Annotation of rpl/lapack/lapack/dla_syrfsx_extended.f, revision 1.5
1.5 ! bertrand 1: *> \brief \b DLA_SYRFSX_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_SYRFSX_EXTENDED + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
! 22: * AF, LDAF, IPIV, COLEQU, C, B, LDB,
! 23: * Y, 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: * INTEGER IPIV( * )
! 38: * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 39: * $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
! 40: * DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
! 41: * $ ERR_BNDS_NORM( NRHS, * ),
! 42: * $ ERR_BNDS_COMP( NRHS, * )
! 43: * ..
! 44: *
! 45: *
! 46: *> \par Purpose:
! 47: * =============
! 48: *>
! 49: *> \verbatim
! 50: *>
! 51: *>
! 52: *> DLA_SYRFSX_EXTENDED improves the computed solution to a system of
! 53: *> linear equations by performing extra-precise iterative refinement
! 54: *> and provides error bounds and backward error estimates for the solution.
! 55: *> This subroutine is called by DSYRFSX to perform iterative refinement.
! 56: *> In addition to normwise error bound, the code provides maximum
! 57: *> componentwise error bound if possible. See comments for ERR_BNDS_NORM
! 58: *> and ERR_BNDS_COMP for details of the error bounds. Note that this
! 59: *> subroutine is only resonsible for setting the second fields of
! 60: *> ERR_BNDS_NORM and ERR_BNDS_COMP.
! 61: *> \endverbatim
! 62: *
! 63: * Arguments:
! 64: * ==========
! 65: *
! 66: *> \param[in] PREC_TYPE
! 67: *> \verbatim
! 68: *> PREC_TYPE is INTEGER
! 69: *> Specifies the intermediate precision to be used in refinement.
! 70: *> The value is defined by ILAPREC(P) where P is a CHARACTER and
! 71: *> P = 'S': Single
! 72: *> = 'D': Double
! 73: *> = 'I': Indigenous
! 74: *> = 'X', 'E': Extra
! 75: *> \endverbatim
! 76: *>
! 77: *> \param[in] UPLO
! 78: *> \verbatim
! 79: *> UPLO is CHARACTER*1
! 80: *> = 'U': Upper triangle of A is stored;
! 81: *> = 'L': Lower triangle of A is stored.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] N
! 85: *> \verbatim
! 86: *> N is INTEGER
! 87: *> The number of linear equations, i.e., the order of the
! 88: *> matrix A. N >= 0.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in] NRHS
! 92: *> \verbatim
! 93: *> NRHS is INTEGER
! 94: *> The number of right-hand-sides, i.e., the number of columns of the
! 95: *> matrix B.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[in] A
! 99: *> \verbatim
! 100: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 101: *> On entry, the N-by-N matrix A.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[in] LDA
! 105: *> \verbatim
! 106: *> LDA is INTEGER
! 107: *> The leading dimension of the array A. LDA >= max(1,N).
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in] AF
! 111: *> \verbatim
! 112: *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
! 113: *> The block diagonal matrix D and the multipliers used to
! 114: *> obtain the factor U or L as computed by DSYTRF.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] LDAF
! 118: *> \verbatim
! 119: *> LDAF is INTEGER
! 120: *> The leading dimension of the array AF. LDAF >= max(1,N).
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[in] IPIV
! 124: *> \verbatim
! 125: *> IPIV is INTEGER array, dimension (N)
! 126: *> Details of the interchanges and the block structure of D
! 127: *> as determined by DSYTRF.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] COLEQU
! 131: *> \verbatim
! 132: *> COLEQU is LOGICAL
! 133: *> If .TRUE. then column equilibration was done to A before calling
! 134: *> this routine. This is needed to compute the solution and error
! 135: *> bounds correctly.
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[in] C
! 139: *> \verbatim
! 140: *> C is DOUBLE PRECISION array, dimension (N)
! 141: *> The column scale factors for A. If COLEQU = .FALSE., C
! 142: *> is not accessed. If C is input, each element of C should be a power
! 143: *> of the radix to ensure a reliable solution and error estimates.
! 144: *> Scaling by powers of the radix does not cause rounding errors unless
! 145: *> the result underflows or overflows. Rounding errors during scaling
! 146: *> lead to refining with a matrix that is not equivalent to the
! 147: *> input matrix, producing error estimates that may not be
! 148: *> 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] Y
! 164: *> \verbatim
! 165: *> Y is DOUBLE PRECISION array, dimension
! 166: *> (LDY,NRHS)
! 167: *> On entry, the solution matrix X, as computed by DSYTRS.
! 168: *> On exit, the improved solution matrix Y.
! 169: *> \endverbatim
! 170: *>
! 171: *> \param[in] LDY
! 172: *> \verbatim
! 173: *> LDY is INTEGER
! 174: *> The leading dimension of the array Y. LDY >= max(1,N).
! 175: *> \endverbatim
! 176: *>
! 177: *> \param[out] BERR_OUT
! 178: *> \verbatim
! 179: *> BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
! 180: *> On exit, BERR_OUT(j) contains the componentwise relative backward
! 181: *> error for right-hand-side j from the formula
! 182: *> max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 183: *> where abs(Z) is the componentwise absolute value of the matrix
! 184: *> or vector Z. This is computed by DLA_LIN_BERR.
! 185: *> \endverbatim
! 186: *>
! 187: *> \param[in] N_NORMS
! 188: *> \verbatim
! 189: *> N_NORMS is INTEGER
! 190: *> Determines which error bounds to return (see ERR_BNDS_NORM
! 191: *> and ERR_BNDS_COMP).
! 192: *> If N_NORMS >= 1 return normwise error bounds.
! 193: *> If N_NORMS >= 2 return componentwise error bounds.
! 194: *> \endverbatim
! 195: *>
! 196: *> \param[in,out] ERR_BNDS_NORM
! 197: *> \verbatim
! 198: *> ERR_BNDS_NORM is DOUBLE PRECISION array, dimension
! 199: *> (NRHS, N_ERR_BNDS)
! 200: *> For each right-hand side, this array contains information about
! 201: *> various error bounds and condition numbers corresponding to the
! 202: *> normwise relative error, which is defined as follows:
! 203: *>
! 204: *> Normwise relative error in the ith solution vector:
! 205: *> max_j (abs(XTRUE(j,i) - X(j,i)))
! 206: *> ------------------------------
! 207: *> max_j abs(X(j,i))
! 208: *>
! 209: *> The array is indexed by the type of error information as described
! 210: *> below. There currently are up to three pieces of information
! 211: *> returned.
! 212: *>
! 213: *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 214: *> right-hand side.
! 215: *>
! 216: *> The second index in ERR_BNDS_NORM(:,err) contains the following
! 217: *> three fields:
! 218: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 219: *> reciprocal condition number is less than the threshold
! 220: *> sqrt(n) * slamch('Epsilon').
! 221: *>
! 222: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 223: *> almost certainly within a factor of 10 of the true error
! 224: *> so long as the next entry is greater than the threshold
! 225: *> sqrt(n) * slamch('Epsilon'). This error bound should only
! 226: *> be trusted if the previous boolean is true.
! 227: *>
! 228: *> err = 3 Reciprocal condition number: Estimated normwise
! 229: *> reciprocal condition number. Compared with the threshold
! 230: *> sqrt(n) * slamch('Epsilon') to determine if the error
! 231: *> estimate is "guaranteed". These reciprocal condition
! 232: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 233: *> appropriately scaled matrix Z.
! 234: *> Let Z = S*A, where S scales each row by a power of the
! 235: *> radix so all absolute row sums of Z are approximately 1.
! 236: *>
! 237: *> This subroutine is only responsible for setting the second field
! 238: *> above.
! 239: *> See Lapack Working Note 165 for further details and extra
! 240: *> cautions.
! 241: *> \endverbatim
! 242: *>
! 243: *> \param[in,out] ERR_BNDS_COMP
! 244: *> \verbatim
! 245: *> ERR_BNDS_COMP is DOUBLE PRECISION array, dimension
! 246: *> (NRHS, N_ERR_BNDS)
! 247: *> For each right-hand side, this array contains information about
! 248: *> various error bounds and condition numbers corresponding to the
! 249: *> componentwise relative error, which is defined as follows:
! 250: *>
! 251: *> Componentwise relative error in the ith solution vector:
! 252: *> abs(XTRUE(j,i) - X(j,i))
! 253: *> max_j ----------------------
! 254: *> abs(X(j,i))
! 255: *>
! 256: *> The array is indexed by the right-hand side i (on which the
! 257: *> componentwise relative error depends), and the type of error
! 258: *> information as described below. There currently are up to three
! 259: *> pieces of information returned for each right-hand side. If
! 260: *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 261: *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 262: *> the first (:,N_ERR_BNDS) entries are returned.
! 263: *>
! 264: *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 265: *> right-hand side.
! 266: *>
! 267: *> The second index in ERR_BNDS_COMP(:,err) contains the following
! 268: *> three fields:
! 269: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 270: *> reciprocal condition number is less than the threshold
! 271: *> sqrt(n) * slamch('Epsilon').
! 272: *>
! 273: *> err = 2 "Guaranteed" error bound: The estimated forward error,
! 274: *> almost certainly within a factor of 10 of the true error
! 275: *> so long as the next entry is greater than the threshold
! 276: *> sqrt(n) * slamch('Epsilon'). This error bound should only
! 277: *> be trusted if the previous boolean is true.
! 278: *>
! 279: *> err = 3 Reciprocal condition number: Estimated componentwise
! 280: *> reciprocal condition number. Compared with the threshold
! 281: *> sqrt(n) * slamch('Epsilon') to determine if the error
! 282: *> estimate is "guaranteed". These reciprocal condition
! 283: *> numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 284: *> appropriately scaled matrix Z.
! 285: *> Let Z = S*(A*diag(x)), where x is the solution for the
! 286: *> current right-hand side and S scales each row of
! 287: *> A*diag(x) by a power of the radix so all absolute row
! 288: *> sums of Z are approximately 1.
! 289: *>
! 290: *> This subroutine is only responsible for setting the second field
! 291: *> above.
! 292: *> See Lapack Working Note 165 for further details and extra
! 293: *> cautions.
! 294: *> \endverbatim
! 295: *>
! 296: *> \param[in] RES
! 297: *> \verbatim
! 298: *> RES is DOUBLE PRECISION array, dimension (N)
! 299: *> Workspace to hold the intermediate residual.
! 300: *> \endverbatim
! 301: *>
! 302: *> \param[in] AYB
! 303: *> \verbatim
! 304: *> AYB is DOUBLE PRECISION array, dimension (N)
! 305: *> Workspace. This can be the same workspace passed for Y_TAIL.
! 306: *> \endverbatim
! 307: *>
! 308: *> \param[in] DY
! 309: *> \verbatim
! 310: *> DY is DOUBLE PRECISION array, dimension (N)
! 311: *> Workspace to hold the intermediate solution.
! 312: *> \endverbatim
! 313: *>
! 314: *> \param[in] Y_TAIL
! 315: *> \verbatim
! 316: *> Y_TAIL is DOUBLE PRECISION array, dimension (N)
! 317: *> Workspace to hold the trailing bits of the intermediate solution.
! 318: *> \endverbatim
! 319: *>
! 320: *> \param[in] RCOND
! 321: *> \verbatim
! 322: *> RCOND is DOUBLE PRECISION
! 323: *> Reciprocal scaled condition number. This is an estimate of the
! 324: *> reciprocal Skeel condition number of the matrix A after
! 325: *> equilibration (if done). If this is less than the machine
! 326: *> precision (in particular, if it is zero), the matrix is singular
! 327: *> to working precision. Note that the error may still be small even
! 328: *> if this number is very small and the matrix appears ill-
! 329: *> conditioned.
! 330: *> \endverbatim
! 331: *>
! 332: *> \param[in] ITHRESH
! 333: *> \verbatim
! 334: *> ITHRESH is INTEGER
! 335: *> The maximum number of residual computations allowed for
! 336: *> refinement. The default is 10. For 'aggressive' set to 100 to
! 337: *> permit convergence using approximate factorizations or
! 338: *> factorizations other than LU. If the factorization uses a
! 339: *> technique other than Gaussian elimination, the guarantees in
! 340: *> ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
! 341: *> \endverbatim
! 342: *>
! 343: *> \param[in] RTHRESH
! 344: *> \verbatim
! 345: *> RTHRESH is DOUBLE PRECISION
! 346: *> Determines when to stop refinement if the error estimate stops
! 347: *> decreasing. Refinement will stop when the next solution no longer
! 348: *> satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
! 349: *> the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
! 350: *> default value is 0.5. For 'aggressive' set to 0.9 to permit
! 351: *> convergence on extremely ill-conditioned matrices. See LAWN 165
! 352: *> for more details.
! 353: *> \endverbatim
! 354: *>
! 355: *> \param[in] DZ_UB
! 356: *> \verbatim
! 357: *> DZ_UB is DOUBLE PRECISION
! 358: *> Determines when to start considering componentwise convergence.
! 359: *> Componentwise convergence is only considered after each component
! 360: *> of the solution Y is stable, which we definte as the relative
! 361: *> change in each component being less than DZ_UB. The default value
! 362: *> is 0.25, requiring the first bit to be stable. See LAWN 165 for
! 363: *> more details.
! 364: *> \endverbatim
! 365: *>
! 366: *> \param[in] IGNORE_CWISE
! 367: *> \verbatim
! 368: *> IGNORE_CWISE is LOGICAL
! 369: *> If .TRUE. then ignore componentwise convergence. Default value
! 370: *> is .FALSE..
! 371: *> \endverbatim
! 372: *>
! 373: *> \param[out] INFO
! 374: *> \verbatim
! 375: *> INFO is INTEGER
! 376: *> = 0: Successful exit.
! 377: *> < 0: if INFO = -i, the ith argument to DSYTRS had an illegal
! 378: *> value
! 379: *> \endverbatim
! 380: *
! 381: * Authors:
! 382: * ========
! 383: *
! 384: *> \author Univ. of Tennessee
! 385: *> \author Univ. of California Berkeley
! 386: *> \author Univ. of Colorado Denver
! 387: *> \author NAG Ltd.
! 388: *
! 389: *> \date November 2011
! 390: *
! 391: *> \ingroup doubleSYcomputational
! 392: *
! 393: * =====================================================================
1.1 bertrand 394: SUBROUTINE DLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
395: $ AF, LDAF, IPIV, COLEQU, C, B, LDB,
396: $ Y, LDY, BERR_OUT, N_NORMS,
397: $ ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
398: $ AYB, DY, Y_TAIL, RCOND, ITHRESH,
399: $ RTHRESH, DZ_UB, IGNORE_CWISE,
400: $ INFO )
401: *
1.5 ! bertrand 402: * -- LAPACK computational routine (version 3.4.0) --
! 403: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 404: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 405: * November 2011
1.1 bertrand 406: *
407: * .. Scalar Arguments ..
408: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
409: $ N_NORMS, ITHRESH
410: CHARACTER UPLO
411: LOGICAL COLEQU, IGNORE_CWISE
412: DOUBLE PRECISION RTHRESH, DZ_UB
413: * ..
414: * .. Array Arguments ..
415: INTEGER IPIV( * )
416: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
417: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
418: DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
419: $ ERR_BNDS_NORM( NRHS, * ),
420: $ ERR_BNDS_COMP( NRHS, * )
421: * ..
422: *
423: * =====================================================================
424: *
425: * .. Local Scalars ..
426: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE
427: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
428: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
429: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
430: $ EPS, HUGEVAL, INCR_THRESH
431: LOGICAL INCR_PREC
432: * ..
433: * .. Parameters ..
434: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
435: $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
436: $ EXTRA_RESIDUAL, EXTRA_Y
437: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
438: $ CONV_STATE = 2, NOPROG_STATE = 3 )
439: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
440: $ EXTRA_Y = 2 )
441: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
442: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
443: INTEGER CMP_ERR_I, PIV_GROWTH_I
444: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
445: $ BERR_I = 3 )
446: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
447: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
448: $ PIV_GROWTH_I = 9 )
449: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
450: $ LA_LINRX_CWISE_I
451: PARAMETER ( LA_LINRX_ITREF_I = 1,
452: $ LA_LINRX_ITHRESH_I = 2 )
453: PARAMETER ( LA_LINRX_CWISE_I = 3 )
454: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
455: $ LA_LINRX_RCOND_I
456: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
457: PARAMETER ( LA_LINRX_RCOND_I = 3 )
458: * ..
459: * .. External Functions ..
460: LOGICAL LSAME
461: EXTERNAL ILAUPLO
462: INTEGER ILAUPLO
463: * ..
464: * .. External Subroutines ..
465: EXTERNAL DAXPY, DCOPY, DSYTRS, DSYMV, BLAS_DSYMV_X,
466: $ BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
467: $ DLA_LIN_BERR
468: DOUBLE PRECISION DLAMCH
469: * ..
470: * .. Intrinsic Functions ..
471: INTRINSIC ABS, MAX, MIN
472: * ..
473: * .. Executable Statements ..
474: *
475: IF ( INFO.NE.0 ) RETURN
476: EPS = DLAMCH( 'Epsilon' )
477: HUGEVAL = DLAMCH( 'Overflow' )
478: * Force HUGEVAL to Inf
479: HUGEVAL = HUGEVAL * HUGEVAL
480: * Using HUGEVAL may lead to spurious underflows.
481: INCR_THRESH = DBLE( N )*EPS
482:
483: IF ( LSAME ( UPLO, 'L' ) ) THEN
484: UPLO2 = ILAUPLO( 'L' )
485: ELSE
486: UPLO2 = ILAUPLO( 'U' )
487: ENDIF
488:
489: DO J = 1, NRHS
490: Y_PREC_STATE = EXTRA_RESIDUAL
491: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
492: DO I = 1, N
493: Y_TAIL( I ) = 0.0D+0
494: END DO
495: END IF
496:
497: DXRAT = 0.0D+0
498: DXRATMAX = 0.0D+0
499: DZRAT = 0.0D+0
500: DZRATMAX = 0.0D+0
501: FINAL_DX_X = HUGEVAL
502: FINAL_DZ_Z = HUGEVAL
503: PREVNORMDX = HUGEVAL
504: PREV_DZ_Z = HUGEVAL
505: DZ_Z = HUGEVAL
506: DX_X = HUGEVAL
507:
508: X_STATE = WORKING_STATE
509: Z_STATE = UNSTABLE_STATE
510: INCR_PREC = .FALSE.
511:
512: DO CNT = 1, ITHRESH
513: *
514: * Compute residual RES = B_s - op(A_s) * Y,
515: * op(A) = A, A**T, or A**H depending on TRANS (and type).
516: *
517: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
518: IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN
519: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
520: $ 1.0D+0, RES, 1 )
521: ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
522: CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
523: $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
524: ELSE
525: CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
526: $ Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
527: END IF
528:
529: ! XXX: RES is no longer needed.
