SUBROUTINE SLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, \$ T, LDT, C, LDC, WORK, LDWORK ) IMPLICIT NONE * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. REAL C( LDC, * ), T( LDT, * ), V( LDV, * ), \$ WORK( LDWORK, * ) * .. * * Purpose * ======= * * SLARFB applies a real block reflector H or its transpose H' to a * real m by n matrix C, from either the left or the right. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': apply H or H' from the Left * = 'R': apply H or H' from the Right * * TRANS (input) CHARACTER*1 * = 'N': apply H (No transpose) * = 'T': apply H' (Transpose) * * DIRECT (input) CHARACTER*1 * Indicates how H is formed from a product of elementary * reflectors * = 'F': H = H(1) H(2) . . . H(k) (Forward) * = 'B': H = H(k) . . . H(2) H(1) (Backward) * * STOREV (input) CHARACTER*1 * Indicates how the vectors which define the elementary * reflectors are stored: * = 'C': Columnwise * = 'R': Rowwise * * M (input) INTEGER * The number of rows of the matrix C. * * N (input) INTEGER * The number of columns of the matrix C. * * K (input) INTEGER * The order of the matrix T (= the number of elementary * reflectors whose product defines the block reflector). * * V (input) REAL array, dimension * (LDV,K) if STOREV = 'C' * (LDV,M) if STOREV = 'R' and SIDE = 'L' * (LDV,N) if STOREV = 'R' and SIDE = 'R' * The matrix V. See further details. * * LDV (input) INTEGER * The leading dimension of the array V. * If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); * if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); * if STOREV = 'R', LDV >= K. * * T (input) REAL array, dimension (LDT,K) * The triangular k by k matrix T in the representation of the * block reflector. * * LDT (input) INTEGER * The leading dimension of the array T. LDT >= K. * * C (input/output) REAL array, dimension (LDC,N) * On entry, the m by n matrix C. * On exit, C is overwritten by H*C or H'*C or C*H or C*H'. * * LDC (input) INTEGER * The leading dimension of the array C. LDA >= max(1,M). * * WORK (workspace) REAL array, dimension (LDWORK,K) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. * If SIDE = 'L', LDWORK >= max(1,N); * if SIDE = 'R', LDWORK >= max(1,M). * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. CHARACTER TRANST INTEGER I, J, LASTV, LASTC * .. * .. External Functions .. LOGICAL LSAME INTEGER ILASLR, ILASLC EXTERNAL LSAME, ILASLR, ILASLC * .. * .. External Subroutines .. EXTERNAL SCOPY, SGEMM, STRMM * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF * IF( LSAME( STOREV, 'C' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 ) (first K rows) * ( V2 ) * where V1 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H' * C where C = ( C1 ) * ( C2 ) * LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC ) * * W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) * * W := C1' * DO 10 J = 1, K CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE * * W := W * V1 * CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C2'*V2 * CALL SGEMM( 'Transpose', 'No transpose', \$ LASTC, K, LASTV-K, \$ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T' or W * T * CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W' * IF( LASTV.GT.K ) THEN * * C2 := C2 - V2 * W' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTV-K, LASTC, K, \$ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, \$ C( K+1, 1 ), LDC ) END IF * * W := W * V1' * CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W' * DO 30 J = 1, K DO 20 I = 1, LASTC C( J, I ) = C( J, I ) - WORK( I, J ) 20 CONTINUE 30 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H' where C = ( C1 C2 ) * LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C1 * DO 40 J = 1, K CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE * * W := W * V1 * CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C2 * V2 * CALL SGEMM( 'No transpose', 'No transpose', \$ LASTC, K, LASTV-K, \$ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T' * CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V' * IF( LASTV.GT.K ) THEN * * C2 := C2 - W * V2' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTC, LASTV-K, K, \$ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, \$ C( 1, K+1 ), LDC ) END IF * * W := W * V1' * CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 60 J = 1, K DO 50 I = 1, LASTC C( I, J ) = C( I, J ) - WORK( I, J ) 50 CONTINUE 60 CONTINUE END IF * ELSE * * Let V = ( V1 ) * ( V2 ) (last K rows) * where V2 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H' * C where C = ( C1 ) * ( C2 ) * LASTV = MAX( K, ILASLR( M, K, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC ) * * W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) * * W := C2' * DO 70 J = 1, K CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, \$ WORK( 1, J ), 1 ) 70 CONTINUE * * W := W * V2 * CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', \$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, \$ WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C1'*V1 * CALL SGEMM( 'Transpose', 'No transpose', \$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T' or W * T * CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W' * IF( LASTV.GT.K ) THEN * * C1 := C1 - V1 * W' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, \$ ONE, C, LDC ) END IF * * W := W * V2' * CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', \$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, \$ WORK, LDWORK ) * * C2 := C2 - W' * DO 90 J = 1, K DO 80 I = 1, LASTC C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) 80 CONTINUE 90 