hemv - {he,sy}mv: Hermitian/symmetric matrix-vector multiply ([cz]symv in LAPACK)

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subroutinechemv(characteruplo,integern,complexalpha,complex,dimension(lda,*)a,integerlda,complex,dimension(*)x,integerincx,complexbeta,complex,dimension(*)y,integerincy)CHEMVPurpose: 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. ParametersUPLO 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. FurtherDetails: 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. subroutinecsymv(characteruplo,integern,complexalpha,complex,dimension(lda,*)a,integerlda,complex,dimension(*)x,integerincx,complexbeta,complex,dimension(*)y,integerincy)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. ParametersUPLO 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. subroutinedsymv(characteruplo,integern,doubleprecisionalpha,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)x,integerincx,doubleprecisionbeta,doubleprecision,dimension(*)y,integerincy)DSYMVPurpose: 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. ParametersUPLO 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. FurtherDetails: 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. subroutinessymv(characteruplo,integern,realalpha,real,dimension(lda,*)a,integerlda,real,dimension(*)x,integerincx,realbeta,real,dimension(*)y,integerincy)SSYMVPurpose: 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. ParametersUPLO 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. FurtherDetails: 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. subroutinezhemv(characteruplo,integern,complex*16alpha,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)x,integerincx,complex*16beta,complex*16,dimension(*)y,integerincy)ZHEMVPurpose: 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. ParametersUPLO 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. FurtherDetails: 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. subroutinezsymv(characteruplo,integern,complex*16alpha,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)x,integerincx,complex*16beta,complex*16,dimension(*)y,integerincy)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. ParametersUPLO 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.

hemv - {he,sy}mv: Hermitian/symmetric matrix-vector multiply ([cz]symv in LAPACK)

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.