SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, & T, LDT, C, LDC, WORK, LDWORK ) ! ! -- LAPACK auxiliary routine (version 3.1) -- ! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. ! November 2006 ! ! .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), & WORK( LDWORK, * ) ! .. ! ! Purpose ! ======= ! ! DLARFB 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) ! .. ! .. Local Scalars .. CHARACTER TRANST INTEGER I, J ! .. ! .. External Functions .. ! LOGICAL LSAME ! EXTERNAL LSAME ! .. ! .. External Subroutines .. ! EXTERNAL DCOPY, DGEMM, DTRMM ! .. ! .. 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 ) ! ! W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) ! ! W := C1' ! DO 10 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, & K, ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN ! ! W := W + C2'*V2 ! CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, & ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, & ONE, WORK, LDWORK ) END IF ! ! W := W * T' or W * T ! CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - V * W' ! IF( M.GT.K ) THEN ! ! C2 := C2 - V2 * W' ! CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, & -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, & C( K+1, 1 ), LDC ) END IF ! ! W := W * V1' ! CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, & ONE, V, LDV, WORK, LDWORK ) ! ! C1 := C1 - W' ! DO 30 J = 1, K DO 20 I = 1, N 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 ) ! ! W := C * V = (C1*V1 + C2*V2) (stored in WORK) ! ! W := C1 ! DO 40 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, & K, ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN ! ! W := W + C2 * V2 ! CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, & ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, & ONE, WORK, LDWORK ) END IF ! ! W := W * T or W * T' ! CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - W * V' ! IF( N.GT.K ) THEN ! ! C2 := C2 - W * V2' ! CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, & -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, & C( 1, K+1 ), LDC ) END IF ! ! W := W * V1' ! CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, & ONE, V, LDV, WORK, LDWORK ) ! ! C1 := C1 - W ! DO 60 J = 1, K DO 50 I = 1, M 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 ) ! ! W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) ! ! W := C2' ! DO 70 J = 1, K CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) 70 CONTINUE ! ! W := W * V2 ! CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, & K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) IF( M.GT.K ) THEN ! ! W := W + C1'*V1 ! CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, & ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF ! ! W := W * T' or W * T ! CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - V * W' ! IF( M.GT.K ) THEN ! ! C1 := C1 - V1 * W' ! CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, & -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) END IF ! ! W := W * V2' ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, & ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) ! ! C2 := C2 - W' ! DO 90 J = 1, K DO 80 I = 1, N C( M-K+J, I ) = C( M-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 ) ! ! W := C * V = (C1*V1 + C2*V2) (stored in WORK) ! ! W := C2 ! DO 100 J = 1, K CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE ! ! W := W * V2 ! CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, & K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) IF( N.GT.K ) THEN ! ! W := W + C1 * V1 ! CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, & ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF ! ! W := W * T or W * T' ! CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - W * V' ! IF( N.GT.K ) THEN ! ! C1 := C1 - W * V1' ! CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, & -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) END IF ! ! W := W * V2' ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, & ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) ! ! C2 := C2 - W ! DO 120 J = 1, K DO 110 I = 1, M C( I, N-K+J ) = C( I, N-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 ) ! ! W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) ! ! W := C1' ! DO 130 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 130 CONTINUE ! ! W := W * V1' ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, & ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN ! ! W := W + C2'*V2' ! CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, & C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, & WORK, LDWORK ) END IF ! ! W := W * T' or W * T ! CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - V' * W' ! IF( M.GT.K ) THEN ! ! C2 := C2 - V2' * W' ! CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, & V( 1, K+1 ), LDV, WORK, LDWORK, ONE, & C( K+1, 1 ), LDC ) END IF ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, & K, ONE, V, LDV, WORK, LDWORK ) ! ! C1 := C1 - W' ! DO 150 J = 1, K DO 140 I = 1, N 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 ) ! ! W := C * V' = (C1*V1' + C2*V2') (stored in WORK) ! ! W := C1 ! DO 160 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE ! ! W := W * V1' ! CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, & ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN ! ! W := W + C2 * V2' ! CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, & ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, & ONE, WORK, LDWORK ) END IF ! ! W := W * T or W * T' ! CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - W * V ! IF( N.GT.K ) THEN ! ! C2 := C2 - W * V2 ! CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, & -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, & C( 1, K+1 ), LDC ) END IF ! ! W := W * V1 ! CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, & K, ONE, V, LDV, WORK, LDWORK ) ! ! C1 := C1 - W ! DO 180 J = 1, K DO 170 I = 1, M 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 ) ! ! W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) ! ! W := C2' ! DO 190 J = 1, K CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) 190 CONTINUE ! ! W := W * V2' ! CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, & ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) IF( M.GT.K ) THEN ! ! W := W + C1'*V1' ! CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, & C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF ! ! W := W * T' or W * T ! CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - V' * W' ! IF( M.GT.K ) THEN ! ! C1 := C1 - V1' * W' ! CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, & V, LDV, WORK, LDWORK, ONE, C, LDC ) END IF ! ! W := W * V2 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, & K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) ! ! C2 := C2 - W' ! DO 210 J = 1, K DO 200 I = 1, N C( M-K+J, I ) = C( M-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 ) ! ! W := C * V' = (C1*V1' + C2*V2') (stored in WORK) ! ! W := C2 ! DO 220 J = 1, K CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 220 CONTINUE ! ! W := W * V2' ! CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, & ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) IF( N.GT.K ) THEN ! ! W := W + C1 * V1' ! CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, & ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF ! ! W := W * T or W * T' ! CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, & ONE, T, LDT, WORK, LDWORK ) ! ! C := C - W * V ! IF( N.GT.K ) THEN ! ! C1 := C1 - W * V1 ! CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, & -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) END IF ! ! W := W * V2 ! CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, & K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) ! ! C1 := C1 - W ! DO 240 J = 1, K DO 230 I = 1, M C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) 230 CONTINUE 240 CONTINUE ! END IF ! END IF END IF ! RETURN ! ! End of DLARFB ! END SUBROUTINE DLARFB