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SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
$ LDC, WORK, LWORK, INFO ) * * -- LAPACK 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 SIDE, TRANS, VECT INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C * with * SIDE = 'L' SIDE = 'R' * TRANS = 'N': Q * C C * Q * TRANS = 'T': Q**T * C C * Q**T * * If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C * with * SIDE = 'L' SIDE = 'R' * TRANS = 'N': P * C C * P * TRANS = 'T': P**T * C C * P**T * * Here Q and P**T are the orthogonal matrices determined by DGEBRD when * reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and * P**T are defined as products of elementary reflectors H(i) and G(i) * respectively. * * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the * order of the orthogonal matrix Q or P**T that is applied. * * If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: * if nq >= k, Q = H(1) H(2) . . . H(k); * if nq < k, Q = H(1) H(2) . . . H(nq-1). * * If VECT = 'P', A is assumed to have been a K-by-NQ matrix: * if k < nq, P = G(1) G(2) . . . G(k); * if k >= nq, P = G(1) G(2) . . . G(nq-1). * * Arguments * ========= * * VECT (input) CHARACTER*1 * = 'Q': apply Q or Q**T; * = 'P': apply P or P**T. * * SIDE (input) CHARACTER*1 * = 'L': apply Q, Q**T, P or P**T from the Left; * = 'R': apply Q, Q**T, P or P**T from the Right. * * TRANS (input) CHARACTER*1 * = 'N': No transpose, apply Q or P; * = 'T': Transpose, apply Q**T or P**T. * * M (input) INTEGER * The number of rows of the matrix C. M >= 0. * * N (input) INTEGER * The number of columns of the matrix C. N >= 0. * * K (input) INTEGER * If VECT = 'Q', the number of columns in the original * matrix reduced by DGEBRD. * If VECT = 'P', the number of rows in the original * matrix reduced by DGEBRD. * K >= 0. * * A (input) DOUBLE PRECISION array, dimension * (LDA,min(nq,K)) if VECT = 'Q' * (LDA,nq) if VECT = 'P' * The vectors which define the elementary reflectors H(i) and * G(i), whose products determine the matrices Q and P, as * returned by DGEBRD. * * LDA (input) INTEGER * The leading dimension of the array A. * If VECT = 'Q', LDA >= max(1,nq); * if VECT = 'P', LDA >= max(1,min(nq,K)). * * TAU (input) DOUBLE PRECISION array, dimension (min(nq,K)) * TAU(i) must contain the scalar factor of the elementary * reflector H(i) or G(i) which determines Q or P, as returned * by DGEBRD in the array argument TAUQ or TAUP. * * C (input/output) DOUBLE PRECISION array, dimension (LDC,N) * On entry, the M-by-N matrix C. * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q * or P*C or P**T*C or C*P or C*P**T. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. * If SIDE = 'L', LWORK >= max(1,N); * if SIDE = 'R', LWORK >= max(1,M). * For optimum performance LWORK >= N*NB if SIDE = 'L', and * LWORK >= M*NB if SIDE = 'R', where NB is the optimal * blocksize. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Local Scalars .. LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DORMLQ, DORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 APPLYQ = LSAME( VECT, 'Q' ) LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q or P and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( K.LT.0 ) THEN INFO = -6 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) $ THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN IF( APPLYQ ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * WORK( 1 ) = 1 IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * IF( APPLYQ ) THEN * * Apply Q * IF( NQ.GE.K ) THEN * * Q was determined by a call to DGEBRD with nq >= k * CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * Q was determined by a call to DGEBRD with nq < k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF ELSE * * Apply P * IF( NOTRAN ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF IF( NQ.GT.K ) THEN * * P was determined by a call to DGEBRD with nq > k * CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * P was determined by a call to DGEBRD with nq <= k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of DORMBR * END |