DGBMV (3) Linux Manual Page

dgbmv.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dgbmv (characterTRANS, integerM, integerN, integerKL, integerKU, double precisionALPHA, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(*)X, integerINCX, double precisionBETA, double precision, dimension(*)Y, integerINCY)

DGBMV Purpose:

 DGBMV performs one of the matrix-vector operations

 y := alpha*A*x + beta*y, or y := alpha*A**T*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**T*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 DOUBLE PRECISION.

 On entry, ALPHA specifies the scalar alpha.

A

 A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION.

 On entry, BETA specifies the scalar beta. When BETA is

 supplied as zero then Y need not be set on input.

Y

 Y is DOUBLE PRECISION 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

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 186 of file dgbmv.f.

Author

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