
NAMEzhbmv.f SYNOPSISFunctions/Subroutinessubroutine zhbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY) Function/Subroutine Documentationsubroutine zhbmv (characterUPLO, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)ZHBMV Purpose:ZHBMV performs the matrixvector 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 hermitian band matrix, with k superdiagonals. UPLO
Author:
UPLO is 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.N N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.K K is INTEGER On entry, K specifies the number of superdiagonals of the matrix A. K must satisfy 0 .le. K.ALPHA ALPHA is COMPLEX*16 On entry, ALPHA specifies the scalar alpha.A A is COMPLEX*16 array of 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 hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first superdiagonal 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 hermitian 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 hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first subdiagonal 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 hermitian 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 Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.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 ( k + 1 ).X X is COMPLEX*16 array of DIMENSION at least ( 1 + ( n  1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x.INCX INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.BETA BETA is COMPLEX*16 On entry, BETA specifies the scalar beta.Y Y is COMPLEX*16 array of 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 INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
Level 2 Blas routine. The vector and matrix arguments are not referenced when N = 0, or M = 0  Written on 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs. AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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