zla_gbamv.f - Man Page

subroutine zla_gbamv (TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY)
ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.

ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.  

Purpose:

 ZLA_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 DOUBLE PRECISION
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.

AB

          AB is COMPLEX*16 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, LDAB 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 COMPLEX*16 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 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

          Y is 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

          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.

Date:

June 2017

Definition at line 188 of file zla_gbamv.f.