ZGBMV
Purpose
ZGBMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
y := alpha*A**H*x + beta*y,
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.
y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
y := alpha*A**H*x + beta*y,
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
| TRANS |
CHARACTER*1.
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**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. Unchanged on exit. |
| M |
INTEGER.
On entry, M specifies the number of rows of the matrix A.
M must be at least zero. Unchanged on exit. |
| N |
INTEGER.
On entry, N specifies the number of columns of the matrix A.
N must be at least zero. Unchanged on exit. |
| KL |
INTEGER.
On entry, KL specifies the number of sub-diagonals of the
matrix A. KL must satisfy 0 .le. KL. Unchanged on exit. |
| KU |
INTEGER.
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy 0 .le. KU. Unchanged on exit. |
| ALPHA |
COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit. |
| A |
COMPLEX*16 array of DIMENSION ( LDA, n ).
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. |
| LDA |
INTEGER.
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. |
| X |
COMPLEX*16 array of DIMENSION at least
( 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 |
INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero. Unchanged on exit. |
| BETA |
COMPLEX*16 .
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 |
COMPLEX*16 array of DIMENSION at least
( 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. |
| INCY |
INTEGER.
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.
The vector and matrix arguments are not referenced when N = 0, or M = 0
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
The vector and matrix arguments are not referenced when N = 0, or M = 0
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.