGED IN THE FOLLOWING ORDER.
C 1,...,K-1,L,K,K+1,...,L-1,L+1,...,P.
C U IS THE PRODUCT OF L-K ROTATIONS U(I), WHERE U(I)
C ACTS IN THE (L-I,L-I+1)-PLANE.
C 2. LEFT CIRCULAR SHIFT (JOB = 2).
C THE COLUMNS ARE REARRANGED IN THE FOLLOWING ORDER
C 1,...,K-1,K+1,K+2,...,L,K,L+1,...,P.
C U IS THE PRODUCT OF L-K ROTATIONS U(I), WHERE U(I)
C ACTS IN THE (K+I-1,K+I)-PLANE.
C ON ENTRY
C R DOUBLE PRECISION(LDR,P), WHERE LDR .GE. P.
C R CONTAINS THE UPPER TRIANGULAR FACTOR
C THAT IS TO BE UPDATED. ELEMENTS OF R
C BELOW THE DIAGONAL ARE NOT REFERENCED.
C LDR INTEGER.
C LDR IS THE LEADING DIMENSION OF THE ARRAY R.
C P INTEGER.
C P IS THE ORDER OF THE MATRIX R.
C K INTEGER.
C K IS THE FIRST COLUMN TO BE PERMUTED.
C L INTEGER.
C L IS THE LAST COLUMN TO BE PERMUTED.
C L MUST BE STRICTLY GREATER THAN K.
C Z DOUBLE PRECISION(LDZ,N)Z), WHERE LDZ .GE. P.
C Z IS AN ARRAY OF NZ P-VECTORS INTO WHICH THE
C TRANSFORMATION U IS MULTIPLIED. Z IS
C NOT REFERENCED IF NZ = 0.
C LDZ INTEGER.
C LDZ IS THE LEADING DIMENSION OF THE ARRAY Z.
C NZ INTEGER.
C NZ IS THE NUMBER OF COLUMNS OF THE MATRIX Z.
C JOB INTEGER.
C JOB DETERMINES THE TYPE OF PERMUTATION.
C JOB = 1 RIGHT CIRCULAR SHIFT.
C JOB = 2 LEFT CIRCULAR SHIFT.
C ON RETURN
C R CONTAINS THE UPDATED FACTOR.
C Z CONTAINS THE UPDATED MATRIX Z.
C C DOUBLE PRECISION(P).
C C CONTAINS THE COSINES OF THE TRANSFORMING ROTATIONS.
C S DOUBLE PRECISION(P).
C S CONTAINS THE SINES OF THE TRANSFORMING ROTATIONS.
C LINPACK. THIS VERSION DATED 08/14/78 .
C G. W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DROTG
C***END PROLOGUE DCHEX
C...SCALAR ARGUMENTS
INTEGER
+ JOB,K,L,LDR,LDZ,NZ,P
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ C(*),R(LDR,*),S(*),Z(LDZ,*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ T,T1
INTEGER
+ I,II,IL,IU,J,JJ,KM1,KP1,LM1,LMK
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DROTG
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MAX0,MIN0
C***FIRST EXECUTABLE STATEMENT DCHEX
KM1 = K - 1
KP1 = K + 1
LMK = L - K
LM1 = L - 1
C PERFORM THE APPROPRIATE TASK.
GO TO (10,130), JOB
C RIGHT CIRCULAR SHIFT.
10 CONTINUE
C REORDER THE COLUMNS.
DO 20 I = 1, L
II = L - I + 1
S(I) = R(II,L)
20 CONTINUE
DO 40 JJ = K, LM1
J = LM1 - JJ + K
DO 30 I = 1, J
R(I,J+1) = R(I,J)
30 CONTINUE
R(J+1,J+1) = 0.0D0
40 CONTINUE
IF (K .EQ. 1) GO TO 60
DO 50 I = 1, KM1
II = L - I + 1
R(I,K) = S(II)
50 CONTINUE
60 CONTINUE
C CALCULATE THE ROTATIONS.
T = S(1)
DO 70 I = 1, LMK
T1 = S(I)
CALL DROTG(S(I+1),T,C(I),T1)
S(I) = T1
T = S(I+1)
70 CONTINUE
R(K,K) = T
DO 90 J = KP1, P
IL = MAX0(1,L-J+1)
DO 80 II = IL, LMK
I = L - II
T = C(II)*R(I,J) + S(II)*R(I+1,J)
R(I+1,J) = C(II)*R(I+1,J) - S(II)*R(I,J)
R(I,J) = T
80 CONTINUE
90 CONTINUE
C IF REQUIRED, APPLY THE TRANSFORMATIONS TO Z.
IF (NZ .LT. 1) GO TO 120
DO 110 J = 1, NZ
DO 100 II = 1, LMK
I = L - II
T = C(II)*Z(I,J) + S(II)*Z(I+1,J)
Z(I+1,J) = C(II)*Z(I+1,J) - S(II)*Z(I,J)
Z(I,J) = T
100 CONTINUE
110 CONTINUE
120 CONTINUE
GO TO 260
C LEFT CIRCULAR SHIFT
130 CONTINUE
C REORDER THE COLUMNS
DO 140 I = 1, K
II = LMK + I
S(II) = R(I,K)
140 CONTINUE
DO 160 J = K, LM1
DO 150 I = 1, J
R(I,J) = R(I,J+1)
150 CONTINUE
JJ = J - KM1
S(JJ) = R(J+1,J+1)
160 CONTINUE
DO 170 I = 1, K
II = LMK + I
R(I,L) = S(II)
170 CONTINUE
DO 180 I = KP1, L
R(I,L) = 0.0D0
180 CONTINUE
C REDUCTION LOOP.
DO 220 J = K, P
IF (J .EQ. K) GO TO 200
C APPLY THE ROTATIONS.
IU = MIN0(J-1,L-1)
DO 190 I = K, IU
II = I - K + 1
T = C(II)*R(I,J) + S(II)*R(I+1,J)
R(I+1,J) = C(II)*R(I+1,J) - S(II)*R(I,J)
R(I,J) = T
190 CONTINUE
200 CONTINUE
IF (J .GE. L) GO TO 210
JJ = J - K + 1
T = S(JJ)
CALL DROTG(R(J,J),T,C(JJ),S(JJ))
210 CONTINUE
220 CONTINUE
C APPLY THE ROTATIONS TO Z.
IF (NZ .LT. 1) GO TO 250
DO 240 J = 1, NZ
DO 230 I = K, LM1
II = I - KM1
T = C(II)*Z(I,J) + S(II)*Z(I+1,J)
Z(I+1,J) = C(II)*Z(I+1,J) - S(II)*Z(I,J)
Z(I,J) = T
230 CONTINUE
240 CONTINUE
250 CONTINUE
260 CONTINUE
RETURN
END
*DCOPY
SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE DCOPY
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A5
C***KEYWORDS BLAS,COPY,DOUBLE PRECISION,LINEAR ALGEBRA,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE D.P. VECTOR COPY Y = X
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C DY DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCY STORAGE SPACING BETWEEN ELEMENTS OF DY
C --OUTPUT--
C DY COPY OF VECTOR DX (UNCHANGED IF N .LE. 0)
C COPY DOUBLE PRECISION DX TO DOUBLE PRECISION DY.
C FOR I = 0 TO N-1, COPY DX(LX+I*INCX) TO DY(LY+I*INCY),
C WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N, AND LY IS
C DEFINED IN A SIMILAR WAY USING INCY.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DCOPY
C...SCALAR ARGUMENTS
INTEGER
+ INCX,INCY,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*),DY(*)
C...LOCAL SCALARS
INTEGER
+ I,IX,IY,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DCOPY
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
5 CONTINUE
C CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DY(IY) = DX(IX)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 7.
20 M = MOD(N,7)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DY(I) = DX(I)
30 CONTINUE
IF( N .LT. 7 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,7
DY(I) = DX(I)
DY(I + 1) = DX(I + 1)
DY(I + 2) = DX(I + 2)
DY(I + 3) = DX(I + 3)
DY(I + 4) = DX(I + 4)
DY(I + 5) = DX(I + 5)
DY(I + 6) = DX(I + 6)
50 CONTINUE
RETURN
C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
60 CONTINUE
NS=N*INCX
DO 70 I=1,NS,INCX
DY(I) = DX(I)
70 CONTINUE
RETURN
END
*DDOT
DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE DDOT
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A4
C***KEYWORDS BLAS,DOUBLE PRECISION,INNER PRODUCT,LINEAR ALGEBRA,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE D.P. INNER PRODUCT OF D.P. VECTORS
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C DY DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCY STORAGE SPACING BETWEEN ELEMENTS OF DY
C --OUTPUT--
C DDOT DOUBLE PRECISION DOT PRODUCT (ZERO IF N .LE. 0)
C RETURNS THE DOT PRODUCT OF DOUBLE PRECISION DX AND DY.
C DDOT = SUM FOR I = 0 TO N-1 OF DX(LX+I*INCX) * DY(LY+I*INCY)
C WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N, AND LY IS
C DEFINED IN A SIMILAR WAY USING INCY.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DDOT
C...SCALAR ARGUMENTS
INTEGER
+ INCX,INCY,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*),DY(*)
C...LOCAL SCALARS
INTEGER
+ I,IX,IY,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DDOT
DDOT = 0.D0
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
5 CONTINUE
C CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DDOT = DDOT + DX(IX)*DY(IY)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C CODE FOR BOTH INCREMENTS EQUAL TO 1.
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5.
20 M = MOD(N,5)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DDOT = DDOT + DX(I)*DY(I)
30 CONTINUE
IF( N .LT. 5 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,5
DDOT = DDOT + DX(I)*DY(I) + DX(I+1)*DY(I+1) +
1 DX(I + 2)*DY(I + 2) + DX(I + 3)*DY(I + 3) + DX(I + 4)*DY(I + 4)
50 CONTINUE
RETURN
C CODE FOR POSITIVE EQUAL INCREMENTS .NE.1.
60 CONTINUE
NS = N*INCX
DO 70 I=1,NS,INCX
DDOT = DDOT + DX(I)*DY(I)
70 CONTINUE
RETURN
END
*DNRM2
DOUBLE PRECISION FUNCTION DNRM2(N,DX,INCX)
C***BEGIN PROLOGUE DNRM2
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A3B
C***KEYWORDS BLAS,DOUBLE PRECISION,EUCLIDEAN,L2,LENGTH,LINEAR ALGEBRA,
C NORM,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE EUCLIDEAN LENGTH (L2 NORM) OF D.P. VECTOR
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C --OUTPUT--
C DNRM2 DOUBLE PRECISION RESULT (ZERO IF N .LE. 0)
C EUCLIDEAN NORM OF THE N-VECTOR STORED IN DX() WITH STORAGE
C INCREMENT INCX .
C IF N .LE. 0 RETURN WITH RESULT = 0.
C IF N .GE. 1 THEN INCX MUST BE .GE. 1
C C.L. LAWSON, 1978 JAN 08
C FOUR PHASE METHOD USING TWO BUILT-IN CONSTANTS THAT ARE
C HOPEFULLY APPLICABLE TO ALL MACHINES.
C CUTLO = MAXIMUM OF DSQRT(U/EPS) OVER ALL KNOWN MACHINES.
C CUTHI = MINIMUM OF DSQRT(V) OVER ALL KNOWN MACHINES.
C WHERE
C EPS = SMALLEST NO. SUCH THAT EPS + 1. .GT. 1.
C U = SMALLEST POSITIVE NO. (UNDERFLOW LIMIT)
C V = LARGEST NO. (OVERFLOW LIMIT)
C BRIEF OUTLINE OF ALGORITHM..
C PHASE 1 SCANS ZERO COMPONENTS.
C MOVE TO PHASE 2 WHEN A COMPONENT IS NONZERO AND .LE. CUTLO
C MOVE TO PHASE 3 WHEN A COMPONENT IS .GT. CUTLO
C MOVE TO PHASE 4 WHEN A COMPONENT IS .GE. CUTHI/M
C WHERE M = N FOR X() REAL AND M = 2*N FOR COMPLEX.
C VALUES FOR CUTLO AND CUTHI..
C FROM THE ENVIRONMENTAL PARAMETERS LISTED IN THE IMSL CONVERTER
C DOCUMENT THE LIMITING VALUES ARE AS FOLLOWS..
C CUTLO, S.P. U/EPS = 2**(-102) FOR HONEYWELL. CLOSE SECONDS ARE
C UNIVAC AND DEC AT 2**(-103)
C THUS CUTLO = 2**(-51) = 4.44089E-16
C CUTHI, S.P. V = 2**127 FOR UNIVAC, HONEYWELL, AND DEC.
C THUS CUTHI = 2**(63.5) = 1.30438E19
C CUTLO, D.P. U/EPS = 2**(-67) FOR HONEYWELL AND DEC.
C THUS CUTLO = 2**(-33.5) = 8.23181D-11
C CUTHI, D.P. SAME AS S.P. CUTHI = 1.30438D19
C DATA CUTLO, CUTHI / 8.232D-11, 1.304D19 /
C DATA CUTLO, CUTHI / 4.441E-16, 1.304E19 /
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DNRM2
C...SCALAR ARGUMENTS
INTEGER
+ INCX,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ CUTHI,CUTLO,HITEST,ONE,SUM,XMAX,ZERO
INTEGER
+ I,J,NEXT,NN
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS,DSQRT,FLOAT
C...DATA STATEMENTS
DATA
+ ZERO,ONE/0.0D0,1.0D0/
DATA
+ CUTLO,CUTHI/8.232D-11,1.304D19/
C***FIRST EXECUTABLE STATEMENT DNRM2
XMAX = ZERO
IF(N .GT. 0) GO TO 10
DNRM2 = ZERO
GO TO 300
10 ASSIGN 30 TO NEXT
SUM = ZERO
NN = N * INCX
C BEGIN MAIN LOOP
I = 1
C 20 GO TO NEXT,(30, 50, 70, 110)
20 GO TO NEXT
30 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
ASSIGN 50 TO NEXT
XMAX = ZERO
C PHASE 1. SUM IS ZERO
50 IF( DX(I) .EQ. ZERO) GO TO 200
IF( DABS(DX(I)) .GT. CUTLO) GO TO 85
C PREPARE FOR PHASE 2.
ASSIGN 70 TO NEXT
GO TO 105
C PREPARE FOR PHASE 4.
100 I = J
ASSIGN 110 TO NEXT
SUM = (SUM / DX(I)) / DX(I)
105 XMAX = DABS(DX(I))
GO TO 115
C PHASE 2. SUM IS SMALL.
C SCALE TO AVOID DESTRUCTIVE UNDERFLOW.
70 IF( DABS(DX(I)) .GT. CUTLO ) GO TO 75
C COMMON CODE FOR PHASES 2 AND 4.
C IN PHASE 4 SUM IS LARGE. SCALE TO AVOID OVERFLOW.
110 IF( DABS(DX(I)) .LE. XMAX ) GO TO 115
SUM = ONE + SUM * (XMAX / DX(I))**2
XMAX = DABS(DX(I))
GO TO 200
115 SUM = SUM + (DX(I)/XMAX)**2
GO TO 200
C PREPARE FOR PHASE 3.
75 SUM = (SUM * XMAX) * XMAX
C FOR REAL OR D.P. SET HITEST = CUTHI/N
C FOR COMPLEX SET HITEST = CUTHI/(2*N)
85 HITEST = CUTHI/FLOAT( N )
C PHASE 3. SUM IS MID-RANGE. NO SCALING.
DO 95 J =I,NN,INCX
IF(DABS(DX(J)) .GE. HITEST) GO TO 100
95 SUM = SUM + DX(J)**2
DNRM2 = DSQRT( SUM )
GO TO 300
200 CONTINUE
I = I + INCX
IF ( I .LE. NN ) GO TO 20
C END OF MAIN LOOP.
C COMPUTE SQUARE ROOT AND ADJUST FOR SCALING.
DNRM2 = XMAX * DSQRT(SUM)
300 CONTINUE
RETURN
END
*DPODI
SUBROUTINE DPODI(A,LDA,N,DET,JOB)
C***BEGIN PROLOGUE DPODI
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D2B1B,D3B1B
C***KEYWORDS DETERMINANT,DOUBLE PRECISION,FACTOR,INVERSE,
C LINEAR ALGEBRA,LINPACK,MATRIX,POSITIVE DEFINITE
C***AUTHOR MOLER, C. B., (U. OF NEW MEXICO)
C***PURPOSE COMPUTES THE DETERMINANT AND INVERSE OF A CERTAIN DOUBLE
C PRECISION SYMMETRIC POSITIVE DEFINITE MATRIX (SEE ABSTRACT)
C USING THE FACTORS COMPUTED BY DPOCO, DPOFA OR DQRDC.
C***DESCRIPTION
C DPODI COMPUTES THE DETERMINANT AND INVERSE OF A CERTAIN
C DOUBLE PRECISION SYMMETRIC POSITIVE DEFINITE MATRIX (SEE BELOW)
C USING THE FACTORS COMPUTED BY DPOCO, DPOFA OR DQRDC.
C ON ENTRY
C A DOUBLE PRECISION(LDA, N)
C THE OUTPUT A FROM DPOCO OR DPOFA
C OR THE OUTPUT X FROM DQRDC.
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY A .
C N INTEGER
C THE ORDER OF THE MATRIX A .
C JOB INTEGER
C = 11 BOTH DETERMINANT AND INVERSE.
C = 01 INVERSE ONLY.
C = 10 DETERMINANT ONLY.
C ON RETURN
C A IF DPOCO OR DPOFA WAS USED TO FACTOR A , THEN
C DPODI PRODUCES THE UPPER HALF OF INVERSE(A) .
C IF DQRDC WAS USED TO DECOMPOSE X , THEN
C DPODI PRODUCES THE UPPER HALF OF INVERSE(TRANS(X)*X)
C WHERE TRANS(X) IS THE TRANSPOSE.
C ELEMENTS OF A BELOW THE DIAGONAL ARE UNCHANGED.
C IF THE UNITS DIGIT OF JOB IS ZERO, A IS UNCHANGED.
C DET DOUBLE PRECISION(2)
C DETERMINANT OF A OR OF TRANS(X)*X IF REQUESTED.
C OTHERWISE NOT REFERENCED.
C DETERMINANT = DET(1) * 10.0**DET(2)
C WITH 1.0 .LE. DET(1) .LT. 10.0
C OR DET(1) .EQ. 0.0 .
C ERROR CONDITION
C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS
C A ZERO ON THE DIAGONAL AND THE INVERSE IS REQUESTED.
C IT WILL NOT OCCUR IF THE SUBROUTINES ARE CALLED CORRECTLY
C AND IF DPOCO OR DPOFA HAS SET INFO .EQ. 0 .
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DAXPY,DSCAL
C***END PROLOGUE DPODI
C...SCALAR ARGUMENTS
INTEGER JOB,LDA,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION A(LDA,*),DET(*)
C...LOCAL SCALARS
DOUBLE PRECISION S,T
INTEGER I,J,JM1,K,KP1
C...EXTERNAL SUBROUTINES
EXTERNAL DAXPY,DSCAL
C...INTRINSIC FUNCTIONS
INTRINSIC MOD
C***FIRST EXECUTABLE STATEMENT DPODI
IF (JOB/10 .EQ. 0) GO TO 70
DET(1) = 1.0D0
DET(2) = 0.0D0
S = 10.0D0
DO 50 I = 1, N
DET(1) = A(I,I)**2*DET(1)
C ...EXIT
IF (DET(1) .EQ. 0.0D0) GO TO 60
10 IF (DET(1) .GE. 1.0D0) GO TO 20
DET(1) = S*DET(1)
DET(2) = DET(2) - 1.0D0
GO TO 10
20 CONTINUE
30 IF (DET(1) .LT. S) GO TO 40
DET(1) = DET(1)/S
DET(2) = DET(2) + 1.0D0
GO TO 30
40 CONTINUE
50 CONTINUE
60 CONTINUE
70 CONTINUE
C COMPUTE INVERSE(R)
IF (MOD(JOB,10) .EQ. 0) GO TO 140
DO 100 K = 1, N
A(K,K) = 1.0D0/A(K,K)
T = -A(K,K)
CALL DSCAL(K-1,T,A(1,K),1)
KP1 = K + 1
IF (N .LT. KP1) GO TO 90
DO 80 J = KP1, N
T = A(K,J)
A(K,J) = 0.0D0
CALL DAXPY(K,T,A(1,K),1,A(1,J),1)
80 CONTINUE
90 CONTINUE
100 CONTINUE
C FORM INVERSE(R) * TRANS(INVERSE(R))
DO 130 J = 1, N
JM1 = J - 1
IF (JM1 .LT. 1) GO TO 120
DO 110 K = 1, JM1
T = A(K,J)
CALL DAXPY(K,T,A(1,J),1,A(1,K),1)
110 CONTINUE
120 CONTINUE
T = A(J,J)
CALL DSCAL(J,T,A(1,J),1)
130 CONTINUE
140 CONTINUE
RETURN
END
*DQRDC
SUBROUTINE DQRDC(X,LDX,N,P,QRAUX,JPVT,WORK,JOB)
C***BEGIN PROLOGUE DQRDC
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D5
C***KEYWORDS DECOMPOSITION,DOUBLE PRECISION,LINEAR ALGEBRA,LINPACK,
C MATRIX,ORTHOGONAL TRIANGULAR
C***AUTHOR STEWART, G. W., (U. OF MARYLAND)
C***PURPOSE USES HOUSEHOLDER TRANSFORMATIONS TO COMPUTE THE QR FACTORI-
C ZATION OF N BY P MATRIX X. COLUMN PIVOTING IS OPTIONAL.
C***DESCRIPTION
C DQRDC USES HOUSEHOLDER TRANSFORMATIONS TO COMPUTE THE QR
C FACTORIZATION OF AN N BY P MATRIX X. COLUMN PIVOTING
C BASED ON THE 2-NORMS OF THE REDUCED COLUMNS MAY BE
C PERFORMED AT THE USER'S OPTION.
C ON ENTRY
C X DOUBLE PRECISION(LDX,P), WHERE LDX .GE. N.
C X CONTAINS THE MATRIX WHOSE DECOMPOSITION IS TO BE
C COMPUTED.
C LDX INTEGER.
C LDX IS THE LEADING DIMENSION OF THE ARRAY X.
C N INTEGER.
C N IS THE NUMBER OF ROWS OF THE MATRIX X.
C P INTEGER.
C P IS THE NUMBER OF COLUMNS OF THE MATRIX X.
C JPVT INTEGER(P).
C JPVT CONTAINS INTEGERS THAT CONTROL THE SELECTION
C OF THE PIVOT COLUMNS. THE K-TH COLUMN X(K) OF X
C IS PLACED IN ONE OF THREE CLASSES ACCORDING TO THE
C VALUE OF JPVT(K).
C IF JPVT(K) .GT. 0, THEN X(K) IS AN INITIAL
C COLUMN.
C IF JPVT(K) .EQ. 0, THEN X(K) IS A FREE COLUMN.
C IF JPVT(K) .LT. 0, THEN X(K) IS A FINAL COLUMN.
C BEFORE THE DECOMPOSITION IS COMPUTED, INITIAL COLUMNS
C ARE MOVED TO THE BEGINNING OF THE ARRAY X AND FINAL
C COLUMNS TO THE END. BOTH INITIAL AND FINAL COLUMNS
C ARE FROZEN IN PLACE DURING THE COMPUTATION AND ONLY
C FREE COLUMNS ARE MOVED. AT THE K-TH STAGE OF THE
C REDUCTION, IF X(K) IS OCCUPIED BY A FREE COLUMN
C IT IS INTERCHANGED WITH THE FREE COLUMN OF LARGEST
C REDUCED NORM. JPVT IS NOT REFERENCED IF
C JOB .EQ. 0.
C WORK DOUBLE PRECISION(P).
C WORK IS A WORK ARRAY. WORK IS NOT REFERENCED IF
C JOB .EQ. 0.
C JOB INTEGER.
C JOB IS AN INTEGER THAT INITIATES COLUMN PIVOTING.
C IF JOB .EQ. 0, NO PIVOTING IS DONE.
C IF JOB .NE. 0, PIVOTING IS DONE.
C ON RETURN
C X X CONTAINS IN ITS UPPER TRIANGLE THE UPPER
C TRIANGULAR MATRIX R OF THE QR FACTORIZATION.
C BELOW ITS DIAGONAL X CONTAINS INFORMATION FROM
C WHICH THE ORTHOGONAL PART OF THE DECOMPOSITION
C CAN BE RECOVERED. NOTE THAT IF PIVOTING HAS
C BEEN REQUESTED, THE DECOMPOSITION IS NOT THAT
C OF THE ORIGINAL MATRIX X BUT THAT OF X
C WITH ITS COLUMNS PERMUTED AS DESCRIBED BY JPVT.
C QRAUX DOUBLE PRECISION(P).
C QRAUX CONTAINS FURTHER INFORMATION REQUIRED TO RECOVER
C THE ORTHOGONAL PART OF THE DECOMPOSITION.
C JPVT JPVT(K) CONTAINS THE INDEX OF THE COLUMN OF THE
C ORIGINAL MATRIX THAT HAS BEEN INTERCHANGED INTO
C THE K-TH COLUMN, IF PIVOTING WAS REQUESTED.
C LINPACK. THIS VERSION DATED 08/14/78 .
C G. W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DAXPY,DDOT,DNRM2,DSCAL,DSWAP
C***END PROLOGUE DQRDC
C...SCALAR ARGUMENTS
INTEGER
+ JOB,LDX,N,P
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ QRAUX(*),WORK(*),X(LDX,*)
INTEGER
+ JPVT(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ MAXNRM,NRMXL,T,TT
INTEGER
+ J,JJ,JP,L,LP1,LUP,MAXJ,PL,PU
LOGICAL
+ NEGJ,SWAPJ
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT,DNRM2
EXTERNAL
+ DDOT,DNRM2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DAXPY,DSCAL,DSWAP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS,DMAX1,DSIGN,DSQRT,MIN0
C***FIRST EXECUTABLE STATEMENT DQRDC
PL = 1
PU = 0
IF (JOB .EQ. 0) GO TO 60
C PIVOTING HAS BEEN REQUESTED. REARRANGE THE COLUMNS
C ACCORDING TO JPVT.
DO 20 J = 1, P
SWAPJ = JPVT(J) .GT. 0
NEGJ = JPVT(J) .LT. 0
JPVT(J) = J
IF (NEGJ) JPVT(J) = -J
IF (.NOT.SWAPJ) GO TO 10
IF (J .NE. PL) CALL DSWAP(N,X(1,PL),1,X(1,J),1)
JPVT(J) = JPVT(PL)
JPVT(PL) = J
PL = PL + 1
10 CONTINUE
20 CONTINUE
PU = P
DO 50 JJ = 1, P
J = P - JJ + 1
IF (JPVT(J) .GE. 0) GO TO 40
JPVT(J) = -JPVT(J)
IF (J .EQ. PU) GO TO 30
CALL DSWAP(N,X(1,PU),1,X(1,J),1)
JP = JPVT(PU)
JPVT(PU) = JPVT(J)
JPVT(J) = JP
30 CONTINUE
PU = PU - 1
40 CONTINUE
50 CONTINUE
60 CONTINUE
C COMPUTE THE NORMS OF THE FREE COLUMNS.
IF (PU .LT. PL) GO TO 80
DO 70 J = PL, PU
QRAUX(J) = DNRM2(N,X(1,J),1)
WORK(J) = QRAUX(J)
70 CONTINUE
80 CONTINUE
C PERFORM THE HOUSEHOLDER REDUCTION OF X.
LUP = MIN0(N,P)
DO 200 L = 1, LUP
IF (L .LT. PL .OR. L .GE. PU) GO TO 120
C LOCATE THE COLUMN OF LARGEST NORM AND BRING IT
C INTO THE PIVOT POSITION.
MAXNRM = 0.0D0
MAXJ = L
DO 100 J = L, PU
IF (QRAUX(J) .LE. MAXNRM) GO TO 90
MAXNRM = QRAUX(J)
MAXJ = J
90 CONTINUE
100 CONTINUE
IF (MAXJ .EQ. L) GO TO 110
CALL DSWAP(N,X(1,L),1,X(1,MAXJ),1)
QRAUX(MAXJ) = QRAUX(L)
WORK(MAXJ) = WORK(L)
JP = JPVT(MAXJ)
JPVT(MAXJ) = JPVT(L)
JPVT(L) = JP
110 CONTINUE
120 CONTINUE
QRAUX(L) = 0.0D0
IF (L .EQ. N) GO TO 190
C COMPUTE THE HOUSEHOLDER TRANSFORMATION FOR COLUMN L.
NRMXL = DNRM2(N-L+1,X(L,L),1)
IF (NRMXL .EQ. 0.0D0) GO TO 180
IF (X(L,L) .NE. 0.0D0) NRMXL = DSIGN(NRMXL,X(L,L))
CALL DSCAL(N-L+1,1.0D0/NRMXL,X(L,L),1)
X(L,L) = 1.0D0 + X(L,L)
C APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS,
C UPDATING THE NORMS.
LP1 = L + 1
IF (P .LT. LP1) GO TO 170
DO 160 J = LP1, P
T = -DDOT(N-L+1,X(L,L),1,X(L,J),1)/X(L,L)
CALL DAXPY(N-L+1,T,X(L,L),1,X(L,J),1)
IF (J .LT. PL .OR. J .GT. PU) GO TO 150
IF (QRAUX(J) .EQ. 0.0D0) GO TO 150
TT = 1.0D0 - (DABS(X(L,J))/QRAUX(J))**2
TT = DMAX1(TT,0.0D0)
T = TT
TT = 1.0D0 + 0.05D0*TT*(QRAUX(J)/WORK(J))**2
IF (TT .EQ. 1.0D0) GO TO 130
QRAUX(J) = QRAUX(J)*DSQRT(T)
GO TO 140
130 CONTINUE
QRAUX(J) = DNRM2(N-L,X(L+1,J),1)
WORK(J) = QRAUX(J)
140 CONTINUE
150 CONTINUE
160 CONTINUE
170 CONTINUE
C SAVE THE TRANSFORMATION.
QRAUX(L) = X(L,L)
X(L,L) = -NRMXL
180 CONTINUE
190 CONTINUE
200 CONTINUE
RETURN
END
*DQRSL
SUBROUTINE DQRSL(X,LDX,N,K,QRAUX,Y,QY,QTY,B,RSD,XB,JOB,INFO)
C***BEGIN PROLOGUE DQRSL
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D9,D2A1
C***KEYWORDS DOUBLE PRECISION,LINEAR ALGEBRA,LINPACK,MATRIX,
C ORTHOGONAL TRIANGULAR,SOLVE
C***AUTHOR STEWART, G. W., (U. OF MARYLAND)
C***PURPOSE APPLIES THE OUTPUT OF DQRDC TO COMPUTE COORDINATE
C TRANSFORMATIONS, PROJECTIONS, AND LEAST SQUARES SOLUTIONS.
C***DESCRIPTION
C DQRSL APPLIES THE OUTPUT OF DQRDC TO COMPUTE COORDINATE
C TRANSFORMATIONS, PROJECTIONS, AND LEAST SQUARES SOLUTIONS.
C FOR K .LE. MIN(N,P), LET XK BE THE MATRIX
C XK = (X(JPVT(1)),X(JPVT(2)), ... ,X(JPVT(K)))
C FORMED FROM COLUMNNS JPVT(1), ... ,JPVT(K) OF THE ORIGINAL
C N X P MATRIX X THAT WAS INPUT TO DQRDC (IF NO PIVOTING WAS
C DONE, XK CONSISTS OF THE FIRST K COLUMNS OF X IN THEIR
C ORIGINAL ORDER). DQRDC PRODUCES A FACTORED ORTHOGONAL MATRIX Q
C AND AN UPPER TRIANGULAR MATRIX R SUCH THAT
C XK = Q * (R)
C (0)
C THIS INFORMATION IS CONTAINED IN CODED FORM IN THE ARRAYS
C X AND QRAUX.
C ON ENTRY
C X DOUBLE PRECISION(LDX,P).
C X CONTAINS THE OUTPUT OF DQRDC.
C LDX INTEGER.
C LDX IS THE LEADING DIMENSION OF THE ARRAY X.
C N INTEGER.
C N IS THE NUMBER OF ROWS OF THE MATRIX XK. IT MUST
C HAVE THE SAME VALUE AS N IN DQRDC.
C K INTEGER.
C K IS THE NUMBER OF COLUMNS OF THE MATRIX XK. K
C MUST NOT BE GREATER THAN MIN(N,P), WHERE P IS THE
C SAME AS IN THE CALLING SEQUENCE TO DQRDC.
C QRAUX DOUBLE PRECISION(P).
C QRAUX CONTAINS THE AUXILIARY OUTPUT FROM DQRDC.
C Y DOUBLE PRECISION(N)
C Y CONTAINS AN N-VECTOR THAT IS TO BE MANIPULATED
C BY DQRSL.
C JOB INTEGER.
C JOB SPECIFIES WHAT IS TO BE COMPUTED. JOB HAS
C THE DECIMAL EXPANSION ABCDE, WITH THE FOLLOWING
C MEANING.
C IF A .NE. 0, COMPUTE QY.
C IF B,C,D, OR E .NE. 0, COMPUTE QTY.
C IF C .NE. 0, COMPUTE B.
C IF D .NE. 0, COMPUTE RSD.
C IF E .NE. 0, COMPUTE XB.
C NOTE THAT A REQUEST TO COMPUTE B, RSD, OR XB
C AUTOMATICALLY TRIGGERS THE COMPUTATION OF QTY, FOR
C WHICH AN ARRAY MUST BE PROVIDED IN THE CALLING
C SEQUENCE.
C ON RETURN
C QY DOUBLE PRECISION(N).
C QY CONTAINS Q*Y, IF ITS COMPUTATION HAS BEEN
C REQUESTED.
C QTY DOUBLE PRECISION(N).
C QTY CONTAINS TRANS(Q)*Y, IF ITS COMPUTATION HAS
C BEEN REQUESTED. HERE TRANS(Q) IS THE
C TRANSPOSE OF THE MATRIX Q.
C B DOUBLE PRECISION(K)
C B CONTAINS THE SOLUTION OF THE LEAST SQUARES PROBLEM
C MINIMIZE NORM2(Y - XK*B),
C IF ITS COMPUTATION HAS BEEN REQUESTED. (NOTE THAT
C IF PIVOTING WAS REQUESTED IN DQRDC, THE J-TH
C COMPONENT OF B WILL BE ASSOCIATED WITH COLUMN JPVT(J)
C OF THE ORIGINAL MATRIX X THAT WAS INPUT INTO DQRDC.)
C RSD DOUBLE PRECISION(N).
C RSD CONTAINS THE LEAST SQUARES RESIDUAL Y - XK*B,
C IF ITS COMPUTATION HAS BEEN REQUESTED. RSD IS
C ALSO THE ORTHOGONAL PROJECTION OF Y ONTO THE
C ORTHOGONAL COMPLEMENT OF THE COLUMN SPACE OF XK.
C XB DOUBLE PRECISION(N).
C XB CONTAINS THE LEAST SQUARES APPROXIMATION XK*B,
C IF ITS COMPUTATION HAS BEEN REQUESTED. XB IS ALSO
C THE ORTHOGONAL PROJECTION OF Y ONTO THE COLUMN SPACE
C OF X.
C INFO INTEGER.
C INFO IS ZERO UNLESS THE COMPUTATION OF B HAS
C BEEN REQUESTED AND R IS EXACTLY SINGULAR. IN
C THIS CASE, INFO IS THE INDEX OF THE FIRST ZERO
C DIAGONAL ELEMENT OF R AND B IS LEFT UNALTERED.
C THE PARAMETERS QY, QTY, B, RSD, AND XB ARE NOT REFERENCED
C IF THEIR COMPUTATION IS NOT REQUESTED AND IN THIS CASE
C CAN BE REPLACED BY DUMMY VARIABLES IN THE CALLING PROGRAM.
C TO SAVE STORAGE, THE USER MAY IN SOME CASES USE THE SAME
C ARRAY FOR DIFFERENT PARAMETERS IN THE CALLING SEQUENCE. A
C FREQUENTLY OCCURING EXAMPLE IS WHEN ONE WISHES TO COMPUTE
C ANY OF B, RSD, OR XB AND DOES NOT NEED Y OR QTY. IN THIS
C CASE ONE MAY IDENTIFY Y, QTY, AND ONE OF B, RSD, OR XB, WHILE
C PROVIDING SEPARATE ARRAYS FOR ANYTHING ELSE THAT IS TO BE
C COMPUTED. THUS THE CALLING SEQUENCE
C CALL DQRSL(X,LDX,N,K,QRAUX,Y,DUM,Y,B,Y,DUM,110,INFO)
C WILL RESULT IN THE COMPUTATION OF B AND RSD, WITH RSD
C OVERWRITING Y. MORE GENERALLY, EACH ITEM IN THE FOLLOWING
C LIST CONTAINS GROUPS OF PERMISSIBLE IDENTIFICATIONS FOR
C A SINGLE CALLING SEQUENCE.
C 1. (Y,QTY,B) (RSD) (XB) (QY)
C 2. (Y,QTY,RSD) (B) (XB) (QY)
C 3. (Y,QTY,XB) (B) (RSD) (QY)
C 4. (Y,QY) (QTY,B) (RSD) (XB)
C 5. (Y,QY) (QTY,RSD) (B) (XB)
C 6. (Y,QY) (QTY,XB) (B) (RSD)
C IN ANY GROUP THE VALUE RETURNED IN THE ARRAY ALLOCATED TO
C THE GROUP CORRESPONDS TO THE LAST MEMBER OF THE GROUP.
C LINPACK. THIS VERSION DATED 08/14/78 .
C G. W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DAXPY,DCOPY,DDOT
C***END PROLOGUE DQRSL
C...SCALAR ARGUMENTS
INTEGER
+ INFO,JOB,K,LDX,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ B(*),QRAUX(*),QTY(*),QY(*),RSD(*),X(LDX,*),XB(*),
+ Y(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ T,TEMP
INTEGER
+ I,J,JJ,JU,KP1
LOGICAL
+ CB,CQTY,CQY,CR,CXB
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT
EXTERNAL
+ DDOT
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DAXPY,DCOPY
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MIN0,MOD
C***FIRST EXECUTABLE STATEMENT DQRSL
INFO = 0
C DETERMINE WHAT IS TO BE COMPUTED.
CQY = JOB/10000 .NE. 0
CQTY = MOD(JOB,10000) .NE. 0
CB = MOD(JOB,1000)/100 .NE. 0
CR = MOD(JOB,100)/10 .NE. 0
CXB = MOD(JOB,10) .NE. 0
JU = MIN0(K,N-1)
C SPECIAL ACTION WHEN N=1.
IF (JU .NE. 0) GO TO 40
IF (CQY) QY(1) = Y(1)
IF (CQTY) QTY(1) = Y(1)
IF (CXB) XB(1) = Y(1)
IF (.NOT.CB) GO TO 30
IF (X(1,1) .NE. 0.0D0) GO TO 10
INFO = 1
GO TO 20
10 CONTINUE
B(1) = Y(1)/X(1,1)
20 CONTINUE
30 CONTINUE
IF (CR) RSD(1) = 0.0D0
GO TO 250
40 CONTINUE
C SET UP TO COMPUTE QY OR QTY.
IF (CQY) CALL DCOPY(N,Y,1,QY,1)
IF (CQTY) CALL DCOPY(N,Y,1,QTY,1)
IF (.NOT.CQY) GO TO 70
C COMPUTE QY.
DO 60 JJ = 1, JU
J = JU - JJ + 1
IF (QRAUX(J) .EQ. 0.0D0) GO TO 50
TEMP = X(J,J)
X(J,J) = QRAUX(J)
T = -DDOT(N-J+1,X(J,J),1,QY(J),1)/X(J,J)
CALL DAXPY(N-J+1,T,X(J,J),1,QY(J),1)
X(J,J) = TEMP
50 CONTINUE
60 CONTINUE
70 CONTINUE
IF (.NOT.CQTY) GO TO 100
C COMPUTE TRANS(Q)*Y.
DO 90 J = 1, JU
IF (QRAUX(J) .EQ. 0.0D0) GO TO 80
TEMP = X(J,J)
X(J,J) = QRAUX(J)
T = -DDOT(N-J+1,X(J,J),1,QTY(J),1)/X(J,J)
CALL DAXPY(N-J+1,T,X(J,J),1,QTY(J),1)
X(J,J) = TEMP
80 CONTINUE
90 CONTINUE
100 CONTINUE
C SET UP TO COMPUTE B, RSD, OR XB.
IF (CB) CALL DCOPY(K,QTY,1,B,1)
KP1 = K + 1
IF (CXB) CALL DCOPY(K,QTY,1,XB,1)
IF (CR .AND. K .LT. N) CALL DCOPY(N-K,QTY(KP1),1,RSD(KP1),1)
IF (.NOT.CXB .OR. KP1 .GT. N) GO TO 120
DO 110 I = KP1, N
XB(I) = 0.0D0
110 CONTINUE
120 CONTINUE
IF (.NOT.CR) GO TO 140
DO 130 I = 1, K
RSD(I) = 0.0D0
130 CONTINUE
140 CONTINUE
IF (.NOT.CB) GO TO 190
C COMPUTE B.
DO 170 JJ = 1, K
J = K - JJ + 1
IF (X(J,J) .NE. 0.0D0) GO TO 150
INFO = J
C ......EXIT
GO TO 180
150 CONTINUE
B(J) = B(J)/X(J,J)
IF (J .EQ. 1) GO TO 160
T = -B(J)
CALL DAXPY(J-1,T,X(1,J),1,B,1)
160 CONTINUE
170 CONTINUE
180 CONTINUE
190 CONTINUE
IF (.NOT.CR .AND. .NOT.CXB) GO TO 240
C COMPUTE RSD OR XB AS REQUIRED.
DO 230 JJ = 1, JU
J = JU - JJ + 1
IF (QRAUX(J) .EQ. 0.0D0) GO TO 220
TEMP = X(J,J)
X(J,J) = QRAUX(J)
IF (.NOT.CR) GO TO 200
T = -DDOT(N-J+1,X(J,J),1,RSD(J),1)/X(J,J)
CALL DAXPY(N-J+1,T,X(J,J),1,RSD(J),1)
200 CONTINUE
IF (.NOT.CXB) GO TO 210
T = -DDOT(N-J+1,X(J,J),1,XB(J),1)/X(J,J)
CALL DAXPY(N-J+1,T,X(J,J),1,XB(J),1)
210 CONTINUE
X(J,J) = TEMP
220 CONTINUE
230 CONTINUE
240 CONTINUE
250 CONTINUE
RETURN
END
*DROT
SUBROUTINE DROT(N,DX,INCX,DY,INCY,DC,DS)
C***BEGIN PROLOGUE DROT
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A8
C***KEYWORDS BLAS,GIVENS ROTATION,LINEAR ALGEBRA,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE APPLY D.P. GIVENS ROTATION
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C DY DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCY STORAGE SPACING BETWEEN ELEMENTS OF DY
C DC D.P. ELEMENT OF ROTATION MATRIX
C DS D.P. ELEMENT OF ROTATION MATRIX
C --OUTPUT--
C DX ROTATED VECTOR (UNCHANGED IF N .LE. 0)
C DY ROTATED VECTOR (UNCHANGED IF N .LE. 0)
C MULTIPLY THE 2 X 2 MATRIX ( DC DS) TIMES THE 2 X N MATRIX (DX**T)
C (-DS DC) (DY**T)
C WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
C DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
C LX = (-INCX)*N, AND SIMILARLY FOR DY USING LY AND INCY.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DROT
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ DC,DS
INTEGER
+ INCX,INCY,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*),DY(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ONE,W,Z,ZERO
INTEGER
+ I,KX,KY,NSTEPS
C...DATA STATEMENTS
DATA
+ ZERO,ONE/0.D0,1.D0/
C***FIRST EXECUTABLE STATEMENT DROT
IF(N .LE. 0 .OR. (DS .EQ. ZERO .AND. DC .EQ. ONE)) GO TO 40
IF(.NOT. (INCX .EQ. INCY .AND. INCX .GT. 0)) GO TO 20
NSTEPS=INCX*N
DO 10 I=1,NSTEPS,INCX
W=DX(I)
Z=DY(I)
DX(I)=DC*W+DS*Z
DY(I)=-DS*W+DC*Z
10 CONTINUE
GO TO 40
20 CONTINUE
KX=1
KY=1
IF(INCX .LT. 0) KX=1-(N-1)*INCX
IF(INCY .LT. 0) KY=1-(N-1)*INCY
DO 30 I=1,N
W=DX(KX)
Z=DY(KY)
DX(KX)=DC*W+DS*Z
DY(KY)=-DS*W+DC*Z
KX=KX+INCX
KY=KY+INCY
30 CONTINUE
40 CONTINUE
RETURN
END
*DROTG
SUBROUTINE DROTG(DA,DB,DC,DS)
C***BEGIN PROLOGUE DROTG
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1B10
C***KEYWORDS BLAS,GIVENS ROTATION,LINEAR ALGEBRA,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE CONSTRUCT D.P. PLANE GIVENS ROTATION
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C DA DOUBLE PRECISION SCALAR
C DB DOUBLE PRECISION SCALAR
C --OUTPUT--
C DA DOUBLE PRECISION RESULT R
C DB DOUBLE PRECISION RESULT Z
C DC DOUBLE PRECISION RESULT
C DS DOUBLE PRECISION RESULT
C DESIGNED BY C. L. LAWSON, JPL, 1977 SEPT 08
C CONSTRUCT THE GIVENS TRANSFORMATION
C ( DC DS )
C G = ( ) , DC**2 + DS**2 = 1 ,
C (-DS DC )
C WHICH ZEROS THE SECOND ENTRY OF THE 2-VECTOR (DA,DB)**T .
C THE QUANTITY R = (+/-)DSQRT(DA**2 + DB**2) OVERWRITES DA IN
C STORAGE. THE VALUE OF DB IS OVERWRITTEN BY A VALUE Z WHICH
C ALLOWS DC AND DS TO BE RECOVERED BY THE FOLLOWING ALGORITHM.
C IF Z=1 SET DC=0.D0 AND DS=1.D0
C IF DABS(Z) .LT. 1 SET DC=DSQRT(1-Z**2) AND DS=Z
C IF DABS(Z) .GT. 1 SET DC=1/Z AND DS=DSQRT(1-DC**2)
C NORMALLY, THE SUBPROGRAM DROT(N,DX,INCX,DY,INCY,DC,DS) WILL
C NEXT BE CALLED TO APPLY THE TRANSFORMATION TO A 2 BY N MATRIX.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DROTG
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ DA,DB,DC,DS
C...LOCAL SCALARS
DOUBLE PRECISION
+ R,U,V
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS,DSQRT
C***FIRST EXECUTABLE STATEMENT DROTG
IF (DABS(DA) .LE. DABS(DB)) GO TO 10
C *** HERE DABS(DA) .GT. DABS(DB) ***
U = DA + DA
V = DB / U
C NOTE THAT U AND R HAVE THE SIGN OF DA
R = DSQRT(.25D0 + V**2) * U
C NOTE THAT DC IS POSITIVE
DC = DA / R
DS = V * (DC + DC)
DB = DS
DA = R
RETURN
C *** HERE DABS(DA) .LE. DABS(DB) ***
10 IF (DB .EQ. 0.D0) GO TO 20
U = DB + DB
V = DA / U
C NOTE THAT U AND R HAVE THE SIGN OF DB
C (R IS IMMEDIATELY STORED IN DA)
DA = DSQRT(.25D0 + V**2) * U
C NOTE THAT DS IS POSITIVE
DS = DB / DA
DC = V * (DS + DS)
IF (DC .EQ. 0.D0) GO TO 15
DB = 1.D0 / DC
RETURN
15 DB = 1.D0
RETURN
C *** HERE DA = DB = 0.D0 ***
20 DC = 1.D0
DS = 0.D0
RETURN
END
*DSCAL
SUBROUTINE DSCAL(N,DA,DX,INCX)
C***BEGIN PROLOGUE DSCAL
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A6
C***KEYWORDS BLAS,LINEAR ALGEBRA,SCALE,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE D.P. VECTOR SCALE X = A*X
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DA DOUBLE PRECISION SCALE FACTOR
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C --OUTPUT--
C DX DOUBLE PRECISION RESULT (UNCHANGED IF N.LE.0)
C REPLACE DOUBLE PRECISION DX BY DOUBLE PRECISION DA*DX.
C FOR I = 0 TO N-1, REPLACE DX(1+I*INCX) WITH DA * DX(1+I*INCX)
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DSCAL
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ DA
INTEGER
+ INCX,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*)
C...LOCAL SCALARS
INTEGER
+ I,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DSCAL
IF(N.LE.0)RETURN
IF(INCX.EQ.1)GOTO 20
C CODE FOR INCREMENTS NOT EQUAL TO 1.
NS = N*INCX
DO 10 I = 1,NS,INCX
DX(I) = DA*DX(I)
10 CONTINUE
RETURN
C CODE FOR INCREMENTS EQUAL TO 1.
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5.
20 M = MOD(N,5)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DX(I) = DA*DX(I)
30 CONTINUE
IF( N .LT. 5 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,5
DX(I) = DA*DX(I)
DX(I + 1) = DA*DX(I + 1)
DX(I + 2) = DA*DX(I + 2)
DX(I + 3) = DA*DX(I + 3)
DX(I + 4) = DA*DX(I + 4)
50 CONTINUE
RETURN
END
*DSWAP
SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
C***BEGIN PROLOGUE DSWAP
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A5
C***KEYWORDS BLAS,DOUBLE PRECISION,INTERCHANGE,LINEAR ALGEBRA,VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE INTERCHANGE D.P. VECTORS
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C DY DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCY STORAGE SPACING BETWEEN ELEMENTS OF DY
C --OUTPUT--
C DX INPUT VECTOR DY (UNCHANGED IF N .LE. 0)
C DY INPUT VECTOR DX (UNCHANGED IF N .LE. 0)
C INTERCHANGE DOUBLE PRECISION DX AND DOUBLE PRECISION DY.
C FOR I = 0 TO N-1, INTERCHANGE DX(LX+I*INCX) AND DY(LY+I*INCY),
C WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N, AND LY IS
C DEFINED IN A SIMILAR WAY USING INCY.
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE DSWAP
C...SCALAR ARGUMENTS
INTEGER
+ INCX,INCY,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*),DY(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ DTEMP1,DTEMP2,DTEMP3
INTEGER
+ I,IX,IY,M,MP1,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DSWAP
IF(N.LE.0)RETURN
IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60
5 CONTINUE
C CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS.
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DTEMP1 = DX(IX)
DX(IX) = DY(IY)
DY(IY) = DTEMP1
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 3.
20 M = MOD(N,3)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DTEMP1 = DX(I)
DX(I) = DY(I)
DY(I) = DTEMP1
30 CONTINUE
IF( N .LT. 3 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,3
DTEMP1 = DX(I)
DTEMP2 = DX(I+1)
DTEMP3 = DX(I+2)
DX(I) = DY(I)
DX(I+1) = DY(I+1)
DX(I+2) = DY(I+2)
DY(I) = DTEMP1
DY(I+1) = DTEMP2
DY(I+2) = DTEMP3
50 CONTINUE
RETURN
60 CONTINUE
C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS.
NS = N*INCX
DO 70 I=1,NS,INCX
DTEMP1 = DX(I)
DX(I) = DY(I)
DY(I) = DTEMP1
70 CONTINUE
RETURN
END
*DTRCO
SUBROUTINE DTRCO(T,LDT,N,RCOND,Z,JOB)
C***BEGIN PROLOGUE DTRCO
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D2A3
C***KEYWORDS CONDITION,DOUBLE PRECISION,FACTOR,LINEAR ALGEBRA,LINPACK,
C MATRIX,TRIANGULAR
C***AUTHOR MOLER, C. B., (U. OF NEW MEXICO)
C***PURPOSE ESTIMATES THE CONDITION OF A DOUBLE PRECISION TRIANGULAR
C MATRIX.
C***DESCRIPTION
C DTRCO ESTIMATES THE CONDITION OF A DOUBLE PRECISION TRIANGULAR
C MATRIX.
C ON ENTRY
C T DOUBLE PRECISION(LDT,N)
C T CONTAINS THE TRIANGULAR MATRIX. THE ZERO
C ELEMENTS OF THE MATRIX ARE NOT REFERENCED, AND
C THE CORRESPONDING ELEMENTS OF THE ARRAY CAN BE
C USED TO STORE OTHER INFORMATION.
C LDT INTEGER
C LDT IS THE LEADING DIMENSION OF THE ARRAY T.
C N INTEGER
C N IS THE ORDER OF THE SYSTEM.
C JOB INTEGER
C = 0 T IS LOWER TRIANGULAR.
C = NONZERO T IS UPPER TRIANGULAR.
C ON RETURN
C RCOND DOUBLE PRECISION
C AN ESTIMATE OF THE RECIPROCAL CONDITION OF T .
C FOR THE SYSTEM T*X = B , RELATIVE PERTURBATIONS
C IN T AND B OF SIZE EPSILON MAY CAUSE
C RELATIVE PERTURBATIONS IN X OF SIZE EPSILON/RCOND .
C IF RCOND IS SO SMALL THAT THE LOGICAL EXPRESSION
C 1.0 + RCOND .EQ. 1.0
C IS TRUE, THEN T MAY BE SINGULAR TO WORKING
C PRECISION. IN PARTICULAR, RCOND IS ZERO IF
C EXACT SINGULARITY IS DETECTED OR THE ESTIMATE
C UNDERFLOWS.
C Z DOUBLE PRECISION(N)
C A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT.
C IF T IS CLOSE TO A SINGULAR MATRIX, THEN Z IS
C AN APPROXIMATE NULL VECTOR IN THE SENSE THAT
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DASUM,DAXPY,DSCAL
C***END PROLOGUE DTRCO
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ RCOND
INTEGER
+ JOB,LDT,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ T(LDT,*),Z(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ EK,S,SM,TNORM,W,WK,WKM,YNORM
INTEGER
+ I1,J,J1,J2,K,KK,L
LOGICAL
+ LOWER
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DASUM
EXTERNAL
+ DASUM
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DAXPY,DSCAL
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS,DMAX1,DSIGN
C***FIRST EXECUTABLE STATEMENT DTRCO
LOWER = JOB .EQ. 0
C COMPUTE 1-NORM OF T
TNORM = 0.0D0
DO 10 J = 1, N
L = J
IF (LOWER) L = N + 1 - J
I1 = 1
IF (LOWER) I1 = J
TNORM = DMAX1(TNORM,DASUM(L,T(I1,J),1))
10 CONTINUE
C RCOND = 1/(NORM(T)*(ESTIMATE OF NORM(INVERSE(T)))) .
C ESTIMATE = NORM(Z)/NORM(Y) WHERE T*Z = Y AND TRANS(T)*Y = E .
C TRANS(T) IS THE TRANSPOSE OF T .
C THE COMPONENTS OF E ARE CHOSEN TO CAUSE MAXIMUM LOCAL
C GROWTH IN THE ELEMENTS OF Y .
C THE VECTORS ARE FREQUENTLY RESCALED TO AVOID OVERFLOW.
C SOLVE TRANS(T)*Y = E
EK = 1.0D0
DO 20 J = 1, N
Z(J) = 0.0D0
20 CONTINUE
DO 100 KK = 1, N
K = KK
IF (LOWER) K = N + 1 - KK
IF (Z(K) .NE. 0.0D0) EK = DSIGN(EK,-Z(K))
IF (DABS(EK-Z(K)) .LE. DABS(T(K,K))) GO TO 30
S = DABS(T(K,K))/DABS(EK-Z(K))
CALL DSCAL(N,S,Z,1)
EK = S*EK
30 CONTINUE
WK = EK - Z(K)
WKM = -EK - Z(K)
S = DABS(WK)
SM = DABS(WKM)
IF (T(K,K) .EQ. 0.0D0) GO TO 40
WK = WK/T(K,K)
WKM = WKM/T(K,K)
GO TO 50
40 CONTINUE
WK = 1.0D0
WKM = 1.0D0
50 CONTINUE
IF (KK .EQ. N) GO TO 90
J1 = K + 1
IF (LOWER) J1 = 1
J2 = N
IF (LOWER) J2 = K - 1
DO 60 J = J1, J2
SM = SM + DABS(Z(J)+WKM*T(K,J))
Z(J) = Z(J) + WK*T(K,J)
S = S + DABS(Z(J))
60 CONTINUE
IF (S .GE. SM) GO TO 80
W = WKM - WK
WK = WKM
DO 70 J = J1, J2
Z(J) = Z(J) + W*T(K,J)
70 CONTINUE
80 CONTINUE
90 CONTINUE
Z(K) = WK
100 CONTINUE
S = 1.0D0/DASUM(N,Z,1)
CALL DSCAL(N,S,Z,1)
YNORM = 1.0D0
C SOLVE T*Z = Y
DO 130 KK = 1, N
K = N + 1 - KK
IF (LOWER) K = KK
IF (DABS(Z(K)) .LE. DABS(T(K,K))) GO TO 110
S = DABS(T(K,K))/DABS(Z(K))
CALL DSCAL(N,S,Z,1)
YNORM = S*YNORM
110 CONTINUE
IF (T(K,K) .NE. 0.0D0) Z(K) = Z(K)/T(K,K)
IF (T(K,K) .EQ. 0.0D0) Z(K) = 1.0D0
I1 = 1
IF (LOWER) I1 = K + 1
IF (KK .GE. N) GO TO 120
W = -Z(K)
CALL DAXPY(N-KK,W,T(I1,K),1,Z(I1),1)
120 CONTINUE
130 CONTINUE
C MAKE ZNORM = 1.0
S = 1.0D0/DASUM(N,Z,1)
CALL DSCAL(N,S,Z,1)
YNORM = S*YNORM
IF (TNORM .NE. 0.0D0) RCOND = YNORM/TNORM
IF (TNORM .EQ. 0.0D0) RCOND = 0.0D0
RETURN
END
*DTRSL
SUBROUTINE DTRSL(T,LDT,N,B,JOB,INFO)
C***BEGIN PROLOGUE DTRSL
C***DATE WRITTEN 780814 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D2A3
C***KEYWORDS DOUBLE PRECISION,LINEAR ALGEBRA,LINPACK,MATRIX,SOLVE,
C TRIANGULAR
C***AUTHOR STEWART, G. W., (U. OF MARYLAND)
C***PURPOSE SOLVES SYSTEMS OF THE FORM T*X=B OR TRANS(T)*X=B WHERE T
C IS A TRIANGULAR MATRIX OF ORDER N.
C***DESCRIPTION
C DTRSL SOLVES SYSTEMS OF THE FORM
C T * X = B
C OR
C TRANS(T) * X = B
C WHERE T IS A TRIANGULAR MATRIX OF ORDER N. HERE TRANS(T)
C DENOTES THE TRANSPOSE OF THE MATRIX T.
C ON ENTRY
C T DOUBLE PRECISION(LDT,N)
C T CONTAINS THE MATRIX OF THE SYSTEM. THE ZERO
C ELEMENTS OF THE MATRIX ARE NOT REFERENCED, AND
C THE CORRESPONDING ELEMENTS OF THE ARRAY CAN BE
C USED TO STORE OTHER INFORMATION.
C LDT INTEGER
C LDT IS THE LEADING DIMENSION OF THE ARRAY T.
C N INTEGER
C N IS THE ORDER OF THE SYSTEM.
C B DOUBLE PRECISION(N).
C B CONTAINS THE RIGHT HAND SIDE OF THE SYSTEM.
C JOB INTEGER
C JOB SPECIFIES WHAT KIND OF SYSTEM IS TO BE SOLVED.
C IF JOB IS
C 00 SOLVE T*X=B, T LOWER TRIANGULAR,
C 01 SOLVE T*X=B, T UPPER TRIANGULAR,
C 10 SOLVE TRANS(T)*X=B, T LOWER TRIANGULAR,
C 11 SOLVE TRANS(T)*X=B, T UPPER TRIANGULAR.
C ON RETURN
C B B CONTAINS THE SOLUTION, IF INFO .EQ. 0.
C OTHERWISE B IS UNALTERED.
C INFO INTEGER
C INFO CONTAINS ZERO IF THE SYSTEM IS NONSINGULAR.
C OTHERWISE INFO CONTAINS THE INDEX OF
C THE FIRST ZERO DIAGONAL ELEMENT OF T.
C LINPACK. THIS VERSION DATED 08/14/78 .
C G. W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***ROUTINES CALLED DAXPY,DDOT
C***END PROLOGUE DTRSL
C...SCALAR ARGUMENTS
INTEGER
+ INFO,JOB,LDT,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ B(*),T(LDT,*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEMP
INTEGER
+ CASE,J,JJ
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT
EXTERNAL
+ DDOT
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DAXPY
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C***FIRST EXECUTABLE STATEMENT DTRSL
C BEGIN BLOCK PERMITTING ...EXITS TO 150
C CHECK FOR ZERO DIAGONAL ELEMENTS.
DO 10 INFO = 1, N
C ......EXIT
IF (T(INFO,INFO) .EQ. 0.0D0) GO TO 150
10 CONTINUE
INFO = 0
C DETERMINE THE TASK AND GO TO IT.
CASE = 1
IF (MOD(JOB,10) .NE. 0) CASE = 2
IF (MOD(JOB,100)/10 .NE. 0) CASE = CASE + 2
GO TO (20,50,80,110), CASE
C SOLVE T*X=B FOR T LOWER TRIANGULAR
20 CONTINUE
B(1) = B(1)/T(1,1)
IF (N .LT. 2) GO TO 40
DO 30 J = 2, N
TEMP = -B(J-1)
CALL DAXPY(N-J+1,TEMP,T(J,J-1),1,B(J),1)
B(J) = B(J)/T(J,J)
30 CONTINUE
40 CONTINUE
GO TO 140
C SOLVE T*X=B FOR T UPPER TRIANGULAR.
50 CONTINUE
B(N) = B(N)/T(N,N)
IF (N .LT. 2) GO TO 70
DO 60 JJ = 2, N
J = N - JJ + 1
TEMP = -B(J+1)
CALL DAXPY(J,TEMP,T(1,J+1),1,B(1),1)
B(J) = B(J)/T(J,J)
60 CONTINUE
70 CONTINUE
GO TO 140
C SOLVE TRANS(T)*X=B FOR T LOWER TRIANGULAR.
80 CONTINUE
B(N) = B(N)/T(N,N)
IF (N .LT. 2) GO TO 100
DO 90 JJ = 2, N
J = N - JJ + 1
B(J) = B(J) - DDOT(JJ-1,T(J+1,J),1,B(J+1),1)
B(J) = B(J)/T(J,J)
90 CONTINUE
100 CONTINUE
GO TO 140
C SOLVE TRANS(T)*X=B FOR T UPPER TRIANGULAR.
110 CONTINUE
B(1) = B(1)/T(1,1)
IF (N .LT. 2) GO TO 130
DO 120 J = 2, N
B(J) = B(J) - DDOT(J-1,T(1,J),1,B(1),1)
B(J) = B(J)/T(J,J)
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
RETURN
END
*IDAMAX
INTEGER FUNCTION IDAMAX(N,DX,INCX)
C***BEGIN PROLOGUE IDAMAX
C***DATE WRITTEN 791001 (YYMMDD)
C***REVISION DATE 820801 (YYMMDD)
C***CATEGORY NO. D1A2
C***KEYWORDS BLAS,DOUBLE PRECISION,LINEAR ALGEBRA,MAXIMUM COMPONENT,
C VECTOR
C***AUTHOR LAWSON, C. L., (JPL)
C HANSON, R. J., (SNLA)
C KINCAID, D. R., (U. OF TEXAS)
C KROGH, F. T., (JPL)
C***PURPOSE FIND LARGEST COMPONENT OF D.P. VECTOR
C***DESCRIPTION
C B L A S SUBPROGRAM
C DESCRIPTION OF PARAMETERS
C --INPUT--
C N NUMBER OF ELEMENTS IN INPUT VECTOR(S)
C DX DOUBLE PRECISION VECTOR WITH N ELEMENTS
C INCX STORAGE SPACING BETWEEN ELEMENTS OF DX
C --OUTPUT--
C IDAMAX SMALLEST INDEX (ZERO IF N .LE. 0)
C FIND SMALLEST INDEX OF MAXIMUM MAGNITUDE OF DOUBLE PRECISION DX.
C IDAMAX = FIRST I, I = 1 TO N, TO MINIMIZE ABS(DX(1-INCX+I*INCX)
C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T.,
C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*,
C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL
C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323
C***ROUTINES CALLED (NONE)
C***END PROLOGUE IDAMAX
C...SCALAR ARGUMENTS
INTEGER
+ INCX,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DX(*)
C...LOCAL SCALARS
DOUBLE PRECISION
+ DMAX,XMAG
INTEGER
+ I,II,NS
C...INTRINSIC FUNCTIONS
INTRINSIC
+ DABS
C***FIRST EXECUTABLE STATEMENT IDAMAX
IDAMAX = 0
IF(N.LE.0) RETURN
IDAMAX = 1
IF(N.LE.1)RETURN
IF(INCX.EQ.1)GOTO 20
C CODE FOR INCREMENTS NOT EQUAL TO 1.
DMAX = DABS(DX(1))
NS = N*INCX
II = 1
DO 10 I = 1,NS,INCX
XMAG = DABS(DX(I))
IF(XMAG.LE.DMAX) GO TO 5
IDAMAX = II
DMAX = XMAG
5 II = II + 1
10 CONTINUE
RETURN
C CODE FOR INCREMENTS EQUAL TO 1.
20 DMAX = DABS(DX(1))
DO 30 I = 2,N
XMAG = DABS(DX(I))
IF(XMAG.LE.DMAX) GO TO 30
IDAMAX = I
DMAX = XMAG
30 CONTINUE
RETURN
END
*DODR
SUBROUTINE DODR
+ (FCN,
+ N,M,NP,NQ,
+ BETA,
+ Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ JOB,
+ IPRINT,LUNERR,LUNRPT,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
C***BEGIN PROLOGUE DODR
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***CATEGORY NO. G2E,I1B1
C***KEYWORDS ORTHOGONAL DISTANCE REGRESSION,
C NONLINEAR LEAST SQUARES,
C MEASUREMENT ERROR MODELS,
C ERRORS IN VARIABLES
C***AUTHOR BOGGS, PAUL T.
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C GAITHERSBURG, MD 20899
C BYRD, RICHARD H.
C DEPARTMENT OF COMPUTER SCIENCE
C UNIVERSITY OF COLORADO, BOULDER, CO 80309
C ROGERS, JANET E.
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C BOULDER, CO 80303-3328
C SCHNABEL, ROBERT B.
C DEPARTMENT OF COMPUTER SCIENCE
C UNIVERSITY OF COLORADO, BOULDER, CO 80309
C AND
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C BOULDER, CO 80303-3328
C***PURPOSE DOUBLE PRECISION DRIVER ROUTINE FOR FINDING
C THE WEIGHTED EXPLICIT OR IMPLICIT ORTHOGONAL DISTANCE
C REGRESSION (ODR) OR ORDINARY LINEAR OR NONLINEAR LEAST
C SQUARES (OLS) SOLUTION (SHORT CALL STATEMENT)
C***DESCRIPTION
C FOR DETAILS, SEE ODRPACK USER'S REFERENCE GUIDE.
C***REFERENCES BOGGS, P. T., R. H. BYRD, J. R. DONALDSON, AND
C R. B. SCHNABEL (1989),
C "ALGORITHM 676 --- ODRPACK: SOFTWARE FOR WEIGHTED
C ORTHOGONAL DISTANCE REGRESSION,"
C ACM TRANS. MATH. SOFTWARE., 15(4):348-364.
C BOGGS, P. T., R. H. BYRD, J. E. ROGERS, AND
C R. B. SCHNABEL (1992),
C "USER'S REFERENCE GUIDE FOR ODRPACK VERSION 2.01,
C SOFTWARE FOR WEIGHTED ORTHOGONAL DISTANCE REGRESSION,"
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C INTERNAL REPORT NUMBER 92-4834.
C BOGGS, P. T., R. H. BYRD, AND R. B. SCHNABEL (1987),
C "A STABLE AND EFFICIENT ALGORITHM FOR NONLINEAR
C ORTHOGONAL DISTANCE REGRESSION,"
C SIAM J. SCI. STAT. COMPUT., 8(6):1052-1078.
C***ROUTINES CALLED DODCNT
C***END PROLOGUE DODR
C...SCALAR ARGUMENTS
INTEGER
+ INFO,JOB,LDWD,LDWE,LDX,LDY,LD2WD,LD2WE,LIWORK,LWORK,
+ M,N,NDIGIT,NP,NQ
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),WORK(LWORK),
+ X(LDX,M),Y(LDY,NQ)
INTEGER
+ IWORK(LIWORK)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ NEGONE,PARTOL,SSTOL,TAUFAC,ZERO
INTEGER
+ IPRINT,LDIFX,LDSCLD,LDSTPD,LUNERR,LUNRPT,MAXIT
LOGICAL
+ SHORT
C...LOCAL ARRAYS
DOUBLE PRECISION
+ SCLB(1),SCLD(1,1),STPB(1),STPD(1,1),WD1(1,1,1)
INTEGER
+ IFIXB(1),IFIXX(1,1)
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DODCNT
C...DATA STATEMENTS
DATA
+ NEGONE,ZERO
+ /-1.0D0,0.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C IPRINT: THE PRINT CONTROL VARIABLE.
C IWORK: THE INTEGER WORK SPACE.
C JOB: THE VARIABLE CONTROLLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERR: THE LOGICAL UNIT NUMBER FOR ERROR MESSAGES.
C LUNRPT: THE LOGICAL UNIT NUMBER FOR COMPUTATION REPORTS.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C N: THE NUMBER OF OBSERVATIONS.
C NEGONE: THE VALUE -1.0D0.
C NDIGIT: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS, AS
C SUPPLIED BY THE USER.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUES FOR DELTA.
C STPB: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=.TRUE.) OR THE LONG-CALL
C (SHORT=.FALSE.).
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C WD: THE DELTA WEIGHTS.
C WD1: A DUMMY ARRAY USED WHEN WD(1,1,1)=0.0D0.
C WE: THE EPSILON WEIGHTS.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C X: THE EXPLANATORY VARIABLE.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C***FIRST EXECUTABLE STATEMENT DODR
C INITIALIZE NECESSARY VARIABLES TO INDICATE USE OF DEFAULT VALUES
IFIXB(1) = -1
IFIXX(1,1) = -1
LDIFX = 1
NDIGIT = -1
TAUFAC = NEGONE
SSTOL = NEGONE
PARTOL = NEGONE
MAXIT = -1
STPB(1) = NEGONE
STPD(1,1) = NEGONE
LDSTPD = 1
SCLB(1) = NEGONE
SCLD(1,1) = NEGONE
LDSCLD = 1
SHORT = .TRUE.
IF (WD(1,1,1).NE.ZERO) THEN
CALL DODCNT
+ (SHORT, FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
ELSE
WD1(1,1,1) = NEGONE
CALL DODCNT
+ (SHORT, FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD1,1,1, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
END IF
RETURN
END
*DODRC
SUBROUTINE DODRC
+ (FCN,
+ N,M,NP,NQ,
+ BETA,
+ Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC,
+ SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD,
+ SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
C***BEGIN PROLOGUE DODRC
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***CATEGORY NO. G2E,I1B1
C***KEYWORDS ORTHOGONAL DISTANCE REGRESSION,
C NONLINEAR LEAST SQUARES,
C MEASUREMENT ERROR MODELS,
C ERRORS IN VARIABLES
C***AUTHOR BOGGS, PAUL T.
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C GAITHERSBURG, MD 20899
C BYRD, RICHARD H.
C DEPARTMENT OF COMPUTER SCIENCE
C UNIVERSITY OF COLORADO, BOULDER, CO 80309
C ROGERS, JANET E.
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C BOULDER, CO 80303-3328
C SCHNABEL, ROBERT B.
C DEPARTMENT OF COMPUTER SCIENCE
C UNIVERSITY OF COLORADO, BOULDER, CO 80309
C AND
C APPLIED AND COMPUTATIONAL MATHEMATICS DIVISION
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C BOULDER, CO 80303-3328
C***PURPOSE DOUBLE PRECISION DRIVER ROUTINE FOR FINDING
C THE WEIGHTED EXPLICIT OR IMPLICIT ORTHOGONAL DISTANCE
C REGRESSION (ODR) OR ORDINARY LINEAR OR NONLINEAR LEAST
C SQUARES (OLS) SOLUTION (LONG CALL STATEMENT)
C***DESCRIPTION
C FOR DETAILS, SEE ODRPACK USER'S REFERENCE GUIDE.
C***REFERENCES BOGGS, P. T., R. H. BYRD, J. R. DONALDSON, AND
C R. B. SCHNABEL (1989),
C "ALGORITHM 676 --- ODRPACK: SOFTWARE FOR WEIGHTED
C ORTHOGONAL DISTANCE REGRESSION,"
C ACM TRANS. MATH. SOFTWARE., 15(4):348-364.
C BOGGS, P. T., R. H. BYRD, J. E. ROGERS, AND
C R. B. SCHNABEL (1992),
C "USER'S REFERENCE GUIDE FOR ODRPACK VERSION 2.01,
C SOFTWARE FOR WEIGHTED ORTHOGONAL DISTANCE REGRESSION,"
C NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
C INTERNAL REPORT NUMBER 92-4834.
C BOGGS, P. T., R. H. BYRD, AND R. B. SCHNABEL (1987),
C "A STABLE AND EFFICIENT ALGORITHM FOR NONLINEAR
C ORTHOGONAL DISTANCE REGRESSION,"
C SIAM J. SCI. STAT. COMPUT., 8(6):1052-1078.
C***ROUTINES CALLED DODCNT
C***END PROLOGUE DODRC
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PARTOL,SSTOL,TAUFAC
INTEGER
+ INFO,IPRINT,JOB,LDIFX,LDSCLD,LDSTPD,LDWD,LDWE,LDX,LDY,
+ LD2WD,LD2WE,LIWORK,LUNERR,LUNRPT,LWORK,M,MAXIT,N,NDIGIT,NP,NQ
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),SCLB(NP),SCLD(LDSCLD,M),STPB(NP),STPD(LDSTPD,M),
+ WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),WORK(LWORK),
+ X(LDX,M),Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),IWORK(LIWORK)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ NEGONE,ZERO
LOGICAL
+ SHORT
C...LOCAL ARRAYS
DOUBLE PRECISION
+ WD1(1,1,1)
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DODCNT
C...DATA STATEMENTS
DATA
+ NEGONE,ZERO
+ /-1.0D0,0.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C IPRINT: THE PRINT CONTROL VARIABLE.
C IWORK: THE INTEGER WORK SPACE.
C JOB: THE VARIABLE CONTROLLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERR: THE LOGICAL UNIT NUMBER FOR ERROR MESSAGES.
C LUNRPT: THE LOGICAL UNIT NUMBER FOR COMPUTATION REPORTS.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C N: THE NUMBER OF OBSERVATIONS.
C NDIGIT: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS, AS
C SUPPLIED BY THE USER.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUES FOR DELTA.
C STPB: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=.TRUE.) OR THE LONG-CALL
C (SHORT=.FALSE.).
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C WD: THE DELTA WEIGHTS.
C WD1: A DUMMY ARRAY USED WHEN WD(1,1,1)=0.0D0.
C WE: THE EPSILON WEIGHTS.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C X: THE EXPLANATORY VARIABLE.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C***FIRST EXECUTABLE STATEMENT DODRC
SHORT = .FALSE.
IF (WD(1,1,1).NE.ZERO) THEN
CALL DODCNT
+ (SHORT, FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
ELSE
WD1(1,1,1) = NEGONE
CALL DODCNT
+ (SHORT, FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD1,1,1, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
END IF
RETURN
END
*DACCES
SUBROUTINE DACCES
+ (N,M,NP,NQ,LDWE,LD2WE,
+ WORK,LWORK,IWORK,LIWORK,
+ ACCESS,ISODR,
+ JPVT,OMEGA,U,QRAUX,SD,VCV,WRK1,WRK2,WRK3,WRK4,WRK5,WRK6,
+ NNZW,NPP,
+ JOB,PARTOL,SSTOL,MAXIT,TAUFAC,ETA,NETA,
+ LUNRPT,IPR1,IPR2,IPR2F,IPR3,
+ WSS,RVAR,IDF,
+ TAU,ALPHA,NITER,NFEV,NJEV,INT2,OLMAVG,
+ RCOND,IRANK,ACTRS,PNORM,PRERS,RNORMS,ISTOP)
C***BEGIN PROLOGUE DACCES
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DIWINF,DWINF
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE ACCESS OR STORE VALUES IN THE WORK ARRAYS
C***END PROLOGUE DACESS
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ACTRS,ALPHA,ETA,OLMAVG,PARTOL,PNORM,PRERS,RCOND,
+ RNORMS,RVAR,SSTOL,TAU,TAUFAC
INTEGER
+ IDF,INT2,IPR1,IPR2,IPR2F,IPR3,IRANK,ISTOP,ISTOPI,JOB,JPVT,
+ LDWE,LD2WE,LIWORK,LUNRPT,LWORK,M,MAXIT,N,NETA,NFEV,NITER,NJEV,
+ NNZW,NP,NPP,NQ,OMEGA,QRAUX,SD,U,VCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK6
LOGICAL
+ ACCESS,ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ WORK(LWORK),WSS(3)
INTEGER
+ IWORK(LIWORK)
C...LOCAL SCALARS
INTEGER
+ ACTRSI,ALPHAI,BETACI,BETANI,BETASI,BETA0I,
+ DELTAI,DELTNI,DELTSI,DIFFI,EPSI,
+ EPSMAI,ETAI,FJACBI,FJACDI,FNI,FSI,IDFI,INT2I,IPRINI,IPRINT,
+ IRANKI,JOBI,JPVTI,LDTTI,LIWKMN,LUNERI,LUNRPI,LWKMN,MAXITI,
+ MSGB,MSGD,NETAI,NFEVI,NITERI,NJEVI,NNZWI,NPPI,NROWI,
+ NTOLI,OLMAVI,OMEGAI,PARTLI,PNORMI,PRERSI,QRAUXI,RCONDI,
+ RNORSI,RVARI,SDI,SI,SSFI,SSI,SSTOLI,TAUFCI,TAUI,TI,TTI,UI,
+ VCVI,WE1I,WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,
+ WSSI,WSSDEI,WSSEPI,XPLUSI
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DIWINF,DWINF
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACCESS: THE VARIABLE DESIGNATING WHETHER INFORMATION IS TO BE
C ACCESSED FROM THE WORK ARRAYS (ACCESS=TRUE) OR STORED IN
C THEM (ACCESS=FALSE).
C ACTRS: THE SAVED ACTUAL RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C ACTRSI: THE LOCATION IN ARRAY WORK OF VARIABLE ACTRS.
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C ALPHAI: THE LOCATION IN ARRAY WORK OF VARIABLE ALPHA.
C BETACI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAC.
C BETANI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAN.
C BETASI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAS.
C BETA0I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETA0.
C DELTAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTA.
C DELTNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAN.
C DELTSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAS.
C DIFFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DIFF.
C EPSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY EPS.
C EPSMAI: THE LOCATION IN ARRAY WORK OF VARIABLE EPSMAC.
C ETA: THE RELATIVE NOISE IN THE FUNCTION RESULTS.
C ETAI: THE LOCATION IN ARRAY WORK OF VARIABLE ETA.
C FJACBI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACB.
C FJACDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACD.
C FNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FN.
C FSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FS.
C IDF: THE DEGREES OF FREEDOM OF THE FIT, EQUAL TO THE NUMBER OF
C OBSERVATIONS WITH NONZERO WEIGHTED DERIVATIVES MINUS THE
C NUMBER OF PARAMETERS BEING ESTIMATED.
C IDFI: THE STARTING LOCATION IN ARRAY IWORK OF VARIABLE IDF.
C INT2: THE NUMBER OF INTERNAL DOUBLING STEPS.
C INT2I: THE LOCATION IN ARRAY IWORK OF VARIABLE INT2.
C IPR1: THE VALUE OF THE FOURTH DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE INITIAL SUMMARY REPORT.
C IPR2: THE VALUE OF THE THIRD DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE ITERATION REPORTS.
C IPR2F: THE VALUE OF THE SECOND DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE FREQUENCY OF THE ITERATION REPORTS.
C IPR3: THE VALUE OF THE FIRST DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE FINAL SUMMARY REPORT.
C IPRINI: THE LOCATION IN ARRAY IWORK OF VARIABLE IPRINT.
C IPRINT: THE PRINT CONTROL VARIABLE.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C IRANKI: THE LOCATION IN ARRAY IWORK OF VARIABLE IRANK.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS TO BE
C FOUND BY ODR (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISTOPI: THE LOCATION IN ARRAY IWORK OF VARIABLE ISTOP.
C IWORK: THE INTEGER WORK SPACE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOBI: THE LOCATION IN ARRAY IWORK OF VARIABLE JOB.
C JPVT: THE PIVOT VECTOR.
C JPVTI: THE STARTING LOCATION IN ARRAY IWORK OF VARIABLE JPVT.
C LDTTI: THE STARTING LOCATION IN ARRAY IWORK OF VARIABLE LDTT.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNERR.
C LUNERR: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C LUNRPI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNRPT.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY WORK.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MAXITI: THE LOCATION IN ARRAY IWORK OF VARIABLE MAXIT.
C MSGB: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGB.
C MSGD: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGD.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C NETAI: THE LOCATION IN ARRAY IWORK OF VARIABLE NETA.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NFEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NFEV.
C NITER: THE NUMBER OF ITERATIONS TAKEN.
C NITERI: THE LOCATION IN ARRAY IWORK OF VARIABLE NITER.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NJEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NJEV.
C NNZW: THE NUMBER OF NONZERO WEIGHTED OBSERVATIONS.
C NNZWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NNZW.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS ACTUALLY ESTIMATED.
C NPPI: THE LOCATION IN ARRAY IWORK OF VARIABLE NPP.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NROW.
C NTOLI: THE LOCATION IN ARRAY IWORK OF VARIABLE NTOL.
C OLMAVG: THE AVERAGE NUMBER OF LEVENBERG-MARQUARDT STEPS PER
C ITERATION.
C OLMAVI: THE LOCATION IN ARRAY WORK OF VARIABLE OLMAVG.
C OMEGA: THE STARTING LOCATION IN ARRAY WORK OF ARRAY OMEGA.
C OMEGAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY OMEGA.
C PARTLI: THE LOCATION IN ARRAY WORK OF VARIABLE PARTOL.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PNORM: THE NORM OF THE SCALED ESTIMATED PARAMETERS.
C PNORMI: THE LOCATION IN ARRAY WORK OF VARIABLE PNORM.
C PRERS: THE SAVED PREDICTED RELATIVE REDUCTION IN THE
C SUM-OF-SQUARES.
C PRERSI: THE LOCATION IN ARRAY WORK OF VARIABLE PRERS.
C QRAUX: THE STARTING LOCATION IN ARRAY WORK OF ARRAY QRAUX.
C QRAUXI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY QRAUX.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION OF FJACB.
C RCONDI: THE LOCATION IN ARRAY WORK OF VARIABLE RCOND.
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C RNORMS: THE NORM OF THE SAVED WEIGHTED EPSILONS AND DELTAS.
C RNORSI: THE LOCATION IN ARRAY WORK OF VARIABLE RNORMS.
C RVAR: THE RESIDUAL VARIANCE, I.E. STANDARD DEVIATION SQUARED.
C RVARI: THE LOCATION IN ARRAY WORK OF VARIABLE RVAR.
C SCLB: THE SCALING VALUES USED FOR BETA.
C SCLD: THE SCALING VALUES USED FOR DELTA.
C SD: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SD.
C SDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SD.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=TRUE) OR THE LONG-
C CALL (SHORT=FALSE).
C SI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY S.
C SSFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SSF.
C SSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SS.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C SSTOLI: THE LOCATION IN ARRAY WORK OF VARIABLE SSTOL.
C TAU: THE TRUST REGION DIAMETER.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TAUFCI: THE LOCATION IN ARRAY WORK OF VARIABLE TAUFAC.
C TAUI: THE LOCATION IN ARRAY WORK OF VARIABLE TAU.
C TI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY T.
C TTI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY TT.
C U: THE STARTING LOCATION IN ARRAY WORK OF ARRAY U.
C UI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY U.
C VCV: THE STARTING LOCATION IN ARRAY WORK OF ARRAY VCV.
C VCVI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY VCV.
C WE1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WE1.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C WRK1: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK1.
C WRK1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK1.
C WRK2: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK2.
C WRK2I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK2.
C WRK3: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK3.
C WRK3I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK3.
C WRK4: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK4.
C WRK4I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK4.
C WRK5: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK5.
C WRK5I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK5.
C WRK6: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK6.
C WRK6I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK6.
C WRK7I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK7.
C WSS: THE SUM OF THE SQUARES OF THE WEIGHTED EPSILONS AND DELTAS,
C THE SUM OF THE SQUARES OF THE WEIGHTED DELTAS, AND
C THE SUM OF THE SQUARES OF THE WEIGHTED EPSILONS.
C WSSI: THE STARTING LOCATION IN ARRAY WORK OF VARIABLE WSS(1).
C WSSDEI: THE STARTING LOCATION IN ARRAY WORK OF VARIABLE WSS(2).
C WSSEPI: THE STARTING LOCATION IN ARRAY WORK OF VARIABLE WSS(3).
C XPLUSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY XPLUSD.
C***FIRST EXECUTABLE STATEMENT DACCES
C FIND STARTING LOCATIONS WITHIN INTEGER WORKSPACE
CALL DIWINF(M,NP,NQ,
+ MSGB,MSGD,JPVTI,ISTOPI,
+ NNZWI,NPPI,IDFI,
+ JOBI,IPRINI,LUNERI,LUNRPI,
+ NROWI,NTOLI,NETAI,
+ MAXITI,NITERI,NFEVI,NJEVI,INT2I,IRANKI,LDTTI,
+ LIWKMN)
C FIND STARTING LOCATIONS WITHIN DOUBLE PRECISION WORK SPACE
CALL DWINF(N,M,NP,NQ,LDWE,LD2WE,ISODR,
+ DELTAI,EPSI,XPLUSI,FNI,SDI,VCVI,
+ RVARI,WSSI,WSSDEI,WSSEPI,RCONDI,ETAI,
+ OLMAVI,TAUI,ALPHAI,ACTRSI,PNORMI,RNORSI,PRERSI,
+ PARTLI,SSTOLI,TAUFCI,EPSMAI,
+ BETA0I,BETACI,BETASI,BETANI,SI,SSI,SSFI,QRAUXI,UI,
+ FSI,FJACBI,WE1I,DIFFI,
+ DELTSI,DELTNI,TI,TTI,OMEGAI,FJACDI,
+ WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,
+ LWKMN)
IF (ACCESS) THEN
C SET STARTING LOCATIONS FOR WORK VECTORS
JPVT = JPVTI
OMEGA = OMEGAI
QRAUX = QRAUXI
SD = SDI
VCV = VCVI
U = UI
WRK1 = WRK1I
WRK2 = WRK2I
WRK3 = WRK3I
WRK4 = WRK4I
WRK5 = WRK5I
WRK6 = WRK6I
C ACCESS VALUES FROM THE WORK VECTORS
ACTRS = WORK(ACTRSI)
ALPHA = WORK(ALPHAI)
ETA = WORK(ETAI)
OLMAVG = WORK(OLMAVI)
PARTOL = WORK(PARTLI)
PNORM = WORK(PNORMI)
PRERS = WORK(PRERSI)
RCOND = WORK(RCONDI)
WSS(1) = WORK(WSSI)
WSS(2) = WORK(WSSDEI)
WSS(3) = WORK(WSSEPI)
RVAR = WORK(RVARI)
RNORMS = WORK(RNORSI)
SSTOL = WORK(SSTOLI)
TAU = WORK(TAUI)
TAUFAC = WORK(TAUFCI)
NETA = IWORK(NETAI)
IRANK = IWORK(IRANKI)
JOB = IWORK(JOBI)
LUNRPT = IWORK(LUNRPI)
MAXIT = IWORK(MAXITI)
NFEV = IWORK(NFEVI)
NITER = IWORK(NITERI)
NJEV = IWORK(NJEVI)
NNZW = IWORK(NNZWI)
NPP = IWORK(NPPI)
IDF = IWORK(IDFI)
INT2 = IWORK(INT2I)
C SET UP PRINT CONTROL VARIABLES
IPRINT = IWORK(IPRINI)
IPR1 = MOD(IPRINT,10000)/1000
IPR2 = MOD(IPRINT,1000)/100
IPR2F = MOD(IPRINT,100)/10
IPR3 = MOD(IPRINT,10)
ELSE
C STORE VALUES INTO THE WORK VECTORS
WORK(ACTRSI) = ACTRS
WORK(ALPHAI) = ALPHA
WORK(OLMAVI) = OLMAVG
WORK(PARTLI) = PARTOL
WORK(PNORMI) = PNORM
WORK(PRERSI) = PRERS
WORK(RCONDI) = RCOND
WORK(WSSI) = WSS(1)
WORK(WSSDEI) = WSS(2)
WORK(WSSEPI) = WSS(3)
WORK(RVARI) = RVAR
WORK(RNORSI) = RNORMS
WORK(SSTOLI) = SSTOL
WORK(TAUI) = TAU
IWORK(IRANKI) = IRANK
IWORK(ISTOPI) = ISTOP
IWORK(NFEVI) = NFEV
IWORK(NITERI) = NITER
IWORK(NJEVI) = NJEV
IWORK(IDFI) = IDF
IWORK(INT2I) = INT2
END IF
RETURN
END
*DESUBI
SUBROUTINE DESUBI
+ (N,M,WD,LDWD,LD2WD,ALPHA,TT,LDTT,I,E)
C***BEGIN PROLOGUE DESUBI
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DZERO
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE E = WD + ALPHA*TT**2
C***END PROLOGUE DESUBI
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ALPHA
INTEGER
+ LDTT,LDWD,LD2WD,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ E(M,M),TT(LDTT,M),WD(LDWD,LD2WD,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ZERO
INTEGER
+ I,J,J1,J2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DZERO
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C E: THE VALUE OF THE ARRAY E = WD + ALPHA*TT**2
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C J1: AN INDEXING VARIABLE.
C J2: AN INDEXING VARIABLE.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NP: THE NUMBER OF RESPONSES PER OBSERVATION.
C TT: THE SCALING VALUES USED FOR DELTA.
C WD: THE SQUARED DELTA WEIGHTS, D**2.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DESUBI
C N.B. THE LOCATIONS OF WD AND TT ACCESSED DEPEND ON THE VALUE
C OF THE FIRST ELEMENT OF EACH ARRAY AND THE LEADING DIMENSIONS
C OF THE MULTIPLY SUBSCRIPTED ARRAYS.
IF (N.EQ.0 .OR. M.EQ.0) RETURN
IF (WD(1,1,1).GE.ZERO) THEN
IF (LDWD.GE.N) THEN
C THE ELEMENTS OF WD HAVE BEEN INDIVIDUALLY SPECIFIED
IF (LD2WD.EQ.1) THEN
C THE ARRAYS STORED IN WD ARE DIAGONAL
CALL DZERO(M,M,E,M)
DO 10 J=1,M
E(J,J) = WD(I,1,J)
10 CONTINUE
ELSE
C THE ARRAYS STORED IN WD ARE FULL POSITIVE SEMIDEFINITE MATRICES
DO 30 J1=1,M
DO 20 J2=1,M
E(J1,J2) = WD(I,J1,J2)
20 CONTINUE
30 CONTINUE
END IF
IF (TT(1,1).GT.ZERO) THEN
IF (LDTT.GE.N) THEN
DO 110 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(I,J)**2
110 CONTINUE
ELSE
DO 120 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(1,J)**2
120 CONTINUE
END IF
ELSE
DO 130 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(1,1)**2
130 CONTINUE
END IF
ELSE
C WD IS AN M BY M MATRIX
IF (LD2WD.EQ.1) THEN
C THE ARRAY STORED IN WD IS DIAGONAL
CALL DZERO(M,M,E,M)
DO 140 J=1,M
E(J,J) = WD(1,1,J)
140 CONTINUE
ELSE
C THE ARRAY STORED IN WD IS A FULL POSITIVE SEMIDEFINITE MATRICES
DO 160 J1=1,M
DO 150 J2=1,M
E(J1,J2) = WD(1,J1,J2)
150 CONTINUE
160 CONTINUE
END IF
IF (TT(1,1).GT.ZERO) THEN
IF (LDTT.GE.N) THEN
DO 210 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(I,J)**2
210 CONTINUE
ELSE
DO 220 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(1,J)**2
220 CONTINUE
END IF
ELSE
DO 230 J=1,M
E(J,J) = E(J,J) + ALPHA*TT(1,1)**2
230 CONTINUE
END IF
END IF
ELSE
C WD IS A DIAGONAL MATRIX WITH ELEMENTS ABS(WD(1,1,1))
CALL DZERO(M,M,E,M)
IF (TT(1,1).GT.ZERO) THEN
IF (LDTT.GE.N) THEN
DO 310 J=1,M
E(J,J) = ABS(WD(1,1,1)) + ALPHA*TT(I,J)**2
310 CONTINUE
ELSE
DO 320 J=1,M
E(J,J) = ABS(WD(1,1,1)) + ALPHA*TT(1,J)**2
320 CONTINUE
END IF
ELSE
DO 330 J=1,M
E(J,J) = ABS(WD(1,1,1)) + ALPHA*TT(1,1)**2
330 CONTINUE
END IF
END IF
RETURN
END
*DETAF
SUBROUTINE DETAF
+ (FCN,
+ N,M,NP,NQ,
+ XPLUSD,BETA,EPSMAC,NROW,
+ PARTMP,PV0,
+ IFIXB,IFIXX,LDIFX,
+ ISTOP,NFEV,ETA,NETA,
+ WRK1,WRK2,WRK6,WRK7)
C***BEGIN PROLOGUE DETAF
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE NOISE AND NUMBER OF GOOD DIGITS IN FUNCTION RESULTS
C (ADAPTED FROM STARPAC SUBROUTINE ETAFUN)
C***END PROLOGUE DETAF
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ EPSMAC,ETA
INTEGER
+ ISTOP,LDIFX,M,N,NETA,NFEV,NP,NQ,NROW
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),PARTMP(NP),PV0(N,NQ),
+ WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),WRK7(-2:2,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ A,B,FAC,HUNDRD,ONE,P1,P2,P5,STP,TWO,ZERO
INTEGER
+ J,K,L
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,INT,LOG10,MAX,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,P1,P2,P5,ONE,TWO,HUNDRD
+ /0.0D0,0.1D0,0.2D0,0.5D0,1.0D0,2.0D0,1.0D2/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C A: PARAMETERS OF THE LOCAL FIT.
C B: PARAMETERS OF THE LOCAL FIT.
C BETA: THE FUNCTION PARAMETERS.
C EPSMAC: THE VALUE OF MACHINE PRECISION.
C ETA: THE NOISE IN THE MODEL RESULTS.
C FAC: A FACTOR USED IN THE COMPUTATIONS.
C HUNDRD: THE VALUE 1.0D2.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: AN INDEX VARIABLE.
C K: AN INDEX VARIABLE.
C L: AN INDEX VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE MODEL RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER AT WHICH THE DERIVATIVE IS TO BE CHECKED.
C ONE: THE VALUE 1.0D0.
C P1: THE VALUE 0.1D0.
C P2: THE VALUE 0.2D0.
C P5: THE VALUE 0.5D0.
C PARTMP: THE MODEL PARAMETERS.
C PV0: THE ORIGINAL PREDICTED VALUES.
C STP: A SMALL VALUE USED TO PERTURB THE PARAMETERS.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C WRK7: A WORK ARRAY OF (5 BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DETAF
STP = HUNDRD*EPSMAC
ETA = EPSMAC
DO 40 J=-2,2
IF (J.EQ.0) THEN
DO 10 L=1,NQ
WRK7(J,L) = PV0(NROW,L)
10 CONTINUE
ELSE
DO 20 K=1,NP
IF (IFIXB(1).LT.0) THEN
PARTMP(K) = BETA(K) + J*STP*BETA(K)
ELSE IF (IFIXB(K).NE.0) THEN
PARTMP(K) = BETA(K) + J*STP*BETA(K)
ELSE
PARTMP(K) = BETA(K)
END IF
20 CONTINUE
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ PARTMP,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 003,WRK2,WRK6,WRK1,ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
END IF
DO 30 L=1,NQ
WRK7(J,L) = WRK2(NROW,L)
30 CONTINUE
END IF
40 CONTINUE
DO 100 L=1,NQ
A = ZERO
B = ZERO
DO 50 J=-2,2
A = A + WRK7(J,L)
B = B + J*WRK7(J,L)
50 CONTINUE
A = P2*A
B = P1*B
IF ((WRK7(0,L).NE.ZERO) .AND.
+ (ABS(WRK7(1,L)+WRK7(-1,L)).GT.HUNDRD*EPSMAC)) THEN
FAC = ONE/ABS(WRK7(0,L))
ELSE
FAC = ONE
END IF
DO 60 J=-2,2
WRK7(J,L) = ABS((WRK7(J,L)-(A+J*B))*FAC)
ETA = MAX(WRK7(J,L),ETA)
60 CONTINUE
100 CONTINUE
NETA = MAX(TWO,P5-LOG10(ETA))
RETURN
END
*DEVJAC
SUBROUTINE DEVJAC
+ (FCN,
+ ANAJAC,CDJAC,
+ N,M,NP,NQ,
+ BETAC,BETA,STPB,
+ IFIXB,IFIXX,LDIFX,
+ X,LDX,DELTA,XPLUSD,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,FN,
+ STP,WRK1,WRK2,WRK3,WRK6,
+ FJACB,ISODR,FJACD,WE1,LDWE,LD2WE,
+ NJEV,NFEV,ISTOP,INFO)
C***BEGIN PROLOGUE DEVJAC
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DDOT,DIFIX,DJACCD,DJACFD,DWGHT,DUNPAC,DXPY
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE THE WEIGHTED JACOBIANS WRT BETA AND DELTA
C***END PROLOGUE DEVJAC
C...SCALAR ARGUMENTS
INTEGER
+ INFO,ISTOP,LDIFX,LDSTPD,LDTT,LDWE,LDX,LD2WE,
+ M,N,NETA,NFEV,NJEV,NP,NQ
LOGICAL
+ ANAJAC,CDJAC,ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),BETAC(NP),DELTA(N,M),FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ FN(N,NQ),SSF(NP),STP(N),STPB(NP),STPD(LDSTPD,M),TT(LDTT,M),
+ WE1(LDWE,LD2WE,NQ),WRK1(N,M,NQ),WRK2(N,NQ),WRK3(NP),
+ WRK6(N,NP,NQ),X(LDX,M),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
INTEGER
+ IDEVAL,J,K,K1,L
DOUBLE PRECISION
+ ZERO
LOGICAL
+ ERROR
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DIFIX,DJACCD,DJACFD,DWGHT,DUNPAC,DXPY
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT
EXTERNAL
+ DDOT
C...DATA STATEMENTS
DATA ZERO
+ /0.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT
C (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C BETAC: THE CURRENT ESTIMATED VALUES OF THE UNFIXED BETA'S.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR BY FORWARD
C DIFFERENCES (CDJAC=FALSE).
C DELTA: THE ESTIMATED VALUES OF DELTA.
C ERROR: THE VARIABLE DESIGNATING WHETHER ODRPACK DETECTED NONZERO
C VALUES IN ARRAY DELTA IN THE OLS CASE, AND THUS WHETHER
C THE USER MAY HAVE OVERWRITTEN IMPORTANT INFORMATION
C BY COMPUTING FJACD IN THE OLS CASE.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FN: THE PREDICTED VALUES OF THE FUNCTION AT THE CURRENT POINT.
C IDEVAL: THE VARIABLE DESIGNATING WHAT COMPUTATIONS ARE TO BE
C PERFORMED BY USER-SUPPLIED SUBROUTINE FCN.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF DELTA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C ISTOP: THE VARIABLE DESIGNATING THAT THE USER WISHES THE
C COMPUTATIONS STOPPED.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR OLS (ISODR=FALSE).
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C K1: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWE: THE LEADING DIMENSION OF ARRAYS WE AND WE1.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LD2WE: THE SECOND DIMENSION OF ARRAYS WE AND WE1.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C SSF: THE SCALE USED FOR THE BETA'S.
C STP: THE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C STPB: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C TT: THE SCALING VALUES USED FOR DELTA.
C WE1: THE SQUARE ROOTS OF THE EPSILON WEIGHTS IN ARRAY WE.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C X: THE INDEPENDENT VARIABLE.
C XPLUSD: THE VALUES OF X + DELTA.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DEVJAC
C INSERT CURRENT UNFIXED BETA ESTIMATES INTO BETA
CALL DUNPAC(NP,BETAC,BETA,IFIXB)
C COMPUTE XPLUSD = X + DELTA
CALL DXPY(N,M,X,LDX,DELTA,N,XPLUSD,N)
C COMPUTE THE JACOBIAN WRT THE ESTIMATED BETAS (FJACB) AND
C THE JACOBIAN WRT DELTA (FJACD)
ISTOP = 0
IF (ISODR) THEN
IDEVAL = 110
ELSE
IDEVAL = 010
END IF
IF (ANAJAC) THEN
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ IDEVAL,WRK2,FJACB,FJACD,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NJEV = NJEV+1
END IF
C MAKE SURE FIXED ELEMENTS OF FJACD ARE ZERO
IF (ISODR) THEN
DO 10 L=1,NQ
CALL DIFIX(N,M,IFIXX,LDIFX,FJACD(1,1,L),N,FJACD(1,1,L),N)
10 CONTINUE
END IF
ELSE IF (CDJAC) THEN
CALL DJACCD(FCN,
+ N,M,NP,NQ,
+ BETA,X,LDX,DELTA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ STPB,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,STP,WRK1,WRK2,WRK3,WRK6,
+ FJACB,ISODR,FJACD,NFEV,ISTOP)
ELSE
CALL DJACFD(FCN,
+ N,M,NP,NQ,
+ BETA,X,LDX,DELTA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ STPB,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,FN,STP,WRK1,WRK2,WRK3,WRK6,
+ FJACB,ISODR,FJACD,NFEV,ISTOP)
END IF
IF (ISTOP.LT.0) THEN
RETURN
ELSE IF (.NOT.ISODR) THEN
C TRY TO DETECT WHETHER THE USER HAS COMPUTED JFACD
C WITHIN FCN IN THE OLS CASE
ERROR = DDOT(N*M,DELTA,1,DELTA,1).NE.ZERO
IF (ERROR) THEN
INFO = 50300
RETURN
END IF
END IF
C WEIGHT THE JACOBIAN WRT THE ESTIMATED BETAS
IF (IFIXB(1).LT.0) THEN
DO 20 K=1,NP
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,
+ FJACB(1,K,1),N*NP,FJACB(1,K,1),N*NP)
20 CONTINUE
ELSE
K1 = 0
DO 30 K=1,NP
IF (IFIXB(K).GE.1) THEN
K1 = K1 + 1
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,
+ FJACB(1,K,1),N*NP,FJACB(1,K1,1),N*NP)
END IF
30 CONTINUE
END IF
C WEIGHT THE JACOBIAN'S WRT DELTA AS APPROPRIATE
IF (ISODR) THEN
DO 40 J=1,M
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,
+ FJACD(1,J,1),N*M,FJACD(1,J,1),N*M)
40 CONTINUE
END IF
RETURN
END
*DFCTR
SUBROUTINE DFCTR(OKSEMI,A,LDA,N,INFO)
C***BEGIN PROLOGUE DFCTR
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DDOT
C***DATE WRITTEN 910706 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE FACTOR THE POSITIVE (SEMI)DEFINITE MATRIX A USING A
C MODIFIED CHOLESKY FACTORIZATION
C (ADAPTED FROM LINPACK SUBROUTINE DPOFA)
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***END PROLOGUE DFCTR
C...SCALAR ARGUMENTS
INTEGER INFO,LDA,N
LOGICAL OKSEMI
C...ARRAY ARGUMENTS
DOUBLE PRECISION A(LDA,N)
C...LOCAL SCALARS
DOUBLE PRECISION XI,S,T,TEN,ZERO
INTEGER J,K
C...EXTERNAL FUNCTIONS
EXTERNAL DMPREC,DDOT
DOUBLE PRECISION DMPREC,DDOT
C...INTRINSIC FUNCTIONS
INTRINSIC SQRT
C...DATA STATEMENTS
DATA
+ ZERO,TEN
+ /0.0D0,10.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C A: THE ARRAY TO BE FACTORED. UPON RETURN, A CONTAINS THE
C UPPER TRIANGULAR MATRIX R SO THAT A = TRANS(R)*R
C WHERE THE STRICT LOWER TRIANGLE IS SET TO ZERO
C IF INFO .NE. 0 , THE FACTORIZATION IS NOT COMPLETE.
C I: AN INDEXING VARIABLE.
C INFO: AN IDICATOR VARIABLE, WHERE IF
C INFO = 0 THEN FACTORIZATION WAS COMPLETED
C INFO = K SIGNALS AN ERROR CONDITION. THE LEADING MINOR
C OF ORDER K IS NOT POSITIVE (SEMI)DEFINITE.
C J: AN INDEXING VARIABLE.
C LDA: THE LEADING DIMENSION OF ARRAY A.
C N: THE NUMBER OF ROWS AND COLUMNS OF DATA IN ARRAY A.
C OKSEMI: THE INDICATING WHETHER THE FACTORED ARRAY CAN BE POSITIVE
C SEMIDEFINITE (OKSEMI=TRUE) OR WHETHER IT MUST BE FOUND TO
C BE POSITIVE DEFINITE (OKSEMI=FALSE).
C TEN: THE VALUE 10.0D0.
C XI: A VALUE USED TO TEST FOR NON POSITIVE SEMIDEFINITENESS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DFCTR
C SET RELATIVE TOLERANCE FOR DETECTING NON POSITIVE SEMIDEFINITENESS.
XI = -TEN*DMPREC()
C COMPUTE FACTORIZATION, STORING IN UPPER TRIANGULAR PORTION OF A
DO 20 J=1,N
INFO = J
S = ZERO
DO 10 K=1,J-1
IF (A(K,K).EQ.ZERO) THEN
T = ZERO
ELSE
T = A(K,J) - DDOT(K-1,A(1,K),1,A(1,J),1)
T = T/A(K,K)
END IF
A(K,J) = T
S = S + T*T
10 CONTINUE
S = A(J,J) - S
C ......EXIT
IF (A(J,J).LT.ZERO .OR. S.LT.XI*ABS(A(J,J))) THEN
RETURN
ELSE IF (.NOT.OKSEMI .AND. S.LE.ZERO) THEN
RETURN
ELSE IF (S.LE.ZERO) THEN
A(J,J) = ZERO
ELSE
A(J,J) = SQRT(S)
END IF
20 CONTINUE
INFO = 0
C ZERO OUT LOWER PORTION OF A
DO 40 J=2,N
DO 30 K=1,J-1
A(J,K) = ZERO
30 CONTINUE
40 CONTINUE
RETURN
END
*DFCTRW
SUBROUTINE DFCTRW
+ (N,M,NQ,NPP,
+ ISODR,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ WRK0,WRK4,
+ WE1,NNZW,INFO)
C***BEGIN PROLOGUE DFCTRW
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DFCTR
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CHECK INPUT PARAMETERS, INDICATING ERRORS FOUND USING
C NONZERO VALUES OF ARGUMENT INFO AS DESCRIBED IN THE
C ODRPACK REFERENCE GUIDE
C***END PROLOGUE DFCTRW
C...SCALAR ARGUMENTS
INTEGER
+ INFO,LDWD,LDWE,LD2WD,LD2WE,
+ M,N,NNZW,NPP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ WE(LDWE,LD2WE,NQ),WE1(LDWE,LD2WE,NQ),WD(LDWD,LD2WD,M),
+ WRK0(NQ,NQ),WRK4(M,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ZERO
INTEGER
+ I,INF,J,J1,J2,L,L1,L2
LOGICAL
+ NOTZRO
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DFCTR
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C J: AN INDEXING VARIABLE.
C J1: AN INDEXING VARIABLE.
C J2: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C L1: AN INDEXING VARIABLE.
C L2: AN INDEXING VARIABLE.
C LAST: THE LAST ROW OF THE ARRAY TO BE ACCESSED.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NNZW: THE NUMBER OF NONZERO WEIGHTED OBSERVATIONS.
C NOTZRO: THE VARIABLE DESIGNATING WHETHER A GIVEN COMPONENT OF THE
C WEIGHT ARRAY WE CONTAINS A NONZERO ELEMENT (NOTZRO=FALSE)
C OR NOT (NOTZRO=TRUE).
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATIONS.
C WE: THE (SQUARED) EPSILON WEIGHTS.
C WE1: THE FACTORED EPSILON WEIGHTS, S.T. TRANS(WE1)*WE1 = WE.
C WD: THE (SQUARED) DELTA WEIGHTS.
C WRK0: A WORK ARRAY OF (NQ BY NQ) ELEMENTS.
C WRK4: A WORK ARRAY OF (M BY M) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DFCTRW
C CHECK EPSILON WEIGHTS, AND STORE FACTORIZATION IN WE1
IF (WE(1,1,1).LT.ZERO) THEN
C WE CONTAINS A SCALAR
WE1(1,1,1) = -SQRT(ABS(WE(1,1,1)))
NNZW = N
ELSE
NNZW = 0
IF (LDWE.EQ.1) THEN
IF (LD2WE.EQ.1) THEN
C WE CONTAINS A DIAGONAL MATRIX
DO 110 L=1,NQ
IF (WE(1,1,L).GT.ZERO) THEN
NNZW = N
WE1(1,1,L) = SQRT(WE(1,1,L))
ELSE IF (WE(1,1,L).LT.ZERO) THEN
INFO = 30010
GO TO 300
END IF
110 CONTINUE
ELSE
C WE CONTAINS A FULL NQ BY NQ SEMIDEFINITE MATRIX
DO 130 L1=1,NQ
DO 120 L2=L1,NQ
WRK0(L1,L2) = WE(1,L1,L2)
120 CONTINUE
130 CONTINUE
CALL DFCTR(.TRUE.,WRK0,NQ,NQ,INF)
IF (INF.NE.0) THEN
INFO = 30010
GO TO 300
ELSE
DO 150 L1=1,NQ
DO 140 L2=1,NQ
WE1(1,L1,L2) = WRK0(L1,L2)
140 CONTINUE
IF (WE1(1,L1,L1).NE.ZERO) THEN
NNZW = N
END IF
150 CONTINUE
END IF
END IF
ELSE
IF (LD2WE.EQ.1) THEN
C WE CONTAINS AN ARRAY OF DIAGONAL MATRIX
DO 220 I=1,N
NOTZRO = .FALSE.
DO 210 L=1,NQ
IF (WE(I,1,L).GT.ZERO) THEN
NOTZRO = .TRUE.
WE1(I,1,L) = SQRT(WE(I,1,L))
ELSE IF (WE(I,1,L).LT.ZERO) THEN
INFO = 30010
GO TO 300
END IF
210 CONTINUE
IF (NOTZRO) THEN
NNZW = NNZW + 1
END IF
220 CONTINUE
ELSE
C WE CONTAINS AN ARRAY OF FULL NQ BY NQ SEMIDEFINITE MATRICES
DO 270 I=1,N
DO 240 L1=1,NQ
DO 230 L2=L1,NQ
WRK0(L1,L2) = WE(I,L1,L2)
230 CONTINUE
240 CONTINUE
CALL DFCTR(.TRUE.,WRK0,NQ,NQ,INF)
IF (INF.NE.0) THEN
INFO = 30010
GO TO 300
ELSE
NOTZRO = .FALSE.
DO 260 L1=1,NQ
DO 250 L2=1,NQ
WE1(I,L1,L2) = WRK0(L1,L2)
250 CONTINUE
IF (WE1(I,L1,L1).NE.ZERO) THEN
NOTZRO = .TRUE.
END IF
260 CONTINUE
END IF
IF (NOTZRO) THEN
NNZW = NNZW + 1
END IF
270 CONTINUE
END IF
END IF
END IF
C CHECK FOR A SUFFICIENT NUMBER OF NONZERO EPSILON WEIGHTS
IF (NNZW.LT.NPP) THEN
INFO = 30020
END IF
C CHECK DELTA WEIGHTS
300 CONTINUE
IF (.NOT.ISODR .OR. WD(1,1,1).LT.ZERO) THEN
C PROBLEM IS NOT ODR, OR WD CONTAINS A SCALAR
RETURN
ELSE
IF (LDWD.EQ.1) THEN
IF (LD2WD.EQ.1) THEN
C WD CONTAINS A DIAGONAL MATRIX
DO 310 J=1,M
IF (WD(1,1,J).LE.ZERO) THEN
INFO = MAX(30001,INFO+1)
RETURN
END IF
310 CONTINUE
ELSE
C WD CONTAINS A FULL M BY M POSITIVE DEFINITE MATRIX
DO 330 J1=1,M
DO 320 J2=J1,M
WRK4(J1,J2) = WD(1,J1,J2)
320 CONTINUE
330 CONTINUE
CALL DFCTR(.FALSE.,WRK4,M,M,INF)
IF (INF.NE.0) THEN
INFO = MAX(30001,INFO+1)
RETURN
END IF
END IF
ELSE
IF (LD2WD.EQ.1) THEN
C WD CONTAINS AN ARRAY OF DIAGONAL MATRICES
DO 420 I=1,N
DO 410 J=1,M
IF (WD(I,1,J).LE.ZERO) THEN
INFO = MAX(30001,INFO+1)
RETURN
END IF
410 CONTINUE
420 CONTINUE
ELSE
C WD CONTAINS AN ARRAY OF FULL M BY M POSITIVE DEFINITE MATRICES
DO 470 I=1,N
DO 440 J1=1,M
DO 430 J2=J1,M
WRK4(J1,J2) = WD(I,J1,J2)
430 CONTINUE
440 CONTINUE
CALL DFCTR(.FALSE.,WRK4,M,M,INF)
IF (INF.NE.0) THEN
INFO = MAX(30001,INFO+1)
RETURN
END IF
470 CONTINUE
END IF
END IF
END IF
RETURN
END
*DFLAGS
SUBROUTINE DFLAGS
+ (JOB,RESTRT,INITD,DOVCV,REDOJ,ANAJAC,CDJAC,CHKJAC,ISODR,IMPLCT)
C***BEGIN PROLOGUE DFLAGS
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SET FLAGS INDICATING CONDITIONS SPECIFIED BY JOB
C***END PROLOGUE DFLAGS
C...SCALAR ARGUMENTS
INTEGER
+ JOB
LOGICAL
+ ANAJAC,CDJAC,CHKJAC,DOVCV,IMPLCT,INITD,ISODR,REDOJ,RESTRT
C...LOCAL SCALARS
INTEGER
+ J
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT (ANAJAC=TRUE).
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR BY FORWARD
C DIFFERENCES (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER-SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX IS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS TO BE INITIALIZED
C TO ZERO (INITD=TRUE) OR TO THE FIRST N BY M ELEMENTS OF
C ARRAY WORK (INITD=FALSE).
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C J: THE VALUE OF A SPECIFIC DIGIT OF JOB.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C***FIRST EXECUTABLE STATEMENT DFLAGS
IF (JOB.GE.0) THEN
RESTRT= JOB.GE.10000
INITD = MOD(JOB,10000)/1000.EQ.0
J = MOD(JOB,1000)/100
IF (J.EQ.0) THEN
DOVCV = .TRUE.
REDOJ = .TRUE.
ELSE IF (J.EQ.1) THEN
DOVCV = .TRUE.
REDOJ = .FALSE.
ELSE
DOVCV = .FALSE.
REDOJ = .FALSE.
END IF
J = MOD(JOB,100)/10
IF (J.EQ.0) THEN
ANAJAC = .FALSE.
CDJAC = .FALSE.
CHKJAC = .FALSE.
ELSE IF (J.EQ.1) THEN
ANAJAC = .FALSE.
CDJAC = .TRUE.
CHKJAC = .FALSE.
ELSE IF (J.EQ.2) THEN
ANAJAC = .TRUE.
CDJAC = .FALSE.
CHKJAC = .TRUE.
ELSE
ANAJAC = .TRUE.
CDJAC = .FALSE.
CHKJAC = .FALSE.
END IF
J = MOD(JOB,10)
IF (J.EQ.0) THEN
ISODR = .TRUE.
IMPLCT = .FALSE.
ELSE IF (J.EQ.1) THEN
ISODR = .TRUE.
IMPLCT = .TRUE.
ELSE
ISODR = .FALSE.
IMPLCT = .FALSE.
END IF
ELSE
RESTRT = .FALSE.
INITD = .TRUE.
DOVCV = .TRUE.
REDOJ = .TRUE.
ANAJAC = .FALSE.
CDJAC = .FALSE.
CHKJAC = .FALSE.
ISODR = .TRUE.
IMPLCT = .FALSE.
END IF
RETURN
END
*DHSTEP
DOUBLE PRECISION FUNCTION DHSTEP
+ (ITYPE,NETA,I,J,STP,LDSTP)
C***BEGIN PROLOGUE DHSTEP
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SET RELATIVE STEP SIZE FOR FINITE DIFFERENCE DERIVATIVES
C***END PROLOGUE DHSTEP
C...SCALAR ARGUMENTS
INTEGER
+ I,ITYPE,J,LDSTP,NETA
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ STP(LDSTP,J)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEN,THREE,TWO,ZERO
C...DATA STATEMENTS
DATA
+ ZERO,TWO,THREE,TEN
+ /0.0D0,2.0D0,3.0D0,10.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN IDENTIFIER FOR SELECTING USER SUPPLIED STEP SIZES.
C ITYPE: THE FINITE DIFFERENCE METHOD BEING USED, WHERE
C ITYPE = 0 INDICATES FORWARD FINITE DIFFERENCES, AND
C ITYPE = 1 INDICATES CENTRAL FINITE DIFFERENCES.
C J: AN IDENTIFIER FOR SELECTING USER SUPPLIED STEP SIZES.
C LDSTP: THE LEADING DIMENSION OF ARRAY STP.
C NETA: THE NUMBER OF GOOD DIGITS IN THE FUNCTION RESULTS.
C STP: THE STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C TEN: THE VALUE 10.0D0.
C THREE: THE VALUE 3.0D0.
C TWO: THE VALUE 2.0D0.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DHSTEP
C SET DHSTEP TO RELATIVE FINITE DIFFERENCE STEP SIZE
IF (STP(1,1).LE.ZERO) THEN
IF (ITYPE.EQ.0) THEN
C USE DEFAULT FORWARD FINITE DIFFERENCE STEP SIZE
DHSTEP = TEN**(-ABS(NETA)/TWO - TWO)
ELSE
C USE DEFAULT CENTRAL FINITE DIFFERENCE STEP SIZE
DHSTEP = TEN**(-ABS(NETA)/THREE)
END IF
ELSE IF (LDSTP.EQ.1) THEN
DHSTEP = STP(1,J)
ELSE
DHSTEP = STP(I,J)
END IF
RETURN
END
*DIFIX
SUBROUTINE DIFIX
+ (N,M,IFIX,LDIFIX,T,LDT,TFIX,LDTFIX)
C***BEGIN PROLOGUE DIFIX
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 910612 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SET ELEMENTS OF T TO ZERO ACCORDING TO IFIX
C***END PROLOGUE DIFIX
C...SCALAR ARGUMENTS
INTEGER
+ LDIFIX,LDT,LDTFIX,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ T(LDT,M),TFIX(LDTFIX,M)
INTEGER
+ IFIX(LDIFIX,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ZERO
INTEGER
+ I,J
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C IFIX: THE ARRAY DESIGNATING WHETHER AN ELEMENT OF T IS TO BE
C SET TO ZERO.
C J: AN INDEXING VARIABLE.
C LDT: THE LEADING DIMENSION OF ARRAY T.
C LDIFIX: THE LEADING DIMENSION OF ARRAY IFIX.
C LDTFIX: THE LEADING DIMENSION OF ARRAY TFIX.
C M: THE NUMBER OF COLUMNS OF DATA IN THE ARRAY.
C N: THE NUMBER OF ROWS OF DATA IN THE ARRAY.
C T: THE ARRAY BEING SET TO ZERO ACCORDING TO THE ELEMENTS
C OF IFIX.
C TFIX: THE RESULTING ARRAY.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DIFIX
IF (N.EQ.0 .OR. M.EQ.0) RETURN
IF (IFIX(1,1).GE.ZERO) THEN
IF (LDIFIX.GE.N) THEN
DO 20 J=1,M
DO 10 I=1,N
IF (IFIX(I,J).EQ.0) THEN
TFIX(I,J) = ZERO
ELSE
TFIX(I,J) = T(I,J)
END IF
10 CONTINUE
20 CONTINUE
ELSE
DO 100 J=1,M
IF (IFIX(1,J).EQ.0) THEN
DO 30 I=1,N
TFIX(I,J) = ZERO
30 CONTINUE
ELSE
DO 90 I=1,N
TFIX(I,J) = T(I,J)
90 CONTINUE
END IF
100 CONTINUE
END IF
END IF
RETURN
END
*DINIWK
SUBROUTINE DINIWK
+ (N,M,NP,WORK,LWORK,IWORK,LIWORK,
+ X,LDX,IFIXX,LDIFX,SCLD,LDSCLD,
+ BETA,SCLB,
+ SSTOL,PARTOL,MAXIT,TAUFAC,
+ JOB,IPRINT,LUNERR,LUNRPT,
+ EPSMAI,SSTOLI,PARTLI,MAXITI,TAUFCI,
+ JOBI,IPRINI,LUNERI,LUNRPI,
+ SSFI,TTI,LDTTI,DELTAI)
C***BEGIN PROLOGUE DINIWK
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DFLAGS,DMPREC,DSCLB,DSCLD,DZERO
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE INITIALIZE WORK VECTORS AS NECESSARY
C***END PROLOGUE DINIWK
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PARTOL,SSTOL,TAUFAC
INTEGER
+ DELTAI,EPSMAI,IPRINI,IPRINT,JOB,JOBI,LDIFX,
+ LDSCLD,LDTTI,LDX,LIWORK,LUNERI,LUNERR,LUNRPI,LUNRPT,LWORK,M,
+ MAXIT,MAXITI,N,NP,PARTLI,SSFI,SSTOLI,TAUFCI,TTI
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),SCLB(NP),SCLD(LDSCLD,M),WORK(LWORK),X(LDX,M)
INTEGER
+ IFIXX(LDIFX,M),IWORK(LIWORK)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ONE,THREE,TWO,ZERO
INTEGER
+ I,J
LOGICAL
+ ANAJAC,CDJAC,CHKJAC,DOVCV,IMPLCT,INITD,ISODR,REDOJ,RESTRT
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DMPREC
EXTERNAL
+ DMPREC
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DCOPY,DFLAGS,DSCLB,DSCLD,DZERO
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MIN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,ONE,TWO,THREE
+ /0.0D0,1.0D0,2.0D0,3.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT
C (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR BY FORWARD
C DIFFERENCES (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER-SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C DELTAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTA.
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX IS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C EPSMAI: THE LOCATION IN ARRAY WORK OF VARIABLE EPSMAC.
C I: AN INDEXING VARIABLE.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE FIXED
C AT THEIR INPUT VALUES OR NOT.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS TO BE INITIALIZED
C TO ZERO (INITD=TRUE) OR TO THE VALUES IN THE FIRST N BY M
C ELEMENTS OF ARRAY WORK (INITD=FALSE).
C IPRINI: THE LOCATION IN ARRAY IWORK OF VARIABLE IPRINT.
C IPRINT: THE PRINT CONTROL VARIABLE.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C IWORK: THE INTEGER WORK SPACE.
C J: AN INDEXING VARIABLE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOBI: THE LOCATION IN ARRAY IWORK OF VARIABLE JOB.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDTTI: THE LEADING DIMENSION OF ARRAY TT.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNERR.
C LUNERR: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C LUNRPI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNRPT.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MAXITI: THE LOCATION IN ARRAY IWORK OF VARIABLE MAXIT.
C N: THE NUMBER OF OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C ONE: THE VALUE 1.0D0.
C PARTLI: THE LOCATION IN ARRAY WORK OF VARIABLE PARTOL.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING CRITERIA.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUES FOR DELTA.
C SSFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SSF.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING CRITERIA.
C SSTOLI: THE LOCATION IN ARRAY WORK OF VARIABLE SSTOL.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TAUFCI: THE LOCATION IN ARRAY WORK OF VARIABLE TAUFAC.
C THREE: THE VALUE 3.0D0.
C TTI: THE STARTING LOCATION IN ARRAY WORK OF THE ARRAY TT.
C TWO: THE VALUE 2.0D0.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C X: THE INDEPENDENT VARIABLE.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DINIWK
CALL DFLAGS(JOB,RESTRT,INITD,DOVCV,REDOJ,
+ ANAJAC,CDJAC,CHKJAC,ISODR,IMPLCT)
C STORE VALUE OF MACHINE PRECISION IN WORK VECTOR
WORK(EPSMAI) = DMPREC()
C SET TOLERANCE FOR STOPPING CRITERIA BASED ON THE CHANGE IN THE
C PARAMETERS (SEE ALSO SUBPROGRAM DODCNT)
IF (PARTOL.LT.ZERO) THEN
WORK(PARTLI) = WORK(EPSMAI)**(TWO/THREE)
ELSE
WORK(PARTLI) = MIN(PARTOL, ONE)
END IF
C SET TOLERANCE FOR STOPPING CRITERIA BASED ON THE CHANGE IN THE
C SUM OF SQUARES OF THE WEIGHTED OBSERVATIONAL ERRORS
IF (SSTOL.LT.ZERO) THEN
WORK(SSTOLI) = SQRT(WORK(EPSMAI))
ELSE
WORK(SSTOLI) = MIN(SSTOL, ONE)
END IF
C SET FACTOR FOR COMPUTING TRUST REGION DIAMETER AT FIRST ITERATION
IF (TAUFAC.LE.ZERO) THEN
WORK(TAUFCI) = ONE
ELSE
WORK(TAUFCI) = MIN(TAUFAC, ONE)
END IF
C SET MAXIMUM NUMBER OF ITERATIONS
IF (MAXIT.LT.0) THEN
IWORK(MAXITI) = 50
ELSE
IWORK(MAXITI) = MAXIT
END IF
C STORE PROBLEM INITIALIZATION AND COMPUTATIONAL METHOD CONTROL
C VARIABLE
IF (JOB.LE.0) THEN
IWORK(JOBI) = 0
ELSE
IWORK(JOBI) = JOB
END IF
C SET PRINT CONTROL
IF (IPRINT.LT.0) THEN
IWORK(IPRINI) = 2001
ELSE
IWORK(IPRINI) = IPRINT
END IF
C SET LOGICAL UNIT NUMBER FOR ERROR MESSAGES
IF (LUNERR.LT.0) THEN
IWORK(LUNERI) = 6
ELSE
IWORK(LUNERI) = LUNERR
END IF
C SET LOGICAL UNIT NUMBER FOR COMPUTATION REPORTS
IF (LUNRPT.LT.0) THEN
IWORK(LUNRPI) = 6
ELSE
IWORK(LUNRPI) = LUNRPT
END IF
C COMPUTE SCALING FOR BETA'S AND DELTA'S
IF (SCLB(1).LE.ZERO) THEN
CALL DSCLB(NP,BETA,WORK(SSFI))
ELSE
CALL DCOPY(NP,SCLB,1,WORK(SSFI),1)
END IF
IF (ISODR) THEN
IF (SCLD(1,1).LE.ZERO) THEN
IWORK(LDTTI) = N
CALL DSCLD(N,M,X,LDX,WORK(TTI),IWORK(LDTTI))
ELSE
IF (LDSCLD.EQ.1) THEN
IWORK(LDTTI) = 1
CALL DCOPY(M,SCLD(1,1),1,WORK(TTI),1)
ELSE
IWORK(LDTTI) = N
DO 10 J=1,M
CALL DCOPY(N,SCLD(1,J),1,
+ WORK(TTI+(J-1)*IWORK(LDTTI)),1)
10 CONTINUE
END IF
END IF
END IF
C INITIALIZE DELTA'S AS NECESSARY
IF (ISODR) THEN
IF (INITD) THEN
CALL DZERO(N,M,WORK(DELTAI),N)
ELSE
IF (IFIXX(1,1).GE.0) THEN
IF (LDIFX.EQ.1) THEN
DO 20 J=1,M
IF (IFIXX(1,J).EQ.0) THEN
CALL DZERO(N,1,WORK(DELTAI+(J-1)*N),N)
END IF
20 CONTINUE
ELSE
DO 40 J=1,M
DO 30 I=1,N
IF (IFIXX(I,J).EQ.0) THEN
WORK(DELTAI-1+I+(J-1)*N) = ZERO
END IF
30 CONTINUE
40 CONTINUE
END IF
END IF
END IF
ELSE
CALL DZERO(N,M,WORK(DELTAI),N)
END IF
RETURN
END
*DIWINF
SUBROUTINE DIWINF
+ (M,NP,NQ,
+ MSGBI,MSGDI,IFIX2I,ISTOPI,
+ NNZWI,NPPI,IDFI,
+ JOBI,IPRINI,LUNERI,LUNRPI,
+ NROWI,NTOLI,NETAI,
+ MAXITI,NITERI,NFEVI,NJEVI,INT2I,IRANKI,LDTTI,
+ LIWKMN)
C***BEGIN PROLOGUE DIWINF
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SET STORAGE LOCATIONS WITHIN INTEGER WORK SPACE
C***END PROLOGUE DIWINF
C...SCALAR ARGUMENTS
INTEGER
+ IDFI,INT2I,IPRINI,IRANKI,ISTOPI,JOBI,IFIX2I,LDTTI,LIWKMN,
+ LUNERI,LUNRPI,M,MAXITI,MSGBI,MSGDI,NETAI,NFEVI,NITERI,NJEVI,
+ NNZWI,NP,NPPI,NQ,NROWI,NTOLI
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C IDFI: THE LOCATION IN ARRAY IWORK OF VARIABLE IDF.
C IFIX2I: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY IFIX2.
C INT2I: THE LOCATION IN ARRAY IWORK OF VARIABLE INT2.
C IPRINI: THE LOCATION IN ARRAY IWORK OF VARIABLE IPRINT.
C IRANKI: THE LOCATION IN ARRAY IWORK OF VARIABLE IRANK.
C ISTOPI: THE LOCATION IN ARRAY IWORK OF VARIABLE ISTOP.
C JOBI: THE LOCATION IN ARRAY IWORK OF VARIABLE JOB.
C LDTTI: THE LOCATION IN ARRAY IWORK OF VARIABLE LDTT.
C LIWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY IWORK.
C LUNERI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNERR.
C LUNRPI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNRPT.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C MAXITI: THE LOCATION IN ARRAY IWORK OF VARIABLE MAXIT.
C MSGBI: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGB.
C MSGDI: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGD.
C NETAI: THE LOCATION IN ARRAY IWORK OF VARIABLE NETA.
C NFEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NFEV.
C NITERI: THE LOCATION IN ARRAY IWORK OF VARIABEL NITER.
C NJEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NJEV.
C NNZWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NNZW.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPPI: THE LOCATION IN ARRAY IWORK OF VARIABLE NPP.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NROW.
C NTOLI: THE LOCATION IN ARRAY IWORK OF VARIABLE NTOL.
C***FIRST EXECUTABLE STATEMENT DIWINF
IF (NP.GE.1 .AND. M.GE.1) THEN
MSGBI = 1
MSGDI = MSGBI + NQ*NP+1
IFIX2I = MSGDI + NQ*M+1
ISTOPI = IFIX2I + NP
NNZWI = ISTOPI + 1
NPPI = NNZWI + 1
IDFI = NPPI + 1
JOBI = IDFI + 1
IPRINI = JOBI + 1
LUNERI = IPRINI + 1
LUNRPI = LUNERI + 1
NROWI = LUNRPI + 1
NTOLI = NROWI + 1
NETAI = NTOLI + 1
MAXITI = NETAI + 1
NITERI = MAXITI + 1
NFEVI = NITERI + 1
NJEVI = NFEVI + 1
INT2I = NJEVI + 1
IRANKI = INT2I + 1
LDTTI = IRANKI + 1
LIWKMN = LDTTI
ELSE
MSGBI = 1
MSGDI = 1
IFIX2I = 1
ISTOPI = 1
NNZWI = 1
NPPI = 1
IDFI = 1
JOBI = 1
IPRINI = 1
LUNERI = 1
LUNRPI = 1
NROWI = 1
NTOLI = 1
NETAI = 1
MAXITI = 1
NITERI = 1
NFEVI = 1
NJEVI = 1
INT2I = 1
IRANKI = 1
LDTTI = 1
LIWKMN = 1
END IF
RETURN
END
*DJACCD
SUBROUTINE DJACCD
+ (FCN,
+ N,M,NP,NQ,
+ BETA,X,LDX,DELTA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ STPB,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,STP,WRK1,WRK2,WRK3,WRK6,
+ FJACB,ISODR,FJACD,NFEV,ISTOP)
C***BEGIN PROLOGUE DJACCD
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DHSTEP,DZERO
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE CENTRAL DIFFERENCE APPROXIMATIONS TO THE
C JACOBIAN WRT THE ESTIMATED BETAS AND WRT THE DELTAS
C***END PROLOGUE DJACCD
C...SCALAR ARGUMENTS
INTEGER
+ ISTOP,LDIFX,LDSTPD,LDTT,LDX,M,N,NETA,NFEV,NP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DELTA(N,M),FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ SSF(NP),STP(N),STPB(NP),STPD(LDSTPD,M),TT(LDTT,M),
+ WRK1(N,M,NQ),WRK2(N,NQ),WRK3(NP),WRK6(N,NP,NQ),
+ X(LDX,M),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ BETAK,ONE,TYPJ,ZERO
INTEGER
+ I,J,K,L
LOGICAL
+ DOIT,SETZRO
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DZERO
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DHSTEP
EXTERNAL
+ DHSTEP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MAX,SIGN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,ONE
+ /0.0D0,1.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C BETAK: THE K-TH FUNCTION PARAMETER.
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DOIT: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVE WRT A GIVEN
C BETA OR DELTA NEEDS TO BE COMPUTED (DOIT=TRUE) OR NOT
C (DOIT=FALSE).
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C I: AN INDEXING VARIABLE.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE FIXED
C AT THEIR INPUT VALUES OR NOT.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF GOOD DIGITS IN THE FUNCTION RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C ONE: THE VALUE 1.0D0.
C SETZRO: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVE WRT SOME
C DELTA NEEDS TO BE SET TO ZERO (SETZRO=TRUE) OR NOT
C (SETZRO=FALSE).
C SSF: THE SCALING VALUES USED FOR BETA.
C STP: THE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO EACH DELTA.
C STPB: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO EACH BETA.
C STPD: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO EACH DELTA.
C TT: THE SCALING VALUES USED FOR DELTA.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C X: THE EXPLANATORY VARIABLE.
C XPLUSD: THE VALUES OF X + DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DJACCD
C COMPUTE THE JACOBIAN WRT THE ESTIMATED BETAS
DO 60 K=1,NP
IF (IFIXB(1).GE.0) THEN
IF (IFIXB(K).EQ.0) THEN
DOIT = .FALSE.
ELSE
DOIT = .TRUE.
END IF
ELSE
DOIT = .TRUE.
END IF
IF (.NOT.DOIT) THEN
DO 10 L=1,NQ
CALL DZERO(N,1,FJACB(1,K,L),N)
10 CONTINUE
ELSE
BETAK = BETA(K)
IF (BETAK.EQ.ZERO) THEN
IF (SSF(1).LT.ZERO) THEN
TYPJ = ONE/ABS(SSF(1))
ELSE
TYPJ = ONE/SSF(K)
END IF
ELSE
TYPJ = ABS(BETAK)
END IF
WRK3(K) = BETAK
+ + SIGN(ONE,BETAK)*TYPJ*DHSTEP(1,NETA,1,K,STPB,1)
WRK3(K) = WRK3(K) - BETAK
BETA(K) = BETAK + WRK3(K)
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
DO 30 L=1,NQ
DO 20 I=1,N
FJACB(I,K,L) = WRK2(I,L)
20 CONTINUE
30 CONTINUE
END IF
BETA(K) = BETAK - WRK3(K)
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
END IF
DO 50 L=1,NQ
DO 40 I=1,N
FJACB(I,K,L) = (FJACB(I,K,L)-WRK2(I,L))/(2*WRK3(K))
40 CONTINUE
50 CONTINUE
BETA(K) = BETAK
END IF
60 CONTINUE
C COMPUTE THE JACOBIAN WRT THE X'S
IF (ISODR) THEN
DO 220 J=1,M
IF (IFIXX(1,1).LT.0) THEN
DOIT = .TRUE.
SETZRO = .FALSE.
ELSE IF (LDIFX.EQ.1) THEN
IF (IFIXX(1,J).EQ.0) THEN
DOIT = .FALSE.
ELSE
DOIT = .TRUE.
END IF
SETZRO = .FALSE.
ELSE
DOIT = .FALSE.
SETZRO = .FALSE.
DO 100 I=1,N
IF (IFIXX(I,J).NE.0) THEN
DOIT = .TRUE.
ELSE
SETZRO = .TRUE.
END IF
100 CONTINUE
END IF
IF (.NOT.DOIT) THEN
DO 110 L=1,NQ
CALL DZERO(N,1,FJACD(1,J,L),N)
110 CONTINUE
ELSE
DO 120 I=1,N
IF (XPLUSD(I,J).EQ.ZERO) THEN
IF (TT(1,1).LT.ZERO) THEN
TYPJ = ONE/ABS(TT(1,1))
ELSE IF (LDTT.EQ.1) THEN
TYPJ = ONE/TT(1,J)
ELSE
TYPJ = ONE/TT(I,J)
END IF
ELSE
TYPJ = ABS(XPLUSD(I,J))
END IF
STP(I) = XPLUSD(I,J)
+ + SIGN(ONE,XPLUSD(I,J))
+ *TYPJ*DHSTEP(1,NETA,I,J,STPD,LDSTPD)
STP(I) = STP(I) - XPLUSD(I,J)
XPLUSD(I,J) = XPLUSD(I,J) + STP(I)
120 CONTINUE
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
DO 140 L=1,NQ
DO 130 I=1,N
FJACD(I,J,L) = WRK2(I,L)
130 CONTINUE
140 CONTINUE
END IF
DO 150 I=1,N
XPLUSD(I,J) = X(I,J) + DELTA(I,J) - STP(I)
150 CONTINUE
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
END IF
IF (SETZRO) THEN
DO 180 I=1,N
IF (IFIXX(I,J).EQ.0) THEN
DO 160 L=1,NQ
FJACD(I,J,L) = ZERO
160 CONTINUE
ELSE
DO 170 L=1,NQ
FJACD(I,J,L) = (FJACD(I,J,L)-WRK2(I,L))/
+ (2*STP(I))
170 CONTINUE
END IF
180 CONTINUE
ELSE
DO 200 L=1,NQ
DO 190 I=1,N
FJACD(I,J,L) = (FJACD(I,J,L)-WRK2(I,L))/
+ (2*STP(I))
190 CONTINUE
200 CONTINUE
END IF
DO 210 I=1,N
XPLUSD(I,J) = X(I,J) + DELTA(I,J)
210 CONTINUE
END IF
220 CONTINUE
END IF
RETURN
END
*DJACFD
SUBROUTINE DJACFD
+ (FCN,
+ N,M,NP,NQ,
+ BETA,X,LDX,DELTA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ STPB,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,FN,STP,WRK1,WRK2,WRK3,WRK6,
+ FJACB,ISODR,FJACD,NFEV,ISTOP)
C***BEGIN PROLOGUE DJACFD
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DHSTEP,DZERO
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE FORWARD DIFFERENCE APPROXIMATIONS TO THE
C JACOBIAN WRT THE ESTIMATED BETAS AND WRT THE DELTAS
C***END PROLOGUE DJACFD
C...SCALAR ARGUMENTS
INTEGER
+ ISTOP,LDIFX,LDSTPD,LDTT,LDX,M,N,NETA,NFEV,NP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DELTA(N,M),FJACB(N,NP,NQ),FJACD(N,M,NQ),FN(N,NQ),
+ SSF(NP),STP(N),STPB(NP),STPD(LDSTPD,M),TT(LDTT,M),
+ WRK1(N,M,NQ),WRK2(N,NQ),WRK3(NP),WRK6(N,NP,NQ),
+ X(LDX,M),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ BETAK,ONE,TYPJ,ZERO
INTEGER
+ I,J,K,L
LOGICAL
+ DOIT,SETZRO
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DZERO
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DHSTEP
EXTERNAL
+ DHSTEP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MAX,SIGN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,ONE
+ /0.0D0,1.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C BETAK: THE K-TH FUNCTION PARAMETER.
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DOIT: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVE WRT A
C GIVEN BETA OR DELTA NEEDS TO BE COMPUTED (DOIT=TRUE)
C OR NOT (DOIT=FALSE).
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FN: THE NEW PREDICTED VALUES FROM THE FUNCTION.
C I: AN INDEXING VARIABLE.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF GOOD DIGITS IN THE FUNCTION RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C ONE: THE VALUE 1.0D0.
C SETZRO: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVE WRT SOME
C DELTA NEEDS TO BE SET TO ZERO (SETZRO=TRUE) OR NOT
C (SETZRO=FALSE).
C SSF: THE SCALE USED FOR THE BETA'S.
C STP: THE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C STPB: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C TT: THE SCALING VALUES USED FOR DELTA.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C X: THE EXPLANATORY VARIABLE.
C XPLUSD: THE VALUES OF X + DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DJACFD
C COMPUTE THE JACOBIAN WRT THE ESTIMATED BETAS
DO 40 K=1,NP
IF (IFIXB(1).GE.0) THEN
IF (IFIXB(K).EQ.0) THEN
DOIT = .FALSE.
ELSE
DOIT = .TRUE.
END IF
ELSE
DOIT = .TRUE.
END IF
IF (.NOT.DOIT) THEN
DO 10 L=1,NQ
CALL DZERO(N,1,FJACB(1,K,L),N)
10 CONTINUE
ELSE
BETAK = BETA(K)
IF (BETAK.EQ.ZERO) THEN
IF (SSF(1).LT.ZERO) THEN
TYPJ = ONE/ABS(SSF(1))
ELSE
TYPJ = ONE/SSF(K)
END IF
ELSE
TYPJ = ABS(BETAK)
END IF
WRK3(K) = BETAK
+ + SIGN(ONE,BETAK)*TYPJ*DHSTEP(0,NETA,1,K,STPB,1)
WRK3(K) = WRK3(K) - BETAK
BETA(K) = BETAK + WRK3(K)
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
END IF
DO 30 L=1,NQ
DO 20 I=1,N
FJACB(I,K,L) = (WRK2(I,L)-FN(I,L))/WRK3(K)
20 CONTINUE
30 CONTINUE
BETA(K) = BETAK
END IF
40 CONTINUE
C COMPUTE THE JACOBIAN WRT THE X'S
IF (ISODR) THEN
DO 220 J=1,M
IF (IFIXX(1,1).LT.0) THEN
DOIT = .TRUE.
SETZRO = .FALSE.
ELSE IF (LDIFX.EQ.1) THEN
IF (IFIXX(1,J).EQ.0) THEN
DOIT = .FALSE.
ELSE
DOIT = .TRUE.
END IF
SETZRO = .FALSE.
ELSE
DOIT = .FALSE.
SETZRO = .FALSE.
DO 100 I=1,N
IF (IFIXX(I,J).NE.0) THEN
DOIT = .TRUE.
ELSE
SETZRO = .TRUE.
END IF
100 CONTINUE
END IF
IF (.NOT.DOIT) THEN
DO 110 L=1,NQ
CALL DZERO(N,1,FJACD(1,J,L),N)
110 CONTINUE
ELSE
DO 120 I=1,N
IF (XPLUSD(I,J).EQ.ZERO) THEN
IF (TT(1,1).LT.ZERO) THEN
TYPJ = ONE/ABS(TT(1,1))
ELSE IF (LDTT.EQ.1) THEN
TYPJ = ONE/TT(1,J)
ELSE
TYPJ = ONE/TT(I,J)
END IF
ELSE
TYPJ = ABS(XPLUSD(I,J))
END IF
STP(I) = XPLUSD(I,J)
+ + SIGN(ONE,XPLUSD(I,J))
+ *TYPJ*DHSTEP(0,NETA,I,J,STPD,LDSTPD)
STP(I) = STP(I) - XPLUSD(I,J)
XPLUSD(I,J) = XPLUSD(I,J) + STP(I)
120 CONTINUE
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 001,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NFEV = NFEV + 1
DO 140 L=1,NQ
DO 130 I=1,N
FJACD(I,J,L) = WRK2(I,L)
130 CONTINUE
140 CONTINUE
END IF
IF (SETZRO) THEN
DO 180 I=1,N
IF (IFIXX(I,J).EQ.0) THEN
DO 160 L=1,NQ
FJACD(I,J,L) = ZERO
160 CONTINUE
ELSE
DO 170 L=1,NQ
FJACD(I,J,L) = (FJACD(I,J,L)-FN(I,L))/STP(I)
170 CONTINUE
END IF
180 CONTINUE
ELSE
DO 200 L=1,NQ
DO 190 I=1,N
FJACD(I,J,L) = (FJACD(I,J,L)-FN(I,L))/STP(I)
190 CONTINUE
200 CONTINUE
END IF
DO 210 I=1,N
XPLUSD(I,J) = X(I,J) + DELTA(I,J)
210 CONTINUE
END IF
220 CONTINUE
END IF
RETURN
END
*DJCK
SUBROUTINE DJCK
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,STPB,STPD,LDSTPD,
+ SSF,TT,LDTT,
+ ETA,NETA,NTOL,NROW,ISODR,EPSMAC,
+ PV0,FJACB,FJACD,
+ MSGB,MSGD,DIFF,ISTOP,NFEV,NJEV,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DJCK
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DHSTEP,DJCKM
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE DRIVER ROUTINE FOR THE DERIVATIVE CHECKING PROCESS
C (ADAPTED FROM STARPAC SUBROUTINE DCKCNT)
C***END PROLOGUE DJCK
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ EPSMAC,ETA
INTEGER
+ ISTOP,LDIFX,LDSTPD,LDTT,
+ M,N,NETA,NFEV,NJEV,NP,NQ,NROW,NTOL
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DIFF(NQ,NP+M),FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ PV0(N,NQ),SSF(NP),STPB(NP),STPD(LDSTPD,M),TT(LDTT,M),
+ WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSGB(1+NQ*NP),MSGD(1+NQ*M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ DIFFJ,H0,HC0,ONE,P5,PV,TOL,TYPJ,ZERO
INTEGER
+ IDEVAL,J,LQ,MSGB1,MSGD1
LOGICAL
+ ISFIXD,ISWRTB
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DJCKM
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DHSTEP
EXTERNAL
+ DHSTEP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,INT,LOG10
C...DATA STATEMENTS
DATA
+ ZERO,P5,ONE
+ /0.0D0,0.5D0,1.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C DIFF: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR EACH DERIVATIVE CHECKED.
C DIFFJ: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR THE DERIVATIVE BEING
C CHECKED.
C EPSMAC: THE VALUE OF MACHINE PRECISION.
C ETA: THE RELATIVE NOISE IN THE FUNCTION RESULTS.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C H0: THE INITIAL RELATIVE STEP SIZE FOR FORWARD DIFFERENCES.
C HC0: THE INITIAL RELATIVE STEP SIZE FOR CENTRAL DIFFERENCES.
C IDEVAL: THE VARIABLE DESIGNATING WHAT COMPUTATIONS ARE TO BE
C PERFORMED BY USER SUPPLIED SUBROUTINE FCN.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISFIXD: THE VARIABLE DESIGNATING WHETHER THE PARAMETER IS FIXED
C (ISFIXD=TRUE) OR NOT (ISFIXD=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=.TRUE.) OR BY OLS (ISODR=.FALSE.).
C ISWRTB: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVES WRT BETA
C (ISWRTB=TRUE) OR DELTA (ISWRTB=FALSE) ARE BEING CHECKED.
C J: AN INDEX VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGB1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C MSGD1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF RELIABLE DIGITS IN THE MODEL RESULTS, EITHER
C SET BY THE USER OR COMPUTED BY DETAF.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT WHICH
C THE DERIVATIVE IS CHECKED.
C NTOL: THE NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN THE
C NUMERICAL DERIVATIVES AND THE USER SUPPLIED DERIVATIVES.
C ONE: THE VALUE 1.0D0.
C P5: THE VALUE 0.5D0.
C PV: THE SCALAR IN WHICH THE PREDICTED VALUE FROM THE MODEL FOR
C ROW NROW IS STORED.
C PV0: THE PREDICTED VALUES USING THE CURRENT PARAMETER ESTIMATES.
C SSF: THE SCALING VALUES USED FOR BETA.
C STPB: THE STEP SIZE FOR FINITE DIFFERENCE DERIVATIVES WRT BETA.
C STPD: THE STEP SIZE FOR FINITE DIFFERENCE DERIVATIVES WRT DELTA.
C TOL: THE AGREEMENT TOLERANCE.
C TT: THE SCALING VALUES USED FOR DELTA.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DJCK
C SET TOLERANCE FOR CHECKING DERIVATIVES
TOL = ETA**(0.25D0)
NTOL = MAX(ONE,P5-LOG10(TOL))
C COMPUTE USER SUPPLIED DERIVATIVE VALUES
ISTOP = 0
IF (ISODR) THEN
IDEVAL = 110
ELSE
IDEVAL = 010
END IF
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ IDEVAL,WRK2,FJACB,FJACD,
+ ISTOP)
IF (ISTOP.NE.0) THEN
RETURN
ELSE
NJEV = NJEV + 1
END IF
C CHECK DERIVATIVES WRT BETA FOR EACH RESPONSE OF OBSERVATION NROW
MSGB1 = 0
MSGD1 = 0
DO 30 LQ=1,NQ
C SET PREDICTED VALUE OF MODEL AT CURRENT PARAMETER ESTIMATES
PV = PV0(NROW,LQ)
ISWRTB = .TRUE.
DO 10 J=1,NP
IF (IFIXB(1).LT.0) THEN
ISFIXD = .FALSE.
ELSE IF (IFIXB(J).EQ.0) THEN
ISFIXD = .TRUE.
ELSE
ISFIXD = .FALSE.
END IF
IF (ISFIXD) THEN
MSGB(1+LQ+(J-1)*NQ) = -1
ELSE
IF (BETA(J).EQ.ZERO) THEN
IF (SSF(1).LT.ZERO) THEN
TYPJ = ONE/ABS(SSF(1))
ELSE
TYPJ = ONE/SSF(J)
END IF
ELSE
TYPJ = ABS(BETA(J))
END IF
H0 = DHSTEP(0,NETA,1,J,STPB,1)
HC0 = H0
C CHECK DERIVATIVE WRT THE J-TH PARAMETER AT THE NROW-TH ROW
CALL DJCKM(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,EPSMAC,J,LQ,TYPJ,H0,HC0,
+ ISWRTB,PV,FJACB(NROW,J,LQ),
+ DIFFJ,MSGB1,MSGB(2),ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
MSGB(1) = -1
RETURN
ELSE
DIFF(LQ,J) = DIFFJ
END IF
END IF
10 CONTINUE
C CHECK DERIVATIVES WRT X FOR EACH RESPONSE OF OBSERVATION NROW
IF (ISODR) THEN
ISWRTB = .FALSE.
DO 20 J=1,M
IF (IFIXX(1,1).LT.0) THEN
ISFIXD = .FALSE.
ELSE IF (LDIFX.EQ.1) THEN
IF (IFIXX(1,J).EQ.0) THEN
ISFIXD = .TRUE.
ELSE
ISFIXD = .FALSE.
END IF
ELSE
ISFIXD = .FALSE.
END IF
IF (ISFIXD) THEN
MSGD(1+LQ+(J-1)*NQ) = -1
ELSE
IF (XPLUSD(NROW,J).EQ.ZERO) THEN
IF (TT(1,1).LT.ZERO) THEN
TYPJ = ONE/ABS(TT(1,1))
ELSE IF (LDTT.EQ.1) THEN
TYPJ = ONE/TT(1,J)
ELSE
TYPJ = ONE/TT(NROW,J)
END IF
ELSE
TYPJ = ABS(XPLUSD(NROW,J))
END IF
H0 = DHSTEP(0,NETA,NROW,J,STPD,LDSTPD)
HC0 = DHSTEP(1,NETA,NROW,J,STPD,LDSTPD)
C CHECK DERIVATIVE WRT THE J-TH COLUMN OF DELTA AT ROW NROW
CALL DJCKM(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,EPSMAC,J,LQ,TYPJ,H0,HC0,
+ ISWRTB,PV,FJACD(NROW,J,LQ),
+ DIFFJ,MSGD1,MSGD(2),ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
MSGD(1) = -1
RETURN
ELSE
DIFF(LQ,NP+J) = DIFFJ
END IF
END IF
20 CONTINUE
END IF
30 CONTINUE
MSGB(1) = MSGB1
MSGD(1) = MSGD1
RETURN
END
*DJCKC
SUBROUTINE DJCKC
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,EPSMAC,J,LQ,HC,ISWRTB,
+ FD,TYPJ,PVPSTP,STP0,
+ PV,D,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DJCKC
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DJCKF,DPVB,DPVD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CHECK WHETHER HIGH CURVATURE COULD BE THE CAUSE OF THE
C DISAGREEMENT BETWEEN THE NUMERICAL AND ANALYTIC DERVIATIVES
C (ADAPTED FROM STARPAC SUBROUTINE DCKCRV)
C***END PROLOGUE DJCKC
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ D,DIFFJ,EPSMAC,ETA,FD,HC,PV,PVPSTP,STP0,TOL,TYPJ
INTEGER
+ ISTOP,J,LDIFX,LQ,M,N,NFEV,NP,NQ,NROW
LOGICAL
+ ISWRTB
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSG(NQ,J)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ CURVE,ONE,PVMCRV,PVPCRV,P01,STP,STPCRV,TEN,TWO
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DJCKF,DPVB,DPVD
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,SIGN
C...DATA STATEMENTS
DATA
+ P01,ONE,TWO,TEN
+ /0.01D0,1.0D0,2.0D0,10.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C CURVE: A MEASURE OF THE CURVATURE IN THE MODEL.
C D: THE DERIVATIVE WITH RESPECT TO THE JTH UNKNOWN PARAMETER.
C DIFFJ: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR THE DERIVATIVE BEING
C CHECKED.
C EPSMAC: THE VALUE OF MACHINE PRECISION.
C ETA: THE RELATIVE NOISE IN THE MODEL
C FD: THE FORWARD DIFFERENCE DERIVATIVE WRT THE JTH PARAMETER.
C HC: THE RELATIVE STEP SIZE FOR CENTRAL FINITE DIFFERENCES.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISWRTB: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVES WRT BETA
C (ISWRTB=TRUE) OR DELTA(ISWRTB=FALSE) ARE BEING CHECKED.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSG: THE ERROR CHECKING RESULTS.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT WHICH
C THE DERIVATIVE IS TO BE CHECKED.
C ONE: THE VALUE 1.0D0.
C PV: THE PREDICTED VALUE OF THE MODEL FOR ROW NROW .
C PVMCRV: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C BASED ON THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J)-STPCRV.
C PVPCRV: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C BASED ON THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J)+STPCRV.
C PVPSTP: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C BASED ON THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J) + STP0.
C P01: THE VALUE 0.01D0.
C STP0: THE INITIAL STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C STP: A STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C STPCRV: THE STEP SIZE SELECTED TO CHECK FOR CURVATURE IN THE MODEL.
C TEN: THE VALUE 10.0D0.
C TOL: THE AGREEMENT TOLERANCE.
C TWO: THE VALUE 2.0D0.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C***FIRST EXECUTABLE STATEMENT DJCKC
IF (ISWRTB) THEN
C PERFORM CENTRAL DIFFERENCE COMPUTATIONS FOR DERIVATIVES WRT BETA
STPCRV = (HC*TYPJ*SIGN(ONE,BETA(J))+BETA(J)) - BETA(J)
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STPCRV,
+ ISTOP,NFEV,PVPCRV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,-STPCRV,
+ ISTOP,NFEV,PVMCRV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
ELSE
C PERFORM CENTRAL DIFFERENCE COMPUTATIONS FOR DERIVATIVES WRT DELTA
STPCRV = (HC*TYPJ*SIGN(ONE,XPLUSD(NROW,J))+XPLUSD(NROW,J)) -
+ XPLUSD(NROW,J)
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STPCRV,
+ ISTOP,NFEV,PVPCRV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,-STPCRV,
+ ISTOP,NFEV,PVMCRV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
END IF
C ESTIMATE CURVATURE BY SECOND DERIVATIVE OF MODEL
CURVE = ABS((PVPCRV-PV)+(PVMCRV-PV)) / (STPCRV*STPCRV)
CURVE = CURVE +
+ ETA*(ABS(PVPCRV)+ABS(PVMCRV)+TWO*ABS(PV)) / (STPCRV**2)
C CHECK IF FINITE PRECISION ARITHMETIC COULD BE THE CULPRIT.
CALL DJCKF(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,J,LQ,ISWRTB,
+ FD,TYPJ,PVPSTP,STP0,CURVE,PV,D,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
IF (MSG(LQ,J).EQ.0) THEN
RETURN
END IF
C CHECK IF HIGH CURVATURE COULD BE THE PROBLEM.
STP = TWO*MAX(TOL*ABS(D)/CURVE,EPSMAC)
IF (STP.LT.ABS(TEN*STP0)) THEN
STP = MIN(STP,P01*ABS(STP0))
END IF
IF (ISWRTB) THEN
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT BETA
STP = (STP*SIGN(ONE,BETA(J)) + BETA(J)) - BETA(J)
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
ELSE
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT DELTA
STP = (STP*SIGN(ONE,XPLUSD(NROW,J)) + XPLUSD(NROW,J)) -
+ XPLUSD(NROW,J)
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
IF (ISTOP.NE.0) THEN
RETURN
END IF
END IF
C COMPUTE THE NEW NUMERICAL DERIVATIVE
FD = (PVPSTP-PV)/STP
DIFFJ = MIN(DIFFJ,ABS(FD-D)/ABS(D))
C CHECK WHETHER THE NEW NUMERICAL DERIVATIVE IS OK
IF (ABS(FD-D).LE.TOL*ABS(D)) THEN
MSG(LQ,J) = 0
C CHECK IF FINITE PRECISION MAY BE THE CULPRIT (FUDGE FACTOR = 2)
ELSE IF (ABS(STP*(FD-D)).LT.TWO*ETA*(ABS(PV)+ABS(PVPSTP))
+ + CURVE*(EPSMAC*TYPJ)**2) THEN
MSG(LQ,J) = 5
END IF
RETURN
END
*DJCKF
SUBROUTINE DJCKF
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,J,LQ,ISWRTB,
+ FD,TYPJ,PVPSTP,STP0,CURVE,PV,D,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DJCKF
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DPVB,DPVD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CHECK WHETHER FINITE PRECISION ARITHMETIC COULD BE THE
C CAUSE OF THE DISAGREEMENT BETWEEN THE DERIVATIVES
C (ADAPTED FROM STARPAC SUBROUTINE DCKFPA)
C***END PROLOGUE DJCKF
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ CURVE,D,DIFFJ,ETA,FD,PV,PVPSTP,STP0,TOL,TYPJ
INTEGER
+ ISTOP,J,LDIFX,LQ,M,N,NFEV,NP,NQ,NROW
LOGICAL
+ ISWRTB
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSG(NQ,J)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ HUNDRD,ONE,P1,STP,TWO
LOGICAL
+ LARGE
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DPVB,DPVD
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,SIGN
C...DATA STATEMENTS
DATA
+ P1,ONE,TWO,HUNDRD
+ /0.1D0,1.0D0,2.0D0,100.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C CURVE: A MEASURE OF THE CURVATURE IN THE MODEL.
C D: THE DERIVATIVE WITH RESPECT TO THE JTH UNKNOWN PARAMETER.
C DIFFJ: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR THE DERIVATIVE BEING
C CHECKED.
C ETA: THE RELATIVE NOISE IN THE MODEL
C FD: THE FORWARD DIFFERENCE DERIVATIVE WRT THE JTH PARAMETER.
C HUNDRD: THE VALUE 100.0D0.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISWRTB: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVES WRT BETA
C (ISWRTB=TRUE) OR DELTA(ISWRTB=FALSE) ARE BEING CHECKED.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LARGE: THE VALUE DESIGNATING WHETHER THE RECOMMENDED INCREASE IN
C THE STEP SIZE WOULD BE GREATER THAN TYPJ.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSG: THE ERROR CHECKING RESULTS.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT WHICH
C THE DERIVATIVE IS TO BE CHECKED.
C ONE: THE VALUE 1.0D0.
C PV: THE PREDICTED VALUE FOR ROW NROW .
C PVPSTP: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C BASED ON THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J) + STP0.
C P1: THE VALUE 0.1D0.
C STP0: THE STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C TOL: THE AGREEMENT TOLERANCE.
C TWO: THE VALUE 2.0D0.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C***FIRST EXECUTABLE STATEMENT DJCKF
C FINITE PRECISION ARITHMETIC COULD BE THE PROBLEM.
