dtbmv.f man page

dtbmv.f —

Synopsis

Functions/Subroutines

subroutine dtbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
DTBMV

Function/Subroutine Documentation

subroutine dtbmv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(*)X, integerINCX)

DTBMV Purpose:

DTBMV  performs one of the matrix-vector operations

   x := A*x,   or   x := A**T*x,

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

Parameters:

UPLO

UPLO is 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.

TRANS

TRANS is 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**T*x.

    TRANS = 'C' or 'c'   x := A**T*x.

DIAG

DIAG is 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.

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 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.

A

A is DOUBLE PRECISION 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 segment 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.

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 DOUBLE PRECISION 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

INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX 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 187 of file dtbmv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK