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# cgbmv.f

Section: LAPACK (3)
Updated: Thu Jun 23 2016
Index

cgbmv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine CGBMV (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV

## Function Documentation

### subroutine CGBMV (CHARACTERTRANS, INTEGERM, INTEGERN, INTEGERKL, INTEGERKU, COMPLEXALPHA, COMPLEX,dimension(lda,*)A, INTEGERLDA, COMPLEX,dimension(*)X, INTEGERINCX, COMPLEXBETA, COMPLEX,dimension(*)Y, INTEGERINCY)

CGBMV Purpose:

` CGBMV  performs one of the matrix-vector operations    y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or    y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals. `

Parameters:

TRANS

`          TRANS is CHARACTER*1           On entry, TRANS specifies the operation to be performed as           follows:              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.              TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.              TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y. `

M

`          M is INTEGER           On entry, M specifies the number of rows of the matrix A.           M must be at least zero. `

N

`          N is INTEGER           On entry, N specifies the number of columns of the matrix A.           N must be at least zero. `

KL

`          KL is INTEGER           On entry, KL specifies the number of sub-diagonals of the           matrix A. KL must satisfy  0 .le. KL. `

KU

`          KU is INTEGER           On entry, KU specifies the number of super-diagonals of the           matrix A. KU must satisfy  0 .le. KU. `

ALPHA

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

A

`          A is COMPLEX array of DIMENSION ( LDA, n ).           Before entry, the leading ( kl + ku + 1 ) by n part of the           array A must contain the matrix of coefficients, supplied           column by column, with the leading diagonal of the matrix in           row ( ku + 1 ) of the array, the first super-diagonal           starting at position 2 in row ku, the first sub-diagonal           starting at position 1 in row ( ku + 2 ), and so on.           Elements in the array A that do not correspond to elements           in the band matrix (such as the top left ku by ku triangle)           are not referenced.           The following program segment will transfer a band matrix           from conventional full matrix storage to band storage:                 DO 20, J = 1, N                    K = KU + 1 - J                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )                       A( K + I, J ) = matrix( I, J )              10    CONTINUE              20 CONTINUE `

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           ( kl + ku + 1 ). `

X

`          X is COMPLEX array of DIMENSION at least           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'           and at least           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.           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. When BETA is           supplied as zero then Y need not be set on input. `

Y

`          Y is COMPLEX array of DIMENSION at least           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'           and at least           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.           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

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 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 188 of file cgbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Index

NAME
SYNOPSIS
Functions/Subroutines
Function Documentation
subroutine CGBMV (CHARACTERTRANS, INTEGERM, INTEGERN, INTEGERKL, INTEGERKU, COMPLEXALPHA, COMPLEX,dimension(lda,*)A, INTEGERLDA, COMPLEX,dimension(*)X, INTEGERINCX, COMPLEXBETA, COMPLEX,dimension(*)Y, INTEGERINCY)
Author

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