version 1.7, 2011/11/21 22:19:55
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version 1.14, 2018/05/29 07:18:32
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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 ZPOEQUB + dependencies |
*> Download ZPOEQUB + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpoequb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpoequb.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpoequb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpoequb.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpoequb.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpoequb.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) |
* SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* INTEGER INFO, LDA, N |
* INTEGER INFO, LDA, N |
* DOUBLE PRECISION AMAX, SCOND |
* DOUBLE PRECISION AMAX, SCOND |
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* COMPLEX*16 A( LDA, * ) |
* COMPLEX*16 A( LDA, * ) |
* DOUBLE PRECISION S( * ) |
* DOUBLE PRECISION S( * ) |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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*> \verbatim |
*> \verbatim |
*> |
*> |
*> ZPOEQUB computes row and column scalings intended to equilibrate a |
*> ZPOEQUB computes row and column scalings intended to equilibrate a |
*> symmetric positive definite matrix A and reduce its condition number |
*> Hermitian positive definite matrix A and reduce its condition number |
*> (with respect to the two-norm). S contains the scale factors, |
*> (with respect to the two-norm). S contains the scale factors, |
*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with |
*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with |
*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This |
*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This |
*> choice of S puts the condition number of B within a factor N of the |
*> choice of S puts the condition number of B within a factor N of the |
*> smallest possible condition number over all possible diagonal |
*> smallest possible condition number over all possible diagonal |
*> scalings. |
*> scalings. |
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*> |
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*> This routine differs from ZPOEQU by restricting the scaling factors |
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*> to a power of the radix. Barring over- and underflow, scaling by |
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*> these factors introduces no additional rounding errors. However, the |
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*> scaled diagonal entries are no longer approximately 1 but lie |
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*> between sqrt(radix) and 1/sqrt(radix). |
*> \endverbatim |
*> \endverbatim |
* |
* |
* Arguments: |
* Arguments: |
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*> \param[in] A |
*> \param[in] A |
*> \verbatim |
*> \verbatim |
*> A is COMPLEX*16 array, dimension (LDA,N) |
*> A is COMPLEX*16 array, dimension (LDA,N) |
*> The N-by-N symmetric positive definite matrix whose scaling |
*> The N-by-N Hermitian positive definite matrix whose scaling |
*> factors are to be computed. Only the diagonal elements of A |
*> factors are to be computed. Only the diagonal elements of A |
*> are referenced. |
*> are referenced. |
*> \endverbatim |
*> \endverbatim |
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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 complex16POcomputational |
*> \ingroup complex16POcomputational |
* |
* |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) |
SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK computational 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 INFO, LDA, N |
INTEGER INFO, LDA, N |