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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine cla_gbamv | ( | integer | TRANS, |
integer | M, | ||
integer | N, | ||
integer | KL, | ||
integer | KU, | ||
real | ALPHA, | ||
complex, dimension( ldab, * ) | AB, | ||
integer | LDAB, | ||
complex, dimension( * ) | X, | ||
integer | INCX, | ||
real | BETA, | ||
real, dimension( * ) | Y, | ||
integer | INCY | ||
) |
CLA_GBAMV performs a matrix-vector operation to calculate error bounds.
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CLA_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.
[in] | 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. |
[in] | 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. |
[in] | 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. |
[in] | KL | KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. |
[in] | KU | KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. |
[in] | ALPHA | ALPHA is REAL On entry, ALPHA specifies the scalar alpha. Unchanged on exit. |
[in] | AB | AB is COMPLEX 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. |
[in] | 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. |
[in] | X | X is COMPLEX 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. |
[in] | INCX | INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. |
[in] | 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. |
[in,out] | 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. |
[in] | 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. |
Definition at line 188 of file cla_gbamv.f.