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LAPACK
3.7.0
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.