TESTING/LIN/csbmv.f(3)     Library Functions Manual     TESTING/LIN/csbmv.f(3)

NAME
       TESTING/LIN/csbmv.f

SYNOPSIS
   Functions/Subroutines
       subroutine csbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
           CSBMV

Function/Subroutine Documentation
   subroutine csbmv (character uplo, integer n, integer k, complex alpha,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x,
       integer incx, complex beta, complex, dimension( * ) y, integer incy)
       CSBMV

       Purpose:


            CSBMV  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.

             UPLO   - 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.

                      Unchanged on exit.

             N      - INTEGER
                      On entry, N specifies the order of the matrix A.
                      N must be at least zero.
                      Unchanged on exit.

             K      - INTEGER
                      On entry, K specifies the number of super-diagonals of the
                      matrix A. K must satisfy  0 .le. K.
                      Unchanged on exit.

             ALPHA  - COMPLEX
                      On entry, ALPHA specifies the scalar alpha.
                      Unchanged on exit.

             A      - COMPLEX array, 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

                      Unchanged on exit.

             LDA    - INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      ( k + 1 ).
                      Unchanged on exit.

             X      - COMPLEX array, dimension at least
                      ( 1 + ( N - 1 )*abs( INCX ) ).
                      Before entry, the incremented array X must contain the
                      vector x.
                      Unchanged on exit.

             INCX   - INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.
                      Unchanged on exit.

             BETA   - COMPLEX
                      On entry, BETA specifies the scalar beta.
                      Unchanged on exit.

             Y      - COMPLEX array, 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   - INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.
                      Unchanged on exit.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 150 of file csbmv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0          TESTING/LIN/csbmv.f(3)