numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/SRC/zgghd3.f | 32483B | -rw-r--r-- |
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*> \brief \b ZGGHD3 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGGHD3 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgghd3.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgghd3.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgghd3.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGGHD3( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, * LDQ, Z, LDZ, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPQ, COMPZ * INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N, LWORK * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), * $ Z( LDZ, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGGHD3 reduces a pair of complex matrices (A,B) to generalized upper *> Hessenberg form using unitary transformations, where A is a *> general matrix and B is upper triangular. The form of the *> generalized eigenvalue problem is *> A*x = lambda*B*x, *> and B is typically made upper triangular by computing its QR *> factorization and moving the unitary matrix Q to the left side *> of the equation. *> *> This subroutine simultaneously reduces A to a Hessenberg matrix H: *> Q**H*A*Z = H *> and transforms B to another upper triangular matrix T: *> Q**H*B*Z = T *> in order to reduce the problem to its standard form *> H*y = lambda*T*y *> where y = Z**H*x. *> *> The unitary matrices Q and Z are determined as products of Givens *> rotations. They may either be formed explicitly, or they may be *> postmultiplied into input matrices Q1 and Z1, so that *> Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H *> Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H *> If Q1 is the unitary matrix from the QR factorization of B in the *> original equation A*x = lambda*B*x, then ZGGHD3 reduces the original *> problem to generalized Hessenberg form. *> *> This is a blocked variant of CGGHRD, using matrix-matrix *> multiplications for parts of the computation to enhance performance. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPQ *> \verbatim *> COMPQ is CHARACTER*1 *> = 'N': do not compute Q; *> = 'I': Q is initialized to the unit matrix, and the *> unitary matrix Q is returned; *> = 'V': Q must contain a unitary matrix Q1 on entry, *> and the product Q1*Q is returned. *> \endverbatim *> *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': do not compute Z; *> = 'I': Z is initialized to the unit matrix, and the *> unitary matrix Z is returned; *> = 'V': Z must contain a unitary matrix Z1 on entry, *> and the product Z1*Z is returned. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> ILO and IHI mark the rows and columns of A which are to be *> reduced. It is assumed that A is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are *> normally set by a previous call to ZGGBAL; otherwise they *> should be set to 1 and N respectively. *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the N-by-N general matrix to be reduced. *> On exit, the upper triangle and the first subdiagonal of A *> are overwritten with the upper Hessenberg matrix H, and the *> rest is set to zero. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB, N) *> On entry, the N-by-N upper triangular matrix B. *> On exit, the upper triangular matrix T = Q**H B Z. The *> elements below the diagonal are set to zero. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ, N) *> On entry, if COMPQ = 'V', the unitary matrix Q1, typically *> from the QR factorization of B. *> On exit, if COMPQ='I', the unitary matrix Q, and if *> COMPQ = 'V', the product Q1*Q. *> Not referenced if COMPQ='N'. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. *> LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, N) *> On entry, if COMPZ = 'V', the unitary matrix Z1. *> On exit, if COMPZ='I', the unitary matrix Z, and if *> COMPZ = 'V', the product Z1*Z. *> Not referenced if COMPZ='N'. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. *> LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. *> \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 length of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= 6*N*NB, 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. *> \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. * *> \ingroup gghd3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> This routine reduces A to Hessenberg form and maintains B in triangular form *> using a blocked variant of Moler and Stewart's original algorithm, *> as described by Kagstrom, Kressner, Quintana-Orti, and Quintana-Orti *> (BIT 2008). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGGHD3( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, $ Q, $ LDQ, Z, LDZ, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * IMPLICIT NONE * * .. Scalar Arguments .. CHARACTER COMPQ, COMPZ INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N, LWORK * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), $ Z( LDZ, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CONE, CZERO PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), $ CZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL BLK22, INITQ, INITZ, LQUERY, WANTQ, WANTZ CHARACTER*1 COMPQ2, COMPZ2 INTEGER COLA, I, IERR, J, J0, JCOL, JJ, JROW, K, $ KACC22, LEN, LWKOPT, N2NB, NB, NBLST, NBMIN, $ NH, NNB, NX, PPW, PPWO, PW, TOP, TOPQ DOUBLE PRECISION C COMPLEX*16 C1, C2, CTEMP, S, S1, S2, TEMP, TEMP1, TEMP2, $ TEMP3 * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL ILAENV, LSAME * .. * .. External Subroutines .. EXTERNAL ZGGHRD, ZLARTG, ZLASET, ZUNM22, ZROT, $ ZGEMM, $ ZGEMV, ZTRMV, ZLACPY, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, DCONJG, MAX * .. * .. Executable Statements .. * * Decode and test the input parameters. * INFO = 0 NB = ILAENV( 1, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) NH = IHI - ILO + 1 IF( NH.LE.1 ) THEN LWKOPT = 1 ELSE LWKOPT = 6*N*NB END IF WORK( 1 ) = DCMPLX( LWKOPT ) INITQ = LSAME( COMPQ, 'I' ) WANTQ = INITQ .OR. LSAME( COMPQ, 'V' ) INITZ = LSAME( COMPZ, 'I' ) WANTZ = INITZ .OR. LSAME( COMPZ, 'V' ) LQUERY = ( LWORK.EQ.-1 ) * IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN INFO = -1 ELSE IF( .NOT.LSAME( COMPZ, 'N' ) .AND. .NOT.WANTZ ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( ILO.LT.1 ) THEN INFO = -4 ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( ( WANTQ .AND. LDQ.LT.N ) .OR. LDQ.LT.1 ) THEN INFO = -11 ELSE IF( ( WANTZ .AND. LDZ.LT.N ) .OR. LDZ.LT.1 ) THEN INFO = -13 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN INFO = -15 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGGHD3', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Initialize Q and Z if desired. * IF( INITQ ) $ CALL ZLASET( 'All', N, N, CZERO, CONE, Q, LDQ ) IF( INITZ ) $ CALL ZLASET( 'All', N, N, CZERO, CONE, Z, LDZ ) * * Zero out lower triangle of B. * IF( N.GT.1 ) $ CALL ZLASET( 'Lower', N-1, N-1, CZERO, CZERO, B(2, 1), LDB ) * * Quick return if possible * IF( NH.LE.1 ) THEN WORK( 1 ) = CONE RETURN END IF * * Determine the blocksize. * NBMIN = ILAENV( 2, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) IF( NB.GT.1 .AND. NB.LT.NH ) THEN * * Determine when to use unblocked instead of blocked code. * NX = MAX( NB, ILAENV( 3, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) ) IF( NX.LT.NH ) THEN * * Determine if workspace is large enough for blocked code. * IF( LWORK.LT.LWKOPT ) THEN * * Not enough workspace to use optimal NB: determine the * minimum value of NB, and reduce NB or force use of * unblocked code. * NBMIN = MAX( 2, ILAENV( 2, 'ZGGHD3', ' ', N, ILO, IHI, $ -1 ) ) IF( LWORK.GE.6*N*NBMIN ) THEN NB = LWORK / ( 6*N ) ELSE NB = 1 END IF END IF END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN * * Use unblocked code below * JCOL = ILO * ELSE * * Use blocked code * KACC22 = ILAENV( 16, 'ZGGHD3', ' ', N, ILO, IHI, -1 ) BLK22 = KACC22.EQ.2 DO JCOL = ILO, IHI-2, NB NNB = MIN( NB, IHI-JCOL-1 ) * * Initialize small unitary factors that will hold the * accumulated Givens rotations in workspace. * N2NB denotes the number of 2*NNB-by-2*NNB factors * NBLST denotes the (possibly smaller) order of the last * factor. * N2NB = ( IHI-JCOL-1 ) / NNB - 1 NBLST = IHI - JCOL - N2NB*NNB CALL ZLASET( 'All', NBLST, NBLST, CZERO, CONE, WORK, $ NBLST ) PW = NBLST * NBLST + 1 DO I = 1, N2NB