330 lines
11 KiB
FortranFixed
330 lines
11 KiB
FortranFixed
SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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* .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA,BETA
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INTEGER K,LDA,LDB,LDC,N
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CHARACTER TRANS,UPLO
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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*
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* Purpose
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* =======
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*
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* DSYR2K performs one of the symmetric rank 2k operations
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*
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* C := alpha*A*B**T + alpha*B*A**T + beta*C,
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*
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* or
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*
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* C := alpha*A**T*B + alpha*B**T*A + beta*C,
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*
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* where alpha and beta are scalars, C is an n by n symmetric matrix
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* and A and B are n by k matrices in the first case and k by n
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* matrices in the second case.
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*
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* Arguments
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* ==========
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*
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* UPLO - CHARACTER*1.
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* On entry, UPLO specifies whether the upper or lower
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* triangular part of the array C is to be referenced as
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* follows:
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*
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* UPLO = 'U' or 'u' Only the upper triangular part of C
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* is to be referenced.
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*
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* UPLO = 'L' or 'l' Only the lower triangular part of C
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* is to be referenced.
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*
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* Unchanged on exit.
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*
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the operation to be performed as
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* follows:
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*
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* TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T +
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* beta*C.
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*
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* TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A +
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* beta*C.
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*
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* TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A +
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* beta*C.
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*
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* Unchanged on exit.
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*
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* N - INTEGER.
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* On entry, N specifies the order of the matrix C. N must be
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* at least zero.
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* Unchanged on exit.
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*
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* K - INTEGER.
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* On entry with TRANS = 'N' or 'n', K specifies the number
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* of columns of the matrices A and B, and on entry with
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* TRANS = 'T' or 't' or 'C' or 'c', K specifies the number
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* of rows of the matrices A and B. K must be at least zero.
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* Unchanged on exit.
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*
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* ALPHA - DOUBLE PRECISION.
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* On entry, ALPHA specifies the scalar alpha.
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* Unchanged on exit.
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*
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* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
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* k when TRANS = 'N' or 'n', and is n otherwise.
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* Before entry with TRANS = 'N' or 'n', the leading n by k
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* part of the array A must contain the matrix A, otherwise
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* the leading k by n part of the array A must contain the
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* matrix A.
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* Unchanged on exit.
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*
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* LDA - INTEGER.
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* On entry, LDA specifies the first dimension of A as declared
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* in the calling (sub) program. When TRANS = 'N' or 'n'
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* then LDA must be at least max( 1, n ), otherwise LDA must
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* be at least max( 1, k ).
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* Unchanged on exit.
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*
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* B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is
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* k when TRANS = 'N' or 'n', and is n otherwise.
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* Before entry with TRANS = 'N' or 'n', the leading n by k
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* part of the array B must contain the matrix B, otherwise
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* the leading k by n part of the array B must contain the
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* matrix B.
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* Unchanged on exit.
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*
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* LDB - INTEGER.
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* On entry, LDB specifies the first dimension of B as declared
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* in the calling (sub) program. When TRANS = 'N' or 'n'
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* then LDB must be at least max( 1, n ), otherwise LDB must
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* be at least max( 1, k ).
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* Unchanged on exit.
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*
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* BETA - DOUBLE PRECISION.
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* On entry, BETA specifies the scalar beta.
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* Unchanged on exit.
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*
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* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
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* Before entry with UPLO = 'U' or 'u', the leading n by n
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* upper triangular part of the array C must contain the upper
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* triangular part of the symmetric matrix and the strictly
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* lower triangular part of C is not referenced. On exit, the
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* upper triangular part of the array C is overwritten by the
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* upper triangular part of the updated matrix.
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* Before entry with UPLO = 'L' or 'l', the leading n by n
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* lower triangular part of the array C must contain the lower
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* triangular part of the symmetric matrix and the strictly
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* upper triangular part of C is not referenced. On exit, the
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* lower triangular part of the array C is overwritten by the
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* lower triangular part of the updated matrix.
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*
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* LDC - INTEGER.
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* On entry, LDC specifies the first dimension of C as declared
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* in the calling (sub) program. LDC must be at least
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* max( 1, n ).
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* Unchanged on exit.
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*
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* Further Details
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* ===============
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*
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* Level 3 Blas routine.
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*
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*
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* -- Written on 8-February-1989.
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* Jack Dongarra, Argonne National Laboratory.
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* Iain Duff, AERE Harwell.
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* Jeremy Du Croz, Numerical Algorithms Group Ltd.
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* Sven Hammarling, Numerical Algorithms Group Ltd.
