sgbmv.f man page

sgbmv.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine sgbmv (characterTRANS, integerM, integerN, integerKL, integerKU, realALPHA, real, dimension(lda,*)A, integerLDA, real, dimension(*)X, integerINCX, realBETA, real, dimension(*)Y, integerINCY)

SGBMV Purpose:

SGBMV  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 REAL
 On entry, ALPHA specifies the scalar alpha.

A

A is REAL 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 REAL 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 REAL
 On entry, BETA specifies the scalar beta. When BETA is
 supplied as zero then Y need not be set on input.

Y

Y is REAL 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 sgbmv.f.

Author

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Referenced By

sgbmv(3) is an alias of sgbmv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK