From de7f36e7f9592366fb7db0bf6fc353924966f340 Mon Sep 17 00:00:00 2001 From: "philippe.theveny" Date: Fri, 14 Aug 2015 22:54:14 +0000 Subject: Added BLAS3 routines for generalised SVD. TODO: LAPACKE wrappers. --- SRC/zggsvp3.f | 580 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 580 insertions(+) create mode 100644 SRC/zggsvp3.f (limited to 'SRC/zggsvp3.f') diff --git a/SRC/zggsvp3.f b/SRC/zggsvp3.f new file mode 100644 index 00000000..b397651c --- /dev/null +++ b/SRC/zggsvp3.f @@ -0,0 +1,580 @@ +*> \brief \b ZGGSVP3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZGGSVP3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZGGSVP3( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, +* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, +* IWORK, RWORK, TAU, WORK, LWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBQ, JOBU, JOBV +* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK +* DOUBLE PRECISION TOLA, TOLB +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION RWORK( * ) +* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), +* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZGGSVP3 computes unitary matrices U, V and Q such that +*> +*> N-K-L K L +*> U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; +*> L ( 0 0 A23 ) +*> M-K-L ( 0 0 0 ) +*> +*> N-K-L K L +*> = K ( 0 A12 A13 ) if M-K-L < 0; +*> M-K ( 0 0 A23 ) +*> +*> N-K-L K L +*> V**H*B*Q = L ( 0 0 B13 ) +*> P-L ( 0 0 0 ) +*> +*> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular +*> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, +*> otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective +*> numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H. +*> +*> This decomposition is the preprocessing step for computing the +*> Generalized Singular Value Decomposition (GSVD), see subroutine +*> ZGGSVD3. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBU +*> \verbatim +*> JOBU is CHARACTER*1 +*> = 'U': Unitary matrix U is computed; +*> = 'N': U is not computed. +*> \endverbatim +*> +*> \param[in] JOBV +*> \verbatim +*> JOBV is CHARACTER*1 +*> = 'V': Unitary matrix V is computed; +*> = 'N': V is not computed. +*> \endverbatim +*> +*> \param[in] JOBQ +*> \verbatim +*> JOBQ is CHARACTER*1 +*> = 'Q': Unitary matrix Q is computed; +*> = 'N': Q is not computed. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] P +*> \verbatim +*> P is INTEGER +*> The number of rows of the matrix B. P >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrices A and B. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, A contains the triangular (or trapezoidal) matrix +*> described in the Purpose section. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX*16 array, dimension (LDB,N) +*> On entry, the P-by-N matrix B. +*> On exit, B contains the triangular matrix described in +*> the Purpose section. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,P). +*> \endverbatim +*> +*> \param[in] TOLA +*> \verbatim +*> TOLA is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] TOLB +*> \verbatim +*> TOLB is DOUBLE PRECISION +*> +*> TOLA and TOLB are the thresholds to determine the effective +*> numerical rank of matrix B and a subblock of A. Generally, +*> they are set to +*> TOLA = MAX(M,N)*norm(A)*MAZHEPS, +*> TOLB = MAX(P,N)*norm(B)*MAZHEPS. +*> The size of TOLA and TOLB may affect the size of backward +*> errors of the decomposition. +*> \endverbatim +*> +*> \param[out] K +*> \verbatim +*> K is INTEGER +*> \endverbatim +*> +*> \param[out] L +*> \verbatim +*> L is INTEGER +*> +*> On exit, K and L specify the dimension of the subblocks +*> described in Purpose section. +*> K + L = effective numerical rank of (A**H,B**H)**H. +*> \endverbatim +*> +*> \param[out] U +*> \verbatim +*> U is COMPLEX*16 array, dimension (LDU,M) +*> If JOBU = 'U', U contains the unitary matrix U. +*> If JOBU = 'N', U is not referenced. +*> \endverbatim +*> +*> \param[in] LDU +*> \verbatim +*> LDU is INTEGER +*> The leading dimension of the array U. LDU >= max(1,M) if +*> JOBU = 'U'; LDU >= 1 otherwise. +*> \endverbatim +*> +*> \param[out] V +*> \verbatim +*> V is COMPLEX*16 array, dimension (LDV,P) +*> If JOBV = 'V', V contains the unitary matrix V. +*> If JOBV = 'N', V is not referenced. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. LDV >= max(1,P) if +*> JOBV = 'V'; LDV >= 1 otherwise. +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is COMPLEX*16 array, dimension (LDQ,N) +*> If JOBQ = 'Q', Q contains the unitary matrix Q. +*> If JOBQ = 'N', Q is not referenced. +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of the array Q. LDQ >= max(1,N) if +*> JOBQ = 'Q'; LDQ >= 1 otherwise. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (N) +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (N) +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. +*> +*> 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. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date August 2015 +* +*> \ingroup complex16OTHERcomputational +* +*> \par Further Details: +* ===================== +* +*> \verbatim +*> +*> The subroutine uses LAPACK subroutine ZGEQP3 for the QR factorization +*> with column pivoting to detect the effective numerical rank of the +*> a matrix. It may be replaced by a better rank determination strategy. +*> +*> ZGGSVP3 replaces the deprecated subroutine ZGGSVP. +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZGGSVP3( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, + $ TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, + $ IWORK, RWORK, TAU, WORK, LWORK, INFO ) +* +* -- LAPACK computational routine (version 3.6.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* August 2015 +* + IMPLICIT NONE +* +* .. Scalar Arguments .. + CHARACTER JOBQ, JOBU, JOBV + INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, + $ LWORK + DOUBLE PRECISION TOLA, TOLB +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION RWORK( * ) + COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), + $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 CZERO, CONE + PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), + $ CONE = ( 1.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + LOGICAL FORWRD, WANTQ, WANTU, WANTV, LQUERY + INTEGER I, J, LWKOPT + COMPLEX*16 T +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZGEQP3, ZGEQR2, ZGERQ2, ZLACPY, ZLAPMT, + $ ZLASET, ZUNG2R, ZUNM2R, ZUNMR2 +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, DIMAG, MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + WANTU = LSAME( JOBU, 'U' ) + WANTV = LSAME( JOBV, 'V' ) + WANTQ = LSAME( JOBQ, 'Q' ) + FORWRD = .TRUE. + LQUERY = ( LWORK.EQ.-1 ) + LWKOPT = 1 +* +* Test the input arguments +* + INFO = 0 + IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN + INFO = -3 + ELSE IF( M.LT.0 ) THEN + INFO = -4 + ELSE IF( P.LT.0 ) THEN + INFO = -5 + ELSE IF( N.LT.0 ) THEN + INFO = -6 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -8 + ELSE IF( LDB.LT.MAX( 1, P ) ) THEN + INFO = -10 + ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN + INFO = -16 + ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN + INFO = -18 + ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN + INFO = -20 + ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN + INFO = -24 + END IF +* +* Compute workspace +* + IF( INFO.EQ.0 ) THEN + CALL ZGEQP3( P, N, B, LDB, IWORK, TAU, WORK, -1, RWORK, INFO ) + LWKOPT = INT( WORK ( 1 ) ) + IF( WANTV ) THEN + LWKOPT = MAX( LWKOPT, P ) + END IF + LWKOPT = MAX( LWKOPT, MIN( N, P ) ) + LWKOPT = MAX( LWKOPT, M ) + IF( WANTQ ) THEN + LWKOPT = MAX( LWKOPT, N ) + END IF + CALL ZGEQP3( M, N, A, LDA, IWORK, TAU, WORK, -1, RWORK, INFO ) + LWKOPT = MAX( LWKOPT, INT( WORK ( 1 ) ) ) + LWKOPT = MAX( 1, LWKOPT ) + WORK( 1 ) = DCMPLX( LWKOPT ) + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZGGSVP3', -INFO ) + RETURN + END IF + IF( LQUERY ) THEN + RETURN + ENDIF +* +* QR with column pivoting of B: B*P = V*( S11 S12 ) +* ( 0 0 ) +* + DO 10 I = 1, N + IWORK( I ) = 0 + 10 CONTINUE + CALL ZGEQP3( P, N, B, LDB, IWORK, TAU, WORK, LWORK, RWORK, INFO ) +* +* Update A := A*P +* + CALL ZLAPMT( FORWRD, M, N, A, LDA, IWORK ) +* +* Determine the effective rank of matrix B. +* + L = 0 + DO 20 I = 1, MIN( P, N ) + IF( ABS( B( I, I ) ).GT.TOLB ) + $ L = L + 1 + 20 CONTINUE +* + IF( WANTV ) THEN +* +* Copy the details of V, and form V. +* + CALL ZLASET( 'Full', P, P, CZERO, CZERO, V, LDV ) + IF( P.GT.1 ) + $ CALL ZLACPY( 'Lower', P-1, N, B( 2, 1 ), LDB, V( 2, 1 ), + $ LDV ) + CALL ZUNG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO ) + END IF +* +* Clean up B +* + DO 40 J = 1, L - 1 + DO 30 I = J + 1, L + B( I, J ) = CZERO + 30 CONTINUE + 40 CONTINUE + IF( P.GT.L ) + $ CALL ZLASET( 'Full', P-L, N, CZERO, CZERO, B( L+1, 1 ), LDB ) +* + IF( WANTQ ) THEN +* +* Set Q = I and Update Q := Q*P +* + CALL ZLASET( 'Full', N, N, CZERO, CONE, Q, LDQ ) + CALL ZLAPMT( FORWRD, N, N, Q, LDQ, IWORK ) + END IF +* + IF( P.GE.L .AND. N.NE.L ) THEN +* +* RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z +* + CALL ZGERQ2( L, N, B, LDB, TAU, WORK, INFO ) +* +* Update A := A*Z**H +* + CALL ZUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB, + $ TAU, A, LDA, WORK, INFO ) + IF( WANTQ ) THEN +* +* Update Q := Q*Z**H +* + CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N, L, B, + $ LDB, TAU, Q, LDQ, WORK, INFO ) + END IF +* +* Clean up B +* + CALL ZLASET( 'Full', L, N-L, CZERO, CZERO, B, LDB ) + DO 60 J = N - L + 1, N + DO 50 I = J - N + L + 1, L + B( I, J ) = CZERO + 50 CONTINUE + 60 CONTINUE +* + END IF +* +* Let N-L L +* A = ( A11 A12 ) M, +* +* then the following does the complete QR decomposition of A11: +* +* A11 = U*( 0 T12 )*P1**H +* ( 0 0 ) +* + DO 70 I = 1, N - L + IWORK( I ) = 0 + 70 CONTINUE + CALL ZGEQP3( M, N-L, A, LDA, IWORK, TAU, WORK, LWORK, RWORK, + $ INFO ) +* +* Determine the effective rank of A11 +* + K = 0 + DO 80 I = 1, MIN( M, N-L ) + IF( ABS( A( I, I ) ).GT.TOLA ) + $ K = K + 1 + 80 CONTINUE +* +* Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N ) +* + CALL ZUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ), + $ A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO ) +* + IF( WANTU ) THEN +* +* Copy the details of U, and form U +* + CALL ZLASET( 'Full', M, M, CZERO, CZERO, U, LDU ) + IF( M.GT.1 ) + $ CALL ZLACPY( 'Lower', M-1, N-L, A( 2, 1 ), LDA, U( 2, 1 ), + $ LDU ) + CALL ZUNG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO ) + END IF +* + IF( WANTQ ) THEN +* +* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 +* + CALL ZLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK ) + END IF +* +* Clean up A: set the strictly lower triangular part of +* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. +* + DO 100 J = 1, K - 1 + DO 90 I = J + 1, K + A( I, J ) = CZERO + 90 CONTINUE + 100 CONTINUE + IF( M.GT.K ) + $ CALL ZLASET( 'Full', M-K, N-L, CZERO, CZERO, A( K+1, 1 ), LDA ) +* + IF( N-L.GT.K ) THEN +* +* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 +* + CALL ZGERQ2( K, N-L, A, LDA, TAU, WORK, INFO ) +* + IF( WANTQ ) THEN +* +* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**H +* + CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A, + $ LDA, TAU, Q, LDQ, WORK, INFO ) + END IF +* +* Clean up A +* + CALL ZLASET( 'Full', K, N-L-K, CZERO, CZERO, A, LDA ) + DO 120 J = N - L - K + 1, N - L + DO 110 I = J - N + L + K + 1, K + A( I, J ) = CZERO + 110 CONTINUE + 120 CONTINUE +* + END IF +* + IF( M.GT.K ) THEN +* +* QR factorization of A( K+1:M,N-L+1:N ) +* + CALL ZGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO ) +* + IF( WANTU ) THEN +* +* Update U(:,K+1:M) := U(:,K+1:M)*U1 +* + CALL ZUNM2R( 'Right', 'No transpose', M, M-K, MIN( M-K, L ), + $ A( K+1, N-L+1 ), LDA, TAU, U( 1, K+1 ), LDU, + $ WORK, INFO ) + END IF +* +* Clean up +* + DO 140 J = N - L + 1, N + DO 130 I = J - N + K + L + 1, M + A( I, J ) = CZERO + 130 CONTINUE + 140 CONTINUE +* + END IF +* + WORK( 1 ) = DCMPLX( LWKOPT ) + RETURN +* +* End of ZGGSVP3 +* + END -- cgit v1.2.3