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version 1.15, 2016/08/27 15:34:24
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*> \brief \b DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. |
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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 DGTTS2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtts2.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/dgtts2.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/dgtts2.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 DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER ITRANS, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
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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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*> DGTTS2 solves one of the systems of equations |
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*> A*X = B or A**T*X = B, |
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*> with a tridiagonal matrix A using the LU factorization computed |
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*> by DGTTRF. |
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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] ITRANS |
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*> \verbatim |
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*> ITRANS is INTEGER |
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*> Specifies the form of the system of equations. |
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*> = 0: A * X = B (No transpose) |
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*> = 1: A**T* X = B (Transpose) |
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*> = 2: A**T* X = B (Conjugate transpose = Transpose) |
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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. |
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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] DL |
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*> \verbatim |
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*> DL is DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) multipliers that define the matrix L from the |
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*> LU factorization of A. |
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*> \endverbatim |
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*> |
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*> \param[in] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> The n diagonal elements of the upper triangular matrix U from |
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*> the LU factorization of A. |
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*> \endverbatim |
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*> |
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*> \param[in] DU |
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*> \verbatim |
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*> DU is DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) elements of the first super-diagonal of U. |
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*> \endverbatim |
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*> |
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*> \param[in] DU2 |
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*> \verbatim |
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*> DU2 is DOUBLE PRECISION array, dimension (N-2) |
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*> The (n-2) elements of the second super-diagonal of U. |
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*> \endverbatim |
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*> |
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*> \param[in] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N) |
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*> The pivot indices; for 1 <= i <= n, row i of the matrix was |
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*> interchanged with row IPIV(i). IPIV(i) will always be either |
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*> i or i+1; IPIV(i) = i indicates a row interchange was not |
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*> required. |
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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 matrix of right hand side vectors B. |
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*> On exit, B is overwritten by the solution vectors 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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* 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 September 2012 |
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* |
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*> \ingroup doubleGTcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) |
SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER ITRANS, LDB, N, NRHS |
INTEGER ITRANS, LDB, N, NRHS |
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DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGTTS2 solves one of the systems of equations |
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* A*X = B or A'*X = B, |
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* with a tridiagonal matrix A using the LU factorization computed |
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* by DGTTRF. |
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* |
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* Arguments |
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* ========= |
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* |
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* ITRANS (input) INTEGER |
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* Specifies the form of the system of equations. |
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* = 0: A * X = B (No transpose) |
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* = 1: A'* X = B (Transpose) |
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* = 2: A'* X = B (Conjugate transpose = Transpose) |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. |
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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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* DL (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) multipliers that define the matrix L from the |
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* LU factorization of A. |
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* |
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* D (input) DOUBLE PRECISION array, dimension (N) |
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* The n diagonal elements of the upper triangular matrix U from |
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* the LU factorization of A. |
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* |
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* DU (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) elements of the first super-diagonal of U. |
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* |
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* DU2 (input) DOUBLE PRECISION array, dimension (N-2) |
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* The (n-2) elements of the second super-diagonal of U. |
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* |
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* IPIV (input) INTEGER array, dimension (N) |
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* The pivot indices; for 1 <= i <= n, row i of the matrix was |
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* interchanged with row IPIV(i). IPIV(i) will always be either |
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* i or i+1; IPIV(i) = i indicates a row interchange was not |
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* required. |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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* On entry, the matrix of right hand side vectors B. |
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* On exit, B is overwritten by the solution vectors 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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END IF |
END IF |
ELSE |
ELSE |
* |
* |
* Solve A' * X = B. |
* Solve A**T * X = B. |
* |
* |
IF( NRHS.LE.1 ) THEN |
IF( NRHS.LE.1 ) THEN |
* |
* |
* Solve U'*x = b. |
* Solve U**T*x = b. |
* |
* |
J = 1 |
J = 1 |
70 CONTINUE |
70 CONTINUE |
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$ B( I-2, J ) ) / D( I ) |
$ B( I-2, J ) ) / D( I ) |
80 CONTINUE |
80 CONTINUE |
* |
* |
* Solve L'*x = b. |
* Solve L**T*x = b. |
* |
* |
DO 90 I = N - 1, 1, -1 |
DO 90 I = N - 1, 1, -1 |
IP = IPIV( I ) |
IP = IPIV( I ) |
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ELSE |
ELSE |
DO 120 J = 1, NRHS |
DO 120 J = 1, NRHS |
* |
* |
* Solve U'*x = b. |
* Solve U**T*x = b. |
* |
* |
B( 1, J ) = B( 1, J ) / D( 1 ) |
B( 1, J ) = B( 1, J ) / D( 1 ) |
IF( N.GT.1 ) |
IF( N.GT.1 ) |