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## man page of LAPACK-3

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

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## NAME

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

SUBROUTINE ZLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY ) IMPLICIT NONE DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS COMPLEX*16 AB( LDAB, * ), X( * ) DOUBLE PRECISION Y( * )## PURPOSE

DLA_GBAMV performs one of the matrix-vector operations or y := alpha*abs(A)'*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an m by n 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

TRANS (input) INTEGER On entry, TRANS specifies the operation to be performed as follows: BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) BLAS_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y) BLAS_CONJ_TRANS y := alpha*abs(A')*abs(x) + beta*abs(y) Unchanged on exit. M (input) INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. 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. KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. ALPHA - DOUBLE PRECISION On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - DOUBLE PRECISION 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, m ). Unchanged on exit. X (input) DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. 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 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. 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. Level 2 Blas routine. LAPACK routine (version 3.2.2)March 2011 LAPACK-3(3)

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