C TRY A LARGER STEP SIZE BASED ON ESTIMATE OF CONDITION ERROR
STP = ETA*(ABS(PV)+ABS(PVPSTP))/(TOL*ABS(D))
IF (STP.GT.ABS(P1*STP0)) THEN
STP = MAX(STP,HUNDRD*ABS(STP0))
END IF
IF (STP.GT.TYPJ) THEN
STP = TYPJ
LARGE = .TRUE.
ELSE
LARGE = .FALSE.
END IF
IF (ISWRTB) THEN
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT BETA
STP = (STP*SIGN(ONE,BETA(J))+BETA(J)) - BETA(J)
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
ELSE
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT DELTA
STP = (STP*SIGN(ONE,XPLUSD(NROW,J)) + XPLUSD(NROW,J)) -
+ XPLUSD(NROW,J)
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
END IF
IF (ISTOP.NE.0) THEN
RETURN
END IF
FD = (PVPSTP-PV)/STP
DIFFJ = MIN(DIFFJ,ABS(FD-D)/ABS(D))
C CHECK FOR AGREEMENT
IF ((ABS(FD-D)).LE.TOL*ABS(D)) THEN
C FORWARD DIFFERENCE QUOTIENT AND ANALYTIC DERIVATIVES AGREE.
MSG(LQ,J) = 0
ELSE IF ((ABS(FD-D).LE.ABS(TWO*CURVE*STP)) .OR. LARGE) THEN
C CURVATURE MAY BE THE CULPRIT (FUDGE FACTOR = 2)
IF (LARGE) THEN
MSG(LQ,J) = 4
ELSE
MSG(LQ,J) = 5
END IF
END IF
RETURN
END
*DJCKM
SUBROUTINE DJCKM
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,EPSMAC,J,LQ,TYPJ,H0,HC0,
+ ISWRTB,PV,D,
+ DIFFJ,MSG1,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DJCKM
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DJCKC,DJCKZ,DPVB,DPVD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CHECK USER SUPPLIED ANALYTIC DERIVATIVES AGAINST NUMERICAL
C DERIVATIVES
C (ADAPTED FROM STARPAC SUBROUTINE DCKMN)
C***END PROLOGUE DJCKM
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ D,DIFFJ,EPSMAC,ETA,H0,HC0,PV,TOL,TYPJ
INTEGER
+ ISTOP,J,LDIFX,LQ,M,MSG1,N,NFEV,NP,NQ,NROW
LOGICAL
+ ISWRTB
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSG(NQ,J)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ BIG,FD,H,HC,H1,HC1,HUNDRD,ONE,PVPSTP,P01,P1,STP0,
+ TEN,THREE,TOL2,TWO,ZERO
INTEGER
+ I
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DJCKC,DJCKZ,DPVB,DPVD
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MAX,SIGN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,P01,P1,ONE,TWO,THREE,TEN,HUNDRD
+ /0.0D0,0.01D0,0.1D0,1.0D0,2.0D0,3.0D0,1.0D1,1.0D2/
DATA
+ BIG,TOL2
+ /1.0D19,5.0D-2/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C BIG: A BIG VALUE, USED TO INITIALIZE DIFFJ.
C D: THE DERIVATIVE WITH RESPECT TO THE JTH UNKNOWN PARAMETER.
C DIFFJ: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR THE DERIVATIVE BEING
C CHECKED.
C EPSMAC: THE VALUE OF MACHINE PRECISION.
C ETA: THE RELATIVE NOISE IN THE FUNCTION RESULTS.
C FD: THE FORWARD DIFFERENCE DERIVATIVE WRT THE JTH PARAMETER.
C H: THE RELATIVE STEP SIZE FOR FORWARD DIFFERENCES.
C H0: THE INITIAL RELATIVE STEP SIZE FOR FORWARD DIFFERENCES.
C H1: THE DEFAULT RELATIVE STEP SIZE FOR FORWARD DIFFERENCES.
C HC: THE RELATIVE STEP SIZE FOR CENTRAL DIFFERENCES.
C HC0: THE INITIAL RELATIVE STEP SIZE FOR CENTRAL DIFFERENCES.
C HC1: THE DEFAULT RELATIVE STEP SIZE FOR CENTRAL DIFFERENCES.
C HUNDRD: THE VALUE 100.0D0.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISWRTB: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVES WRT BETA
C (ISWRTB=TRUE) OR DELTAS (ISWRTB=FALSE) ARE BEING CHECKED.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSG: THE ERROR CHECKING RESULTS.
C MSG1: THE ERROR CHECKING RESULTS SUMMARY.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT WHICH
C THE DERIVATIVE IS TO BE CHECKED.
C ONE: THE VALUE 1.0D0.
C PV: THE PREDICTED VALUE FROM THE MODEL FOR ROW NROW .
C PVPSTP: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C USING THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE JTH
C PARAMETER VALUE, WHICH IS BETA(J) + STP0.
C P01: THE VALUE 0.01D0.
C P1: THE VALUE 0.1D0.
C STP0: THE INITIAL STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C TEN: THE VALUE 10.0D0.
C THREE: THE VALUE 3.0D0.
C TWO: THE VALUE 2.0D0.
C TOL: THE AGREEMENT TOLERANCE.
C TOL2: A MINIMUM AGREEMENT TOLERANCE.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DJCKM
C CALCULATE THE JTH PARTIAL DERIVATIVE USING FORWARD DIFFERENCE
C QUOTIENTS AND DECIDE IF IT AGREES WITH USER SUPPLIED VALUES
H1 = SQRT(ETA)
HC1 = ETA**(ONE/THREE)
MSG(LQ,J) = 7
DIFFJ = BIG
DO 10 I=1,3
IF (I.EQ.1) THEN
C TRY INITIAL RELATIVE STEP SIZE
H = H0
HC = HC0
ELSE IF (I.EQ.2) THEN
C TRY LARGER RELATIVE STEP SIZE
H = MAX(TEN*H1, MIN(HUNDRD*H0, ONE))
HC = MAX(TEN*HC1,MIN(HUNDRD*HC0,ONE))
ELSE IF (I.EQ.3) THEN
C TRY SMALLER RELATIVE STEP SIZE
H = MIN(P1*H1, MAX(P01*H,TWO*EPSMAC))
HC = MIN(P1*HC1,MAX(P01*HC,TWO*EPSMAC))
END IF
IF (ISWRTB) THEN
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT BETA
STP0 = (H*TYPJ*SIGN(ONE,BETA(J))+BETA(J)) - BETA(J)
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP0,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
ELSE
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT DELTA
STP0 = (H*TYPJ*SIGN(ONE,XPLUSD(NROW,J))+XPLUSD(NROW,J))
+ - XPLUSD(NROW,J)
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP0,
+ ISTOP,NFEV,PVPSTP,
+ WRK1,WRK2,WRK6)
END IF
IF (ISTOP.NE.0) THEN
RETURN
END IF
FD = (PVPSTP-PV)/STP0
C CHECK FOR AGREEMENT
IF (ABS(FD-D).LE.TOL*ABS(D)) THEN
C NUMERICAL AND ANALYTIC DERIVATIVES AGREE
C SET RELATIVE DIFFERENCE FOR DERIVATIVE CHECKING REPORT
IF ((D.EQ.ZERO) .OR. (FD.EQ.ZERO)) THEN
DIFFJ = ABS(FD-D)
ELSE
DIFFJ = ABS(FD-D)/ABS(D)
END IF
C SET MSG FLAG.
IF (D.EQ.ZERO) THEN
C JTH ANALYTIC AND NUMERICAL DERIVATIVES ARE BOTH ZERO.
MSG(LQ,J) = 1
ELSE
C JTH ANALYTIC AND NUMERICAL DERIVATIVES ARE BOTH NONZERO.
MSG(LQ,J) = 0
END IF
ELSE
C NUMERICAL AND ANALYTIC DERIVATIVES DISAGREE. CHECK WHY
IF ((D.EQ.ZERO) .OR. (FD.EQ.ZERO)) THEN
CALL DJCKZ(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,EPSMAC,J,LQ,ISWRTB,
+ TOL,D,FD,TYPJ,PVPSTP,STP0,PV,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
ELSE
CALL DJCKC(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ ETA,TOL,NROW,EPSMAC,J,LQ,HC,ISWRTB,
+ FD,TYPJ,PVPSTP,STP0,PV,D,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
END IF
IF (MSG(LQ,J).LE.2) THEN
GO TO 20
END IF
END IF
10 CONTINUE
C SET SUMMARY FLAG TO INDICATE QUESTIONABLE RESULTS
20 CONTINUE
IF ((MSG(LQ,J).GE.7) .AND. (DIFFJ.LE.TOL2)) MSG(LQ,J) = 6
IF ((MSG(LQ,J).GE.1) .AND. (MSG(LQ,J).LE.6)) THEN
MSG1 = MAX(MSG1,1)
ELSE IF (MSG(LQ,J).GE.7) THEN
MSG1 = 2
END IF
RETURN
END
*DJCKZ
SUBROUTINE DJCKZ
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,EPSMAC,J,LQ,ISWRTB,
+ TOL,D,FD,TYPJ,PVPSTP,STP0,PV,
+ DIFFJ,MSG,ISTOP,NFEV,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DJCKZ
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DPVB,DPVD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE RECHECK THE DERIVATIVES IN THE CASE WHERE THE FINITE
C DIFFERENCE DERIVATIVE DISAGREES WITH THE ANALYTIC
C DERIVATIVE AND THE ANALYTIC DERIVATIVE IS ZERO
C (ADAPTED FROM STARPAC SUBROUTINE DCKZRO)
C***END PROLOGUE DJCKZ
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ D,DIFFJ,EPSMAC,FD,PV,PVPSTP,STP0,TOL,TYPJ
INTEGER
+ ISTOP,J,LDIFX,LQ,M,N,NFEV,NP,NQ,NROW
LOGICAL
+ ISWRTB
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSG(NQ,J)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ CD,ONE,PVMSTP,THREE,TWO,ZERO
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DPVB,DPVD
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MIN
C...DATA STATEMENTS
DATA
+ ZERO,ONE,TWO,THREE
+ /0.0D0,1.0D0,2.0D0,3.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C CD: THE CENTRAL DIFFERENCE DERIVATIVE WRT THE JTH PARAMETER.
C D: THE DERIVATIVE WITH RESPECT TO THE JTH UNKNOWN PARAMETER.
C DIFFJ: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR THE DERIVATIVE BEING
C CHECKED.
C EPSMAC: THE VALUE OF MACHINE PRECISION.
C FD: THE FORWARD DIFFERENCE DERIVATIVE WRT THE JTH PARAMETER.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISWRTB: THE VARIABLE DESIGNATING WHETHER THE DERIVATIVES WRT BETA
C (ISWRTB=TRUE) OR X (ISWRTB=FALSE) ARE BEING CHECKED.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSG: THE ERROR CHECKING RESULTS.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT WHICH
C THE DERIVATIVE IS TO BE CHECKED.
C ONE: THE VALUE 1.0D0.
C PV: THE PREDICTED VALUE FROM THE MODEL FOR ROW NROW .
C PVMSTP: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C USING THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J) - STP0.
C PVPSTP: THE PREDICTED VALUE FOR ROW NROW OF THE MODEL
C USING THE CURRENT PARAMETER ESTIMATES FOR ALL BUT THE
C JTH PARAMETER VALUE, WHICH IS BETA(J) + STP0.
C STP0: THE INITIAL STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C THREE: THE VALUE 3.0D0.
C TWO: THE VALUE 2.0D0.
C TOL: THE AGREEMENT TOLERANCE.
C TYPJ: THE TYPICAL SIZE OF THE J-TH UNKNOWN BETA OR DELTA.
C WRK1: A WORK ARRAY OF (N BY M BY NQ) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK6: A WORK ARRAY OF (N BY NP BY NQ) ELEMENTS.
C XPLUSD: THE VALUES OF X + DELTA.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DJCKZ
C RECALCULATE NUMERICAL DERIVATIVE USING CENTRAL DIFFERENCE AND STEP
C SIZE OF 2*STP0
IF (ISWRTB) THEN
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT BETA
CALL DPVB(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,-STP0,
+ ISTOP,NFEV,PVMSTP,
+ WRK1,WRK2,WRK6)
ELSE
C PERFORM COMPUTATIONS FOR DERIVATIVES WRT DELTA
CALL DPVD(FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,-STP0,
+ ISTOP,NFEV,PVMSTP,
+ WRK1,WRK2,WRK6)
END IF
IF (ISTOP.NE.0) THEN
RETURN
END IF
CD = (PVPSTP-PVMSTP)/(TWO*STP0)
DIFFJ = MIN(ABS(CD-D),ABS(FD-D))
C CHECK FOR AGREEMENT
IF (DIFFJ.LE.TOL*ABS(D)) THEN
C FINITE DIFFERENCE AND ANALYTIC DERIVATIVES NOW AGREE.
IF (D.EQ.ZERO) THEN
MSG(LQ,J) = 1
ELSE
MSG(LQ,J) = 0
END IF
ELSE IF (DIFFJ*TYPJ.LE.ABS(PV*EPSMAC**(ONE/THREE))) THEN
C DERIVATIVES ARE BOTH CLOSE TO ZERO
MSG(LQ,J) = 2
ELSE
C DERIVATIVES ARE NOT BOTH CLOSE TO ZERO
MSG(LQ,J) = 3
END IF
RETURN
END
*DODCHK
SUBROUTINE DODCHK
+ (N,M,NP,NQ,
+ ISODR,ANAJAC,IMPLCT,
+ IFIXB,
+ LDX,LDIFX,LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LDY,
+ LWORK,LWKMN,LIWORK,LIWKMN,
+ SCLB,SCLD,STPB,STPD,
+ INFO)
C***BEGIN PROLOGUE DODCHK
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CHECK INPUT PARAMETERS, INDICATING ERRORS FOUND USING
C NONZERO VALUES OF ARGUMENT INFO
C***END PROLOGUE DODCHK
C...SCALAR ARGUMENTS
INTEGER
+ INFO,LDIFX,LDSCLD,LDSTPD,LDWD,LDWE,LDX,LDY,LD2WD,LD2WE,
+ LIWKMN,LIWORK,LWKMN,LWORK,M,N,NP,NQ
LOGICAL
+ ANAJAC,IMPLCT,ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ SCLB(NP),SCLD(LDSCLD,M),STPB(NP),STPD(LDSTPD,M)
INTEGER
+ IFIXB(NP)
C...LOCAL SCALARS
INTEGER
+ I,J,K,LAST,NPP
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT
C (ANAJAC=TRUE).
C I: AN INDEXING VARIABLE.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C LAST: THE LAST ROW OF THE ARRAY TO BE ACCESSED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY X.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY IWORK.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY WORK.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATIONS.
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUE FOR DELTA.
C STPB: THE STEP FOR THE FINITE DIFFERENCE DERIVITIVE WRT BETA.
C STPD: THE STEP FOR THE FINITE DIFFERENCE DERIVITIVE WRT DELTA.
C***FIRST EXECUTABLE STATEMENT DODCHK
C FIND ACTUAL NUMBER OF PARAMETERS BEING ESTIMATED
IF (NP.LE.0 .OR. IFIXB(1).LT.0) THEN
NPP = NP
ELSE
NPP = 0
DO 10 K=1,NP
IF (IFIXB(K).NE.0) THEN
NPP = NPP + 1
END IF
10 CONTINUE
END IF
C CHECK PROBLEM SPECIFICATION PARAMETERS
IF (N.LE.0 .OR.
+ M.LE.0 .OR.
+ (NPP.LE.0 .OR. NPP.GT.N) .OR.
+ (NQ.LE.0)) THEN
INFO = 10000
IF (N.LE.0) THEN
INFO = INFO + 1000
END IF
IF (M.LE.0) THEN
INFO = INFO + 100
END IF
IF (NPP.LE.0 .OR. NPP.GT.N) THEN
INFO = INFO + 10
END IF
IF (NQ.LE.0) THEN
INFO = INFO + 1
END IF
RETURN
END IF
C CHECK DIMENSION SPECIFICATION PARAMETERS
IF ((.NOT.IMPLCT .AND. LDY.LT.N) .OR.
+ (LDX.LT.N) .OR.
+ (LDWE.NE.1 .AND. LDWE.LT.N) .OR.
+ (LD2WE.NE.1 .AND. LD2WE.LT.NQ) .OR.
+ (ISODR .AND. (LDWD.NE.1 .AND. LDWD.LT.N)) .OR.
+ (ISODR .AND. (LD2WD.NE.1 .AND. LD2WD.LT.M)) .OR.
+ (ISODR .AND. (LDIFX.NE.1 .AND. LDIFX.LT.N)) .OR.
+ (ISODR .AND. (LDSTPD.NE.1 .AND. LDSTPD.LT.N)) .OR.
+ (ISODR .AND. (LDSCLD.NE.1 .AND. LDSCLD.LT.N)) .OR.
+ (LWORK.LT.LWKMN) .OR.
+ (LIWORK.LT.LIWKMN)) THEN
INFO = 20000
IF (.NOT.IMPLCT .AND. LDY.LT.N) THEN
INFO = INFO + 1000
END IF
IF (LDX.LT.N) THEN
INFO = INFO + 2000
END IF
IF ((LDWE.NE.1 .AND. LDWE.LT.N) .OR.
+ (LD2WE.NE.1 .AND. LD2WE.LT.NQ)) THEN
INFO = INFO + 100
END IF
IF (ISODR .AND. ((LDWD.NE.1 .AND. LDWD.LT.N) .OR.
+ (LD2WD.NE.1 .AND. LD2WD.LT.M))) THEN
INFO = INFO + 200
END IF
IF (ISODR .AND. (LDIFX.NE.1 .AND. LDIFX.LT.N)) THEN
INFO = INFO + 10
END IF
IF (ISODR .AND. (LDSTPD.NE.1 .AND. LDSTPD.LT.N)) THEN
INFO = INFO + 20
END IF
IF (ISODR .AND. (LDSCLD.NE.1 .AND. LDSCLD.LT.N)) THEN
INFO = INFO + 40
END IF
IF (LWORK.LT.LWKMN) THEN
INFO = INFO + 1
END IF
IF (LIWORK.LT.LIWKMN) THEN
INFO = INFO + 2
END IF
RETURN
END IF
C CHECK DELTA SCALING
IF (ISODR .AND. SCLD(1,1).GT.0) THEN
IF (LDSCLD.GE.N) THEN
LAST = N
ELSE
LAST = 1
END IF
DO 120 J=1,M
DO 110 I=1,LAST
IF (SCLD(I,J).LE.0) THEN
INFO = 30200
GO TO 130
END IF
110 CONTINUE
120 CONTINUE
END IF
130 CONTINUE
C CHECK BETA SCALING
IF (SCLB(1).GT.0) THEN
DO 210 K=1,NP
IF (SCLB(K).LE.0) THEN
IF (INFO.EQ.0) THEN
INFO = 30100
ELSE
INFO = INFO + 100
END IF
GO TO 220
END IF
210 CONTINUE
END IF
220 CONTINUE
C CHECK DELTA FINITE DIFFERENCE STEP SIZES
IF (ANAJAC .AND. ISODR .AND. STPD(1,1).GT.0) THEN
IF (LDSTPD.GE.N) THEN
LAST = N
ELSE
LAST = 1
END IF
DO 320 J=1,M
DO 310 I=1,LAST
IF (STPD(I,J).LE.0) THEN
IF (INFO.EQ.0) THEN
INFO = 32000
ELSE
INFO = INFO + 2000
END IF
GO TO 330
END IF
310 CONTINUE
320 CONTINUE
END IF
330 CONTINUE
C CHECK BETA FINITE DIFFERENCE STEP SIZES
IF (ANAJAC .AND. STPB(1).GT.0) THEN
DO 410 K=1,NP
IF (STPB(K).LE.0) THEN
IF (INFO.EQ.0) THEN
INFO = 31000
ELSE
INFO = INFO + 1000
END IF
GO TO 420
END IF
410 CONTINUE
END IF
420 CONTINUE
RETURN
END
*DODCNT
SUBROUTINE DODCNT
+ (SHORT, FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT, IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ INFO)
C***BEGIN PROLOGUE DODCNT
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DODDRV
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE DOUBLE PRECISION DRIVER ROUTINE FOR FINDING
C THE WEIGHTED EXPLICIT OR IMPLICIT ORTHOGONAL DISTANCE
C REGRESSION (ODR) OR ORDINARY LINEAR OR NONLINEAR LEAST
C SQUARES (OLS) SOLUTION
C***END PROLOGUE DODCNT
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PARTOL,SSTOL,TAUFAC
INTEGER
+ INFO,IPRINT,JOB,LDIFX,LDSCLD,LDSTPD,LDWD,LDWE,LDX,LDY,
+ LD2WD,LD2WE,LIWORK,LUNERR,LUNRPT,LWORK,M,MAXIT,N,NDIGIT,NP,NQ
LOGICAL
+ SHORT
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),SCLB(NP),SCLD(LDSCLD,M),STPB(NP),STPD(LDSTPD,M),
+ WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),WORK(LWORK),
+ X(LDX,M),Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),IWORK(LIWORK)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ CNVTOL,ONE,PCHECK,PFAC,PSTART,THREE,TSTIMP,ZERO
INTEGER
+ IPRNTI,IPR1,IPR2,IPR2F,IPR3,JOBI,JOB1,JOB2,JOB3,JOB4,JOB5,
+ MAXITI,MAXIT1
LOGICAL
+ DONE,FSTITR,HEAD,IMPLCT,PRTPEN
C...LOCAL ARRAYS
DOUBLE PRECISION
+ PNLTY(1,1,1)
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DODDRV
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DMPREC
EXTERNAL
+ DMPREC
C...DATA STATEMENTS
DATA
+ PCHECK,PSTART,PFAC,ZERO,ONE,THREE
+ /1.0D3,1.0D1,1.0D1,0.0D0,1.0D0,3.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C CNVTOL: THE CONVERGENCE TOLERANCE FOR IMPLICIT MODELS.
C DONE: THE VARIABLE DESIGNATING WHETHER THE INPLICIT SOLUTION HAS
C BEEN FOUND (DONE=TRUE) OR NOT (DONE=FALSE).
C FSTITR: THE VARIABLE DESIGNATING WHETHER THIS IS THE FIRST
C ITERATION (FSTITR=TRUE) OR NOT (FSTITR=FALSE).
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=TRUE) OR NOT (HEAD=FALSE).
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C IPRINT: THE PRINT CONTROL VARIABLES.
C IPRNTI: THE PRINT CONTROL VARIABLES.
C IPR1: THE 1ST DIGIT OF THE PRINT CONTROL VARIABLE.
C IPR2: THE 2ND DIGIT OF THE PRINT CONTROL VARIABLE.
C IPR3: THE 3RD DIGIT OF THE PRINT CONTROL VARIABLE.
C IPR4: THE 4TH DIGIT OF THE PRINT CONTROL VARIABLE.
C IWORK: THE INTEGER WORK SPACE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOBI: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOB1: THE 1ST DIGIT OF THE VARIABLE CONTROLING PROBLEM
C INITIALIZATION AND COMPUTATIONAL METHOD.
C JOB2: THE 2ND DIGIT OF THE VARIABLE CONTROLING PROBLEM
C INITIALIZATION AND COMPUTATIONAL METHOD.
C JOB3: THE 3RD DIGIT OF THE VARIABLE CONTROLING PROBLEM
C INITIALIZATION AND COMPUTATIONAL METHOD.
C JOB4: THE 4TH DIGIT OF THE VARIABLE CONTROLING PROBLEM
C INITIALIZATION AND COMPUTATIONAL METHOD.
C JOB5: THE 5TH DIGIT OF THE VARIABLE CONTROLING PROBLEM
C INITIALIZATION AND COMPUTATIONAL METHOD.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERR: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LWORK: THE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MAXITI: FOR IMPLICIT MODELS, THE NUMBER OF ITERATIONS ALLOWED FOR
C THE CURRENT PENALTY PARAMETER VALUE.
C MAXIT1: FOR IMPLICIT MODELS, THE NUMBER OF ITERATIONS ALLOWED FOR
C THE NEXT PENALTY PARAMETER VALUE.
C N: THE NUMBER OF OBSERVATIONS.
C NDIGIT: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS, AS
C SUPPLIED BY THE USER.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C ONE: THE VALUE 1.0D0.
C PARTOL: THE USER SUPPLIED PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PCHECK: THE VALUE DESIGNATING THE MINIMUM PENALTY PARAMETER ALLOWED
C BEFORE THE IMPLICIT PROBLEM CAN BE CONSIDERED SOLVED.
C PFAC: THE FACTOR FOR INCREASING THE PENALTY PARAMETER.
C PNLTY: THE PENALTY PARAMETER FOR AN IMPLICIT MODEL.
C PRTPEN: THE VALUE DESIGNATING WHETHER THE PENALTY PARAMETER IS TO BE
C PRINTED IN THE ITERATION REPORT (PRTPEN=TRUE) OR NOT
C (PRTPEN=FALSE).
C PSTART: THE FACTOR FOR INCREASING THE PENALTY PARAMETER.
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUES FOR DELTA.
C STPB: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=.TRUE.) OR THE LONG-CALL
C (SHORT=.FALSE.).
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C THREE: THE VALUE 3.0D0.
C TSTIMP: THE RELATIVE CHANGE IN THE PARAMETERS BETWEEN THE INITIAL
C VALUES AND THE SOLUTION.
C WD: THE DELTA WEIGHTS.
C WE: THE EPSILON WEIGHTS.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C X: THE INDEPENDENT VARIABLE.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODCNT
IMPLCT = MOD(JOB,10).EQ.1
FSTITR = .TRUE.
HEAD = .TRUE.
PRTPEN = .FALSE.
IF (IMPLCT) THEN
C SET UP FOR IMPLICIT PROBLEM
IF (IPRINT.GE.0) THEN
IPR1 = MOD(IPRINT,10000)/1000
IPR2 = MOD(IPRINT,1000)/100
IPR2F = MOD(IPRINT,100)/10
IPR3 = MOD(IPRINT,10)
ELSE
IPR1 = 2
IPR2 = 0
IPR2F = 0
IPR3 = 1
END IF
IPRNTI = IPR1*1000 + IPR2*100 + IPR2F*10
JOB5 = MOD(JOB,100000)/10000
JOB4 = MOD(JOB,10000)/1000
JOB3 = MOD(JOB,1000)/100
JOB2 = MOD(JOB,100)/10
JOB1 = MOD(JOB,10)
JOBI = JOB5*10000 + JOB4*1000 + JOB3*100 + JOB2*10 + JOB1
IF (WE(1,1,1).LE.ZERO) THEN
PNLTY(1,1,1) = -PSTART
ELSE
PNLTY(1,1,1) = -WE(1,1,1)
END IF
IF (PARTOL.LT.ZERO) THEN
CNVTOL = DMPREC()**(ONE/THREE)
ELSE
CNVTOL = MIN(PARTOL,ONE)
END IF
IF (MAXIT.GE.1) THEN
MAXITI = MAXIT
ELSE
MAXITI = 100
END IF
DONE = MAXITI.EQ.0
PRTPEN = .TRUE.
10 CONTINUE
CALL DODDRV
+ (SHORT,HEAD,FSTITR,PRTPEN,
+ FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ PNLTY,1,1,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOBI,NDIGIT,TAUFAC, SSTOL,CNVTOL,MAXITI,
+ IPRNTI,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ MAXIT1,TSTIMP, INFO)
IF (DONE) THEN
RETURN
ELSE
DONE = MAXIT1.LE.0 .OR.
+ (ABS(PNLTY(1,1,1)).GE.PCHECK .AND.
+ TSTIMP.LE.CNVTOL)
END IF
IF (DONE) THEN
IF (TSTIMP.LE.CNVTOL) THEN
INFO = (INFO/10)*10 + 2
ELSE
INFO = (INFO/10)*10 + 4
END IF
JOBI = 10000 + 1000 + JOB3*100 + JOB2*10 + JOB1
MAXITI = 0
IPRNTI = IPR3
ELSE
PRTPEN = .TRUE.
PNLTY(1,1,1) = PFAC*PNLTY(1,1,1)
JOBI = 10000 + 1000 + 000 + JOB2*10 + JOB1
MAXITI = MAXIT1
IPRNTI = 0000 + IPR2*100 + IPR2F*10
END IF
GO TO 10
ELSE
CALL DODDRV
+ (SHORT,HEAD,FSTITR,PRTPEN,
+ FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ MAXIT1,TSTIMP, INFO)
END IF
RETURN
END
*DODDRV
SUBROUTINE DODDRV
+ (SHORT,HEAD,FSTITR,PRTPEN,
+ FCN, N,M,NP,NQ, BETA, Y,LDY,X,LDX,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD, IFIXB,IFIXX,LDIFX,
+ JOB,NDIGIT,TAUFAC, SSTOL,PARTOL,MAXIT,
+ IPRINT,LUNERR,LUNRPT,
+ STPB,STPD,LDSTPD, SCLB,SCLD,LDSCLD,
+ WORK,LWORK,IWORK,LIWORK,
+ MAXIT1,TSTIMP, INFO)
C***BEGIN PROLOGUE DODDRV
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DCOPY,DDOT,DETAF,DFCTRW,DFLAGS,
C DINIWK,DIWINF,DJCK,DNRM2,DODCHK,DODMN,
C DODPER,DPACK,DSETN,DUNPAC,DWGHT,DWINF,DXMY,DXPY
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE PERFORM ERROR CHECKING AND INITIALIZATION, AND BEGIN
C PROCEDURE FOR PERFORMING ORTHOGONAL DISTANCE REGRESSION
C (ODR) OR ORDINARY LINEAR OR NONLINEAR LEAST SQUARES (OLS)
C***END PROLOGUE DODDRV
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PARTOL,SSTOL,TAUFAC,TSTIMP
INTEGER
+ INFO,IPRINT,JOB,LDIFX,LDSCLD,LDSTPD,LDWD,LDWE,LDX,LDY,
+ LD2WD,LD2WE,LIWORK,LUNERR,LUNRPT,LWORK,M,MAXIT,MAXIT1,
+ N,NDIGIT,NP,NQ
LOGICAL
+ FSTITR,HEAD,PRTPEN,SHORT
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),SCLB(NP),SCLD(LDSCLD,M),STPB(NP),STPD(LDSTPD,M),
+ WE(LDWE,LD2WE,NQ),WD(LDWD,LD2WD,M),WORK(LWORK),
+ X(LDX,M),Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),IWORK(LIWORK)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ EPSMAC,ETA,P5,ONE,TEN,ZERO
INTEGER
+ ACTRSI,ALPHAI,BETACI,BETANI,BETASI,BETA0I,DELTAI,DELTNI,DELTSI,
+ DIFFI,EPSMAI,ETAI,FI,FJACBI,FJACDI,FNI,FSI,I,IDFI,INT2I,IPRINI,
+ IRANKI,ISTOP,ISTOPI,JOBI,JPVTI,K,LDTT,LDTTI,LIWKMN,
+ LUNERI,LUNRPI,LWKMN,LWRK,MAXITI,MSGB,MSGD,NETA,NETAI,
+ NFEV,NFEVI,NITERI,NJEV,NJEVI,NNZW,NNZWI,NPP,NPPI,NROW,NROWI,
+ NTOL,NTOLI,OLMAVI,OMEGAI,PARTLI,PNORMI,PRERSI,QRAUXI,RCONDI,
+ RNORSI,RVARI,SDI,SI,SSFI,SSI,SSTOLI,TAUFCI,TAUI,TI,TTI,UI,
+ VCVI,WE1I,WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,WRK,
+ WSSI,WSSDEI,WSSEPI,XPLUSI
LOGICAL
+ ANAJAC,CDJAC,CHKJAC,DOVCV,IMPLCT,INITD,ISODR,REDOJ,RESTRT
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT,DNRM2
EXTERNAL
+ DDOT,DNRM2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DCOPY,DETAF,DFCTRW,DFLAGS,DINIWK,DIWINF,DJCK,DODCHK,
+ DODMN,DODPER,DPACK,DSETN,DUNPAC,DWGHT,DWINF,DXMY,DXPY
C...DATA STATEMENTS
DATA
+ ZERO,P5,ONE,TEN
+ /0.0D0,0.5D0,1.0D0,10.0D0/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACTRSI: THE LOCATION IN ARRAY WORK OF VARIABLE ACTRS.
C ALPHAI: THE LOCATION IN ARRAY WORK OF VARIABLE ALPHA.
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT
C (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C BETACI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAC.
C BETANI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAN.
C BETASI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAS.
C BETA0I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETA0.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE
C COMPUTED BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR FORWARD
C DIFFERENCES (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C DELTAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTA.
C DELTNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAN.
C DELTSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAS.
C DIFFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DIFF.
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX IS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C EPSMAI: THE LOCATION IN ARRAY WORK OF VARIABLE EPSMAC.
C ETA: THE RELATIVE NOISE IN THE FUNCTION RESULTS.
C ETAI: THE LOCATION IN ARRAY WORK OF VARIABLE ETA.
C FI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY F.
C FJACBI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACB.
C FJACDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACD.
C FNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FN.
C FSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FS.
C FSTITR: THE VARIABLE DESIGNATING WHETHER THIS IS THE FIRST
C ITERATION (FSTITR=TRUE) OR NOT (FSTITR=FALSE).
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=TRUE) OR NOT (HEAD=FALSE).
C I: AN INDEX VARIABLE.
C IDFI: THE LOCATION IN ARRAY IWORK OF VARIABLE IDF.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS TO BE INITIALIZED
C TO ZERO (INITD=TRUE) OR TO THE VALUES IN THE FIRST N BY M
C ELEMENTS OF ARRAY WORK (INITD=FALSE).
C INT2I: THE IN ARRAY IWORK OF VARIABLE INT2.
C IPRINI: THE LOCATION IN ARRAY IWORK OF VARIABLE IPRINT.
C IPRINT: THE PRINT CONTROL VARIABLE.
C IRANKI: THE LOCATION IN ARRAY IWORK OF VARIABLE IRANK.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISTOPI: THE LOCATION IN ARRAY IWORK OF VARIABLE ISTOP.
C IWORK: THE INTEGER WORK SPACE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOBI: THE LOCATION IN ARRAY IWORK OF VARIABLE JOB.
C JPVTI: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY JPVT.
C K: AN INDEX VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDTTI: THE LOCATION IN ARRAY IWORK OF VARIABLE LDTT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY IWORK.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LUNERI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNERR.
C LUNERR: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C LUNRPI: THE LOCATION IN ARRAY IWORK OF VARIABLE LUNRPT.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY WORK.
C LWORK: THE LENGTH OF VECTOR WORK.
C LWRK: THE LENGTH OF VECTOR WRK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MAXIT1: FOR IMPLICIT MODELS, THE ITERATIONS ALLOWED FOR THE NEXT
C PENALTY PARAMETER VALUE.
C MAXITI: THE LOCATION IN ARRAY IWORK OF VARIABLE MAXIT.
C MSGB: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGB.
C MSGD: THE STARTING LOCATION IN ARRAY IWORK OF ARRAY MSGD.
C N: THE NUMBER OF OBSERVATIONS.
C NDIGIT: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS, AS
C SUPPLIED BY THE USER.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C NETAI: THE LOCATION IN ARRAY IWORK OF VARIABLE NETA.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NFEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NFEV.
C NITERI: THE LOCATION IN ARRAY IWORK OF VARIABLE NITER.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NJEVI: THE LOCATION IN ARRAY IWORK OF VARIABLE NJEV.
C NNZW: THE NUMBER OF NONZERO OBSERVATIONAL ERROR WEIGHTS.
C NNZWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NNZW.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NPPI: THE LOCATION IN ARRAY IWORK OF VARIABLE NPP.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER AT WHICH THE DERIVATIVE IS TO BE CHECKED.
C NROWI: THE LOCATION IN ARRAY IWORK OF VARIABLE NROW.
C NTOL: THE NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN THE
C NUMERICAL DERIVATIVES AND THE USER SUPPLIED DERIVATIVES,
C SET BY DJCK.
C NTOLI: THE LOCATION IN ARRAY IWORK OF VARIABLE NTOL.
C OLMAVI: THE LOCATION IN ARRAY WORK OF VARIABLE OLMAVG.
C OMEGAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY OMEGA.
C ONE: THE VALUE 1.0D0.
C PARTLI: THE LOCATION IN ARRAY WORK OF VARIABLE PARTOL.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PNORM: THE NORM OF THE SCALED ESTIMATED PARAMETERS.
C PNORMI: THE LOCATION IN ARRAY WORK OF VARIABLE PNORM.
C PRERSI: THE LOCATION IN ARRAY WORK OF VARIABLE PRERS.
C PRTPEN: THE VARIABLE DESIGNATING WHETHER THE PENALTY PARAMETER IS
C TO BE PRINTED IN THE ITERATION REPORT (PRTPEN=TRUE) OR NOT
C (PRTPEN=FALSE).
C P5: THE VALUE 0.5D0.
C QRAUXI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY QRAUX.
C RCONDI: THE LOCATION IN ARRAY WORK OF VARIABLE RCOND.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C RNORSI: THE LOCATION IN ARRAY WORK OF VARIABLE RNORMS.
C RVARI: THE LOCATION IN ARRAY WORK OF VARIABLE RVAR.
C SCLB: THE SCALING VALUES FOR BETA.
C SCLD: THE SCALING VALUES FOR DELTA.
C SDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SD.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=TRUE) OR THE LONG-CALL
C (SHORT=FALSE).
C SI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY S.
C SSFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SSF.
C SSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SS.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C SSTOLI: THE LOCATION IN ARRAY WORK OF VARIABLE SSTOL.
C STPB: THE STEP SIZE FOR FINITE DIFFERENCE DERIVATIVES WRT BETA.
C STPD: THE STEP SIZE FOR FINITE DIFFERENCE DERIVATIVES WRT DELTA.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TAUFCI: THE LOCATION IN ARRAY WORK OF VARIABLE TAUFAC.
C TAUI: THE LOCATION IN ARRAY WORK OF VARIABLE TAU.
C TEN: THE VALUE 10.0D0.
C TI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY T.
C TSTIMP: THE RELATIVE CHANGE IN THE PARAMETERS BETWEEN THE INITIAL
C VALUES AND THE SOLUTION.
C TTI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY TT.
C UI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY U.
C VCVI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY VCV.
C WD: THE DELTA WEIGHTS.
C WE: THE EPSILON WEIGHTS.
C WE1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WE1.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C WRK: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK,
C EQUIVALENCED TO WRK1 AND WRK2.
C WRK1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK1.
C WRK2I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK2.
C WRK3I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK3.
C WRK4I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK4.
C WRK5I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK5.
C WRK6I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK6.
C WRK7I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK7.
C WSSI: THE LOCATION IN ARRAY WORK OF VARIABLE WSS.
C WSSDEI: THE LOCATION IN ARRAY WORK OF VARIABLE WSSDEL.
C WSSEPI: THE LOCATION IN ARRAY WORK OF VARIABLE WSSEPS.
C X: THE EXPLANATORY VARIABLE.
C XPLUSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY XPLUSD.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODDRV
C INITIALIZE NECESSARY VARIABLES
CALL DFLAGS(JOB,RESTRT,INITD,DOVCV,REDOJ,
+ ANAJAC,CDJAC,CHKJAC,ISODR,IMPLCT)
C SET STARTING LOCATIONS WITHIN INTEGER WORKSPACE
C (INVALID VALUES OF M, NP AND/OR NQ ARE HANDLED REASONABLY BY DIWINF)
CALL DIWINF(M,NP,NQ,
+ MSGB,MSGD,JPVTI,ISTOPI,
+ NNZWI,NPPI,IDFI,
+ JOBI,IPRINI,LUNERI,LUNRPI,
+ NROWI,NTOLI,NETAI,
+ MAXITI,NITERI,NFEVI,NJEVI,INT2I,IRANKI,LDTTI,
+ LIWKMN)
C SET STARTING LOCATIONS WITHIN DOUBLE PRECISION WORK SPACE
C (INVALID VALUES OF N, M, NP, NQ, LDWE AND/OR LD2WE
C ARE HANDLED REASONABLY BY DWINF)
CALL DWINF(N,M,NP,NQ,LDWE,LD2WE,ISODR,
+ DELTAI,FI,XPLUSI,FNI,SDI,VCVI,
+ RVARI,WSSI,WSSDEI,WSSEPI,RCONDI,ETAI,
+ OLMAVI,TAUI,ALPHAI,ACTRSI,PNORMI,RNORSI,PRERSI,
+ PARTLI,SSTOLI,TAUFCI,EPSMAI,
+ BETA0I,BETACI,BETASI,BETANI,SI,SSI,SSFI,QRAUXI,UI,
+ FSI,FJACBI,WE1I,DIFFI,
+ DELTSI,DELTNI,TI,TTI,OMEGAI,FJACDI,
+ WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,
+ LWKMN)
IF (ISODR) THEN
WRK = WRK1I
LWRK = N*M*NQ + N*NQ
ELSE
WRK = WRK2I
LWRK = N*NQ
END IF
C UPDATE THE PENALTY PARAMETERS
C (WE(1,1,1) IS NOT A USER SUPPLIED ARRAY IN THIS CASE)
IF (RESTRT .AND. IMPLCT) THEN
WE(1,1,1) = MAX(WORK(WE1I)**2,ABS(WE(1,1,1)))
WORK(WE1I) = -SQRT(ABS(WE(1,1,1)))
END IF
IF (RESTRT) THEN
C RESET MAXIMUM NUMBER OF ITERATIONS
IF (MAXIT.GE.0) THEN
IWORK(MAXITI) = IWORK(NITERI) + MAXIT
ELSE
IWORK(MAXITI) = IWORK(NITERI) + 10
END IF
IF (IWORK(NITERI).LT.IWORK(MAXITI)) THEN
INFO = 0
END IF
IF (JOB.GE.0) IWORK(JOBI) = JOB
IF (IPRINT.GE.0) IWORK(IPRINI) = IPRINT
IF (PARTOL.GE.ZERO .AND. PARTOL.LT.ONE) WORK(PARTLI) = PARTOL
IF (SSTOL.GE.ZERO .AND. SSTOL.LT.ONE) WORK(SSTOLI) = SSTOL
WORK(OLMAVI) = WORK(OLMAVI)*IWORK(NITERI)
IF (IMPLCT) THEN
CALL DCOPY(N*NQ,WORK(FNI),1,WORK(FI),1)
ELSE
CALL DXMY(N,NQ,WORK(FNI),N,Y,LDY,WORK(FI),N)
END IF
CALL DWGHT(N,NQ,WORK(WE1I),LDWE,LD2WE,WORK(FI),N,WORK(FI),N)
WORK(WSSEPI) = DDOT(N*NQ,WORK(FI),1,WORK(FI),1)
WORK(WSSI) = WORK(WSSEPI) + WORK(WSSDEI)
ELSE
C PERFORM ERROR CHECKING
INFO = 0
CALL DODCHK(N,M,NP,NQ,
+ ISODR,ANAJAC,IMPLCT,
+ IFIXB,
+ LDX,LDIFX,LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LDY,
+ LWORK,LWKMN,LIWORK,LIWKMN,
+ SCLB,SCLD,STPB,STPD,
+ INFO)
IF (INFO.GT.0) THEN
GO TO 50
END IF
C INITIALIZE WORK VECTORS AS NECESSARY
DO 10 I=N*M+N*NQ+1,LWORK
WORK(I) = ZERO
10 CONTINUE
DO 20 I=1,LIWORK
IWORK(I) = 0
20 CONTINUE
CALL DINIWK(N,M,NP,
+ WORK,LWORK,IWORK,LIWORK,
+ X,LDX,IFIXX,LDIFX,SCLD,LDSCLD,
+ BETA,SCLB,
+ SSTOL,PARTOL,MAXIT,TAUFAC,
+ JOB,IPRINT,LUNERR,LUNRPT,
+ EPSMAI,SSTOLI,PARTLI,MAXITI,TAUFCI,
+ JOBI,IPRINI,LUNERI,LUNRPI,
+ SSFI,TTI,LDTTI,DELTAI)
IWORK(MSGB) = -1
IWORK(MSGD) = -1
WORK(TAUI) = -WORK(TAUFCI)
C SET UP FOR PARAMETER ESTIMATION -
C PULL BETA'S TO BE ESTIMATED AND CORRESPONDING SCALE VALUES
C AND STORE IN WORK(BETACI) AND WORK(SSI), RESPECTIVELY
CALL DPACK(NP,IWORK(NPPI),WORK(BETACI),BETA,IFIXB)
CALL DPACK(NP,IWORK(NPPI),WORK(SSI),WORK(SSFI),IFIXB)
NPP = IWORK(NPPI)
C CHECK THAT WD IS POSITIVE DEFINITE AND WE IS POSITIVE SEMIDEFINITE,
C SAVING FACTORIZATION OF WE, AND COUNTING NUMBER OF NONZERO WEIGHTS
CALL DFCTRW(N,M,NQ,NPP,
+ ISODR,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ WORK(WRK2I),WORK(WRK4I),
+ WORK(WE1I),NNZW,INFO)
IWORK(NNZWI) = NNZW
IF (INFO.NE.0) THEN
GO TO 50
END IF
C EVALUATE THE PREDICTED VALUES AND
C WEIGHTED EPSILONS AT THE STARTING POINT
CALL DUNPAC(NP,WORK(BETACI),BETA,IFIXB)
CALL DXPY(N,M,X,LDX,WORK(DELTAI),N,WORK(XPLUSI),N)
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,WORK(XPLUSI),
+ IFIXB,IFIXX,LDIFX,
+ 002,WORK(FNI),WORK(WRK6I),WORK(WRK1I),
+ ISTOP)
IWORK(ISTOPI) = ISTOP
IF (ISTOP.EQ.0) THEN
IWORK(NFEVI) = IWORK(NFEVI) + 1
IF (IMPLCT) THEN
CALL DCOPY(N*NQ,WORK(FNI),1,WORK(FI),1)
ELSE
CALL DXMY(N,NQ,WORK(FNI),N,Y,LDY,WORK(FI),N)
END IF
CALL DWGHT(N,NQ,WORK(WE1I),LDWE,LD2WE,WORK(FI),N,WORK(FI),N)
ELSE
INFO = 52000
GO TO 50
END IF
C COMPUTE NORM OF THE INITIAL ESTIMATES
CALL DWGHT(NPP,1,WORK(SSI),NPP,1,WORK(BETACI),NPP,
+ WORK(WRK),NPP)
IF (ISODR) THEN
CALL DWGHT(N,M,WORK(TTI),IWORK(LDTTI),1,WORK(DELTAI),N,
+ WORK(WRK+NPP),N)
WORK(PNORMI) = DNRM2(NPP+N*M,WORK(WRK),1)
ELSE
WORK(PNORMI) = DNRM2(NPP,WORK(WRK),1)
END IF
C COMPUTE SUM OF SQUARES OF THE WEIGHTED EPSILONS AND WEIGHTED DELTAS
WORK(WSSEPI) = DDOT(N*NQ,WORK(FI),1,WORK(FI),1)
IF (ISODR) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,WORK(DELTAI),N,WORK(WRK),N)
WORK(WSSDEI) = DDOT(N*M,WORK(DELTAI),1,WORK(WRK),1)
ELSE
WORK(WSSDEI) = ZERO
END IF
WORK(WSSI) = WORK(WSSEPI) + WORK(WSSDEI)
C SELECT FIRST ROW OF X + DELTA THAT CONTAINS NO ZEROS
NROW = -1
CALL DSETN(N,M,WORK(XPLUSI),N,NROW)
IWORK(NROWI) = NROW
C SET NUMBER OF GOOD DIGITS IN FUNCTION RESULTS
EPSMAC = WORK(EPSMAI)
IF (NDIGIT.LT.2) THEN
IWORK(NETAI) = -1
NFEV = IWORK(NFEVI)
CALL DETAF(FCN,
+ N,M,NP,NQ,
+ WORK(XPLUSI),BETA,EPSMAC,NROW,
+ WORK(BETANI),WORK(FNI),
+ IFIXB,IFIXX,LDIFX,
+ ISTOP,NFEV,ETA,NETA,
+ WORK(WRK1I),WORK(WRK2I),WORK(WRK6I),WORK(WRK7I))
IWORK(ISTOPI) = ISTOP
IWORK(NFEVI) = NFEV
IF (ISTOP.NE.0) THEN
INFO = 53000
IWORK(NETAI) = 0
WORK(ETAI) = ZERO
GO TO 50
ELSE
IWORK(NETAI) = -NETA
WORK(ETAI) = ETA
END IF
ELSE
IWORK(NETAI) = MIN(NDIGIT,INT(P5-LOG10(EPSMAC)))
WORK(ETAI) = MAX(EPSMAC,TEN**(-NDIGIT))
END IF
C CHECK DERIVATIVES IF NECESSARY
IF (CHKJAC .AND. ANAJAC) THEN
NTOL = -1
NFEV = IWORK(NFEVI)
NJEV = IWORK(NJEVI)
NETA = IWORK(NETAI)
LDTT = IWORK(LDTTI)
ETA = WORK(ETAI)
EPSMAC = WORK(EPSMAI)
CALL DJCK(FCN,
+ N,M,NP,NQ,
+ BETA,WORK(XPLUSI),
+ IFIXB,IFIXX,LDIFX,STPB,STPD,LDSTPD,
+ WORK(SSFI),WORK(TTI),LDTT,
+ ETA,NETA,NTOL,NROW,ISODR,EPSMAC,
+ WORK(FNI),WORK(FJACBI),WORK(FJACDI),
+ IWORK(MSGB),IWORK(MSGD),WORK(DIFFI),
+ ISTOP,NFEV,NJEV,
+ WORK(WRK1I),WORK(WRK2I),WORK(WRK6I))
IWORK(ISTOPI) = ISTOP
IWORK(NFEVI) = NFEV
IWORK(NJEVI) = NJEV
IWORK(NTOLI) = NTOL
IF (ISTOP.NE.0) THEN
INFO = 54000
ELSE IF (IWORK(MSGB).NE.0 .OR. IWORK(MSGD).NE.0) THEN
INFO = 40000
END IF
ELSE
C INDICATE USER SUPPLIED DERIVATIVES WERE NOT CHECKED
IWORK(MSGB) = -1
IWORK(MSGD) = -1
END IF
C PRINT APPROPRIATE ERROR MESSAGES
50 IF ((INFO.NE.0) .OR. (IWORK(MSGB).NE.-1)) THEN
IF (LUNERR.NE.0 .AND. IPRINT.NE.0) THEN
CALL DODPER
+ (INFO,LUNERR,SHORT,
+ N,M,NP,NQ,
+ LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LWKMN,LIWKMN,
+ WORK(FJACBI),WORK(FJACDI),
+ WORK(DIFFI),IWORK(MSGB),ISODR,IWORK(MSGD),
+ WORK(XPLUSI),IWORK(NROWI),IWORK(NETAI),IWORK(NTOLI))
END IF
C SET INFO TO REFLECT ERRORS IN THE USER SUPPLIED JACOBIANS
IF (INFO.EQ.40000) THEN
IF (IWORK(MSGB).EQ.2 .OR. IWORK(MSGD).EQ.2) THEN
IF (IWORK(MSGB).EQ.2) THEN
INFO = INFO + 1000
END IF
IF (IWORK(MSGD).EQ.2) THEN
INFO = INFO + 100
END IF
ELSE
INFO = 0
END IF
END IF
IF (INFO.NE.0) THEN
RETURN
END IF
END IF
END IF
C SAVE THE INITIAL VALUES OF BETA
CALL DCOPY(NP,BETA,1,WORK(BETA0I),1)
C FIND LEAST SQUARES SOLUTION
CALL DCOPY(N*NQ,WORK(FNI),1,WORK(FSI),1)
LDTT = IWORK(LDTTI)
CALL DODMN(HEAD,FSTITR,PRTPEN,
+ FCN, N,M,NP,NQ, JOB, BETA,Y,LDY,X,LDX,
+ WE,WORK(WE1I),LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ WORK(BETACI),WORK(BETANI),WORK(BETASI),WORK(SI),
+ WORK(DELTAI),WORK(DELTNI),WORK(DELTSI),
+ WORK(TI),WORK(FI),WORK(FNI),WORK(FSI),
+ WORK(FJACBI),IWORK(MSGB),WORK(FJACDI),IWORK(MSGD),
+ WORK(SSFI),WORK(SSI),WORK(TTI),LDTT,
+ STPB,STPD,LDSTPD,
+ WORK(XPLUSI),WORK(WRK),LWRK,
+ WORK,LWORK,IWORK,LIWORK,INFO)
MAXIT1 = IWORK(MAXITI) - IWORK(NITERI)
TSTIMP = ZERO
DO 100 K=1,NP
IF (BETA(K).EQ.ZERO) THEN
TSTIMP = MAX(TSTIMP,
+ ABS(BETA(K)-WORK(BETA0I-1+K))/WORK(SSFI-1+K))
ELSE
TSTIMP = MAX(TSTIMP,
+ ABS(BETA(K)-WORK(BETA0I-1+K))/ABS(BETA(K)))
END IF
100 CONTINUE
RETURN
END
*DODLM
SUBROUTINE DODLM
+ (N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ALPHA2,TAU,EPSFCN,ISODR,
+ TFJACB,OMEGA,U,QRAUX,JPVT,
+ S,T,NLMS,RCOND,IRANK,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
C***BEGIN PROLOGUE DODLM
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DDOT,DNRM2,DODSTP,DSCALE,DWGHT
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE LEVENBERG-MARQUARDT PARAMETER AND STEPS S AND T
C USING ANALOG OF THE TRUST-REGION LEVENBERG-MARQUARDT
C ALGORITHM
C***END PROLOGUE DODLM
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ALPHA2,EPSFCN,RCOND,TAU
INTEGER
+ IRANK,ISTOPC,LDTT,LDWD,LD2WD,LWRK,M,N,NLMS,NP,NPP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DELTA(N,M),F(N,NQ),FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ OMEGA(NQ,NQ),QRAUX(NP),S(NP),SS(NP),
+ T(N,M),TFJACB(N,NQ,NP),TT(LDTT,M),U(NP),WD(LDWD,LD2WD,M),
+ WRK(LWRK),WRK1(N,NQ,M),WRK2(N,NQ),WRK3(NP),WRK4(M,M),WRK5(M)
INTEGER
+ JPVT(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ALPHA1,ALPHAN,BOT,P001,P1,PHI1,PHI2,SA,TOP,ZERO
INTEGER
+ I,IWRK,J,K,L
LOGICAL
+ FORVCV
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT,DNRM2
EXTERNAL
+ DDOT,DNRM2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DODSTP,DSCALE,DWGHT
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MAX,MIN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,P001,P1
+ /0.0D0,0.001D0,0.1D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ALPHAN: THE NEW LEVENBERG-MARQUARDT PARAMETER.
