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RedHat 9 (Linux i386) - man page for cgbmv (redhat section l)

CGBMV(l)				   BLAS routine 				 CGBMV(l)

NAME
       CGBMV  -  perform  one  of the matrix-vector operations	 y := alpha*A*x + beta*y, or y :=
       alpha*A'*x + beta*y, or	 y := alpha*conjg( A' )*x + beta*y,

SYNOPSIS
       SUBROUTINE CGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

	   COMPLEX	ALPHA, BETA

	   INTEGER	INCX, INCY, KL, KU, LDA, M, N

	   CHARACTER*1	TRANS

	   COMPLEX	A( LDA, * ), X( * ), Y( * )

PURPOSE
       CGBMV  performs one of the matrix-vector operations

       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  - 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'*x + beta*y.

	      TRANS = 'C' or 'c'   y := alpha*conjg( A' )*x + beta*y.

	      Unchanged on exit.

       M      - INTEGER.
	      On entry, M specifies the number of rows of the matrix A.  M must be at least zero.
	      Unchanged on exit.

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

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

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

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

       A      - COMPLEX 	 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 posi-
	      tion 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

	      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 ( kl + ku + 1 ).  Unchanged on exit.

       X      - COMPLEX 	 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.  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. When BETA is supplied as zero then Y need
	      not be set on input.  Unchanged on exit.

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

	      Level 2 Blas routine.

	      --  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.

BLAS routine				 16 October 1992				 CGBMV(l)


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