--- rpl/lapack/lapack/dgttrf.f	2010/08/06 15:28:38	1.3
+++ rpl/lapack/lapack/dgttrf.f	2023/08/07 08:38:52	1.18
@@ -1,9 +1,130 @@
+*> \brief \b DGTTRF
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGTTRF + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgttrf.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgttrf.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgttrf.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
+*
+*       .. Scalar Arguments ..
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       INTEGER            IPIV( * )
+*       DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DGTTRF computes an LU factorization of a real tridiagonal matrix A
+*> using elimination with partial pivoting and row interchanges.
+*>
+*> The factorization has the form
+*>    A = L * U
+*> where L is a product of permutation and unit lower bidiagonal
+*> matrices and U is upper triangular with nonzeros in only the main
+*> diagonal and first two superdiagonals.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in,out] DL
+*> \verbatim
+*>          DL is DOUBLE PRECISION array, dimension (N-1)
+*>          On entry, DL must contain the (n-1) sub-diagonal elements of
+*>          A.
+*>
+*>          On exit, DL is overwritten by the (n-1) multipliers that
+*>          define the matrix L from the LU factorization of A.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          On entry, D must contain the diagonal elements of A.
+*>
+*>          On exit, D is overwritten by the n diagonal elements of the
+*>          upper triangular matrix U from the LU factorization of A.
+*> \endverbatim
+*>
+*> \param[in,out] DU
+*> \verbatim
+*>          DU is DOUBLE PRECISION array, dimension (N-1)
+*>          On entry, DU must contain the (n-1) super-diagonal elements
+*>          of A.
+*>
+*>          On exit, DU is overwritten by the (n-1) elements of the first
+*>          super-diagonal of U.
+*> \endverbatim
+*>
+*> \param[out] DU2
+*> \verbatim
+*>          DU2 is DOUBLE PRECISION array, dimension (N-2)
+*>          On exit, DU2 is overwritten by the (n-2) elements of the
+*>          second super-diagonal of U.
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*>          IPIV is INTEGER array, dimension (N)
+*>          The pivot indices; for 1 <= i <= n, row i of the matrix was
+*>          interchanged with row IPIV(i).  IPIV(i) will always be either
+*>          i or i+1; IPIV(i) = i indicates a row interchange was not
+*>          required.
+*> \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 doubleGTcomputational
+*
+*  =====================================================================
       SUBROUTINE DGTTRF( N, DL, D, DU, DU2, 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, N
@@ -13,62 +134,6 @@
       DOUBLE PRECISION   D( * ), DL( * ), DU( * ), DU2( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  DGTTRF computes an LU factorization of a real tridiagonal matrix A
-*  using elimination with partial pivoting and row interchanges.
-*
-*  The factorization has the form
-*     A = L * U
-*  where L is a product of permutation and unit lower bidiagonal
-*  matrices and U is upper triangular with nonzeros in only the main
-*  diagonal and first two superdiagonals.
-*
-*  Arguments
-*  =========
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.
-*
-*  DL      (input/output) DOUBLE PRECISION array, dimension (N-1)
-*          On entry, DL must contain the (n-1) sub-diagonal elements of
-*          A.
-*
-*          On exit, DL is overwritten by the (n-1) multipliers that
-*          define the matrix L from the LU factorization of A.
-*
-*  D       (input/output) DOUBLE PRECISION array, dimension (N)
-*          On entry, D must contain the diagonal elements of A.
-*
-*          On exit, D is overwritten by the n diagonal elements of the
-*          upper triangular matrix U from the LU factorization of A.
-*
-*  DU      (input/output) DOUBLE PRECISION array, dimension (N-1)
-*          On entry, DU must contain the (n-1) super-diagonal elements
-*          of A.
-*
-*          On exit, DU is overwritten by the (n-1) elements of the first
-*          super-diagonal of U.
-*
-*  DU2     (output) DOUBLE PRECISION array, dimension (N-2)
-*          On exit, DU2 is overwritten by the (n-2) elements of the
-*          second super-diagonal of U.
-*
-*  IPIV    (output) INTEGER array, dimension (N)
-*          The pivot indices; for 1 <= i <= n, row i of the matrix was
-*          interchanged with row IPIV(i).  IPIV(i) will always be either
-*          i or i+1; IPIV(i) = i indicates a row interchange was not
-*          required.
-*
-*  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 ..