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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| subroutine csbmv | ( | character | UPLO, |
| integer | N, | ||
| integer | K, | ||
| complex | ALPHA, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| complex, dimension( * ) | X, | ||
| integer | INCX, | ||
| complex | BETA, | ||
| complex, dimension( * ) | Y, | ||
| integer | INCY | ||
| ) |
CSBMV
CSBMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric band matrix, with k super-diagonals. UPLO - CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:
UPLO = 'U' or 'u' The upper triangular part of A is
being supplied.
UPLO = 'L' or 'l' The lower triangular part of A is
being supplied.
Unchanged on exit.
N - INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
K - INTEGER
On entry, K specifies the number of super-diagonals of the
matrix A. K must satisfy 0 .le. K.
Unchanged on exit.
ALPHA - COMPLEX
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
A - COMPLEX array, dimension( LDA, N )
Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the symmetric matrix, supplied column by
column, with the leading diagonal of the matrix in row
( k + 1 ) of the array, the first super-diagonal starting at
position 2 in row k, and so on. The top left k by k triangle
of the array A is not referenced.
The following program segment will transfer the upper
triangular part of a symmetric band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = K + 1 - J
DO 10, I = MAX( 1, J - K ), J
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE
Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the symmetric matrix, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer the lower
triangular part of a symmetric band matrix from conventional
full matrix storage to band storage:
DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + 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
( k + 1 ).
Unchanged on exit.
X - COMPLEX array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ).
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
On entry, BETA specifies the scalar beta.
Unchanged on exit.
Y - COMPLEX array, dimension at least
( 1 + ( N - 1 )*abs( INCY ) ).
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. Definition at line 154 of file csbmv.f.
1.8.10