sla_geamv (l) - Linux Manuals

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

NAME

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

SYNOPSIS

SUBROUTINE SLA_GEAMV
( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

    
IMPLICIT NONE

    
REAL ALPHA, BETA

    
INTEGER INCX, INCY, LDA, M, N, TRANS

    
REAL A( LDA, * ), X( * ), Y( * )

PURPOSE

SLA_GEAMV performs one of the matrix-vector operations
or   y := alpha*abs(A)aq*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 - 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(Aaq)*abs(x) + beta*abs(y)
BLAS_CONJ_TRANS y := alpha*abs(Aaq)*abs(x) + beta*abs(y) Unchanged on exit.
M - INTEGER
On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N - INTEGER
On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA - REAL
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A - REAL 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 - 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 - REAL array of DIMENSION at least
( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = aqNaq or aqnaq and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. Unchanged on exit.
INCX - INTEGER
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA - 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 - REAL
Array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = aqNaq or aqnaq 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 - INTEGER
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine.

Pages related to sla_geamv

  • sla_geamv (3)
  • sla_gercond (l) - SLA_GERCOND estimate the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number
  • sla_gerfsx_extended (l) - computes ..
  • sla_gbamv (l) - performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y),
  • sla_gbrcond (l) - SLA_GERCOND Estimate the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number
  • sla_gbrfsx_extended (l) - computes ..
  • sla_lin_berr (l) - SLA_LIN_BERR compute component-wise relative backward error from the formula max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) where abs(Z) is the component-wise absolute value of the matrix or vector Z
  • sla_porcond (l) - SLA_PORCOND Estimate the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C) The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number