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H' where C = ( C1 C2 ) * LASTV = MAX( K, ILASLR( N, K, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C2 * DO 100 J = 1, K CALL SCOPY( LASTC, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE * * W := W * V2 * CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', \$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, \$ WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C1 * V1 * CALL SGEMM( 'No transpose', 'No transpose', \$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T' * CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V' * IF( LASTV.GT.K ) THEN * * C1 := C1 - W * V1' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, \$ ONE, C, LDC ) END IF * * W := W * V2' * CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', \$ LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV, \$ WORK, LDWORK ) * * C2 := C2 - W * DO 120 J = 1, K DO 110 I = 1, LASTC C( I, LASTV-K+J ) = C( I, LASTV-K+J ) - WORK(I, J) 110 CONTINUE 120 CONTINUE END IF END IF * ELSE IF( LSAME( STOREV, 'R' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 V2 ) (V1: first K columns) * where V1 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H' * C where C = ( C1 ) * ( C2 ) * LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC ) * * W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) * * W := C1' * DO 130 J = 1, K CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 130 CONTINUE * * W := W * V1' * CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C2'*V2' * CALL SGEMM( 'Transpose', 'Transpose', \$ LASTC, K, LASTV-K, \$ ONE, C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T' or W * T * CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - V' * W' * IF( LASTV.GT.K ) THEN * * C2 := C2 - V2' * W' * CALL SGEMM( 'Transpose', 'Transpose', \$ LASTV-K, LASTC, K, \$ -ONE, V( 1, K+1 ), LDV, WORK, LDWORK, \$ ONE, C( K+1, 1 ), LDC ) END IF * * W := W * V1 * CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W' * DO 150 J = 1, K DO 140 I = 1, LASTC C( J, I ) = C( J, I ) - WORK( I, J ) 140 CONTINUE 150 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H' where C = ( C1 C2 ) * LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC ) * * W := C * V' = (C1*V1' + C2*V2') (stored in WORK) * * W := C1 * DO 160 J = 1, K CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE * * W := W * V1' * CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C2 * V2' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTC, K, LASTV-K, \$ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T' * CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( LASTV.GT.K ) THEN * * C2 := C2 - W * V2 * CALL SGEMM( 'No transpose', 'No transpose', \$ LASTC, LASTV-K, K, \$ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, \$ ONE, C( 1, K+1 ), LDC ) END IF * * W := W * V1 * CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit', \$ LASTC, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 180 J = 1, K DO 170 I = 1, LASTC C( I, J ) = C( I, J ) - WORK( I, J ) 170 CONTINUE 180 CONTINUE * END IF * ELSE * * Let V = ( V1 V2 ) (V2: last K columns) * where V2 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H' * C where C = ( C1 ) * ( C2 ) * LASTV = MAX( K, ILASLC( K, M, V, LDV ) ) LASTC = ILASLC( LASTV, N, C, LDC ) * * W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) * * W := C2' * DO 190 J = 1, K CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC, \$ WORK( 1, J ), 1 ) 190 CONTINUE * * W := W * V2' * CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', \$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, \$ WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C1'*V1' * CALL SGEMM( 'Transpose', 'Transpose', \$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T' or W * T * CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - V' * W' * IF( LASTV.GT.K ) THEN * * C1 := C1 - V1' * W' * CALL SGEMM( 'Transpose', 'Transpose', \$ LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK, \$ ONE, C, LDC ) END IF * * W := W * V2 * CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', \$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, \$ WORK, LDWORK ) * * C2 := C2 - W' * DO 210 J = 1, K DO 200 I = 1, LASTC C( LASTV-K+J, I ) = C( LASTV-K+J, I ) - WORK(I, J) 200 CONTINUE 210 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H' where C = ( C1 C2 ) * LASTV = MAX( K, ILASLC( K, N, V, LDV ) ) LASTC = ILASLR( M, LASTV, C, LDC ) * * W := C * V' = (C1*V1' + C2*V2') (stored in WORK) * * W := C2 * DO 220 J = 1, K CALL SCOPY( LASTC, C( 1, LASTV-K+J ), 1, \$ WORK( 1, J ), 1 ) 220 CONTINUE * * W := W * V2' * CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit', \$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, \$ WORK, LDWORK ) IF( LASTV.GT.K ) THEN * * W := W + C1 * V1' * CALL SGEMM( 'No transpose', 'Transpose', \$ LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, \$ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T' * CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', \$ LASTC, K, ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( LASTV.GT.K ) THEN * * C1 := C1 - W * V1 * CALL SGEMM( 'No transpose', 'No transpose', \$ LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV, \$ ONE, C, LDC ) END IF * * W := W * V2 * CALL STRMM( 'Right', 'Lower', 'No transpose', 'Unit', \$ LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV, \$ WORK, LDWORK ) * * C1 := C1 - W * DO 240 J = 1, K DO 230 I = 1, LASTC C( I, LASTV-K+J ) = C( I, LASTV-K+J ) \$ - WORK( I, J ) 230 CONTINUE 240 CONTINUE * END IF * END IF END IF * RETURN * * End of SLARFB * END