SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * -- LAPACK auxiliary routine (version 3.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * October 31, 1992 * * .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE INTEGER LDA, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), C( * ), S( * ) * .. * * Purpose * ======= * * SLASR performs the transformation * * A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) * * A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) * * where A is an m by n real matrix and P is an orthogonal matrix, * consisting of a sequence of plane rotations determined by the * parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' * and z = n when SIDE = 'R' or 'r' ): * * When DIRECT = 'F' or 'f' ( Forward sequence ) then * * P = P( z - 1 )*...*P( 2 )*P( 1 ), * * and when DIRECT = 'B' or 'b' ( Backward sequence ) then * * P = P( 1 )*P( 2 )*...*P( z - 1 ), * * where P( k ) is a plane rotation matrix for the following planes: * * when PIVOT = 'V' or 'v' ( Variable pivot ), * the plane ( k, k + 1 ) * * when PIVOT = 'T' or 't' ( Top pivot ), * the plane ( 1, k + 1 ) * * when PIVOT = 'B' or 'b' ( Bottom pivot ), * the plane ( k, z ) * * c( k ) and s( k ) must contain the cosine and sine that define the * matrix P( k ). The two by two plane rotation part of the matrix * P( k ), R( k ), is assumed to be of the form * * R( k ) = ( c( k ) s( k ) ). * ( -s( k ) c( k ) ) * * This version vectorises across rows of the array A when SIDE = 'L'. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * Specifies whether the plane rotation matrix P is applied to * A on the left or the right. * = 'L': Left, compute A := P*A * = 'R': Right, compute A:= A*P' * * DIRECT (input) CHARACTER*1 * Specifies whether P is a forward or backward sequence of * plane rotations. * = 'F': Forward, P = P( z - 1 )*...*P( 2 )*P( 1 ) * = 'B': Backward, P = P( 1 )*P( 2 )*...*P( z - 1 ) * * PIVOT (input) CHARACTER*1 * Specifies the plane for which P(k) is a plane rotation * matrix. * = 'V': Variable pivot, the plane (k,k+1) * = 'T': Top pivot, the plane (1,k+1) * = 'B': Bottom pivot, the plane (k,z) * * M (input) INTEGER * The number of rows of the matrix A. If m <= 1, an immediate * return is effected. * * N (input) INTEGER * The number of columns of the matrix A. If n <= 1, an * immediate return is effected. * * C, S (input) REAL arrays, dimension * (M-1) if SIDE = 'L' * (N-1) if SIDE = 'R' * c(k) and s(k) contain the cosine and sine that define the * matrix P(k). The two by two plane rotation part of the * matrix P(k), R(k), is assumed to be of the form * R( k ) = ( c( k ) s( k ) ). * ( -s( k ) c( k ) ) * * A (input/output) REAL array, dimension (LDA,N) * The m by n matrix A. On exit, A is overwritten by P*A if * SIDE = 'R' or by A*P' if SIDE = 'L'. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J REAL CTEMP, STEMP, TEMP * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN INFO = 1 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN INFO = 2 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) $ THEN INFO = 3 ELSE IF( M.LT.0 ) THEN INFO = 4 ELSE IF( N.LT.0 ) THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = 9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLASR ', INFO ) RETURN END IF * * Quick return if possible * IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) $ RETURN IF( LSAME( SIDE, 'L' ) ) THEN * * Form P * A * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 20 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 10 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 10 CONTINUE END IF 20 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 40 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 30 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 30 CONTINUE END IF 40 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 60 J = 2, M CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 50 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 50 CONTINUE END IF 60 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 80 J = M, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 70 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 100 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 90 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 90 CONTINUE END IF 100 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 120 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 110 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 110 CONTINUE END IF 120 CONTINUE END IF END IF ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form A * P' * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 140 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 130 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 130 CONTINUE END IF 140 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 160 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 150 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 150 CONTINUE END IF 160 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 180 J = 2, N CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 170 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 170 CONTINUE END IF 180 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 200 J = N, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 190 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 190 CONTINUE END IF 200 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 220 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 210 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 210 CONTINUE END IF 220 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 240 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 230 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 230 CONTINUE END IF 240 CONTINUE END IF END IF END IF * RETURN * * End of SLASR * END