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version 1.18, 2023/08/07 08:38:50
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*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm). |
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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 DGETF2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetf2.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/dgetf2.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/dgetf2.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 DGETF2( M, N, A, LDA, IPIV, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDA, M, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION A( LDA, * ) |
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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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*> DGETF2 computes an LU factorization of a general m-by-n matrix A |
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*> using partial pivoting with row interchanges. |
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*> |
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*> The factorization has the form |
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*> A = P * L * U |
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*> where P is a permutation matrix, L is lower triangular with unit |
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*> diagonal elements (lower trapezoidal if m > n), and U is upper |
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*> triangular (upper trapezoidal if m < n). |
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*> |
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*> This is the right-looking Level 2 BLAS version of the algorithm. |
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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] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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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 number of columns of the matrix A. N >= 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 DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the m by n matrix to be factored. |
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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,M). |
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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 (min(M,N)) |
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*> The pivot indices; for 1 <= i <= min(M,N), row i of the |
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*> matrix was interchanged with row IPIV(i). |
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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 = -k, the k-th argument had an illegal value |
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*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization |
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*> has been completed, but the factor U is exactly |
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*> singular, and division by zero will occur if it is used |
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*> to solve a system of equations. |
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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 doubleGEcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) |
SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine -- |
* -- 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 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, LDA, M, N |
INTEGER INFO, LDA, M, N |
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DOUBLE PRECISION A( LDA, * ) |
DOUBLE PRECISION A( LDA, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGETF2 computes an LU factorization of a general m-by-n matrix A |
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* using partial pivoting with row interchanges. |
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* |
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* The factorization has the form |
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* A = P * L * U |
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* where P is a permutation matrix, L is lower triangular with unit |
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* diagonal elements (lower trapezoidal if m > n), and U is upper |
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* triangular (upper trapezoidal if m < n). |
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* |
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* This is the right-looking Level 2 BLAS version of the algorithm. |
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* |
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* Arguments |
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* ========= |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the m by n matrix to be factored. |
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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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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,M). |
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* |
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* IPIV (output) INTEGER array, dimension (min(M,N)) |
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* The pivot indices; for 1 <= i <= min(M,N), row i of the |
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* matrix was interchanged with row IPIV(i). |
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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 = -k, the k-th argument had an illegal value |
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* > 0: if INFO = k, U(k,k) is exactly zero. The factorization |
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* has been completed, but the factor U is exactly |
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* singular, and division by zero will occur if it is used |
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* to solve a system of equations. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE PRECISION SFMIN |
DOUBLE PRECISION SFMIN |
INTEGER I, J, JP |
INTEGER I, J, JP |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
DOUBLE PRECISION DLAMCH |
DOUBLE PRECISION DLAMCH |
INTEGER IDAMAX |
INTEGER IDAMAX |
EXTERNAL DLAMCH, IDAMAX |
EXTERNAL DLAMCH, IDAMAX |
* .. |
* .. |
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IF( M.EQ.0 .OR. N.EQ.0 ) |
IF( M.EQ.0 .OR. N.EQ.0 ) |
$ RETURN |
$ RETURN |
* |
* |
* Compute machine safe minimum |
* Compute machine safe minimum |
* |
* |
SFMIN = DLAMCH('S') |
SFMIN = DLAMCH('S') |
* |
* |
DO 10 J = 1, MIN( M, N ) |
DO 10 J = 1, MIN( M, N ) |
* |
* |
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* |
* |
* Compute elements J+1:M of J-th column. |
* Compute elements J+1:M of J-th column. |
* |
* |
IF( J.LT.M ) THEN |
IF( J.LT.M ) THEN |
IF( ABS(A( J, J )) .GE. SFMIN ) THEN |
IF( ABS(A( J, J )) .GE. SFMIN ) THEN |
CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) |
CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) |
ELSE |
ELSE |
DO 20 I = 1, M-J |
DO 20 I = 1, M-J |
A( J+I, J ) = A( J+I, J ) / A( J, J ) |
A( J+I, J ) = A( J+I, J ) / A( J, J ) |
20 CONTINUE |
20 CONTINUE |
END IF |
END IF |
END IF |
END IF |
* |
* |
ELSE IF( INFO.EQ.0 ) THEN |
ELSE IF( INFO.EQ.0 ) THEN |
* |
* |