*> \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGESV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGESV computes the solution to a real system of linear equations *> A * X = B, *> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. *> *> The LU decomposition with partial pivoting and row interchanges is *> used to factor A as *> A = P * L * U, *> where P is a permutation matrix, L is unit lower triangular, and U is *> upper triangular. The factored form of A is then used to solve the *> system of equations A * X = B. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., the order of the *> matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the N-by-N coefficient matrix A. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices that define the permutation matrix P; *> row i of the matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the N-by-NRHS matrix of right hand side matrix B. *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, so the solution could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEsolve * * ===================================================================== SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Subroutines .. EXTERNAL DGETRF, DGETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( NRHS.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGESV ', -INFO ) RETURN END IF * * Compute the LU factorization of A. * CALL DGETRF( N, N, A, LDA, IPIV, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB, \$ INFO ) END IF RETURN * * End of DGESV * END