--- rpl/lapack/lapack/dgetc2.f 2010/01/26 15:22:46 1.1.1.1
+++ rpl/lapack/lapack/dgetc2.f 2020/05/21 21:45:57 1.21
@@ -1,9 +1,120 @@
+*> \brief \b DGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGETC2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * ), JPIV( * )
+* DOUBLE PRECISION A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGETC2 computes an LU factorization with complete pivoting of the
+*> n-by-n matrix A. The factorization has the form A = P * L * U * Q,
+*> where P and Q are permutation matrices, L is lower triangular with
+*> unit diagonal elements and U is upper triangular.
+*>
+*> This is the Level 2 BLAS algorithm.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA, N)
+*> On entry, the n-by-n matrix A to be factored.
+*> On exit, the factors L and U from the factorization
+*> A = P*L*U*Q; the unit diagonal elements of L are not stored.
+*> If U(k, k) appears to be less than SMIN, U(k, k) is given the
+*> value of SMIN, i.e., giving a nonsingular perturbed system.
+*> \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; for 1 <= i <= N, row i of the
+*> matrix has been interchanged with row IPIV(i).
+*> \endverbatim
+*>
+*> \param[out] JPIV
+*> \verbatim
+*> JPIV is INTEGER array, dimension(N).
+*> The pivot indices; for 1 <= j <= N, column j of the
+*> matrix has been interchanged with column JPIV(j).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> > 0: if INFO = k, U(k, k) is likely to produce overflow if
+*> we try to solve for x in Ax = b. So U is perturbed to
+*> avoid the overflow.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date June 2016
+*
+*> \ingroup doubleGEauxiliary
+*
+*> \par Contributors:
+* ==================
+*>
+*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
+*> Umea University, S-901 87 Umea, Sweden.
+*
+* =====================================================================
SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
*
-* -- LAPACK auxiliary routine (version 3.2) --
+* -- LAPACK auxiliary routine (version 3.8.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* June 2016
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, N
@@ -13,53 +124,6 @@
DOUBLE PRECISION A( LDA, * )
* ..
*
-* Purpose
-* =======
-*
-* DGETC2 computes an LU factorization with complete pivoting of the
-* n-by-n matrix A. The factorization has the form A = P * L * U * Q,
-* where P and Q are permutation matrices, L is lower triangular with
-* unit diagonal elements and U is upper triangular.
-*
-* This is the Level 2 BLAS algorithm.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-* On entry, the n-by-n matrix A to be factored.
-* On exit, the factors L and U from the factorization
-* A = P*L*U*Q; the unit diagonal elements of L are not stored.
-* If U(k, k) appears to be less than SMIN, U(k, k) is given the
-* value of SMIN, i.e., giving a nonsingular perturbed system.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* IPIV (output) INTEGER array, dimension(N).
-* The pivot indices; for 1 <= i <= N, row i of the
-* matrix has been interchanged with row IPIV(i).
-*
-* JPIV (output) INTEGER array, dimension(N).
-* The pivot indices; for 1 <= j <= N, column j of the
-* matrix has been interchanged with column JPIV(j).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* > 0: if INFO = k, U(k, k) is likely to produce owerflow if
-* we try to solve for x in Ax = b. So U is perturbed to
-* avoid the overflow.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
-* Umea University, S-901 87 Umea, Sweden.
-*
* =====================================================================
*
* .. Parameters ..
@@ -71,7 +135,7 @@
DOUBLE PRECISION BIGNUM, EPS, SMIN, SMLNUM, XMAX
* ..
* .. External Subroutines ..
- EXTERNAL DGER, DSWAP
+ EXTERNAL DGER, DSWAP, DLABAD
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
@@ -82,14 +146,32 @@
* ..
* .. Executable Statements ..
*
+ INFO = 0
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
* Set constants to control overflow
*
- INFO = 0
EPS = DLAMCH( 'P' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
+* Handle the case N=1 by itself
+*
+ IF( N.EQ.1 ) THEN
+ IPIV( 1 ) = 1
+ JPIV( 1 ) = 1
+ IF( ABS( A( 1, 1 ) ).LT.SMLNUM ) THEN
+ INFO = 1
+ A( 1, 1 ) = SMLNUM
+ END IF
+ RETURN
+ END IF
+*
* Factorize A using complete pivoting.
* Set pivots less than SMIN to SMIN.
*
@@ -140,6 +222,11 @@
A( N, N ) = SMIN
END IF
*
+* Set last pivots to N
+*
+ IPIV( N ) = N
+ JPIV( N ) = N
+*
RETURN
*
* End of DGETC2