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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine sgbmv | ( | character | trans, |
| integer | m, | ||
| integer | n, | ||
| integer | kl, | ||
| integer | ku, | ||
| real | alpha, | ||
| real, dimension(lda,*) | a, | ||
| integer | lda, | ||
| real, dimension(*) | x, | ||
| integer | incx, | ||
| real | beta, | ||
| real, dimension(*) | y, | ||
| integer | incy | ||
| ) |
SGBMV
SGBMV performs one of the matrix-vector operations
y := alpha*A*x + beta*y, or y := alpha*A**T*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. | [in] | TRANS | TRANS is 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**T*x + beta*y. |
| [in] | M | M is INTEGER
On entry, M specifies the number of rows of the matrix A.
M must be at least zero. |
| [in] | N | N is INTEGER
On entry, N specifies the number of columns of the matrix A.
N must be at least zero. |
| [in] | KL | KL is INTEGER
On entry, KL specifies the number of sub-diagonals of the
matrix A. KL must satisfy 0 .le. KL. |
| [in] | KU | KU is INTEGER
On entry, KU specifies the number of super-diagonals of the
matrix A. KU must satisfy 0 .le. KU. |
| [in] | ALPHA | ALPHA is REAL
On entry, ALPHA specifies the scalar alpha. |
| [in] | A | A is REAL array, 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 |
| [in] | LDA | LDA is 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 ). |
| [in] | X | X is REAL array, 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. |
| [in] | INCX | INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero. |
| [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. |
| [in,out] | Y | Y is REAL array, 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.
If either m or n is zero, then Y not referenced and the function
performs a quick return. |
| [in] | INCY | INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero. |
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- 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. Definition at line 186 of file sgbmv.f.
1.9.7