SRC/sla_gbamv.f(3)

NAME
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

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