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## man page of LAPACK-3

### LAPACK-3: performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y),

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## NAME

LAPACK-3 - performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y),## SYNOPSIS

SUBROUTINE ZLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY ) IMPLICIT NONE DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, N, UPLO COMPLEX*16 A( LDA, * ), X( * ) DOUBLE PRECISION Y( * )## PURPOSE

ZLA_SYAMV performs the matrix-vector operation where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, "symbolically" zero components are not perturbed. A zero entry is considered "symbolic" if all multiplications involved in computing that entry have at least one zero multiplicand.ARGUMENTS

UPLO (input) INTEGER On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = BLAS_UPPER Only the upper triangular part of A is to be referenced. UPLO = BLAS_LOWER Only the lower triangular part of A is to be referenced. Unchanged on exit. N (input) INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit. LDA (input) 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 - COMPLEX*16 array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the 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 - DOUBLE PRECISION . 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) DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the 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.## FURTHER DETAILS

Level 2 Blas routine. -- 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. -- Modified for the absolute-value product, April 2006 Jason Riedy, UC Berkeley LAPACK routine (version 3.2.2)March 2011 LAPACK-3(3)

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