SLA_GBAMV
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.
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.
Arguments
| TRANS |
(input) 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 |
(input) INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero. Unchanged on exit. |
| N |
(input) INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero. Unchanged on exit. |
| KL |
(input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
|
| KU |
(input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
|
| ALPHA |
(input) REAL
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit. |
| AB |
(input) REAL array of 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 |
(input) 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 |
(input) 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 |
(input) INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero. Unchanged on exit. |
| BETA |
(input) 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 |
(input/output) 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 |
(input) INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero. Unchanged on exit. Level 2 Blas routine. |