# chbmv.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **chbmv** (UPLO, **N**, K, ALPHA, A, **LDA**, X, INCX, BETA, Y, INCY)**CHBMV**

## Function/Subroutine Documentation

### subroutine chbmv (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)

**CHBMV**

**Purpose:**

CHBMV 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 hermitian band matrix, with k super-diagonals.

**Parameters:***UPLO*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 super-diagonals of the matrix A. K must satisfy 0 .le. K.

*ALPHA*ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.

*A*A is 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 hermitian 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 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 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 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 array, 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 On entry, BETA specifies the scalar beta.

*Y*Y is 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*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

**Further Details:**

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 189 of file chbmv.f.

## Author

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## Referenced By

The man page chbmv(3) is an alias of chbmv.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK