--- name: "hemv" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/hemv" --- # hemv(3) {he,sy}mv: Hermitian/symmetric matrix-vector multiply (\[cz\]symv in LAPACK) ## NAME hemv - {he,sy}mv: Hermitian/symmetric matrix-vector multiply (\[cz\]symv in LAPACK) ## SYNOPSIS ### Functions subroutine **chemv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **CHEMV** subroutine **dsymv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **DSYMV** subroutine **ssymv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **SSYMV** subroutine **zhemv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **ZHEMV** subroutine **csymv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **CSYMV** computes a matrix-vector product for a complex symmetric matrix. subroutine **zsymv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)\ **ZSYMV** computes a matrix-vector product for a complex symmetric matrix. ## Detailed Description ## Function Documentation ### subroutine chemv (character uplo, integer n, complex alpha, complex, dimension(lda,\*) a, integer lda, complex, dimension(\*) x, integer incx, complex beta, complex, dimension(\*) y, integer incy) **CHEMV** **Purpose:** ``` !> !> CHEMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n hermitian matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> ``` *ALPHA* ``` !> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !> ``` *A* ``` !> A is COMPLEX array, dimension ( LDA, N ) !> Before entry with 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. !> Before entry with 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 and 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. LDA must be at least !> max( 1, n ). !> ``` *X* ``` !> X is COMPLEX array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *BETA* ``` !> BETA is COMPLEX !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> ``` *Y* ``` !> Y is COMPLEX array, dimension at least !> ( 1 + ( n - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` !> !> Level 2 Blas routine. !> The vector and matrix arguments are not referenced when N = 0, or M = 0 !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !> ``` Definition at line **153** of file **chemv.f**. ### subroutine csymv (character uplo, integer n, complex alpha, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) x, integer incx, complex beta, complex, dimension( \* ) y, integer incy) **CSYMV** computes a matrix-vector product for a complex symmetric matrix. **Purpose:** ``` !> !> CSYMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n symmetric matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> !> Unchanged on exit. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !> ``` *ALPHA* ``` !> ALPHA is COMPLEX !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !> ``` *A* ``` !> A is COMPLEX array, dimension ( LDA, N ) !> Before entry, with 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. !> Before entry, with 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. !> Unchanged on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, N ). !> Unchanged on exit. !> ``` *X* ``` !> X is COMPLEX array, dimension at least !> ( 1 + ( N - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the N- !> element vector x. !> Unchanged on exit. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !> ``` *BETA* ``` !> BETA is COMPLEX !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> Unchanged on exit. !> ``` *Y* ``` !> Y is COMPLEX array, dimension at least !> ( 1 + ( N - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> Unchanged on exit. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **156** of file **csymv.f**. ### subroutine dsymv (character uplo, integer n, double precision alpha, double precision, dimension(lda,\*) a, integer lda, double precision, dimension(\*) x, integer incx, double precision beta, double precision, dimension(\*) y, integer incy) **DSYMV** **Purpose:** ``` !> !> DSYMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n symmetric matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> 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, N ) !> Before entry with 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. !> Before entry with 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. LDA must be at least !> max( 1, n ). !> ``` *X* ``` !> X is DOUBLE PRECISION array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *BETA* ``` !> BETA is DOUBLE PRECISION. !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> ``` *Y* ``` !> Y is DOUBLE PRECISION array, dimension at least !> ( 1 + ( n - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` !> !> Level 2 Blas routine. !> The vector and matrix arguments are not referenced when N = 0, or M = 0 !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !> ``` Definition at line **151** of file **dsymv.f**. ### subroutine ssymv (character uplo, integer n, real alpha, real, dimension(lda,\*) a, integer lda, real, dimension(\*) x, integer incx, real beta, real, dimension(\*) y, integer incy) **SSYMV** **Purpose:** ``` !> !> SSYMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n symmetric matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> ``` *ALPHA* ``` !> ALPHA is REAL !> On entry, ALPHA specifies the scalar alpha. !> ``` *A* ``` !> A is REAL array, dimension ( LDA, N ) !> Before entry with 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. !> Before entry with 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. LDA must be at least !> max( 1, n ). !> ``` *X* ``` !> X is REAL array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *BETA* ``` !> BETA is REAL !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> ``` *Y* ``` !> Y is REAL array, dimension at least !> ( 1 + ( n - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` !> !> Level 2 Blas routine. !> The vector and matrix arguments are not referenced when N = 0, or M = 0 !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !> ``` Definition at line **151** of file **ssymv.f**. ### subroutine zhemv (character uplo, integer n, complex\*16 alpha, complex\*16, dimension(lda,\*) a, integer lda, complex\*16, dimension(\*) x, integer incx, complex\*16 beta, complex\*16, dimension(\*) y, integer incy) **ZHEMV** **Purpose:** ``` !> !> ZHEMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n hermitian matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> 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, N ) !> Before entry with 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. !> Before entry with 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 and 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. LDA must be at least !> max( 1, n ). !> ``` *X* ``` !> X is COMPLEX*16 array, dimension at least !> ( 1 + ( n - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the n !> element vector x. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> ``` *BETA* ``` !> BETA is COMPLEX*16 !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> ``` *Y* ``` !> Y is COMPLEX*16 array, dimension at least !> ( 1 + ( n - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` !> !> Level 2 Blas routine. !> The vector and matrix arguments are not referenced when N = 0, or M = 0 !> !> -- Written on 22-October-1986. !> Jack Dongarra, Argonne National Lab. !> Jeremy Du Croz, Nag Central Office. !> Sven Hammarling, Nag Central Office. !> Richard Hanson, Sandia National Labs. !> ``` Definition at line **153** of file **zhemv.f**. ### subroutine zsymv (character uplo, integer n, complex\*16 alpha, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) x, integer incx, complex\*16 beta, complex\*16, dimension( \* ) y, integer incy) **ZSYMV** computes a matrix-vector product for a complex symmetric matrix. **Purpose:** ``` !> !> ZSYMV performs the matrix-vector operation !> !> y := alpha*A*x + beta*y, !> !> where alpha and beta are scalars, x and y are n element vectors and !> A is an n by n symmetric matrix. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> On entry, UPLO specifies whether the upper or lower !> triangular part of the array A is to be referenced as !> follows: !> !> UPLO = 'U' or 'u' Only the upper triangular part of A !> is to be referenced. !> !> UPLO = 'L' or 'l' Only the lower triangular part of A !> is to be referenced. !> !> Unchanged on exit. !> ``` *N* ``` !> N is INTEGER !> On entry, N specifies the order of the matrix A. !> N must be at least zero. !> Unchanged on exit. !> ``` *ALPHA* ``` !> ALPHA is COMPLEX*16 !> On entry, ALPHA specifies the scalar alpha. !> Unchanged on exit. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension ( LDA, N ) !> Before entry, with 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. !> Before entry, with 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. !> Unchanged on exit. !> ``` *LDA* ``` !> LDA is INTEGER !> On entry, LDA specifies the first dimension of A as declared !> in the calling (sub) program. LDA must be at least !> max( 1, N ). !> Unchanged on exit. !> ``` *X* ``` !> X is COMPLEX*16 array, dimension at least !> ( 1 + ( N - 1 )*abs( INCX ) ). !> Before entry, the incremented array X must contain the N- !> element vector x. !> Unchanged on exit. !> ``` *INCX* ``` !> INCX is INTEGER !> On entry, INCX specifies the increment for the elements of !> X. INCX must not be zero. !> Unchanged on exit. !> ``` *BETA* ``` !> BETA is COMPLEX*16 !> On entry, BETA specifies the scalar beta. When BETA is !> supplied as zero then Y need not be set on input. !> Unchanged on exit. !> ``` *Y* ``` !> Y is COMPLEX*16 array, dimension at least !> ( 1 + ( N - 1 )*abs( INCY ) ). !> Before entry, the incremented array Y must contain the n !> element vector y. On exit, Y is overwritten by the updated !> vector y. !> ``` *INCY* ``` !> INCY is INTEGER !> On entry, INCY specifies the increment for the elements of !> Y. INCY must not be zero. !> Unchanged on exit. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **156** of file **zsymv.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.