version 1.3, 2010/08/06 15:28:59
|
version 1.15, 2017/06/17 11:06:59
|
Line 1
|
Line 1
|
|
*> \brief \b ZPOEQU |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZPOEQU + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpoequ.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpoequ.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpoequ.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* INTEGER INFO, LDA, N |
|
* DOUBLE PRECISION AMAX, SCOND |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION S( * ) |
|
* COMPLEX*16 A( LDA, * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZPOEQU computes row and column scalings intended to equilibrate a |
|
*> Hermitian positive definite matrix A and reduce its condition number |
|
*> (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 |
|
*> 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 |
|
*> smallest possible condition number over all possible diagonal |
|
*> scalings. |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The order of the matrix A. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] A |
|
*> \verbatim |
|
*> A is COMPLEX*16 array, dimension (LDA,N) |
|
*> The N-by-N Hermitian positive definite matrix whose scaling |
|
*> factors are to be computed. Only the diagonal elements of A |
|
*> are referenced. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of the array A. LDA >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] S |
|
*> \verbatim |
|
*> S is DOUBLE PRECISION array, dimension (N) |
|
*> If INFO = 0, S contains the scale factors for A. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] SCOND |
|
*> \verbatim |
|
*> SCOND is DOUBLE PRECISION |
|
*> If INFO = 0, S contains the ratio of the smallest S(i) to |
|
*> the largest S(i). If SCOND >= 0.1 and AMAX is neither too |
|
*> large nor too small, it is not worth scaling by S. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] AMAX |
|
*> \verbatim |
|
*> AMAX is DOUBLE PRECISION |
|
*> Absolute value of largest matrix element. If AMAX is very |
|
*> close to overflow or very close to underflow, the matrix |
|
*> should be scaled. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] INFO |
|
*> \verbatim |
|
*> INFO is INTEGER |
|
*> = 0: successful exit |
|
*> < 0: if INFO = -i, the i-th argument had an illegal value |
|
*> > 0: if INFO = i, the i-th diagonal element is nonpositive. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date December 2016 |
|
* |
|
*> \ingroup complex16POcomputational |
|
* |
|
* ===================================================================== |
SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) |
SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- 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 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, N |
INTEGER INFO, LDA, N |
Line 14
|
Line 127
|
COMPLEX*16 A( LDA, * ) |
COMPLEX*16 A( LDA, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZPOEQU computes row and column scalings intended to equilibrate a |
|
* Hermitian positive definite matrix A and reduce its condition number |
|
* (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 |
|
* 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 |
|
* smallest possible condition number over all possible diagonal |
|
* scalings. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrix A. N >= 0. |
|
* |
|
* A (input) COMPLEX*16 array, dimension (LDA,N) |
|
* The N-by-N Hermitian positive definite matrix whose scaling |
|
* factors are to be computed. Only the diagonal elements of A |
|
* are referenced. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,N). |
|
* |
|
* S (output) DOUBLE PRECISION array, dimension (N) |
|
* If INFO = 0, S contains the scale factors for A. |
|
* |
|
* SCOND (output) DOUBLE PRECISION |
|
* If INFO = 0, S contains the ratio of the smallest S(i) to |
|
* the largest S(i). If SCOND >= 0.1 and AMAX is neither too |
|
* large nor too small, it is not worth scaling by S. |
|
* |
|
* AMAX (output) DOUBLE PRECISION |
|
* Absolute value of largest matrix element. If AMAX is very |
|
* close to overflow or very close to underflow, the matrix |
|
* should be scaled. |
|
* |
|
* INFO (output) INTEGER |
|
* = 0: successful exit |
|
* < 0: if INFO = -i, the i-th argument had an illegal value |
|
* > 0: if INFO = i, the i-th diagonal element is nonpositive. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |