--- rpl/lapack/lapack/dporfsx.f 2010/12/21 13:53:36 1.4
+++ rpl/lapack/lapack/dporfsx.f 2011/11/21 20:43:02 1.5
@@ -1,18 +1,404 @@
+*> \brief \b DPORFSX
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DPORFSX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
+* LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
+* ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
+* WORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO, EQUED
+* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
+* $ N_ERR_BNDS
+* DOUBLE PRECISION RCOND
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
+* $ X( LDX, * ), WORK( * )
+* DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
+* $ ERR_BNDS_NORM( NRHS, * ),
+* $ ERR_BNDS_COMP( NRHS, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DPORFSX improves the computed solution to a system of linear
+*> equations when the coefficient matrix is symmetric positive
+*> definite, and provides error bounds and backward error estimates
+*> for the solution. In addition to normwise error bound, the code
+*> provides maximum componentwise error bound if possible. See
+*> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
+*> error bounds.
+*>
+*> The original system of linear equations may have been equilibrated
+*> before calling this routine, as described by arguments EQUED and S
+*> below. In this case, the solution and error bounds returned are
+*> for the original unequilibrated system.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \verbatim
+*> Some optional parameters are bundled in the PARAMS array. These
+*> settings determine how refinement is performed, but often the
+*> defaults are acceptable. If the defaults are acceptable, users
+*> can pass NPARAMS = 0 which prevents the source code from accessing
+*> the PARAMS argument.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored;
+*> = 'L': Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] EQUED
+*> \verbatim
+*> EQUED is CHARACTER*1
+*> Specifies the form of equilibration that was done to A
+*> before calling this routine. This is needed to compute
+*> the solution and error bounds correctly.
+*> = 'N': No equilibration
+*> = 'Y': Both row and column equilibration, i.e., A has been
+*> replaced by diag(S) * A * diag(S).
+*> The right hand side B has been changed accordingly.
+*> \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 DOUBLE PRECISION array, dimension (LDA,N)
+*> The symmetric matrix A. If UPLO = 'U', the leading N-by-N
+*> upper triangular part of A contains the upper triangular part
+*> of the matrix A, and the strictly lower triangular part of A
+*> is not referenced. If UPLO = 'L', the leading N-by-N lower
+*> triangular part of A contains the lower triangular part of
+*> the matrix A, and the strictly upper triangular part of A is
+*> not referenced.
+*> \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 DOUBLE PRECISION array, dimension (LDAF,N)
+*> The triangular factor U or L from the Cholesky factorization
+*> A = U**T*U or A = L*L**T, as computed by DPOTRF.
+*> \endverbatim
+*>
+*> \param[in] LDAF
+*> \verbatim
+*> LDAF is INTEGER
+*> The leading dimension of the array AF. LDAF >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] S
+*> \verbatim
+*> S is or output) DOUBLE PRECISION array, dimension (N)
+*> The row scale factors for A. If EQUED = 'Y', A is multiplied on
+*> the left and right by diag(S). S is an input argument if FACT =
+*> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
+*> = 'Y', each element of S must be positive. If S is output, each
+*> element of S is a power of the radix. If S is input, each element
+*> of S should be a power of the radix to ensure a reliable solution
+*> and error estimates. Scaling by powers of the radix does not cause
+*> rounding errors unless the result underflows or overflows.
+*> Rounding errors during scaling lead to refining with a matrix that
+*> is not equivalent to the input matrix, producing error estimates
+*> that may not be reliable.
+*> \endverbatim
+*>
+*> \param[in] B
+*> \verbatim
+*> B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
+*> On entry, the solution matrix X, as computed by DGETRS.
+*> 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] RCOND
+*> \verbatim
+*> RCOND is DOUBLE PRECISION
+*> Reciprocal scaled condition number. This is an estimate of the
+*> reciprocal Skeel condition number of the matrix A after
+*> equilibration (if done). If this is less than the machine
+*> precision (in particular, if it is zero), the matrix is singular
+*> to working precision. Note that the error may still be small even
+*> if this number is very small and the matrix appears ill-
+*> conditioned.
+*> \endverbatim
+*>
+*> \param[out] BERR
+*> \verbatim
+*> BERR is DOUBLE PRECISION array, dimension (NRHS)
+*> Componentwise relative backward error. This is 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[in] N_ERR_BNDS
+*> \verbatim
+*> N_ERR_BNDS is INTEGER
+*> Number of error bounds to return for each right hand side
+*> and each type (normwise or componentwise). See ERR_BNDS_NORM and
+*> ERR_BNDS_COMP below.
+*> \endverbatim
+*>
+*> \param[out] ERR_BNDS_NORM
+*> \verbatim
+*> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
+*> For each right-hand side, this array contains information about
+*> various error bounds and condition numbers corresponding to the
+*> normwise relative error, which is defined as follows:
+*>
+*> Normwise relative error in the ith solution vector:
+*> max_j (abs(XTRUE(j,i) - X(j,i)))
+*> ------------------------------
+*> max_j abs(X(j,i))
+*>
+*> The array is indexed by the type of error information as described
+*> below. There currently are up to three pieces of information
+*> returned.
+*>
+*> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
+*> right-hand side.
+*>
+*> The second index in ERR_BNDS_NORM(:,err) contains the following
+*> three fields:
+*> err = 1 "Trust/don't trust" boolean. Trust the answer if the
+*> reciprocal condition number is less than the threshold
+*> sqrt(n) * dlamch('Epsilon').
+*>
+*> err = 2 "Guaranteed" error bound: The estimated forward error,
+*> almost certainly within a factor of 10 of the true error
+*> so long as the next entry is greater than the threshold
+*> sqrt(n) * dlamch('Epsilon'). This error bound should only
+*> be trusted if the previous boolean is true.
+*>
+*> err = 3 Reciprocal condition number: Estimated normwise
+*> reciprocal condition number. Compared with the threshold
+*> sqrt(n) * dlamch('Epsilon') to determine if the error
+*> estimate is "guaranteed". These reciprocal condition
+*> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
+*> appropriately scaled matrix Z.
+*> Let Z = S*A, where S scales each row by a power of the
+*> radix so all absolute row sums of Z are approximately 1.
+*>
+*> See Lapack Working Note 165 for further details and extra
+*> cautions.
+*> \endverbatim
+*>
+*> \param[out] ERR_BNDS_COMP
+*> \verbatim
+*> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
+*> For each right-hand side, this array contains information about
+*> various error bounds and condition numbers corresponding to the
+*> componentwise relative error, which is defined as follows:
+*>
+*> Componentwise relative error in the ith solution vector:
+*> abs(XTRUE(j,i) - X(j,i))
+*> max_j ----------------------
+*> abs(X(j,i))
+*>
+*> The array is indexed by the right-hand side i (on which the
+*> componentwise relative error depends), and the type of error
+*> information as described below. There currently are up to three
+*> pieces of information returned for each right-hand side. If
+*> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
+*> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
+*> the first (:,N_ERR_BNDS) entries are returned.
+*>
+*> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
+*> right-hand side.
+*>
+*> The second index in ERR_BNDS_COMP(:,err) contains the following
+*> three fields:
+*> err = 1 "Trust/don't trust" boolean. Trust the answer if the
+*> reciprocal condition number is less than the threshold
+*> sqrt(n) * dlamch('Epsilon').
+*>
+*> err = 2 "Guaranteed" error bound: The estimated forward error,
+*> almost certainly within a factor of 10 of the true error
+*> so long as the next entry is greater than the threshold
+*> sqrt(n) * dlamch('Epsilon'). This error bound should only
+*> be trusted if the previous boolean is true.
+*>
+*> err = 3 Reciprocal condition number: Estimated componentwise
+*> reciprocal condition number. Compared with the threshold
+*> sqrt(n) * dlamch('Epsilon') to determine if the error
+*> estimate is "guaranteed". These reciprocal condition
+*> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
+*> appropriately scaled matrix Z.
+*> Let Z = S*(A*diag(x)), where x is the solution for the
+*> current right-hand side and S scales each row of
+*> A*diag(x) by a power of the radix so all absolute row
+*> sums of Z are approximately 1.
+*>
+*> See Lapack Working Note 165 for further details and extra
+*> cautions.
+*> \endverbatim
+*>
+*> \param[in] NPARAMS
+*> \verbatim
+*> NPARAMS is INTEGER
+*> Specifies the number of parameters set in PARAMS. If .LE. 0, the
+*> PARAMS array is never referenced and default values are used.
+*> \endverbatim
+*>
+*> \param[in,out] PARAMS
+*> \verbatim
+*> PARAMS is / output) DOUBLE PRECISION array, dimension (NPARAMS)
+*> Specifies algorithm parameters. If an entry is .LT. 0.0, then
+*> that entry will be filled with default value used for that
+*> parameter. Only positions up to NPARAMS are accessed; defaults
+*> are used for higher-numbered parameters.
+*>
+*> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
+*> refinement or not.
+*> Default: 1.0D+0
+*> = 0.0 : No refinement is performed, and no error bounds are
+*> computed.
+*> = 1.0 : Use the double-precision refinement algorithm,
+*> possibly with doubled-single computations if the
+*> compilation environment does not support DOUBLE
+*> PRECISION.
+*> (other values are reserved for future use)
+*>
+*> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
+*> computations allowed for refinement.
+*> Default: 10
+*> Aggressive: Set to 100 to permit convergence using approximate
+*> factorizations or factorizations other than LU. If
+*> the factorization uses a technique other than
+*> Gaussian elimination, the guarantees in
+*> err_bnds_norm and err_bnds_comp may no longer be
+*> trustworthy.
+*>
+*> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
+*> will attempt to find a solution with small componentwise
+*> relative error in the double-precision algorithm. Positive
+*> is true, 0.0 is false.
+*> Default: 1.0 (attempt componentwise convergence)
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (4*N)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: Successful exit. The solution to every right-hand side is
+*> guaranteed.
+*> < 0: If INFO = -i, the i-th argument had an illegal value
+*> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
+*> has been completed, but the factor U is exactly singular, so
+*> the solution and error bounds could not be computed. RCOND = 0
+*> is returned.
+*> = N+J: The solution corresponding to the Jth right-hand side is
+*> not guaranteed. The solutions corresponding to other right-
+*> hand sides K with K > J may not be guaranteed as well, but
+*> only the first such right-hand side is reported. If a small
+*> componentwise error is not requested (PARAMS(3) = 0.0) then
+*> the Jth right-hand side is the first with a normwise error
+*> bound that is not guaranteed (the smallest J such
+*> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
+*> the Jth right-hand side is the first with either a normwise or
+*> componentwise error bound that is not guaranteed (the smallest
+*> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
+*> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
+*> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
+*> about all of the right-hand sides check ERR_BNDS_NORM or
+*> ERR_BNDS_COMP.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doublePOcomputational
+*
+* =====================================================================
SUBROUTINE DPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
$ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
$ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
$ WORK, IWORK, INFO )
*
-* -- LAPACK routine (version 3.2.2) --
-* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
-* -- Jason Riedy of Univ. of California Berkeley. --
-* -- June 2010 --
-*
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley and NAG Ltd. --
+* -- 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 2011
*
- IMPLICIT NONE
-* ..
* .. Scalar Arguments ..
CHARACTER UPLO, EQUED
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
@@ -28,270 +414,7 @@
$ ERR_BNDS_COMP( NRHS, * )
* ..
*
-* Purpose
-* =======
-*
-* DPORFSX improves the computed solution to a system of linear
-* equations when the coefficient matrix is symmetric positive
-* definite, and provides error bounds and backward error estimates
-* for the solution. In addition to normwise error bound, the code
-* provides maximum componentwise error bound if possible. See
-* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
-* error bounds.
-*
-* The original system of linear equations may have been equilibrated
-* before calling this routine, as described by arguments EQUED and S
-* below. In this case, the solution and error bounds returned are
-* for the original unequilibrated system.
-*
-* Arguments
-* =========
-*
-* Some optional parameters are bundled in the PARAMS array. These
-* settings determine how refinement is performed, but often the
-* defaults are acceptable. If the defaults are acceptable, users
-* can pass NPARAMS = 0 which prevents the source code from accessing
-* the PARAMS argument.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored;
-* = 'L': Lower triangle of A is stored.
-*
-* EQUED (input) CHARACTER*1
-* Specifies the form of equilibration that was done to A
-* before calling this routine. This is needed to compute
-* the solution and error bounds correctly.
-* = 'N': No equilibration
-* = 'Y': Both row and column equilibration, i.e., A has been
-* replaced by diag(S) * A * diag(S).
-* The right hand side B has been changed accordingly.
-*
-* 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) DOUBLE PRECISION array, dimension (LDA,N)
-* The symmetric matrix A. If UPLO = 'U', the leading N-by-N
-* upper triangular part of A contains the upper triangular part
-* of the matrix A, and the strictly lower triangular part of A
-* is not referenced. If UPLO = 'L', the leading N-by-N lower
-* triangular part of A contains the lower triangular part of
-* the matrix A, and the strictly upper triangular part of A is
-* not referenced.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
-* The triangular factor U or L from the Cholesky factorization
-* A = U**T*U or A = L*L**T, as computed by DPOTRF.
-*
-* LDAF (input) INTEGER
-* The leading dimension of the array AF. LDAF >= max(1,N).
-*
-* S (input or output) DOUBLE PRECISION array, dimension (N)
-* The row scale factors for A. If EQUED = 'Y', A is multiplied on
-* the left and right by diag(S). S is an input argument if FACT =
-* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
-* = 'Y', each element of S must be positive. If S is output, each
-* element of S is a power of the radix. If S is input, each element
-* of S should be a power of the radix to ensure a reliable solution
-* and error estimates. Scaling by powers of the radix does not cause
-* rounding errors unless the result underflows or overflows.
-* Rounding errors during scaling lead to refining with a matrix that
-* is not equivalent to the input matrix, producing error estimates
-* that may not be reliable.
-*
-* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
-* On entry, the solution matrix X, as computed by DGETRS.
-* On exit, the improved solution matrix X.
-*
-* LDX (input) INTEGER
-* The leading dimension of the array X. LDX >= max(1,N).
-*
-* RCOND (output) DOUBLE PRECISION
-* Reciprocal scaled condition number. This is an estimate of the
-* reciprocal Skeel condition number of the matrix A after
-* equilibration (if done). If this is less than the machine
-* precision (in particular, if it is zero), the matrix is singular
-* to working precision. Note that the error may still be small even
-* if this number is very small and the matrix appears ill-
-* conditioned.
-*
-* BERR (output) DOUBLE PRECISION array, dimension (NRHS)
-* Componentwise relative backward error. This is 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).
-*
-* N_ERR_BNDS (input) INTEGER
-* Number of error bounds to return for each right hand side
-* and each type (normwise or componentwise). See ERR_BNDS_NORM and
-* ERR_BNDS_COMP below.
-*
-* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
-* For each right-hand side, this array contains information about
-* various error bounds and condition numbers corresponding to the
-* normwise relative error, which is defined as follows:
-*
-* Normwise relative error in the ith solution vector:
-* max_j (abs(XTRUE(j,i) - X(j,i)))
-* ------------------------------
-* max_j abs(X(j,i))
-*
-* The array is indexed by the type of error information as described
-* below. There currently are up to three pieces of information
-* returned.
-*
-* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
-* right-hand side.
-*
-* The second index in ERR_BNDS_NORM(:,err) contains the following
-* three fields:
-* err = 1 "Trust/don't trust" boolean. Trust the answer if the
-* reciprocal condition number is less than the threshold
-* sqrt(n) * dlamch('Epsilon').
-*
-* err = 2 "Guaranteed" error bound: The estimated forward error,
-* almost certainly within a factor of 10 of the true error
-* so long as the next entry is greater than the threshold
-* sqrt(n) * dlamch('Epsilon'). This error bound should only
-* be trusted if the previous boolean is true.
-*
-* err = 3 Reciprocal condition number: Estimated normwise
-* reciprocal condition number. Compared with the threshold
-* sqrt(n) * dlamch('Epsilon') to determine if the error
-* estimate is "guaranteed". These reciprocal condition
-* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
-* appropriately scaled matrix Z.
-* Let Z = S*A, where S scales each row by a power of the
-* radix so all absolute row sums of Z are approximately 1.
-*
-* See Lapack Working Note 165 for further details and extra
-* cautions.
-*
-* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
-* For each right-hand side, this array contains information about
-* various error bounds and condition numbers corresponding to the
-* componentwise relative error, which is defined as follows:
-*
-* Componentwise relative error in the ith solution vector:
-* abs(XTRUE(j,i) - X(j,i))
-* max_j ----------------------
-* abs(X(j,i))
-*
-* The array is indexed by the right-hand side i (on which the
-* componentwise relative error depends), and the type of error
-* information as described below. There currently are up to three
-* pieces of information returned for each right-hand side. If
-* componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
-* the first (:,N_ERR_BNDS) entries are returned.
-*
-* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
-* right-hand side.
-*
-* The second index in ERR_BNDS_COMP(:,err) contains the following
-* three fields:
-* err = 1 "Trust/don't trust" boolean. Trust the answer if the
-* reciprocal condition number is less than the threshold
-* sqrt(n) * dlamch('Epsilon').
-*
-* err = 2 "Guaranteed" error bound: The estimated forward error,
-* almost certainly within a factor of 10 of the true error
-* so long as the next entry is greater than the threshold
-* sqrt(n) * dlamch('Epsilon'). This error bound should only
-* be trusted if the previous boolean is true.
-*
-* err = 3 Reciprocal condition number: Estimated componentwise
-* reciprocal condition number. Compared with the threshold
-* sqrt(n) * dlamch('Epsilon') to determine if the error
-* estimate is "guaranteed". These reciprocal condition
-* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
-* appropriately scaled matrix Z.
-* Let Z = S*(A*diag(x)), where x is the solution for the
-* current right-hand side and S scales each row of
-* A*diag(x) by a power of the radix so all absolute row
-* sums of Z are approximately 1.
-*
-* See Lapack Working Note 165 for further details and extra
-* cautions.
-*
-* NPARAMS (input) INTEGER
-* Specifies the number of parameters set in PARAMS. If .LE. 0, the
-* PARAMS array is never referenced and default values are used.
-*
-* PARAMS (input / output) DOUBLE PRECISION array, dimension (NPARAMS)
-* Specifies algorithm parameters. If an entry is .LT. 0.0, then
-* that entry will be filled with default value used for that
-* parameter. Only positions up to NPARAMS are accessed; defaults
-* are used for higher-numbered parameters.
-*
-* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
-* refinement or not.
-* Default: 1.0D+0
-* = 0.0 : No refinement is performed, and no error bounds are
-* computed.
-* = 1.0 : Use the double-precision refinement algorithm,
-* possibly with doubled-single computations if the
-* compilation environment does not support DOUBLE
-* PRECISION.
-* (other values are reserved for future use)
-*
-* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
-* computations allowed for refinement.
-* Default: 10
-* Aggressive: Set to 100 to permit convergence using approximate
-* factorizations or factorizations other than LU. If
-* the factorization uses a technique other than
-* Gaussian elimination, the guarantees in
-* err_bnds_norm and err_bnds_comp may no longer be
-* trustworthy.
-*
-* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
-* will attempt to find a solution with small componentwise
-* relative error in the double-precision algorithm. Positive
-* is true, 0.0 is false.
-* Default: 1.0 (attempt componentwise convergence)
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (4*N)
-*
-* IWORK (workspace) INTEGER array, dimension (N)
-*
-* INFO (output) INTEGER
-* = 0: Successful exit. The solution to every right-hand side is
-* guaranteed.
-* < 0: If INFO = -i, the i-th argument had an illegal value
-* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
-* has been completed, but the factor U is exactly singular, so
-* the solution and error bounds could not be computed. RCOND = 0
-* is returned.
-* = N+J: The solution corresponding to the Jth right-hand side is
-* not guaranteed. The solutions corresponding to other right-
-* hand sides K with K > J may not be guaranteed as well, but
-* only the first such right-hand side is reported. If a small
-* componentwise error is not requested (PARAMS(3) = 0.0) then
-* the Jth right-hand side is the first with a normwise error
-* bound that is not guaranteed (the smallest J such
-* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
-* the Jth right-hand side is the first with either a normwise or
-* componentwise error bound that is not guaranteed (the smallest
-* J such that either ERR_BNDS_NORM(J,1) = 0.0 or
-* ERR_BNDS_COMP(J,1) = 0.0). See the definition of
-* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
-* about all of the right-hand sides check ERR_BNDS_NORM or
-* ERR_BNDS_COMP.
-*
-* ==================================================================
+* ==================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE