372 lines
11 KiB
Fortran
372 lines
11 KiB
Fortran
*> \brief \b ZHEMM
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*
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* .. Scalar Arguments ..
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* COMPLEX*16 ALPHA,BETA
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* INTEGER LDA,LDB,LDC,M,N
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* CHARACTER SIDE,UPLO
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZHEMM performs one of the matrix-matrix operations
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*>
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*> C := alpha*A*B + beta*C,
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*>
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*> or
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*>
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*> C := alpha*B*A + beta*C,
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*>
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*> where alpha and beta are scalars, A is an hermitian matrix and B and
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*> C are m by n matrices.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] SIDE
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*> \verbatim
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*> SIDE is CHARACTER*1
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*> On entry, SIDE specifies whether the hermitian matrix A
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*> appears on the left or right in the operation as follows:
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*>
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*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
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*>
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*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> On entry, UPLO specifies whether the upper or lower
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*> triangular part of the hermitian matrix A is to be
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*> referenced as follows:
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*>
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*> UPLO = 'U' or 'u' Only the upper triangular part of the
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*> hermitian matrix is to be referenced.
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*>
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*> UPLO = 'L' or 'l' Only the lower triangular part of the
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*> hermitian matrix is to be referenced.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> On entry, M specifies the number of rows of the matrix C.
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*> M must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> On entry, N specifies the number of columns of the matrix C.
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*> N must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is COMPLEX*16
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*> On entry, ALPHA specifies the scalar alpha.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
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*> m when SIDE = 'L' or 'l' and is n otherwise.
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*> Before entry with SIDE = 'L' or 'l', the m by m part of
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*> the array A must contain the hermitian matrix, such that
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*> when UPLO = 'U' or 'u', the leading m by m upper triangular
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*> part of the array A must contain the upper triangular part
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*> of the hermitian matrix and the strictly lower triangular
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*> part of A is not referenced, and when UPLO = 'L' or 'l',
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*> the leading m by m lower triangular part of the array A
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*> must contain the lower triangular part of the hermitian
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*> matrix and the strictly upper triangular part of A is not
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*> referenced.
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*> Before entry with SIDE = 'R' or 'r', the n by n part of
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*> the array A must contain the hermitian matrix, such that
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*> when UPLO = 'U' or 'u', the leading n by n upper triangular
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*> part of the array A must contain the upper triangular part
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*> of the hermitian matrix and the strictly lower triangular
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*> part of A is not referenced, and when UPLO = 'L' or 'l',
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*> the leading n by n lower triangular part of the array A
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*> must contain the lower triangular part of the hermitian
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*> matrix and the strictly upper triangular part of A is not
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*> referenced.
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*> Note that the imaginary parts of the diagonal elements need
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*> not be set, they are assumed to be zero.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is 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 SIDE = 'L' or 'l' then
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*> LDA must be at least max( 1, m ), otherwise LDA must be at
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*> least max( 1, n ).
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension ( LDB, N )
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*> Before entry, the leading m by n part of the array B must
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*> contain the matrix B.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is 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. LDB must be at least
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*> max( 1, m ).
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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is COMPLEX*16
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*> On entry, BETA specifies the scalar beta. When BETA is
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*> supplied as zero then C need not be set on input.
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*> \endverbatim
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*>
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*> \param[in,out] C
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*> \verbatim
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*> C is COMPLEX*16 array, dimension ( LDC, N )
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*> Before entry, the leading m by n part of the array C must
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*> contain the matrix C, except when beta is zero, in which
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*> case C need not be set on entry.
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*> On exit, the array C is overwritten by the m by n updated
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*> matrix.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is 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, m ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex16_blas_level3
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> Level 3 Blas routine.
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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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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*
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* -- Reference BLAS level3 routine (version 3.7.0) --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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COMPLEX*16 ALPHA,BETA
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INTEGER LDA,LDB,LDC,M,N
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CHARACTER SIDE,UPLO
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
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* ..
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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 DBLE,DCONJG,MAX
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* ..
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* .. Local Scalars ..
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COMPLEX*16 TEMP1,TEMP2
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INTEGER I,INFO,J,K,NROWA
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LOGICAL UPPER
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* ..
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* .. Parameters ..
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COMPLEX*16 ONE
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PARAMETER (ONE= (1.0D+0,0.0D+0))
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COMPLEX*16 ZERO
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PARAMETER (ZERO= (0.0D+0,0.0D+0))
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* ..
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*
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* Set NROWA as the number of rows of A.
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*
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IF (LSAME(SIDE,'L')) THEN
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NROWA = M
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ELSE
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NROWA = N
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END IF
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UPPER = LSAME(UPLO,'U')
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*
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* Test the input parameters.
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*
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INFO = 0
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IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
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INFO = 1
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ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
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INFO = 2
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ELSE IF (M.LT.0) THEN
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INFO = 3
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ELSE IF (N.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,M)) THEN
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INFO = 9
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ELSE IF (LDC.LT.MAX(1,M)) 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('ZHEMM ',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 ((M.EQ.0) .OR. (N.EQ.0) .OR.
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+ ((ALPHA.EQ.ZERO).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 (BETA.EQ.ZERO) THEN
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DO 20 J = 1,N
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DO 10 I = 1,M
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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,M
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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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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(SIDE,'L')) THEN
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*
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* Form C := alpha*A*B + beta*C.
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*
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IF (UPPER) THEN
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DO 70 J = 1,N
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DO 60 I = 1,M
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TEMP1 = ALPHA*B(I,J)
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TEMP2 = ZERO
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DO 50 K = 1,I - 1
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C(K,J) = C(K,J) + TEMP1*A(K,I)
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TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
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50 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
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+ ALPHA*TEMP2
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END IF
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60 CONTINUE
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70 CONTINUE
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ELSE
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DO 100 J = 1,N
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DO 90 I = M,1,-1
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TEMP1 = ALPHA*B(I,J)
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TEMP2 = ZERO
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DO 80 K = I + 1,M
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C(K,J) = C(K,J) + TEMP1*A(K,I)
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TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
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80 CONTINUE
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IF (BETA.EQ.ZERO) THEN
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C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
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ELSE
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C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
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+ ALPHA*TEMP2
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END IF
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90 CONTINUE
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100 CONTINUE
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END IF
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ELSE
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*
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* Form C := alpha*B*A + beta*C.
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*
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DO 170 J = 1,N
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TEMP1 = ALPHA*DBLE(A(J,J))
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IF (BETA.EQ.ZERO) THEN
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DO 110 I = 1,M
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C(I,J) = TEMP1*B(I,J)
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110 CONTINUE
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ELSE
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DO 120 I = 1,M
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C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
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120 CONTINUE
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END IF
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DO 140 K = 1,J - 1
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IF (UPPER) THEN
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TEMP1 = ALPHA*A(K,J)
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ELSE
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TEMP1 = ALPHA*DCONJG(A(J,K))
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END IF
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DO 130 I = 1,M
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C(I,J) = C(I,J) + TEMP1*B(I,K)
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130 CONTINUE
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140 CONTINUE
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DO 160 K = J + 1,N
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IF (UPPER) THEN
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TEMP1 = ALPHA*DCONJG(A(J,K))
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ELSE
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TEMP1 = ALPHA*A(K,J)
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END IF
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DO 150 I = 1,M
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C(I,J) = C(I,J) + TEMP1*B(I,K)
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150 CONTINUE
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160 CONTINUE
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170 CONTINUE
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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 ZHEMM .
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*
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END
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