Scroll to navigation

ZGBMV(1) BLAS routine ZGBMV(1)

NAME

ZGBMV - performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y,

SYNOPSIS

DOUBLE COMPLEX ALPHA,BETA INTEGER INCX,INCY,KL,KU,LDA,M,N CHARACTER TRANS DOUBLE COMPLEX A(LDA,*),X(*),Y(*)

PURPOSE

ZGBMV performs one of the matrix-vector operations

where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

ARGUMENTS

On entry, TRANS specifies the operation to be performed as follows:

TRANS = 'N' or 'n' y := alpha*A*x + beta*y.

TRANS = 'T' or 't' y := alpha*A'*x + beta*y.

TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.

Unchanged on exit.

On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL. Unchanged on exit.
On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU. Unchanged on exit.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage:

DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE

Unchanged on exit.

On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( kl + ku + 1 ). Unchanged on exit.
( 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.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.
( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

FURTHER DETAILS

Level 2 Blas routine.

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.

November 2008 BLAS routine