--- rpl/lapack/lapack/dgetf2.f 2010/08/06 15:28:37 1.3
+++ rpl/lapack/lapack/dgetf2.f 2023/08/07 08:38:50 1.18
@@ -1,9 +1,114 @@
+*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGETF2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> 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.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the m by n matrix to be factored.
+*> 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,M).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (min(M,N))
+*> The pivot indices; for 1 <= i <= min(M,N), row i of the
+*> matrix was interchanged with row IPIV(i).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th argument had an illegal value
+*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
+*> has been completed, but the factor U is exactly
+*> singular, and division by zero will occur if it is used
+*> to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleGEcomputational
+*
+* =====================================================================
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, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
@@ -13,49 +118,6 @@
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
-* The number of rows of the matrix A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the m by n matrix to be factored.
-* On exit, the factors L and U from the factorization
-* A = P*L*U; the unit diagonal elements of L are not stored.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* IPIV (output) INTEGER array, dimension (min(M,N))
-* The pivot indices; for 1 <= i <= min(M,N), row i of the
-* matrix was interchanged with row IPIV(i).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -k, the k-th argument had an illegal value
-* > 0: if INFO = k, U(k,k) is exactly zero. The factorization
-* has been completed, but the factor U is exactly
-* singular, and division by zero will occur if it is used
-* to solve a system of equations.
-*
* =====================================================================
*
* .. Parameters ..
@@ -63,11 +125,11 @@
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
- DOUBLE PRECISION SFMIN
+ DOUBLE PRECISION SFMIN
INTEGER I, J, JP
* ..
* .. External Functions ..
- DOUBLE PRECISION DLAMCH
+ DOUBLE PRECISION DLAMCH
INTEGER IDAMAX
EXTERNAL DLAMCH, IDAMAX
* ..
@@ -99,9 +161,9 @@
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
-* Compute machine safe minimum
-*
- SFMIN = DLAMCH('S')
+* Compute machine safe minimum
+*
+ SFMIN = DLAMCH('S')
*
DO 10 J = 1, MIN( M, N )
*
@@ -118,15 +180,15 @@
*
* Compute elements J+1:M of J-th column.
*
- IF( J.LT.M ) THEN
- IF( ABS(A( J, J )) .GE. SFMIN ) THEN
- CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
- ELSE
- DO 20 I = 1, M-J
- A( J+I, J ) = A( J+I, J ) / A( J, J )
- 20 CONTINUE
- END IF
- END IF
+ IF( J.LT.M ) THEN
+ IF( ABS(A( J, J )) .GE. SFMIN ) THEN
+ CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
+ ELSE
+ DO 20 I = 1, M-J
+ A( J+I, J ) = A( J+I, J ) / A( J, J )
+ 20 CONTINUE
+ END IF
+ END IF
*
ELSE IF( INFO.EQ.0 ) THEN
*