version 1.3, 2010/08/06 15:28:46
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version 1.17, 2018/05/29 07:18:04
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*> \brief \b DPPCON |
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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 DPPCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppcon.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/dppcon.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/dppcon.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 DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, 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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* DOUBLE PRECISION ANORM, RCOND |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION AP( * ), WORK( * ) |
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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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*> DPPCON estimates the reciprocal of the condition number (in the |
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*> 1-norm) of a real symmetric positive definite packed matrix using |
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*> the Cholesky factorization A = U**T*U or A = L*L**T computed by |
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*> DPPTRF. |
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*> |
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*> An estimate is obtained for norm(inv(A)), and the reciprocal of the |
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*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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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] AP |
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*> \verbatim |
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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*> The triangular factor U or L from the Cholesky factorization |
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*> A = U**T*U or A = L*L**T, packed columnwise in a linear |
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*> array. The j-th column of U or L is stored in the array AP |
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*> as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. |
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*> \endverbatim |
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*> |
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*> \param[in] ANORM |
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*> \verbatim |
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*> ANORM is DOUBLE PRECISION |
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*> The 1-norm (or infinity-norm) of the symmetric matrix A. |
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*> \endverbatim |
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*> |
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*> \param[out] RCOND |
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*> \verbatim |
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*> RCOND is DOUBLE PRECISION |
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*> The reciprocal of the condition number of the matrix A, |
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*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an |
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*> estimate of the 1-norm of inv(A) computed in this routine. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (3*N) |
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*> \endverbatim |
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*> |
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*> \param[out] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER array, dimension (N) |
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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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*> \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 December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO ) |
SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, 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 |
* |
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* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION AP( * ), WORK( * ) |
DOUBLE PRECISION AP( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPPCON estimates the reciprocal of the condition number (in the |
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* 1-norm) of a real symmetric positive definite packed matrix using |
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* the Cholesky factorization A = U**T*U or A = L*L**T computed by |
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* DPPTRF. |
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* |
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* An estimate is obtained for norm(inv(A)), and the reciprocal of the |
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* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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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) DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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* The triangular factor U or L from the Cholesky factorization |
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* A = U**T*U or A = L*L**T, packed columnwise in a linear |
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* array. The j-th column of U or L is stored in the array AP |
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* as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. |
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* |
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* ANORM (input) DOUBLE PRECISION |
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* The 1-norm (or infinity-norm) of the symmetric matrix A. |
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* |
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* RCOND (output) DOUBLE PRECISION |
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* The reciprocal of the condition number of the matrix A, |
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* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an |
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* estimate of the 1-norm of inv(A) computed in this routine. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) |
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* |
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* IWORK (workspace) INTEGER array, dimension (N) |
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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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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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IF( KASE.NE.0 ) THEN |
IF( KASE.NE.0 ) THEN |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Multiply by inv(U'). |
* Multiply by inv(U**T). |
* |
* |
CALL DLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, |
CALL DLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, |
$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) |
$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) |
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$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) |
$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO ) |
NORMIN = 'Y' |
NORMIN = 'Y' |
* |
* |
* Multiply by inv(L'). |
* Multiply by inv(L**T). |
* |
* |
CALL DLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, |
CALL DLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, |
$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) |
$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO ) |