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version 1.6, 2010/08/13 21:03:45
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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 |
|
| * ======= |
|
| * |
|
| * DGETF2 computes an LU factorization of a general m-by-n matrix A |
|
| * using partial pivoting with row interchanges. |
|
| * |
|
| * The factorization has the form |
|
| * A = P * L * U |
|
| * where P is a permutation matrix, L is lower triangular with unit |
|
| * diagonal elements (lower trapezoidal if m > n), and U is upper |
|
| * triangular (upper trapezoidal if m < n). |
|
| * |
|
| * This is the right-looking Level 2 BLAS version of the algorithm. |
|
| * |
|
| * Arguments |
|
| * ========= |
|
| * |
|
| * 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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| * ===================================================================== |
* ===================================================================== |
| * |
* |
| * .. 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 |
| * |
* |
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