zspmv (l) - Linux Manuals

zspmv: performs the matrix-vector operation y := alpha*A*x + beta*y,

NAME

ZSPMV - performs the matrix-vector operation y := alpha*A*x + beta*y,

SYNOPSIS

SUBROUTINE ZSPMV(
UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )

    
CHARACTER UPLO

    
INTEGER INCX, INCY, N

    
COMPLEX*16 ALPHA, BETA

    
COMPLEX*16 AP( * ), X( * ), Y( * )

PURPOSE

ZSPMV performs the matrix-vector operation where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

ARGUMENTS

UPLO (input) CHARACTER*1
On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = aqUaq or aquaq The upper triangular part of A is supplied in AP. UPLO = aqLaq or aqlaq The lower triangular part of A is supplied in AP. Unchanged on exit.
N (input) INTEGER
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA (input) COMPLEX*16
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
AP (input) COMPLEX*16 array, dimension at least
( ( N*( N + 1 ) )/2 ). Before entry, with UPLO = aqUaq or aquaq, the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry, with UPLO = aqLaq or aqlaq, the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Unchanged on exit.
X (input) 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 (input) INTEGER
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA (input) 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 (input/output) 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 (input) INTEGER
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Pages related to zspmv

  • zspmv (3)
  • zspcon (l) - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
  • zspr (l) - performs the symmetric rank 1 operation A := alpha*x*conjg( xaq ) + A,
  • zsprfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
  • zspsv (l) - computes the solution to a complex system of linear equations A * X = B,
  • zspsvx (l) - uses the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices
  • zsptrf (l) - computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
  • zsptri (l) - computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
  • zsptrs (l) - solves a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF