Annotation of rpl/lapack/lapack/dgerfsx.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b DGERFSX
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGERFSX + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerfsx.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgerfsx.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgerfsx.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
! 22: * R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
! 23: * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
! 24: * WORK, IWORK, INFO )
! 25: *
! 26: * .. Scalar Arguments ..
! 27: * CHARACTER TRANS, EQUED
! 28: * INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
! 29: * $ N_ERR_BNDS
! 30: * DOUBLE PRECISION RCOND
! 31: * ..
! 32: * .. Array Arguments ..
! 33: * INTEGER IPIV( * ), IWORK( * )
! 34: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 35: * $ X( LDX , * ), WORK( * )
! 36: * DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ),
! 37: * $ ERR_BNDS_NORM( NRHS, * ),
! 38: * $ ERR_BNDS_COMP( NRHS, * )
! 39: * ..
! 40: *
! 41: *
! 42: *> \par Purpose:
! 43: * =============
! 44: *>
! 45: *> \verbatim
! 46: *>
! 47: *> DGERFSX improves the computed solution to a system of linear
! 48: *> equations and provides error bounds and backward error estimates
! 49: *> for the solution. In addition to normwise error bound, the code
! 50: *> provides maximum componentwise error bound if possible. See
! 51: *> comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
! 52: *> error bounds.
! 53: *>
! 54: *> The original system of linear equations may have been equilibrated
! 55: *> before calling this routine, as described by arguments EQUED, R
! 56: *> and C below. In this case, the solution and error bounds returned
! 57: *> are for the original unequilibrated system.
! 58: *> \endverbatim
! 59: *
! 60: * Arguments:
! 61: * ==========
! 62: *
! 63: *> \verbatim
! 64: *> Some optional parameters are bundled in the PARAMS array. These
! 65: *> settings determine how refinement is performed, but often the
! 66: *> defaults are acceptable. If the defaults are acceptable, users
! 67: *> can pass NPARAMS = 0 which prevents the source code from accessing
! 68: *> the PARAMS argument.
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] TRANS
! 72: *> \verbatim
! 73: *> TRANS is CHARACTER*1
! 74: *> Specifies the form of the system of equations:
! 75: *> = 'N': A * X = B (No transpose)
! 76: *> = 'T': A**T * X = B (Transpose)
! 77: *> = 'C': A**H * X = B (Conjugate transpose = Transpose)
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] EQUED
! 81: *> \verbatim
! 82: *> EQUED is CHARACTER*1
! 83: *> Specifies the form of equilibration that was done to A
! 84: *> before calling this routine. This is needed to compute
! 85: *> the solution and error bounds correctly.
! 86: *> = 'N': No equilibration
! 87: *> = 'R': Row equilibration, i.e., A has been premultiplied by
! 88: *> diag(R).
! 89: *> = 'C': Column equilibration, i.e., A has been postmultiplied
! 90: *> by diag(C).
! 91: *> = 'B': Both row and column equilibration, i.e., A has been
! 92: *> replaced by diag(R) * A * diag(C).
! 93: *> The right hand side B has been changed accordingly.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] N
! 97: *> \verbatim
! 98: *> N is INTEGER
! 99: *> The order of the matrix A. N >= 0.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] NRHS
! 103: *> \verbatim
! 104: *> NRHS is INTEGER
! 105: *> The number of right hand sides, i.e., the number of columns
! 106: *> of the matrices B and X. NRHS >= 0.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] A
! 110: *> \verbatim
! 111: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 112: *> The original N-by-N matrix A.
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[in] LDA
! 116: *> \verbatim
! 117: *> LDA is INTEGER
! 118: *> The leading dimension of the array A. LDA >= max(1,N).
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] AF
! 122: *> \verbatim
! 123: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 124: *> The factors L and U from the factorization A = P*L*U
! 125: *> as computed by DGETRF.
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[in] LDAF
! 129: *> \verbatim
! 130: *> LDAF is INTEGER
! 131: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 132: *> \endverbatim
! 133: *>
! 134: *> \param[in] IPIV
! 135: *> \verbatim
! 136: *> IPIV is INTEGER array, dimension (N)
! 137: *> The pivot indices from DGETRF; for 1<=i<=N, row i of the
! 138: *> matrix was interchanged with row IPIV(i).
! 139: *> \endverbatim
! 140: *>
! 141: *> \param[in] R
! 142: *> \verbatim
! 143: *> R is DOUBLE PRECISION array, dimension (N)
! 144: *> The row scale factors for A. If EQUED = 'R' or 'B', A is
! 145: *> multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
! 146: *> is not accessed.
! 147: *> If R is accessed, each element of R should be a power of the radix
! 148: *> to ensure a reliable solution and error estimates. Scaling by
! 149: *> powers of the radix does not cause rounding errors unless the
! 150: *> result underflows or overflows. Rounding errors during scaling
! 151: *> lead to refining with a matrix that is not equivalent to the
! 152: *> input matrix, producing error estimates that may not be
! 153: *> reliable.
! 154: *> \endverbatim
! 155: *>
! 156: *> \param[in] C
! 157: *> \verbatim
! 158: *> C is DOUBLE PRECISION array, dimension (N)
! 159: *> The column scale factors for A. If EQUED = 'C' or 'B', A is
! 160: *> multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
! 161: *> is not accessed.
! 162: *> If C is accessed, each element of C should be a power of the radix
! 163: *> to ensure a reliable solution and error estimates. Scaling by
! 164: *> powers of the radix does not cause rounding errors unless the
! 165: *> result underflows or overflows. Rounding errors during scaling
! 166: *> lead to refining with a matrix that is not equivalent to the
! 167: *> input matrix, producing error estimates that may not be
! 168: *> reliable.
! 169: *> \endverbatim
! 170: *>
! 171: *> \param[in] B
! 172: *> \verbatim
! 173: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 174: *> The right hand side matrix B.
! 175: *> \endverbatim
! 176: *>
! 177: *> \param[in] LDB
! 178: *> \verbatim
! 179: *> LDB is INTEGER
! 180: *> The leading dimension of the array B. LDB >= max(1,N).
! 181: *> \endverbatim
! 182: *>
! 183: *> \param[in,out] X
! 184: *> \verbatim
! 185: *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
! 186: *> On entry, the solution matrix X, as computed by DGETRS.
! 187: *> On exit, the improved solution matrix X.
! 188: *> \endverbatim
! 189: *>
! 190: *> \param[in] LDX
! 191: *> \verbatim
! 192: *> LDX is INTEGER
! 193: *> The leading dimension of the array X. LDX >= max(1,N).
! 194: *> \endverbatim
! 195: *>
! 196: *> \param[out] RCOND
! 197: *> \verbatim
! 198: *> RCOND is DOUBLE PRECISION
! 199: *> Reciprocal scaled condition number. This is an estimate of the
! 200: *> reciprocal Skeel condition number of the matrix A after
! 201: *> equilibration (if done). If this is less than the machine
! 202: *> precision (in particular, if it is zero), the matrix is singular
! 203: *> to working precision. Note that the error may still be small even
! 204: *> if this number is very small and the matrix appears ill-
! 205: *> conditioned.
! 206: *> \endverbatim
! 207: *>
! 208: *> \param[out] BERR
! 209: *> \verbatim
! 210: *> BERR is DOUBLE PRECISION array, dimension (NRHS)
! 211: *> Componentwise relative backward error. This is the
! 212: *> componentwise relative backward error of each solution vector X(j)
! 213: *> (i.e., the smallest relative change in any element of A or B that
! 214: *> makes X(j) an exact solution).
! 215: *> \endverbatim
! 216: *>
! 217: *> \param[in] N_ERR_BNDS
! 218: *> \verbatim
! 219: *> N_ERR_BNDS is INTEGER
! 220: *> Number of error bounds to return for each right hand side
! 221: *> and each type (normwise or componentwise). See ERR_BNDS_NORM and
! 222: *> ERR_BNDS_COMP below.
! 223: *> \endverbatim
! 224: *>
! 225: *> \param[out] ERR_BNDS_NORM
! 226: *> \verbatim
! 227: *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 228: *> For each right-hand side, this array contains information about
! 229: *> various error bounds and condition numbers corresponding to the
! 230: *> normwise relative error, which is defined as follows:
! 231: *>
! 232: *> Normwise relative error in the ith solution vector:
! 233: *> max_j (abs(XTRUE(j,i) - X(j,i)))
! 234: *> ------------------------------
! 235: *> max_j abs(X(j,i))
! 236: *>
! 237: *> The array is indexed by the type of error information as described
! 238: *> below. There currently are up to three pieces of information
! 239: *> returned.
! 240: *>
! 241: *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 242: *> right-hand side.
! 243: *>
! 244: *> The second index in ERR_BNDS_NORM(:,err) contains the following
! 245: *> three fields:
! 246: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 247: *> reciprocal condition number is less than the threshold
! 248: *> sqrt(n) * dlamch('Epsilon').
! 249: *>
! 250: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 251: *> almost certainly within a factor of 10 of the true error
! 252: *> so long as the next entry is greater than the threshold
! 253: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
! 254: *> be trusted if the previous boolean is true.
! 255: *>
! 256: *> err = 3 Reciprocal condition number: Estimated normwise
! 257: *> reciprocal condition number. Compared with the threshold
! 258: *> sqrt(n) * dlamch('Epsilon') to determine if the error
! 259: *> estimate is "guaranteed". These reciprocal condition
! 260: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 261: *> appropriately scaled matrix Z.
! 262: *> Let Z = S*A, where S scales each row by a power of the
! 263: *> radix so all absolute row sums of Z are approximately 1.
! 264: *>
! 265: *> See Lapack Working Note 165 for further details and extra
! 266: *> cautions.
! 267: *> \endverbatim
! 268: *>
! 269: *> \param[out] ERR_BNDS_COMP
! 270: *> \verbatim
! 271: *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 272: *> For each right-hand side, this array contains information about
! 273: *> various error bounds and condition numbers corresponding to the
! 274: *> componentwise relative error, which is defined as follows:
! 275: *>
! 276: *> Componentwise relative error in the ith solution vector:
! 277: *> abs(XTRUE(j,i) - X(j,i))
! 278: *> max_j ----------------------
! 279: *> abs(X(j,i))
! 280: *>
! 281: *> The array is indexed by the right-hand side i (on which the
! 282: *> componentwise relative error depends), and the type of error
! 283: *> information as described below. There currently are up to three
! 284: *> pieces of information returned for each right-hand side. If
! 285: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 286: *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 287: *> the first (:,N_ERR_BNDS) entries are returned.
! 288: *>
! 289: *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 290: *> right-hand side.
! 291: *>
! 292: *> The second index in ERR_BNDS_COMP(:,err) contains the following
! 293: *> three fields:
! 294: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 295: *> reciprocal condition number is less than the threshold
! 296: *> sqrt(n) * dlamch('Epsilon').
! 297: *>
! 298: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 299: *> almost certainly within a factor of 10 of the true error
! 300: *> so long as the next entry is greater than the threshold
! 301: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
! 302: *> be trusted if the previous boolean is true.
! 303: *>
! 304: *> err = 3 Reciprocal condition number: Estimated componentwise
! 305: *> reciprocal condition number. Compared with the threshold
! 306: *> sqrt(n) * dlamch('Epsilon') to determine if the error
! 307: *> estimate is "guaranteed". These reciprocal condition
! 308: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 309: *> appropriately scaled matrix Z.
! 310: *> Let Z = S*(A*diag(x)), where x is the solution for the
! 311: *> current right-hand side and S scales each row of
! 312: *> A*diag(x) by a power of the radix so all absolute row
! 313: *> sums of Z are approximately 1.
! 314: *>
! 315: *> See Lapack Working Note 165 for further details and extra
! 316: *> cautions.
! 317: *> \endverbatim
! 318: *>
! 319: *> \param[in] NPARAMS
! 320: *> \verbatim
! 321: *> NPARAMS is INTEGER
! 322: *> Specifies the number of parameters set in PARAMS. If .LE. 0, the
! 323: *> PARAMS array is never referenced and default values are used.
! 324: *> \endverbatim
! 325: *>
! 326: *> \param[in,out] PARAMS
! 327: *> \verbatim
! 328: *> PARAMS is / output) DOUBLE PRECISION array, dimension (NPARAMS)
! 329: *> Specifies algorithm parameters. If an entry is .LT. 0.0, then
! 330: *> that entry will be filled with default value used for that
! 331: *> parameter. Only positions up to NPARAMS are accessed; defaults
! 332: *> are used for higher-numbered parameters.
! 333: *>
! 334: *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
! 335: *> refinement or not.
! 336: *> Default: 1.0D+0
! 337: *> = 0.0 : No refinement is performed, and no error bounds are
! 338: *> computed.
! 339: *> = 1.0 : Use the double-precision refinement algorithm,
! 340: *> possibly with doubled-single computations if the
! 341: *> compilation environment does not support DOUBLE
! 342: *> PRECISION.
! 343: *> (other values are reserved for future use)
! 344: *>
! 345: *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
! 346: *> computations allowed for refinement.
! 347: *> Default: 10
! 348: *> Aggressive: Set to 100 to permit convergence using approximate
! 349: *> factorizations or factorizations other than LU. If
! 350: *> the factorization uses a technique other than
! 351: *> Gaussian elimination, the guarantees in
! 352: *> err_bnds_norm and err_bnds_comp may no longer be
! 353: *> trustworthy.
! 354: *>
! 355: *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
! 356: *> will attempt to find a solution with small componentwise
! 357: *> relative error in the double-precision algorithm. Positive
! 358: *> is true, 0.0 is false.
! 359: *> Default: 1.0 (attempt componentwise convergence)
! 360: *> \endverbatim
! 361: *>
! 362: *> \param[out] WORK
! 363: *> \verbatim
! 364: *> WORK is DOUBLE PRECISION array, dimension (4*N)
! 365: *> \endverbatim
! 366: *>
! 367: *> \param[out] IWORK
! 368: *> \verbatim
! 369: *> IWORK is INTEGER array, dimension (N)
! 370: *> \endverbatim
! 371: *>
! 372: *> \param[out] INFO
! 373: *> \verbatim
! 374: *> INFO is INTEGER
! 375: *> = 0: Successful exit. The solution to every right-hand side is
! 376: *> guaranteed.
! 377: *> < 0: If INFO = -i, the i-th argument had an illegal value
! 378: *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
! 379: *> has been completed, but the factor U is exactly singular, so
! 380: *> the solution and error bounds could not be computed. RCOND = 0
! 381: *> is returned.
! 382: *> = N+J: The solution corresponding to the Jth right-hand side is
! 383: *> not guaranteed. The solutions corresponding to other right-
! 384: *> hand sides K with K > J may not be guaranteed as well, but
! 385: *> only the first such right-hand side is reported. If a small
! 386: *> componentwise error is not requested (PARAMS(3) = 0.0) then
! 387: *> the Jth right-hand side is the first with a normwise error
! 388: *> bound that is not guaranteed (the smallest J such
! 389: *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
! 390: *> the Jth right-hand side is the first with either a normwise or
! 391: *> componentwise error bound that is not guaranteed (the smallest
! 392: *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
! 393: *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
! 394: *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
! 395: *> about all of the right-hand sides check ERR_BNDS_NORM or
! 396: *> ERR_BNDS_COMP.
! 397: *> \endverbatim
! 398: *
! 399: * Authors:
! 400: * ========
! 401: *
! 402: *> \author Univ. of Tennessee
! 403: *> \author Univ. of California Berkeley
! 404: *> \author Univ. of Colorado Denver
! 405: *> \author NAG Ltd.
! 406: *
! 407: *> \date November 2011
! 408: *
! 409: *> \ingroup doubleGEcomputational
! 410: *
! 411: * =====================================================================
1.1 bertrand 412: SUBROUTINE DGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
413: $ R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
414: $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
415: $ WORK, IWORK, INFO )
416: *
1.5 ! bertrand 417: * -- LAPACK computational routine (version 3.4.0) --
! 418: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 419: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 420: * November 2011
1.1 bertrand 421: *
422: * .. Scalar Arguments ..
423: CHARACTER TRANS, EQUED
424: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
425: $ N_ERR_BNDS
426: DOUBLE PRECISION RCOND
427: * ..
428: * .. Array Arguments ..
429: INTEGER IPIV( * ), IWORK( * )
430: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
431: $ X( LDX , * ), WORK( * )
432: DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ),
433: $ ERR_BNDS_NORM( NRHS, * ),
434: $ ERR_BNDS_COMP( NRHS, * )
435: * ..
436: *
1.5 ! bertrand 437: * ==================================================================
1.1 bertrand 438: *
439: * .. Parameters ..
440: DOUBLE PRECISION ZERO, ONE
441: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
442: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
443: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
444: DOUBLE PRECISION DZTHRESH_DEFAULT
445: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
446: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
447: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
448: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
449: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
450: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
451: $ LA_LINRX_CWISE_I
452: PARAMETER ( LA_LINRX_ITREF_I = 1,
453: $ LA_LINRX_ITHRESH_I = 2 )
454: PARAMETER ( LA_LINRX_CWISE_I = 3 )
455: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
456: $ LA_LINRX_RCOND_I
457: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
458: PARAMETER ( LA_LINRX_RCOND_I = 3 )
459: * ..
460: * .. Local Scalars ..
461: CHARACTER(1) NORM
462: LOGICAL ROWEQU, COLEQU, NOTRAN
463: INTEGER J, TRANS_TYPE, PREC_TYPE, REF_TYPE
464: INTEGER N_NORMS
465: DOUBLE PRECISION ANORM, RCOND_TMP
466: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
467: LOGICAL IGNORE_CWISE
468: INTEGER ITHRESH
469: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
470: * ..
471: * .. External Subroutines ..
472: EXTERNAL XERBLA, DGECON, DLA_GERFSX_EXTENDED
473: * ..
474: * .. Intrinsic Functions ..
475: INTRINSIC MAX, SQRT
476: * ..
477: * .. External Functions ..
478: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
479: EXTERNAL DLAMCH, DLANGE, DLA_GERCOND
480: DOUBLE PRECISION DLAMCH, DLANGE, DLA_GERCOND
481: LOGICAL LSAME
482: INTEGER BLAS_FPINFO_X
483: INTEGER ILATRANS, ILAPREC
484: * ..
485: * .. Executable Statements ..
486: *
487: * Check the input parameters.
488: *
489: INFO = 0
490: TRANS_TYPE = ILATRANS( TRANS )
491: REF_TYPE = INT( ITREF_DEFAULT )
492: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
493: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
494: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
495: ELSE
496: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
497: END IF
498: END IF
499: *
500: * Set default parameters.
501: *
502: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
503: ITHRESH = INT( ITHRESH_DEFAULT )
504: RTHRESH = RTHRESH_DEFAULT
505: UNSTABLE_THRESH = DZTHRESH_DEFAULT
506: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
507: *
508: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
509: IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
510: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
511: ELSE
512: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
513: END IF
514: END IF
515: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
516: IF ( PARAMS( LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
517: IF ( IGNORE_CWISE ) THEN
518: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
519: ELSE
520: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
521: END IF
522: ELSE
523: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
524: END IF
525: END IF
526: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
527: N_NORMS = 0
528: ELSE IF ( IGNORE_CWISE ) THEN
529: N_NORMS = 1
530: ELSE
531: N_NORMS = 2
532: END IF
533: *
534: NOTRAN = LSAME( TRANS, 'N' )
535: ROWEQU = LSAME( EQUED, 'R' ) .OR. LSAME( EQUED, 'B' )
536: COLEQU = LSAME( EQUED, 'C' ) .OR. LSAME( EQUED, 'B' )
537: *
538: * Test input parameters.
539: *
540: IF( TRANS_TYPE.EQ.-1 ) THEN
541: INFO = -1
542: ELSE IF( .NOT.ROWEQU .AND. .NOT.COLEQU .AND.
543: $ .NOT.LSAME( EQUED, 'N' ) ) THEN
544: INFO = -2
545: ELSE IF( N.LT.0 ) THEN
546: INFO = -3
547: ELSE IF( NRHS.LT.0 ) THEN
548: INFO = -4
549: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
550: INFO = -6
551: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
552: INFO = -8
553: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
554: INFO = -13
555: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
556: INFO = -15
557: END IF
558: IF( INFO.NE.0 ) THEN
559: CALL XERBLA( 'DGERFSX', -INFO )
560: RETURN
561: END IF
562: *
563: * Quick return if possible.
564: *
565: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
566: RCOND = 1.0D+0
567: DO J = 1, NRHS
568: BERR( J ) = 0.0D+0
569: IF ( N_ERR_BNDS .GE. 1 ) THEN
570: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I) = 1.0D+0
571: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
572: END IF
573: IF ( N_ERR_BNDS .GE. 2 ) THEN
574: ERR_BNDS_NORM( J, LA_LINRX_ERR_I) = 0.0D+0
575: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
576: END IF
577: IF ( N_ERR_BNDS .GE. 3 ) THEN
578: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I) = 1.0D+0
579: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
580: END IF
581: END DO
582: RETURN
583: END IF
584: *
585: * Default to failure.
586: *
587: RCOND = 0.0D+0
588: DO J = 1, NRHS
589: BERR( J ) = 1.0D+0
590: IF ( N_ERR_BNDS .GE. 1 ) THEN
591: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
592: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
593: END IF
594: IF ( N_ERR_BNDS .GE. 2 ) THEN
595: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
596: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
597: END IF
598: IF ( N_ERR_BNDS .GE. 3 ) THEN
599: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
600: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
601: END IF
602: END DO
603: *
604: * Compute the norm of A and the reciprocal of the condition
605: * number of A.
606: *
607: IF( NOTRAN ) THEN
608: NORM = 'I'
609: ELSE
610: NORM = '1'
611: END IF
612: ANORM = DLANGE( NORM, N, N, A, LDA, WORK )
613: CALL DGECON( NORM, N, AF, LDAF, ANORM, RCOND, WORK, IWORK, INFO )
614: *
615: * Perform refinement on each right-hand side
616: *
617: IF ( REF_TYPE .NE. 0 ) THEN
618:
619: PREC_TYPE = ILAPREC( 'E' )
620:
621: IF ( NOTRAN ) THEN
622: CALL DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N,
623: $ NRHS, A, LDA, AF, LDAF, IPIV, COLEQU, C, B,
624: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM,
625: $ ERR_BNDS_COMP, WORK(N+1), WORK(1), WORK(2*N+1),
626: $ WORK(1), RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH,
627: $ IGNORE_CWISE, INFO )
628: ELSE
629: CALL DLA_GERFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N,
630: $ NRHS, A, LDA, AF, LDAF, IPIV, ROWEQU, R, B,
631: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM,
632: $ ERR_BNDS_COMP, WORK(N+1), WORK(1), WORK(2*N+1),
633: $ WORK(1), RCOND, ITHRESH, RTHRESH, UNSTABLE_THRESH,
634: $ IGNORE_CWISE, INFO )
635: END IF
636: END IF
637:
638: ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
639: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
640: *
641: * Compute scaled normwise condition number cond(A*C).
642: *
643: IF ( COLEQU .AND. NOTRAN ) THEN
644: RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
645: $ -1, C, INFO, WORK, IWORK )
646: ELSE IF ( ROWEQU .AND. .NOT. NOTRAN ) THEN
647: RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
648: $ -1, R, INFO, WORK, IWORK )
649: ELSE
650: RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF, IPIV,
651: $ 0, R, INFO, WORK, IWORK )
652: END IF
653: DO J = 1, NRHS
654: *
655: * Cap the error at 1.0.
656: *
657: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
658: $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
659: $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
660: *
661: * Threshold the error (see LAWN).
662: *
663: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
664: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
665: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
666: IF ( INFO .LE. N ) INFO = N + J
667: ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
668: $ THEN
669: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
670: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
671: END IF
672: *
673: * Save the condition number.
674: *
675: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
676: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
677: END IF
678: END DO
679: END IF
680:
681: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
682: *
683: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
684: * each right-hand side using the current solution as an estimate of
685: * the true solution. If the componentwise error estimate is too
686: * large, then the solution is a lousy estimate of truth and the
687: * estimated RCOND may be too optimistic. To avoid misleading users,
688: * the inverse condition number is set to 0.0 when the estimated
689: * cwise error is at least CWISE_WRONG.
690: *
691: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
692: DO J = 1, NRHS
693: IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
694: $ THEN
695: RCOND_TMP = DLA_GERCOND( TRANS, N, A, LDA, AF, LDAF,
696: $ IPIV, 1, X(1,J), INFO, WORK, IWORK )
697: ELSE
698: RCOND_TMP = 0.0D+0
699: END IF
700: *
701: * Cap the error at 1.0.
702: *
703: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
704: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
705: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
706: *
707: * Threshold the error (see LAWN).
708: *
709: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
710: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
711: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
712: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
713: $ .AND. INFO.LT.N + J ) INFO = N + J
714: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
715: $ .LT. ERR_LBND ) THEN
716: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
717: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
718: END IF
719: *
720: * Save the condition number.
721: *
722: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
723: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
724: END IF
725: END DO
726: END IF
727: *
728: RETURN
729: *
730: * End of DGERFSX
731: *
732: END
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