CALL ZLASET( 'All', 2*NNB, 2*NNB, CZERO, CONE, $ WORK( PW ), 2*NNB ) PW = PW + 4*NNB*NNB END DO * * Reduce columns JCOL:JCOL+NNB-1 of A to Hessenberg form. * DO J = JCOL, JCOL+NNB-1 * * Reduce Jth column of A. Store cosines and sines in Jth * column of A and B, respectively. * DO I = IHI, J+2, -1 TEMP = A( I-1, J ) CALL ZLARTG( TEMP, A( I, J ), C, S, A( I-1, J ) ) A( I, J ) = DCMPLX( C ) B( I, J ) = S END DO * * Accumulate Givens rotations into workspace array. * PPW = ( NBLST + 1 )*( NBLST - 2 ) - J + JCOL + 1 LEN = 2 + J - JCOL JROW = J + N2NB*NNB + 2 DO I = IHI, JROW, -1 CTEMP = A( I, J ) S = B( I, J ) DO JJ = PPW, PPW+LEN-1 TEMP = WORK( JJ + NBLST ) WORK( JJ + NBLST ) = CTEMP*TEMP - S*WORK( JJ ) WORK( JJ ) = DCONJG( S )*TEMP + CTEMP*WORK( JJ ) END DO LEN = LEN + 1 PPW = PPW - NBLST - 1 END DO * PPWO = NBLST*NBLST + ( NNB+J-JCOL-1 )*2*NNB + NNB J0 = JROW - NNB DO JROW = J0, J+2, -NNB PPW = PPWO LEN = 2 + J - JCOL DO I = JROW+NNB-1, JROW, -1 CTEMP = A( I, J ) S = B( I, J ) DO JJ = PPW, PPW+LEN-1 TEMP = WORK( JJ + 2*NNB ) WORK( JJ + 2*NNB ) = CTEMP*TEMP - S*WORK( JJ ) WORK( JJ ) = DCONJG( S )*TEMP + CTEMP*WORK( JJ ) END DO LEN = LEN + 1 PPW = PPW - 2*NNB - 1 END DO PPWO = PPWO + 4*NNB*NNB END DO * * TOP denotes the number of top rows in A and B that will * not be updated during the next steps. * IF( JCOL.LE.2 ) THEN TOP = 0 ELSE TOP = JCOL END IF * * Propagate transformations through B and replace stored * left sines/cosines by right sines/cosines. * DO JJ = N, J+1, -1 * * Update JJth column of B. * DO I = MIN( JJ+1, IHI ), J+2, -1 CTEMP = A( I, J ) S = B( I, J ) TEMP = B( I, JJ ) B( I, JJ ) = CTEMP*TEMP - DCONJG( S )*B( I-1, JJ ) B( I-1, JJ ) = S*TEMP + CTEMP*B( I-1, JJ ) END DO * * Annihilate B( JJ+1, JJ ). * IF( JJ.LT.IHI ) THEN TEMP = B( JJ+1, JJ+1 ) CALL ZLARTG( TEMP, B( JJ+1, JJ ), C, S, $ B( JJ+1, JJ+1 ) ) B( JJ+1, JJ ) = CZERO CALL ZROT( JJ-TOP, B( TOP+1, JJ+1 ), 1, $ B( TOP+1, JJ ), 1, C, S ) A( JJ+1, J ) = DCMPLX( C ) B( JJ+1, J ) = -DCONJG( S ) END IF END DO * * Update A by transformations from right. * JJ = MOD( IHI-J-1, 3 ) DO I = IHI-J-3, JJ+1, -3 CTEMP = A( J+1+I, J ) S = -B( J+1+I, J ) C1 = A( J+2+I, J ) S1 = -B( J+2+I, J ) C2 = A( J+3+I, J ) S2 = -B( J+3+I, J ) * DO K = TOP+1, IHI TEMP = A( K, J+I ) TEMP1 = A( K, J+I+1 ) TEMP2 = A( K, J+I+2 ) TEMP3 = A( K, J+I+3 ) A( K, J+I+3 ) = C2*TEMP3 + DCONJG( S2 )*TEMP2 TEMP2 = -S2*TEMP3 + C2*TEMP2 A( K, J+I+2 ) = C1*TEMP2 + DCONJG( S1 )*TEMP1 TEMP1 = -S1*TEMP2 + C1*TEMP1 A( K, J+I+1 ) = CTEMP*TEMP1 + DCONJG( S )*TEMP A( K, J+I ) = -S*TEMP1 + CTEMP*TEMP END DO END DO * IF( JJ.GT.0 ) THEN DO I = JJ, 1, -1 C = DBLE( A( J+1+I, J ) ) CALL ZROT( IHI-TOP, A( TOP+1, J+I+1 ), 1, $ A( TOP+1, J+I ), 1, C, $ -DCONJG( B( J+1+I, J ) ) ) END DO END IF * * Update (J+1)th column of A by transformations from left. * IF ( J .LT. JCOL + NNB - 1 ) THEN LEN = 1 + J - JCOL * * Multiply with the trailing accumulated unitary * matrix, which takes the form * * [ U11 U12 ] * U = [ ], * [ U21 U22 ] * * where U21 is a LEN-by-LEN matrix and U12 is lower * triangular. * JROW = IHI - NBLST + 1 CALL ZGEMV( 'Conjugate', NBLST, LEN, CONE, WORK, $ NBLST, A( JROW, J+1 ), 1, CZERO, $ WORK( PW ), 1 ) PPW = PW + LEN DO I = JROW, JROW+NBLST-LEN-1 WORK( PPW ) = A( I, J+1 ) PPW = PPW + 1 END DO CALL ZTRMV( 'Lower', 'Conjugate', 'Non-unit', $ NBLST-LEN, WORK( LEN*NBLST + 1 ), NBLST, $ WORK( PW+LEN ), 1 ) CALL ZGEMV( 'Conjugate', LEN, NBLST-LEN, CONE, $ WORK( (LEN+1)*NBLST - LEN + 1 ), NBLST, $ A( JROW+NBLST-LEN, J+1 ), 1, CONE, $ WORK( PW+LEN ), 1 ) PPW = PW DO I = JROW, JROW+NBLST-1 A( I, J+1 ) = WORK( PPW ) PPW = PPW + 1 END DO * * Multiply with the other accumulated unitary * matrices, which take the form * * [ U11 U12 0 ] * [ ] * U = [ U21 U22 0 ], * [ ] * [ 0 0 I ] * * where I denotes the (NNB-LEN)-by-(NNB-LEN) identity * matrix, U21 is a LEN-by-LEN upper triangular matrix * and U12 is an NNB-by-NNB lower triangular matrix. * PPWO = 1 + NBLST*NBLST J0 = JROW - NNB DO JROW = J0, JCOL+1, -NNB PPW = PW + LEN DO I = JROW, JROW+NNB-1 WORK( PPW ) = A( I, J+1 ) PPW = PPW + 1 END DO PPW = PW DO I = JROW+NNB, JROW+NNB+LEN-1 WORK( PPW ) = A( I, J+1 ) PPW = PPW + 1 END DO CALL ZTRMV( 'Upper', 'Conjugate', 'Non-unit', $ LEN, $ WORK( PPWO + NNB ), 2*NNB, WORK( PW ), $ 1 ) CALL ZTRMV( 'Lower', 'Conjugate', 'Non-unit', $ NNB, $ WORK( PPWO + 2*LEN*NNB ), $ 2*NNB, WORK( PW + LEN ), 1 ) CALL ZGEMV( 'Conjugate', NNB, LEN, CONE, $ WORK( PPWO ), 2*NNB, A( JROW, J+1 ), 1, $ CONE, WORK( PW ), 1 ) CALL ZGEMV( 'Conjugate', LEN, NNB, CONE, $ WORK( PPWO + 2*LEN*NNB + NNB ), 2*NNB, $ A( JROW+NNB, J+1 ), 1, CONE, $ WORK( PW+LEN ), 1 ) PPW = PW DO I = JROW, JROW+LEN+NNB-1 A( I, J+1 ) = WORK( PPW ) PPW = PPW + 1 END DO PPWO = PPWO + 4*NNB*NNB END DO END IF END DO * * Apply accumulated unitary matrices to A. * COLA = N - JCOL - NNB + 1 J = IHI - NBLST + 1 CALL ZGEMM( 'Conjugate', 'No Transpose', NBLST, $ COLA, NBLST, CONE, WORK, NBLST, $ A( J, JCOL+NNB ), LDA, CZERO, WORK( PW ), $ NBLST ) CALL ZLACPY( 'All', NBLST, COLA, WORK( PW ), NBLST, $ A( J, JCOL+NNB ), LDA ) PPWO = NBLST*NBLST + 1 J0 = J - NNB DO J = J0, JCOL+1, -NNB IF ( BLK22 ) THEN * * Exploit the structure of * * [ U11 U12 ] * U = [ ] * [ U21 U22 ], * * where all blocks are NNB-by-NNB, U21 is upper * triangular and U12 is lower triangular. * CALL ZUNM22( 'Left', 'Conjugate', 2*NNB, COLA, NNB, $ NNB, WORK( PPWO ), 2*NNB, $ A( J, JCOL+NNB ), LDA, WORK( PW ), $ LWORK-PW+1, IERR ) ELSE * * Ignore the structure of U. * CALL ZGEMM( 'Conjugate', 'No Transpose', 2*NNB, $ COLA, 2*NNB, CONE, WORK( PPWO ), 2*NNB, $ A( J, JCOL+NNB ), LDA, CZERO, WORK( PW ), $ 2*NNB ) CALL ZLACPY( 'All', 2*NNB, COLA, WORK( PW ), 2*NNB, $ A( J, JCOL+NNB ), LDA ) END IF PPWO = PPWO + 4*NNB*NNB END DO * * Apply accumulated unitary matrices to Q. * IF( WANTQ ) THEN J = IHI - NBLST + 1 IF ( INITQ ) THEN TOPQ = MAX( 2, J - JCOL + 1 ) NH = IHI - TOPQ + 1 ELSE TOPQ = 1 NH = N END IF CALL ZGEMM( 'No Transpose', 'No Transpose', NH, $ NBLST, NBLST, CONE, Q( TOPQ, J ), LDQ, $ WORK, NBLST, CZERO, WORK( PW ), NH ) CALL ZLACPY( 'All', NH, NBLST, WORK( PW ), NH, $ Q( TOPQ, J ), LDQ ) PPWO = NBLST*NBLST + 1 J0 = J - NNB DO J = J0, JCOL+1, -NNB IF ( INITQ ) THEN TOPQ = MAX( 2, J - JCOL + 1 ) NH = IHI - TOPQ + 1 END IF IF ( BLK22 ) THEN * * Exploit the structure of U. * CALL ZUNM22( 'Right', 'No Transpose', NH, 2*NNB, $ NNB, NNB, WORK( PPWO ), 2*NNB, $ Q( TOPQ, J ), LDQ, WORK( PW ), $ LWORK-PW+1, IERR ) ELSE * * Ignore the structure of U. * CALL ZGEMM( 'No Transpose', 'No Transpose', NH, $ 2*NNB, 2*NNB, CONE, Q( TOPQ, J ), LDQ, $ WORK( PPWO ), 2*NNB, CZERO, WORK( PW ), $ NH ) CALL ZLACPY( 'All', NH, 2*NNB, WORK( PW ), NH, $ Q( TOPQ, J ), LDQ ) END IF PPWO = PPWO + 4*NNB*NNB END DO END IF * * Accumulate right Givens rotations if required. * IF ( WANTZ .OR. TOP.GT.0 ) THEN * * Initialize small unitary factors that will hold the * accumulated Givens rotations in workspace. * CALL ZLASET( 'All', NBLST, NBLST, CZERO, CONE, WORK, $ NBLST ) PW = NBLST * NBLST + 1 DO I = 1, N2NB CALL ZLASET( 'All', 2*NNB, 2*NNB, CZERO, CONE, $ WORK( PW ), 2*NNB ) PW = PW + 4*NNB*NNB END DO * * Accumulate Givens rotations into workspace array. * DO J = JCOL, JCOL+NNB-1 PPW = ( NBLST + 1 )*( NBLST - 2 ) - J + JCOL + 1 LEN = 2 + J - JCOL JROW = J + N2NB*NNB + 2 DO I = IHI, JROW, -1 CTEMP = A( I, J ) A( I, J ) = CZERO S = B( I, J ) B( I, J ) = CZERO DO JJ = PPW, PPW+LEN-1 TEMP = WORK( JJ + NBLST ) WORK( JJ + NBLST ) = CTEMP*TEMP - $ DCONJG( S )*WORK( JJ ) WORK( JJ ) = S*TEMP + CTEMP*WORK( JJ ) END DO LEN = LEN + 1 PPW = PPW - NBLST - 1 END DO * PPWO = NBLST*NBLST + ( NNB+J-JCOL-1 )*2*NNB + NNB J0 = JROW - NNB DO JROW = J0, J+2, -NNB PPW = PPWO LEN = 2 + J - JCOL DO I = JROW+NNB-1, JROW, -1 CTEMP = A( I, J ) A( I, J ) = CZERO S = B( I, J ) B( I, J ) = CZERO DO JJ = PPW, PPW+LEN-1 TEMP = WORK( JJ + 2*NNB ) WORK( JJ + 2*NNB ) = CTEMP*TEMP - $ DCONJG( S )*WORK( JJ ) WORK( JJ ) = S*TEMP + CTEMP*WORK( JJ ) END DO LEN = LEN + 1 PPW = PPW - 2*NNB - 1 END DO PPWO = PPWO + 4*NNB*NNB END DO END DO ELSE * CALL ZLASET( 'Lower', IHI - JCOL - 1, NNB, CZERO, $ CZERO, $ A( JCOL + 2, JCOL ), LDA ) CALL ZLASET( 'Lower', IHI - JCOL - 1, NNB, CZERO, $ CZERO, $ B( JCOL + 2, JCOL ), LDB ) END IF * * Apply accumulated unitary matrices to A and B. * IF ( TOP.GT.0 ) THEN J = IHI - NBLST + 1 CALL ZGEMM( 'No Transpose', 'No Transpose', TOP, $ NBLST, NBLST, CONE, A( 1, J ), LDA, $ WORK, NBLST, CZERO, WORK( PW ), TOP ) CALL ZLACPY( 'All', TOP, NBLST, WORK( PW ), TOP, $ A( 1, J ), LDA ) PPWO = NBLST*NBLST + 1 J0 = J - NNB DO J = J0, JCOL+1, -NNB IF ( BLK22 ) THEN * * Exploit the structure of U. * CALL ZUNM22( 'Right', 'No Transpose', TOP, $ 2*NNB, $ NNB, NNB, WORK( PPWO ), 2*NNB, $ A( 1, J ), LDA, WORK( PW ), $ LWORK-PW+1, IERR ) ELSE * * Ignore the structure of U. * CALL ZGEMM( 'No Transpose', 'No Transpose', TOP, $ 2*NNB, 2*NNB, CONE, A( 1, J ), LDA, $ WORK( PPWO ), 2*NNB, CZERO, $ WORK( PW ), TOP ) CALL ZLACPY( 'All', TOP, 2*NNB, WORK( PW ), TOP, $ A( 1, J ), LDA ) END IF PPWO = PPWO + 4*NNB*NNB END DO * J = IHI - NBLST + 1 CALL ZGEMM( 'No Transpose', 'No Transpose', TOP, $ NBLST, NBLST, CONE, B( 1, J ), LDB, $ WORK, NBLST, CZERO, WORK( PW ), TOP ) CALL ZLACPY( 'All', TOP, NBLST, WORK( PW ), TOP, $ B( 1, J ), LDB ) PPWO = NBLST*NBLST + 1 J0 = J - NNB DO J = J0, JCOL+1, -NNB IF ( BLK22 ) THEN * * Exploit the structure of U. * CALL ZUNM22( 'Right', 'No Transpose', TOP, $ 2*NNB, $ NNB, NNB, WORK( PPWO ), 2*NNB, $ B( 1, J ), LDB, WORK( PW ), $ LWORK-PW+1, IERR ) ELSE * * Ignore the structure of U. * CALL ZGEMM( 'No Transpose', 'No Transpose', TOP, $ 2*NNB, 2*NNB, CONE, B( 1, J ), LDB, $ WORK( PPWO ), 2*NNB, CZERO, $ WORK( PW ), TOP ) CALL ZLACPY( 'All', TOP, 2*NNB, WORK( PW ), TOP, $ B( 1, J ), LDB ) END IF PPWO = PPWO + 4*NNB*NNB END DO END IF * * Apply accumulated unitary matrices to Z. * IF( WANTZ ) THEN J = IHI - NBLST + 1 IF ( INITQ ) THEN TOPQ = MAX( 2, J - JCOL + 1 ) NH = IHI - TOPQ + 1 ELSE TOPQ = 1 NH = N END IF CALL ZGEMM( 'No Transpose', 'No Transpose', NH, $ NBLST, NBLST, CONE, Z( TOPQ, J ), LDZ, $ WORK, NBLST, CZERO, WORK( PW ), NH ) CALL ZLACPY( 'All', NH, NBLST, WORK( PW ), NH, $ Z( TOPQ, J ), LDZ ) PPWO = NBLST*NBLST + 1 J0 = J - NNB DO J = J0, JCOL+1, -NNB IF ( INITQ ) THEN TOPQ = MAX( 2, J - JCOL + 1 ) NH = IHI - TOPQ + 1 END IF IF ( BLK22 ) THEN * * Exploit the structure of U. * CALL ZUNM22( 'Right', 'No Transpose', NH, 2*NNB, $ NNB, NNB, WORK( PPWO ), 2*NNB, $ Z( TOPQ, J ), LDZ, WORK( PW ), $ LWORK-PW+1, IERR ) ELSE * * Ignore the structure of U. * CALL ZGEMM( 'No Transpose', 'No Transpose', NH, $ 2*NNB, 2*NNB, CONE, Z( TOPQ, J ), LDZ, $ WORK( PPWO ), 2*NNB, CZERO, WORK( PW ), $ NH ) CALL ZLACPY( 'All', NH, 2*NNB, WORK( PW ), NH, $ Z( TOPQ, J ), LDZ ) END IF PPWO = PPWO + 4*NNB*NNB END DO END IF END DO END IF * * Use unblocked code to reduce the rest of the matrix * Avoid re-initialization of modified Q and Z. * COMPQ2 = COMPQ COMPZ2 = COMPZ IF ( JCOL.NE.ILO ) THEN IF ( WANTQ ) $ COMPQ2 = 'V' IF ( WANTZ ) $ COMPZ2 = 'V' END IF * IF ( JCOL.LT.IHI ) $ CALL ZGGHRD( COMPQ2, COMPZ2, N, JCOL, IHI, A, LDA, B, LDB, $ Q, $ LDQ, Z, LDZ, IERR ) * WORK( 1 ) = DCMPLX( LWKOPT ) * RETURN * * End of ZGGHD3 * END