dsbmv.f (3) Linux Manual Page

dsbmv.f –

Synopsis

Functions/Subroutines

subroutine dsbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV

Function/Subroutine Documentation

subroutine dsbmv (characterUPLO, integerN, integerK, double precisionALPHA, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(*)X, integerINCX, double precisionBETA, double precision, dimension(*)Y, integerINCY)

DSBMV Purpose:

 DSBMV 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.

 

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 DOUBLE PRECISION.

 On entry, ALPHA specifies the scalar alpha.

A

 A is DOUBLE PRECISION 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 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

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 DOUBLE PRECISION 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 DOUBLE PRECISION.

 On entry, BETA specifies the scalar beta.

Y

 Y is DOUBLE PRECISION 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.

 

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 185 of file dsbmv.f.

Author

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