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version 1.8, 2011/11/21 20:43:18
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*> \brief \b ZLATDF |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZLATDF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatdf.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatdf.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatdf.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, |
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* JPIV ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER IJOB, LDZ, N |
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* DOUBLE PRECISION RDSCAL, RDSUM |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ), JPIV( * ) |
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* COMPLEX*16 RHS( * ), Z( LDZ, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZLATDF computes the contribution to the reciprocal Dif-estimate |
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*> by solving for x in Z * x = b, where b is chosen such that the norm |
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*> of x is as large as possible. It is assumed that LU decomposition |
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*> of Z has been computed by ZGETC2. On entry RHS = f holds the |
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*> contribution from earlier solved sub-systems, and on return RHS = x. |
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*> |
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*> The factorization of Z returned by ZGETC2 has the form |
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*> Z = P * L * U * Q, where P and Q are permutation matrices. L is lower |
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*> triangular with unit diagonal elements and U is upper triangular. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] IJOB |
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*> \verbatim |
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*> IJOB is INTEGER |
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*> IJOB = 2: First compute an approximative null-vector e |
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*> of Z using ZGECON, e is normalized and solve for |
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*> Zx = +-e - f with the sign giving the greater value of |
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*> 2-norm(x). About 5 times as expensive as Default. |
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*> IJOB .ne. 2: Local look ahead strategy where |
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*> all entries of the r.h.s. b is choosen as either +1 or |
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*> -1. Default. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The number of columns of the matrix Z. |
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*> \endverbatim |
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*> |
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*> \param[in] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension (LDZ, N) |
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*> On entry, the LU part of the factorization of the n-by-n |
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*> matrix Z computed by ZGETC2: Z = P * L * U * Q |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDA >= max(1, N). |
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*> \endverbatim |
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*> |
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*> \param[in,out] RHS |
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*> \verbatim |
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*> RHS is DOUBLE PRECISION array, dimension (N). |
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*> On entry, RHS contains contributions from other subsystems. |
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*> On exit, RHS contains the solution of the subsystem with |
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*> entries according to the value of IJOB (see above). |
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*> \endverbatim |
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*> |
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*> \param[in,out] RDSUM |
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*> \verbatim |
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*> RDSUM is DOUBLE PRECISION |
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*> On entry, the sum of squares of computed contributions to |
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*> the Dif-estimate under computation by ZTGSYL, where the |
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*> scaling factor RDSCAL (see below) has been factored out. |
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*> On exit, the corresponding sum of squares updated with the |
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*> contributions from the current sub-system. |
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*> If TRANS = 'T' RDSUM is not touched. |
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*> NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL. |
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*> \endverbatim |
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*> |
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*> \param[in,out] RDSCAL |
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*> \verbatim |
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*> RDSCAL is DOUBLE PRECISION |
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*> On entry, scaling factor used to prevent overflow in RDSUM. |
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*> On exit, RDSCAL is updated w.r.t. the current contributions |
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*> in RDSUM. |
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*> If TRANS = 'T', RDSCAL is not touched. |
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*> NOTE: RDSCAL only makes sense when ZTGSY2 is called by |
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*> ZTGSYL. |
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*> \endverbatim |
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*> |
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*> \param[in] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N). |
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*> The pivot indices; for 1 <= i <= N, row i of the |
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*> matrix has been interchanged with row IPIV(i). |
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*> \endverbatim |
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*> |
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*> \param[in] JPIV |
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*> \verbatim |
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*> JPIV is INTEGER array, dimension (N). |
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*> The pivot indices; for 1 <= j <= N, column j of the |
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*> matrix has been interchanged with column JPIV(j). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup complex16OTHERauxiliary |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> This routine is a further developed implementation of algorithm |
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*> BSOLVE in [1] using complete pivoting in the LU factorization. |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
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*> Umea University, S-901 87 Umea, Sweden. |
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* |
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*> \par References: |
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* ================ |
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*> |
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*> [1] Bo Kagstrom and Lars Westin, |
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*> Generalized Schur Methods with Condition Estimators for |
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*> Solving the Generalized Sylvester Equation, IEEE Transactions |
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*> on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. |
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*>\n |
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*> [2] Peter Poromaa, |
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*> On Efficient and Robust Estimators for the Separation |
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*> between two Regular Matrix Pairs with Applications in |
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*> Condition Estimation. Report UMINF-95.05, Department of |
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*> Computing Science, Umea University, S-901 87 Umea, Sweden, |
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*> 1995. |
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* |
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* ===================================================================== |
SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, |
SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, |
$ JPIV ) |
$ JPIV ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- 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 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER IJOB, LDZ, N |
INTEGER IJOB, LDZ, N |
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COMPLEX*16 RHS( * ), Z( LDZ, * ) |
COMPLEX*16 RHS( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZLATDF computes the contribution to the reciprocal Dif-estimate |
|
* by solving for x in Z * x = b, where b is chosen such that the norm |
|
* of x is as large as possible. It is assumed that LU decomposition |
|
* of Z has been computed by ZGETC2. On entry RHS = f holds the |
|
* contribution from earlier solved sub-systems, and on return RHS = x. |
|
* |
|
* The factorization of Z returned by ZGETC2 has the form |
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* Z = P * L * U * Q, where P and Q are permutation matrices. L is lower |
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* triangular with unit diagonal elements and U is upper triangular. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* IJOB (input) INTEGER |
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* IJOB = 2: First compute an approximative null-vector e |
|
* of Z using ZGECON, e is normalized and solve for |
|
* Zx = +-e - f with the sign giving the greater value of |
|
* 2-norm(x). About 5 times as expensive as Default. |
|
* IJOB .ne. 2: Local look ahead strategy where |
|
* all entries of the r.h.s. b is choosen as either +1 or |
|
* -1. Default. |
|
* |
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* N (input) INTEGER |
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* The number of columns of the matrix Z. |
|
* |
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* Z (input) DOUBLE PRECISION array, dimension (LDZ, N) |
|
* On entry, the LU part of the factorization of the n-by-n |
|
* matrix Z computed by ZGETC2: Z = P * L * U * Q |
|
* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDA >= max(1, N). |
|
* |
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* RHS (input/output) DOUBLE PRECISION array, dimension (N). |
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* On entry, RHS contains contributions from other subsystems. |
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* On exit, RHS contains the solution of the subsystem with |
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* entries according to the value of IJOB (see above). |
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* |
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* RDSUM (input/output) DOUBLE PRECISION |
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* On entry, the sum of squares of computed contributions to |
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* the Dif-estimate under computation by ZTGSYL, where the |
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* scaling factor RDSCAL (see below) has been factored out. |
|
* On exit, the corresponding sum of squares updated with the |
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* contributions from the current sub-system. |
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* If TRANS = 'T' RDSUM is not touched. |
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* NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL. |
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* |
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* RDSCAL (input/output) DOUBLE PRECISION |
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* On entry, scaling factor used to prevent overflow in RDSUM. |
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* On exit, RDSCAL is updated w.r.t. the current contributions |
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* in RDSUM. |
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* If TRANS = 'T', RDSCAL is not touched. |
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* NOTE: RDSCAL only makes sense when ZTGSY2 is called by |
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* ZTGSYL. |
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* |
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* IPIV (input) INTEGER array, dimension (N). |
|
* The pivot indices; for 1 <= i <= N, row i of the |
|
* matrix has been interchanged with row IPIV(i). |
|
* |
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* JPIV (input) INTEGER array, dimension (N). |
|
* The pivot indices; for 1 <= j <= N, column j of the |
|
* matrix has been interchanged with column JPIV(j). |
|
* |
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* Further Details |
|
* =============== |
|
* |
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* Based on contributions by |
|
* Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
|
* Umea University, S-901 87 Umea, Sweden. |
|
* |
|
* This routine is a further developed implementation of algorithm |
|
* BSOLVE in [1] using complete pivoting in the LU factorization. |
|
* |
|
* [1] Bo Kagstrom and Lars Westin, |
|
* Generalized Schur Methods with Condition Estimators for |
|
* Solving the Generalized Sylvester Equation, IEEE Transactions |
|
* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. |
|
* |
|
* [2] Peter Poromaa, |
|
* On Efficient and Robust Estimators for the Separation |
|
* between two Regular Matrix Pairs with Applications in |
|
* Condition Estimation. Report UMINF-95.05, Department of |
|
* Computing Science, Umea University, S-901 87 Umea, Sweden, |
|
* 1995. |
|
* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |