177 lines
5.0 KiB
Fortran
177 lines
5.0 KiB
Fortran
*> \brief <b> ZGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver) </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 ZGESV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesv.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/zgesv.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/zgesv.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 ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 A( LDA, * ), 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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*> ZGESV computes the solution to a complex system of linear equations
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*> A * X = B,
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*> where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
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*>
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*> The LU decomposition with partial pivoting and row interchanges is
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*> used to factor A as
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*> A = P * L * U,
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*> where P is a permutation matrix, L is unit lower triangular, and U is
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*> upper triangular. The factored form of A is then used to solve the
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*> system of 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] 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] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> On entry, the N-by-N coefficient matrix A.
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*> On exit, the factors L and U from the factorization
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*> A = P*L*U; the unit diagonal elements of L are not stored.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices that define the permutation matrix P;
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*> row i of the matrix was interchanged with row IPIV(i).
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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 N-by-NRHS matrix of 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, U(i,i) is exactly zero. The factorization
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*> has been completed, but the factor U is exactly
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*> singular, so the solution could not be 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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*> \ingroup complex16GEsolve
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*
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* =====================================================================
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SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
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*
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* -- LAPACK driver routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 A( LDA, * ), B( LDB, * )
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* ..
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*
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* =====================================================================
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*
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZGETRF, ZGETRS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGESV ', -INFO )
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RETURN
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END IF
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*
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* Compute the LU factorization of A.
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*
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CALL ZGETRF( N, N, A, LDA, IPIV, INFO )
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IF( INFO.EQ.0 ) THEN
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*
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* Solve the system A*X = B, overwriting B with X.
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*
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CALL ZGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB,
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$ INFO )
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END IF
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RETURN
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*
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* End of ZGESV
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*
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END
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