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*
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* =====================================================================
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*
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION TEMP1,TEMP2
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INTEGER I,INFO,J,L,NROWA
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LOGICAL UPPER
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* ..
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* .. Parameters ..
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DOUBLE PRECISION ONE,ZERO
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PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
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* ..
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*
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* Test the input parameters.
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*
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IF (LSAME(TRANS,'N')) THEN
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NROWA = N
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ELSE
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NROWA = K
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END IF
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UPPER = LSAME(UPLO,'U')
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*
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INFO = 0
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IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
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INFO = 1
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ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
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+ (.NOT.LSAME(TRANS,'T')) .AND.
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+ (.NOT.LSAME(TRANS,'C'))) THEN
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INFO = 2
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ELSE IF (N.LT.0) THEN
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INFO = 3
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ELSE IF (K.LT.0) THEN
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INFO = 4
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
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INFO = 7
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ELSE IF (LDB.LT.MAX(1,NROWA)) THEN
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INFO = 9
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ELSE IF (LDC.LT.MAX(1,N)) THEN
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INFO = 12
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END IF
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IF (INFO.NE.0) THEN
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CALL XERBLA('DSYR2K',INFO)
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RETURN
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END IF
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*
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* Quick return if possible.
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*
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IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
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+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
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*
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* And when alpha.eq.zero.
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*
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IF (ALPHA.EQ.ZERO) THEN
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IF (UPPER) THEN
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IF (BETA.EQ.ZERO) THEN
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DO 20 J = 1,N
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DO 10 I = 1,J
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C(I,J) = ZERO
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1,N
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DO 30 I = 1,J
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C(I,J) = BETA*C(I,J)
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30 CONTINUE
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40 CONTINUE
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END IF
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ELSE
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IF (BETA.EQ.ZERO) THEN
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DO 60 J = 1,N
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DO 50 I = J,N
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C(I,J) = ZERO
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50 CONTINUE
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60 CONTINUE
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ELSE
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DO 80 J = 1,N
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DO 70 I = J,N
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C(I,J) = BETA*C(I,J)
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70 CONTINUE
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80 CONTINUE
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END IF
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END IF
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RETURN
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END IF
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*
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* Start the operations.
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*
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IF (LSAME(TRANS,'N')) THEN
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*
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* Form C := alpha*A*B**T + alpha*B*A**T + C.
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*
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IF (UPPER) THEN
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DO 130 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 90 I = 1,J
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C(I,J) = ZERO
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90 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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DO 100 I = 1,J
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C(I,J) = BETA*C(I,J)
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100 CONTINUE
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END IF
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DO 120 L = 1,K
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
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TEMP1 = ALPHA*B(J,L)
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TEMP2 = ALPHA*A(J,L)
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DO 110 I = 1,J
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C(I,J) = C(I,J) + A(I,L)*TEMP1 +
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+ B(I,L)*TEMP2
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110 CONTINUE
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END IF
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120 CONTINUE
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130 CONTINUE
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ELSE
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DO 180 J = 1,N
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IF (BETA.EQ.ZERO) THEN
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DO 140 I = J,N
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C(I,J) = ZERO
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140 CONTINUE
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ELSE IF (BETA.NE.ONE) THEN
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DO 150 I = J,N
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C(I,J) = BETA*C(I,J)
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150 CONTINUE
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END IF
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DO 170 L = 1,K
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN
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TEMP1 = ALPHA*B(J,L)
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TEMP2 = ALPHA*A(J,L)
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DO 160 I = J,N
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C(I,J) = C(I,J) + A(I,L)*TEMP1 +
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+ B(I,L)*TEMP2
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160 CONTINUE
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END IF
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170 CONTINUE
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180 CONTINUE
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END IF
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ELSE
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*
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* Form C := alpha*A**T*B + alpha*B**T*A + C.
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*
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IF (UPPER) THEN
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DO 210 J = 1,N
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DO 200 I = 1,J
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TEMP1 = ZERO
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TEMP2 = ZERO
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DO 190 L = 1,K
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TEMP1 = TEMP1 + A(L,I)*B(L,J)
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TEMP2 = TEMP2 + B(L,I)*A(L,J)
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190 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
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+ ALPHA*TEMP2
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END IF
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200 CONTINUE
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210 CONTINUE
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ELSE
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DO 240 J = 1,N
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DO 230 I = J,N
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TEMP1 = ZERO
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TEMP2 = ZERO
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DO 220 L = 1,K
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TEMP1 = TEMP1 + A(L,I)*B(L,J)
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TEMP2 = TEMP2 + B(L,I)*A(L,J)
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220 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 +
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+ ALPHA*TEMP2
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END IF
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230 CONTINUE
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240 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of DSYR2K.
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*
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END
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