Annotation of rpl/lapack/lapack/dla_porfsx_extended.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b DLA_PORFSX_EXTENDED
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLA_PORFSX_EXTENDED + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_porfsx_extended.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_porfsx_extended.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_porfsx_extended.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
! 22: * AF, LDAF, COLEQU, C, B, LDB, Y,
! 23: * LDY, BERR_OUT, N_NORMS,
! 24: * ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
! 25: * AYB, DY, Y_TAIL, RCOND, ITHRESH,
! 26: * RTHRESH, DZ_UB, IGNORE_CWISE,
! 27: * INFO )
! 28: *
! 29: * .. Scalar Arguments ..
! 30: * INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
! 31: * $ N_NORMS, ITHRESH
! 32: * CHARACTER UPLO
! 33: * LOGICAL COLEQU, IGNORE_CWISE
! 34: * DOUBLE PRECISION RTHRESH, DZ_UB
! 35: * ..
! 36: * .. Array Arguments ..
! 37: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 38: * $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
! 39: * DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ),
! 40: * $ ERR_BNDS_NORM( NRHS, * ),
! 41: * $ ERR_BNDS_COMP( NRHS, * )
! 42: * ..
! 43: *
! 44: *
! 45: *> \par Purpose:
! 46: * =============
! 47: *>
! 48: *> \verbatim
! 49: *>
! 50: *> DLA_PORFSX_EXTENDED improves the computed solution to a system of
! 51: *> linear equations by performing extra-precise iterative refinement
! 52: *> and provides error bounds and backward error estimates for the solution.
! 53: *> This subroutine is called by DPORFSX to perform iterative refinement.
! 54: *> In addition to normwise error bound, the code provides maximum
! 55: *> componentwise error bound if possible. See comments for ERR_BNDS_NORM
! 56: *> and ERR_BNDS_COMP for details of the error bounds. Note that this
! 57: *> subroutine is only resonsible for setting the second fields of
! 58: *> ERR_BNDS_NORM and ERR_BNDS_COMP.
! 59: *> \endverbatim
! 60: *
! 61: * Arguments:
! 62: * ==========
! 63: *
! 64: *> \param[in] PREC_TYPE
! 65: *> \verbatim
! 66: *> PREC_TYPE is INTEGER
! 67: *> Specifies the intermediate precision to be used in refinement.
! 68: *> The value is defined by ILAPREC(P) where P is a CHARACTER and
! 69: *> P = 'S': Single
! 70: *> = 'D': Double
! 71: *> = 'I': Indigenous
! 72: *> = 'X', 'E': Extra
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] UPLO
! 76: *> \verbatim
! 77: *> UPLO is CHARACTER*1
! 78: *> = 'U': Upper triangle of A is stored;
! 79: *> = 'L': Lower triangle of A is stored.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] N
! 83: *> \verbatim
! 84: *> N is INTEGER
! 85: *> The number of linear equations, i.e., the order of the
! 86: *> matrix A. N >= 0.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] NRHS
! 90: *> \verbatim
! 91: *> NRHS is INTEGER
! 92: *> The number of right-hand-sides, i.e., the number of columns of the
! 93: *> matrix B.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] A
! 97: *> \verbatim
! 98: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 99: *> On entry, the N-by-N matrix A.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] LDA
! 103: *> \verbatim
! 104: *> LDA is INTEGER
! 105: *> The leading dimension of the array A. LDA >= max(1,N).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] AF
! 109: *> \verbatim
! 110: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 111: *> The triangular factor U or L from the Cholesky factorization
! 112: *> A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[in] LDAF
! 116: *> \verbatim
! 117: *> LDAF is INTEGER
! 118: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] COLEQU
! 122: *> \verbatim
! 123: *> COLEQU is LOGICAL
! 124: *> If .TRUE. then column equilibration was done to A before calling
! 125: *> this routine. This is needed to compute the solution and error
! 126: *> bounds correctly.
! 127: *> \endverbatim
! 128: *>
! 129: *> \param[in] C
! 130: *> \verbatim
! 131: *> C is DOUBLE PRECISION array, dimension (N)
! 132: *> The column scale factors for A. If COLEQU = .FALSE., C
! 133: *> is not accessed. If C is input, each element of C should be a power
! 134: *> of the radix to ensure a reliable solution and error estimates.
! 135: *> Scaling by powers of the radix does not cause rounding errors unless
! 136: *> the result underflows or overflows. Rounding errors during scaling
! 137: *> lead to refining with a matrix that is not equivalent to the
! 138: *> input matrix, producing error estimates that may not be
! 139: *> reliable.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] B
! 143: *> \verbatim
! 144: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
! 145: *> The right-hand-side matrix B.
! 146: *> \endverbatim
! 147: *>
! 148: *> \param[in] LDB
! 149: *> \verbatim
! 150: *> LDB is INTEGER
! 151: *> The leading dimension of the array B. LDB >= max(1,N).
! 152: *> \endverbatim
! 153: *>
! 154: *> \param[in,out] Y
! 155: *> \verbatim
! 156: *> Y is DOUBLE PRECISION array, dimension
! 157: *> (LDY,NRHS)
! 158: *> On entry, the solution matrix X, as computed by DPOTRS.
! 159: *> On exit, the improved solution matrix Y.
! 160: *> \endverbatim
! 161: *>
! 162: *> \param[in] LDY
! 163: *> \verbatim
! 164: *> LDY is INTEGER
! 165: *> The leading dimension of the array Y. LDY >= max(1,N).
! 166: *> \endverbatim
! 167: *>
! 168: *> \param[out] BERR_OUT
! 169: *> \verbatim
! 170: *> BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
! 171: *> On exit, BERR_OUT(j) contains the componentwise relative backward
! 172: *> error for right-hand-side j from the formula
! 173: *> max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 174: *> where abs(Z) is the componentwise absolute value of the matrix
! 175: *> or vector Z. This is computed by DLA_LIN_BERR.
! 176: *> \endverbatim
! 177: *>
! 178: *> \param[in] N_NORMS
! 179: *> \verbatim
! 180: *> N_NORMS is INTEGER
! 181: *> Determines which error bounds to return (see ERR_BNDS_NORM
! 182: *> and ERR_BNDS_COMP).
! 183: *> If N_NORMS >= 1 return normwise error bounds.
! 184: *> If N_NORMS >= 2 return componentwise error bounds.
! 185: *> \endverbatim
! 186: *>
! 187: *> \param[in,out] ERR_BNDS_NORM
! 188: *> \verbatim
! 189: *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension
! 190: *> (NRHS, N_ERR_BNDS)
! 191: *> For each right-hand side, this array contains information about
! 192: *> various error bounds and condition numbers corresponding to the
! 193: *> normwise relative error, which is defined as follows:
! 194: *>
! 195: *> Normwise relative error in the ith solution vector:
! 196: *> max_j (abs(XTRUE(j,i) - X(j,i)))
! 197: *> ------------------------------
! 198: *> max_j abs(X(j,i))
! 199: *>
! 200: *> The array is indexed by the type of error information as described
! 201: *> below. There currently are up to three pieces of information
! 202: *> returned.
! 203: *>
! 204: *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 205: *> right-hand side.
! 206: *>
! 207: *> The second index in ERR_BNDS_NORM(:,err) contains the following
! 208: *> three fields:
! 209: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 210: *> reciprocal condition number is less than the threshold
! 211: *> sqrt(n) * slamch('Epsilon').
! 212: *>
! 213: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 214: *> almost certainly within a factor of 10 of the true error
! 215: *> so long as the next entry is greater than the threshold
! 216: *> sqrt(n) * slamch('Epsilon'). This error bound should only
! 217: *> be trusted if the previous boolean is true.
! 218: *>
! 219: *> err = 3 Reciprocal condition number: Estimated normwise
! 220: *> reciprocal condition number. Compared with the threshold
! 221: *> sqrt(n) * slamch('Epsilon') to determine if the error
! 222: *> estimate is "guaranteed". These reciprocal condition
! 223: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 224: *> appropriately scaled matrix Z.
! 225: *> Let Z = S*A, where S scales each row by a power of the
! 226: *> radix so all absolute row sums of Z are approximately 1.
! 227: *>
! 228: *> This subroutine is only responsible for setting the second field
! 229: *> above.
! 230: *> See Lapack Working Note 165 for further details and extra
! 231: *> cautions.
! 232: *> \endverbatim
! 233: *>
! 234: *> \param[in,out] ERR_BNDS_COMP
! 235: *> \verbatim
! 236: *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension
! 237: *> (NRHS, N_ERR_BNDS)
! 238: *> For each right-hand side, this array contains information about
! 239: *> various error bounds and condition numbers corresponding to the
! 240: *> componentwise relative error, which is defined as follows:
! 241: *>
! 242: *> Componentwise relative error in the ith solution vector:
! 243: *> abs(XTRUE(j,i) - X(j,i))
! 244: *> max_j ----------------------
! 245: *> abs(X(j,i))
! 246: *>
! 247: *> The array is indexed by the right-hand side i (on which the
! 248: *> componentwise relative error depends), and the type of error
! 249: *> information as described below. There currently are up to three
! 250: *> pieces of information returned for each right-hand side. If
! 251: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 252: *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 253: *> the first (:,N_ERR_BNDS) entries are returned.
! 254: *>
! 255: *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 256: *> right-hand side.
! 257: *>
! 258: *> The second index in ERR_BNDS_COMP(:,err) contains the following
! 259: *> three fields:
! 260: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 261: *> reciprocal condition number is less than the threshold
! 262: *> sqrt(n) * slamch('Epsilon').
! 263: *>
! 264: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 265: *> almost certainly within a factor of 10 of the true error
! 266: *> so long as the next entry is greater than the threshold
! 267: *> sqrt(n) * slamch('Epsilon'). This error bound should only
! 268: *> be trusted if the previous boolean is true.
! 269: *>
! 270: *> err = 3 Reciprocal condition number: Estimated componentwise
! 271: *> reciprocal condition number. Compared with the threshold
! 272: *> sqrt(n) * slamch('Epsilon') to determine if the error
! 273: *> estimate is "guaranteed". These reciprocal condition
! 274: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 275: *> appropriately scaled matrix Z.
! 276: *> Let Z = S*(A*diag(x)), where x is the solution for the
! 277: *> current right-hand side and S scales each row of
! 278: *> A*diag(x) by a power of the radix so all absolute row
! 279: *> sums of Z are approximately 1.
! 280: *>
! 281: *> This subroutine is only responsible for setting the second field
! 282: *> above.
! 283: *> See Lapack Working Note 165 for further details and extra
! 284: *> cautions.
! 285: *> \endverbatim
! 286: *>
! 287: *> \param[in] RES
! 288: *> \verbatim
! 289: *> RES is DOUBLE PRECISION array, dimension (N)
! 290: *> Workspace to hold the intermediate residual.
! 291: *> \endverbatim
! 292: *>
! 293: *> \param[in] AYB
! 294: *> \verbatim
! 295: *> AYB is DOUBLE PRECISION array, dimension (N)
! 296: *> Workspace. This can be the same workspace passed for Y_TAIL.
! 297: *> \endverbatim
! 298: *>
! 299: *> \param[in] DY
! 300: *> \verbatim
! 301: *> DY is DOUBLE PRECISION array, dimension (N)
! 302: *> Workspace to hold the intermediate solution.
! 303: *> \endverbatim
! 304: *>
! 305: *> \param[in] Y_TAIL
! 306: *> \verbatim
! 307: *> Y_TAIL is DOUBLE PRECISION array, dimension (N)
! 308: *> Workspace to hold the trailing bits of the intermediate solution.
! 309: *> \endverbatim
! 310: *>
! 311: *> \param[in] RCOND
! 312: *> \verbatim
! 313: *> RCOND is DOUBLE PRECISION
! 314: *> Reciprocal scaled condition number. This is an estimate of the
! 315: *> reciprocal Skeel condition number of the matrix A after
! 316: *> equilibration (if done). If this is less than the machine
! 317: *> precision (in particular, if it is zero), the matrix is singular
! 318: *> to working precision. Note that the error may still be small even
! 319: *> if this number is very small and the matrix appears ill-
! 320: *> conditioned.
! 321: *> \endverbatim
! 322: *>
! 323: *> \param[in] ITHRESH
! 324: *> \verbatim
! 325: *> ITHRESH is INTEGER
! 326: *> The maximum number of residual computations allowed for
! 327: *> refinement. The default is 10. For 'aggressive' set to 100 to
! 328: *> permit convergence using approximate factorizations or
! 329: *> factorizations other than LU. If the factorization uses a
! 330: *> technique other than Gaussian elimination, the guarantees in
! 331: *> ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
! 332: *> \endverbatim
! 333: *>
! 334: *> \param[in] RTHRESH
! 335: *> \verbatim
! 336: *> RTHRESH is DOUBLE PRECISION
! 337: *> Determines when to stop refinement if the error estimate stops
! 338: *> decreasing. Refinement will stop when the next solution no longer
! 339: *> satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
! 340: *> the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
! 341: *> default value is 0.5. For 'aggressive' set to 0.9 to permit
! 342: *> convergence on extremely ill-conditioned matrices. See LAWN 165
! 343: *> for more details.
! 344: *> \endverbatim
! 345: *>
! 346: *> \param[in] DZ_UB
! 347: *> \verbatim
! 348: *> DZ_UB is DOUBLE PRECISION
! 349: *> Determines when to start considering componentwise convergence.
! 350: *> Componentwise convergence is only considered after each component
! 351: *> of the solution Y is stable, which we definte as the relative
! 352: *> change in each component being less than DZ_UB. The default value
! 353: *> is 0.25, requiring the first bit to be stable. See LAWN 165 for
! 354: *> more details.
! 355: *> \endverbatim
! 356: *>
! 357: *> \param[in] IGNORE_CWISE
! 358: *> \verbatim
! 359: *> IGNORE_CWISE is LOGICAL
! 360: *> If .TRUE. then ignore componentwise convergence. Default value
! 361: *> is .FALSE..
! 362: *> \endverbatim
! 363: *>
! 364: *> \param[out] INFO
! 365: *> \verbatim
! 366: *> INFO is INTEGER
! 367: *> = 0: Successful exit.
! 368: *> < 0: if INFO = -i, the ith argument to DPOTRS had an illegal
! 369: *> value
! 370: *> \endverbatim
! 371: *
! 372: * Authors:
! 373: * ========
! 374: *
! 375: *> \author Univ. of Tennessee
! 376: *> \author Univ. of California Berkeley
! 377: *> \author Univ. of Colorado Denver
! 378: *> \author NAG Ltd.
! 379: *
! 380: *> \date November 2011
! 381: *
! 382: *> \ingroup doublePOcomputational
! 383: *
! 384: * =====================================================================
1.1 bertrand 385: SUBROUTINE DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
386: $ AF, LDAF, COLEQU, C, B, LDB, Y,
387: $ LDY, BERR_OUT, N_NORMS,
388: $ ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
389: $ AYB, DY, Y_TAIL, RCOND, ITHRESH,
390: $ RTHRESH, DZ_UB, IGNORE_CWISE,
391: $ INFO )
392: *
1.5 ! bertrand 393: * -- LAPACK computational routine (version 3.4.0) --
! 394: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 395: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 396: * November 2011
1.1 bertrand 397: *
398: * .. Scalar Arguments ..
399: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
400: $ N_NORMS, ITHRESH
401: CHARACTER UPLO
402: LOGICAL COLEQU, IGNORE_CWISE
403: DOUBLE PRECISION RTHRESH, DZ_UB
404: * ..
405: * .. Array Arguments ..
406: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
407: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
408: DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ),
409: $ ERR_BNDS_NORM( NRHS, * ),
410: $ ERR_BNDS_COMP( NRHS, * )
411: * ..
412: *
413: * =====================================================================
414: *
415: * .. Local Scalars ..
416: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE
417: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
418: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
419: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
420: $ EPS, HUGEVAL, INCR_THRESH
421: LOGICAL INCR_PREC
422: * ..
423: * .. Parameters ..
424: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
425: $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
426: $ EXTRA_RESIDUAL, EXTRA_Y
427: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
428: $ CONV_STATE = 2, NOPROG_STATE = 3 )
429: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
430: $ EXTRA_Y = 2 )
431: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
432: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
433: INTEGER CMP_ERR_I, PIV_GROWTH_I
434: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
435: $ BERR_I = 3 )
436: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
437: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
438: $ PIV_GROWTH_I = 9 )
439: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
440: $ LA_LINRX_CWISE_I
441: PARAMETER ( LA_LINRX_ITREF_I = 1,
442: $ LA_LINRX_ITHRESH_I = 2 )
443: PARAMETER ( LA_LINRX_CWISE_I = 3 )
444: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
445: $ LA_LINRX_RCOND_I
446: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
447: PARAMETER ( LA_LINRX_RCOND_I = 3 )
448: * ..
449: * .. External Functions ..
450: LOGICAL LSAME
451: EXTERNAL ILAUPLO
452: INTEGER ILAUPLO
453: * ..
454: * .. External Subroutines ..
455: EXTERNAL DAXPY, DCOPY, DPOTRS, DSYMV, BLAS_DSYMV_X,
456: $ BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
457: $ DLA_LIN_BERR
458: DOUBLE PRECISION DLAMCH
459: * ..
460: * .. Intrinsic Functions ..
461: INTRINSIC ABS, MAX, MIN
462: * ..
463: * .. Executable Statements ..
464: *
465: IF (INFO.NE.0) RETURN
466: EPS = DLAMCH( 'Epsilon' )
467: HUGEVAL = DLAMCH( 'Overflow' )
468: * Force HUGEVAL to Inf
469: HUGEVAL = HUGEVAL * HUGEVAL
470: * Using HUGEVAL may lead to spurious underflows.
471: INCR_THRESH = DBLE( N ) * EPS
472:
473: IF ( LSAME ( UPLO, 'L' ) ) THEN
474: UPLO2 = ILAUPLO( 'L' )
475: ELSE
476: UPLO2 = ILAUPLO( 'U' )
477: ENDIF
478:
479: DO J = 1, NRHS
480: Y_PREC_STATE = EXTRA_RESIDUAL
481: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
482: DO I = 1, N
483: Y_TAIL( I ) = 0.0D+0
484: END DO
485: END IF
486:
487: DXRAT = 0.0D+0
488: DXRATMAX = 0.0D+0
489: DZRAT = 0.0D+0
490: DZRATMAX = 0.0D+0
491: FINAL_DX_X = HUGEVAL
492: FINAL_DZ_Z = HUGEVAL
493: PREVNORMDX = HUGEVAL
494: PREV_DZ_Z = HUGEVAL
495: DZ_Z = HUGEVAL
496: DX_X = HUGEVAL
497:
498: X_STATE = WORKING_STATE
499: Z_STATE = UNSTABLE_STATE
500: INCR_PREC = .FALSE.
501:
502: DO CNT = 1, ITHRESH
503: *
504: * Compute residual RES = B_s - op(A_s) * Y,
505: * op(A) = A, A**T, or A**H depending on TRANS (and type).
506: *
507: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
508: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
509: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
510: $ 1.0D+0, RES, 1 )
511: ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
512: CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
513: $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
514: ELSE
515: CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
516: $ Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
517: END IF
518:
519: ! XXX: RES is no longer needed.
520: CALL DCOPY( N, RES, 1, DY, 1 )
521: CALL DPOTRS( UPLO, N, 1, AF, LDAF, DY, N, INFO )
522: *
523: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
524: *
525: NORMX = 0.0D+0
526: NORMY = 0.0D+0
527: NORMDX = 0.0D+0
528: DZ_Z = 0.0D+0
529: YMIN = HUGEVAL
530:
531: DO I = 1, N
532: YK = ABS( Y( I, J ) )
533: DYK = ABS( DY( I ) )
534:
535: IF ( YK .NE. 0.0D+0 ) THEN
536: DZ_Z = MAX( DZ_Z, DYK / YK )
537: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
538: DZ_Z = HUGEVAL
539: END IF
540:
541: YMIN = MIN( YMIN, YK )
542:
543: NORMY = MAX( NORMY, YK )
544:
545: IF ( COLEQU ) THEN
546: NORMX = MAX( NORMX, YK * C( I ) )
547: NORMDX = MAX( NORMDX, DYK * C( I ) )
548: ELSE
549: NORMX = NORMY
550: NORMDX = MAX( NORMDX, DYK )
551: END IF
552: END DO
553:
554: IF ( NORMX .NE. 0.0D+0 ) THEN
555: DX_X = NORMDX / NORMX
556: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
557: DX_X = 0.0D+0
558: ELSE
559: DX_X = HUGEVAL
560: END IF
561:
562: DXRAT = NORMDX / PREVNORMDX
563: DZRAT = DZ_Z / PREV_DZ_Z
564: *
565: * Check termination criteria.
566: *
567: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
568: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
569: $ INCR_PREC = .TRUE.
570:
571: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
572: $ X_STATE = WORKING_STATE
573: IF ( X_STATE .EQ. WORKING_STATE ) THEN
574: IF ( DX_X .LE. EPS ) THEN
575: X_STATE = CONV_STATE
576: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
577: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
578: INCR_PREC = .TRUE.
579: ELSE
580: X_STATE = NOPROG_STATE
581: END IF
582: ELSE
583: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
584: END IF
585: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
586: END IF
587:
588: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
589: $ Z_STATE = WORKING_STATE
590: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
591: $ Z_STATE = WORKING_STATE
592: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
593: IF ( DZ_Z .LE. EPS ) THEN
594: Z_STATE = CONV_STATE
595: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
596: Z_STATE = UNSTABLE_STATE
597: DZRATMAX = 0.0D+0
598: FINAL_DZ_Z = HUGEVAL
599: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
600: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
601: INCR_PREC = .TRUE.
602: ELSE
603: Z_STATE = NOPROG_STATE
604: END IF
605: ELSE
606: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
607: END IF
608: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
609: END IF
610:
611: IF ( X_STATE.NE.WORKING_STATE.AND.
612: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
613: $ GOTO 666
614:
615: IF ( INCR_PREC ) THEN
616: INCR_PREC = .FALSE.
617: Y_PREC_STATE = Y_PREC_STATE + 1
618: DO I = 1, N
619: Y_TAIL( I ) = 0.0D+0
620: END DO
621: END IF
622:
623: PREVNORMDX = NORMDX
624: PREV_DZ_Z = DZ_Z
625: *
626: * Update soluton.
627: *
628: IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
629: CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
630: ELSE
631: CALL DLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
632: END IF
633:
634: END DO
635: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
636: 666 CONTINUE
637: *
638: * Set final_* when cnt hits ithresh.
639: *
640: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
641: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
642: *
643: * Compute error bounds.
644: *
645: IF ( N_NORMS .GE. 1 ) THEN
646: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
647: $ FINAL_DX_X / (1 - DXRATMAX)
648: END IF
649: IF ( N_NORMS .GE. 2 ) THEN
650: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
651: $ FINAL_DZ_Z / (1 - DZRATMAX)
652: END IF
653: *
654: * Compute componentwise relative backward error from formula
655: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
656: * where abs(Z) is the componentwise absolute value of the matrix
657: * or vector Z.
658: *
659: * Compute residual RES = B_s - op(A_s) * Y,
660: * op(A) = A, A**T, or A**H depending on TRANS (and type).
661: *
662: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
663: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
664: $ 1 )
665:
666: DO I = 1, N
667: AYB( I ) = ABS( B( I, J ) )
668: END DO
669: *
670: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
671: *
672: CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
673: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
674:
675: CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
676: *
677: * End of loop for each RHS.
678: *
679: END DO
680: *
681: RETURN
682: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dla_porfsx_extended.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack