LAGEAMB - 5.2 English - 68552

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

Purpose:

   LA_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.
   Level 2 Blas routine.

Parameters:

• TRANS – [in]

  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 – [in]

  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 – [in]

  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 – [in]

  KL is INTEGER

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

• KU – [in]

  KU is INTEGER

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

• ALPHA – [in]

  ALPHA is REAL

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

• AB – [in]

  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 – [in]

  LDAB is INTEGER

  On entry, LDA specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least fla_max(1, m).

  Unchanged on exit.

• X – [in]

  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 – [in]

  INCX is INTEGER

  On entry, INCX specifies the increment for the elements of X. INCX must not be zero.

  Unchanged on exit.

• BETA – [in]

  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 – [inout]

  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.

• INCY – [in]

  INCY is INTEGER

  On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

  Unchanged on exit.