# hemm - Man Page

{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**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**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

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**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**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

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**UPLO**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**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**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Definition at line **188** of file **zsymm.f**.

## Author

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