zhbmv.f man page

zhbmv.f —

Synopsis

Functions/Subroutines

subroutine zhbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHBMV

Function/Subroutine Documentation

subroutine zhbmv (characterUPLO, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

ZHBMV Purpose:

ZHBMV  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 hermitian 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 COMPLEX*16
 On entry, ALPHA specifies the scalar alpha.

A

A is COMPLEX*16 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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 the imaginary parts of the diagonal elements need
 not be set and are assumed to be zero.

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*16 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 COMPLEX*16
 On entry, BETA specifies the scalar beta.

Y

Y is COMPLEX*16 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 188 of file zhbmv.f.

Author

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Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK