--- rpl/lapack/lapack/zgeql2.f	2010/08/06 15:28:52	1.3
+++ rpl/lapack/lapack/zgeql2.f	2023/08/07 08:39:18	1.20
@@ -1,9 +1,129 @@
+*> \brief \b ZGEQL2 computes the QL 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 ZGEQL2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeql2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeql2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeql2.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, LDA, M, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZGEQL2 computes a QL factorization of a complex m by n matrix A:
+*> A = Q * L.
+*> \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 COMPLEX*16 array, dimension (LDA,N)
+*>          On entry, the m by n matrix A.
+*>          On exit, if m >= n, the lower triangle of the subarray
+*>          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
+*>          if m <= n, the elements on and below the (n-m)-th
+*>          superdiagonal contain the m by n lower trapezoidal matrix L;
+*>          the remaining elements, with the array TAU, represent the
+*>          unitary 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 COMPLEX*16 array, dimension (min(M,N))
+*>          The scalar factors of the elementary reflectors (see Further
+*>          Details).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension (N)
+*> \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 complex16GEcomputational
+*
+*> \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**H
+*>
+*>  where tau is a complex scalar, and v is a complex vector with
+*>  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
+*>  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE ZGEQL2( 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
@@ -12,59 +132,6 @@
       COMPLEX*16         A( LDA, * ), TAU( * ), WORK( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZGEQL2 computes a QL factorization of a complex m by n matrix A:
-*  A = Q * L.
-*
-*  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) COMPLEX*16 array, dimension (LDA,N)
-*          On entry, the m by n matrix A.
-*          On exit, if m >= n, the lower triangle of the subarray
-*          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
-*          if m <= n, the elements on and below the (n-m)-th
-*          superdiagonal contain the m by n lower trapezoidal matrix L;
-*          the remaining elements, with the array TAU, represent the
-*          unitary 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) COMPLEX*16 array, dimension (min(M,N))
-*          The scalar factors of the elementary reflectors (see Further
-*          Details).
-*
-*  WORK    (workspace) COMPLEX*16 array, dimension (N)
-*
-*  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 complex scalar, and v is a complex vector with
-*  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
-*  A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -76,7 +143,7 @@
       COMPLEX*16         ALPHA
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           XERBLA, ZLARF, ZLARFP
+      EXTERNAL           XERBLA, ZLARF, ZLARFG
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          DCONJG, MAX, MIN
@@ -106,9 +173,9 @@
 *        A(1:m-k+i-1,n-k+i)
 *
          ALPHA = A( M-K+I, N-K+I )
-         CALL ZLARFP( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
+         CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
 *
-*        Apply H(i)' to A(1:m-k+i,1:n-k+i-1) from the left
+*        Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
 *
          A( M-K+I, N-K+I ) = ONE
          CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1,