--- rpl/lapack/lapack/zptrfs.f 2011/07/22 07:38:19 1.8
+++ rpl/lapack/lapack/zptrfs.f 2011/11/21 20:43:20 1.9
@@ -1,10 +1,192 @@
+*> \brief \b ZPTRFS
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPTRFS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \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.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERcomputational
+*
+* =====================================================================
SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
$ FERR, BERR, WORK, RWORK, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -17,87 +199,6 @@
$ 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 ..