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# ctbmv.f

Section: LAPACK (3)
Updated: Wed Oct 17 2018
Index

ctbmv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine CTBMV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBMV

## Function/Subroutine Documentation

### subroutine CTBMV (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex, dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX)

CTBMV Purpose:

` CTBMV  performs one of the matrix-vector operations    x := A*x,   or   x := A**T*x,   or   x := A**H*x, where x is an n element vector and  A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.`

Parameters:

UPLO

`          UPLO is CHARACTER*1           On entry, UPLO specifies whether the matrix is an upper or           lower triangular matrix as follows:              UPLO = 'U' or 'u'   A is an upper triangular matrix.              UPLO = 'L' or 'l'   A is a lower triangular matrix.`

TRANS

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

DIAG

`          DIAG is CHARACTER*1           On entry, DIAG specifies whether or not A is unit           triangular as follows:              DIAG = 'U' or 'u'   A is assumed to be unit triangular.              DIAG = 'N' or 'n'   A is not assumed to be unit                                  triangular.`

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 with UPLO = 'U' or 'u', K specifies the number of           super-diagonals of the matrix A.           On entry with UPLO = 'L' or 'l', K specifies the number of           sub-diagonals of the matrix A.           K must satisfy  0 .le. K.`

A

`          A is COMPLEX 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 matrix of coefficients, 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 an upper           triangular 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 matrix of coefficients, 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 a lower           triangular 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 when DIAG = 'U' or 'u' the elements of the array A           corresponding to the diagonal elements of the matrix are not           referenced, but are assumed to be unity.`

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 of dimension at least           ( 1 + ( n - 1 )*abs( INCX ) ).           Before entry, the incremented array X must contain the n           element vector x. On exit, X is overwritten with the           tranformed vector x.`

INCX

`          INCX is INTEGER           On entry, INCX specifies the increment for the elements of           X. INCX must not be zero.`

Author:

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 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 187 of file ctbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine CTBMV (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex, dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX)
Author

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