version 1.10, 2011/11/21 22:19:27
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version 1.19, 2023/08/07 08:38:48
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* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download DGEHRD + dependencies |
*> Download DGEHRD + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgehrd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgehrd.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgehrd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgehrd.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgehrd.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgehrd.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
* SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER IHI, ILO, INFO, LDA, LWORK, N |
* INTEGER IHI, ILO, INFO, LDA, LWORK, N |
* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> \verbatim |
*> \verbatim |
*> LWORK is INTEGER |
*> LWORK is INTEGER |
*> The length of the array WORK. LWORK >= max(1,N). |
*> The length of the array WORK. LWORK >= max(1,N). |
*> For optimum performance LWORK >= N*NB, where NB is the |
*> For good performance, LWORK should generally be larger. |
*> optimal blocksize. |
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*> |
*> |
*> If LWORK = -1, then a workspace query is assumed; the routine |
*> If LWORK = -1, then a workspace query is assumed; the routine |
*> only calculates the optimal size of the WORK array, returns |
*> only calculates the optimal size of the WORK array, returns |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
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*> \date November 2011 |
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* |
* |
*> \ingroup doubleGEcomputational |
*> \ingroup doubleGEcomputational |
* |
* |
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* ===================================================================== |
* ===================================================================== |
SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
SUBROUTINE DGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2011 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER IHI, ILO, INFO, LDA, LWORK, N |
INTEGER IHI, ILO, INFO, LDA, LWORK, N |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
INTEGER NBMAX, LDT |
INTEGER NBMAX, LDT, TSIZE |
PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) |
PARAMETER ( NBMAX = 64, LDT = NBMAX+1, |
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$ TSIZE = LDT*NBMAX ) |
DOUBLE PRECISION ZERO, ONE |
DOUBLE PRECISION ZERO, ONE |
PARAMETER ( ZERO = 0.0D+0, |
PARAMETER ( ZERO = 0.0D+0, |
$ ONE = 1.0D+0 ) |
$ ONE = 1.0D+0 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
LOGICAL LQUERY |
LOGICAL LQUERY |
INTEGER I, IB, IINFO, IWS, J, LDWORK, LWKOPT, NB, |
INTEGER I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB, |
$ NBMIN, NH, NX |
$ NBMIN, NH, NX |
DOUBLE PRECISION EI |
DOUBLE PRECISION EI |
* .. |
* .. |
* .. Local Arrays .. |
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DOUBLE PRECISION T( LDT, NBMAX ) |
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* .. |
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* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DAXPY, DGEHD2, DGEMM, DLAHR2, DLARFB, DTRMM, |
EXTERNAL DAXPY, DGEHD2, DGEMM, DLAHR2, DLARFB, DTRMM, |
$ XERBLA |
$ XERBLA |
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* Test the input parameters |
* Test the input parameters |
* |
* |
INFO = 0 |
INFO = 0 |
NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) ) |
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LWKOPT = N*NB |
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WORK( 1 ) = LWKOPT |
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LQUERY = ( LWORK.EQ.-1 ) |
LQUERY = ( LWORK.EQ.-1 ) |
IF( N.LT.0 ) THEN |
IF( N.LT.0 ) THEN |
INFO = -1 |
INFO = -1 |
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ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN |
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN |
INFO = -8 |
INFO = -8 |
END IF |
END IF |
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* |
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IF( INFO.EQ.0 ) THEN |
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* |
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* Compute the workspace requirements |
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* |
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NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) ) |
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LWKOPT = N*NB + TSIZE |
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WORK( 1 ) = LWKOPT |
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END IF |
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* |
IF( INFO.NE.0 ) THEN |
IF( INFO.NE.0 ) THEN |
CALL XERBLA( 'DGEHRD', -INFO ) |
CALL XERBLA( 'DGEHRD', -INFO ) |
RETURN |
RETURN |
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* |
* |
NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) ) |
NB = MIN( NBMAX, ILAENV( 1, 'DGEHRD', ' ', N, ILO, IHI, -1 ) ) |
NBMIN = 2 |
NBMIN = 2 |
IWS = 1 |
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IF( NB.GT.1 .AND. NB.LT.NH ) THEN |
IF( NB.GT.1 .AND. NB.LT.NH ) THEN |
* |
* |
* Determine when to cross over from blocked to unblocked code |
* Determine when to cross over from blocked to unblocked code |
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* |
* |
* Determine if workspace is large enough for blocked code |
* Determine if workspace is large enough for blocked code |
* |
* |
IWS = N*NB |
IF( LWORK.LT.N*NB+TSIZE ) THEN |
IF( LWORK.LT.IWS ) THEN |
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* |
* |
* Not enough workspace to use optimal NB: determine the |
* Not enough workspace to use optimal NB: determine the |
* minimum value of NB, and reduce NB or force use of |
* minimum value of NB, and reduce NB or force use of |
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* |
* |
NBMIN = MAX( 2, ILAENV( 2, 'DGEHRD', ' ', N, ILO, IHI, |
NBMIN = MAX( 2, ILAENV( 2, 'DGEHRD', ' ', N, ILO, IHI, |
$ -1 ) ) |
$ -1 ) ) |
IF( LWORK.GE.N*NBMIN ) THEN |
IF( LWORK.GE.(N*NBMIN + TSIZE) ) THEN |
NB = LWORK / N |
NB = (LWORK-TSIZE) / N |
ELSE |
ELSE |
NB = 1 |
NB = 1 |
END IF |
END IF |
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* |
* |
* Use blocked code |
* Use blocked code |
* |
* |
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IWT = 1 + N*NB |
DO 40 I = ILO, IHI - 1 - NX, NB |
DO 40 I = ILO, IHI - 1 - NX, NB |
IB = MIN( NB, IHI-I ) |
IB = MIN( NB, IHI-I ) |
* |
* |
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* matrices V and T of the block reflector H = I - V*T*V**T |
* matrices V and T of the block reflector H = I - V*T*V**T |
* which performs the reduction, and also the matrix Y = A*V*T |
* which performs the reduction, and also the matrix Y = A*V*T |
* |
* |
CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT, |
CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), |
$ WORK, LDWORK ) |
$ WORK( IWT ), LDT, WORK, LDWORK ) |
* |
* |
* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the |
* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the |
* right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set |
* right, computing A := A - Y * V**T. V(i+ib,ib-1) must be set |
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* |
* |
EI = A( I+IB, I+IB-1 ) |
EI = A( I+IB, I+IB-1 ) |
A( I+IB, I+IB-1 ) = ONE |
A( I+IB, I+IB-1 ) = ONE |
CALL DGEMM( 'No transpose', 'Transpose', |
CALL DGEMM( 'No transpose', 'Transpose', |
$ IHI, IHI-I-IB+1, |
$ IHI, IHI-I-IB+1, |
$ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE, |
$ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE, |
$ A( 1, I+IB ), LDA ) |
$ A( 1, I+IB ), LDA ) |
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* |
* |
CALL DLARFB( 'Left', 'Transpose', 'Forward', |
CALL DLARFB( 'Left', 'Transpose', 'Forward', |
$ 'Columnwise', |
$ 'Columnwise', |
$ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, T, LDT, |
$ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, |
$ A( I+1, I+IB ), LDA, WORK, LDWORK ) |
$ WORK( IWT ), LDT, A( I+1, I+IB ), LDA, |
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$ WORK, LDWORK ) |
40 CONTINUE |
40 CONTINUE |
END IF |
END IF |
* |
* |
* Use unblocked code to reduce the rest of the matrix |
* Use unblocked code to reduce the rest of the matrix |
* |
* |
CALL DGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) |
CALL DGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) |
WORK( 1 ) = IWS |
WORK( 1 ) = LWKOPT |
* |
* |
RETURN |
RETURN |
* |
* |