version 1.3, 2010/08/06 15:29:00
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version 1.18, 2023/08/07 08:39:34
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*> \brief \b ZPPTRF |
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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 ZPPTRF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpptrf.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/zpptrf.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/zpptrf.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 ZPPTRF( UPLO, N, AP, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 AP( * ) |
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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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*> ZPPTRF computes the Cholesky factorization of a complex Hermitian |
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*> positive definite matrix A stored in packed format. |
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*> |
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*> The factorization has the form |
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*> A = U**H * U, if UPLO = 'U', or |
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*> A = L * L**H, if UPLO = 'L', |
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*> where U is an upper triangular matrix and L is lower 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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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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 order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AP |
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*> \verbatim |
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*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) |
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*> On entry, the upper or lower triangle of the Hermitian matrix |
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*> A, packed columnwise in a linear array. The j-th column of A |
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*> is stored in the array AP as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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*> See below for further details. |
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*> |
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*> On exit, if INFO = 0, the triangular factor U or L from the |
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*> Cholesky factorization A = U**H*U or A = L*L**H, in the same |
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*> storage format as A. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, the leading minor of order i is not |
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*> positive definite, and the factorization could not be |
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*> completed. |
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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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*> \ingroup complex16OTHERcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> The packed storage scheme is illustrated by the following example |
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*> when N = 4, UPLO = 'U': |
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*> |
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*> Two-dimensional storage of the Hermitian matrix A: |
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*> |
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*> a11 a12 a13 a14 |
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*> a22 a23 a24 |
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*> a33 a34 (aij = conjg(aji)) |
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*> a44 |
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*> |
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*> Packed storage of the upper triangle of A: |
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*> |
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*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) |
SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational 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 2006 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 AP( * ) |
COMPLEX*16 AP( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZPPTRF computes the Cholesky factorization of a complex Hermitian |
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* positive definite matrix A stored in packed format. |
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* |
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* The factorization has the form |
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* A = U**H * U, if UPLO = 'U', or |
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* A = L * L**H, if UPLO = 'L', |
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* where U is an upper triangular matrix and L is lower triangular. |
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* |
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* Arguments |
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* ========= |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) |
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* On entry, the upper or lower triangle of the Hermitian matrix |
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* A, packed columnwise in a linear array. The j-th column of A |
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* is stored in the array AP as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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* See below for further details. |
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* |
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* On exit, if INFO = 0, the triangular factor U or L from the |
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* Cholesky factorization A = U**H*U or A = L*L**H, in the same |
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* storage format as A. |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* > 0: if INFO = i, the leading minor of order i is not |
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* positive definite, and the factorization could not be |
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* completed. |
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* |
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* Further Details |
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* =============== |
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* |
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* The packed storage scheme is illustrated by the following example |
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* when N = 4, UPLO = 'U': |
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* |
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* Two-dimensional storage of the Hermitian matrix A: |
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* |
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* a11 a12 a13 a14 |
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* a22 a23 a24 |
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* a33 a34 (aij = conjg(aji)) |
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* a44 |
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* |
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* Packed storage of the upper triangle of A: |
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* |
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* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute the Cholesky factorization A = U'*U. |
* Compute the Cholesky factorization A = U**H * U. |
* |
* |
JJ = 0 |
JJ = 0 |
DO 10 J = 1, N |
DO 10 J = 1, N |
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* |
* |
* Compute U(J,J) and test for non-positive-definiteness. |
* Compute U(J,J) and test for non-positive-definiteness. |
* |
* |
AJJ = DBLE( AP( JJ ) ) - ZDOTC( J-1, AP( JC ), 1, AP( JC ), |
AJJ = DBLE( AP( JJ ) ) - DBLE( ZDOTC( J-1, |
$ 1 ) |
$ AP( JC ), 1, AP( JC ), 1 ) ) |
IF( AJJ.LE.ZERO ) THEN |
IF( AJJ.LE.ZERO ) THEN |
AP( JJ ) = AJJ |
AP( JJ ) = AJJ |
GO TO 30 |
GO TO 30 |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
* |
* |
* Compute the Cholesky factorization A = L*L'. |
* Compute the Cholesky factorization A = L * L**H. |
* |
* |
JJ = 1 |
JJ = 1 |
DO 20 J = 1, N |
DO 20 J = 1, N |