version 1.10, 2012/08/22 09:48:35
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version 1.19, 2020/05/21 21:46:07
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*> \brief \b ZLAHQR |
*> \brief \b ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. |
* |
* |
* =========== 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 ZLAHQR + dependencies |
*> Download ZLAHQR + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlahqr.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlahqr.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlahqr.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, |
* SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, |
* IHIZ, Z, LDZ, INFO ) |
* IHIZ, Z, LDZ, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
* LOGICAL WANTT, WANTZ |
* LOGICAL WANTT, WANTZ |
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* .. Array Arguments .. |
* .. Array Arguments .. |
* COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) |
* COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> \param[out] INFO |
*> \param[out] INFO |
*> \verbatim |
*> \verbatim |
*> INFO is INTEGER |
*> INFO is INTEGER |
*> = 0: successful exit |
*> = 0: successful exit |
*> .GT. 0: if INFO = i, ZLAHQR failed to compute all the |
*> > 0: if INFO = i, ZLAHQR failed to compute all the |
*> eigenvalues ILO to IHI in a total of 30 iterations |
*> eigenvalues ILO to IHI in a total of 30 iterations |
*> per eigenvalue; elements i+1:ihi of W contain |
*> per eigenvalue; elements i+1:ihi of W contain |
*> those eigenvalues which have been successfully |
*> those eigenvalues which have been successfully |
*> computed. |
*> computed. |
*> |
*> |
*> If INFO .GT. 0 and WANTT is .FALSE., then on exit, |
*> If INFO > 0 and WANTT is .FALSE., then on exit, |
*> the remaining unconverged eigenvalues are the |
*> the remaining unconverged eigenvalues are the |
*> eigenvalues of the upper Hessenberg matrix |
*> eigenvalues of the upper Hessenberg matrix |
*> rows and columns ILO thorugh INFO of the final, |
*> rows and columns ILO through INFO of the final, |
*> output value of H. |
*> output value of H. |
*> |
*> |
*> If INFO .GT. 0 and WANTT is .TRUE., then on exit |
*> If INFO > 0 and WANTT is .TRUE., then on exit |
*> (*) (initial value of H)*U = U*(final value of H) |
*> (*) (initial value of H)*U = U*(final value of H) |
*> where U is an orthognal matrix. The final |
*> where U is an orthogonal matrix. The final |
*> value of H is upper Hessenberg and triangular in |
*> value of H is upper Hessenberg and triangular in |
*> rows and columns INFO+1 through IHI. |
*> rows and columns INFO+1 through IHI. |
*> |
*> |
*> If INFO .GT. 0 and WANTZ is .TRUE., then on exit |
*> If INFO > 0 and WANTZ is .TRUE., then on exit |
*> (final value of Z) = (initial value of Z)*U |
*> (final value of Z) = (initial value of Z)*U |
*> where U is the orthogonal matrix in (*) |
*> where U is the orthogonal matrix in (*) |
*> (regardless of the value of WANTT.) |
*> (regardless of the value of WANTT.) |
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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. |
* |
* |
*> \date November 2011 |
*> \date December 2016 |
* |
* |
*> \ingroup complex16OTHERauxiliary |
*> \ingroup complex16OTHERauxiliary |
* |
* |
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SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, |
SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, |
$ IHIZ, Z, LDZ, INFO ) |
$ IHIZ, Z, LDZ, INFO ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK auxiliary routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
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* ========================================================= |
* ========================================================= |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
INTEGER ITMAX |
|
PARAMETER ( ITMAX = 30 ) |
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COMPLEX*16 ZERO, ONE |
COMPLEX*16 ZERO, ONE |
PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), |
PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), |
$ ONE = ( 1.0d0, 0.0d0 ) ) |
$ ONE = ( 1.0d0, 0.0d0 ) ) |
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$ V2, X, Y |
$ V2, X, Y |
DOUBLE PRECISION AA, AB, BA, BB, H10, H21, RTEMP, S, SAFMAX, |
DOUBLE PRECISION AA, AB, BA, BB, H10, H21, RTEMP, S, SAFMAX, |
$ SAFMIN, SMLNUM, SX, T2, TST, ULP |
$ SAFMIN, SMLNUM, SX, T2, TST, ULP |
INTEGER I, I1, I2, ITS, J, JHI, JLO, K, L, M, NH, NZ |
INTEGER I, I1, I2, ITS, ITMAX, J, JHI, JLO, K, L, M, |
|
$ NH, NZ |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
COMPLEX*16 V( 2 ) |
COMPLEX*16 V( 2 ) |
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I2 = N |
I2 = N |
END IF |
END IF |
* |
* |
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* ITMAX is the total number of QR iterations allowed. |
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* |
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ITMAX = 30 * MAX( 10, NH ) |
|
* |
* The main loop begins here. I is the loop index and decreases from |
* The main loop begins here. I is the loop index and decreases from |
* IHI to ILO in steps of 1. Each iteration of the loop works |
* IHI to ILO in steps of 1. Each iteration of the loop works |
* with the active submatrix in rows and columns L to I. |
* with the active submatrix in rows and columns L to I. |