--- rpl/lapack/lapack/zptrfs.f	2010/01/26 15:22:46	1.1.1.1
+++ rpl/lapack/lapack/zptrfs.f	2023/08/07 08:39:36	1.19
@@ -1,10 +1,189 @@
+*> \brief \b ZPTRFS
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPTRFS + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptrfs.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptrfs.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptrfs.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
+*                          FERR, BERR, WORK, RWORK, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, LDB, LDX, N, NRHS
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   BERR( * ), D( * ), DF( * ), FERR( * ),
+*      $                   RWORK( * )
+*       COMPLEX*16         B( LDB, * ), E( * ), EF( * ), WORK( * ),
+*      $                   X( LDX, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZPTRFS improves the computed solution to a system of linear
+*> equations when the coefficient matrix is Hermitian positive definite
+*> and tridiagonal, and provides error bounds and backward error
+*> estimates for the solution.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the superdiagonal or the subdiagonal of the
+*>          tridiagonal matrix A is stored and the form of the
+*>          factorization:
+*>          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
+*>          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
+*>          (The two forms are equivalent if A is real.)
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in] NRHS
+*> \verbatim
+*>          NRHS is INTEGER
+*>          The number of right hand sides, i.e., the number of columns
+*>          of the matrix B.  NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          The n real diagonal elements of the tridiagonal matrix A.
+*> \endverbatim
+*>
+*> \param[in] E
+*> \verbatim
+*>          E is COMPLEX*16 array, dimension (N-1)
+*>          The (n-1) off-diagonal elements of the tridiagonal matrix A
+*>          (see UPLO).
+*> \endverbatim
+*>
+*> \param[in] DF
+*> \verbatim
+*>          DF is DOUBLE PRECISION array, dimension (N)
+*>          The n diagonal elements of the diagonal matrix D from
+*>          the factorization computed by ZPTTRF.
+*> \endverbatim
+*>
+*> \param[in] EF
+*> \verbatim
+*>          EF is COMPLEX*16 array, dimension (N-1)
+*>          The (n-1) off-diagonal elements of the unit bidiagonal
+*>          factor U or L from the factorization computed by ZPTTRF
+*>          (see UPLO).
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
+*>          The right hand side matrix B.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] X
+*> \verbatim
+*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
+*>          On entry, the solution matrix X, as computed by ZPTTRS.
+*>          On exit, the improved solution matrix X.
+*> \endverbatim
+*>
+*> \param[in] LDX
+*> \verbatim
+*>          LDX is INTEGER
+*>          The leading dimension of the array X.  LDX >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] FERR
+*> \verbatim
+*>          FERR is DOUBLE PRECISION array, dimension (NRHS)
+*>          The forward error bound for each solution vector
+*>          X(j) (the j-th column of the solution matrix X).
+*>          If XTRUE is the true solution corresponding to X(j), FERR(j)
+*>          is an estimated upper bound for the magnitude of the largest
+*>          element in (X(j) - XTRUE) divided by the magnitude of the
+*>          largest element in X(j).
+*> \endverbatim
+*>
+*> \param[out] BERR
+*> \verbatim
+*>          BERR is DOUBLE PRECISION array, dimension (NRHS)
+*>          The componentwise relative backward error of each solution
+*>          vector X(j) (i.e., the smallest relative change in
+*>          any element of A or B that makes X(j) an exact solution).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*>          WORK is COMPLEX*16 array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] RWORK
+*> \verbatim
+*>          RWORK is DOUBLE PRECISION 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
+*
+*> \par Internal Parameters:
+*  =========================
+*>
+*> \verbatim
+*>  ITMAX is the maximum number of steps of iterative refinement.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16PTcomputational
+*
+*  =====================================================================
       SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
      $                   FERR, BERR, WORK, RWORK, 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 ..
       CHARACTER          UPLO
@@ -17,87 +196,6 @@
      $                   X( LDX, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZPTRFS improves the computed solution to a system of linear
-*  equations when the coefficient matrix is Hermitian positive definite
-*  and tridiagonal, and provides error bounds and backward error
-*  estimates for the solution.
-*
-*  Arguments
-*  =========
-*
-*  UPLO    (input) CHARACTER*1
-*          Specifies whether the superdiagonal or the subdiagonal of the
-*          tridiagonal matrix A is stored and the form of the
-*          factorization:
-*          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
-*          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
-*          (The two forms are equivalent if A is real.)
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.  N >= 0.
-*
-*  NRHS    (input) INTEGER
-*          The number of right hand sides, i.e., the number of columns
-*          of the matrix B.  NRHS >= 0.
-*
-*  D       (input) DOUBLE PRECISION array, dimension (N)
-*          The n real diagonal elements of the tridiagonal matrix A.
-*
-*  E       (input) COMPLEX*16 array, dimension (N-1)
-*          The (n-1) off-diagonal elements of the tridiagonal matrix A
-*          (see UPLO).
-*
-*  DF      (input) DOUBLE PRECISION array, dimension (N)
-*          The n diagonal elements of the diagonal matrix D from
-*          the factorization computed by ZPTTRF.
-*
-*  EF      (input) COMPLEX*16 array, dimension (N-1)
-*          The (n-1) off-diagonal elements of the unit bidiagonal
-*          factor U or L from the factorization computed by ZPTTRF
-*          (see UPLO).
-*
-*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
-*          The right hand side matrix B.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max(1,N).
-*
-*  X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
-*          On entry, the solution matrix X, as computed by ZPTTRS.
-*          On exit, the improved solution matrix X.
-*
-*  LDX     (input) INTEGER
-*          The leading dimension of the array X.  LDX >= max(1,N).
-*
-*  FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
-*          The forward error bound for each solution vector
-*          X(j) (the j-th column of the solution matrix X).
-*          If XTRUE is the true solution corresponding to X(j), FERR(j)
-*          is an estimated upper bound for the magnitude of the largest
-*          element in (X(j) - XTRUE) divided by the magnitude of the
-*          largest element in X(j).
-*
-*  BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
-*          The componentwise relative backward error of each solution
-*          vector X(j) (i.e., the smallest relative change in
-*          any element of A or B that makes X(j) an exact solution).
-*
-*  WORK    (workspace) COMPLEX*16 array, dimension (N)
-*
-*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit
-*          < 0:  if INFO = -i, the i-th argument had an illegal value
-*
-*  Internal Parameters
-*  ===================
-*
-*  ITMAX is the maximum number of steps of iterative refinement.
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -327,7 +425,7 @@
 *           m(i,j) =  abs(A(i,j)), i = j,
 *           m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*        and e = [ 1, 1, ..., 1 ]**T.  Note M(A) = M(L)*D*M(L)**H.
 *
 *        Solve M(L) * x = e.
 *
@@ -336,7 +434,7 @@
             RWORK( I ) = ONE + RWORK( I-1 )*ABS( EF( I-1 ) )
    70    CONTINUE
 *
-*        Solve D * M(L)' * x = b.
+*        Solve D * M(L)**H * x = b.
 *
          RWORK( N ) = RWORK( N ) / DF( N )
          DO 80 I = N - 1, 1, -1