version 1.11, 2012/12/14 12:30:22
|
version 1.19, 2020/05/21 21:45:59
|
Line 2
|
Line 2
|
* |
* |
* =========== 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 |
Line 28
|
Line 28
|
* .. Array Arguments .. |
* .. Array Arguments .. |
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * ) |
* DOUBLE PRECISION H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
Line 150
|
Line 150
|
*> \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.) |
Line 178
|
Line 178
|
* 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 September 2012 |
*> \date December 2016 |
* |
* |
*> \ingroup doubleOTHERauxiliary |
*> \ingroup doubleOTHERauxiliary |
* |
* |
Line 207
|
Line 207
|
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 ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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..-- |
* September 2012 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N |
Line 223
|
Line 223
|
* ========================================================= |
* ========================================================= |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
INTEGER ITMAX |
|
PARAMETER ( ITMAX = 30 ) |
|
DOUBLE PRECISION ZERO, ONE, TWO |
DOUBLE PRECISION ZERO, ONE, TWO |
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 |
Line 235
|
Line 233
|
$ 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, J, K, L, M, NH, NR, NZ |
INTEGER I, I1, I2, ITS, ITMAX, J, K, L, M, NH, NR, NZ |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
DOUBLE PRECISION V( 3 ) |
DOUBLE PRECISION V( 3 ) |
Line 292
|
Line 290
|
I2 = N |
I2 = N |
END IF |
END IF |
* |
* |
|
* ITMAX is the total number of QR iterations allowed. |
|
* |
|
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 or 2. Each iteration of the loop works |
* IHI to ILO in steps of 1 or 2. 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. |