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