version 1.3, 2010/08/06 15:28:45
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version 1.13, 2014/01/27 09:28:25
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*> \brief \b DPBTRS |
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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 DPBTRS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrs.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/dpbtrs.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/dpbtrs.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 DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, 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, KD, LDAB, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), 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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*> DPBTRS solves a system of linear equations A*X = B with a symmetric |
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*> positive definite band matrix A using the Cholesky factorization |
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*> A = U**T*U or A = L*L**T computed by DPBTRF. |
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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 triangular factor stored in AB; |
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*> = 'L': Lower triangular factor stored in AB. |
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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] KD |
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*> \verbatim |
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*> KD is INTEGER |
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*> The number of superdiagonals of the matrix A if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KD >= 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] AB |
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*> \verbatim |
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N) |
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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 of the band matrix A, stored in the |
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*> first KD+1 rows of the array. The j-th column of U or L is |
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*> stored in the j-th column of the array AB as follows: |
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*> if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDAB >= KD+1. |
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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 right hand side matrix B. |
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*> On exit, the 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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*> \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 November 2011 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) |
SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ) |
DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPBTRS solves a system of linear equations A*X = B with a symmetric |
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* positive definite band matrix A using the Cholesky factorization |
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* A = U**T*U or A = L*L**T computed by DPBTRF. |
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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 triangular factor stored in AB; |
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* = 'L': Lower triangular factor stored in AB. |
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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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* KD (input) INTEGER |
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* The number of superdiagonals of the matrix A if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KD >= 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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* AB (input) DOUBLE PRECISION array, dimension (LDAB,N) |
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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 of the band matrix A, stored in the |
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* first KD+1 rows of the array. The j-th column of U or L is |
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* stored in the j-th column of the array AB as follows: |
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* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KD+1. |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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* On entry, the right hand side matrix B. |
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* On exit, the 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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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Solve A*X = B where A = U'*U. |
* Solve A*X = B where A = U**T *U. |
* |
* |
DO 10 J = 1, NRHS |
DO 10 J = 1, NRHS |
* |
* |
* Solve U'*X = B, overwriting B with X. |
* Solve U**T *X = B, overwriting B with X. |
* |
* |
CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB, |
CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB, |
$ LDAB, B( 1, J ), 1 ) |
$ LDAB, B( 1, J ), 1 ) |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
* |
* |
* Solve A*X = B where A = L*L'. |
* Solve A*X = B where A = L*L**T. |
* |
* |
DO 20 J = 1, NRHS |
DO 20 J = 1, NRHS |
* |
* |
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CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB, |
CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB, |
$ LDAB, B( 1, J ), 1 ) |
$ LDAB, B( 1, J ), 1 ) |
* |
* |
* Solve L'*X = B, overwriting B with X. |
* Solve L**T *X = B, overwriting B with X. |
* |
* |
CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB, |
CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB, |
$ LDAB, B( 1, J ), 1 ) |
$ LDAB, B( 1, J ), 1 ) |