Annotation of rpl/lapack/lapack/zherfsx.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b ZHERFSX
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHERFSX + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zherfsx.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zherfsx.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zherfsx.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
! 22: * S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
! 23: * ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
! 24: * WORK, RWORK, 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 IPIV( * )
! 34: * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 35: * $ X( LDX, * ), WORK( * )
! 36: * DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
! 37: * $ ERR_BNDS_NORM( NRHS, * ),
! 38: * $ ERR_BNDS_COMP( NRHS, * )
! 39: *
! 40: *
! 41: *> \par Purpose:
! 42: * =============
! 43: *>
! 44: *> \verbatim
! 45: *>
! 46: *> ZHERFSX improves the computed solution to a system of linear
! 47: *> equations when the coefficient matrix is Hermitian indefinite, and
! 48: *> provides error bounds and backward error estimates for the
! 49: *> solution. In addition to normwise error bound, the code provides
! 50: *> maximum componentwise error bound if possible. See comments for
! 51: *> ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds.
! 52: *>
! 53: *> The original system of linear equations may have been equilibrated
! 54: *> before calling this routine, as described by arguments EQUED and S
! 55: *> below. In this case, the solution and error bounds returned are
! 56: *> for the original unequilibrated system.
! 57: *> \endverbatim
! 58: *
! 59: * Arguments:
! 60: * ==========
! 61: *
! 62: *> \verbatim
! 63: *> Some optional parameters are bundled in the PARAMS array. These
! 64: *> settings determine how refinement is performed, but often the
! 65: *> defaults are acceptable. If the defaults are acceptable, users
! 66: *> can pass NPARAMS = 0 which prevents the source code from accessing
! 67: *> the PARAMS argument.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] UPLO
! 71: *> \verbatim
! 72: *> UPLO is CHARACTER*1
! 73: *> = 'U': Upper triangle of A is stored;
! 74: *> = 'L': Lower triangle of A is stored.
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] EQUED
! 78: *> \verbatim
! 79: *> EQUED is CHARACTER*1
! 80: *> Specifies the form of equilibration that was done to A
! 81: *> before calling this routine. This is needed to compute
! 82: *> the solution and error bounds correctly.
! 83: *> = 'N': No equilibration
! 84: *> = 'Y': Both row and column equilibration, i.e., A has been
! 85: *> replaced by diag(S) * A * diag(S).
! 86: *> The right hand side B has been changed accordingly.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] N
! 90: *> \verbatim
! 91: *> N is INTEGER
! 92: *> The order of the matrix A. N >= 0.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] NRHS
! 96: *> \verbatim
! 97: *> NRHS is INTEGER
! 98: *> The number of right hand sides, i.e., the number of columns
! 99: *> of the matrices B and X. NRHS >= 0.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] A
! 103: *> \verbatim
! 104: *> A is COMPLEX*16 array, dimension (LDA,N)
! 105: *> The symmetric matrix A. If UPLO = 'U', the leading N-by-N
! 106: *> upper triangular part of A contains the upper triangular
! 107: *> part of the matrix A, and the strictly lower triangular
! 108: *> part of A is not referenced. If UPLO = 'L', the leading
! 109: *> N-by-N lower triangular part of A contains the lower
! 110: *> triangular part of the matrix A, and the strictly upper
! 111: *> triangular part of A is not referenced.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in] LDA
! 115: *> \verbatim
! 116: *> LDA is INTEGER
! 117: *> The leading dimension of the array A. LDA >= max(1,N).
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[in] AF
! 121: *> \verbatim
! 122: *> AF is COMPLEX*16 array, dimension (LDAF,N)
! 123: *> The factored form of the matrix A. AF contains the block
! 124: *> diagonal matrix D and the multipliers used to obtain the
! 125: *> factor U or L from the factorization A = U*D*U**T or A =
! 126: *> L*D*L**T as computed by DSYTRF.
! 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] IPIV
! 136: *> \verbatim
! 137: *> IPIV is INTEGER array, dimension (N)
! 138: *> Details of the interchanges and the block structure of D
! 139: *> as determined by DSYTRF.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in,out] S
! 143: *> \verbatim
! 144: *> S is or output) DOUBLE PRECISION array, dimension (N)
! 145: *> The scale factors for A. If EQUED = 'Y', A is multiplied on
! 146: *> the left and right by diag(S). S is an input argument if FACT =
! 147: *> 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
! 148: *> = 'Y', each element of S must be positive. If S is output, each
! 149: *> element of S is a power of the radix. If S is input, each element
! 150: *> of S should be a power of the radix to ensure a reliable solution
! 151: *> and error estimates. Scaling by powers of the radix does not cause
! 152: *> rounding errors unless the result underflows or overflows.
! 153: *> Rounding errors during scaling lead to refining with a matrix that
! 154: *> is not equivalent to the input matrix, producing error estimates
! 155: *> that may not be reliable.
! 156: *> \endverbatim
! 157: *>
! 158: *> \param[in] B
! 159: *> \verbatim
! 160: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
! 161: *> The right hand side matrix B.
! 162: *> \endverbatim
! 163: *>
! 164: *> \param[in] LDB
! 165: *> \verbatim
! 166: *> LDB is INTEGER
! 167: *> The leading dimension of the array B. LDB >= max(1,N).
! 168: *> \endverbatim
! 169: *>
! 170: *> \param[in,out] X
! 171: *> \verbatim
! 172: *> X is COMPLEX*16 array, dimension (LDX,NRHS)
! 173: *> On entry, the solution matrix X, as computed by DGETRS.
! 174: *> On exit, the improved solution matrix X.
! 175: *> \endverbatim
! 176: *>
! 177: *> \param[in] LDX
! 178: *> \verbatim
! 179: *> LDX is INTEGER
! 180: *> The leading dimension of the array X. LDX >= max(1,N).
! 181: *> \endverbatim
! 182: *>
! 183: *> \param[out] RCOND
! 184: *> \verbatim
! 185: *> RCOND is DOUBLE PRECISION
! 186: *> Reciprocal scaled condition number. This is an estimate of the
! 187: *> reciprocal Skeel condition number of the matrix A after
! 188: *> equilibration (if done). If this is less than the machine
! 189: *> precision (in particular, if it is zero), the matrix is singular
! 190: *> to working precision. Note that the error may still be small even
! 191: *> if this number is very small and the matrix appears ill-
! 192: *> conditioned.
! 193: *> \endverbatim
! 194: *>
! 195: *> \param[out] BERR
! 196: *> \verbatim
! 197: *> BERR is DOUBLE PRECISION array, dimension (NRHS)
! 198: *> Componentwise relative backward error. This is the
! 199: *> componentwise relative backward error of each solution vector X(j)
! 200: *> (i.e., the smallest relative change in any element of A or B that
! 201: *> makes X(j) an exact solution).
! 202: *> \endverbatim
! 203: *>
! 204: *> \param[in] N_ERR_BNDS
! 205: *> \verbatim
! 206: *> N_ERR_BNDS is INTEGER
! 207: *> Number of error bounds to return for each right hand side
! 208: *> and each type (normwise or componentwise). See ERR_BNDS_NORM and
! 209: *> ERR_BNDS_COMP below.
! 210: *> \endverbatim
! 211: *>
! 212: *> \param[out] ERR_BNDS_NORM
! 213: *> \verbatim
! 214: *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 215: *> For each right-hand side, this array contains information about
! 216: *> various error bounds and condition numbers corresponding to the
! 217: *> normwise relative error, which is defined as follows:
! 218: *>
! 219: *> Normwise relative error in the ith solution vector:
! 220: *> max_j (abs(XTRUE(j,i) - X(j,i)))
! 221: *> ------------------------------
! 222: *> max_j abs(X(j,i))
! 223: *>
! 224: *> The array is indexed by the type of error information as described
! 225: *> below. There currently are up to three pieces of information
! 226: *> returned.
! 227: *>
! 228: *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 229: *> right-hand side.
! 230: *>
! 231: *> The second index in ERR_BNDS_NORM(:,err) contains the following
! 232: *> three fields:
! 233: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 234: *> reciprocal condition number is less than the threshold
! 235: *> sqrt(n) * dlamch('Epsilon').
! 236: *>
! 237: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 238: *> almost certainly within a factor of 10 of the true error
! 239: *> so long as the next entry is greater than the threshold
! 240: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
! 241: *> be trusted if the previous boolean is true.
! 242: *>
! 243: *> err = 3 Reciprocal condition number: Estimated normwise
! 244: *> reciprocal condition number. Compared with the threshold
! 245: *> sqrt(n) * dlamch('Epsilon') to determine if the error
! 246: *> estimate is "guaranteed". These reciprocal condition
! 247: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 248: *> appropriately scaled matrix Z.
! 249: *> Let Z = S*A, where S scales each row by a power of the
! 250: *> radix so all absolute row sums of Z are approximately 1.
! 251: *>
! 252: *> See Lapack Working Note 165 for further details and extra
! 253: *> cautions.
! 254: *> \endverbatim
! 255: *>
! 256: *> \param[out] ERR_BNDS_COMP
! 257: *> \verbatim
! 258: *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 259: *> For each right-hand side, this array contains information about
! 260: *> various error bounds and condition numbers corresponding to the
! 261: *> componentwise relative error, which is defined as follows:
! 262: *>
! 263: *> Componentwise relative error in the ith solution vector:
! 264: *> abs(XTRUE(j,i) - X(j,i))
! 265: *> max_j ----------------------
! 266: *> abs(X(j,i))
! 267: *>
! 268: *> The array is indexed by the right-hand side i (on which the
! 269: *> componentwise relative error depends), and the type of error
! 270: *> information as described below. There currently are up to three
! 271: *> pieces of information returned for each right-hand side. If
! 272: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 273: *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 274: *> the first (:,N_ERR_BNDS) entries are returned.
! 275: *>
! 276: *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 277: *> right-hand side.
! 278: *>
! 279: *> The second index in ERR_BNDS_COMP(:,err) contains the following
! 280: *> three fields:
! 281: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 282: *> reciprocal condition number is less than the threshold
! 283: *> sqrt(n) * dlamch('Epsilon').
! 284: *>
! 285: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 286: *> almost certainly within a factor of 10 of the true error
! 287: *> so long as the next entry is greater than the threshold
! 288: *> sqrt(n) * dlamch('Epsilon'). This error bound should only
! 289: *> be trusted if the previous boolean is true.
! 290: *>
! 291: *> err = 3 Reciprocal condition number: Estimated componentwise
! 292: *> reciprocal condition number. Compared with the threshold
! 293: *> sqrt(n) * dlamch('Epsilon') to determine if the error
! 294: *> estimate is "guaranteed". These reciprocal condition
! 295: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 296: *> appropriately scaled matrix Z.
! 297: *> Let Z = S*(A*diag(x)), where x is the solution for the
! 298: *> current right-hand side and S scales each row of
! 299: *> A*diag(x) by a power of the radix so all absolute row
! 300: *> sums of Z are approximately 1.
! 301: *>
! 302: *> See Lapack Working Note 165 for further details and extra
! 303: *> cautions.
! 304: *> \endverbatim
! 305: *>
! 306: *> \param[in] NPARAMS
! 307: *> \verbatim
! 308: *> NPARAMS is INTEGER
! 309: *> Specifies the number of parameters set in PARAMS. If .LE. 0, the
! 310: *> PARAMS array is never referenced and default values are used.
! 311: *> \endverbatim
! 312: *>
! 313: *> \param[in,out] PARAMS
! 314: *> \verbatim
! 315: *> PARAMS is / output) DOUBLE PRECISION array, dimension NPARAMS
! 316: *> Specifies algorithm parameters. If an entry is .LT. 0.0, then
! 317: *> that entry will be filled with default value used for that
! 318: *> parameter. Only positions up to NPARAMS are accessed; defaults
! 319: *> are used for higher-numbered parameters.
! 320: *>
! 321: *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
! 322: *> refinement or not.
! 323: *> Default: 1.0D+0
! 324: *> = 0.0 : No refinement is performed, and no error bounds are
! 325: *> computed.
! 326: *> = 1.0 : Use the double-precision refinement algorithm,
! 327: *> possibly with doubled-single computations if the
! 328: *> compilation environment does not support DOUBLE
! 329: *> PRECISION.
! 330: *> (other values are reserved for future use)
! 331: *>
! 332: *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
! 333: *> computations allowed for refinement.
! 334: *> Default: 10
! 335: *> Aggressive: Set to 100 to permit convergence using approximate
! 336: *> factorizations or factorizations other than LU. If
! 337: *> the factorization uses a technique other than
! 338: *> Gaussian elimination, the guarantees in
! 339: *> err_bnds_norm and err_bnds_comp may no longer be
! 340: *> trustworthy.
! 341: *>
! 342: *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
! 343: *> will attempt to find a solution with small componentwise
! 344: *> relative error in the double-precision algorithm. Positive
! 345: *> is true, 0.0 is false.
! 346: *> Default: 1.0 (attempt componentwise convergence)
! 347: *> \endverbatim
! 348: *>
! 349: *> \param[out] WORK
! 350: *> \verbatim
! 351: *> WORK is COMPLEX*16 array, dimension (2*N)
! 352: *> \endverbatim
! 353: *>
! 354: *> \param[out] RWORK
! 355: *> \verbatim
! 356: *> RWORK is DOUBLE PRECISION array, dimension (2*N)
! 357: *> \endverbatim
! 358: *>
! 359: *> \param[out] INFO
! 360: *> \verbatim
! 361: *> INFO is INTEGER
! 362: *> = 0: Successful exit. The solution to every right-hand side is
! 363: *> guaranteed.
! 364: *> < 0: If INFO = -i, the i-th argument had an illegal value
! 365: *> > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
! 366: *> has been completed, but the factor U is exactly singular, so
! 367: *> the solution and error bounds could not be computed. RCOND = 0
! 368: *> is returned.
! 369: *> = N+J: The solution corresponding to the Jth right-hand side is
! 370: *> not guaranteed. The solutions corresponding to other right-
! 371: *> hand sides K with K > J may not be guaranteed as well, but
! 372: *> only the first such right-hand side is reported. If a small
! 373: *> componentwise error is not requested (PARAMS(3) = 0.0) then
! 374: *> the Jth right-hand side is the first with a normwise error
! 375: *> bound that is not guaranteed (the smallest J such
! 376: *> that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
! 377: *> the Jth right-hand side is the first with either a normwise or
! 378: *> componentwise error bound that is not guaranteed (the smallest
! 379: *> J such that either ERR_BNDS_NORM(J,1) = 0.0 or
! 380: *> ERR_BNDS_COMP(J,1) = 0.0). See the definition of
! 381: *> ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
! 382: *> about all of the right-hand sides check ERR_BNDS_NORM or
! 383: *> ERR_BNDS_COMP.
! 384: *> \endverbatim
! 385: *
! 386: * Authors:
! 387: * ========
! 388: *
! 389: *> \author Univ. of Tennessee
! 390: *> \author Univ. of California Berkeley
! 391: *> \author Univ. of Colorado Denver
! 392: *> \author NAG Ltd.
! 393: *
! 394: *> \date November 2011
! 395: *
! 396: *> \ingroup complex16HEcomputational
! 397: *
! 398: * =====================================================================
1.1 bertrand 399: SUBROUTINE ZHERFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV,
400: $ S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
401: $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
402: $ WORK, RWORK, INFO )
403: *
1.5 ! bertrand 404: * -- LAPACK computational routine (version 3.4.0) --
! 405: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 406: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 407: * November 2011
1.1 bertrand 408: *
409: * .. Scalar Arguments ..
410: CHARACTER UPLO, EQUED
411: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
412: $ N_ERR_BNDS
413: DOUBLE PRECISION RCOND
414: * ..
415: * .. Array Arguments ..
416: INTEGER IPIV( * )
417: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
418: $ X( LDX, * ), WORK( * )
419: DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
420: $ ERR_BNDS_NORM( NRHS, * ),
421: $ ERR_BNDS_COMP( NRHS, * )
422: *
1.5 ! bertrand 423: * ==================================================================
1.1 bertrand 424: *
425: * .. Parameters ..
426: DOUBLE PRECISION ZERO, ONE
427: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
428: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
429: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
430: DOUBLE PRECISION DZTHRESH_DEFAULT
431: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
432: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
433: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
434: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
435: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
436: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
437: $ LA_LINRX_CWISE_I
438: PARAMETER ( LA_LINRX_ITREF_I = 1,
439: $ LA_LINRX_ITHRESH_I = 2 )
440: PARAMETER ( LA_LINRX_CWISE_I = 3 )
441: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
442: $ LA_LINRX_RCOND_I
443: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
444: PARAMETER ( LA_LINRX_RCOND_I = 3 )
445: * ..
446: * .. Local Scalars ..
447: CHARACTER(1) NORM
448: LOGICAL RCEQU
449: INTEGER J, PREC_TYPE, REF_TYPE
450: INTEGER N_NORMS
451: DOUBLE PRECISION ANORM, RCOND_TMP
452: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
453: LOGICAL IGNORE_CWISE
454: INTEGER ITHRESH
455: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
456: * ..
457: * .. External Subroutines ..
458: EXTERNAL XERBLA, ZHECON, ZLA_HERFSX_EXTENDED
459: * ..
460: * .. Intrinsic Functions ..
461: INTRINSIC MAX, SQRT, TRANSFER
462: * ..
463: * .. External Functions ..
464: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
465: EXTERNAL DLAMCH, ZLANHE, ZLA_HERCOND_X, ZLA_HERCOND_C
466: DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_HERCOND_X, ZLA_HERCOND_C
467: LOGICAL LSAME
468: INTEGER BLAS_FPINFO_X
469: INTEGER ILATRANS, ILAPREC
470: * ..
471: * .. Executable Statements ..
472: *
473: * Check the input parameters.
474: *
475: INFO = 0
476: REF_TYPE = INT( ITREF_DEFAULT )
477: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
478: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
479: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
480: ELSE
481: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
482: END IF
483: END IF
484: *
485: * Set default parameters.
486: *
487: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
488: ITHRESH = INT( ITHRESH_DEFAULT )
489: RTHRESH = RTHRESH_DEFAULT
490: UNSTABLE_THRESH = DZTHRESH_DEFAULT
491: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
492: *
493: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
494: IF ( PARAMS( LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
495: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
496: ELSE
497: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
498: END IF
499: END IF
500: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
501: IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
502: IF ( IGNORE_CWISE ) THEN
503: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
504: ELSE
505: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
506: END IF
507: ELSE
508: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
509: END IF
510: END IF
511: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
512: N_NORMS = 0
513: ELSE IF ( IGNORE_CWISE ) THEN
514: N_NORMS = 1
515: ELSE
516: N_NORMS = 2
517: END IF
518: *
519: RCEQU = LSAME( EQUED, 'Y' )
520: *
521: * Test input parameters.
522: *
523: IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
524: INFO = -1
525: ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
526: INFO = -2
527: ELSE IF( N.LT.0 ) THEN
528: INFO = -3
529: ELSE IF( NRHS.LT.0 ) THEN
530: INFO = -4
531: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
532: INFO = -6
533: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
534: INFO = -8
535: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
536: INFO = -11
537: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
538: INFO = -13
539: END IF
540: IF( INFO.NE.0 ) THEN
541: CALL XERBLA( 'ZHERFSX', -INFO )
542: RETURN
543: END IF
544: *
545: * Quick return if possible.
546: *
547: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
548: RCOND = 1.0D+0
549: DO J = 1, NRHS
550: BERR( J ) = 0.0D+0
551: IF ( N_ERR_BNDS .GE. 1 ) THEN
552: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
553: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
554: END IF
555: IF ( N_ERR_BNDS .GE. 2 ) THEN
556: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
557: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
558: END IF
559: IF ( N_ERR_BNDS .GE. 3 ) THEN
560: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
561: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
562: END IF
563: END DO
564: RETURN
565: END IF
566: *
567: * Default to failure.
568: *
569: RCOND = 0.0D+0
570: DO J = 1, NRHS
571: BERR( J ) = 1.0D+0
572: IF ( N_ERR_BNDS .GE. 1 ) THEN
573: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
574: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
575: END IF
576: IF ( N_ERR_BNDS .GE. 2 ) THEN
577: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
578: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
579: END IF
580: IF ( N_ERR_BNDS .GE. 3 ) THEN
581: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
582: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
583: END IF
584: END DO
585: *
586: * Compute the norm of A and the reciprocal of the condition
587: * number of A.
588: *
589: NORM = 'I'
590: ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK )
591: CALL ZHECON( UPLO, N, AF, LDAF, IPIV, ANORM, RCOND, WORK,
592: $ INFO )
593: *
594: * Perform refinement on each right-hand side
595: *
596: IF ( REF_TYPE .NE. 0 ) THEN
597:
598: PREC_TYPE = ILAPREC( 'E' )
599:
600: CALL ZLA_HERFSX_EXTENDED( PREC_TYPE, UPLO, N,
601: $ NRHS, A, LDA, AF, LDAF, IPIV, RCEQU, S, B,
602: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
603: $ WORK, RWORK, WORK(N+1),
604: $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND,
605: $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
606: $ INFO )
607: END IF
608:
609: ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
610: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
611: *
612: * Compute scaled normwise condition number cond(A*C).
613: *
614: IF ( RCEQU ) THEN
615: RCOND_TMP = ZLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV,
616: $ S, .TRUE., INFO, WORK, RWORK )
617: ELSE
618: RCOND_TMP = ZLA_HERCOND_C( UPLO, N, A, LDA, AF, LDAF, IPIV,
619: $ S, .FALSE., INFO, WORK, RWORK )
620: END IF
621: DO J = 1, NRHS
622: *
623: * Cap the error at 1.0.
624: *
625: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
626: $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
627: $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
628: *
629: * Threshold the error (see LAWN).
630: *
631: IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN
632: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
633: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
634: IF ( INFO .LE. N ) INFO = N + J
635: ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
636: $ THEN
637: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
638: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
639: END IF
640: *
641: * Save the condition number.
642: *
643: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
644: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
645: END IF
646: END DO
647: END IF
648:
649: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2 ) THEN
650: *
651: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
652: * each right-hand side using the current solution as an estimate of
653: * the true solution. If the componentwise error estimate is too
654: * large, then the solution is a lousy estimate of truth and the
655: * estimated RCOND may be too optimistic. To avoid misleading users,
656: * the inverse condition number is set to 0.0 when the estimated
657: * cwise error is at least CWISE_WRONG.
658: *
659: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
660: DO J = 1, NRHS
661: IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
662: $ THEN
663: RCOND_TMP = ZLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF,
664: $ IPIV, X( 1, J ), INFO, WORK, RWORK )
665: ELSE
666: RCOND_TMP = 0.0D+0
667: END IF
668: *
669: * Cap the error at 1.0.
670: *
671: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
672: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
673: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
674: *
675: * Threshold the error (see LAWN).
676: *
677: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
678: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
679: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
680: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
681: $ .AND. INFO.LT.N + J ) INFO = N + J
682: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
683: $ .LT. ERR_LBND ) THEN
684: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
685: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
686: END IF
687: *
688: * Save the condition number.
689: *
690: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
691: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
692: END IF
693:
694: END DO
695: END IF
696: *
697: RETURN
698: *
699: * End of ZHERFSX
700: *
701: END
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