zgbmv.f man page

zgbmv.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zgbmv (characterTRANS, integerM, integerN, integerKL, integerKU, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

ZGBMV Purpose:

ZGBMV  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*16
 On entry, ALPHA specifies the scalar alpha.

A

A is COMPLEX*16 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*16 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*16
 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*16 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 188 of file zgbmv.f.

Author

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Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK