version 1.5, 2010/08/07 13:22:45
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version 1.8, 2011/11/21 20:43:22
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*> \brief \b ZTBTRS |
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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 ZTBTRS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztbtrs.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/ztbtrs.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/ztbtrs.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 ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, |
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* LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER DIAG, TRANS, 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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* COMPLEX*16 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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*> ZTBTRS solves a triangular system of the form |
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*> |
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*> A * X = B, A**T * X = B, or A**H * X = B, |
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*> |
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*> where A is a triangular band matrix of order N, and B is an |
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*> N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
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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': A is upper triangular; |
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*> = 'L': A is lower triangular. |
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*> \endverbatim |
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*> |
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*> \param[in] TRANS |
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*> \verbatim |
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*> TRANS is CHARACTER*1 |
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*> Specifies the form of the system of equations: |
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*> = 'N': A * X = B (No transpose) |
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*> = 'T': A**T * X = B (Transpose) |
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*> = 'C': A**H * X = B (Conjugate transpose) |
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*> \endverbatim |
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*> |
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*> \param[in] DIAG |
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*> \verbatim |
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*> DIAG is CHARACTER*1 |
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*> = 'N': A is non-unit triangular; |
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*> = 'U': A is unit triangular. |
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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 or subdiagonals of the |
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*> triangular band matrix A. 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 COMPLEX*16 array, dimension (LDAB,N) |
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*> The upper or lower triangular band matrix A, stored in the |
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*> first kd+1 rows of AB. The j-th column of A is stored |
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*> in the j-th column of the array AB as follows: |
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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*> If DIAG = 'U', the diagonal elements of A are not referenced |
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*> and are assumed to be 1. |
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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 COMPLEX*16 array, dimension (LDB,NRHS) |
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*> On entry, the right hand side matrix B. |
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*> On exit, if INFO = 0, 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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*> > 0: if INFO = i, the i-th diagonal element of A is zero, |
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*> indicating that the matrix is singular and the |
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*> solutions X have 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 November 2011 |
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* |
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*> \ingroup complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, |
SUBROUTINE ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, |
$ LDB, INFO ) |
$ 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 DIAG, TRANS, UPLO |
CHARACTER DIAG, TRANS, UPLO |
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COMPLEX*16 AB( LDAB, * ), B( LDB, * ) |
COMPLEX*16 AB( LDAB, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZTBTRS solves a triangular system of the form |
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* |
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* A * X = B, A**T * X = B, or A**H * X = B, |
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* |
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* where A is a triangular band matrix of order N, and B is an |
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* N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
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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': A is upper triangular; |
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* = 'L': A is lower triangular. |
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* |
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* TRANS (input) CHARACTER*1 |
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* Specifies the form of the system of equations: |
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* = 'N': A * X = B (No transpose) |
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* = 'T': A**T * X = B (Transpose) |
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* = 'C': A**H * X = B (Conjugate transpose) |
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* |
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* DIAG (input) CHARACTER*1 |
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* = 'N': A is non-unit triangular; |
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* = 'U': A is unit triangular. |
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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 or subdiagonals of the |
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* triangular band matrix A. 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) COMPLEX*16 array, dimension (LDAB,N) |
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* The upper or lower triangular band matrix A, stored in the |
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* first kd+1 rows of AB. The j-th column of A is stored |
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* in the j-th column of the array AB as follows: |
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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* If DIAG = 'U', the diagonal elements of A are not referenced |
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* and are assumed to be 1. |
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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) COMPLEX*16 array, dimension (LDB,NRHS) |
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* On entry, the right hand side matrix B. |
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* On exit, if INFO = 0, 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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* > 0: if INFO = i, the i-th diagonal element of A is zero, |
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* indicating that the matrix is singular and the |
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* solutions X have not been computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |