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hemm(3) Library Functions Manual hemm(3)

NAME

hemm - {he,sy}mm: Hermitian/symmetric matrix-matrix multiply

SYNOPSIS

Functions


subroutine CHEMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
CHEMM subroutine CSYMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
CSYMM subroutine DSYMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
DSYMM subroutine SSYMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
SSYMM subroutine ZHEMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZHEMM subroutine ZSYMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)
ZSYMM

Detailed Description

Function Documentation

subroutine CHEMM (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

CHEMM

Purpose:

!>
!> CHEMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where alpha and beta are scalars, A is an hermitian matrix and  B and
!> C are m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  hermitian matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  hermitian  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  hermitian matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  hermitian matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is COMPLEX array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  hermitian matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  hermitian matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  hermitian
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  hermitian matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  hermitian matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  hermitian
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Note that the imaginary parts  of the diagonal elements need
!>           not be set, they are assumed to be zero.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least max( 1, n ).
!>

B

!>          B is COMPLEX array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is COMPLEX
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is COMPLEX array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 190 of file chemm.f.

subroutine CSYMM (character side, character uplo, integer m, integer n, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

CSYMM

Purpose:

!>
!> CSYMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where  alpha and beta are scalars, A is a symmetric matrix and  B and
!> C are m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  symmetric matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  symmetric  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  symmetric matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  symmetric matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is COMPLEX array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least max( 1, n ).
!>

B

!>          B is COMPLEX array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is COMPLEX
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is COMPLEX array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 188 of file csymm.f.

subroutine DSYMM (character side, character uplo, integer m, integer n, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision, dimension(ldb,*) b, integer ldb, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYMM

Purpose:

!>
!> DSYMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where alpha and beta are scalars,  A is a symmetric matrix and  B and
!> C are  m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  symmetric matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  symmetric  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  symmetric matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  symmetric matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is DOUBLE PRECISION.
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least  max( 1, n ).
!>

B

!>          B is DOUBLE PRECISION array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is DOUBLE PRECISION.
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is DOUBLE PRECISION array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 188 of file dsymm.f.

subroutine SSYMM (character side, character uplo, integer m, integer n, real alpha, real, dimension(lda,*) a, integer lda, real, dimension(ldb,*) b, integer ldb, real beta, real, dimension(ldc,*) c, integer ldc)

SSYMM

Purpose:

!>
!> SSYMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where alpha and beta are scalars,  A is a symmetric matrix and  B and
!> C are  m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  symmetric matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  symmetric  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  symmetric matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  symmetric matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is REAL array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least  max( 1, n ).
!>

B

!>          B is REAL array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is REAL
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is REAL array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 188 of file ssymm.f.

subroutine ZHEMM (character side, character uplo, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)

ZHEMM

Purpose:

!>
!> ZHEMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where alpha and beta are scalars, A is an hermitian matrix and  B and
!> C are m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  hermitian matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  hermitian  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  hermitian matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  hermitian matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  hermitian matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  hermitian matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  hermitian
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  hermitian matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  hermitian matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  hermitian
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Note that the imaginary parts  of the diagonal elements need
!>           not be set, they are assumed to be zero.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least max( 1, n ).
!>

B

!>          B is COMPLEX*16 array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is COMPLEX*16
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is COMPLEX*16 array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 190 of file zhemm.f.

subroutine ZSYMM (character side, character uplo, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc)

ZSYMM

Purpose:

!>
!> ZSYMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*A*B + beta*C,
!>
!> or
!>
!>    C := alpha*B*A + beta*C,
!>
!> where  alpha and beta are scalars, A is a symmetric matrix and  B and
!> C are m by n matrices.
!>

Parameters

SIDE 

!>          SIDE is CHARACTER*1
!>           On entry,  SIDE  specifies whether  the  symmetric matrix  A
!>           appears on the  left or right  in the  operation as follows:
!>
!>              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
!>
!>              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
!>

UPLO

!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of  the  symmetric  matrix   A  is  to  be
!>           referenced as follows:
!>
!>              UPLO = 'U' or 'u'   Only the upper triangular part of the
!>                                  symmetric matrix is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the lower triangular part of the
!>                                  symmetric matrix is to be referenced.
!>

M

!>          M is INTEGER
!>           On entry,  M  specifies the number of rows of the matrix  C.
!>           M  must be at least zero.
!>

N

!>          N is INTEGER
!>           On entry, N specifies the number of columns of the matrix C.
!>           N  must be at least zero.
!>

ALPHA

!>          ALPHA is COMPLEX*16
!>           On entry, ALPHA specifies the scalar alpha.
!>

A

!>          A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
!>           m  when  SIDE = 'L' or 'l'  and is n  otherwise.
!>           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading m by m upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  m by m  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
!>           the array  A  must contain the  symmetric matrix,  such that
!>           when  UPLO = 'U' or 'u', the leading n by n upper triangular
!>           part of the array  A  must contain the upper triangular part
!>           of the  symmetric matrix and the  strictly  lower triangular
!>           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
!>           the leading  n by n  lower triangular part  of the  array  A
!>           must  contain  the  lower triangular part  of the  symmetric
!>           matrix and the  strictly upper triangular part of  A  is not
!>           referenced.
!>

LDA

!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the  calling (sub) program. When  SIDE = 'L' or 'l'  then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least max( 1, n ).
!>

B

!>          B is COMPLEX*16 array, dimension ( LDB, N )
!>           Before entry, the leading  m by n part of the array  B  must
!>           contain the matrix B.
!>

LDB

!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>

BETA

!>          BETA is COMPLEX*16
!>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
!>           supplied as zero then C need not be set on input.
!>

C

!>          C is COMPLEX*16 array, dimension ( LDC, N )
!>           Before entry, the leading  m by n  part of the array  C must
!>           contain the matrix  C,  except when  beta  is zero, in which
!>           case C need not be set on entry.
!>           On exit, the array  C  is overwritten by the  m by n updated
!>           matrix.
!>

LDC

!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, m ).
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 188 of file zsymm.f.

Author

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