# sla_gbamv.f - Man Page

SRC/sla_gbamv.f

## Synopsis

### Functions/Subroutines

subroutine **sla_gbamv** (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)**SLA_GBAMV** performs a matrix-vector operation to calculate error bounds.

## Function/Subroutine Documentation

### subroutine sla_gbamv (integer trans, integer m, integer n, integer kl, integer ku, real alpha, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

**SLA_GBAMV** performs a matrix-vector operation to calculate error bounds.

**Purpose:**

SLA_GBAMV performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y), or y := alpha*abs(A)**T*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.

**Parameters***TRANS*TRANS is 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**T)*abs(x) + beta*abs(y) BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) Unchanged on exit.

*M*M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.

*KL*KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

*KU*KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

*ALPHA*ALPHA is REAL On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*AB*AB is REAL array, dimension ( LDAB, n ) Before entry, the leading m by n part of the array AB must contain the matrix of coefficients. Unchanged on exit.

*LDAB*LDAB is INTEGER On entry, LDA specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit.

*X*X is REAL 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*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 REAL 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 REAL 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. If either m or n is zero, then Y not referenced and the function performs a quick return.

*INCY*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **185** of file **sla_gbamv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sla_gbamv(3) is an alias of sla_gbamv.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK