--- rpl/lapack/lapack/zgerfs.f 2010/12/21 13:53:44 1.7
+++ rpl/lapack/lapack/zgerfs.f 2011/11/21 20:43:09 1.8
@@ -1,12 +1,195 @@
+*> \brief \b ZGERFS
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGERFS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
+* X, LDX, FERR, BERR, WORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER TRANS
+* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
+* COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
+* $ WORK( * ), X( LDX, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGERFS improves the computed solution to a system of linear
+*> equations and provides error bounds and backward error estimates for
+*> the solution.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] TRANS
+*> \verbatim
+*> TRANS is CHARACTER*1
+*> Specifies the form of the system of equations:
+*> = 'N': A * X = B (No transpose)
+*> = 'T': A**T * X = B (Transpose)
+*> = 'C': A**H * X = B (Conjugate transpose)
+*> \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 matrices B and X. NRHS >= 0.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> The original N-by-N matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] AF
+*> \verbatim
+*> AF is COMPLEX*16 array, dimension (LDAF,N)
+*> The factors L and U from the factorization A = P*L*U
+*> as computed by ZGETRF.
+*> \endverbatim
+*>
+*> \param[in] LDAF
+*> \verbatim
+*> LDAF is INTEGER
+*> The leading dimension of the array AF. LDAF >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> The pivot indices from ZGETRF; for 1<=i<=N, row i of the
+*> matrix was interchanged with row IPIV(i).
+*> \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 ZGETRS.
+*> 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 estimated 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). The estimate is as reliable as
+*> the estimate for RCOND, and is almost always a slight
+*> overestimate of the true error.
+*> \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 (2*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 complex16GEcomputational
+*
+* =====================================================================
SUBROUTINE ZGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
$ X, LDX, FERR, BERR, WORK, RWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- 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..--
-* November 2006
-*
-* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER TRANS
@@ -19,87 +202,6 @@
$ WORK( * ), X( LDX, * )
* ..
*
-* Purpose
-* =======
-*
-* ZGERFS improves the computed solution to a system of linear
-* equations and provides error bounds and backward error estimates for
-* the solution.
-*
-* Arguments
-* =========
-*
-* TRANS (input) CHARACTER*1
-* Specifies the form of the system of equations:
-* = 'N': A * X = B (No transpose)
-* = 'T': A**T * X = B (Transpose)
-* = 'C': A**H * X = B (Conjugate transpose)
-*
-* 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 matrices B and X. NRHS >= 0.
-*
-* A (input) COMPLEX*16 array, dimension (LDA,N)
-* The original N-by-N matrix A.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* AF (input) COMPLEX*16 array, dimension (LDAF,N)
-* The factors L and U from the factorization A = P*L*U
-* as computed by ZGETRF.
-*
-* LDAF (input) INTEGER
-* The leading dimension of the array AF. LDAF >= max(1,N).
-*
-* IPIV (input) INTEGER array, dimension (N)
-* The pivot indices from ZGETRF; for 1<=i<=N, row i of the
-* matrix was interchanged with row IPIV(i).
-*
-* 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 ZGETRS.
-* 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 estimated 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). The estimate is as reliable as
-* the estimate for RCOND, and is almost always a slight
-* overestimate of the true error.
-*
-* 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 (2*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 ..