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