New changes from l2g

w

dataassim/math/algebra/eigen.f

@@ -0,0 +1,111 @@
+      SUBROUTINE EIGEN(NM,N,A,WR,WI,Z)
+      COMMON/CSTAK/DSTAK(500)
+C
+      REAL A(NM,N),WR(N),WI(N),Z(NM,N)
+      REAL RSTAK(1000)
+C
+      EQUIVALENCE (DSTAK(1),RSTAK(1))
+C
+C EIGEN FINDS THE EIGENVALUES AND EIGENVECTORS
+C OF A REAL MATRIX (NOT IMAGINARY) BY
+C CALLING THE SEQUENCE OF SUBROUTINES
+C ORTHE,ORTRA, AND HQR2, WHICH, IN TURN, ARE
+C THE EISPACK ROUTINES ORTHES, ORTRAN, AND HQR2,
+C ADJUSTED FOR USE IN THE PORT LIBRARY.
+C
+C ON INPUT -
+C
+C   NM - AN INTEGER INPUT VARIABLE SET EQUAL TO
+C        THE ROW DIMENSION OF THE TWO-DIMENSIONAL ARRAYS
+C        A AND Z AS SPECIFIED IN THE DIMENSION STATEMENTS
+C        FOR A AND Z IN THE CALLING PROGRAM.
+C
+C   N -  AN INTEGER INPUT VARIABLE SET EQUAL TO THE
+C        ORDER OF THE MATRIX A.
+C
+C     N MUST NOT BE GREATER THAN NM.
+C
+C   A - THE MATRIX, A REAL TWO-DIMENSIONAL
+C       ARRAY WITH ROW DIMENSION NM AND COLUMN
+C       DIMENSION AT LEAST N.
+C
+C     A IS OVERWRITTEN.
+C
+C
+C
+C ON OUTPUT -
+C
+C   WR - A REAL ARRAY OF DIMENSION
+C        AT LEAST N CONTAINING THE REAL PARTS OF THE EIGENVALUES
+C
+C   WI - A REAL ARRAY OF DIMENSION
+C        AT LEAST N CONTAINING THE IMAGINARY PARTS OF THE EIGENVALUES.
+C
+C     THE EIGENVALUES ARE UNORDERED EXCEPT THAT
+C     COMPLEX CONJUGATE PAIRS OF EIGENVALUES
+C     APPEAR CONSECUTIVELY WITH THE EIGENVALUE HAVING
+C     THE POSITIVE IMAGINARY PART FIRST.
+C
+C   Z - A REAL TWO-DIMENSIONAL ARRAY
+C       WITH ROW DIMENSION NM AND COLUMN DIMENSION
+C       AT LEAST N CONTAINING THE REAL AND IMAGINARY PARTS
+C       OF THE EIGENVECTORS.
+C
+C       IF THE J-TH EIGENVALUE IS REAL, THE J-TH
+C       COLUMN OF Z CONTAINS ITS EIGENVECTOR.
+C
+C       IF THE J-TH EIGENVALUE IS COMPLEX WITH
+C       POSITIVE REAL PART, THE J-TH AND (J+1)-TH
+C       COLUMNS OF Z CONTAIN THE REAL AND IMAGINARY
+C       PARTS OF ITS EIGENVECTOR.
+C
+C       THE CONJUGATE OF THIS VECTOR IS THE
+C       EIGENVECTOR FOR THE CONJUGATE EIGENVALUE.
+C       THE EIGENVECTORS ARE NOT NORMALIZED.
+C
+C
+C ERROR STATES -
+C
+C          1 - N IS GREATER THAN NM
+C
+C          K - THE K-TH EIGENVALUE COULD NOT BE COMPUTED
+C              WITHIN 30 ITERATIONS.
+C
+C              THE EIGENVALUES IN THE WR AND WRI ARRAYS
+C              SHOULD BE CORRECT FOR INDICES
+C              K+1, K+2,...,N, BUT NO EIGENVECTORS ARE COMPUTED.
+C
+C
+C
+C
+C CHECK FOR INPUT ERROR IN N
+C
+C/6S
+C     IF (N .GT. NM) CALL SETERR(
+C    1   29H EIGEN - N IS GREATER THAN NM,29,1,2)
+C/7S
+      IF (N .GT. NM) CALL SETERR(
+     1   ' EIGEN - N IS GREATER THAN NM',29,1,2)
+C/
+C
+C ALLOCATE A SCRATCH VECTOR
+      IORT = ISTKGT(N,3)
+C
+      CALL ORTHE (NM,N,1,N,A,RSTAK(IORT))
+      CALL ORTRA (NM,N,1,N,A,RSTAK(IORT),Z)
+      CALL HQR2 (NM,N,1,N,A,WR,WI,Z,IERR)
+C
+      IF (IERR .NE. 0) GO TO 10
+      CALL ISTKRL(1)
+      RETURN
+C/6S
+C 10  CALL SETERR(
+C    1   34H EIGEN - FAILED ON THAT EIGENVALUE,34,IERR,1)
+C/7S
+  10  CALL SETERR(
+     1   ' EIGEN - FAILED ON THAT EIGENVALUE',34,IERR,1)
+C/
+C
+      CALL ISTKRL(1)
+      RETURN
+      END