530: CALL DCOPY( N, RES, 1, DY, 1 )
531: CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
532: *
533: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
534: *
535: NORMX = 0.0D+0
536: NORMY = 0.0D+0
537: NORMDX = 0.0D+0
538: DZ_Z = 0.0D+0
539: YMIN = HUGEVAL
540:
541: DO I = 1, N
542: YK = ABS( Y( I, J ) )
543: DYK = ABS( DY( I ) )
544:
545: IF ( YK .NE. 0.0D+0 ) THEN
546: DZ_Z = MAX( DZ_Z, DYK / YK )
547: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
548: DZ_Z = HUGEVAL
549: END IF
550:
551: YMIN = MIN( YMIN, YK )
552:
553: NORMY = MAX( NORMY, YK )
554:
555: IF ( COLEQU ) THEN
556: NORMX = MAX( NORMX, YK * C( I ) )
557: NORMDX = MAX( NORMDX, DYK * C( I ) )
558: ELSE
559: NORMX = NORMY
560: NORMDX = MAX(NORMDX, DYK)
561: END IF
562: END DO
563:
564: IF ( NORMX .NE. 0.0D+0 ) THEN
565: DX_X = NORMDX / NORMX
566: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
567: DX_X = 0.0D+0
568: ELSE
569: DX_X = HUGEVAL
570: END IF
571:
572: DXRAT = NORMDX / PREVNORMDX
573: DZRAT = DZ_Z / PREV_DZ_Z
574: *
575: * Check termination criteria.
576: *
577: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
578: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
579: $ INCR_PREC = .TRUE.
580:
581: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
582: $ X_STATE = WORKING_STATE
583: IF ( X_STATE .EQ. WORKING_STATE ) THEN
584: IF ( DX_X .LE. EPS ) THEN
585: X_STATE = CONV_STATE
586: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
587: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
588: INCR_PREC = .TRUE.
589: ELSE
590: X_STATE = NOPROG_STATE
591: END IF
592: ELSE
593: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
594: END IF
595: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
596: END IF
597:
598: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
599: $ Z_STATE = WORKING_STATE
600: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
601: $ Z_STATE = WORKING_STATE
602: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
603: IF ( DZ_Z .LE. EPS ) THEN
604: Z_STATE = CONV_STATE
605: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
606: Z_STATE = UNSTABLE_STATE
607: DZRATMAX = 0.0D+0
608: FINAL_DZ_Z = HUGEVAL
609: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
610: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
611: INCR_PREC = .TRUE.
612: ELSE
613: Z_STATE = NOPROG_STATE
614: END IF
615: ELSE
616: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
617: END IF
618: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
619: END IF
620:
621: IF ( X_STATE.NE.WORKING_STATE.AND.
622: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
623: $ GOTO 666
624:
625: IF ( INCR_PREC ) THEN
626: INCR_PREC = .FALSE.
627: Y_PREC_STATE = Y_PREC_STATE + 1
628: DO I = 1, N
629: Y_TAIL( I ) = 0.0D+0
630: END DO
631: END IF
632:
633: PREVNORMDX = NORMDX
634: PREV_DZ_Z = DZ_Z
635: *
636: * Update soluton.
637: *
638: IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
639: CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
640: ELSE
641: CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
642: END IF
643:
644: END DO
645: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
646: 666 CONTINUE
647: *
648: * Set final_* when cnt hits ithresh.
649: *
650: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
651: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
652: *
653: * Compute error bounds.
654: *
655: IF ( N_NORMS .GE. 1 ) THEN
656: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
657: $ FINAL_DX_X / (1 - DXRATMAX)
658: END IF
659: IF ( N_NORMS .GE. 2 ) THEN
660: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
661: $ FINAL_DZ_Z / (1 - DZRATMAX)
662: END IF
663: *
664: * Compute componentwise relative backward error from formula
665: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
666: * where abs(Z) is the componentwise absolute value of the matrix
667: * or vector Z.
668: *
669: * Compute residual RES = B_s - op(A_s) * Y,
670: * op(A) = A, A**T, or A**H depending on TRANS (and type).
671: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
672: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
673: $ 1 )
674:
675: DO I = 1, N
676: AYB( I ) = ABS( B( I, J ) )
677: END DO
678: *
679: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
680: *
681: CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
682: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
683:
684: CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
685: *
686: * End of loop for each RHS.
687: *
688: END DO
689: *
690: RETURN
691: END
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