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SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
$ LDV, T, LDT, C, LDC, WORK, LDWORK ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * ) * .. * * Purpose * ======= * * DLARZB applies a real block reflector H or its transpose H**T to * a real distributed M-by-N C from the left or the right. * * Currently, only STOREV = 'R' and DIRECT = 'B' are supported. * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': apply H or H**T from the Left * = 'R': apply H or H**T from the Right * * TRANS (input) CHARACTER*1 * = 'N': apply H (No transpose) * = 'C': apply H**T (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, not supported yet) * = '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 (not supported yet) * = '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). * * L (input) INTEGER * The number of columns of the matrix V containing the * meaningful part of the Householder reflectors. * If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. * * V (input) DOUBLE PRECISION array, dimension (LDV,NV). * If STOREV = 'C', NV = K; if STOREV = 'R', NV = L. * * LDV (input) INTEGER * The leading dimension of the array V. * If STOREV = 'C', LDV >= L; 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**T*C or C*H or C*H**T. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= 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). * * Further Details * =============== * * Based on contributions by * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. CHARACTER TRANST INTEGER I, INFO, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * * Check for currently supported options * INFO = 0 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN INFO = -3 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLARZB', -INFO ) RETURN END IF * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**T * C * * W( 1:n, 1:k ) = C( 1:k, 1:n )**T * DO 10 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE * * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ... * C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T * IF( L.GT.0 ) $ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE, $ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK ) * * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T * CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T, $ LDT, WORK, LDWORK ) * * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T * DO 30 J = 1, N DO 20 I = 1, K C( I, J ) = C( I, J ) - WORK( J, I ) 20 CONTINUE 30 CONTINUE * * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T * IF( L.GT.0 ) $ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV, $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC ) * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**T * * W( 1:m, 1:k ) = C( 1:m, 1:k ) * DO 40 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE * * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ... * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T * IF( L.GT.0 ) $ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE, $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK ) * * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T * CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T, $ LDT, WORK, LDWORK ) * * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k ) * DO 60 J = 1, K DO 50 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 50 CONTINUE 60 CONTINUE * * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... * W( 1:m, 1:k ) * V( 1:k, 1:l ) * IF( L.GT.0 ) $ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE, $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC ) * END IF * RETURN * * End of DLARZB * END |