version 1.6, 2010/08/13 21:03:55
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version 1.17, 2018/05/29 07:18:04
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*> \brief <b> DPPSV computes the solution to system of linear equations A * X = B for OTHER matrices</b> |
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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 DPPSV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dppsv.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/dppsv.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/dppsv.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 DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AP( * ), B( LDB, * ) |
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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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*> DPPSV computes the solution to a real system of linear equations |
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*> A * X = B, |
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*> where A is an N-by-N symmetric positive definite matrix stored in |
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*> packed format and X and B are N-by-NRHS matrices. |
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*> |
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*> The Cholesky decomposition is used to factor A as |
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*> A = U**T* U, if UPLO = 'U', or |
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*> A = L * L**T, if UPLO = 'L', |
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*> where U is an upper triangular matrix and L is a lower triangular |
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*> matrix. The factored form of A is then used to solve the system of |
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*> equations A * X = B. |
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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 number of linear equations, i.e., the order of the |
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*> matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 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 DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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*> On entry, the upper or lower triangle of the symmetric 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 factor U or L from the Cholesky |
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*> factorization A = U**T*U or A = L*L**T, in the same storage |
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*> format as A. |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) |
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*> On entry, the N-by-NRHS right hand side matrix B. |
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,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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*> > 0: if INFO = i, the leading minor of order i of A is not |
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*> positive definite, so the factorization could not be |
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*> completed, and the solution has not been computed. |
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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 doubleOTHERsolve |
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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 symmetric 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 DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) |
SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver 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 .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION AP( * ), B( LDB, * ) |
DOUBLE PRECISION AP( * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPPSV computes the solution to a real system of linear equations |
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* A * X = B, |
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* where A is an N-by-N symmetric positive definite matrix stored in |
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* packed format and X and B are N-by-NRHS matrices. |
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* |
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* The Cholesky decomposition is used to factor A as |
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* A = U**T* U, if UPLO = 'U', or |
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* A = L * L**T, if UPLO = 'L', |
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* where U is an upper triangular matrix and L is a lower triangular |
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* matrix. The factored form of A is then used to solve the system of |
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* equations A * X = B. |
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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 number of linear equations, i.e., the order of the |
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* matrix A. N >= 0. |
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* |
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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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* On entry, the upper or lower triangle of the symmetric 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 factor U or L from the Cholesky |
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* factorization A = U**T*U or A = L*L**T, in the same storage |
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* format as A. |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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* On entry, the N-by-NRHS right hand side matrix B. |
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* On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,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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* > 0: if INFO = i, the leading minor of order i of A is not |
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* positive definite, so the factorization could not be |
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* completed, and the solution has not been computed. |
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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 symmetric 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Functions .. |
* .. External Functions .. |
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RETURN |
RETURN |
END IF |
END IF |
* |
* |
* Compute the Cholesky factorization A = U'*U or A = L*L'. |
* Compute the Cholesky factorization A = U**T*U or A = L*L**T. |
* |
* |
CALL DPPTRF( UPLO, N, AP, INFO ) |
CALL DPPTRF( UPLO, N, AP, INFO ) |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |