250 lines
8.1 KiB
Fortran
250 lines
8.1 KiB
Fortran
SUBROUTINE MB01ND( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
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C
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C SLICOT RELEASE 5.0.
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C
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C Copyright (c) 2002-2009 NICONET e.V.
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C
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C This program is free software: you can redistribute it and/or
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C modify it under the terms of the GNU General Public License as
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C published by the Free Software Foundation, either version 2 of
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C the License, or (at your option) any later version.
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C
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C This program is distributed in the hope that it will be useful,
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C but WITHOUT ANY WARRANTY; without even the implied warranty of
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C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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C GNU General Public License for more details.
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C
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C You should have received a copy of the GNU General Public License
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C along with this program. If not, see
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C <http://www.gnu.org/licenses/>.
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C
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C PURPOSE
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C
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C To perform the skew-symmetric rank 2 operation
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C
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C A := alpha*x*y' - alpha*y*x' + A,
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C
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C where alpha is a scalar, x and y are vectors of length n and A is
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C an n-by-n skew-symmetric matrix.
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C
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C This is a modified version of the vanilla implemented BLAS
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C routine DSYR2 written by Jack Dongarra, Jeremy Du Croz,
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C Sven Hammarling, and Richard Hanson.
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C
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C ARGUMENTS
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C
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C Mode Parameters
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C
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C UPLO CHARACTER*1
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C Specifies whether the upper or lower triangular part of
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C the array A is to be referenced as follows:
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C = 'U': only the strictly upper triangular part of A is to
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C be referenced;
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C = 'L': only the strictly lower triangular part of A is to
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C be referenced.
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C
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C Input/Output Parameters
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C
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C N (input) INTEGER
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C The order of the matrix A. N >= 0.
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C
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C ALPHA (input) DOUBLE PRECISION
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C The scalar alpha. If alpha is zero X and Y are not
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C referenced.
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C
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C X (input) DOUBLE PRECISION array, dimension
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C ( 1 + ( N - 1 )*abs( INCX ) ).
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C On entry, elements 1, INCX+1, .., ( N - 1 )*INCX + 1 of
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C this array must contain the elements of the vector X.
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C
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C INCX (input) INTEGER
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C The increment for the elements of X. IF INCX < 0 then the
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C elements of X are accessed in reversed order. INCX <> 0.
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C
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C Y (input) DOUBLE PRECISION array, dimension
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C ( 1 + ( N - 1 )*abs( INCY ) ).
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C On entry, elements 1, INCY+1, .., ( N - 1 )*INCY + 1 of
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C this array must contain the elements of the vector Y.
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C
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C INCY (input) INTEGER
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C The increment for the elements of Y. IF INCY < 0 then the
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C elements of Y are accessed in reversed order. INCY <> 0.
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C
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C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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C On entry with UPLO = 'U', the leading N-by-N part of this
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C array must contain the strictly upper triangular part of
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C the matrix A. The lower triangular part of this array is
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C not referenced.
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C On entry with UPLO = 'L', the leading N-by-N part of this
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C array must contain the strictly lower triangular part of
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C the matrix A. The upper triangular part of this array is
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C not referenced.
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C On exit with UPLO = 'U', the leading N-by-N part of this
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C array contains the strictly upper triangular part of the
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C updated matrix A.
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C On exit with UPLO = 'L', the leading N-by-N part of this
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C array contains the strictly lower triangular part of the
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C updated matrix A.
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C
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C LDA INTEGER
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C The leading dimension of the array A. LDA >= MAX(1,N)
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C
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C NUMERICAL ASPECTS
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C
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C Though being almost identical with the vanilla implementation
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C of the BLAS routine DSYR2 the performance of this routine could
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C be significantly lower in the case of vendor supplied, highly
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C optimized BLAS.
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C
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C CONTRIBUTORS
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C
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C D. Kressner, Technical Univ. Berlin, Germany, and
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C P. Benner, Technical Univ. Chemnitz, Germany, December 2003.
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C
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C REVISIONS
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C
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C V. Sima, May 2008 (SLICOT version of the HAPACK routine DSKR2).
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C
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C KEYWORDS
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C
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C Elementary matrix operations.
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C
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C ******************************************************************
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C
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C .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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C .. Scalar Arguments ..
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DOUBLE PRECISION ALPHA
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INTEGER INCX, INCY, LDA, N
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CHARACTER UPLO
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C .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
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C .. Local Scalars ..
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DOUBLE PRECISION TEMP1, TEMP2
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INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
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C .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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C .. External Subroutines ..
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EXTERNAL XERBLA
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C .. Intrinsic Functions ..
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INTRINSIC MAX
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C
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C .. Executable Statements ..
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C
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C Test the input parameters.
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C
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INFO = 0
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IF ( .NOT.LSAME( UPLO, 'U' ).AND.
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$ .NOT.LSAME( UPLO, 'L' ) )THEN
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INFO = 1
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ELSE IF ( N.LT.0 )THEN
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INFO = 2
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ELSE IF ( INCX.EQ.0 )THEN
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INFO = 5
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ELSE IF ( INCY.EQ.0 )THEN
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INFO = 7
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ELSE IF ( LDA.LT.MAX( 1, N ) )THEN
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INFO = 9
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END IF
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C
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IF ( INFO.NE.0 )THEN
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CALL XERBLA( 'MB01ND', INFO )
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RETURN
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END IF
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C
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C Quick return if possible.
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C
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IF ( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
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$ RETURN
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C
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C Set up the start points in X and Y if the increments are not both
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C unity.
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C
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IF ( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
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IF ( INCX.GT.0 )THEN
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KX = 1
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ELSE
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KX = 1 - ( N - 1 )*INCX
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END IF
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IF ( INCY.GT.0 )THEN
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KY = 1
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ELSE
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KY = 1 - ( N - 1 )*INCY
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END IF
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JX = KX
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JY = KY
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END IF
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C
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C Start the operations. In this version the elements of A are
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C accessed sequentially with one pass through the triangular part
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C of A.
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C
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IF ( LSAME( UPLO, 'U' ) )THEN
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C
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C Form A when A is stored in the upper triangle.
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C
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IF ( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 20 J = 2, N
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IF ( ( X(J).NE.ZERO ).OR.( Y(J).NE.ZERO ) )THEN
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TEMP1 = ALPHA*Y(J)
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TEMP2 = ALPHA*X(J)
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DO 10 I = 1, J-1
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A(I,J) = A(I,J) + X(I)*TEMP1 - Y(I)*TEMP2
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10 CONTINUE
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END IF
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20 CONTINUE
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ELSE
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DO 40 J = 2, N
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IF ( ( X(JX).NE.ZERO ).OR.( Y(JY).NE.ZERO ) )THEN
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TEMP1 = ALPHA*Y(JY)
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TEMP2 = ALPHA*X(JX)
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IX = KX
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IY = KY
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DO 30 I = 1, J-1
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A(I,J) = A(I,J) + X(IX)*TEMP1 - Y(IY)*TEMP2
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IX = IX + INCX
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IY = IY + INCY
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30 CONTINUE
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END IF
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JX = JX + INCX
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JY = JY + INCY
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40 CONTINUE
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END IF
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ELSE
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C
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C Form A when A is stored in the lower triangle.
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C
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IF ( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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DO 60 J = 1, N-1
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IF ( ( X(J).NE.ZERO ).OR.( Y(J).NE.ZERO ) )THEN
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TEMP1 = ALPHA*Y(J)
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TEMP2 = ALPHA*X(J)
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DO 50 I = J+1, N
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A(I,J) = A(I,J) + X(I)*TEMP1 - Y(I)*TEMP2
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE
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DO 80 J = 1, N-1
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IF ( ( X(JX).NE.ZERO ).OR.( Y(JY).NE.ZERO ) )THEN
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TEMP1 = ALPHA*Y(JY)
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TEMP2 = ALPHA*X(JX)
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IX = JX
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IY = JY
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DO 70 I = J+1, N
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A(I,J) = A(I,J) + X(IX)*TEMP1 - Y(IY)*TEMP2
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IX = IX + INCX
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IY = IY + INCY
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70 CONTINUE
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END IF
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JX = JX + INCX
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JY = JY + INCY
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80 CONTINUE
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END IF
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END IF
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RETURN
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C *** Last line of MB01ND ***
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END
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