--- rpl/lapack/lapack/dgelq2.f 2010/08/06 15:28:36 1.3
+++ rpl/lapack/lapack/dgelq2.f 2023/08/07 08:38:48 1.21
@@ -1,9 +1,135 @@
+*> \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGELQ2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGELQ2 computes an LQ factorization of a real m-by-n matrix A:
+*>
+*> A = ( L 0 ) * Q
+*>
+*> where:
+*>
+*> Q is a n-by-n orthogonal matrix;
+*> L is a lower-triangular m-by-m matrix;
+*> 0 is a m-by-(n-m) zero matrix, if m < n.
+*>
+*> \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 A.
+*> On exit, the elements on and below the diagonal of the array
+*> contain the m by min(m,n) lower trapezoidal matrix L (L is
+*> lower triangular if m <= n); the elements above the diagonal,
+*> with the array TAU, represent the orthogonal matrix Q as a
+*> product of elementary reflectors (see Further Details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (min(M,N))
+*> The scalar factors of the elementary reflectors (see Further
+*> Details).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (M)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleGEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The matrix Q is represented as a product of elementary reflectors
+*>
+*> Q = H(k) . . . H(2) H(1), where k = min(m,n).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**T
+*>
+*> where tau is a real scalar, and v is a real vector with
+*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
+*> and tau in TAU(i).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, 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
@@ -12,57 +138,6 @@
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGELQ2 computes an LQ factorization of a real m by n matrix A:
-* A = L * Q.
-*
-* 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 A.
-* On exit, the elements on and below the diagonal of the array
-* contain the m by min(m,n) lower trapezoidal matrix L (L is
-* lower triangular if m <= n); the elements above the diagonal,
-* with the array TAU, represent the orthogonal matrix Q as a
-* product of elementary reflectors (see Further Details).
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
-* The scalar factors of the elementary reflectors (see Further
-* Details).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (M)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of elementary reflectors
-*
-* Q = H(k) . . . H(2) H(1), where k = min(m,n).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a real scalar, and v is a real vector with
-* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
-* and tau in TAU(i).
-*
* =====================================================================
*
* .. Parameters ..
@@ -74,7 +149,7 @@
DOUBLE PRECISION AII
* ..
* .. External Subroutines ..
- EXTERNAL DLARF, DLARFP, XERBLA
+ EXTERNAL DLARF, DLARFG, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
@@ -102,7 +177,7 @@
*
* Generate elementary reflector H(i) to annihilate A(i,i+1:n)
*
- CALL DLARFP( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA,
+ CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA,
$ TAU( I ) )
IF( I.LT.M ) THEN
*