C ALPHA1: THE PREVIOUS LEVENBERG-MARQUARDT PARAMETER.
C ALPHA2: THE CURRENT LEVENBERG-MARQUARDT PARAMETER.
C BOT: THE LOWER LIMIT FOR SETTING ALPHA.
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C EPSFCN: THE FUNCTION'S PRECISION.
C F: THE (WEIGHTED) ESTIMATED VALUES OF EPSILON.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FORVCV: THE VARIABLE DESIGNATING WHETHER THIS SUBROUTINE WAS
C CALLED TO SET UP FOR THE COVARIANCE MATRIX COMPUTATIONS
C (FORVCV=TRUE) OR NOT (FORVCV=FALSE).
C I: AN INDEXING VARIABLE.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOPC: THE VARIABLE DESIGNATING WHETHER THE COMPUTATIONS WERE
C STOPED DUE TO SOME NUMERICAL ERROR DETECTED WITHIN
C SUBROUTINE DODSTP.
C IWRK: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C JPVT: THE PIVOT VECTOR.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LWRK: THE LENGTH OF VECTOR WRK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NLMS: THE NUMBER OF LEVENBERG-MARQUARDT STEPS TAKEN.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C OMEGA: THE ARRAY (I-FJACD*INV(P)*TRANS(FJACD))**(-1/2) WHERE
C P = TRANS(FJACD)*FJACD + D**2 + ALPHA*TT**2
C P001: THE VALUE 0.001D0
C P1: THE VALUE 0.1D0
C PHI1: THE PREVIOUS DIFFERENCE BETWEEN THE NORM OF THE SCALED STEP
C AND THE TRUST REGION DIAMETER.
C PHI2: THE CURRENT DIFFERENCE BETWEEN THE NORM OF THE SCALED STEP
C AND THE TRUST REGION DIAMETER.
C QRAUX: THE ARRAY REQUIRED TO RECOVER THE ORTHOGONAL PART OF THE
C Q-R DECOMPOSITION.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION OF TFJACB.
C S: THE STEP FOR BETA.
C SA: THE SCALAR PHI2*(ALPHA1-ALPHA2)/(PHI1-PHI2).
C SS: THE SCALING VALUES USED FOR THE UNFIXED BETAS.
C T: THE STEP FOR DELTA.
C TAU: THE TRUST REGION DIAMETER.
C TFJACB: THE ARRAY OMEGA*FJACB.
C TOP: THE UPPER LIMIT FOR SETTING ALPHA.
C TT: THE SCALE USED FOR THE DELTA'S.
C U: THE APPROXIMATE NULL VECTOR FOR TFJACB.
C WD: THE DELTA WEIGHTS.
C WRK: A WORK ARRAY OF (LWRK) ELEMENTS,
C EQUIVALENCED TO WRK1 AND WRK2.
C WRK1: A WORK ARRAY OF (N BY NQ BY M) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK4: A WORK ARRAY OF (M BY M) ELEMENTS.
C WRK5: A WORK ARRAY OF (M) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODLM
FORVCV = .FALSE.
ISTOPC = 0
C COMPUTE FULL GAUSS-NEWTON STEP (ALPHA=0)
ALPHA1 = ZERO
CALL DODSTP(N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ALPHA1,EPSFCN,ISODR,
+ TFJACB,OMEGA,U,QRAUX,JPVT,
+ S,T,PHI1,IRANK,RCOND,FORVCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
IF (ISTOPC.NE.0) THEN
RETURN
END IF
C INITIALIZE TAU IF NECESSARY
IF (TAU.LT.ZERO) THEN
TAU = ABS(TAU)*PHI1
END IF
C CHECK IF FULL GAUSS-NEWTON STEP IS OPTIMAL
IF ((PHI1-TAU).LE.P1*TAU) THEN
NLMS = 1
ALPHA2 = ZERO
RETURN
END IF
C FULL GAUSS-NEWTON STEP IS OUTSIDE TRUST REGION -
C FIND LOCALLY CONSTRAINED OPTIMAL STEP
PHI1 = PHI1 - TAU
C INITIALIZE UPPER AND LOWER BOUNDS FOR ALPHA
BOT = ZERO
DO 30 K=1,NPP
DO 20 L=1,NQ
DO 10 I=1,N
TFJACB(I,L,K) = FJACB(I,K,L)
10 CONTINUE
20 CONTINUE
WRK(K) = DDOT(N*NQ,TFJACB(1,1,K),1,F(1,1),1)
30 CONTINUE
CALL DSCALE(NPP,1,SS,NPP,WRK,NPP,WRK,NPP)
IF (ISODR) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,DELTA,N,WRK(NPP+1),N)
IWRK = NPP
DO 50 J=1,M
DO 40 I=1,N
IWRK = IWRK + 1
WRK(IWRK) = WRK(IWRK) +
+ DDOT(NQ,FJACD(I,J,1),N*M,F(I,1),N)
40 CONTINUE
50 CONTINUE
CALL DSCALE(N,M,TT,LDTT,WRK(NPP+1),N,WRK(NPP+1),N)
TOP = DNRM2(NPP+N*M,WRK,1)/TAU
ELSE
TOP = DNRM2(NPP,WRK,1)/TAU
END IF
IF (ALPHA2.GT.TOP .OR. ALPHA2.EQ.ZERO) THEN
ALPHA2 = P001*TOP
END IF
C MAIN LOOP
DO 60 I=1,10
C COMPUTE LOCALLY CONSTRAINED STEPS S AND T AND PHI(ALPHA) FOR
C CURRENT VALUE OF ALPHA
CALL DODSTP(N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ALPHA2,EPSFCN,ISODR,
+ TFJACB,OMEGA,U,QRAUX,JPVT,
+ S,T,PHI2,IRANK,RCOND,FORVCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
IF (ISTOPC.NE.0) THEN
RETURN
END IF
PHI2 = PHI2-TAU
C CHECK WHETHER CURRENT STEP IS OPTIMAL
IF (ABS(PHI2).LE.P1*TAU .OR.
+ (ALPHA2.EQ.BOT .AND. PHI2.LT.ZERO)) THEN
NLMS = I+1
RETURN
END IF
C CURRENT STEP IS NOT OPTIMAL
C UPDATE BOUNDS FOR ALPHA AND COMPUTE NEW ALPHA
IF (PHI1-PHI2.EQ.ZERO) THEN
NLMS = 12
RETURN
END IF
SA = PHI2*(ALPHA1-ALPHA2)/(PHI1-PHI2)
IF (PHI2.LT.ZERO) THEN
TOP = MIN(TOP,ALPHA2)
ELSE
BOT = MAX(BOT,ALPHA2)
END IF
IF (PHI1*PHI2.GT.ZERO) THEN
BOT = MAX(BOT,ALPHA2-SA)
ELSE
TOP = MIN(TOP,ALPHA2-SA)
END IF
ALPHAN = ALPHA2 - SA*(PHI1+TAU)/TAU
IF (ALPHAN.GE.TOP .OR. ALPHAN.LE.BOT) THEN
ALPHAN = MAX(P001*TOP,SQRT(TOP*BOT))
END IF
C GET READY FOR NEXT ITERATION
ALPHA1 = ALPHA2
ALPHA2 = ALPHAN
PHI1 = PHI2
60 CONTINUE
C SET NLMS TO INDICATE AN OPTIMAL STEP COULD NOT BE FOUND IN 10 TRYS
NLMS = 12
RETURN
END
*DODMN
SUBROUTINE DODMN
+ (HEAD,FSTITR,PRTPEN,
+ FCN, N,M,NP,NQ, JOB, BETA,Y,LDY,X,LDX,
+ WE,WE1,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ BETAC,BETAN,BETAS,S,DELTA,DELTAN,DELTAS,
+ T,F,FN,FS,FJACB,MSGB,FJACD,MSGD,
+ SSF,SS,TT,LDTT,STPB,STPD,LDSTPD,
+ XPLUSD,WRK,LWRK,WORK,LWORK,IWORK,LIWORK,INFO)
C***BEGIN PROLOGUE DODMN
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN,DACCES,DCOPY,DDOT,DEVJAC,DFLAGS,DNRM2,DODLM,
C DODPCR,DODVCV,DUNPAC,DWGHT,DXMY,DXPY
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE ITERATIVELY COMPUTE LEAST SQUARES SOLUTION
C***END PROLOGUE DODMN
C...SCALAR ARGUMENTS
INTEGER
+ INFO,JOB,LDIFX,LDSTPD,LDTT,LDWD,LDWE,LDX,LDY,LD2WD,LD2WE,
+ LIWORK,LWORK,LWRK,M,N,NP,NQ
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),BETAC(NP),BETAN(NP),BETAS(NP),
+ DELTA(N,M),DELTAN(N,M),DELTAS(N,M),
+ F(N,NQ),FJACB(N,NP,NQ),FJACD(N,M,NQ),FN(N,NQ),FS(N,NQ),
+ S(NP),SS(NP),SSF(NP),STPB(NP),STPD(LDSTPD,M),
+ T(N,M),TT(LDTT,M),
+ WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),WE1(LDWE,LD2WE,NQ),
+ WORK(LWORK),X(LDX,M),XPLUSD(N,M),WRK(LWRK),Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),IWORK(LIWORK),
+ MSGB(NQ*NP+1),MSGD(NQ*M+1)
LOGICAL
+ FSTITR,HEAD,PRTPEN
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ ACTRED,ACTRS,ALPHA,DIRDER,ETA,OLMAVG,ONE,
+ P0001,P1,P25,P5,P75,PARTOL,PNORM,PRERED,PRERS,
+ RATIO,RCOND,RNORM,RNORMN,RNORMS,RSS,RVAR,SSTOL,TAU,TAUFAC,
+ TEMP,TEMP1,TEMP2,TSNORM,ZERO
INTEGER
+ I,IDF,IFLAG,INT2,IPR,IPR1,IPR2,IPR2F,IPR3,IRANK,
+ ISTOP,ISTOPC,IWRK,J,JPVT,L,LOOPED,LUDFLT,LUNR,LUNRPT,
+ MAXIT,NETA,NFEV,NITER,NJEV,NLMS,NNZW,NPP,NPR,OMEGA,QRAUX,
+ SD,U,VCV,WRK1,WRK2,WRK3,WRK4,WRK5,WRK6
LOGICAL
+ ACCESS,ANAJAC,CDJAC,CHKJAC,CNVPAR,CNVSS,DIDVCV,DOVCV,
+ IMPLCT,INITD,INTDBL,ISODR,LSTEP,REDOJ,RESTRT
C...LOCAL ARRAYS
DOUBLE PRECISION
+ WSS(3)
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT,DNRM2
EXTERNAL
+ DDOT,DNRM2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DACCES,DCOPY,DEVJAC,DFLAGS,
+ DODLM,DODPCR,DODVCV,DUNPAC,DWGHT,DXMY,DXPY
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MIN,MOD,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,P0001,P1,P25,P5,P75,ONE
+ /0.0D0,0.00010D0,0.10D0,0.250D0,
+ 0.50D0,0.750D0,1.0D0/
DATA
+ LUDFLT
+ /6/
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACCESS: THE VARIABLE DESIGNATING WHETHER INFORMATION IS TO BE
C ACCESSED FROM THE WORK ARRAYS (ACCESS=TRUE) OR STORED IN
C THEM (ACCESS=FALSE).
C ACTRED: THE ACTUAL RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C ACTRS: THE SAVED ACTUAL RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C BETAC: THE CURRENT ESTIMATED VALUES OF THE UNFIXED BETA'S.
C BETAN: THE NEW ESTIMATED VALUES OF THE UNFIXED BETA'S.
C BETAS: THE SAVED ESTIMATED VALUES OF THE UNFIXED BETA'S.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR BY FORWARD
C DIFFERENCES (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C CNVPAR: THE VARIABLE DESIGNATING WHETHER PARAMETER CONVERGENCE WAS
C ATTAINED (CNVPAR=TRUE) OR NOT (CNVPAR=FALSE).
C CNVSS: THE VARIABLE DESIGNATING WHETHER SUM-OF-SQUARES CONVERGENCE
C WAS ATTAINED (CNVSS=TRUE) OR NOT (CNVSS=FALSE).
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DELTAN: THE NEW ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DELTAS: THE SAVED ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DIDVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX WAS
C COMPUTED (DIDVCV=TRUE) OR NOT (DIDVCV=FALSE).
C DIRDER: THE DIRECTIONAL DERIVATIVE.
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX
C SHOULD TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C ETA: THE RELATIVE NOISE IN THE FUNCTION RESULTS.
C F: THE (WEIGHTED) ESTIMATED VALUES OF EPSILON.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FN: THE NEW PREDICTED VALUES FROM THE FUNCTION.
C FS: THE SAVED PREDICTED VALUES FROM THE FUNCTION.
C FSTITR: THE VARIABLE DESIGNATING WHETHER THIS IS THE FIRST
C ITERATION (FSTITR=TRUE) OR NOT (FSTITR=FALSE).
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=TRUE) OR NOT (HEAD=FALSE).
C I: AN INDEXING VARIABLE.
C IDF: THE DEGREES OF FREEDOM OF THE FIT, EQUAL TO THE NUMBER OF
C OBSERVATIONS WITH NONZERO WEIGHTED DERIVATIVES MINUS THE
C NUMBER OF PARAMETERS BEING ESTIMATED.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFLAG: THE VARIABLE DESIGNATING WHICH REPORT IS TO BE PRINTED.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS INITIALIZED TO
C ZERO (INITD=TRUE) OR TO THE VALUES IN THE FIRST N BY M
C ELEMENTS OF ARRAY WORK (INITD=FALSE).
C INT2: THE NUMBER OF INTERNAL DOUBLING STEPS TAKEN.
C INTDBL: THE VARIABLE DESIGNATING WHETHER INTERNAL DOUBLING IS TO BE
C USED (INTDBL=TRUE) OR NOT (INTDBL=FALSE).
C IPR: THE VALUES DESIGNATING THE LENGTH OF THE PRINTED REPORT.
C IPR1: THE VALUE OF THE 4TH DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE INITIAL SUMMARY REPORT.
C IPR2: THE VALUE OF THE 3RD DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE ITERATION REPORT.
C IPR2F: THE VALUE OF THE 2ND DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE FREQUENCY OF THE ITERATION REPORTS.
C IPR3: THE VALUE OF THE 1ST DIGIT (FROM THE RIGHT) OF IPRINT,
C WHICH CONTROLS THE FINAL SUMMARY REPORT.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C ISTOPC: THE VARIABLE DESIGNATING WHETHER THE COMPUTATIONS WERE
C STOPED DUE TO SOME NUMERICAL ERROR WITHIN ROUTINE DODSTP.
C IWORK: THE INTEGER WORK SPACE.
C IWRK: AN INDEX VARIABLE.
C J: AN INDEX VARIABLE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JPVT: THE STARTING LOCATION IN IWORK OF ARRAY JPVT.
C L: AN INDEX VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE AND WE1.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE AND WE1.
C LIWORK: THE LENGTH OF VECTOR IWORK.
C LOOPED: A COUNTER USED TO DETERMINE HOW MANY TIMES THE SUBLOOP
C HAS BEEN EXECUTED, WHERE IF THE COUNT BECOMES LARGE
C ENOUGH THE COMPUTATIONS WILL BE STOPPED.
C LSTEP: THE VARIABLE DESIGNATING WHETHER A SUCCESSFUL STEP HAS
C BEEN FOUND (LSTEP=TRUE) OR NOT (LSTEP=FALSE).
C LUDFLT: THE DEFAULT LOGICAL UNIT NUMBER, USED FOR COMPUTATION
C REPORTS TO THE SCREEN.
C LUNR: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C LWORK: THE LENGTH OF VECTOR WORK.
C LWRK: THE LENGTH OF VECTOR WRK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NITER: THE NUMBER OF ITERATIONS TAKEN.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NLMS: THE NUMBER OF LEVENBERG-MARQUARDT STEPS TAKEN.
C NNZW: THE NUMBER OF NONZERO WEIGHTED OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NPR: THE NUMBER OF TIMES THE REPORT IS TO BE WRITTEN.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C OLMAVG: THE AVERAGE NUMBER OF LEVENBERG-MARQUARDT STEPS PER
C ITERATION.
C OMEGA: THE STARTING LOCATION IN WORK OF ARRAY OMEGA.
C ONE: THE VALUE 1.0D0.
C P0001: THE VALUE 0.0001D0.
C P1: THE VALUE 0.1D0.
C P25: THE VALUE 0.25D0.
C P5: THE VALUE 0.5D0.
C P75: THE VALUE 0.75D0.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PNORM: THE NORM OF THE SCALED ESTIMATED PARAMETERS.
C PRERED: THE PREDICTED RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C PRERS: THE OLD PREDICTED RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C PRTPEN: THE VALUE DESIGNATING WHETHER THE PENALTY PARAMETER IS TO
C BE PRINTED IN THE ITERATION REPORT (PRTPEN=TRUE) OR NOT
C (PRTPEN=FALSE).
C QRAUX: THE STARTING LOCATION IN ARRAY WORK OF ARRAY QRAUX.
C RATIO: THE RATIO OF THE ACTUAL RELATIVE REDUCTION TO THE PREDICTED
C RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION OF FJACB.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C RNORM: THE NORM OF THE WEIGHTED ERRORS.
C RNORMN: THE NEW NORM OF THE WEIGHTED ERRORS.
C RNORMS: THE SAVED NORM OF THE WEIGHTED ERRORS.
C RSS: THE RESIDUAL SUM OF SQUARES.
C RVAR: THE RESIDUAL VARIANCE.
C S: THE STEP FOR BETA.
C SD: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SD.
C SS: THE SCALING VALUES USED FOR THE UNFIXED BETAS.
C SSF: THE SCALING VALUES USED FOR BETA.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C STPB: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO EACH BETA.
C STPD: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C T: THE STEP FOR DELTA.
C TAU: THE TRUST REGION DIAMETER.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TEMP: A TEMPORARY STORAGE LOCATION.
C TEMP1: A TEMPORARY STORAGE LOCATION.
C TEMP2: A TEMPORARY STORAGE LOCATION.
C TSNORM: THE NORM OF THE SCALED STEP.
C TT: THE SCALING VALUES USED FOR DELTA.
C U: THE STARTING LOCATION IN ARRAY WORK OF ARRAY U.
C VCV: THE STARTING LOCATION IN ARRAY WORK OF ARRAY VCV.
C WE: THE EPSILON WEIGHTS.
C WE1: THE SQUARE ROOT OF THE EPSILON WEIGHTS.
C WD: THE DELTA WEIGHTS.
C WORK: THE DOUBLE PRECISION WORK SPACE.
C WSS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS AND DELTAS,
C THE SUM-OF-SQUARES OF THE WEIGHTED DELTAS, AND
C THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS.
C WRK: A WORK ARRAY, EQUIVALENCED TO WRK1 AND WRK2
C WRK1: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK1.
C WRK2: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK2.
C WRK3: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK3.
C WRK4: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK4.
C WRK5: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK5.
C WRK6: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK6.
C X: THE EXPLANATORY VARIABLE.
C XPLUSD: THE VALUES OF X + DELTA.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODMN
C INITIALIZE NECESSARY VARIABLES
CALL DFLAGS(JOB,RESTRT,INITD,DOVCV,REDOJ,
+ ANAJAC,CDJAC,CHKJAC,ISODR,IMPLCT)
ACCESS = .TRUE.
CALL DACCES(N,M,NP,NQ,LDWE,LD2WE,
+ WORK,LWORK,IWORK,LIWORK,
+ ACCESS,ISODR,
+ JPVT,OMEGA,U,QRAUX,SD,VCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK6,
+ NNZW,NPP,
+ JOB,PARTOL,SSTOL,MAXIT,TAUFAC,ETA,NETA,
+ LUNRPT,IPR1,IPR2,IPR2F,IPR3,
+ WSS,RVAR,IDF,
+ TAU,ALPHA,NITER,NFEV,NJEV,INT2,OLMAVG,
+ RCOND,IRANK,ACTRS,PNORM,PRERS,RNORMS,ISTOP)
RNORM = SQRT(WSS(1))
DIDVCV = .FALSE.
INTDBL = .FALSE.
LSTEP = .TRUE.
C PRINT INITIAL SUMMARY IF DESIRED
IF (IPR1.NE.0 .AND. LUNRPT.NE.0) THEN
IFLAG = 1
IF (IPR1.GE.3 .AND. LUNRPT.NE.LUDFLT) THEN
NPR = 2
ELSE
NPR = 1
END IF
IF (IPR1.GE.6) THEN
IPR = 2
ELSE
IPR = 2 - MOD(IPR1,2)
END IF
LUNR = LUNRPT
DO 10 I=1,NPR
CALL DODPCR(IPR,LUNR,
+ HEAD,PRTPEN,FSTITR,DIDVCV,IFLAG,
+ N,M,NP,NQ,NPP,NNZW,
+ MSGB,MSGD, BETA,Y,LDY,X,LDX,DELTA,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ SSF,TT,LDTT,STPB,STPD,LDSTPD,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS,RVAR,IDF,WORK(SD),
+ NITER,NFEV,NJEV,ACTRED,PRERED,
+ TAU,PNORM,ALPHA,F,RCOND,IRANK,INFO,ISTOP)
IF (IPR1.GE.5) THEN
IPR = 2
ELSE
IPR = 1
END IF
LUNR = LUDFLT
10 CONTINUE
END IF
C STOP IF INITIAL ESTIMATES ARE EXACT SOLUTION
IF (RNORM.EQ.ZERO) THEN
INFO = 1
OLMAVG = ZERO
ISTOP = 0
GO TO 150
END IF
C STOP IF NUMBER OF ITERATIONS ALREADY EQUALS MAXIMUM PERMITTED
IF (RESTRT .AND. (NITER.GE.MAXIT)) THEN
ISTOP = 0
GO TO 150
ELSE IF (NITER.GE.MAXIT) THEN
INFO = 4
ISTOP = 0
GO TO 150
END IF
C MAIN LOOP
100 CONTINUE
NITER = NITER + 1
RNORMS = RNORM
LOOPED = 0
C EVALUATE JACOBIAN USING BEST ESTIMATE OF FUNCTION (FS)
IF ((NITER.EQ.1) .AND. (ANAJAC.AND.CHKJAC)) THEN
ISTOP = 0
ELSE
CALL DEVJAC(FCN,
+ ANAJAC,CDJAC,
+ N,M,NP,NQ,
+ BETAC,BETA,STPB,
+ IFIXB,IFIXX,LDIFX,
+ X,LDX,DELTA,XPLUSD,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,FS,
+ T,WORK(WRK1),WORK(WRK2),WORK(WRK3),WORK(WRK6),
+ FJACB,ISODR,FJACD,WE1,LDWE,LD2WE,
+ NJEV,NFEV,ISTOP,INFO)
END IF
IF (ISTOP.NE.0) THEN
INFO = 51000
GO TO 200
ELSE IF (INFO.EQ.50300) THEN
GO TO 200
END IF
C SUB LOOP FOR
C INTERNAL DOUBLING OR
C COMPUTING NEW STEP WHEN OLD FAILED
110 CONTINUE
C COMPUTE STEPS S AND T
IF (LOOPED.GT.100) THEN
INFO = 60000
GO TO 200
ELSE
LOOPED = LOOPED + 1
CALL DODLM(N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ALPHA,TAU,ETA,ISODR,
+ WORK(WRK6),WORK(OMEGA),
+ WORK(U),WORK(QRAUX),IWORK(JPVT),
+ S,T,NLMS,RCOND,IRANK,
+ WORK(WRK1),WORK(WRK2),WORK(WRK3),WORK(WRK4),
+ WORK(WRK5),WRK,LWRK,ISTOPC)
END IF
IF (ISTOPC.NE.0) THEN
INFO = ISTOPC
GO TO 200
END IF
OLMAVG = OLMAVG+NLMS
C COMPUTE BETAN = BETAC + S
C DELTAN = DELTA + T
CALL DXPY(NPP,1,BETAC,NPP,S,NPP,BETAN,NPP)
IF (ISODR) CALL DXPY(N,M,DELTA,N,T,N,DELTAN,N)
C COMPUTE NORM OF SCALED STEPS S AND T (TSNORM)
CALL DWGHT(NPP,1,SS,NPP,1,S,NPP,WRK,NPP)
IF (ISODR) THEN
CALL DWGHT(N,M,TT,LDTT,1,T,N,WRK(NPP+1),N)
TSNORM = DNRM2(NPP+N*M,WRK,1)
ELSE
TSNORM = DNRM2(NPP,WRK,1)
END IF
C COMPUTE SCALED PREDICTED REDUCTION
IWRK = 0
DO 130 L=1,NQ
DO 120 I=1,N
IWRK = IWRK + 1
WRK(IWRK) = DDOT(NPP,FJACB(I,1,L),N,S,1)
IF (ISODR) WRK(IWRK) = WRK(IWRK) +
+ DDOT(M,FJACD(I,1,L),N,T(I,1),N)
120 CONTINUE
130 CONTINUE
IF (ISODR) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,T,N,WRK(N*NQ+1),N)
TEMP1 = DDOT(N*NQ,WRK,1,WRK,1) + DDOT(N*M,T,1,WRK(N*NQ+1),1)
TEMP1 = SQRT(TEMP1)/RNORM
ELSE
TEMP1 = DNRM2(N*NQ,WRK,1)/RNORM
END IF
TEMP2 = SQRT(ALPHA)*TSNORM/RNORM
PRERED = TEMP1**2+TEMP2**2/P5
DIRDER = -(TEMP1**2+TEMP2**2)
C EVALUATE PREDICTED VALUES AT NEW POINT
CALL DUNPAC(NP,BETAN,BETA,IFIXB)
CALL DXPY(N,M,X,LDX,DELTAN,N,XPLUSD,N)
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 002,FN,WORK(WRK6),WORK(WRK1),
+ ISTOP)
IF (ISTOP.EQ.0) THEN
NFEV = NFEV + 1
END IF
IF (ISTOP.LT.0) THEN
C SET INFO TO INDICATE USER HAS STOPPED THE COMPUTATIONS IN FCN
INFO = 51000
GO TO 200
ELSE IF (ISTOP.GT.0) THEN
C SET NORM TO INDICATE STEP SHOULD BE REJECTED
RNORMN = RNORM/(P1*P75)
ELSE
C COMPUTE NORM OF NEW WEIGHTED EPSILONS AND WEIGHTED DELTAS (RNORMN)
IF (IMPLCT) THEN
CALL DCOPY(N*NQ,FN,1,WRK,1)
ELSE
CALL DXMY(N,NQ,FN,N,Y,LDY,WRK,N)
END IF
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,WRK,N,WRK,N)
IF (ISODR) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,DELTAN,N,WRK(N*NQ+1),N)
RNORMN = SQRT(DDOT(N*NQ,WRK,1,WRK,1) +
+ DDOT(N*M,DELTAN,1,WRK(N*NQ+1),1))
ELSE
RNORMN = DNRM2(N*NQ,WRK,1)
END IF
END IF
C COMPUTE SCALED ACTUAL REDUCTION
IF (P1*RNORMN.LT.RNORM) THEN
ACTRED = ONE - (RNORMN/RNORM)**2
ELSE
ACTRED = -ONE
END IF
C COMPUTE RATIO OF ACTUAL REDUCTION TO PREDICTED REDUCTION
IF(PRERED .EQ. ZERO) THEN
RATIO = ZERO
ELSE
RATIO = ACTRED/PRERED
END IF
C CHECK ON LACK OF REDUCTION IN INTERNAL DOUBLING CASE
IF (INTDBL .AND. (RATIO.LT.P0001 .OR. RNORMN.GT.RNORMS)) THEN
ISTOP = 0
TAU = TAU*P5
ALPHA = ALPHA/P5
CALL DCOPY(NPP,BETAS,1,BETAN,1)
CALL DCOPY(N*M,DELTAS,1,DELTAN,1)
CALL DCOPY(N*NQ,FS,1,FN,1)
ACTRED = ACTRS
PRERED = PRERS
RNORMN = RNORMS
RATIO = P5
END IF
C UPDATE STEP BOUND
INTDBL = .FALSE.
IF (RATIO.LT.P25) THEN
IF (ACTRED.GE.ZERO) THEN
TEMP = P5
ELSE
TEMP = P5*DIRDER/(DIRDER+P5*ACTRED)
END IF
IF (P1*RNORMN.GE.RNORM .OR. TEMP.LT.P1) THEN
TEMP = P1
END IF
TAU = TEMP*MIN(TAU,TSNORM/P1)
ALPHA = ALPHA/TEMP
ELSE IF (ALPHA.EQ.ZERO) THEN
TAU = TSNORM/P5
ELSE IF (RATIO.GE.P75 .AND. NLMS.LE.11) THEN
C STEP QUALIFIES FOR INTERNAL DOUBLING
C - UPDATE TAU AND ALPHA
C - SAVE INFORMATION FOR CURRENT POINT
INTDBL = .TRUE.
TAU = TSNORM/P5
ALPHA = ALPHA*P5
CALL DCOPY(NPP,BETAN,1,BETAS,1)
CALL DCOPY(N*M,DELTAN,1,DELTAS,1)
CALL DCOPY(N*NQ,FN,1,FS,1)
ACTRS = ACTRED
PRERS = PRERED
RNORMS = RNORMN
END IF
C IF INTERNAL DOUBLING, SKIP CONVERGENCE CHECKS
IF (INTDBL .AND. TAU.GT.ZERO) THEN
INT2 = INT2+1
GO TO 110
END IF
C CHECK ACCEPTANCE
IF (RATIO.GE.P0001) THEN
CALL DCOPY(N*NQ,FN,1,FS,1)
IF (IMPLCT) THEN
CALL DCOPY(N*NQ,FS,1,F,1)
ELSE
CALL DXMY(N,NQ,FS,N,Y,LDY,F,N)
END IF
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,F,N,F,N)
CALL DCOPY(NPP,BETAN,1,BETAC,1)
CALL DCOPY(N*M,DELTAN,1,DELTA,1)
RNORM = RNORMN
CALL DWGHT(NPP,1,SS,NPP,1,BETAC,NPP,WRK,NPP)
IF (ISODR) THEN
CALL DWGHT(N,M,TT,LDTT,1,DELTA,N,WRK(NPP+1),N)
PNORM = DNRM2(NPP+N*M,WRK,1)
ELSE
PNORM = DNRM2(NPP,WRK,1)
END IF
LSTEP = .TRUE.
ELSE
LSTEP = .FALSE.
END IF
C TEST CONVERGENCE
INFO = 0
CNVSS = RNORM.EQ.ZERO
+ .OR.
+ (ABS(ACTRED).LE.SSTOL .AND.
+ PRERED.LE.SSTOL .AND.
+ P5*RATIO.LE.ONE)
CNVPAR = (TAU.LE.PARTOL*PNORM) .AND. (.NOT.IMPLCT)
IF (CNVSS) INFO = 1
IF (CNVPAR) INFO = 2
IF (CNVSS .AND. CNVPAR) INFO = 3
C PRINT ITERATION REPORT
IF (INFO.NE.0 .OR. LSTEP) THEN
IF (IPR2.NE.0 .AND. IPR2F.NE.0 .AND. LUNRPT.NE.0) THEN
IF (IPR2F.EQ.1 .OR. MOD(NITER,IPR2F).EQ.1) THEN
IFLAG = 2
CALL DUNPAC(NP,BETAC,BETA,IFIXB)
WSS(1) = RNORM*RNORM
IF (IPR2.GE.3. AND. LUNRPT.NE.LUDFLT) THEN
NPR = 2
ELSE
NPR = 1
END IF
IF (IPR2.GE.6) THEN
IPR = 2
ELSE
IPR = 2 - MOD(IPR2,2)
END IF
LUNR = LUNRPT
DO 140 I=1,NPR
CALL DODPCR(IPR,LUNR,
+ HEAD,PRTPEN,FSTITR,DIDVCV,IFLAG,
+ N,M,NP,NQ,NPP,NNZW,
+ MSGB,MSGD, BETA,Y,LDY,X,LDX,DELTA,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ SSF,TT,LDTT,STPB,STPD,LDSTPD,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS,RVAR,IDF,WORK(SD),
+ NITER,NFEV,NJEV,ACTRED,PRERED,
+ TAU,PNORM,ALPHA,F,RCOND,IRANK,INFO,ISTOP)
IF (IPR2.GE.5) THEN
IPR = 2
ELSE
IPR = 1
END IF
LUNR = LUDFLT
140 CONTINUE
FSTITR = .FALSE.
PRTPEN = .FALSE.
END IF
END IF
END IF
C CHECK IF FINISHED
IF (INFO.EQ.0) THEN
IF (LSTEP) THEN
C BEGIN NEXT INTERATION UNLESS A STOPPING CRITERIA HAS BEEN MET
IF (NITER.GE.MAXIT) THEN
INFO = 4
ELSE
GO TO 100
END IF
ELSE
C STEP FAILED - RECOMPUTE UNLESS A STOPPING CRITERIA HAS BEEN MET
GO TO 110
END IF
END IF
150 CONTINUE
IF (ISTOP.GT.0) INFO = INFO + 100
C STORE UNWEIGHTED EPSILONS AND X+DELTA TO RETURN TO USER
IF (IMPLCT) THEN
CALL DCOPY(N*NQ,FS,1,F,1)
ELSE
CALL DXMY(N,NQ,FS,N,Y,LDY,F,N)
END IF
CALL DUNPAC(NP,BETAC,BETA,IFIXB)
CALL DXPY(N,M,X,LDX,DELTA,N,XPLUSD,N)
C COMPUTE COVARIANCE MATRIX OF ESTIMATED PARAMETERS
C IN UPPER NP BY NP PORTION OF WORK(VCV) IF REQUESTED
IF (DOVCV .AND. ISTOP.EQ.0) THEN
C RE-EVALUATE JACOBIAN AT FINAL SOLUTION, IF REQUESTED
C OTHERWISE, JACOBIAN FROM BEGINNING OF LAST ITERATION WILL BE USED
C TO COMPUTE COVARIANCE MATRIX
IF (REDOJ) THEN
CALL DEVJAC(FCN,
+ ANAJAC,CDJAC,
+ N,M,NP,NQ,
+ BETAC,BETA,STPB,
+ IFIXB,IFIXX,LDIFX,
+ X,LDX,DELTA,XPLUSD,STPD,LDSTPD,
+ SSF,TT,LDTT,NETA,FS,
+ T,WORK(WRK1),WORK(WRK2),WORK(WRK3),WORK(WRK6),
+ FJACB,ISODR,FJACD,WE1,LDWE,LD2WE,
+ NJEV,NFEV,ISTOP,INFO)
IF (ISTOP.NE.0) THEN
INFO = 51000
GO TO 200
ELSE IF (INFO.EQ.50300) THEN
GO TO 200
END IF
END IF
IF (IMPLCT) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,DELTA,N,WRK(N*NQ+1),N)
RSS = DDOT(N*M,DELTA,1,WRK(N*NQ+1),1)
ELSE
RSS = RNORM*RNORM
END IF
IF (REDOJ .OR. NITER.GE.1) THEN
CALL DODVCV(N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SSF,SS,TT,LDTT,DELTA,
+ ETA,ISODR,
+ WORK(VCV),WORK(SD),
+ WORK(WRK6),WORK(OMEGA),
+ WORK(U),WORK(QRAUX),IWORK(JPVT),
+ S,T,IRANK,RCOND,RSS,IDF,RVAR,IFIXB,
+ WORK(WRK1),WORK(WRK2),WORK(WRK3),WORK(WRK4),
+ WORK(WRK5),WRK,LWRK,ISTOPC)
IF (ISTOPC.NE.0) THEN
INFO = ISTOPC
GO TO 200
END IF
DIDVCV = .TRUE.
END IF
END IF
C SET JPVT TO INDICATE DROPPED, FIXED AND ESTIMATED PARAMETERS
200 DO 210 I=0,NP-1
WORK(WRK3+I) = IWORK(JPVT+I)
IWORK(JPVT+I) = -2
210 CONTINUE
IF (REDOJ .OR. NITER.GE.1) THEN
DO 220 I=0,NPP-1
J = WORK(WRK3+I) - 1
IF (I.LE.NPP-IRANK-1) THEN
IWORK(JPVT+J) = 1
ELSE
IWORK(JPVT+J) = -1
END IF
220 CONTINUE
IF (NPP.LT.NP) THEN
J = NPP-1
DO 230 I=NP-1,0,-1
IF (IFIXB(I+1).EQ.0) THEN
IWORK(JPVT+I) = 0
ELSE
IWORK(JPVT+I) = IWORK(JPVT+J)
J = J - 1
END IF
230 CONTINUE
END IF
END IF
C STORE VARIOUS SCALARS IN WORK ARRAYS FOR RETURN TO USER
IF (NITER.GE.1) THEN
OLMAVG = OLMAVG/NITER
ELSE
OLMAVG = ZERO
END IF
C COMPUTE WEIGHTED SUMS OF SQUARES FOR RETURN TO USER
CALL DWGHT(N,NQ,WE1,LDWE,LD2WE,F,N,WRK,N)
WSS(3) = DDOT(N*NQ,WRK,1,WRK,1)
IF (ISODR) THEN
CALL DWGHT(N,M,WD,LDWD,LD2WD,DELTA,N,WRK(N*NQ+1),N)
WSS(2) = DDOT(N*M,DELTA,1,WRK(N*NQ+1),1)
ELSE
WSS(2) = ZERO
END IF
WSS(1) = WSS(2) + WSS(3)
ACCESS = .FALSE.
CALL DACCES(N,M,NP,NQ,LDWE,LD2WE,
+ WORK,LWORK,IWORK,LIWORK,
+ ACCESS,ISODR,
+ JPVT,OMEGA,U,QRAUX,SD,VCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK6,
+ NNZW,NPP,
+ JOB,PARTOL,SSTOL,MAXIT,TAUFAC,ETA,NETA,
+ LUNRPT,IPR1,IPR2,IPR2F,IPR3,
+ WSS,RVAR,IDF,
+ TAU,ALPHA,NITER,NFEV,NJEV,INT2,OLMAVG,
+ RCOND,IRANK,ACTRS,PNORM,PRERS,RNORMS,ISTOP)
C ENCODE EXISTANCE OF QUESTIONABLE RESULTS INTO INFO
IF (INFO.LE.9 .OR. INFO.GE.60000) THEN
IF (MSGB(1).EQ.1 .OR. MSGD(1).EQ.1) THEN
INFO = INFO + 1000
END IF
IF (ISTOP.NE.0) THEN
INFO = INFO + 100
END IF
IF (IRANK.GE.1) THEN
IF (NPP.GT.IRANK) THEN
INFO = INFO + 10
ELSE
INFO = INFO + 20
END IF
END IF
END IF
C PRINT FINAL SUMMARY
IF (IPR3.NE.0 .AND. LUNRPT.NE.0) THEN
IFLAG = 3
IF (IPR3.GE.3. AND. LUNRPT.NE.LUDFLT) THEN
NPR = 2
ELSE
NPR = 1
END IF
IF (IPR3.GE.6) THEN
IPR = 2
ELSE
IPR = 2 - MOD(IPR3,2)
END IF
LUNR = LUNRPT
DO 240 I=1,NPR
CALL DODPCR(IPR,LUNR,
+ HEAD,PRTPEN,FSTITR,DIDVCV,IFLAG,
+ N,M,NP,NQ,NPP,NNZW,
+ MSGB,MSGD, BETA,Y,LDY,X,LDX,DELTA,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IWORK(JPVT),IFIXX,LDIFX,
+ SSF,TT,LDTT,STPB,STPD,LDSTPD,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS,RVAR,IDF,WORK(SD),
+ NITER,NFEV,NJEV,ACTRED,PRERED,
+ TAU,PNORM,ALPHA,F,RCOND,IRANK,INFO,ISTOP)
IF (IPR3.GE.5) THEN
IPR = 2
ELSE
IPR = 1
END IF
LUNR = LUDFLT
240 CONTINUE
END IF
RETURN
END
*DODPC1
SUBROUTINE DODPC1
+ (IPR,LUNRPT,
+ ANAJAC,CDJAC,CHKJAC,INITD,RESTRT,ISODR,IMPLCT,DOVCV,REDOJ,
+ MSGB1,MSGB,MSGD1,MSGD,
+ N,M,NP,NQ,NPP,NNZW,
+ X,LDX,IFIXX,LDIFX,DELTA,WD,LDWD,LD2WD,TT,LDTT,STPD,LDSTPD,
+ Y,LDY,WE,LDWE,LD2WE,PNLTY,
+ BETA,IFIXB,SSF,STPB,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS,WSSDEL,WSSEPS)
C***BEGIN PROLOGUE DODPC1
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DHSTEP
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE GENERATE INITIAL SUMMARY REPORT
C***END PROLOGUE DODPC1
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PARTOL,PNLTY,SSTOL,TAUFAC,WSS,WSSDEL,WSSEPS
INTEGER
+ IPR,JOB,LDIFX,LDSTPD,LDTT,LDWD,LDWE,LDX,LDY,LD2WD,LD2WE,
+ LUNRPT,M,MAXIT,MSGB1,MSGD1,N,NETA,NNZW,NP,NPP,NQ
LOGICAL
+ ANAJAC,CDJAC,CHKJAC,DOVCV,IMPLCT,INITD,ISODR,REDOJ,RESTRT
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DELTA(N,M),SSF(NP),STPB(NP),STPD(LDSTPD,M),
+ TT(LDTT,M),WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),X(LDX,M),
+ Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSGB(NQ,NP),MSGD(NQ,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEMP1,TEMP2,TEMP3,ZERO
INTEGER
+ I,ITEMP,J,JOB1,JOB2,JOB3,JOB4,JOB5,L
C...LOCAL ARRAYS
CHARACTER TEMPC0*2,TEMPC1*5,TEMPC2*13
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DHSTEP
EXTERNAL
+ DHSTEP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,MIN
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR FORWARD DIFFERENCES
C (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX IS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C I: AN INDEXING VARIABLE.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS INITIALIZED TO
C ZERO (INITD=TRUE) OR TO THE VALUES IN THE FIRST N BY M
C ELEMENTS OF ARRAY WORK (INITD=FALSE).
C IPR: THE VALUE INDICATING THE REPORT TO BE PRINTED.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ITEMP: A TEMPORARY INTEGER VALUE.
C J: AN INDEXING VARIABLE.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C JOB1: THE 1ST DIGIT (FROM THE LEFT) OF VARIABLE JOB.
C JOB2: THE 2ND DIGIT (FROM THE LEFT) OF VARIABLE JOB.
C JOB3: THE 3RD DIGIT (FROM THE LEFT) OF VARIABLE JOB.
C JOB4: THE 4TH DIGIT (FROM THE LEFT) OF VARIABLE JOB.
C JOB5: THE 5TH DIGIT (FROM THE LEFT) OF VARIABLE JOB.
C L: AN INDEXING VARIABLE.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LUNRPT: THE LOGICAL UNIT NUMBER FOR THE COMPUTATION REPORTS.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGB1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C MSGD1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C A NEGATIVE VALUE INDICATES THAT NETA WAS ESTIMATED BY
C ODRPACK. A POSITIVE VALUE INDICTES THE VALUE WAS SUPPLIED
C BY THE USER.
C NNZW: THE NUMBER OF NONZERO OBSERVATIONAL ERROR WEIGHTS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PNLTY: THE PENALTY PARAMETER FOR AN IMPLICIT MODEL.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C SSF: THE SCALING VALUES FOR BETA.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C STPB: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP USED FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TEMPC0: A TEMPORARY CHARACTER*2 VALUE.
C TEMPC1: A TEMPORARY CHARACTER*5 VALUE.
C TEMPC2: A TEMPORARY CHARACTER*13 VALUE.
C TEMP1: A TEMPORARY DOUBLE PRECISION VALUE.
C TEMP2: A TEMPORARY DOUBLE PRECISION VALUE.
C TEMP3: A TEMPORARY DOUBLE PRECISION VALUE.
C TT: THE SCALING VALUES FOR DELTA.
C WD: THE DELTA WEIGHTS.
C WE: THE EPSILON WEIGHTS.
C WSS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS AND DELTAS.
C WSSDEL: THE SUM-OF-SQUARES OF THE WEIGHTED DELTAS.
C WSSEPS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS.
C X: THE EXPLANATORY VARIABLE.
C Y: THE RESPONSE VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODPC1
C PRINT PROBLEM SIZE SPECIFICATION
WRITE (LUNRPT,1000) N,NNZW,NQ,M,NP,NPP
C PRINT CONTROL VALUES
JOB1 = JOB/10000
JOB2 = MOD(JOB,10000)/1000
JOB3 = MOD(JOB,1000)/100
JOB4 = MOD(JOB,100)/10
JOB5 = MOD(JOB,10)
WRITE (LUNRPT,1100) JOB
IF (RESTRT) THEN
WRITE (LUNRPT,1110) JOB1
ELSE
WRITE (LUNRPT,1111) JOB1
END IF
IF (ISODR) THEN
IF (INITD) THEN
WRITE (LUNRPT,1120) JOB2
ELSE
WRITE (LUNRPT,1121) JOB2
END IF
ELSE
WRITE (LUNRPT,1122) JOB2,JOB5
END IF
IF (DOVCV) THEN
WRITE (LUNRPT,1130) JOB3
IF (REDOJ) THEN
WRITE (LUNRPT,1131)
ELSE
WRITE (LUNRPT,1132)
END IF
ELSE
WRITE (LUNRPT,1133) JOB3
END IF
IF (ANAJAC) THEN
WRITE (LUNRPT,1140) JOB4
IF (CHKJAC) THEN
IF (MSGB1.GE.1 .OR. MSGD1.GE.1) THEN
WRITE (LUNRPT,1141)
ELSE
WRITE (LUNRPT,1142)
END IF
ELSE
WRITE (LUNRPT,1143)
END IF
ELSE IF (CDJAC) THEN
WRITE (LUNRPT,1144) JOB4
ELSE
WRITE (LUNRPT,1145) JOB4
END IF
IF (ISODR) THEN
IF (IMPLCT) THEN
WRITE (LUNRPT,1150) JOB5
ELSE
WRITE (LUNRPT,1151) JOB5
END IF
ELSE
WRITE (LUNRPT,1152) JOB5
END IF
IF (NETA.LT.0) THEN
WRITE (LUNRPT,1200) -NETA
ELSE
WRITE (LUNRPT,1210) NETA
END IF
WRITE (LUNRPT,1300) TAUFAC
C PRINT STOPPING CRITERIA
WRITE (LUNRPT,1400) SSTOL,PARTOL,MAXIT
C PRINT INITIAL SUM OF SQUARES
IF (IMPLCT) THEN
WRITE (LUNRPT,1500) WSSDEL
IF (ISODR) THEN
WRITE (LUNRPT,1510) WSS,WSSEPS,PNLTY
END IF
ELSE
WRITE (LUNRPT,1600) WSS
IF (ISODR) THEN
WRITE (LUNRPT,1610) WSSDEL,WSSEPS
END IF
END IF
IF (IPR.GE.2) THEN
C PRINT FUNCTION PARAMETER DATA
WRITE (LUNRPT,4000)
IF (CHKJAC .AND. ((MSGB1.GE.1) .OR. (MSGD1.GE.1))) THEN
WRITE (LUNRPT,4110)
ELSE IF (ANAJAC) THEN
WRITE (LUNRPT,4120)
ELSE
WRITE (LUNRPT,4200)
END IF
DO 130 J=1,NP
IF (IFIXB(1).LT.0) THEN
TEMPC1 = ' NO'
ELSE
IF (IFIXB(J).NE.0) THEN
TEMPC1 = ' NO'
ELSE
TEMPC1 = ' YES'
END IF
END IF
IF (ANAJAC) THEN
IF (CHKJAC .AND. ((MSGB1.GE.1) .OR. (MSGD1.GE.1))) THEN
ITEMP = -1
DO 110 L=1,NQ
ITEMP = MAX(ITEMP,MSGB(L,J))
110 CONTINUE
IF (ITEMP.LE.-1) THEN
TEMPC2 = ' UNCHECKED'
ELSE IF (ITEMP.EQ.0) THEN
TEMPC2 = ' VERIFIED'
ELSE IF (ITEMP.GE.1) THEN
TEMPC2 = ' QUESTIONABLE'
END IF
ELSE
TEMPC2 = ' '
END IF
ELSE
TEMPC2 = ' '
END IF
IF (SSF(1).LT.ZERO) THEN
TEMP1 = ABS(SSF(1))
ELSE
TEMP1 = SSF(J)
END IF
IF (ANAJAC) THEN
WRITE (LUNRPT,4310) J,BETA(J),TEMPC1,TEMP1,TEMPC2
ELSE
IF (CDJAC) THEN
TEMP2 = DHSTEP(1,NETA,1,J,STPB,1)
ELSE
TEMP2 = DHSTEP(0,NETA,1,J,STPB,1)
END IF
WRITE (LUNRPT,4320) J,BETA(J),TEMPC1,TEMP1,TEMP2
END IF
130 CONTINUE
C PRINT EXPLANATORY VARIABLE DATA
IF (ISODR) THEN
WRITE (LUNRPT,2010)
IF (CHKJAC .AND. ((MSGB1.GE.1) .OR. (MSGD1.GE.1))) THEN
WRITE (LUNRPT,2110)
ELSE IF (ANAJAC) THEN
WRITE (LUNRPT,2120)
ELSE
WRITE (LUNRPT,2130)
END IF
ELSE
WRITE (LUNRPT,2020)
WRITE (LUNRPT,2140)
END IF
IF (ISODR) THEN
DO 240 J = 1,M
TEMPC0 = '1,'
DO 230 I=1,N,N-1
IF (IFIXX(1,1).LT.0) THEN
TEMPC1 = ' NO'
ELSE
IF (LDIFX.EQ.1) THEN
IF (IFIXX(1,J).EQ.0) THEN
TEMPC1 = ' YES'
ELSE
TEMPC1 = ' NO'
END IF
ELSE
IF (IFIXX(I,J).EQ.0) THEN
TEMPC1 = ' YES'
ELSE
TEMPC1 = ' NO'
END IF
END IF
END IF
IF (TT(1,1).LT.ZERO) THEN
TEMP1 = ABS(TT(1,1))
ELSE
IF (LDTT.EQ.1) THEN
TEMP1 = TT(1,J)
ELSE
TEMP1 = TT(I,J)
END IF
END IF
IF (WD(1,1,1).LT.ZERO) THEN
TEMP2 = ABS(WD(1,1,1))
ELSE
IF (LDWD.EQ.1) THEN
IF (LD2WD.EQ.1) THEN
TEMP2 = WD(1,1,J)
ELSE
TEMP2 = WD(1,J,J)
END IF
ELSE
IF (LD2WD.EQ.1) THEN
TEMP2 = WD(I,1,J)
ELSE
TEMP2 = WD(I,J,J)
END IF
END IF
END IF
IF (ANAJAC) THEN
IF (CHKJAC .AND.
+ (((MSGB1.GE.1) .OR. (MSGD1.GE.1)) .AND.
+ (I.EQ.1))) THEN
ITEMP = -1
DO 210 L=1,NQ
ITEMP = MAX(ITEMP,MSGD(L,J))
210 CONTINUE
IF (ITEMP.LE.-1) THEN
TEMPC2 = ' UNCHECKED'
ELSE IF (ITEMP.EQ.0) THEN
TEMPC2 = ' VERIFIED'
ELSE IF (ITEMP.GE.1) THEN
TEMPC2 = ' QUESTIONABLE'
END IF
ELSE
TEMPC2 = ' '
END IF
IF (M.LE.9) THEN
WRITE (LUNRPT,5110)
+ TEMPC0,J,X(I,J),
+ DELTA(I,J),TEMPC1,TEMP1,TEMP2,TEMPC2
ELSE
WRITE (LUNRPT,5120)
+ TEMPC0,J,X(I,J),
+ DELTA(I,J),TEMPC1,TEMP1,TEMP2,TEMPC2
END IF
ELSE
TEMPC2 = ' '
IF (CDJAC) THEN
TEMP3 = DHSTEP(1,NETA,I,J,STPD,LDSTPD)
ELSE
TEMP3 = DHSTEP(0,NETA,I,J,STPD,LDSTPD)
END IF
IF (M.LE.9) THEN
WRITE (LUNRPT,5210)
+ TEMPC0,J,X(I,J),
+ DELTA(I,J),TEMPC1,TEMP1,TEMP2,TEMP3
ELSE
WRITE (LUNRPT,5220)
+ TEMPC0,J,X(I,J),
+ DELTA(I,J),TEMPC1,TEMP1,TEMP2,TEMP3
END IF
END IF
TEMPC0 = 'N,'
230 CONTINUE
IF (J.LT.M) WRITE (LUNRPT,6000)
240 CONTINUE
ELSE
DO 260 J = 1,M
TEMPC0 = '1,'
DO 250 I=1,N,N-1
IF (M.LE.9) THEN
WRITE (LUNRPT,5110)
+ TEMPC0,J,X(I,J)
ELSE
WRITE (LUNRPT,5120)
+ TEMPC0,J,X(I,J)
END IF
TEMPC0 = 'N,'
250 CONTINUE
IF (J.LT.M) WRITE (LUNRPT,6000)
260 CONTINUE
END IF
C PRINT RESPONSE VARIABLE DATA AND OBSERVATION ERROR WEIGHTS
IF (.NOT.IMPLCT) THEN
WRITE (LUNRPT,3000)
WRITE (LUNRPT,3100)
DO 310 L=1,NQ
TEMPC0 = '1,'
DO 300 I=1,N,N-1
IF (WE(1,1,1).LT.ZERO) THEN
TEMP1 = ABS(WE(1,1,1))
ELSE IF (LDWE.EQ.1) THEN
IF (LD2WE.EQ.1) THEN
TEMP1 = WE(1,1,L)
ELSE
TEMP1 = WE(1,L,L)
END IF
ELSE
IF (LD2WE.EQ.1) THEN
TEMP1 = WE(I,1,L)
ELSE
TEMP1 = WE(I,L,L)
END IF
END IF
IF (NQ.LE.9) THEN
WRITE (LUNRPT,5110)
+ TEMPC0,L,Y(I,L),TEMP1
ELSE
WRITE (LUNRPT,5120)
+ TEMPC0,L,Y(I,L),TEMP1
END IF
TEMPC0 = 'N,'
300 CONTINUE
IF (L.LT.NQ) WRITE (LUNRPT,6000)
310 CONTINUE
END IF
END IF
RETURN
C FORMAT STATEMENTS
1000 FORMAT
+ (/' --- PROBLEM SIZE:'/
+ ' N = ',I5,
+ ' (NUMBER WITH NONZERO WEIGHT = ',I5,')'/
+ ' NQ = ',I5/
+ ' M = ',I5/
+ ' NP = ',I5,
+ ' (NUMBER UNFIXED = ',I5,')')
1100 FORMAT
+ (/' --- CONTROL VALUES:'/
+ ' JOB = ',I5.5/
+ ' = ABCDE, WHERE')
1110 FORMAT
+ (' A=',I1,' ==> FIT IS A RESTART.')
1111 FORMAT
+ (' A=',I1,' ==> FIT IS NOT A RESTART.')
1120 FORMAT
+ (' B=',I1,' ==> DELTAS ARE INITIALIZED',
+ ' TO ZERO.')
1121 FORMAT
+ (' B=',I1,' ==> DELTAS ARE INITIALIZED',
+ ' BY USER.')
1122 FORMAT
+ (' B=',I1,' ==> DELTAS ARE FIXED AT',
+ ' ZERO SINCE E=',I1,'.')
1130 FORMAT
+ (' C=',I1,' ==> COVARIANCE MATRIX WILL',
+ ' BE COMPUTED USING')
1131 FORMAT
+ (' DERIVATIVES RE-',
+ 'EVALUATED AT THE SOLUTION.')
1132 FORMAT
+ (' DERIVATIVES FROM THE',
+ ' LAST ITERATION.')
1133 FORMAT
+ (' C=',I1,' ==> COVARIANCE MATRIX WILL',
+ ' NOT BE COMPUTED.')
1140 FORMAT
+ (' D=',I1,' ==> DERIVATIVES ARE',
+ ' SUPPLIED BY USER.')
1141 FORMAT
+ (' DERIVATIVES WERE CHECKED.'/
+ ' RESULTS APPEAR QUESTIONABLE.')
1142 FORMAT
+ (' DERIVATIVES WERE CHECKED.'/
+ ' RESULTS APPEAR CORRECT.')
1143 FORMAT
+ (' DERIVATIVES WERE NOT',
+ ' CHECKED.')
1144 FORMAT
+ (' D=',I1,' ==> DERIVATIVES ARE',
+ ' ESTIMATED BY CENTRAL',
+ ' DIFFERENCES.')
1145 FORMAT
+ (' D=',I1,' ==> DERIVATIVES ARE',
+ ' ESTIMATED BY FORWARD',
+ ' DIFFERENCES.')
1150 FORMAT
+ (' E=',I1,' ==> METHOD IS IMPLICIT ODR.')
1151 FORMAT
+ (' E=',I1,' ==> METHOD IS EXPLICIT ODR.')
1152 FORMAT
+ (' E=',I1,' ==> METHOD IS EXPLICIT OLS.')
1200 FORMAT
+ (' NDIGIT = ',I5,' (ESTIMATED BY ODRPACK)')
1210 FORMAT
+ (' NDIGIT = ',I5,' (SUPPLIED BY USER)')
1300 FORMAT
+ (' TAUFAC = ',1P,D12.2)
1400 FORMAT
+ (/' --- STOPPING CRITERIA:'/
+ ' SSTOL = ',1P,D12.2,
+ ' (SUM OF SQUARES STOPPING TOLERANCE)'/
+ ' PARTOL = ',1P,D12.2,
+ ' (PARAMETER STOPPING TOLERANCE)'/
+ ' MAXIT = ',I5,
+ ' (MAXIMUM NUMBER OF ITERATIONS)')
1500 FORMAT
+ (/' --- INITIAL SUM OF SQUARED WEIGHTED DELTAS =',
+ 17X,1P,D17.8)
1510 FORMAT
+ ( ' INITIAL PENALTY FUNCTION VALUE =',1P,D17.8/
+ ' PENALTY TERM =',1P,D17.8/
+ ' PENALTY PARAMETER =',1P,D10.1)
1600 FORMAT
+ (/' --- INITIAL WEIGHTED SUM OF SQUARES =',
+ 17X,1P,D17.8)
1610 FORMAT
+ ( ' SUM OF SQUARED WEIGHTED DELTAS =',1P,D17.8/
+ ' SUM OF SQUARED WEIGHTED EPSILONS =',1P,D17.8)
2010 FORMAT
+ (/' --- EXPLANATORY VARIABLE AND DELTA WEIGHT SUMMARY:')
2020 FORMAT
+ (/' --- EXPLANATORY VARIABLE SUMMARY:')
2110 FORMAT
+ (/' INDEX X(I,J) DELTA(I,J) FIXED',
+ ' SCALE WEIGHT DERIVATIVE'/
+ ' ',
+ ' ASSESSMENT'/,
+ ' (I,J) (IFIXX)',
+ ' (SCLD) (WD) '/)
2120 FORMAT
+ (/' INDEX X(I,J) DELTA(I,J) FIXED',
+ ' SCALE WEIGHT '/
+ ' ',
+ ' '/,
+ ' (I,J) (IFIXX)',
+ ' (SCLD) (WD) '/)
2130 FORMAT
+ (/' INDEX X(I,J) DELTA(I,J) FIXED',
+ ' SCALE WEIGHT DERIVATIVE'/
+ ' ',
+ ' STEP SIZE'/,
+ ' (I,J) (IFIXX)',
+ ' (SCLD) (WD) (STPD)'/)
2140 FORMAT
+ (/' INDEX X(I,J)'/
+ ' (I,J) '/)
3000 FORMAT
+ (/' --- RESPONSE VARIABLE AND EPSILON ERROR WEIGHT',
+ ' SUMMARY:')
3100 FORMAT
+ (/' INDEX Y(I,L) WEIGHT'/
+ ' (I,L) (WE)'/)
4000 FORMAT
+ (/' --- FUNCTION PARAMETER SUMMARY:')
4110 FORMAT
+ (/' INDEX BETA(K) FIXED SCALE',
+ ' DERIVATIVE'/
+ ' ',
+ ' ASSESSMENT'/,
+ ' (K) (IFIXB) (SCLB)',
+ ' '/)
4120 FORMAT
+ (/' INDEX BETA(K) FIXED SCALE',
+ ' '/
+ ' ',
+ ' '/,
+ ' (K) (IFIXB) (SCLB)',
+ ' '/)
4200 FORMAT
+ (/' INDEX BETA(K) FIXED SCALE',
+ ' DERIVATIVE'/
+ ' ',
+ ' STEP SIZE'/,
+ ' (K) (IFIXB) (SCLB)',
+ ' (STPB)'/)
4310 FORMAT
+ (7X,I5,1P,D16.8,4X,A5,D16.8,1X,A13)
4320 FORMAT
+ (7X,I5,1P,D16.8,4X,A5,D16.8,1X,D13.5)
5110 FORMAT
+ (9X,A2,I1,1P,2D12.3,4X,A5,2D10.2,1X,A13)
5120 FORMAT
+ (8X,A2,I2,1P,2D12.3,4X,A5,2D10.2,1X,A13)
5210 FORMAT
+ (9X,A2,I1,1P,2D12.3,4X,A5,2D10.2,1X,D13.5)
5220 FORMAT
+ (8X,A2,I2,1P,2D12.3,4X,A5,2D10.2,1X,D13.5)
6000 FORMAT
+ (' ')
END
*DODPC2
SUBROUTINE DODPC2
+ (IPR,LUNRPT, FSTITR,IMPLCT,PRTPEN,
+ PNLTY,
+ NITER,NFEV,WSS,ACTRED,PRERED,ALPHA,TAU,PNORM,NP,BETA)
C***BEGIN PROLOGUE DODPC2
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE GENERATE ITERATION REPORTS
C***END PROLOGUE DODPC2
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ACTRED,ALPHA,PNLTY,PNORM,PRERED,TAU,WSS
INTEGER
+ IPR,LUNRPT,NFEV,NITER,NP
LOGICAL
+ FSTITR,IMPLCT,PRTPEN
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ RATIO,ZERO
INTEGER
+ J,K,L
CHARACTER GN*3
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MIN
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACTRED: THE ACTUAL RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C BETA: THE FUNCTION PARAMETERS.
C FSTITR: THE VARIABLE DESIGNATING WHETHER THIS IS THE FIRST
C ITERATION (FSTITR=.TRUE.) OR NOT (FSTITR=.FALSE.).
C GN: THE CHARACTER*3 VARIABLE INDICATING WHETHER A GAUSS-NEWTON
C STEP WAS TAKEN.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C IPR: THE VALUE INDICATING THE REPORT TO BE PRINTED.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NITER: THE NUMBER OF ITERATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C PNLTY: THE PENALTY PARAMETER FOR AN IMPLICIT MODEL.
C PNORM: THE NORM OF THE SCALED ESTIMATED PARAMETERS.
C PRERED: THE PREDICTED RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C PRTPEN: THE VARIABLE DESIGNATING WHETHER THE PENALTY PARAMETER IS
C TO BE PRINTED IN THE ITERATION REPORT (PRTPEN=TRUE) OR NOT
C (PRTPEN=FALSE).
C RATIO: THE RATIO OF TAU TO PNORM.
C TAU: THE TRUST REGION DIAMETER.
C WSS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS AND DELTAS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODPC2
IF (FSTITR) THEN
IF (IPR.EQ.1) THEN
IF (IMPLCT) THEN
WRITE (LUNRPT,1121)
ELSE
WRITE (LUNRPT,1122)
END IF
ELSE
IF (IMPLCT) THEN
WRITE (LUNRPT,1131)
ELSE
WRITE (LUNRPT,1132)
END IF
END IF
END IF
IF (PRTPEN) THEN
WRITE (LUNRPT,1133) PNLTY
END IF
IF (ALPHA.EQ.ZERO) THEN
GN = 'YES'
ELSE
GN = ' NO'
END IF
IF (PNORM.NE.ZERO) THEN
RATIO = TAU/PNORM
ELSE
RATIO = ZERO
END IF
IF (IPR.EQ.1) THEN
WRITE (LUNRPT,1141) NITER,NFEV,WSS,ACTRED,PRERED,
+ RATIO,GN
ELSE
J = 1
K = MIN(3,NP)
IF (J.EQ.K) THEN
WRITE (LUNRPT,1141) NITER,NFEV,WSS,ACTRED,PRERED,
+ RATIO,GN,J,BETA(J)
ELSE
WRITE (LUNRPT,1142) NITER,NFEV,WSS,ACTRED,PRERED,
+ RATIO,GN,J,K,(BETA(L),L=J,K)
END IF
IF (NP.GT.3) THEN
DO 10 J=4,NP,3
K = MIN(J+2,NP)
IF (J.EQ.K) THEN
WRITE (LUNRPT,1151) J,BETA(J)
ELSE
WRITE (LUNRPT,1152) J,K,(BETA(L),L=J,K)
END IF
10 CONTINUE
END IF
END IF
RETURN
C FORMAT STATEMENTS
1121 FORMAT
+ (//
+ ' CUM. PENALTY ACT. REL. PRED. REL.'/
+ ' IT. NO. FN FUNCTION SUM-OF-SQS SUM-OF-SQS',
+ ' G-N'/
+ ' NUM. EVALS VALUE REDUCTION REDUCTION',
+ ' TAU/PNORM STEP'/
+ ' ---- ------ ----------- ----------- -----------',
+ ' --------- ----')
1122 FORMAT
+ (//
+ ' CUM. ACT. REL. PRED. REL.'/
+ ' IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS',
+ ' G-N'/
+ ' NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION',
+ ' TAU/PNORM STEP'/
+ ' ---- ------ ----------- ----------- -----------',
+ ' --------- ----'/)
1131 FORMAT
+ (//
+ ' CUM. PENALTY ACT. REL. PRED. REL.'/
+ ' IT. NO. FN FUNCTION SUM-OF-SQS SUM-OF-SQS',
+ ' G-N BETA -------------->'/
+ ' NUM. EVALS VALUE REDUCTION REDUCTION',
+ ' TAU/PNORM STEP INDEX VALUE'/
+ ' ---- ------ ----------- ----------- -----------',
+ ' --------- ---- ----- -----')
1132 FORMAT
+ (//
+ ' CUM. ACT. REL. PRED. REL.'/
+ ' IT. NO. FN WEIGHTED SUM-OF-SQS SUM-OF-SQS',
+ ' G-N BETA -------------->'/
+ ' NUM. EVALS SUM-OF-SQS REDUCTION REDUCTION',
+ ' TAU/PNORM STEP INDEX VALUE'/
+ ' ---- ------ ----------- ----------- -----------',
+ ' --------- ---- ----- -----'/)
1133 FORMAT
+ (/' PENALTY PARAMETER VALUE = ', 1P,E10.1)
1141 FORMAT
+ (1X,I4,I8,1X,1P,D12.5,2D13.4,D11.3,3X,A3,7X,I3,3D16.8)
1142 FORMAT
+ (1X,I4,I8,1X,1P,D12.5,2D13.4,D11.3,3X,A3,1X,I3,' TO',I3,3D16.8)
1151 FORMAT
+ (76X,I3,1P,D16.8)
1152 FORMAT
+ (70X,I3,' TO',I3,1P,3D16.8)
END
*DODPC3
SUBROUTINE DODPC3
+ (IPR,LUNRPT,
+ ISODR,IMPLCT,DIDVCV,DOVCV,REDOJ,ANAJAC,
+ N,M,NP,NQ,NPP,
+ INFO,NITER,NFEV,NJEV,IRANK,RCOND,ISTOP,
+ WSS,WSSDEL,WSSEPS,PNLTY,RVAR,IDF,
+ BETA,SDBETA,IFIXB2,F,DELTA)
C***BEGIN PROLOGUE DODPC3
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DPPT
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE GENERATE FINAL SUMMARY REPORT
C***END PROLOGUE DODPC3
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PNLTY,RCOND,RVAR,WSS,WSSDEL,WSSEPS
INTEGER
+ IDF,INFO,IPR,IRANK,ISTOP,LUNRPT,M,
+ N,NFEV,NITER,NJEV,NP,NPP,NQ
LOGICAL
+ ANAJAC,DIDVCV,DOVCV,IMPLCT,ISODR,REDOJ
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DELTA(N,M),F(N,NQ),SDBETA(NP)
INTEGER
+ IFIXB2(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TVAL
INTEGER
+ D1,D2,D3,D4,D5,I,J,K,L,NPLM1
CHARACTER FMT1*90
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DPPT
EXTERNAL
+ DPPT
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MIN,MOD
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C D1: THE FIRST DIGIT OF INFO.
C D2: THE SECOND DIGIT OF INFO.
C D3: THE THIRD DIGIT OF INFO.
C D4: THE FOURTH DIGIT OF INFO.
C D5: THE FIFTH DIGIT OF INFO.
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DIDVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX WAS
C COMPUTED (DIDVCV=TRUE) OR NOT (DIDVCV=FALSE).
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX WAS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C F: THE ESTIMATED VALUES OF EPSILON.
C FMT1: A CHARACTER*90 VARIABLE USED FOR FORMATS.
C I: AN INDEXING VARIABLE.
C IDF: THE DEGREES OF FREEDOM OF THE FIT, EQUAL TO THE NUMBER OF
C OBSERVATIONS WITH NONZERO WEIGHTED DERIVATIVES MINUS THE
C NUMBER OF PARAMETERS BEING ESTIMATED.
C IFIXB2: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA WERE
C ESTIMATED, FIXED, OR DROPPED BECAUSE THEY CAUSED RANK
C DEFICIENCY, CORRESPONDING TO VALUES OF IFIXB2 EQUALING 1,
C 0, AND -1, RESPECTIVELY. IF IFIXB2 IS -2, THEN NO ATTEMPT
C WAS MADE TO ESTIMATE THE PARAMETERS BECAUSE MAXIT = 0.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C IPR: THE VARIABLE INDICATING WHAT IS TO BE PRINTED.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C L: AN INDEXING VARIABLE.
C LUNRPT: THE LOGICAL UNIT NUMBER USED FOR COMPUTATION REPORTS.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NITER: THE NUMBER OF ITERATIONS.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPLM1: THE NUMBER OF ITEMS TO BE PRINTED PER LINE, MINUS ONE.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C PNLTY: THE PENALTY PARAMETER FOR AN IMPLICIT MODEL.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION OF TFJACB.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS
C TO BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE
C MATRIX (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RVAR: THE RESIDUAL VARIANCE.
C SDBETA: THE STANDARD ERRORS OF THE ESTIMATED PARAMETERS.
C TVAL: THE VALUE OF THE 97.5 PERCENT POINT FUNCTION FOR THE
C T DISTRIBUTION.
C WSS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS AND DELTAS.
C WSSDEL: THE SUM-OF-SQUARES OF THE WEIGHTED DELTAS.
C WSSEPS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS.
C***FIRST EXECUTABLE STATEMENT DODPC3
D1 = INFO/10000
D2 = MOD(INFO,10000)/1000
D3 = MOD(INFO,1000)/100
D4 = MOD(INFO,100)/10
D5 = MOD(INFO,10)
C PRINT STOPPING CONDITIONS
WRITE (LUNRPT,1000)
IF (INFO.LE.9) THEN
IF (INFO.EQ.1) THEN
WRITE (LUNRPT,1011) INFO
ELSE IF (INFO.EQ.2) THEN
WRITE (LUNRPT,1012) INFO
ELSE IF (INFO.EQ.3) THEN
WRITE (LUNRPT,1013) INFO
ELSE IF (INFO.EQ.4) THEN
WRITE (LUNRPT,1014) INFO
ELSE IF (INFO.LE.9) THEN
WRITE (LUNRPT,1015) INFO
END IF
ELSE IF (INFO.LE.9999) THEN
C PRINT WARNING DIAGNOSTICS
WRITE (LUNRPT,1020) INFO
IF (D2.EQ.1) WRITE (LUNRPT,1021)
IF (D3.EQ.1) WRITE (LUNRPT,1022)
IF (D4.EQ.1) WRITE (LUNRPT,1023)
IF (D4.EQ.2) WRITE (LUNRPT,1024)
IF (D5.EQ.1) THEN
WRITE (LUNRPT,1031)
ELSE IF (D5.EQ.2) THEN
WRITE (LUNRPT,1032)
ELSE IF (D5.EQ.3) THEN
WRITE (LUNRPT,1033)
ELSE IF (D5.EQ.4) THEN
WRITE (LUNRPT,1034)
ELSE IF (D5.LE.9) THEN
WRITE (LUNRPT,1035) D5
END IF
ELSE
C PRINT ERROR MESSAGES
WRITE (LUNRPT,1040) INFO
IF (D1.EQ.5) THEN
WRITE (LUNRPT,1042)
IF (D2.NE.0) WRITE (LUNRPT,1043) D2
IF (D3.EQ.3) THEN
WRITE (LUNRPT,1044) D3
ELSE IF (D3.NE.0) THEN
WRITE (LUNRPT,1045) D3
END IF
ELSE IF (D1.EQ.6) THEN
WRITE (LUNRPT,1050)
ELSE
WRITE (LUNRPT,1060) D1
END IF
END IF
C PRINT MISC. STOPPING INFO
WRITE (LUNRPT,1300) NITER
WRITE (LUNRPT,1310) NFEV
IF (ANAJAC) WRITE (LUNRPT,1320) NJEV
WRITE (LUNRPT,1330) IRANK
WRITE (LUNRPT,1340) RCOND
WRITE (LUNRPT,1350) ISTOP
C PRINT FINAL SUM OF SQUARES
IF (IMPLCT) THEN
WRITE (LUNRPT,2000) WSSDEL
IF (ISODR) THEN
WRITE (LUNRPT,2010) WSS,WSSEPS,PNLTY
END IF
ELSE
WRITE (LUNRPT,2100) WSS
IF (ISODR) THEN
WRITE (LUNRPT,2110) WSSDEL,WSSEPS
END IF
END IF
IF (DIDVCV) THEN
WRITE (LUNRPT,2200) SQRT(RVAR),IDF
END IF
NPLM1 = 3
C PRINT ESTIMATED BETA'S, AND,
C IF, FULL RANK, THEIR STANDARD ERRORS
WRITE (LUNRPT,3000)
IF (DIDVCV) THEN
WRITE (LUNRPT,7300)
TVAL = DPPT(0.975D0,IDF)
DO 10 J=1,NP
IF (IFIXB2(J).GE.1) THEN
WRITE (LUNRPT,8400) J,BETA(J),SDBETA(J),
+ BETA(J)-TVAL*SDBETA(J),
+ BETA(J)+TVAL*SDBETA(J)
ELSE IF (IFIXB2(J).EQ.0) THEN
WRITE (LUNRPT,8600) J,BETA(J)
ELSE
WRITE (LUNRPT,8700) J,BETA(J)
END IF
10 CONTINUE
IF (.NOT.REDOJ) WRITE (LUNRPT,7310)
ELSE
IF (DOVCV) THEN
IF (D1.LE.5) THEN
WRITE (LUNRPT,7410)
ELSE
WRITE (LUNRPT,7420)
END IF
END IF
IF ((IRANK.EQ.0 .AND. NPP.EQ.NP) .OR. NITER.EQ.0) THEN
IF (NP.EQ.1) THEN
WRITE (LUNRPT,7100)
ELSE
WRITE (LUNRPT,7200)
END IF
DO 20 J=1,NP,NPLM1+1
K = MIN(J+NPLM1,NP)
IF (K.EQ.J) THEN
WRITE (LUNRPT,8100) J,BETA(J)
ELSE
WRITE (LUNRPT,8200) J,K,(BETA(L),L=J,K)
END IF
20 CONTINUE
IF (NITER.GE.1) THEN
WRITE (LUNRPT,8800)
ELSE
WRITE (LUNRPT,8900)
END IF
ELSE
WRITE (LUNRPT,7500)
DO 30 J=1,NP
IF (IFIXB2(J).GE.1) THEN
WRITE (LUNRPT,8500) J,BETA(J)
ELSE IF (IFIXB2(J).EQ.0) THEN
WRITE (LUNRPT,8600) J,BETA(J)
ELSE
WRITE (LUNRPT,8700) J,BETA(J)
END IF
30 CONTINUE
END IF
END IF
IF (IPR.EQ.1) RETURN
C PRINT EPSILON'S AND DELTA'S TOGETHER IN A COLUMN IF THE NUMBER OF
C COLUMNS OF DATA IN EPSILON AND DELTA IS LESS THAN OR EQUAL TO THREE.
IF (IMPLCT .AND. (M.LE.4)) THEN
WRITE (LUNRPT,4100)
WRITE (FMT1,9110) M
WRITE (LUNRPT,FMT1) (J,J=1,M)
DO 40 I=1,N
WRITE (LUNRPT,4130) I,(DELTA(I,J),J=1,M)
40 CONTINUE
ELSE IF (ISODR .AND. (NQ+M.LE.4)) THEN
WRITE (LUNRPT,4110)
WRITE (FMT1,9120) NQ,M
WRITE (LUNRPT,FMT1) (L,L=1,NQ),(J,J=1,M)
DO 50 I=1,N
WRITE (LUNRPT,4130) I,(F(I,L),L=1,NQ),(DELTA(I,J),J=1,M)
50 CONTINUE
ELSE IF (.NOT.ISODR .AND. ((NQ.GE.2) .AND. (NQ.LE.4))) THEN
WRITE (LUNRPT,4120)
WRITE (FMT1,9130) NQ
WRITE (LUNRPT,FMT1) (L,L=1,NQ)
DO 60 I=1,N
WRITE (LUNRPT,4130) I,(F(I,L),L=1,NQ)
60 CONTINUE
ELSE
C PRINT EPSILON'S AND DELTA'S SEPARATELY
IF (.NOT.IMPLCT) THEN
C PRINT EPSILON'S
DO 80 J=1,NQ
WRITE (LUNRPT,4200) J
IF (N.EQ.1) THEN
WRITE (LUNRPT,7100)
ELSE
WRITE (LUNRPT,7200)
END IF
DO 70 I=1,N,NPLM1+1
K = MIN(I+NPLM1,N)
IF (I.EQ.K) THEN
WRITE (LUNRPT,8100) I,F(I,J)
ELSE
WRITE (LUNRPT,8200) I,K,(F(L,J),L=I,K)
END IF
70 CONTINUE
80 CONTINUE
END IF
C PRINT DELTA'S
IF (ISODR) THEN
DO 100 J=1,M
WRITE (LUNRPT,4300) J
IF (N.EQ.1) THEN
WRITE (LUNRPT,7100)
ELSE
WRITE (LUNRPT,7200)
END IF
DO 90 I=1,N,NPLM1+1
K = MIN(I+NPLM1,N)
IF (I.EQ.K) THEN
WRITE (LUNRPT,8100) I,DELTA(I,J)
ELSE
WRITE (LUNRPT,8200) I,K,(DELTA(L,J),L=I,K)
END IF
90 CONTINUE
100 CONTINUE
END IF
END IF
RETURN
C FORMAT STATEMENTS
1000 FORMAT
+ (/' --- STOPPING CONDITIONS:')
1011 FORMAT
+ (' INFO = ',I5,' ==> SUM OF SQUARES CONVERGENCE.')
1012 FORMAT
+ (' INFO = ',I5,' ==> PARAMETER CONVERGENCE.')
1013 FORMAT
+ (' INFO = ',I5,' ==> SUM OF SQUARES CONVERGENCE AND',
+ ' PARAMETER CONVERGENCE.')
1014 FORMAT
+ (' INFO = ',I5,' ==> ITERATION LIMIT REACHED.')
1015 FORMAT
+ (' INFO = ',I5,' ==> UNEXPECTED VALUE,',
+ ' PROBABLY INDICATING'/
+ ' INCORRECTLY SPECIFIED',
+ ' USER INPUT.')
1020 FORMAT
+ (' INFO = ',I5.4/
+ ' = ABCD, WHERE A NONZERO VALUE FOR DIGIT A,',
+ ' B, OR C INDICATES WHY'/
+ ' THE RESULTS MIGHT BE QUESTIONABLE,',
+ ' AND DIGIT D INDICATES'/
+ ' THE ACTUAL STOPPING CONDITION.')
1021 FORMAT
+ (' A=1 ==> DERIVATIVES ARE',
+ ' QUESTIONABLE.')
1022 FORMAT
+ (' B=1 ==> USER SET ISTOP TO',
+ ' NONZERO VALUE DURING LAST'/
+ ' CALL TO SUBROUTINE FCN.')
1023 FORMAT
+ (' C=1 ==> DERIVATIVES ARE NOT',
+ ' FULL RANK AT THE SOLUTION.')
1024 FORMAT
+ (' C=2 ==> DERIVATIVES ARE ZERO',
+ ' RANK AT THE SOLUTION.')
1031 FORMAT
+ (' D=1 ==> SUM OF SQUARES CONVERGENCE.')
1032 FORMAT
+ (' D=2 ==> PARAMETER CONVERGENCE.')
1033 FORMAT
+ (' D=3 ==> SUM OF SQUARES CONVERGENCE',
+ ' AND PARAMETER CONVERGENCE.')
1034 FORMAT
+ (' D=4 ==> ITERATION LIMIT REACHED.')
1035 FORMAT
+ (' D=',I1,' ==> UNEXPECTED VALUE,',
+ ' PROBABLY INDICATING'/
+ ' INCORRECTLY SPECIFIED',
+ ' USER INPUT.')
1040 FORMAT
+ (' INFO = ',I5.5/
+ ' = ABCDE, WHERE A NONZERO VALUE FOR A GIVEN',
+ ' DIGIT INDICATES AN'/
+ ' ABNORMAL STOPPING CONDITION.')
1042 FORMAT
+ (' A=5 ==> USER STOPPED COMPUTATIONS',
+ ' IN SUBROUTINE FCN.')
1043 FORMAT
+ (' B=',I1,' ==> COMPUTATIONS WERE',
+ ' STOPPED DURING THE'/
+ ' FUNCTION EVALUATION.')
1044 FORMAT
+ (' C=',I1,' ==> COMPUTATIONS WERE',
+ ' STOPPED BECAUSE'/
+ ' DERIVATIVES WITH',
+ ' RESPECT TO DELTA WERE'/
+ ' COMPUTED BY',
+ ' SUBROUTINE FCN WHEN'/
+ ' FIT IS OLS.')
1045 FORMAT
+ (' C=',I1,' ==> COMPUTATIONS WERE',
+ ' STOPPED DURING THE'/
+ ' JACOBIAN EVALUATION.')
1050 FORMAT
+ (' A=6 ==> NUMERICAL INSTABILITIES',
+ ' HAVE BEEN DETECTED,'/
+ ' POSSIBLY INDICATING',
+ ' A DISCONTINUITY IN THE'/
+ ' DERIVATIVES OR A POOR',
+ ' POOR CHOICE OF PROBLEM'/
+ ' SCALE OR WEIGHTS.')
1060 FORMAT
+ (' A=',I1,' ==> UNEXPECTED VALUE,',
+ ' PROBABLY INDICATING'/
+ ' INCORRECTLY SPECIFIED',
+ ' USER INPUT.')
1300 FORMAT
+ (' NITER = ',I5,
+ ' (NUMBER OF ITERATIONS)')
1310 FORMAT
+ (' NFEV = ',I5,
+ ' (NUMBER OF FUNCTION EVALUATIONS)')
1320 FORMAT
+ (' NJEV = ',I5,
+ ' (NUMBER OF JACOBIAN EVALUATIONS)')
1330 FORMAT
+ (' IRANK = ',I5,
+ ' (RANK DEFICIENCY)')
1340 FORMAT
+ (' RCOND = ',1P,D12.2,
+ ' (INVERSE CONDITION NUMBER)')
*1341 FORMAT
* + (' ==> POSSIBLY FEWER THAN 2 SIGNIFICANT',
* + ' DIGITS IN RESULTS;'/
* + ' SEE ODRPACK REFERENCE',
* + ' GUIDE, SECTION 4.C.')
1350 FORMAT
+ (' ISTOP = ',I5,
+ ' (RETURNED BY USER FROM',
+ ' SUBROUTINE FCN)')
2000 FORMAT
+ (/' --- FINAL SUM OF SQUARED WEIGHTED DELTAS = ',
+ 17X,1P,D17.8)
2010 FORMAT
+ ( ' FINAL PENALTY FUNCTION VALUE = ',1P,D17.8/
+ ' PENALTY TERM = ',1P,D17.8/
+ ' PENALTY PARAMETER = ',1P,D10.1)
2100 FORMAT
+ (/' --- FINAL WEIGHTED SUMS OF SQUARES = ',17X,1P,D17.8)
2110 FORMAT
+ ( ' SUM OF SQUARED WEIGHTED DELTAS = ',1P,D17.8/
+ ' SUM OF SQUARED WEIGHTED EPSILONS = ',1P,D17.8)
2200 FORMAT
+ (/' --- RESIDUAL STANDARD DEVIATION = ',
+ 17X,1P,D17.8/
+ ' DEGREES OF FREEDOM =',I5)
3000 FORMAT
+ (/' --- ESTIMATED BETA(J), J = 1, ..., NP:')
4100 FORMAT
+ (/' --- ESTIMATED DELTA(I,*), I = 1, ..., N:')
4110 FORMAT
+ (/' --- ESTIMATED EPSILON(I) AND DELTA(I,*), I = 1, ..., N:')
4120 FORMAT
+ (/' --- ESTIMATED EPSILON(I), I = 1, ..., N:')
4130 FORMAT(5X,I5,1P,5D16.8)
4200 FORMAT
+ (/' --- ESTIMATED EPSILON(I,',I3,'), I = 1, ..., N:')
4300 FORMAT
+ (/' --- ESTIMATED DELTA(I,',I3,'), I = 1, ..., N:')
7100 FORMAT
+ (/' INDEX VALUE'/)
7200 FORMAT
+ (/' INDEX VALUE -------------->'/)
7300 FORMAT
+ (/' BETA S.D. BETA',
+ ' ---- 95% CONFIDENCE INTERVAL ----'/)
7310 FORMAT
+ (/' N.B. STANDARD ERRORS AND CONFIDENCE INTERVALS ARE',
+ ' COMPUTED USING'/
+ ' DERIVATIVES CALCULATED AT THE BEGINNING',
+ ' OF THE LAST ITERATION,'/
+ ' AND NOT USING DERIVATIVES RE-EVALUATED AT THE',
+ ' FINAL SOLUTION.')
7410 FORMAT
+ (/' N.B. THE STANDARD ERRORS OF THE ESTIMATED BETAS WERE',
+ ' NOT COMPUTED BECAUSE'/
+ ' THE DERIVATIVES WERE NOT AVAILABLE. EITHER MAXIT',
+ ' IS 0 AND THE THIRD'/
+ ' DIGIT OF JOB IS GREATER THAN 1, OR THE MOST',
+ ' RECENTLY TRIED VALUES OF'/
+ ' BETA AND/OR X+DELTA WERE IDENTIFIED AS',
+ ' UNACCEPTABLE BY USER SUPPLIED'/
+ ' SUBROUTINE FCN.')
7420 FORMAT
+ (/' N.B. THE STANDARD ERRORS OF THE ESTIMATED BETAS WERE',
+ ' NOT COMPUTED.'/
+ ' (SEE INFO ABOVE.)')
7500 FORMAT
+ (/' BETA STATUS')
8100 FORMAT
+ (11X,I5,1P,D16.8)
8200 FORMAT
+ (3X,I5,' TO',I5,1P,7D16.8)
8400 FORMAT
+ (3X,I5,1X,1P,D16.8,3X,D12.4,3X,D16.8,1X,'TO',D16.8)
8500 FORMAT
+ (3X,I5,1X,1P,D16.8,6X,'ESTIMATED')
8600 FORMAT
+ (3X,I5,1X,1P,D16.8,6X,' FIXED')
8700 FORMAT
+ (3X,I5,1X,1P,D16.8,6X,' DROPPED')
8800 FORMAT
+ (/' N.B. NO PARAMETERS WERE FIXED BY THE USER OR',
+ ' DROPPED AT THE LAST'/
+ ' ITERATION BECAUSE THEY CAUSED THE MODEL TO BE',
+ ' RANK DEFICIENT.')
8900 FORMAT
+ (/' N.B. NO CHANGE WAS MADE TO THE USER SUPPLIED PARAMETER',
+ ' VALUES BECAUSE'/
+ ' MAXIT=0.')
9110 FORMAT
+ ('(/'' I'',',
+ I2,'('' DELTA(I,'',I1,'')'')/)')
9120 FORMAT
+ ('(/'' I'',',
+ I2,'('' EPSILON(I,'',I1,'')''),',
+ I2,'('' DELTA(I,'',I1,'')'')/)')
9130 FORMAT
+ ('(/'' I'',',
+ I2,'('' EPSILON(I,'',I1,'')'')/)')
END
*DODPCR
SUBROUTINE DODPCR
+ (IPR,LUNRPT,
+ HEAD,PRTPEN,FSTITR,DIDVCV,IFLAG,
+ N,M,NP,NQ,NPP,NNZW,
+ MSGB,MSGD, BETA,Y,LDY,X,LDX,DELTA,
+ WE,LDWE,LD2WE,WD,LDWD,LD2WD,
+ IFIXB,IFIXX,LDIFX,
+ SSF,TT,LDTT,STPB,STPD,LDSTPD,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS,RVAR,IDF,SDBETA,
+ NITER,NFEV,NJEV,ACTRED,PRERED,
+ TAU,PNORM,ALPHA,F,RCOND,IRANK,INFO,ISTOP)
C***BEGIN PROLOGUE DODPCR
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DFLAGS,DODPC1,DODPC2,DODPC3,DODPHD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE GENERATE COMPUTATION REPORTS
C***END PROLOGUE DODPCR
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ACTRED,ALPHA,PARTOL,PNORM,PRERED,RCOND,RVAR,
+ SSTOL,TAU,TAUFAC
INTEGER
+ IDF,IFLAG,INFO,IPR,IRANK,ISTOP,JOB,LDIFX,LDSTPD,LDTT,LDWD,LDWE,
+ LDX,LDY,LD2WD,LD2WE,LUNRPT,M,MAXIT,N,NETA,NFEV,
+ NITER,NJEV,NNZW,NP,NPP,NQ
LOGICAL
+ DIDVCV,FSTITR,HEAD,PRTPEN
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),DELTA(N,M),F(N,NQ),SDBETA(NP),SSF(NP),
+ STPB(NP),STPD(LDSTPD,M),TT(LDTT,M),
+ WD(LDWD,LD2WD,M),WE(LDWE,LD2WE,NQ),WSS(3),X(LDX,M),Y(LDY,NQ)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M),MSGB(NQ*NP+1),MSGD(NQ*M+1)
C...LOCAL SCALARS
DOUBLE PRECISION
+ PNLTY
LOGICAL
+ ANAJAC,CDJAC,CHKJAC,DOVCV,IMPLCT,INITD,ISODR,REDOJ,RESTRT
CHARACTER TYP*3
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DFLAGS,DODPC1,DODPC2,DODPC3,DODPHD
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACTRED: THE ACTUAL RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C ANAJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY FINITE DIFFERENCES (ANAJAC=FALSE) OR NOT (ANAJAC=TRUE).
C BETA: THE FUNCTION PARAMETERS.
C CDJAC: THE VARIABLE DESIGNATING WHETHER THE JACOBIANS ARE COMPUTED
C BY CENTRAL DIFFERENCES (CDJAC=TRUE) OR BY FORWARD
C DIFFERENCES (CDJAC=FALSE).
C CHKJAC: THE VARIABLE DESIGNATING WHETHER THE USER SUPPLIED
C JACOBIANS ARE TO BE CHECKED (CHKJAC=TRUE) OR NOT
C (CHKJAC=FALSE).
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DIDVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX WAS
C COMPUTED (DIDVCV=TRUE) OR NOT (DIDVCV=FALSE).
C DOVCV: THE VARIABLE DESIGNATING WHETHER THE COVARIANCE MATRIX IS
C TO BE COMPUTED (DOVCV=TRUE) OR NOT (DOVCV=FALSE).
C F: THE (WEIGHTED) ESTIMATED VALUES OF EPSILON.
C FSTITR: THE VARIABLE DESIGNATING WHETHER THIS IS THE FIRST
C ITERATION (FSTITR=TRUE) OR NOT (FSTITR=FALSE).
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=TRUE) OR NOT (HEAD=FALSE).
C IDF: THE DEGREES OF FREEDOM OF THE FIT, EQUAL TO THE NUMBER OF
C OBSERVATIONS WITH NONZERO WEIGHTED DERIVATIVES MINUS THE
C NUMBER OF PARAMETERS BEING ESTIMATED.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFLAG: THE VARIABLE DESIGNATING WHAT IS TO BE PRINTED.
C IMPLCT: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY
C IMPLICIT ODR (IMPLCT=TRUE) OR EXPLICIT ODR (IMPLCT=FALSE).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C INITD: THE VARIABLE DESIGNATING WHETHER DELTA IS INITIALIZED TO
C ZERO (INITD=TRUE) OR TO THE VALUES IN THE FIRST N BY M
C ELEMENTS OF ARRAY WORK (INITD=FALSE).
C IPR: THE VALUE INDICATING THE REPORT TO BE PRINTED.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C JOB: THE VARIABLE CONTROLING PROBLEM INITIALIZATION AND
C COMPUTATIONAL METHOD.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LUNRPT: THE LOGICAL UNIT NUMBER FOR COMPUTATION REPORTS.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF ACCURATE DIGITS IN THE FUNCTION RESULTS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NITER: THE NUMBER OF ITERATIONS.
C NJEV: THE NUMBER OF JACOBIAN EVALUATIONS.
C NNZW: THE NUMBER OF NONZERO WEIGHTED OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C PARTOL: THE PARAMETER CONVERGENCE STOPPING TOLERANCE.
C PNLTY: THE PENALTY PARAMETER FOR AN IMPLICIT MODEL.
C PNORM: THE NORM OF THE SCALED ESTIMATED PARAMETERS.
C PRERED: THE PREDICTED RELATIVE REDUCTION IN THE SUM-OF-SQUARES.
C PRTPEN: THE VARIABLE DESIGNATING WHETHER THE PENALTY PARAMETER IS
C TO BE PRINTED IN THE ITERATION REPORT (PRTPEN=TRUE) OR NOT
C (PRTPEN=FALSE).
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION NUMBER OF TFJACB.
C REDOJ: THE VARIABLE DESIGNATING WHETHER THE JACOBIAN MATRIX IS TO
C BE RECOMPUTED FOR THE COMPUTATION OF THE COVARIANCE MATRIX
C (REDOJ=TRUE) OR NOT (REDOJ=FALSE).
C RESTRT: THE VARIABLE DESIGNATING WHETHER THE CALL IS A RESTART
C (RESTRT=TRUE) OR NOT (RESTRT=FALSE).
C RVAR: THE RESIDUAL VARIANCE.
C SDBETA: THE STANDARD DEVIATIONS OF THE ESTIMATED BETA'S.
C SSF: THE SCALING VALUES FOR BETA.
C SSTOL: THE SUM-OF-SQUARES CONVERGENCE STOPPING TOLERANCE.
C STPB: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO BETA.
C STPD: THE RELATIVE STEP FOR COMPUTING FINITE DIFFERENCE
C DERIVATIVES WITH RESPECT TO DELTA.
C TAU: THE TRUST REGION DIAMETER.
C TAUFAC: THE FACTOR USED TO COMPUTE THE INITIAL TRUST REGION
C DIAMETER.
C TT: THE SCALING VALUES FOR DELTA.
C TYP: THE CHARACTER*3 STRING "ODR" OR "OLS".
C WE: THE EPSILON WEIGHTS.
C WD: THE DELTA WEIGHTS.
C WSS: THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS AND DELTAS,
C THE SUM-OF-SQUARES OF THE WEIGHTED DELTAS, AND
C THE SUM-OF-SQUARES OF THE WEIGHTED EPSILONS.
C X: THE EXPLANATORY VARIABLE.
C Y: THE DEPENDENT VARIABLE. UNUSED WHEN THE MODEL IS IMPLICIT.
C***FIRST EXECUTABLE STATEMENT DODPCR
CALL DFLAGS(JOB,RESTRT,INITD,DOVCV,REDOJ,
+ ANAJAC,CDJAC,CHKJAC,ISODR,IMPLCT)
PNLTY = ABS(WE(1,1,1))
IF (HEAD) THEN
CALL DODPHD(HEAD,LUNRPT)
END IF
IF (ISODR) THEN
TYP = 'ODR'
ELSE
TYP = 'OLS'
END IF
C PRINT INITIAL SUMMARY
IF (IFLAG.EQ.1) THEN
WRITE (LUNRPT,1200) TYP
CALL DODPC1
+ (IPR,LUNRPT,
+ ANAJAC,CDJAC,CHKJAC,INITD,RESTRT,ISODR,IMPLCT,DOVCV,REDOJ,
+ MSGB(1),MSGB(2),MSGD(1),MSGD(2),
+ N,M,NP,NQ,NPP,NNZW,
+ X,LDX,IFIXX,LDIFX,DELTA,WD,LDWD,LD2WD,TT,LDTT,STPD,LDSTPD,
+ Y,LDY,WE,LDWE,LD2WE,PNLTY,
+ BETA,IFIXB,SSF,STPB,
+ JOB,NETA,TAUFAC,SSTOL,PARTOL,MAXIT,
+ WSS(1),WSS(2),WSS(3))
C PRINT ITERATION REPORTS
ELSE IF (IFLAG.EQ.2) THEN
IF (FSTITR) THEN
WRITE (LUNRPT,1300) TYP
END IF
CALL DODPC2
+ (IPR,LUNRPT, FSTITR,IMPLCT,PRTPEN,
+ PNLTY,
+ NITER,NFEV,WSS(1),ACTRED,PRERED,ALPHA,TAU,PNORM,NP,BETA)
C PRINT FINAL SUMMARY
ELSE IF (IFLAG.EQ.3) THEN
WRITE (LUNRPT,1400) TYP
CALL DODPC3
+ (IPR,LUNRPT,
+ ISODR,IMPLCT,DIDVCV,DOVCV,REDOJ,ANAJAC,
+ N,M,NP,NQ,NPP,
+ INFO,NITER,NFEV,NJEV,IRANK,RCOND,ISTOP,
+ WSS(1),WSS(2),WSS(3),PNLTY,RVAR,IDF,
+ BETA,SDBETA,IFIXB,F,DELTA)
END IF
RETURN
C FORMAT STATEMENTS
1200 FORMAT
+ (/' *** INITIAL SUMMARY FOR FIT BY METHOD OF ',A3, ' ***')
1300 FORMAT
+ (/' *** ITERATION REPORTS FOR FIT BY METHOD OF ',A3, ' ***')
1400 FORMAT
+ (/' *** FINAL SUMMARY FOR FIT BY METHOD OF ',A3, ' ***')
END
*DODPE1
SUBROUTINE DODPE1
+ (UNIT,D1,D2,D3,D4,D5,
+ N,M,NQ,
+ LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LWKMN,LIWKMN)
C***BEGIN PROLOGUE DODPE1
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE PRINT ERROR REPORTS
C***END PROLOGUE DODPE1
C...SCALAR ARGUMENTS
INTEGER
+ D1,D2,D3,D4,D5,LDSCLD,LDSTPD,LDWD,LDWE,LD2WD,LD2WE,
+ LIWKMN,LWKMN,M,N,NQ,UNIT
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C D1: THE 1ST DIGIT (FROM THE LEFT) OF INFO.
C D2: THE 2ND DIGIT (FROM THE LEFT) OF INFO.
C D3: THE 3RD DIGIT (FROM THE LEFT) OF INFO.
C D4: THE 4TH DIGIT (FROM THE LEFT) OF INFO.
C D5: THE 5TH DIGIT (FROM THE LEFT) OF INFO.
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LIWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY IWORK.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY WORK.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C UNIT: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C***FIRST EXECUTABLE STATEMENT DODPE1
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN PROBLEM SPECIFICATION
C PARAMETERS
IF (D1.EQ.1) THEN
IF (D2.NE.0) THEN
WRITE(UNIT,1100)
END IF
IF (D3.NE.0) THEN
WRITE(UNIT,1200)
END IF
IF (D4.NE.0) THEN
WRITE(UNIT,1300)
END IF
IF (D5.NE.0) THEN
WRITE(UNIT,1400)
END IF
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN DIMENSION SPECIFICATION
C PARAMETERS
ELSE IF (D1.EQ.2) THEN
IF (D2.NE.0) THEN
IF (D2.EQ.1 .OR. D2.EQ.3) THEN
WRITE(UNIT,2110)
END IF
IF (D2.EQ.2 .OR. D2.EQ.3) THEN
WRITE(UNIT,2120)
END IF
END IF
IF (D3.NE.0) THEN
IF (D3.EQ.1 .OR. D3.EQ.3 .OR. D3.EQ.5 .OR. D3.EQ.7) THEN
WRITE(UNIT,2210)
END IF
IF (D3.EQ.2 .OR. D3.EQ.3 .OR. D3.EQ.6 .OR. D3.EQ.7) THEN
WRITE(UNIT,2220)
END IF
IF (D3.EQ.4 .OR. D3.EQ.5 .OR. D3.EQ.6 .OR. D3.EQ.7) THEN
WRITE(UNIT,2230)
END IF
END IF
IF (D4.NE.0) THEN
IF (D4.EQ.1 .OR. D4.EQ.3) THEN
WRITE(UNIT,2310)
END IF
IF (D4.EQ.2 .OR. D4.EQ.3) THEN
WRITE(UNIT,2320)
END IF
END IF
IF (D5.NE.0) THEN
IF (D5.EQ.1 .OR. D5.EQ.3) THEN
WRITE(UNIT,2410) LWKMN
END IF
IF (D5.EQ.2 .OR. D5.EQ.3) THEN
WRITE(UNIT,2420) LIWKMN
END IF
END IF
ELSE IF (D1.EQ.3) THEN
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN SCALE VALUES
IF (D2.NE.0) THEN
IF (D2.EQ.1 .OR. D2.EQ.3) THEN
IF (LDSCLD.GE.N) THEN
WRITE(UNIT,3110)
ELSE
WRITE(UNIT,3120)
END IF
END IF
IF (D2.EQ.2 .OR. D2.EQ.3) THEN
WRITE(UNIT,3130)
END IF
END IF
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN DERIVATIVE STEP VALUES
IF (D3.NE.0) THEN
IF (D3.EQ.1 .OR. D3.EQ.3) THEN
IF (LDSTPD.GE.N) THEN
WRITE(UNIT,3210)
ELSE
WRITE(UNIT,3220)
END IF
END IF
IF (D3.EQ.2 .OR. D3.EQ.3) THEN
WRITE(UNIT,3230)
END IF
END IF
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN OBSERVATIONAL ERROR WEIGHTS
IF (D4.NE.0) THEN
IF (D4.EQ.1) THEN
IF (LDWE.GE.N) THEN
IF (LD2WE.GE.NQ) THEN
WRITE(UNIT,3310)
ELSE
WRITE(UNIT,3320)
END IF
ELSE
IF (LD2WE.GE.NQ) THEN
WRITE(UNIT,3410)
ELSE
WRITE(UNIT,3420)
END IF
END IF
END IF
IF (D4.EQ.2) THEN
WRITE(UNIT,3500)
END IF
END IF
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN DELTA WEIGHTS
IF (D5.NE.0) THEN
IF (LDWD.GE.N) THEN
IF (LD2WD.GE.M) THEN
WRITE(UNIT,4310)
ELSE
WRITE(UNIT,4320)
END IF
ELSE
IF (LD2WD.GE.M) THEN
WRITE(UNIT,4410)
ELSE
WRITE(UNIT,4420)
END IF
END IF
END IF
END IF
C FORMAT STATEMENTS
1100 FORMAT
+ (/' ERROR : N IS LESS THAN ONE.')
1200 FORMAT
+ (/' ERROR : M IS LESS THAN ONE.')
1300 FORMAT
+ (/' ERROR : NP IS LESS THAN ONE'/
+ ' OR NP IS GREATER THAN N.')
1400 FORMAT
+ (/' ERROR : NQ IS LESS THAN ONE.')
2110 FORMAT
+ (/' ERROR : LDX IS LESS THAN N.')
2120 FORMAT
+ (/' ERROR : LDY IS LESS THAN N.')
2210 FORMAT
+ (/' ERROR : LDIFX IS LESS THAN N'/
+ ' AND LDIFX IS NOT EQUAL TO ONE.')
2220 FORMAT
+ (/' ERROR : LDSCLD IS LESS THAN N'/
+ ' AND LDSCLD IS NOT EQUAL TO ONE.')
2230 FORMAT
+ (/' ERROR : LDSTPD IS LESS THAN N'/
+ ' AND LDSTPD IS NOT EQUAL TO ONE.')
2310 FORMAT
+ (/' ERROR : LDWE IS LESS THAN N'/
+ ' AND LDWE IS NOT EQUAL TO ONE OR'/
+ ' OR'/
+ ' LD2WE IS LESS THAN NQ'/
+ ' AND LD2WE IS NOT EQUAL TO ONE.')
2320 FORMAT
+ (/' ERROR : LDWD IS LESS THAN N'/
+ ' AND LDWD IS NOT EQUAL TO ONE.')
2410 FORMAT
+ (/' ERROR : LWORK IS LESS THAN ',I7, ','/
+ ' THE SMALLEST ACCEPTABLE DIMENSION OF ARRAY WORK.')
2420 FORMAT
+ (/' ERROR : LIWORK IS LESS THAN ',I7, ','/
+ ' THE SMALLEST ACCEPTABLE DIMENSION OF ARRAY',
+ ' IWORK.')
3110 FORMAT
+ (/' ERROR : SCLD(I,J) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME I = 1, ..., N AND J = 1, ..., M.'//
+ ' WHEN SCLD(1,1) IS GREATER THAN ZERO'/
+ ' AND LDSCLD IS GREATER THAN OR EQUAL TO N THEN'/
+ ' EACH OF THE N BY M ELEMENTS OF'/
+ ' SCLD MUST BE GREATER THAN ZERO.')
3120 FORMAT
+ (/' ERROR : SCLD(1,J) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME J = 1, ..., M.'//
+ ' WHEN SCLD(1,1) IS GREATER THAN ZERO'/
+ ' AND LDSCLD IS EQUAL TO ONE THEN'/
+ ' EACH OF THE 1 BY M ELEMENTS OF'/
+ ' SCLD MUST BE GREATER THAN ZERO.')
3130 FORMAT
+ (/' ERROR : SCLB(K) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME K = 1, ..., NP.'//
+ ' ALL NP ELEMENTS OF',
+ ' SCLB MUST BE GREATER THAN ZERO.')
3210 FORMAT
+ (/' ERROR : STPD(I,J) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME I = 1, ..., N AND J = 1, ..., M.'//
+ ' WHEN STPD(1,1) IS GREATER THAN ZERO'/
+ ' AND LDSTPD IS GREATER THAN OR EQUAL TO N THEN'/
+ ' EACH OF THE N BY M ELEMENTS OF'/
+ ' STPD MUST BE GREATER THAN ZERO.')
3220 FORMAT
+ (/' ERROR : STPD(1,J) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME J = 1, ..., M.'//
+ ' WHEN STPD(1,1) IS GREATER THAN ZERO'/
+ ' AND LDSTPD IS EQUAL TO ONE THEN'/
+ ' EACH OF THE 1 BY M ELEMENTS OF'/
+ ' STPD MUST BE GREATER THAN ZERO.')
3230 FORMAT
+ (/' ERROR : STPB(K) IS LESS THAN OR EQUAL TO ZERO'/
+ ' FOR SOME K = 1, ..., NP.'//
+ ' ALL NP ELEMENTS OF',
+ ' STPB MUST BE GREATER THAN ZERO.')
3310 FORMAT
+ (/' ERROR : AT LEAST ONE OF THE (NQ BY NQ) ARRAYS STARTING'/
+ ' IN WE(I,1,1), I = 1, ..., N, IS NOT POSITIVE'/
+ ' SEMIDEFINITE. WHEN WE(1,1,1) IS GREATER THAN'/
+ ' OR EQUAL TO ZERO, AND LDWE IS GREATER THAN OR'/
+ ' EQUAL TO N, AND LD2WE IS GREATER THAN OR EQUAL'/
+ ' TO NQ, THEN EACH OF THE (NQ BY NQ) ARRAYS IN WE'/
+ ' MUST BE POSITIVE SEMIDEFINITE.')
3320 FORMAT
+ (/' ERROR : AT LEAST ONE OF THE (1 BY NQ) ARRAYS STARTING'/
+ ' IN WE(I,1,1), I = 1, ..., N, HAS A NEGATIVE'/
+ ' ELEMENT. WHEN WE(1,1,1) IS GREATER THAN OR'/
+ ' EQUAL TO ZERO, AND LDWE IS GREATER THAN OR EQUAL'/
+ ' TO N, AND LD2WE IS EQUAL TO 1, THEN EACH OF THE'/
+ ' (1 BY NQ) ARRAYS IN WE MUST HAVE ONLY NON-'/
+ ' NEGATIVE ELEMENTS.')
3410 FORMAT
+ (/' ERROR : THE (NQ BY NQ) ARRAY STARTING IN WE(1,1,1) IS'/
+ ' NOT POSITIVE SEMIDEFINITE. WHEN WE(1,1,1) IS'/
+ ' GREATER THAN OR EQUAL TO ZERO, AND LDWE IS EQUAL'/
+ ' TO 1, AND LD2WE IS GREATER THAN OR EQUAL TO NQ,'/
+ ' THEN THE (NQ BY NQ) ARRAY IN WE MUST BE POSITIVE'/
+ ' SEMIDEFINITE.')
3420 FORMAT
+ (/' ERROR : THE (1 BY NQ) ARRAY STARTING IN WE(1,1,1) HAS'/
+ ' A NEGATIVE ELEMENT. WHEN WE(1,1,1) IS GREATER'/
+ ' THAN OR EQUAL TO ZERO, AND LDWE IS EQUAL TO 1,'/
+ ' AND LD2WE IS EQUAL TO 1, THEN THE (1 BY NQ)'/
+ ' ARRAY IN WE MUST HAVE ONLY NONNEGATIVE ELEMENTS.')
3500 FORMAT
+ (/' ERROR : THE NUMBER OF NONZERO ARRAYS IN ARRAY WE IS'/
+ ' LESS THAN NP.')
4310 FORMAT
+ (/' ERROR : AT LEAST ONE OF THE (M BY M) ARRAYS STARTING'/
+ ' IN WD(I,1,1), I = 1, ..., N, IS NOT POSITIVE'/
+ ' DEFINITE. WHEN WD(1,1,1) IS GREATER THAN ZERO,'/
+ ' AND LDWD IS GREATER THAN OR EQUAL TO N, AND'/
+ ' LD2WD IS GREATER THAN OR EQUAL TO M, THEN EACH'/
+ ' OF THE (M BY M) ARRAYS IN WD MUST BE POSITIVE'/
+ ' DEFINITE.')
4320 FORMAT
+ (/' ERROR : AT LEAST ONE OF THE (1 BY M) ARRAYS STARTING'/
+ ' IN WD(I,1,1), I = 1, ..., N, HAS A NONPOSITIVE'/
+ ' ELEMENT. WHEN WD(1,1,1) IS GREATER THAN ZERO,'/
+ ' AND LDWD IS GREATER THAN OR EQUAL TO N, AND'/
+ ' LD2WD IS EQUAL TO 1, THEN EACH OF THE (1 BY M)'/
+ ' ARRAYS IN WD MUST HAVE ONLY POSITIVE ELEMENTS.')
4410 FORMAT
+ (/' ERROR : THE (M BY M) ARRAY STARTING IN WD(1,1,1) IS'/
+ ' NOT POSITIVE DEFINITE. WHEN WD(1,1,1) IS'/
+ ' GREATER THAN ZERO, AND LDWD IS EQUAL TO 1, AND'/
+ ' LD2WD IS GREATER THAN OR EQUAL TO M, THEN THE'/
+ ' (M BY M) ARRAY IN WD MUST BE POSITIVE DEFINITE.')
4420 FORMAT
+ (/' ERROR : THE (1 BY M) ARRAY STARTING IN WD(1,1,1) HAS A'/
+ ' NONPOSITIVE ELEMENT. WHEN WD(1,1,1) IS GREATER'/
+ ' THAN ZERO, AND LDWD IS EQUAL TO 1, AND LD2WD IS'/
+ ' EQUAL TO 1, THEN THE (1 BY M) ARRAY IN WD MUST'/
+ ' HAVE ONLY POSITIVE ELEMENTS.')
END
*DODPE2
SUBROUTINE DODPE2
+ (UNIT,
+ N,M,NP,NQ,
+ FJACB,FJACD,
+ DIFF,MSGB1,MSGB,ISODR,MSGD1,MSGD,
+ XPLUSD,NROW,NETA,NTOL)
C***BEGIN PROLOGUE DODPE2
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE GENERATE THE DERIVATIVE CHECKING REPORT
C***END PROLOGUE DODPE2
C...SCALAR ARGUMENTS
INTEGER
+ M,MSGB1,MSGD1,N,NETA,NP,NQ,NROW,NTOL,UNIT
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DIFF(NQ,NP+M),FJACB(N,NP,NQ),FJACD(N,M,NQ),XPLUSD(N,M)
INTEGER
+ MSGB(NQ,NP),MSGD(NQ,M)
C...LOCAL SCALARS
INTEGER
+ I,J,K,L
CHARACTER FLAG*1,TYP*3
C...LOCAL ARRAYS
LOGICAL
+ FTNOTE(0:7)
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C DIFF: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR EACH DERIVATIVE CHECKED.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FLAG: THE CHARACTER STRING INDICATING HIGHLY QUESTIONABLE RESULTS.
C FTNOTE: THE ARRAY CONTROLING FOOTNOTES.
C I: AN INDEX VARIABLE.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=.TRUE.) OR BY OLS (ISODR=.FALSE.).
C J: AN INDEX VARIABLE.
C K: AN INDEX VARIABLE.
C L: AN INDEX VARIABLE.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGB1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C MSGD1: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF RELIABLE DIGITS IN THE MODEL.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT
C WHICH THE DERIVATIVE IS TO BE CHECKED.
C NTOL: THE NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN THE
C FINITE DIFFERENCE AND THE USER SUPPLIED DERIVATIVES.
C TYP: THE CHARACTER STRING INDICATING SOLUTION TYPE, ODR OR OLS.
C UNIT: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C XPLUSD: THE VALUES OF X + DELTA.
C***FIRST EXECUTABLE STATEMENT DODPE2
C SET UP FOR FOOTNOTES
DO 10 I=0,7
FTNOTE(I) = .FALSE.
10 CONTINUE
DO 40 L=1,NQ
IF (MSGB1.GE.1) THEN
DO 20 I=1,NP
IF (MSGB(L,I).GE.1) THEN
FTNOTE(0) = .TRUE.
FTNOTE(MSGB(L,I)) = .TRUE.
END IF
20 CONTINUE
END IF
IF (MSGD1.GE.1) THEN
DO 30 I=1,M
IF (MSGD(L,I).GE.1) THEN
FTNOTE(0) = .TRUE.
FTNOTE(MSGD(L,I)) = .TRUE.
END IF
30 CONTINUE
END IF
40 CONTINUE
C PRINT REPORT
IF (ISODR) THEN
TYP = 'ODR'
ELSE
TYP = 'OLS'
END IF
WRITE (UNIT,1000) TYP
DO 70 L=1,NQ
WRITE (UNIT,2100) L,NROW
WRITE (UNIT,2200)
DO 50 I=1,NP
K = MSGB(L,I)
IF (K.GE.7) THEN
FLAG = '*'
ELSE
FLAG = ' '
END IF
IF (K.LE.-1) THEN
WRITE (UNIT,3100) I
ELSE IF (K.EQ.0) THEN
WRITE (UNIT,3200) I,FJACB(NROW,I,L),DIFF(L,I),FLAG
ELSE IF (K.GE.1) THEN
WRITE (UNIT,3300) I,FJACB(NROW,I,L),DIFF(L,I),FLAG,K
END IF
50 CONTINUE
IF (ISODR) THEN
DO 60 I=1,M
K = MSGD(L,I)
IF (K.GE.7) THEN
FLAG = '*'
ELSE
FLAG = ' '
END IF
IF (K.LE.-1) THEN
WRITE (UNIT,4100) NROW,I
ELSE IF (K.EQ.0) THEN
WRITE (UNIT,4200) NROW,I,
+ FJACD(NROW,I,L),DIFF(L,NP+I),FLAG
ELSE IF (K.GE.1) THEN
WRITE (UNIT,4300) NROW,I,
+ FJACD(NROW,I,L),DIFF(L,NP+I),FLAG,K
END IF
60 CONTINUE
END IF
70 CONTINUE
C PRINT FOOTNOTES
IF (FTNOTE(0)) THEN
WRITE (UNIT,5000)
IF (FTNOTE(1)) WRITE (UNIT,5100)
IF (FTNOTE(2)) WRITE (UNIT,5200)
IF (FTNOTE(3)) WRITE (UNIT,5300)
IF (FTNOTE(4)) WRITE (UNIT,5400)
IF (FTNOTE(5)) WRITE (UNIT,5500)
IF (FTNOTE(6)) WRITE (UNIT,5600)
IF (FTNOTE(7)) WRITE (UNIT,5700)
END IF
IF (NETA.LT.0) THEN
WRITE (UNIT,6000) -NETA
ELSE
WRITE (UNIT,6100) NETA
END IF
WRITE (UNIT,7000) NTOL
C PRINT OUT ROW OF EXPLANATORY VARIABLE WHICH WAS CHECKED.
WRITE (UNIT,8100) NROW
DO 80 J=1,M
WRITE (UNIT,8110) NROW,J,XPLUSD(NROW,J)
80 CONTINUE
RETURN
C FORMAT STATEMENTS
1000 FORMAT
+ (//' *** DERIVATIVE CHECKING REPORT FOR FIT BY METHOD OF ',A3,
+ ' ***'/)
2100 FORMAT (/' FOR RESPONSE ',I2,' OF OBSERVATION ', I5/)
2200 FORMAT (' ',' USER',
+ ' ',' '/
+ ' ',' SUPPLIED',
+ ' RELATIVE',' DERIVATIVE '/
+ ' DERIVATIVE WRT',' VALUE',
+ ' DIFFERENCE',' ASSESSMENT '/)
3100 FORMAT (' BETA(',I3,')', ' --- ',
+ ' --- ',' UNCHECKED')
3200 FORMAT (' BETA(',I3,')', 1P,2D13.2,3X,A1,
+ 'VERIFIED')
3300 FORMAT (' BETA(',I3,')', 1P,2D13.2,3X,A1,
+ 'QUESTIONABLE (SEE NOTE ',I1,')')
4100 FORMAT (' DELTA(',I2,',',I2,')', ' --- ',
+ ' --- ',' UNCHECKED')
4200 FORMAT (' DELTA(',I2,',',I2,')', 1P,2D13.2,3X,A1,
+ 'VERIFIED')
4300 FORMAT (' DELTA(',I2,',',I2,')', 1P,2D13.2,3X,A1,
+ 'QUESTIONABLE (SEE NOTE ',I1,')')
5000 FORMAT
+ (/' NOTES:')
5100 FORMAT
+ (/' (1) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' AGREE, BUT'/
+ ' RESULTS ARE QUESTIONABLE BECAUSE BOTH ARE ZERO.')
5200 FORMAT
+ (/' (2) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' AGREE, BUT'/
+ ' RESULTS ARE QUESTIONABLE BECAUSE ONE IS',
+ ' IDENTICALLY ZERO'/
+ ' AND THE OTHER IS ONLY APPROXIMATELY ZERO.')
5300 FORMAT
+ (/' (3) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' DISAGREE, BUT'/
+ ' RESULTS ARE QUESTIONABLE BECAUSE ONE IS',
+ ' IDENTICALLY ZERO'/
+ ' AND THE OTHER IS NOT.')
5400 FORMAT
+ (/' (4) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' DISAGREE, BUT'/
+ ' FINITE DIFFERENCE DERIVATIVE IS QUESTIONABLE',
+ ' BECAUSE EITHER'/
+ ' THE RATIO OF RELATIVE CURVATURE TO RELATIVE',
+ ' SLOPE IS TOO HIGH'/
+ ' OR THE SCALE IS WRONG.')
5500 FORMAT
+ (/' (5) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' DISAGREE, BUT'/
+ ' FINITE DIFFERENCE DERIVATIVE IS QUESTIONABLE',
+ ' BECAUSE THE'/
+ ' RATIO OF RELATIVE CURVATURE TO RELATIVE SLOPE IS',
+ ' TOO HIGH.')
5600 FORMAT
+ (/' (6) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' DISAGREE, BUT'/
+ ' HAVE AT LEAST 2 DIGITS IN COMMON.')
5700 FORMAT
+ (/' (7) USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVES',
+ ' DISAGREE, AND'/
+ ' HAVE FEWER THAN 2 DIGITS IN COMMON. DERIVATIVE',
+ ' CHECKING MUST'/
+ ' BE TURNED OFF IN ORDER TO PROCEED.')
6000 FORMAT
+ (/' NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS ',
+ I5/
+ ' (ESTIMATED BY ODRPACK)')
6100 FORMAT
+ (/' NUMBER OF RELIABLE DIGITS IN FUNCTION RESULTS ',
+ I5/
+ ' (SUPPLIED BY USER)')
7000 FORMAT
+ (/' NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN '/
+ ' USER SUPPLIED AND FINITE DIFFERENCE DERIVATIVE FOR '/
+ ' USER SUPPLIED DERIVATIVE TO BE CONSIDERED VERIFIED ',
+ I5)
8100 FORMAT
+ (/' ROW NUMBER AT WHICH DERIVATIVES WERE CHECKED ',
+ I5//
+ ' -VALUES OF THE EXPLANATORY VARIABLES AT THIS ROW'/)
8110 FORMAT
+ (10X,'X(',I2,',',I2,')',1X,1P,3D16.8)
END
*DODPE3
SUBROUTINE DODPE3
+ (UNIT,D2,D3)
C***BEGIN PROLOGUE DODPE3
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE PRINT ERROR REPORTS INDICATING THAT COMPUTATIONS WERE
C STOPPED IN USER SUPPLIED SUBROUTINES FCN
C***END PROLOGUE DODPE3
C...SCALAR ARGUMENTS
INTEGER
+ D2,D3,UNIT
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C D2: THE 2ND DIGIT (FROM THE LEFT) OF INFO.
C D3: THE 3RD DIGIT (FROM THE LEFT) OF INFO.
C UNIT: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C***FIRST EXECUTABLE STATEMENT DODPE3
C PRINT APPROPRIATE MESSAGES TO INDICATE WHERE COMPUTATIONS WERE
C STOPPED
IF (D2.EQ.2) THEN
WRITE(UNIT,1100)
ELSE IF (D2.EQ.3) THEN
WRITE(UNIT,1200)
ELSE IF (D2.EQ.4) THEN
WRITE(UNIT,1300)
END IF
IF (D3.EQ.2) THEN
WRITE(UNIT,1400)
END IF
C FORMAT STATEMENTS
1100 FORMAT
+ (//' VARIABLE ISTOP HAS BEEN RETURNED WITH A NONZERO VALUE '/
+ ' FROM USER SUPPLIED SUBROUTINE FCN WHEN INVOKED USING THE'/
+ ' INITIAL ESTIMATES OF BETA AND DELTA SUPPLIED BY THE '/
+ ' USER. THE INITIAL ESTIMATES MUST BE ADJUSTED TO ALLOW '/
+ ' PROPER EVALUATION OF SUBROUTINE FCN BEFORE THE '/
+ ' REGRESSION PROCEDURE CAN CONTINUE.')
1200 FORMAT
+ (//' VARIABLE ISTOP HAS BEEN RETURNED WITH A NONZERO VALUE '/
+ ' FROM USER SUPPLIED SUBROUTINE FCN. THIS OCCURRED DURING'/
+ ' THE COMPUTATION OF THE NUMBER OF RELIABLE DIGITS IN THE '/
+ ' PREDICTED VALUES (F) RETURNED FROM SUBROUTINE FCN, INDI-'/
+ ' CATING THAT CHANGES IN THE INITIAL ESTIMATES OF BETA(K),'/
+ ' K=1,NP, AS SMALL AS 2*BETA(K)*SQRT(MACHINE PRECISION), '/
+ ' WHERE MACHINE PRECISION IS DEFINED AS THE SMALLEST VALUE'/
+ ' E SUCH THAT 1+E>1 ON THE COMPUTER BEING USED, PREVENT '/
+ ' SUBROUTINE FCN FROM BEING PROPERLY EVALUATED. THE '/
+ ' INITIAL ESTIMATES MUST BE ADJUSTED TO ALLOW PROPER '/
+ ' EVALUATION OF SUBROUTINE FCN DURING THESE COMPUTATIONS '/
+ ' BEFORE THE REGRESSION PROCEDURE CAN CONTINUE.')
1300 FORMAT
+ (//' VARIABLE ISTOP HAS BEEN RETURNED WITH A NONZERO VALUE '/
+ ' FROM USER SUPPLIED SUBROUTINE FCN. THIS OCCURRED DURING'/
+ ' THE DERIVATIVE CHECKING PROCEDURE, INDICATING THAT '/
+ ' CHANGES IN THE INITIAL ESTIMATES OF BETA(K), K=1,NP, AS '/
+ ' SMALL AS MAX[BETA(K),1/SCLB(K)]*10**(-NETA/2), AND/OR '/
+ ' OF DELTA(I,J), I=1,N AND J=1,M, AS SMALL AS '/
+ ' MAX[DELTA(I,J),1/SCLD(I,J)]*10**(-NETA/2), WHERE NETA '/
+ ' IS DEFINED TO BE THE NUMBER OF RELIABLE DIGITS IN '/
+ ' PREDICTED VALUES (F) RETURNED FROM SUBROUTINE FCN, '/
+ ' PREVENT SUBROUTINE FCN FROM BEING PROPERLY EVALUATED. '/
+ ' THE INITIAL ESTIMATES MUST BE ADJUSTED TO ALLOW PROPER '/
+ ' EVALUATION OF SUBROUTINE FCN DURING THESE COMPUTATIONS '/
+ ' BEFORE THE REGRESSION PROCEDURE CAN CONTINUE.')
1400 FORMAT
+ (//' VARIABLE ISTOP HAS BEEN RETURNED WITH A NONZERO VALUE '/
+ ' FROM USER SUPPLIED SUBROUTINE FCN WHEN INVOKED FOR '/
+ ' DERIVATIVE EVALUATIONS USING THE INITIAL ESTIMATES OF '/
+ ' BETA AND DELTA SUPPLIED BY THE USER. THE INITIAL '/
+ ' ESTIMATES MUST BE ADJUSTED TO ALLOW PROPER EVALUATION '/
+ ' OF SUBROUTINE FCN BEFORE THE REGRESSION PROCEDURE CAN '/
+ ' CONTINUE.')
END
*DODPER
SUBROUTINE DODPER
+ (INFO,LUNERR,SHORT,
+ N,M,NP,NQ,
+ LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LWKMN,LIWKMN,
+ FJACB,FJACD,
+ DIFF,MSGB,ISODR,MSGD,
+ XPLUSD,NROW,NETA,NTOL)
C***BEGIN PROLOGUE DODPER
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DODPE1,DODPE2,DODPE3,DODPHD
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE CONTROLLING ROUTINE FOR PRINTING ERROR REPORTS
C***END PROLOGUE DODPER
C...SCALAR ARGUMENTS
INTEGER
+ INFO,LDSCLD,LDSTPD,LDWD,LDWE,LD2WD,LD2WE,LIWKMN,LUNERR,LWKMN,
+ M,N,NETA,NP,NQ,NROW,NTOL
LOGICAL
+ ISODR,SHORT
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DIFF(NQ,NP+M),FJACB(N,NP,NQ),FJACD(N,M,NQ),XPLUSD(N,M)
INTEGER
+ MSGB(NQ*NP+1),MSGD(NQ*M+1)
C...LOCAL SCALARS
INTEGER
+ D1,D2,D3,D4,D5,UNIT
LOGICAL
+ HEAD
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DODPE1,DODPE2,DODPE3,DODPHD
C...INTRINSIC FUNCTIONS
INTRINSIC
+ MOD
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C D1: THE 1ST DIGIT (FROM THE LEFT) OF INFO.
C D2: THE 2ND DIGIT (FROM THE LEFT) OF INFO.
C D3: THE 3RD DIGIT (FROM THE LEFT) OF INFO.
C D4: THE 4TH DIGIT (FROM THE LEFT) OF INFO.
C D5: THE 5TH DIGIT (FROM THE LEFT) OF INFO.
C DIFF: THE RELATIVE DIFFERENCES BETWEEN THE USER SUPPLIED AND
C FINITE DIFFERENCE DERIVATIVES FOR EACH DERIVATIVE CHECKED.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=.TRUE.) OR NOT (HEAD=.FALSE.).
C INFO: THE VARIABLE DESIGNATING WHY THE COMPUTATIONS WERE STOPPED.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=.TRUE.) OR BY OLS (ISODR=.FALSE.).
C LDSCLD: THE LEADING DIMENSION OF ARRAY SCLD.
C LDSTPD: THE LEADING DIMENSION OF ARRAY STPD.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LIWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY IWORK.
C LUNERR: THE LOGICAL UNIT NUMBER USED FOR ERROR MESSAGES.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF ARRAY WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C MSGB: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT BETA.
C MSGD: THE ERROR CHECKING RESULTS FOR THE JACOBIAN WRT DELTA.
C N: THE NUMBER OF OBSERVATIONS.
C NETA: THE NUMBER OF RELIABLE DIGITS IN THE MODEL.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE EXPLANATORY VARIABLE ARRAY AT
C WHICH THE DERIVATIVE IS TO BE CHECKED.
C NTOL: THE NUMBER OF DIGITS OF AGREEMENT REQUIRED BETWEEN THE
C FINITE DIFFERENCE AND THE USER SUPPLIED DERIVATIVES.
C SHORT: THE VARIABLE DESIGNATING WHETHER THE USER HAS INVOKED
C ODRPACK BY THE SHORT-CALL (SHORT=.TRUE.) OR THE LONG-CALL
C (SHORT=.FALSE.).
C UNIT: THE LOGICAL UNIT NUMBER FOR ERROR MESSAGES.
C XPLUSD: THE VALUES X + DELTA.
C***FIRST EXECUTABLE STATEMENT DODPER
C SET LOGICAL UNIT NUMBER FOR ERROR REPORT
IF (LUNERR.EQ.0) THEN
RETURN
ELSE IF (LUNERR.LT.0) THEN
UNIT = 6
ELSE
UNIT = LUNERR
END IF
C PRINT HEADING
HEAD = .TRUE.
CALL DODPHD(HEAD,UNIT)
C EXTRACT INDIVIDUAL DIGITS FROM VARIABLE INFO
D1 = MOD(INFO,100000)/10000
D2 = MOD(INFO,10000)/1000
D3 = MOD(INFO,1000)/100
D4 = MOD(INFO,100)/10
D5 = MOD(INFO,10)
C PRINT APPROPRIATE ERROR MESSAGES FOR ODRPACK INVOKED STOP
IF (D1.GE.1 .AND. D1.LE.3) THEN
C PRINT APPROPRIATE MESSAGES FOR ERRORS IN
C PROBLEM SPECIFICATION PARAMETERS
C DIMENSION SPECIFICATION PARAMETERS
C NUMBER OF GOOD DIGITS IN X
C WEIGHTS
CALL DODPE1(UNIT,D1,D2,D3,D4,D5,
+ N,M,NQ,
+ LDSCLD,LDSTPD,LDWE,LD2WE,LDWD,LD2WD,
+ LWKMN,LIWKMN)
ELSE IF ((D1.EQ.4) .OR. (MSGB(1).GE.0)) THEN
C PRINT APPROPRIATE MESSAGES FOR DERIVATIVE CHECKING
CALL DODPE2(UNIT,
+ N,M,NP,NQ,
+ FJACB,FJACD,
+ DIFF,MSGB(1),MSGB(2),ISODR,MSGD(1),MSGD(2),
+ XPLUSD,NROW,NETA,NTOL)
ELSE IF (D1.EQ.5) THEN
C PRINT APPROPRIATE ERROR MESSAGE FOR USER INVOKED STOP FROM FCN
CALL DODPE3(UNIT,D2,D3)
END IF
C PRINT CORRECT FORM OF CALL STATEMENT
IF ((D1.GE.1 .AND. D1.LE.3) .OR.
+ (D1.EQ.4 .AND. (D2.EQ.2 .OR. D3.EQ.2)) .OR.
+ (D1.EQ.5)) THEN
IF (SHORT) THEN
WRITE (UNIT,1100)
ELSE
WRITE (UNIT,1200)
END IF
END IF
RETURN
C FORMAT STATEMENTS
1100 FORMAT
+ (//' THE CORRECT FORM OF THE CALL STATEMENT IS '//
+ ' CALL DODR'/
+ ' + (FCN,'/
+ ' + N,M,NP,NQ,'/
+ ' + BETA,'/
+ ' + Y,LDY,X,LDX,'/
+ ' + WE,LDWE,LD2WE,WD,LDWD,LD2WD,'/
+ ' + JOB,'/
+ ' + IPRINT,LUNERR,LUNRPT,'/
+ ' + WORK,LWORK,IWORK,LIWORK,'/
+ ' + INFO)')
1200 FORMAT
+ (//' THE CORRECT FORM OF THE CALL STATEMENT IS '//
+ ' CALL DODRC'/
+ ' + (FCN,'/
+ ' + N,M,NP,NQ,'/
+ ' + BETA,'/
+ ' + Y,LDY,X,LDX,'/
+ ' + WE,LDWE,LD2WE,WD,LDWD,LD2WD,'/
+ ' + IFIXB,IFIXX,LDIFX,'/
+ ' + JOB,NDIGIT,TAUFAC,'/
+ ' + SSTOL,PARTOL,MAXIT,'/
+ ' + IPRINT,LUNERR,LUNRPT,'/
+ ' + STPB,STPD,LDSTPD,'/
+ ' + SCLB,SCLD,LDSCLD,'/
+ ' + WORK,LWORK,IWORK,LIWORK,'/
+ ' + INFO)')
END
*DODPHD
SUBROUTINE DODPHD
+ (HEAD,UNIT)
C***BEGIN PROLOGUE DODPHD
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE PRINT ODRPACK HEADING
C***END PROLOGUE DODPHD
C...SCALAR ARGUMENTS
INTEGER
+ UNIT
LOGICAL
+ HEAD
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C HEAD: THE VARIABLE DESIGNATING WHETHER THE HEADING IS TO BE
C PRINTED (HEAD=.TRUE.) OR NOT (HEAD=.FALSE.).
C UNIT: THE LOGICAL UNIT NUMBER TO WHICH THE HEADING IS WRITTEN.
C***FIRST EXECUTABLE STATEMENT DODPHD
IF (HEAD) THEN
WRITE(UNIT,1000)
HEAD = .FALSE.
END IF
RETURN
C FORMAT STATEMENTS
1000 FORMAT (
+ ' ******************************************************* '/
+ ' * ODRPACK VERSION 2.01 OF 06-19-92 (DOUBLE PRECISION) * '/
+ ' ******************************************************* '/)
END
*DODSTP
SUBROUTINE DODSTP
+ (N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ALPHA,EPSFCN,ISODR,
+ TFJACB,OMEGA,U,QRAUX,KPVT,
+ S,T,PHI,IRANK,RCOND,FORVCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
C***BEGIN PROLOGUE DODSTP
C***REFER TO DODR,DODRC
C***ROUTINES CALLED IDAMAX,DCHEX,DESUBI,DFCTR,DNRM2,DQRDC,DQRSL,DROT,
C DROTG,DSOLVE,DTRCO,DTRSL,DVEVTR,DWGHT,DZERO
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE LOCALLY CONSTRAINED STEPS S AND T, AND PHI(ALPHA)
C***END PROLOGUE DODSTP
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ ALPHA,EPSFCN,PHI,RCOND
INTEGER
+ IRANK,ISTOPC,LDTT,LDWD,LD2WD,LWRK,M,N,NP,NPP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DELTA(N,M),F(N,NQ),FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ OMEGA(NQ,NQ),QRAUX(NP),S(NP),SS(NP),
+ T(N,M),TFJACB(N,NQ,NP),TT(LDTT,M),U(NP),WD(LDWD,LD2WD,M),
+ WRK1(N,NQ,M),WRK2(N,NQ),WRK3(NP),WRK4(M,M),WRK5(M),WRK(LWRK)
INTEGER
+ KPVT(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ CO,ONE,SI,TEMP,ZERO
INTEGER
+ I,IMAX,INF,IPVT,J,K,K1,K2,KP,L
LOGICAL
+ ELIM,FORVCV
C...LOCAL ARRAYS
DOUBLE PRECISION
+ DUM(2)
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DNRM2
INTEGER
+ IDAMAX
EXTERNAL
+ DNRM2,IDAMAX
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DCHEX,DESUBI,DFCTR,DQRDC,DQRSL,DROT,DROTG,
+ DSOLVE,DTRCO,DTRSL,DVEVTR,DWGHT,DZERO
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,ONE
+ /0.0D0,1.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ALPHA: THE LEVENBERG-MARQUARDT PARAMETER.
C CO: THE COSINE FROM THE PLANE ROTATION.
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C DUM: A DUMMY ARRAY.
C ELIM: THE VARIABLE DESIGNATING WHETHER COLUMNS OF THE JACOBIAN
C WRT BETA HAVE BEEN ELIMINATED (ELIM=TRUE) OR NOT
C (ELIM=FALSE).
C EPSFCN: THE FUNCTION'S PRECISION.
C F: THE (WEIGHTED) ESTIMATED VALUES OF EPSILON.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FORVCV: THE VARIABLE DESIGNATING WHETHER THIS SUBROUTINE WAS
C CALLED TO SET UP FOR THE COVARIANCE MATRIX COMPUTATIONS
C (FORVCV=TRUE) OR NOT (FORVCV=FALSE).
C I: AN INDEXING VARIABLE.
C IMAX: THE INDEX OF THE ELEMENT OF U HAVING THE LARGEST ABSOLUTE
C VALUE.
C INF: THE RETURN CODE FROM LINPACK ROUTINES.
C IPVT: THE VARIABLE DESIGNATING WHETHER PIVOTING IS TO BE DONE.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOPC: THE VARIABLE DESIGNATING WHETHER THE COMPUTATIONS WERE
C STOPED DUE TO A NUMERICAL ERROR WITHIN SUBROUTINE DODSTP.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C K1: AN INDEXING VARIABLE.
C K2: AN INDEXING VARIABLE.
C KP: THE RANK OF THE JACOBIAN WRT BETA.
C KPVT: THE PIVOT VECTOR.
C L: AN INDEXING VARIABLE.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LWRK: THE LENGTH OF VECTOR WRK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C OMEGA: THE ARRAY DEFINED S.T.
C OMEGA*TRANS(OMEGA) = INV(I+FJACD*INV(E)*TRANS(FJACD))
C = (I-FJACD*INV(P)*TRANS(FJACD))
C WHERE E = D**2 + ALPHA*TT**2
C P = TRANS(FJACD)*FJACD + D**2 + ALPHA*TT**2
C ONE: THE VALUE 1.0D0.
C PHI: THE DIFFERENCE BETWEEN THE NORM OF THE SCALED STEP
C AND THE TRUST REGION DIAMETER.
C QRAUX: THE ARRAY REQUIRED TO RECOVER THE ORTHOGONAL PART OF THE
C Q-R DECOMPOSITION.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION NUMBER OF TFJACB.
C S: THE STEP FOR BETA.
C SI: THE SINE FROM THE PLANE ROTATION.
C SS: THE SCALING VALUES FOR THE UNFIXED BETAS.
C T: THE STEP FOR DELTA.
C TEMP: A TEMPORARY STORAGE LOCATION.
C TFJACB: THE ARRAY OMEGA*FJACB.
C TT: THE SCALING VALUES FOR DELTA.
C U: THE APPROXIMATE NULL VECTOR FOR TFJACB.
C WD: THE (SQUARED) DELTA WEIGHTS.
C WRK: A WORK ARRAY OF (LWRK) ELEMENTS,
C EQUIVALENCED TO WRK1 AND WRK2.
C WRK1: A WORK ARRAY OF (N BY NQ BY M) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK4: A WORK ARRAY OF (M BY M) ELEMENTS.
C WRK5: A WORK ARRAY OF (M) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODSTP
C COMPUTE LOOP PARAMETERS WHICH DEPEND ON WEIGHT STRUCTURE
C SET UP KPVT IF ALPHA = 0
IF (ALPHA.EQ.ZERO) THEN
KP = NPP
DO 10 K=1,NP
KPVT(K) = K
10 CONTINUE
ELSE
IF (NPP.GE.1) THEN
KP = NPP-IRANK
ELSE
KP = NPP
END IF
END IF
IF (ISODR) THEN
C T = WD * DELTA = D*G2
CALL DWGHT(N,M,WD,LDWD,LD2WD,DELTA,N,T,N)
DO 300 I=1,N
C COMPUTE WRK4, SUCH THAT
C TRANS(WRK4)*WRK4 = E = (D**2 + ALPHA*TT**2)
CALL DESUBI(N,M,WD,LDWD,LD2WD,ALPHA,TT,LDTT,I,WRK4)
CALL DFCTR(.FALSE.,WRK4,M,M,INF)
IF (INF.NE.0) THEN
ISTOPC = 60000
RETURN
END IF
C COMPUTE OMEGA, SUCH THAT
C TRANS(OMEGA)*OMEGA = I+FJACD*INV(E)*TRANS(FJACD)
C INV(TRANS(OMEGA)*OMEGA) = I-FJACD*INV(P)*TRANS(FJACD)
CALL DVEVTR(M,NQ,I,
+ FJACD,N,M, WRK4,M, WRK1,N,NQ, OMEGA,NQ, WRK5)
DO 110 L=1,NQ
OMEGA(L,L) = ONE + OMEGA(L,L)
110 CONTINUE
CALL DFCTR(.FALSE.,OMEGA,NQ,NQ,INF)
IF (INF.NE.0) THEN
ISTOPC = 60000
RETURN
END IF
C COMPUTE WRK1 = TRANS(FJACD)*(I-FJACD*INV(P)*TRANS(JFACD))
C = TRANS(FJACD)*INV(TRANS(OMEGA)*OMEGA)
DO 130 J=1,M
DO 120 L=1,NQ
WRK1(I,L,J) = FJACD(I,J,L)
120 CONTINUE
CALL DSOLVE(NQ,OMEGA,NQ,WRK1(I,1,J),N,4)
CALL DSOLVE(NQ,OMEGA,NQ,WRK1(I,1,J),N,2)
130 CONTINUE
C COMPUTE WRK5 = INV(E)*D*G2
DO 140 J=1,M
WRK5(J) = T(I,J)
140 CONTINUE
CALL DSOLVE(M,WRK4,M,WRK5,1,4)
CALL DSOLVE(M,WRK4,M,WRK5,1,2)
C COMPUTE TFJACB = INV(TRANS(OMEGA))*FJACB
DO 170 K=1,KP
DO 150 L=1,NQ
TFJACB(I,L,K) = FJACB(I,KPVT(K),L)
150 CONTINUE
CALL DSOLVE(NQ,OMEGA,NQ,TFJACB(I,1,K),N,4)
DO 160 L=1,NQ
IF (SS(1).GT.ZERO) THEN
TFJACB(I,L,K) = TFJACB(I,L,K)/SS(KPVT(K))
ELSE
TFJACB(I,L,K) = TFJACB(I,L,K)/ABS(SS(1))
END IF
160 CONTINUE
170 CONTINUE
C COMPUTE WRK2 = (V*INV(E)*D**2*G2 - G1)
DO 190 L=1,NQ
WRK2(I,L) = ZERO
DO 180 J=1,M
WRK2(I,L) = WRK2(I,L) + FJACD(I,J,L)*WRK5(J)
180 CONTINUE
WRK2(I,L) = WRK2(I,L) - F(I,L)
190 CONTINUE
C COMPUTE WRK2 = INV(TRANS(OMEGA))*(V*INV(E)*D**2*G2 - G1)
CALL DSOLVE(NQ,OMEGA,NQ,WRK2(I,1),N,4)
300 CONTINUE
ELSE
DO 360 I=1,N
DO 350 L=1,NQ
DO 340 K=1,KP
TFJACB(I,L,K) = FJACB(I,KPVT(K),L)
IF (SS(1).GT.ZERO) THEN
TFJACB(I,L,K) = TFJACB(I,L,K)/SS(KPVT(K))
ELSE
TFJACB(I,L,K) = TFJACB(I,L,K)/ABS(SS(1))
END IF
340 CONTINUE
WRK2(I,L) = -F(I,L)
350 CONTINUE
360 CONTINUE
END IF
C COMPUTE S
C DO QR FACTORIZATION (WITH COLUMN PIVOTING OF TRJACB IF ALPHA = 0)
IF (ALPHA.EQ.ZERO) THEN
IPVT = 1
DO 410 K=1,NP
KPVT(K) = 0
410 CONTINUE
ELSE
IPVT = 0
END IF
CALL DQRDC(TFJACB,N*NQ,N*NQ,KP,QRAUX,KPVT,WRK3,IPVT)
CALL DQRSL(TFJACB,N*NQ,N*NQ,KP,
+ QRAUX,WRK2,DUM,WRK2,DUM,DUM,DUM,1000,INF)
IF (INF.NE.0) THEN
ISTOPC = 60000
RETURN
END IF
C ELIMINATE ALPHA PART USING GIVENS ROTATIONS
IF (ALPHA.NE.ZERO) THEN
CALL DZERO(NPP,1,S,NPP)
DO 430 K1=1,KP
CALL DZERO(KP,1,WRK3,KP)
WRK3(K1) = SQRT(ALPHA)
DO 420 K2=K1,KP
CALL DROTG(TFJACB(K2,1,K2),WRK3(K2),CO,SI)
IF (KP-K2.GE.1) THEN
CALL DROT(KP-K2,TFJACB(K2,1,K2+1),N*NQ,
+ WRK3(K2+1),1,CO,SI)
END IF
TEMP = CO*WRK2(K2,1) + SI*S(KPVT(K1))
S(KPVT(K1)) = -SI*WRK2(K2,1) + CO*S(KPVT(K1))
WRK2(K2,1) = TEMP
420 CONTINUE
430 CONTINUE
END IF
C COMPUTE SOLUTION - ELIMINATE VARIABLES IF NECESSARY
IF (NPP.GE.1) THEN
IF (ALPHA.EQ.ZERO) THEN
KP = NPP
C ESTIMATE RCOND - U WILL CONTAIN APPROX NULL VECTOR
440 CALL DTRCO(TFJACB,N*NQ,KP,RCOND,U,1)
IF (RCOND.LE.EPSFCN) THEN
ELIM = .TRUE.
IMAX = IDAMAX(KP,U,1)
C IMAX IS THE COLUMN TO REMOVE - USE DCHEX AND FIX KPVT
IF (IMAX.NE.KP) THEN
CALL DCHEX(TFJACB,N*NQ,KP,IMAX,KP,WRK2,N*NQ,1,
+ QRAUX,WRK3,2)
K = KPVT(IMAX)
DO 450 I=IMAX,KP-1
KPVT(I) = KPVT(I+1)
450 CONTINUE
KPVT(KP) = K
END IF
KP = KP-1
ELSE
ELIM = .FALSE.
END IF
IF (ELIM .AND. KP.GE.1) THEN
GO TO 440
ELSE
IRANK = NPP-KP
END IF
END IF
END IF
IF (FORVCV) RETURN
C BACKSOLVE AND UNSCRAMBLE
IF (NPP.GE.1) THEN
DO 510 I=KP+1,NPP
WRK2(I,1) = ZERO
510 CONTINUE
IF (KP.GE.1) THEN
CALL DTRSL(TFJACB,N*NQ,KP,WRK2,01,INF)
IF (INF.NE.0) THEN
ISTOPC = 60000
RETURN
END IF
END IF
DO 520 I=1,NPP
IF (SS(1).GT.ZERO) THEN
S(KPVT(I)) = WRK2(I,1)/SS(KPVT(I))
ELSE
S(KPVT(I)) = WRK2(I,1)/ABS(SS(1))
END IF
520 CONTINUE
END IF
IF (ISODR) THEN
C NOTE: T AND WRK1 HAVE BEEN INITIALIZED ABOVE,
C WHERE T = WD * DELTA = D*G2
C WRK1 = TRANS(FJACD)*(I-FJACD*INV(P)*TRANS(JFACD))
DO 670 I=1,N
C COMPUTE WRK4, SUCH THAT
C TRANS(WRK4)*WRK4 = E = (D**2 + ALPHA*TT**2)
CALL DESUBI(N,M,WD,LDWD,LD2WD,ALPHA,TT,LDTT,I,WRK4)
CALL DFCTR(.FALSE.,WRK4,M,M,INF)
IF (INF.NE.0) THEN
ISTOPC = 60000
RETURN
END IF
C COMPUTE WRK5 = INV(E)*D*G2
DO 610 J=1,M
WRK5(J) = T(I,J)
610 CONTINUE
CALL DSOLVE(M,WRK4,M,WRK5,1,4)
CALL DSOLVE(M,WRK4,M,WRK5,1,2)
DO 640 L=1,NQ
WRK2(I,L) = F(I,L)
DO 620 K=1,NPP
WRK2(I,L) = WRK2(I,L) + FJACB(I,K,L)*S(K)
620 CONTINUE
DO 630 J=1,M
WRK2(I,L) = WRK2(I,L) - FJACD(I,J,L)*WRK5(J)
630 CONTINUE
640 CONTINUE
DO 660 J=1,M
WRK5(J) = ZERO
DO 650 L=1,NQ
WRK5(J) = WRK5(J) + WRK1(I,L,J)*WRK2(I,L)
650 CONTINUE
T(I,J) = -(WRK5(J) + T(I,J))
660 CONTINUE
CALL DSOLVE(M,WRK4,M,T(I,1),N,4)
CALL DSOLVE(M,WRK4,M,T(I,1),N,2)
670 CONTINUE
END IF
C COMPUTE PHI(ALPHA) FROM SCALED S AND T
CALL DWGHT(NPP,1,SS,NPP,1,S,NPP,WRK,NPP)
IF (ISODR) THEN
CALL DWGHT(N,M,TT,LDTT,1,T,N,WRK(NPP+1),N)
PHI = DNRM2(NPP+N*M,WRK,1)
ELSE
PHI = DNRM2(NPP,WRK,1)
END IF
RETURN
END
*DODVCV
SUBROUTINE DODVCV
+ (N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SSF,SS,TT,LDTT,DELTA,
+ EPSFCN,ISODR,
+ VCV,SD,
+ WRK6,OMEGA,U,QRAUX,JPVT,
+ S,T,IRANK,RCOND,RSS,IDF,RVAR,IFIXB,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
C***BEGIN PROLOGUE DODVCV
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DPODI,DODSTP
C***DATE WRITTEN 901207 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE COMPUTE COVARIANCE MATRIX OF ESTIMATED PARAMETERS
C***END PROLOGUE DODVCV
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ EPSFCN,RCOND,RSS,RVAR
INTEGER
+ IDF,IRANK,ISTOPC,LDTT,LDWD,LD2WD,LWRK,M,N,NP,NPP,NQ
LOGICAL
+ ISODR
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ DELTA(N,M),F(N,NQ),
+ FJACB(N,NP,NQ),FJACD(N,M,NQ),
+ OMEGA(NQ,NQ),QRAUX(NP),S(NP),SD(NP),SS(NP),SSF(NP),
+ T(N,M),TT(LDTT,M),U(NP),VCV(NP,NP),WD(LDWD,LD2WD,M),
+ WRK1(N,NQ,M),WRK2(N,NQ),WRK3(NP),WRK4(M,M),WRK5(M),
+ WRK6(N*NQ,NP),WRK(LWRK)
INTEGER
+ IFIXB(NP),JPVT(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEMP,ZERO
INTEGER
+ I,IUNFIX,J,JUNFIX,KP,L
LOGICAL
+ FORVCV
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DPODI,DODSTP
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,SQRT
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C DELTA: THE ESTIMATED ERRORS IN THE EXPLANATORY VARIABLES.
C EPSFCN: THE FUNCTION'S PRECISION.
C F: THE (WEIGHTED) ESTIMATED VALUES OF EPSILON.
C FJACB: THE JACOBIAN WITH RESPECT TO BETA.
C FJACD: THE JACOBIAN WITH RESPECT TO DELTA.
C FORVCV: THE VARIABLE DESIGNATING WHETHER SUBROUTINE DODSTP IS
C CALLED TO SET UP FOR THE COVARIANCE MATRIX COMPUTATIONS
C (FORVCV=TRUE) OR NOT (FORVCV=FALSE).
C I: AN INDEXING VARIABLE.
C IDF: THE DEGREES OF FREEDOM OF THE FIT, EQUAL TO THE NUMBER OF
C OBSERVATIONS WITH NONZERO WEIGHTED DERIVATIVES MINUS THE
C NUMBER OF PARAMETERS BEING ESTIMATED.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IMAX: THE INDEX OF THE ELEMENT OF U HAVING THE LARGEST ABSOLUTE
C VALUE.
C IRANK: THE RANK DEFICIENCY OF THE JACOBIAN WRT BETA.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C ISTOPC: THE VARIABLE DESIGNATING WHETHER THE COMPUTATIONS WERE
C STOPED DUE TO A NUMERICAL ERROR WITHIN SUBROUTINE DODSTP.
C IUNFIX: THE INDEX OF THE NEXT UNFIXED PARAMETER.
C J: AN INDEXING VARIABLE.
C JPVT: THE PIVOT VECTOR.
C JUNFIX: THE INDEX OF THE NEXT UNFIXED PARAMETER.
C KP: THE RANK OF THE JACOBIAN WRT BETA.
C L: AN INDEXING VARIABLE.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDWD: THE LEADING DIMENSION OF ARRAY WD.
C LD2WD: THE SECOND DIMENSION OF ARRAY WD.
C LWRK: THE LENGTH OF VECTOR WRK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NPP: THE NUMBER OF FUNCTION PARAMETERS BEING ESTIMATED.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C OMEGA: THE ARRAY DEFINED S.T.
C OMEGA*TRANS(OMEGA) = INV(I+FJACD*INV(E)*TRANS(FJACD))
C = (I-FJACD*INV(P)*TRANS(FJACD))
C WHERE E = D**2 + ALPHA*TT**2
C P = TRANS(FJACD)*FJACD + D**2 + ALPHA*TT**2
C QRAUX: THE ARRAY REQUIRED TO RECOVER THE ORTHOGONAL PART OF THE
C Q-R DECOMPOSITION.
C RCOND: THE APPROXIMATE RECIPROCAL CONDITION OF FJACB.
C RSS: THE RESIDUAL SUM OF SQUARES.
C RVAR: THE RESIDUAL VARIANCE.
C S: THE STEP FOR BETA.
C SD: THE STANDARD DEVIATIONS OF THE ESTIMATED BETAS.
C SS: THE SCALING VALUES FOR THE UNFIXED BETAS.
C SSF: THE SCALING VALUES USED FOR BETA.
C T: THE STEP FOR DELTA.
C TEMP: A TEMPORARY STORAGE LOCATION
C TT: THE SCALING VALUES FOR DELTA.
C U: THE APPROXIMATE NULL VECTOR FOR FJACB.
C VCV: THE COVARIANCE MATRIX OF THE ESTIMATED BETAS.
C WD: THE DELTA WEIGHTS.
C WRK: A WORK ARRAY OF (LWRK) ELEMENTS,
C EQUIVALENCED TO WRK1 AND WRK2.
C WRK1: A WORK ARRAY OF (N BY NQ BY M) ELEMENTS.
C WRK2: A WORK ARRAY OF (N BY NQ) ELEMENTS.
C WRK3: A WORK ARRAY OF (NP) ELEMENTS.
C WRK4: A WORK ARRAY OF (M BY M) ELEMENTS.
C WRK5: A WORK ARRAY OF (M) ELEMENTS.
C WRK6: A WORK ARRAY OF (N*NQ BY P) ELEMENTS.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DODVCV
FORVCV = .TRUE.
ISTOPC = 0
CALL DODSTP(N,M,NP,NQ,NPP,
+ F,FJACB,FJACD,
+ WD,LDWD,LD2WD,SS,TT,LDTT,DELTA,
+ ZERO,EPSFCN,ISODR,
+ WRK6,OMEGA,U,QRAUX,JPVT,
+ S,T,TEMP,IRANK,RCOND,FORVCV,
+ WRK1,WRK2,WRK3,WRK4,WRK5,WRK,LWRK,ISTOPC)
IF (ISTOPC.NE.0) THEN
RETURN
END IF
KP = NPP - IRANK
CALL DPODI (WRK6,N*NQ,KP,WRK3,1)
IDF = 0
DO 150 I=1,N
DO 120 J=1,NPP
DO 110 L=1,NQ
IF (FJACB(I,J,L).NE.ZERO) THEN
IDF = IDF + 1
GO TO 150
END IF
110 CONTINUE
120 CONTINUE
IF (ISODR) THEN
DO 140 J=1,M
DO 130 L=1,NQ
IF (FJACD(I,J,L).NE.ZERO) THEN
IDF = IDF + 1
GO TO 150
END IF
130 CONTINUE
140 CONTINUE
END IF
150 CONTINUE
IF (IDF.GT.KP) THEN
IDF = IDF - KP
RVAR = RSS/IDF
ELSE
IDF = 0
RVAR = RSS
END IF
C STORE VARIANCES IN SD, RESTORING ORIGINAL ORDER
DO 200 I=1,NP
SD(I) = ZERO
200 CONTINUE
DO 210 I=1,KP
SD(JPVT(I)) = WRK6(I,I)
210 CONTINUE
IF (NP.GT.NPP) THEN
JUNFIX = NPP
DO 220 J=NP,1,-1
IF (IFIXB(J).EQ.0) THEN
SD(J) = ZERO
ELSE
SD(J) = SD(JUNFIX)
JUNFIX = JUNFIX - 1
END IF
220 CONTINUE
END IF
C STORE COVARIANCE MATRIX IN VCV, RESTORING ORIGINAL ORDER
DO 310 I=1,NP
DO 300 J=1,I
VCV(I,J) = ZERO
300 CONTINUE
310 CONTINUE
DO 330 I=1,KP
DO 320 J=I+1,KP
IF (JPVT(I).GT.JPVT(J)) THEN
VCV(JPVT(I),JPVT(J))=WRK6(I,J)
ELSE
VCV(JPVT(J),JPVT(I))=WRK6(I,J)
END IF
320 CONTINUE
330 CONTINUE
IF (NP.GT.NPP) THEN
IUNFIX = NPP
DO 360 I=NP,1,-1
IF (IFIXB(I).EQ.0) THEN
DO 340 J=I,1,-1
VCV(I,J) = ZERO
340 CONTINUE
ELSE
JUNFIX = NPP
DO 350 J=NP,1,-1
IF (IFIXB(J).EQ.0) THEN
VCV(I,J) = ZERO
ELSE
VCV(I,J) = VCV(IUNFIX,JUNFIX)
JUNFIX = JUNFIX - 1
END IF
350 CONTINUE
IUNFIX = IUNFIX - 1
END IF
360 CONTINUE
END IF
DO 380 I=1,NP
VCV(I,I) = SD(I)
SD(I) = SQRT(RVAR*SD(I))
DO 370 J=1,I
VCV(J,I) = VCV(I,J)
370 CONTINUE
380 CONTINUE
C UNSCALE STANDARD ERRORS AND COVARIANCE MATRIX
DO 410 I=1,NP
IF (SSF(1).GT.ZERO) THEN
SD(I) = SD(I)/SSF(I)
ELSE
SD(I) = SD(I)/ABS(SSF(1))
END IF
DO 400 J=1,NP
IF (SSF(1).GT.ZERO) THEN
VCV(I,J) = VCV(I,J)/(SSF(I)*SSF(J))
ELSE
VCV(I,J) = VCV(I,J)/(SSF(1)*SSF(1))
END IF
400 CONTINUE
410 CONTINUE
RETURN
END
*DPACK
SUBROUTINE DPACK
+ (N2,N1,V1,V2,IFIX)
C***BEGIN PROLOGUE DPACK
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DCOPY
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SELECT THE UNFIXED ELEMENTS OF V2 AND RETURN THEM IN V1
C***END PROLOGUE DPACK
C...SCALAR ARGUMENTS
INTEGER
+ N1,N2
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ V1(N2),V2(N2)
INTEGER
+ IFIX(N2)
C...LOCAL SCALARS
INTEGER
+ I
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DCOPY
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C IFIX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF V2 ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C N1: THE NUMBER OF ITEMS IN V1.
C N2: THE NUMBER OF ITEMS IN V2.
C V1: THE VECTOR OF THE UNFIXED ITEMS FROM V2.
C V2: THE VECTOR OF THE FIXED AND UNFIXED ITEMS FROM WHICH THE
C UNFIXED ELEMENTS ARE TO BE EXTRACTED.
C***FIRST EXECUTABLE STATEMENT DPACK
N1 = 0
IF (IFIX(1).GE.0) THEN
DO 10 I=1,N2
IF (IFIX(I).NE.0) THEN
N1 = N1+1
V1(N1) = V2(I)
END IF
10 CONTINUE
ELSE
N1 = N2
CALL DCOPY(N2,V2,1,V1,1)
END IF
RETURN
END
*DPPNML
DOUBLE PRECISION FUNCTION DPPNML
+ (P)
C***BEGIN PROLOGUE DPPNML
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 901207 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***AUTHOR FILLIBEN, JAMES J.,
C STATISTICAL ENGINEERING DIVISION
C NATIONAL BUREAU OF STANDARDS
C WASHINGTON, D. C. 20234
C (ORIGINAL VERSION--JUNE 1972.
C (UPDATED --SEPTEMBER 1975,
C NOVEMBER 1975, AND
C OCTOBER 1976.
C***PURPOSE COMPUTE THE PERCENT POINT FUNCTION VALUE FOR THE
C NORMAL (GAUSSIAN) DISTRIBUTION WITH MEAN 0 AND STANDARD
C DEVIATION 1, AND WITH PROBABILITY DENSITY FUNCTION
C F(X) = (1/SQRT(2*PI))*EXP(-X*X/2).
C (ADAPTED FROM DATAPAC SUBROUTINE TPPF, WITH MODIFICATIONS
C TO FACILITATE CONVERSION TO DOUBLE PRECISION AUTOMATICALLY)
C***DESCRIPTION
C --THE CODING AS PRESENTED BELOW IS ESSENTIALLY
C IDENTICAL TO THAT PRESENTED BY ODEH AND EVANS
C AS ALGORTIHM 70 OF APPLIED STATISTICS.
C --AS POINTED OUT BY ODEH AND EVANS IN APPLIED
C STATISTICS, THEIR ALGORITHM REPRESENTES A
C SUBSTANTIAL IMPROVEMENT OVER THE PREVIOUSLY EMPLOYED
C HASTINGS APPROXIMATION FOR THE NORMAL PERCENT POINT
C FUNCTION, WITH ACCURACY IMPROVING FROM 4.5*(10**-4)
C TO 1.5*(10**-8).
C***REFERENCES ODEH AND EVANS, THE PERCENTAGE POINTS OF THE NORMAL
C DISTRIBUTION, ALGORTIHM 70, APPLIED STATISTICS, 1974,
C PAGES 96-97.
C EVANS, ALGORITHMS FOR MINIMAL DEGREE POLYNOMIAL AND
C RATIONAL APPROXIMATION, M. SC. THESIS, 1972,
C UNIVERSITY OF VICTORIA, B. C., CANADA.
C HASTINGS, APPROXIMATIONS FOR DIGITAL COMPUTERS, 1955,
C PAGES 113, 191, 192.
C NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS
C SERIES 55, 1964, PAGE 933, FORMULA 26.2.23.
C FILLIBEN, SIMPLE AND ROBUST LINEAR ESTIMATION OF THE
C LOCATION PARAMETER OF A SYMMETRIC DISTRIBUTION
C (UNPUBLISHED PH.D. DISSERTATION, PRINCETON
C UNIVERSITY), 1969, PAGES 21-44, 229-231.
C FILLIBEN, "THE PERCENT POINT FUNCTION",
C (UNPUBLISHED MANUSCRIPT), 1970, PAGES 28-31.
C JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE DISTRIBUTIONS,
C VOLUME 1, 1970, PAGES 40-111.
C KELLEY STATISTICAL TABLES, 1948.
C OWEN, HANDBOOK OF STATISTICAL TABLES, 1962, PAGES 3-16.
C PEARSON AND HARTLEY, BIOMETRIKA TABLES FOR
C STATISTICIANS, VOLUME 1, 1954, PAGES 104-113.
C***END PROLOGUE DPPNML
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ P
C...LOCAL SCALARS
DOUBLE PRECISION
+ ADEN,ANUM,HALF,ONE,P0,P1,P2,P3,P4,Q0,Q1,Q2,Q3,Q4,R,T,TWO,ZERO
C...INTRINSIC FUNCTIONS
INTRINSIC
+ LOG,SQRT
C...DATA STATEMENTS
DATA
+ P0,P1,P2,P3,P4
+ /-0.322232431088D0,-1.0D0,-0.342242088547D0,
+ -0.204231210245D-1,-0.453642210148D-4/
DATA
+ Q0,Q1,Q2,Q3,Q4
+ /0.993484626060D-1,0.588581570495D0,
+ 0.531103462366D0,0.103537752850D0,0.38560700634D-2/
DATA
+ ZERO,HALF,ONE,TWO
+ /0.0D0,0.5D0,1.0D0,2.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ADEN: A VALUE USED IN THE APPROXIMATION.
C ANUM: A VALUE USED IN THE APPROXIMATION.
C HALF: THE VALUE 0.5D0.
C ONE: THE VALUE 1.0D0.
C P: THE PROBABILITY AT WHICH THE PERCENT POINT IS TO BE
C EVALUATED. P MUST BE BETWEEN 0.0D0 AND 1.0D0, EXCLUSIVE.
C P0: A PARAMETER USED IN THE APPROXIMATION.
C P1: A PARAMETER USED IN THE APPROXIMATION.
C P2: A PARAMETER USED IN THE APPROXIMATION.
C P3: A PARAMETER USED IN THE APPROXIMATION.
C P4: A PARAMETER USED IN THE APPROXIMATION.
C Q0: A PARAMETER USED IN THE APPROXIMATION.
C Q1: A PARAMETER USED IN THE APPROXIMATION.
C Q2: A PARAMETER USED IN THE APPROXIMATION.
C Q3: A PARAMETER USED IN THE APPROXIMATION.
C Q4: A PARAMETER USED IN THE APPROXIMATION.
C R: THE PROBABILITY AT WHICH THE PERCENT POINT IS EVALUATED.
C T: A VALUE USED IN THE APPROXIMATION.
C TWO: THE VALUE 2.0D0.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DPPT
IF (P.EQ.HALF) THEN
DPPNML = ZERO
ELSE
R = P
IF (P.GT.HALF) R = ONE - R
T = SQRT(-TWO*LOG(R))
ANUM = ((((T*P4+P3)*T+P2)*T+P1)*T+P0)
ADEN = ((((T*Q4+Q3)*T+Q2)*T+Q1)*T+Q0)
DPPNML = T + (ANUM/ADEN)
IF (P.LT.HALF) DPPNML = -DPPNML
END IF
RETURN
END
*DPPT
DOUBLE PRECISION FUNCTION DPPT
+ (P, IDF)
C***BEGIN PROLOGUE DPPT
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DPPNML
C***DATE WRITTEN 901207 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***AUTHOR FILLIBEN, JAMES J.,
C STATISTICAL ENGINEERING DIVISION
C NATIONAL BUREAU OF STANDARDS
C WASHINGTON, D. C. 20234
C (ORIGINAL VERSION--OCTOBER 1975.)
C (UPDATED --NOVEMBER 1975.)
C***PURPOSE COMPUTE THE PERCENT POINT FUNCTION VALUE FOR THE
C STUDENT'S T DISTRIBUTION WITH IDF DEGREES OF FREEDOM.
C (ADAPTED FROM DATAPAC SUBROUTINE TPPF, WITH MODIFICATIONS
C TO FACILITATE CONVERSION TO DOUBLE PRECISION AUTOMATICALLY)
C***DESCRIPTION
C --FOR IDF = 1 AND IDF = 2, THE PERCENT POINT FUNCTION
C FOR THE T DISTRIBUTION EXISTS IN SIMPLE CLOSED FORM
C AND SO THE COMPUTED PERCENT POINTS ARE EXACT.
C --FOR IDF BETWEEN 3 AND 6, INCLUSIVELY, THE APPROXIMATION
C IS AUGMENTED BY 3 ITERATIONS OF NEWTON'S METHOD TO
C IMPROVE THE ACCURACY, ESPECIALLY FOR P NEAR 0 OR 1.
C***REFERENCES NATIONAL BUREAU OF STANDARDS APPLIED MATHMATICS
C SERIES 55, 1964, PAGE 949, FORMULA 26.7.5.
C JOHNSON AND KOTZ, CONTINUOUS UNIVARIATE DISTRIBUTIONS,
C VOLUME 2, 1970, PAGE 102, FORMULA 11.
C FEDERIGHI, "EXTENDED TABLES OF THE PERCENTAGE POINTS
C OF STUDENT"S T DISTRIBUTION, JOURNAL OF THE AMERICAN
C STATISTICAL ASSOCIATION, 1969, PAGES 683-688.
C HASTINGS AND PEACOCK, STATISTICAL DISTRIBUTIONS, A
C HANDBOOK FOR STUDENTS AND PRACTITIONERS, 1975,
C PAGES 120-123.
C***END PROLOGUE DPPT
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ P
INTEGER
+ IDF
C...LOCAL SCALARS
DOUBLE PRECISION
+ ARG,B21,B31,B32,B33,B34,B41,B42,B43,B44,B45,
+ B51,B52,B53,B54,B55,B56,C,CON,D1,D3,D5,D7,D9,DF,EIGHT,FIFTN,
+ HALF,ONE,PI,PPFN,S,TERM1,TERM2,TERM3,TERM4,TERM5,THREE,TWO,
+ Z,ZERO
INTEGER
+ IPASS,MAXIT
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DPPNML
EXTERNAL
+ DPPNML
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ATAN,COS,SIN,SQRT
C...DATA STATEMENTS
DATA
+ B21
+ /4.0D0/
DATA
+ B31, B32, B33, B34
+ /96.0D0,5.0D0,16.0D0,3.0D0/
DATA
+ B41, B42, B43, B44, B45
+ /384.0D0,3.0D0,19.0D0,17.0D0,-15.0D0/
DATA
+ B51,B52,B53,B54,B55,B56
+ /9216.0D0,79.0D0,776.0D0,1482.0D0,-1920.0D0,-945.0D0/
DATA
+ ZERO,HALF,ONE,TWO,THREE,EIGHT,FIFTN
+ /0.0D0,0.5D0,1.0D0,2.0D0,3.0D0,8.0D0,15.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ARG: A VALUE USED IN THE APPROXIMATION.
C B21: A PARAMETER USED IN THE APPROXIMATION.
C B31: A PARAMETER USED IN THE APPROXIMATION.
C B32: A PARAMETER USED IN THE APPROXIMATION.
C B33: A PARAMETER USED IN THE APPROXIMATION.
C B34: A PARAMETER USED IN THE APPROXIMATION.
C B41: A PARAMETER USED IN THE APPROXIMATION.
C B42: A PARAMETER USED IN THE APPROXIMATION.
C B43: A PARAMETER USED IN THE APPROXIMATION.
C B44: A PARAMETER USED IN THE APPROXIMATION.
C B45: A PARAMETER USED IN THE APPROXIMATION.
C B51: A PARAMETER USED IN THE APPROXIMATION.
C B52: A PARAMETER USED IN THE APPROXIMATION.
C B53: A PARAMETER USED IN THE APPROXIMATION.
C B54: A PARAMETER USED IN THE APPROXIMATION.
C B55: A PARAMETER USED IN THE APPROXIMATION.
C B56: A PARAMETER USED IN THE APPROXIMATION.
C C: A VALUE USED IN THE APPROXIMATION.
C CON: A VALUE USED IN THE APPROXIMATION.
C DF: THE DEGREES OF FREEDOM.
C D1: A VALUE USED IN THE APPROXIMATION.
C D3: A VALUE USED IN THE APPROXIMATION.
C D5: A VALUE USED IN THE APPROXIMATION.
C D7: A VALUE USED IN THE APPROXIMATION.
C D9: A VALUE USED IN THE APPROXIMATION.
C EIGHT: THE VALUE 8.0D0.
C FIFTN: THE VALUE 15.0D0.
C HALF: THE VALUE 0.5D0.
C IDF: THE (POSITIVE INTEGER) DEGREES OF FREEDOM.
C IPASS: A VALUE USED IN THE APPROXIMATION.
C MAXIT: THE MAXIMUM NUMBER OF ITERATIONS ALLOWED FOR THE APPROX.
C ONE: THE VALUE 1.0D0.
C P: THE PROBABILITY AT WHICH THE PERCENT POINT IS TO BE
C EVALUATED. P MUST LIE BETWEEN 0.0DO AND 1.0D0, EXCLUSIVE.
C PI: THE VALUE OF PI.
C PPFN: THE NORMAL PERCENT POINT VALUE.
C S: A VALUE USED IN THE APPROXIMATION.
C TERM1: A VALUE USED IN THE APPROXIMATION.
C TERM2: A VALUE USED IN THE APPROXIMATION.
C TERM3: A VALUE USED IN THE APPROXIMATION.
C TERM4: A VALUE USED IN THE APPROXIMATION.
C TERM5: A VALUE USED IN THE APPROXIMATION.
C THREE: THE VALUE 3.0D0.
C TWO: THE VALUE 2.0D0.
C Z: A VALUE USED IN THE APPROXIMATION.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DPPT
PI = 3.141592653589793238462643383279D0
DF = IDF
MAXIT = 5
IF (IDF.LE.0) THEN
C TREAT THE IDF < 1 CASE
DPPT = ZERO
ELSE IF (IDF.EQ.1) THEN
C TREAT THE IDF = 1 (CAUCHY) CASE
ARG = PI*P
DPPT = -COS(ARG)/SIN(ARG)
ELSE IF (IDF.EQ.2) THEN
C TREAT THE IDF = 2 CASE
TERM1 = SQRT(TWO)/TWO
TERM2 = TWO*P - ONE
TERM3 = SQRT(P*(ONE-P))
DPPT = TERM1*TERM2/TERM3
ELSE IF (IDF.GE.3) THEN
C TREAT THE IDF GREATER THAN OR EQUAL TO 3 CASE
PPFN = DPPNML(P)
D1 = PPFN
D3 = PPFN**3
D5 = PPFN**5
D7 = PPFN**7
D9 = PPFN**9
TERM1 = D1
TERM2 = (ONE/B21)*(D3+D1)/DF
TERM3 = (ONE/B31)*(B32*D5+B33*D3+B34*D1)/(DF**2)
TERM4 = (ONE/B41)*(B42*D7+B43*D5+B44*D3+B45*D1)/(DF**3)
TERM5 = (ONE/B51)*(B52*D9+B53*D7+B54*D5+B55*D3+B56*D1)/(DF**4)
DPPT = TERM1 + TERM2 + TERM3 + TERM4 + TERM5
IF (IDF.EQ.3) THEN
C AUGMENT THE RESULTS FOR THE IDF = 3 CASE
CON = PI*(P-HALF)
ARG = DPPT/SQRT(DF)
Z = ATAN(ARG)
DO 70 IPASS=1,MAXIT
S = SIN(Z)
C = COS(Z)
Z = Z - (Z+S*C-CON)/(TWO*C**2)
70 CONTINUE
DPPT = SQRT(DF)*S/C
ELSE IF (IDF.EQ.4) THEN
C AUGMENT THE RESULTS FOR THE IDF = 4 CASE
CON = TWO*(P-HALF)
ARG = DPPT/SQRT(DF)
Z = ATAN(ARG)
DO 90 IPASS=1,MAXIT
S = SIN(Z)
C = COS(Z)
Z = Z - ((ONE+HALF*C**2)*S-CON)/((ONE+HALF)*C**3)
90 CONTINUE
DPPT = SQRT(DF)*S/C
ELSE IF (IDF.EQ.5) THEN
C AUGMENT THE RESULTS FOR THE IDF = 5 CASE
CON = PI*(P-HALF)
ARG = DPPT/SQRT(DF)
Z = ATAN(ARG)
DO 110 IPASS=1,MAXIT
S = SIN(Z)
C = COS(Z)
Z = Z - (Z+(C+(TWO/THREE)*C**3)*S-CON)/
+ ((EIGHT/THREE)*C**4)
110 CONTINUE
DPPT = SQRT(DF)*S/C
ELSE IF (IDF.EQ.6) THEN
C AUGMENT THE RESULTS FOR THE IDF = 6 CASE
CON = TWO*(P-HALF)
ARG = DPPT/SQRT(DF)
Z = ATAN(ARG)
DO 130 IPASS=1,MAXIT
S = SIN(Z)
C = COS(Z)
Z = Z - ((ONE+HALF*C**2 + (THREE/EIGHT)*C**4)*S-CON)/
+ ((FIFTN/EIGHT)*C**5)
130 CONTINUE
DPPT = SQRT(DF)*S/C
END IF
END IF
RETURN
END
*DPVB
SUBROUTINE DPVB
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVB,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DPVB
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE THE NROW-TH FUNCTION VALUE USING BETA(J) + STP
C***END PROLOGUE DPVB
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PVB,STP
INTEGER
+ ISTOP,J,LDIFX,LQ,M,N,NFEV,NP,NQ,NROW
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ BETAJ
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C BETAJ: THE CURRENT ESTIMATE OF THE JTH PARAMETER.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE INDEPENDENT VARIABLE ARRAY AT
C WHICH THE DERIVATIVE IS TO BE CHECKED.
C PVB: THE FUNCTION VALUE FOR THE SELECTED OBSERVATION & RESPONSE.
C STP: THE STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C XPLUSD: THE VALUES OF X + DELTA.
C***FIRST EXECUTABLE STATEMENT DPVB
C COMPUTE PREDICTED VALUES
BETAJ = BETA(J)
BETA(J) = BETA(J) + STP
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 003,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.EQ.0) THEN
NFEV = NFEV + 1
ELSE
RETURN
END IF
BETA(J) = BETAJ
PVB = WRK2(NROW,LQ)
RETURN
END
*DPVD
SUBROUTINE DPVD
+ (FCN,
+ N,M,NP,NQ,
+ BETA,XPLUSD,IFIXB,IFIXX,LDIFX,
+ NROW,J,LQ,STP,
+ ISTOP,NFEV,PVD,
+ WRK1,WRK2,WRK6)
C***BEGIN PROLOGUE DPVD
C***REFER TO DODR,DODRC
C***ROUTINES CALLED FCN
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE NROW-TH FUNCTION VALUE USING
C X(NROW,J) + DELTA(NROW,J) + STP
C***END PROLOGUE DPVD
C...SCALAR ARGUMENTS
DOUBLE PRECISION
+ PVD,STP
INTEGER
+ ISTOP,J,LDIFX,LQ,M,N,NFEV,NP,NQ,NROW
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),WRK1(N,M,NQ),WRK2(N,NQ),WRK6(N,NP,NQ),XPLUSD(N,M)
INTEGER
+ IFIXB(NP),IFIXX(LDIFX,M)
C...SUBROUTINE ARGUMENTS
EXTERNAL
+ FCN
C...LOCAL SCALARS
DOUBLE PRECISION
+ XPDJ
C...ROUTINE NAMES USED AS SUBPROGRAM ARGUMENTS
C FCN: THE USER-SUPPLIED SUBROUTINE FOR EVALUATING THE MODEL.
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C IFIXB: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF BETA ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C IFIXX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF X ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ISTOP: THE VARIABLE DESIGNATING WHETHER THERE ARE PROBLEMS
C COMPUTING THE FUNCTION AT THE CURRENT BETA AND DELTA.
C J: THE INDEX OF THE PARTIAL DERIVATIVE BEING EXAMINED.
C LDIFX: THE LEADING DIMENSION OF ARRAY IFIXX.
C LQ: THE RESPONSE CURRENTLY BEING EXAMINED.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NFEV: THE NUMBER OF FUNCTION EVALUATIONS.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C NROW: THE ROW NUMBER OF THE INDEPENDENT VARIABLE ARRAY AT
C WHICH THE DERIVATIVE IS TO BE CHECKED.
C PVD: THE FUNCTION VALUE FOR THE SELECTED OBSERVATION & RESPONSE.
C STP: THE STEP SIZE FOR THE FINITE DIFFERENCE DERIVATIVE.
C XPDJ: THE (NROW,J)TH ELEMENT OF XPLUSD.
C XPLUSD: THE VALUES OF X + DELTA.
C***FIRST EXECUTABLE STATEMENT DPVD
C COMPUTE PREDICTED VALUES
XPDJ = XPLUSD(NROW,J)
XPLUSD(NROW,J) = XPLUSD(NROW,J) + STP
ISTOP = 0
CALL FCN(N,M,NP,NQ,
+ N,M,NP,
+ BETA,XPLUSD,
+ IFIXB,IFIXX,LDIFX,
+ 003,WRK2,WRK6,WRK1,
+ ISTOP)
IF (ISTOP.EQ.0) THEN
NFEV = NFEV + 1
ELSE
RETURN
END IF
XPLUSD(NROW,J) = XPDJ
PVD = WRK2(NROW,LQ)
RETURN
END
*DSCALE
SUBROUTINE DSCALE
+ (N,M,SCL,LDSCL,T,LDT,SCLT,LDSCLT)
C***BEGIN PROLOGUE DSCALE
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SCALE T BY THE INVERSE OF SCL, I.E., COMPUTE T/SCL
C***END PROLOGUE DSCALE
C...SCALAR ARGUMENTS
INTEGER
+ LDT,LDSCL,LDSCLT,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ T(LDT,M),SCL(LDSCL,M),SCLT(LDSCLT,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ONE,TEMP,ZERO
INTEGER
+ I,J
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS
C...DATA STATEMENTS
DATA
+ ONE,ZERO
+ /1.0D0,0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C LDSCL: THE LEADING DIMENSION OF ARRAY SCL.
C LDSCLT: THE LEADING DIMENSION OF ARRAY SCLT.
C LDT: THE LEADING DIMENSION OF ARRAY T.
C M: THE NUMBER OF COLUMNS OF DATA IN T.
C N: THE NUMBER OF ROWS OF DATA IN T.
C ONE: THE VALUE 1.0D0.
C SCL: THE SCALE VALUES.
C SCLT: THE INVERSELY SCALED MATRIX.
C T: THE ARRAY TO BE INVERSELY SCALED BY SCL.
C TEMP: A TEMPORARY SCALAR.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DSCALE
IF (N.EQ.0 .OR. M.EQ.0) RETURN
IF (SCL(1,1).GE.ZERO) THEN
IF (LDSCL.GE.N) THEN
DO 80 J=1,M
DO 70 I=1,N
SCLT(I,J) = T(I,J)/SCL(I,J)
70 CONTINUE
80 CONTINUE
ELSE
DO 100 J=1,M
TEMP = ONE/SCL(1,J)
DO 90 I=1,N
SCLT(I,J) = T(I,J)*TEMP
90 CONTINUE
100 CONTINUE
END IF
ELSE
TEMP = ONE/ABS(SCL(1,1))
DO 120 J=1,M
DO 110 I=1,N
SCLT(I,J) = T(I,J)*TEMP
110 CONTINUE
120 CONTINUE
END IF
RETURN
END
*DSCLB
SUBROUTINE DSCLB
+ (NP,BETA,SSF)
C***BEGIN PROLOGUE DSCLB
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SELECT SCALING VALUES FOR BETA ACCORDING TO THE
C ALGORITHM GIVEN IN THE ODRPACK REFERENCE GUIDE
C***END PROLOGUE DSCLB
C...SCALAR ARGUMENTS
INTEGER
+ NP
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ BETA(NP),SSF(NP)
C...LOCAL SCALARS
DOUBLE PRECISION
+ BMAX,BMIN,ONE,TEN,ZERO
INTEGER
+ K
LOGICAL
+ BIGDIF
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,LOG10,MAX,MIN,SQRT
C...DATA STATEMENTS
DATA
+ ZERO,ONE,TEN
+ /0.0D0,1.0D0,10.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BETA: THE FUNCTION PARAMETERS.
C BIGDIF: THE VARIABLE DESIGNATING WHETHER THERE IS A SIGNIFICANT
C DIFFERENCE IN THE MAGNITUDES OF THE NONZERO ELEMENTS OF
C BETA (BIGDIF=.TRUE.) OR NOT (BIGDIF=.FALSE.).
C BMAX: THE LARGEST NONZERO MAGNITUDE.
C BMIN: THE SMALLEST NONZERO MAGNITUDE.
C K: AN INDEXING VARIABLE.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C ONE: THE VALUE 1.0D0.
C SSF: THE SCALING VALUES FOR BETA.
C TEN: THE VALUE 10.0D0.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DSCLB
BMAX = ABS(BETA(1))
DO 10 K=2,NP
BMAX = MAX(BMAX,ABS(BETA(K)))
10 CONTINUE
IF (BMAX.EQ.ZERO) THEN
C ALL INPUT VALUES OF BETA ARE ZERO
DO 20 K=1,NP
SSF(K) = ONE
20 CONTINUE
ELSE
C SOME OF THE INPUT VALUES ARE NONZERO
BMIN = BMAX
DO 30 K=1,NP
IF (BETA(K).NE.ZERO) THEN
BMIN = MIN(BMIN,ABS(BETA(K)))
END IF
30 CONTINUE
BIGDIF = LOG10(BMAX)-LOG10(BMIN).GE.ONE
DO 40 K=1,NP
IF (BETA(K).EQ.ZERO) THEN
SSF(K) = TEN/BMIN
ELSE
IF (BIGDIF) THEN
SSF(K) = ONE/ABS(BETA(K))
ELSE
SSF(K) = ONE/BMAX
END IF
END IF
40 CONTINUE
END IF
RETURN
END
*DSCLD
SUBROUTINE DSCLD
+ (N,M,X,LDX,TT,LDTT)
C***BEGIN PROLOGUE DSCLD
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SELECT SCALING VALUES FOR DELTA ACCORDING TO THE
C ALGORITHM GIVEN IN THE ODRPACK REFERENCE GUIDE
C***END PROLOGUE DSCLD
C...SCALAR ARGUMENTS
INTEGER
+ LDTT,LDX,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ TT(LDTT,M),X(LDX,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ONE,TEN,XMAX,XMIN,ZERO
INTEGER
+ I,J
LOGICAL
+ BIGDIF
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS,LOG10,MAX,MIN
C...DATA STATEMENTS
DATA
+ ZERO,ONE,TEN
+ /0.0D0,1.0D0,10.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C BIGDIF: THE VARIABLE DESIGNATING WHETHER THERE IS A SIGNIFICANT
C DIFFERENCE IN THE MAGNITUDES OF THE NONZERO ELEMENTS OF
C X (BIGDIF=.TRUE.) OR NOT (BIGDIF=.FALSE.).
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C LDTT: THE LEADING DIMENSION OF ARRAY TT.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C ONE: THE VALUE 1.0D0.
C TT: THE SCALING VALUES FOR DELTA.
C X: THE INDEPENDENT VARIABLE.
C XMAX: THE LARGEST NONZERO MAGNITUDE.
C XMIN: THE SMALLEST NONZERO MAGNITUDE.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DSCLD
DO 50 J=1,M
XMAX = ABS(X(1,J))
DO 10 I=2,N
XMAX = MAX(XMAX,ABS(X(I,J)))
10 CONTINUE
IF (XMAX.EQ.ZERO) THEN
C ALL INPUT VALUES OF X(I,J), I=1,...,N, ARE ZERO
DO 20 I=1,N
TT(I,J) = ONE
20 CONTINUE
ELSE
C SOME OF THE INPUT VALUES ARE NONZERO
XMIN = XMAX
DO 30 I=1,N
IF (X(I,J).NE.ZERO) THEN
XMIN = MIN(XMIN,ABS(X(I,J)))
END IF
30 CONTINUE
BIGDIF = LOG10(XMAX)-LOG10(XMIN).GE.ONE
DO 40 I=1,N
IF (X(I,J).NE.ZERO) THEN
IF (BIGDIF) THEN
TT(I,J) = ONE/ABS(X(I,J))
ELSE
TT(I,J) = ONE/XMAX
END IF
ELSE
TT(I,J) = TEN/XMIN
END IF
40 CONTINUE
END IF
50 CONTINUE
RETURN
END
*DSETN
SUBROUTINE DSETN
+ (N,M,X,LDX,NROW)
C***BEGIN PROLOGUE DSETN
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SELECT THE ROW AT WHICH THE DERIVATIVE WILL BE CHECKED
C***END PROLOGUE DSETN
C...SCALAR ARGUMENTS
INTEGER
+ LDX,M,N,NROW
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ X(LDX,M)
C...LOCAL SCALARS
INTEGER
+ I,J
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEX VARIABLE.
C J: AN INDEX VARIABLE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NROW: THE SELECTED ROW NUMBER OF THE INDEPENDENT VARIABLE.
C X: THE INDEPENDENT VARIABLE.
C***FIRST EXECUTABLE STATEMENT DSETN
IF ((NROW.GE.1) .AND. (NROW.LE.N)) RETURN
C SELECT FIRST ROW OF INDEPENDENT VARIABLES WHICH CONTAINS NO ZEROS
C IF THERE IS ONE, OTHERWISE FIRST ROW IS USED.
DO 20 I = 1, N
DO 10 J = 1, M
IF (X(I,J).EQ.0.0) GO TO 20
10 CONTINUE
NROW = I
RETURN
20 CONTINUE
NROW = 1
RETURN
END
*DSOLVE
SUBROUTINE DSOLVE(N,T,LDT,B,LDB,JOB)
C***BEGIN PROLOGUE DSOLVE
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DAXPY,DDOT
C***DATE WRITTEN 920220 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE SOLVE SYSTEMS OF THE FORM
C T * X = B OR TRANS(T) * X = B
C WHERE T IS AN UPPER OR LOWER TRIANGULAR MATRIX OF ORDER N,
C AND THE SOLUTION X OVERWRITES THE RHS B.
C (ADAPTED FROM LINPACK SUBROUTINE DTRSL)
C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C *LINPACK USERS GUIDE*, SIAM, 1979.
C***END PROLOGUE DSOLVE
C...SCALAR ARGUMENTS
INTEGER
+ JOB,LDB,LDT,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ B(LDB,N),T(LDT,N)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEMP,ZERO
INTEGER
+ J1,J,JN
C...EXTERNAL FUNCTIONS
DOUBLE PRECISION
+ DDOT
EXTERNAL
+ DDOT
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DAXPY
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C B: ON INPUT: THE RIGHT HAND SIDE; ON EXIT: THE SOLUTION
C J1: THE FIRST NONZERO ENTRY IN T.
C J: AN INDEXING VARIABLE.
C JN: THE LAST NONZERO ENTRY IN T.
C JOB: WHAT KIND OF SYSTEM IS TO BE SOLVED, WHERE IF JOB IS
C 1 SOLVE T*X=B, T LOWER TRIANGULAR,
C 2 SOLVE T*X=B, T UPPER TRIANGULAR,
C 3 SOLVE TRANS(T)*X=B, T LOWER TRIANGULAR,
C 4 SOLVE TRANS(T)*X=B, T UPPER TRIANGULAR.
C LDB: THE LEADING DIMENSION OF ARRAY B.
C LDT: THE LEADING DIMENSION OF ARRAY T.
C N: THE NUMBER OF ROWS AND COLUMNS OF DATA IN ARRAY T.
C T: THE UPPER OR LOWER TRIDIAGONAL SYSTEM.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DSOLVE
C FIND FIRST NONZERO DIAGONAL ENTRY IN T
J1 = 0
DO 10 J=1,N
IF (J1.EQ.0 .AND. T(J,J).NE.ZERO) THEN
J1 = J
ELSE IF (T(J,J).EQ.ZERO) THEN
B(1,J) = ZERO
END IF
10 CONTINUE
IF (J1.EQ.0) RETURN
C FIND LAST NONZERO DIAGONAL ENTRY IN T
JN = 0
DO 20 J=N,J1,-1
IF (JN.EQ.0 .AND. T(J,J).NE.ZERO) THEN
JN = J
ELSE IF (T(J,J).EQ.ZERO) THEN
B(1,J) = ZERO
END IF
20 CONTINUE
IF (JOB.EQ.1) THEN
C SOLVE T*X=B FOR T LOWER TRIANGULAR
B(1,J1) = B(1,J1)/T(J1,J1)
DO 30 J = J1+1, JN
TEMP = -B(1,J-1)
CALL DAXPY(JN-J+1,TEMP,T(J,J-1),1,B(1,J),LDB)
IF (T(J,J).NE.ZERO) THEN
B(1,J) = B(1,J)/T(J,J)
ELSE
B(1,J) = ZERO
END IF
30 CONTINUE
ELSE IF (JOB.EQ.2) THEN
C SOLVE T*X=B FOR T UPPER TRIANGULAR.
B(1,JN) = B(1,JN)/T(JN,JN)
DO 40 J = JN-1,J1,-1
TEMP = -B(1,J+1)
CALL DAXPY(J,TEMP,T(1,J+1),1,B(1,1),LDB)
IF (T(J,J).NE.ZERO) THEN
B(1,J) = B(1,J)/T(J,J)
ELSE
B(1,J) = ZERO
END IF
40 CONTINUE
ELSE IF (JOB.EQ.3) THEN
C SOLVE TRANS(T)*X=B FOR T LOWER TRIANGULAR.
B(1,JN) = B(1,JN)/T(JN,JN)
DO 50 J = JN-1,J1,-1
B(1,J) = B(1,J) - DDOT(JN-J+1,T(J+1,J),1,B(1,J+1),LDB)
IF (T(J,J).NE.ZERO) THEN
B(1,J) = B(1,J)/T(J,J)
ELSE
B(1,J) = ZERO
END IF
50 CONTINUE
ELSE IF (JOB.EQ.4) THEN
C SOLVE TRANS(T)*X=B FOR T UPPER TRIANGULAR.
B(1,J1) = B(1,J1)/T(J1,J1)
DO 60 J = J1+1,JN
B(1,J) = B(1,J) - DDOT(J-1,T(1,J),1,B(1,1),LDB)
IF (T(J,J).NE.ZERO) THEN
B(1,J) = B(1,J)/T(J,J)
ELSE
B(1,J) = ZERO
END IF
60 CONTINUE
END IF
RETURN
END
*DUNPAC
SUBROUTINE DUNPAC
+ (N2,V1,V2,IFIX)
C***BEGIN PROLOGUE DUNPAC
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DCOPY
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COPY THE ELEMENTS OF V1 INTO THE LOCATIONS OF V2 WHICH ARE
C UNFIXED
C***END PROLOGUE DUNPAC
C...SCALAR ARGUMENTS
INTEGER
+ N2
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ V1(N2),V2(N2)
INTEGER
+ IFIX(N2)
C...LOCAL SCALARS
INTEGER
+ I,N1
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DCOPY
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C IFIX: THE VALUES DESIGNATING WHETHER THE ELEMENTS OF V2 ARE
C FIXED AT THEIR INPUT VALUES OR NOT.
C ODRPACK REFERENCE GUIDE.)
C N1: THE NUMBER OF ITEMS IN V1.
C N2: THE NUMBER OF ITEMS IN V2.
C V1: THE VECTOR OF THE UNFIXED ITEMS.
C V2: THE VECTOR OF THE FIXED AND UNFIXED ITEMS INTO WHICH THE
C ELEMENTS OF V1 ARE TO BE INSERTED.
C***FIRST EXECUTABLE STATEMENT DUNPAC
N1 = 0
IF (IFIX(1).GE.0) THEN
DO 10 I = 1,N2
IF (IFIX(I).NE.0) THEN
N1 = N1 + 1
V2(I) = V1(N1)
END IF
10 CONTINUE
ELSE
N1 = N2
CALL DCOPY(N2,V1,1,V2,1)
END IF
RETURN
END
*DVEVTR
SUBROUTINE DVEVTR
+ (M,NQ,INDX,
+ V,LDV,LD2V, E,LDE, VE,LDVE,LD2VE, VEV,LDVEV,
+ WRK5)
C***BEGIN PROLOGUE DVEVTR
C***REFER TO DODR,DODRC
C***ROUTINES CALLED DSOLVE
C***DATE WRITTEN 910613 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE V*E*TRANS(V) FOR THE (INDX)TH M BY NQ ARRAY IN V
C***END PROLOGUE DVEVTR
C...SCALAR ARGUMENTS
INTEGER
+ INDX,LDE,LDV,LDVE,LDVEV,LD2V,LD2VE,M,NQ
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ E(LDE,M),V(LDV,LD2V,NQ),VE(LDVE,LD2VE,M),VEV(LDVEV,NQ),WRK5(M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ZERO
INTEGER
+ J,L1,L2
C...EXTERNAL SUBROUTINES
EXTERNAL
+ DSOLVE
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C INDX: THE ROW IN V IN WHICH THE M BY NQ ARRAY IS STORED.
C J: AN INDEXING VARIABLE.
C LDE: THE LEADING DIMENSION OF ARRAY E.
C LDV: THE LEADING DIMENSION OF ARRAY V.
C LDVE: THE LEADING DIMENSION OF ARRAY VE.
C LDVEV: THE LEADING DIMENSION OF ARRAY VEV.
C LD2V: THE SECOND DIMENSION OF ARRAY V.
C L1: AN INDEXING VARIABLE.
C L2: AN INDEXING VARIABLE.
C M: THE NUMBER OF COLUMNS OF DATA IN THE INDEPENDENT VARIABLE.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C E: THE M BY M MATRIX OF THE FACTORS SO ETE = (D**2 + ALPHA*T**2).
C V: AN ARRAY OF NQ BY M MATRICES.
C VE: THE NQ BY M ARRAY VE = V * INV(E)
C VEV: THE NQ BY NQ ARRAY VEV = V * INV(ETE) * TRANS(V).
C WRK5: AN M WORK VECTOR.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DVEVTR
IF (NQ.EQ.0 .OR. M.EQ.0) RETURN
DO 140 L1 = 1,NQ
DO 110 J = 1,M
WRK5(J) = V(INDX,J,L1)
110 CONTINUE
CALL DSOLVE(M,E,LDE,WRK5,1,4)
DO 120 J = 1,M
VE(INDX,L1,J) = WRK5(J)
120 CONTINUE
140 CONTINUE
DO 230 L1 = 1,NQ
DO 220 L2 = 1,L1
VEV(L1,L2) = ZERO
DO 210 J = 1,M
VEV(L1,L2) = VEV(L1,L2) + VE(INDX,L1,J)*VE(INDX,L2,J)
210 CONTINUE
VEV(L2,L1) = VEV(L1,L2)
220 CONTINUE
230 CONTINUE
RETURN
END
*DWGHT
SUBROUTINE DWGHT
+ (N,M,WT,LDWT,LD2WT,T,LDT,WTT,LDWTT)
C***BEGIN PROLOGUE DWGHT
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SCALE MATRIX T USING WT, I.E., COMPUTE WTT = WT*T
C***END PROLOGUE DWGHT
C...SCALAR ARGUMENTS
INTEGER
+ LDT,LDWT,LDWTT,LD2WT,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ T(LDT,M),WT(LDWT,LD2WT,M),WTT(LDWTT,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ TEMP,ZERO
INTEGER
+ I,J,K
C...INTRINSIC FUNCTIONS
INTRINSIC
+ ABS
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C K: AN INDEXING VARIABLE.
C LDT: THE LEADING DIMENSION OF ARRAY T.
C LDWT: THE LEADING DIMENSION OF ARRAY WT.
C LDWTT: THE LEADING DIMENSION OF ARRAY WTT.
C LD2WT: THE SECOND DIMENSION OF ARRAY WT.
C M: THE NUMBER OF COLUMNS OF DATA IN T.
C N: THE NUMBER OF ROWS OF DATA IN T.
C T: THE ARRAY BEING SCALED BY WT.
C TEMP: A TEMPORARY SCALAR.
C WT: THE WEIGHTS.
C WTT: THE RESULTS OF WEIGHTING ARRAY T BY WT.
C ARRAY WTT CAN BE THE SAME AS T ONLY IF THE ARRAYS IN WT
C ARE UPPER TRIANGULAR WITH ZEROS BELOW THE DIAGONAL.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DWGHT
IF (N.EQ.0 .OR. M.EQ.0) RETURN
IF (WT(1,1,1).GE.ZERO) THEN
IF (LDWT.GE.N) THEN
IF (LD2WT.GE.M) THEN
C WT IS AN N-ARRAY OF M BY M MATRICES
DO 130 I=1,N
DO 120 J=1,M
TEMP = ZERO
DO 110 K=1,M
TEMP = TEMP + WT(I,J,K)*T(I,K)
110 CONTINUE
WTT(I,J) = TEMP
120 CONTINUE
130 CONTINUE
ELSE
C WT IS AN N-ARRAY OF DIAGONAL MATRICES
DO 230 I=1,N
DO 220 J=1,M
WTT(I,J) = WT(I,1,J)*T(I,J)
220 CONTINUE
230 CONTINUE
END IF
ELSE
IF (LD2WT.GE.M) THEN
C WT IS AN M BY M MATRIX
DO 330 I=1,N
DO 320 J=1,M
TEMP = ZERO
DO 310 K=1,M
TEMP = TEMP + WT(1,J,K)*T(I,K)
310 CONTINUE
WTT(I,J) = TEMP
320 CONTINUE
330 CONTINUE
ELSE
C WT IS A DIAGONAL MATRICE
DO 430 I=1,N
DO 420 J=1,M
WTT(I,J) = WT(1,1,J)*T(I,J)
420 CONTINUE
430 CONTINUE
END IF
END IF
ELSE
C WT IS A SCALAR
DO 520 J=1,M
DO 510 I=1,N
WTT(I,J) = ABS(WT(1,1,1))*T(I,J)
510 CONTINUE
520 CONTINUE
END IF
RETURN
END
*DWINF
SUBROUTINE DWINF
+ (N,M,NP,NQ,LDWE,LD2WE,ISODR,
+ DELTAI,EPSI,XPLUSI,FNI,SDI,VCVI,
+ RVARI,WSSI,WSSDEI,WSSEPI,RCONDI,ETAI,
+ OLMAVI,TAUI,ALPHAI,ACTRSI,PNORMI,RNORSI,PRERSI,
+ PARTLI,SSTOLI,TAUFCI,EPSMAI,
+ BETA0I,BETACI,BETASI,BETANI,SI,SSI,SSFI,QRAUXI,UI,
+ FSI,FJACBI,WE1I,DIFFI,
+ DELTSI,DELTNI,TI,TTI,OMEGAI,FJACDI,
+ WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,
+ LWKMN)
C***BEGIN PROLOGUE DWINF
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920619 (YYMMDD)
C***PURPOSE SET STORAGE LOCATIONS WITHIN DOUBLE PRECISION WORK SPACE
C***END PROLOGUE DWINF
C...SCALAR ARGUMENTS
INTEGER
+ ACTRSI,ALPHAI,BETACI,BETANI,BETASI,BETA0I,DELTAI,DELTNI,DELTSI,
+ DIFFI,EPSI,EPSMAI,ETAI,FJACBI,FJACDI,FNI,FSI,LDWE,LD2WE,LWKMN,
+ M,N,NP,NQ,OLMAVI,OMEGAI,PARTLI,PNORMI,PRERSI,QRAUXI,RCONDI,
+ RNORSI,RVARI,SDI,SI,SSFI,SSI,SSTOLI,TAUFCI,TAUI,TI,TTI,UI,VCVI,
+ WE1I,WRK1I,WRK2I,WRK3I,WRK4I,WRK5I,WRK6I,WRK7I,
+ WSSI,WSSDEI,WSSEPI,XPLUSI
LOGICAL
+ ISODR
C...LOCAL SCALARS
INTEGER
+ NEXT
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C ACTRSI: THE LOCATION IN ARRAY WORK OF VARIABLE ACTRS.
C ALPHAI: THE LOCATION IN ARRAY WORK OF VARIABLE ALPHA.
C BETACI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAC.
C BETANI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAN.
C BETASI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETAS.
C BETA0I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY BETA0.
C DELTAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTA.
C DELTNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAN.
C DELTSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DELTAS.
C DIFFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY DIFF.
C EPSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY EPS.
C EPSMAI: THE LOCATION IN ARRAY WORK OF VARIABLE EPSMAC.
C ETAI: THE LOCATION IN ARRAY WORK OF VARIABLE ETA.
C FJACBI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACB.
C FJACDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FJACD.
C FNI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FN.
C FSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY FS.
C ISODR: THE VARIABLE DESIGNATING WHETHER THE SOLUTION IS BY ODR
C (ISODR=TRUE) OR BY OLS (ISODR=FALSE).
C LDWE: THE LEADING DIMENSION OF ARRAY WE.
C LD2WE: THE SECOND DIMENSION OF ARRAY WE.
C LWKMN: THE MINIMUM ACCEPTABLE LENGTH OF VECTOR WORK.
C M: THE NUMBER OF COLUMNS OF DATA IN THE EXPLANATORY VARIABLE.
C N: THE NUMBER OF OBSERVATIONS.
C NEXT: THE NEXT AVAILABLE LOCATION WITH WORK.
C NP: THE NUMBER OF FUNCTION PARAMETERS.
C NQ: THE NUMBER OF RESPONSES PER OBSERVATION.
C OLMAVI: THE LOCATION IN ARRAY WORK OF VARIABLE OLMAVG.
C OMEGAI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY OMEGA.
C PARTLI: THE LOCATION IN ARRAY WORK OF VARIABLE PARTOL.
C PNORMI: THE LOCATION IN ARRAY WORK OF VARIABLE PNORM.
C PRERSI: THE LOCATION IN ARRAY WORK OF VARIABLE PRERS.
C QRAUXI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY QRAUX.
C RCONDI: THE LOCATION IN ARRAY WORK OF VARIABLE RCONDI.
C RNORSI: THE LOCATION IN ARRAY WORK OF VARIABLE RNORMS.
C RVARI: THE LOCATION IN ARRAY WORK OF VARIABLE RVAR.
C SDI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SD.
C SI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY S.
C SSFI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SSF.
C SSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY SS.
C SSTOLI: THE LOCATION IN ARRAY WORK OF VARIABLE SSTOL.
C TAUFCI: THE LOCATION IN ARRAY WORK OF VARIABLE TAUFAC.
C TAUI: THE LOCATION IN ARRAY WORK OF VARIABLE TAU.
C TI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY T.
C TTI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY TT.
C UI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY U.
C VCVI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY VCV.
C WE1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WE1.
C WRK1I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK1.
C WRK2I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK2.
C WRK3I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK3.
C WRK4I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK4.
C WRK5I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK5.
C WRK6I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK6.
C WRK7I: THE STARTING LOCATION IN ARRAY WORK OF ARRAY WRK7.
C WSSI: THE LOCATION IN ARRAY WORK OF VARIABLE WSS.
C WSSDEI: THE LOCATION IN ARRAY WORK OF VARIABLE WSSDEL.
C WSSEPI: THE LOCATION IN ARRAY WORK OF VARIABLE WSSEPS.
C XPLUSI: THE STARTING LOCATION IN ARRAY WORK OF ARRAY XPLUSD.
C***FIRST EXECUTABLE STATEMENT DWINF
IF (N.GE.1 .AND. M.GE.1 .AND. NP.GE.1 .AND. NQ.GE.1 .AND.
+ LDWE.GE.1 .AND. LD2WE.GE.1) THEN
DELTAI = 1
EPSI = DELTAI + N*M
XPLUSI = EPSI + N*NQ
FNI = XPLUSI + N*M
SDI = FNI + N*NQ
VCVI = SDI + NP
RVARI = VCVI + NP*NP
WSSI = RVARI + 1
WSSDEI = WSSI + 1
WSSEPI = WSSDEI + 1
RCONDI = WSSEPI + 1
ETAI = RCONDI + 1
OLMAVI = ETAI + 1
TAUI = OLMAVI + 1
ALPHAI = TAUI + 1
ACTRSI = ALPHAI + 1
PNORMI = ACTRSI + 1
RNORSI = PNORMI + 1
PRERSI = RNORSI + 1
PARTLI = PRERSI + 1
SSTOLI = PARTLI + 1
TAUFCI = SSTOLI + 1
EPSMAI = TAUFCI + 1
BETA0I = EPSMAI + 1
BETACI = BETA0I + NP
BETASI = BETACI + NP
BETANI = BETASI + NP
SI = BETANI + NP
SSI = SI + NP
SSFI = SSI + NP
QRAUXI = SSFI + NP
UI = QRAUXI + NP
FSI = UI + NP
FJACBI = FSI + N*NQ
WE1I = FJACBI + N*NP*NQ
DIFFI = WE1I + LDWE*LD2WE*NQ
NEXT = DIFFI + NQ*(NP+M)
IF (ISODR) THEN
DELTSI = NEXT
DELTNI = DELTSI + N*M
TI = DELTNI + N*M
TTI = TI + N*M
OMEGAI = TTI + N*M
FJACDI = OMEGAI + NQ*NQ
WRK1I = FJACDI + N*M*NQ
NEXT = WRK1I + N*M*NQ
ELSE
DELTSI = DELTAI
DELTNI = DELTAI
TI = DELTAI
TTI = DELTAI
OMEGAI = DELTAI
FJACDI = DELTAI
WRK1I = DELTAI
END IF
WRK2I = NEXT
WRK3I = WRK2I + N*NQ
WRK4I = WRK3I + NP
WRK5I = WRK4I + M*M
WRK6I = WRK5I + M
WRK7I = WRK6I + N*NQ*NP
NEXT = WRK7I + 5*NQ
LWKMN = NEXT
ELSE
DELTAI = 1
EPSI = 1
XPLUSI = 1
FNI = 1
SDI = 1
VCVI = 1
RVARI = 1
WSSI = 1
WSSDEI = 1
WSSEPI = 1
RCONDI = 1
ETAI = 1
OLMAVI = 1
TAUI = 1
ALPHAI = 1
ACTRSI = 1
PNORMI = 1
RNORSI = 1
PRERSI = 1
PARTLI = 1
SSTOLI = 1
TAUFCI = 1
EPSMAI = 1
BETA0I = 1
BETACI = 1
BETASI = 1
BETANI = 1
SI = 1
SSI = 1
SSFI = 1
QRAUXI = 1
FSI = 1
UI = 1
FJACBI = 1
WE1I = 1
DIFFI = 1
DELTSI = 1
DELTNI = 1
TI = 1
TTI = 1
FJACDI = 1
OMEGAI = 1
WRK1I = 1
WRK2I = 1
WRK3I = 1
WRK4I = 1
WRK5I = 1
WRK6I = 1
WRK7I = 1
LWKMN = 1
END IF
RETURN
END
*DXMY
SUBROUTINE DXMY
+ (N,M,X,LDX,Y,LDY,XMY,LDXMY)
C***BEGIN PROLOGUE DXMY
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE XMY = X - Y
C***END PROLOGUE DXMY
C...SCALAR ARGUMENTS
INTEGER
+ LDX,LDXMY,LDY,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ X(LDX,M),XMY(LDXMY,M),Y(LDY,M)
C...LOCAL SCALARS
INTEGER
+ I,J
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDXMY: THE LEADING DIMENSION OF ARRAY XMY.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C M: THE NUMBER OF COLUMNS OF DATA IN ARRAYS X AND Y.
C N: THE NUMBER OF ROWS OF DATA IN ARRAYS X AND Y.
C X: THE FIRST OF THE TWO ARRAYS.
C XMY: THE VALUES OF X-Y.
C Y: THE SECOND OF THE TWO ARRAYS.
C***FIRST EXECUTABLE STATEMENT DXMY
DO 20 J=1,M
DO 10 I=1,N
XMY(I,J) = X(I,J) - Y(I,J)
10 CONTINUE
20 CONTINUE
RETURN
END
*DXPY
SUBROUTINE DXPY
+ (N,M,X,LDX,Y,LDY,XPY,LDXPY)
C***BEGIN PROLOGUE DXPY
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE COMPUTE XPY = X + Y
C***END PROLOGUE DXPY
C...SCALAR ARGUMENTS
INTEGER
+ LDX,LDXPY,LDY,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ X(LDX,M),XPY(LDXPY,M),Y(LDY,M)
C...LOCAL SCALARS
INTEGER
+ I,J
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C LDX: THE LEADING DIMENSION OF ARRAY X.
C LDXPY: THE LEADING DIMENSION OF ARRAY XPY.
C LDY: THE LEADING DIMENSION OF ARRAY Y.
C M: THE NUMBER OF COLUMNS OF DATA IN ARRAYS X AND Y.
C N: THE NUMBER OF ROWS OF DATA IN ARRAYS X AND Y.
C X: THE FIRST OF THE TWO ARRAYS TO BE ADDED TOGETHER.
C XPY: THE VALUES OF X+Y.
C Y: THE SECOND OF THE TWO ARRAYS TO BE ADDED TOGETHER.
C***FIRST EXECUTABLE STATEMENT DXPY
DO 20 J=1,M
DO 10 I=1,N
XPY(I,J) = X(I,J) + Y(I,J)
10 CONTINUE
20 CONTINUE
RETURN
END
*DZERO
SUBROUTINE DZERO
+ (N,M,A,LDA)
C***BEGIN PROLOGUE DZERO
C***REFER TO DODR,DODRC
C***ROUTINES CALLED (NONE)
C***DATE WRITTEN 860529 (YYMMDD)
C***REVISION DATE 920304 (YYMMDD)
C***PURPOSE SET A = ZERO
C***END PROLOGUE DZERO
C...SCALAR ARGUMENTS
INTEGER
+ LDA,M,N
C...ARRAY ARGUMENTS
DOUBLE PRECISION
+ A(LDA,M)
C...LOCAL SCALARS
DOUBLE PRECISION
+ ZERO
INTEGER
+ I,J
C...DATA STATEMENTS
DATA
+ ZERO
+ /0.0D0/
C...VARIABLE DEFINITIONS (ALPHABETICALLY)
C A: THE ARRAY TO BE SET TO ZERO.
C I: AN INDEXING VARIABLE.
C J: AN INDEXING VARIABLE.
C LDA: THE LEADING DIMENSION OF ARRAY A.
C M: THE NUMBER OF COLUMNS TO BE SET TO ZERO.
C N: THE NUMBER OF ROWS TO BE SET TO ZERO.
C ZERO: THE VALUE 0.0D0.
C***FIRST EXECUTABLE STATEMENT DZERO
DO 20 J=1,M
DO 10 I=1,N
A(I,J) = ZERO
10 CONTINUE
20 CONTINUE
RETURN
END
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