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

ZTBMV(l)				   BLAS routine 				 ZTBMV(l)

NAME
       ZTBMV  -  perform  one  of  the matrix-vector operations   x := A*x, or x := A'*x, or x :=
       conjg( A' )*x,

SYNOPSIS
       SUBROUTINE ZTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )

	   INTEGER	INCX, K, LDA, N

	   CHARACTER*1	DIAG, TRANS, UPLO

	   COMPLEX*16	A( LDA, * ), X( * )

PURPOSE
       ZTBMV  performs one of the matrix-vector operations

       where x is an n element vector and  A is an n by n unit, or non-unit, upper or lower  tri-
       angular band matrix, with ( k + 1 ) diagonals.

PARAMETERS
       UPLO   - CHARACTER*1.
	      On  entry, UPLO specifies whether the matrix is an upper or lower triangular matrix
	      as follows:

	      UPLO = 'U' or 'u'   A is an upper triangular matrix.

	      UPLO = 'L' or 'l'   A is a lower triangular matrix.

	      Unchanged on exit.

       TRANS  - CHARACTER*1.
	      On entry, TRANS specifies the operation to be performed as follows:

	      TRANS = 'N' or 'n'   x := A*x.

	      TRANS = 'T' or 't'   x := A'*x.

	      TRANS = 'C' or 'c'   x := conjg( A' )*x.

	      Unchanged on exit.

       DIAG   - CHARACTER*1.
	      On entry, DIAG specifies whether or not A is unit triangular as follows:

	      DIAG = 'U' or 'u'   A is assumed to be unit triangular.

	      DIAG = 'N' or 'n'   A is not assumed to be unit triangular.

	      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  with UPLO = 'U' or 'u', K specifies the number of super-diagonals of the
	      matrix A.  On entry with UPLO = 'L' or 'l', K specifies the number of sub-diagonals
	      of the matrix A.	K must satisfy	0 .le. K.  Unchanged on exit.

       A      - 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 matrix of coefficients, 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 seg-
	      ment will transfer an upper triangular 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 matrix of coefficients, 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 a lower triangular 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  when DIAG = 'U' or 'u' the elements of the array A corresponding to the
	      diagonal elements of the matrix are not referenced, but are assumed  to  be  unity.
	      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*16	 array of dimension at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must  contain
	      the n element vector x. On exit, X is overwritten with the tranformed vector x.

       INCX   - INTEGER.
	      On  entry,  INCX	specifies  the	increment for the elements of X. INCX 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				 ZTBMV(l)


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