# zsbmv.f - Man Page

TESTING/LIN/zsbmv.f

## Synopsis

### Functions/Subroutines

subroutine **zsbmv** (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)**ZSBMV**

## Function/Subroutine Documentation

### subroutine zsbmv (character uplo, integer n, integer k, complex*16 alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, complex*16 beta, complex*16, dimension( * ) y, integer incy)

**ZSBMV**

**Purpose:**

ZSBMV 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*16 On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - COMPLEX*16 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*16 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*16 On entry, BETA specifies the scalar beta. Unchanged on exit. Y - COMPLEX*16 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **150** of file **zsbmv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK