version 1.15, 2016/08/27 15:34:27
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version 1.20, 2023/08/07 08:38:54
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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 DLAHQR + dependencies |
*> Download DLAHQR + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahqr.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahqr.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahqr.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, |
* SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, |
* ILOZ, IHIZ, Z, LDZ, INFO ) |
* ILOZ, 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 .. |
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * ) |
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), 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, DLAHQR failed to compute all the |
*> > 0: If INFO = i, DLAHQR 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 WR and WI |
*> per eigenvalue; elements i+1:ihi of WR and WI |
*> contain those eigenvalues which have been |
*> contain those eigenvalues which have been |
*> successfully computed. |
*> successfully 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 rows |
*> eigenvalues of the upper Hessenberg matrix rows |
*> and columns ILO thorugh INFO of the final, output |
*> and columns ILO through INFO of the final, output |
*> value of H. |
*> 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 2015 |
|
* |
* |
*> \ingroup doubleOTHERauxiliary |
*> \ingroup doubleOTHERauxiliary |
* |
* |
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* ===================================================================== |
* ===================================================================== |
SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, |
SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, |
$ ILOZ, IHIZ, Z, LDZ, INFO ) |
$ ILOZ, IHIZ, Z, LDZ, INFO ) |
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IMPLICIT NONE |
* |
* |
* -- LAPACK auxiliary routine (version 3.6.0) -- |
* -- LAPACK auxiliary 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 2015 |
|
* |
* |
* .. 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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PARAMETER ( ZERO = 0.0d0, ONE = 1.0d0, TWO = 2.0d0 ) |
PARAMETER ( ZERO = 0.0d0, ONE = 1.0d0, TWO = 2.0d0 ) |
DOUBLE PRECISION DAT1, DAT2 |
DOUBLE PRECISION DAT1, DAT2 |
PARAMETER ( DAT1 = 3.0d0 / 4.0d0, DAT2 = -0.4375d0 ) |
PARAMETER ( DAT1 = 3.0d0 / 4.0d0, DAT2 = -0.4375d0 ) |
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INTEGER KEXSH |
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PARAMETER ( KEXSH = 10 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE PRECISION AA, AB, BA, BB, CS, DET, H11, H12, H21, H21S, |
DOUBLE PRECISION AA, AB, BA, BB, CS, DET, H11, H12, H21, H21S, |
$ H22, RT1I, RT1R, RT2I, RT2R, RTDISC, S, SAFMAX, |
$ H22, RT1I, RT1R, RT2I, RT2R, RTDISC, S, SAFMAX, |
$ SAFMIN, SMLNUM, SN, SUM, T1, T2, T3, TR, TST, |
$ SAFMIN, SMLNUM, SN, SUM, T1, T2, T3, TR, TST, |
$ ULP, V2, V3 |
$ ULP, V2, V3 |
INTEGER I, I1, I2, ITS, ITMAX, J, K, L, M, NH, NR, NZ |
INTEGER I, I1, I2, ITS, ITMAX, J, K, L, M, NH, NR, NZ, |
|
$ KDEFL |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
DOUBLE PRECISION V( 3 ) |
DOUBLE PRECISION V( 3 ) |
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* |
* |
* ITMAX is the total number of QR iterations allowed. |
* ITMAX is the total number of QR iterations allowed. |
* |
* |
ITMAX = 30 * MAX( 10, NH ) |
ITMAX = 30 * MAX( 10, NH ) |
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* |
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* KDEFL counts the number of iterations since a deflation |
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* |
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KDEFL = 0 |
* |
* |
* 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 or 2. Each iteration of the loop works |
* IHI to ILO in steps of 1 or 2. Each iteration of the loop works |
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* |
* |
IF( L.GE.I-1 ) |
IF( L.GE.I-1 ) |
$ GO TO 150 |
$ GO TO 150 |
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KDEFL = KDEFL + 1 |
* |
* |
* Now the active submatrix is in rows and columns L to I. If |
* Now the active submatrix is in rows and columns L to I. If |
* eigenvalues only are being computed, only the active submatrix |
* eigenvalues only are being computed, only the active submatrix |
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I2 = I |
I2 = I |
END IF |
END IF |
* |
* |
IF( ITS.EQ.10 ) THEN |
IF( MOD(KDEFL,2*KEXSH).EQ.0 ) THEN |
* |
* |
* Exceptional shift. |
* Exceptional shift. |
* |
* |
S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) ) |
S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) ) |
H11 = DAT1*S + H( L, L ) |
H11 = DAT1*S + H( I, I ) |
H12 = DAT2*S |
H12 = DAT2*S |
H21 = S |
H21 = S |
H22 = H11 |
H22 = H11 |
ELSE IF( ITS.EQ.20 ) THEN |
ELSE IF( MOD(KDEFL,KEXSH).EQ.0 ) THEN |
* |
* |
* Exceptional shift. |
* Exceptional shift. |
* |
* |
S = ABS( H( I, I-1 ) ) + ABS( H( I-1, I-2 ) ) |
S = ABS( H( L+1, L ) ) + ABS( H( L+2, L+1 ) ) |
H11 = DAT1*S + H( I, I ) |
H11 = DAT1*S + H( L, L ) |
H12 = DAT2*S |
H12 = DAT2*S |
H21 = S |
H21 = S |
H22 = H11 |
H22 = H11 |
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CALL DROT( NZ, Z( ILOZ, I-1 ), 1, Z( ILOZ, I ), 1, CS, SN ) |
CALL DROT( NZ, Z( ILOZ, I-1 ), 1, Z( ILOZ, I ), 1, CS, SN ) |
END IF |
END IF |
END IF |
END IF |
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* reset deflation counter |
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KDEFL = 0 |
* |
* |
* return to start of the main loop with new value of I. |
* return to start of the main loop with new value of I. |
* |
* |