Annotation of rpl/lapack/lapack/dla_porfsx_extended.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
! 2: $ AF, LDAF, COLEQU, C, B, LDB, Y,
! 3: $ LDY, BERR_OUT, N_NORMS,
! 4: $ ERR_BNDS_NORM, ERR_BNDS_COMP, RES,
! 5: $ AYB, DY, Y_TAIL, RCOND, ITHRESH,
! 6: $ RTHRESH, DZ_UB, IGNORE_CWISE,
! 7: $ INFO )
! 8: *
! 9: * -- LAPACK routine (version 3.2.2) --
! 10: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 11: * -- Jason Riedy of Univ. of California Berkeley. --
! 12: * -- June 2010 --
! 13: *
! 14: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 15: * -- Univ. of California Berkeley and NAG Ltd. --
! 16: *
! 17: IMPLICIT NONE
! 18: * ..
! 19: * .. Scalar Arguments ..
! 20: INTEGER INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
! 21: $ N_NORMS, ITHRESH
! 22: CHARACTER UPLO
! 23: LOGICAL COLEQU, IGNORE_CWISE
! 24: DOUBLE PRECISION RTHRESH, DZ_UB
! 25: * ..
! 26: * .. Array Arguments ..
! 27: DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 28: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
! 29: DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ),
! 30: $ ERR_BNDS_NORM( NRHS, * ),
! 31: $ ERR_BNDS_COMP( NRHS, * )
! 32: * ..
! 33: *
! 34: * Purpose
! 35: * =======
! 36: *
! 37: * DLA_PORFSX_EXTENDED improves the computed solution to a system of
! 38: * linear equations by performing extra-precise iterative refinement
! 39: * and provides error bounds and backward error estimates for the solution.
! 40: * This subroutine is called by DPORFSX to perform iterative refinement.
! 41: * In addition to normwise error bound, the code provides maximum
! 42: * componentwise error bound if possible. See comments for ERR_BNDS_NORM
! 43: * and ERR_BNDS_COMP for details of the error bounds. Note that this
! 44: * subroutine is only resonsible for setting the second fields of
! 45: * ERR_BNDS_NORM and ERR_BNDS_COMP.
! 46: *
! 47: * Arguments
! 48: * =========
! 49: *
! 50: * PREC_TYPE (input) INTEGER
! 51: * Specifies the intermediate precision to be used in refinement.
! 52: * The value is defined by ILAPREC(P) where P is a CHARACTER and
! 53: * P = 'S': Single
! 54: * = 'D': Double
! 55: * = 'I': Indigenous
! 56: * = 'X', 'E': Extra
! 57: *
! 58: * UPLO (input) CHARACTER*1
! 59: * = 'U': Upper triangle of A is stored;
! 60: * = 'L': Lower triangle of A is stored.
! 61: *
! 62: * N (input) INTEGER
! 63: * The number of linear equations, i.e., the order of the
! 64: * matrix A. N >= 0.
! 65: *
! 66: * NRHS (input) INTEGER
! 67: * The number of right-hand-sides, i.e., the number of columns of the
! 68: * matrix B.
! 69: *
! 70: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 71: * On entry, the N-by-N matrix A.
! 72: *
! 73: * LDA (input) INTEGER
! 74: * The leading dimension of the array A. LDA >= max(1,N).
! 75: *
! 76: * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
! 77: * The triangular factor U or L from the Cholesky factorization
! 78: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 79: *
! 80: * LDAF (input) INTEGER
! 81: * The leading dimension of the array AF. LDAF >= max(1,N).
! 82: *
! 83: * COLEQU (input) LOGICAL
! 84: * If .TRUE. then column equilibration was done to A before calling
! 85: * this routine. This is needed to compute the solution and error
! 86: * bounds correctly.
! 87: *
! 88: * C (input) DOUBLE PRECISION array, dimension (N)
! 89: * The column scale factors for A. If COLEQU = .FALSE., C
! 90: * is not accessed. If C is input, each element of C should be a power
! 91: * of the radix to ensure a reliable solution and error estimates.
! 92: * Scaling by powers of the radix does not cause rounding errors unless
! 93: * the result underflows or overflows. Rounding errors during scaling
! 94: * lead to refining with a matrix that is not equivalent to the
! 95: * input matrix, producing error estimates that may not be
! 96: * reliable.
! 97: *
! 98: * B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
! 99: * The right-hand-side matrix B.
! 100: *
! 101: * LDB (input) INTEGER
! 102: * The leading dimension of the array B. LDB >= max(1,N).
! 103: *
! 104: * Y (input/output) DOUBLE PRECISION array, dimension
! 105: * (LDY,NRHS)
! 106: * On entry, the solution matrix X, as computed by DPOTRS.
! 107: * On exit, the improved solution matrix Y.
! 108: *
! 109: * LDY (input) INTEGER
! 110: * The leading dimension of the array Y. LDY >= max(1,N).
! 111: *
! 112: * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS)
! 113: * On exit, BERR_OUT(j) contains the componentwise relative backward
! 114: * error for right-hand-side j from the formula
! 115: * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 116: * where abs(Z) is the componentwise absolute value of the matrix
! 117: * or vector Z. This is computed by DLA_LIN_BERR.
! 118: *
! 119: * N_NORMS (input) INTEGER
! 120: * Determines which error bounds to return (see ERR_BNDS_NORM
! 121: * and ERR_BNDS_COMP).
! 122: * If N_NORMS >= 1 return normwise error bounds.
! 123: * If N_NORMS >= 2 return componentwise error bounds.
! 124: *
! 125: * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension
! 126: * (NRHS, N_ERR_BNDS)
! 127: * For each right-hand side, this array contains information about
! 128: * various error bounds and condition numbers corresponding to the
! 129: * normwise relative error, which is defined as follows:
! 130: *
! 131: * Normwise relative error in the ith solution vector:
! 132: * max_j (abs(XTRUE(j,i) - X(j,i)))
! 133: * ------------------------------
! 134: * max_j abs(X(j,i))
! 135: *
! 136: * The array is indexed by the type of error information as described
! 137: * below. There currently are up to three pieces of information
! 138: * returned.
! 139: *
! 140: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 141: * right-hand side.
! 142: *
! 143: * The second index in ERR_BNDS_NORM(:,err) contains the following
! 144: * three fields:
! 145: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 146: * reciprocal condition number is less than the threshold
! 147: * sqrt(n) * slamch('Epsilon').
! 148: *
! 149: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 150: * almost certainly within a factor of 10 of the true error
! 151: * so long as the next entry is greater than the threshold
! 152: * sqrt(n) * slamch('Epsilon'). This error bound should only
! 153: * be trusted if the previous boolean is true.
! 154: *
! 155: * err = 3 Reciprocal condition number: Estimated normwise
! 156: * reciprocal condition number. Compared with the threshold
! 157: * sqrt(n) * slamch('Epsilon') to determine if the error
! 158: * estimate is "guaranteed". These reciprocal condition
! 159: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 160: * appropriately scaled matrix Z.
! 161: * Let Z = S*A, where S scales each row by a power of the
! 162: * radix so all absolute row sums of Z are approximately 1.
! 163: *
! 164: * This subroutine is only responsible for setting the second field
! 165: * above.
! 166: * See Lapack Working Note 165 for further details and extra
! 167: * cautions.
! 168: *
! 169: * ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension
! 170: * (NRHS, N_ERR_BNDS)
! 171: * For each right-hand side, this array contains information about
! 172: * various error bounds and condition numbers corresponding to the
! 173: * componentwise relative error, which is defined as follows:
! 174: *
! 175: * Componentwise relative error in the ith solution vector:
! 176: * abs(XTRUE(j,i) - X(j,i))
! 177: * max_j ----------------------
! 178: * abs(X(j,i))
! 179: *
! 180: * The array is indexed by the right-hand side i (on which the
! 181: * componentwise relative error depends), and the type of error
! 182: * information as described below. There currently are up to three
! 183: * pieces of information returned for each right-hand side. If
! 184: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 185: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 186: * the first (:,N_ERR_BNDS) entries are returned.
! 187: *
! 188: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 189: * right-hand side.
! 190: *
! 191: * The second index in ERR_BNDS_COMP(:,err) contains the following
! 192: * three fields:
! 193: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 194: * reciprocal condition number is less than the threshold
! 195: * sqrt(n) * slamch('Epsilon').
! 196: *
! 197: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 198: * almost certainly within a factor of 10 of the true error
! 199: * so long as the next entry is greater than the threshold
! 200: * sqrt(n) * slamch('Epsilon'). This error bound should only
! 201: * be trusted if the previous boolean is true.
! 202: *
! 203: * err = 3 Reciprocal condition number: Estimated componentwise
! 204: * reciprocal condition number. Compared with the threshold
! 205: * sqrt(n) * slamch('Epsilon') to determine if the error
! 206: * estimate is "guaranteed". These reciprocal condition
! 207: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 208: * appropriately scaled matrix Z.
! 209: * Let Z = S*(A*diag(x)), where x is the solution for the
! 210: * current right-hand side and S scales each row of
! 211: * A*diag(x) by a power of the radix so all absolute row
! 212: * sums of Z are approximately 1.
! 213: *
! 214: * This subroutine is only responsible for setting the second field
! 215: * above.
! 216: * See Lapack Working Note 165 for further details and extra
! 217: * cautions.
! 218: *
! 219: * RES (input) DOUBLE PRECISION array, dimension (N)
! 220: * Workspace to hold the intermediate residual.
! 221: *
! 222: * AYB (input) DOUBLE PRECISION array, dimension (N)
! 223: * Workspace. This can be the same workspace passed for Y_TAIL.
! 224: *
! 225: * DY (input) DOUBLE PRECISION array, dimension (N)
! 226: * Workspace to hold the intermediate solution.
! 227: *
! 228: * Y_TAIL (input) DOUBLE PRECISION array, dimension (N)
! 229: * Workspace to hold the trailing bits of the intermediate solution.
! 230: *
! 231: * RCOND (input) DOUBLE PRECISION
! 232: * Reciprocal scaled condition number. This is an estimate of the
! 233: * reciprocal Skeel condition number of the matrix A after
! 234: * equilibration (if done). If this is less than the machine
! 235: * precision (in particular, if it is zero), the matrix is singular
! 236: * to working precision. Note that the error may still be small even
! 237: * if this number is very small and the matrix appears ill-
! 238: * conditioned.
! 239: *
! 240: * ITHRESH (input) INTEGER
! 241: * The maximum number of residual computations allowed for
! 242: * refinement. The default is 10. For 'aggressive' set to 100 to
! 243: * permit convergence using approximate factorizations or
! 244: * factorizations other than LU. If the factorization uses a
! 245: * technique other than Gaussian elimination, the guarantees in
! 246: * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
! 247: *
! 248: * RTHRESH (input) DOUBLE PRECISION
! 249: * Determines when to stop refinement if the error estimate stops
! 250: * decreasing. Refinement will stop when the next solution no longer
! 251: * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
! 252: * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
! 253: * default value is 0.5. For 'aggressive' set to 0.9 to permit
! 254: * convergence on extremely ill-conditioned matrices. See LAWN 165
! 255: * for more details.
! 256: *
! 257: * DZ_UB (input) DOUBLE PRECISION
! 258: * Determines when to start considering componentwise convergence.
! 259: * Componentwise convergence is only considered after each component
! 260: * of the solution Y is stable, which we definte as the relative
! 261: * change in each component being less than DZ_UB. The default value
! 262: * is 0.25, requiring the first bit to be stable. See LAWN 165 for
! 263: * more details.
! 264: *
! 265: * IGNORE_CWISE (input) LOGICAL
! 266: * If .TRUE. then ignore componentwise convergence. Default value
! 267: * is .FALSE..
! 268: *
! 269: * INFO (output) INTEGER
! 270: * = 0: Successful exit.
! 271: * < 0: if INFO = -i, the ith argument to DPOTRS had an illegal
! 272: * value
! 273: *
! 274: * =====================================================================
! 275: *
! 276: * .. Local Scalars ..
! 277: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE
! 278: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
! 279: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
! 280: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
! 281: $ EPS, HUGEVAL, INCR_THRESH
! 282: LOGICAL INCR_PREC
! 283: * ..
! 284: * .. Parameters ..
! 285: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
! 286: $ NOPROG_STATE, Y_PREC_STATE, BASE_RESIDUAL,
! 287: $ EXTRA_RESIDUAL, EXTRA_Y
! 288: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
! 289: $ CONV_STATE = 2, NOPROG_STATE = 3 )
! 290: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
! 291: $ EXTRA_Y = 2 )
! 292: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
! 293: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
! 294: INTEGER CMP_ERR_I, PIV_GROWTH_I
! 295: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
! 296: $ BERR_I = 3 )
! 297: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
! 298: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
! 299: $ PIV_GROWTH_I = 9 )
! 300: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
! 301: $ LA_LINRX_CWISE_I
! 302: PARAMETER ( LA_LINRX_ITREF_I = 1,
! 303: $ LA_LINRX_ITHRESH_I = 2 )
! 304: PARAMETER ( LA_LINRX_CWISE_I = 3 )
! 305: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
! 306: $ LA_LINRX_RCOND_I
! 307: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
! 308: PARAMETER ( LA_LINRX_RCOND_I = 3 )
! 309: * ..
! 310: * .. External Functions ..
! 311: LOGICAL LSAME
! 312: EXTERNAL ILAUPLO
! 313: INTEGER ILAUPLO
! 314: * ..
! 315: * .. External Subroutines ..
! 316: EXTERNAL DAXPY, DCOPY, DPOTRS, DSYMV, BLAS_DSYMV_X,
! 317: $ BLAS_DSYMV2_X, DLA_SYAMV, DLA_WWADDW,
! 318: $ DLA_LIN_BERR
! 319: DOUBLE PRECISION DLAMCH
! 320: * ..
! 321: * .. Intrinsic Functions ..
! 322: INTRINSIC ABS, MAX, MIN
! 323: * ..
! 324: * .. Executable Statements ..
! 325: *
! 326: IF (INFO.NE.0) RETURN
! 327: EPS = DLAMCH( 'Epsilon' )
! 328: HUGEVAL = DLAMCH( 'Overflow' )
! 329: * Force HUGEVAL to Inf
! 330: HUGEVAL = HUGEVAL * HUGEVAL
! 331: * Using HUGEVAL may lead to spurious underflows.
! 332: INCR_THRESH = DBLE( N ) * EPS
! 333:
! 334: IF ( LSAME ( UPLO, 'L' ) ) THEN
! 335: UPLO2 = ILAUPLO( 'L' )
! 336: ELSE
! 337: UPLO2 = ILAUPLO( 'U' )
! 338: ENDIF
! 339:
! 340: DO J = 1, NRHS
! 341: Y_PREC_STATE = EXTRA_RESIDUAL
! 342: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
! 343: DO I = 1, N
! 344: Y_TAIL( I ) = 0.0D+0
! 345: END DO
! 346: END IF
! 347:
! 348: DXRAT = 0.0D+0
! 349: DXRATMAX = 0.0D+0
! 350: DZRAT = 0.0D+0
! 351: DZRATMAX = 0.0D+0
! 352: FINAL_DX_X = HUGEVAL
! 353: FINAL_DZ_Z = HUGEVAL
! 354: PREVNORMDX = HUGEVAL
! 355: PREV_DZ_Z = HUGEVAL
! 356: DZ_Z = HUGEVAL
! 357: DX_X = HUGEVAL
! 358:
! 359: X_STATE = WORKING_STATE
! 360: Z_STATE = UNSTABLE_STATE
! 361: INCR_PREC = .FALSE.
! 362:
! 363: DO CNT = 1, ITHRESH
! 364: *
! 365: * Compute residual RES = B_s - op(A_s) * Y,
! 366: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 367: *
! 368: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
! 369: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
! 370: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1,
! 371: $ 1.0D+0, RES, 1 )
! 372: ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
! 373: CALL BLAS_DSYMV_X( UPLO2, N, -1.0D+0, A, LDA,
! 374: $ Y( 1, J ), 1, 1.0D+0, RES, 1, PREC_TYPE )
! 375: ELSE
! 376: CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
! 377: $ Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
! 378: END IF
! 379:
! 380: ! XXX: RES is no longer needed.
! 381: CALL DCOPY( N, RES, 1, DY, 1 )
! 382: CALL DPOTRS( UPLO, N, 1, AF, LDAF, DY, N, INFO )
! 383: *
! 384: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
! 385: *
! 386: NORMX = 0.0D+0
! 387: NORMY = 0.0D+0
! 388: NORMDX = 0.0D+0
! 389: DZ_Z = 0.0D+0
! 390: YMIN = HUGEVAL
! 391:
! 392: DO I = 1, N
! 393: YK = ABS( Y( I, J ) )
! 394: DYK = ABS( DY( I ) )
! 395:
! 396: IF ( YK .NE. 0.0D+0 ) THEN
! 397: DZ_Z = MAX( DZ_Z, DYK / YK )
! 398: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
! 399: DZ_Z = HUGEVAL
! 400: END IF
! 401:
! 402: YMIN = MIN( YMIN, YK )
! 403:
! 404: NORMY = MAX( NORMY, YK )
! 405:
! 406: IF ( COLEQU ) THEN
! 407: NORMX = MAX( NORMX, YK * C( I ) )
! 408: NORMDX = MAX( NORMDX, DYK * C( I ) )
! 409: ELSE
! 410: NORMX = NORMY
! 411: NORMDX = MAX( NORMDX, DYK )
! 412: END IF
! 413: END DO
! 414:
! 415: IF ( NORMX .NE. 0.0D+0 ) THEN
! 416: DX_X = NORMDX / NORMX
! 417: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
! 418: DX_X = 0.0D+0
! 419: ELSE
! 420: DX_X = HUGEVAL
! 421: END IF
! 422:
! 423: DXRAT = NORMDX / PREVNORMDX
! 424: DZRAT = DZ_Z / PREV_DZ_Z
! 425: *
! 426: * Check termination criteria.
! 427: *
! 428: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
! 429: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
! 430: $ INCR_PREC = .TRUE.
! 431:
! 432: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
! 433: $ X_STATE = WORKING_STATE
! 434: IF ( X_STATE .EQ. WORKING_STATE ) THEN
! 435: IF ( DX_X .LE. EPS ) THEN
! 436: X_STATE = CONV_STATE
! 437: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
! 438: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
! 439: INCR_PREC = .TRUE.
! 440: ELSE
! 441: X_STATE = NOPROG_STATE
! 442: END IF
! 443: ELSE
! 444: IF ( DXRAT .GT. DXRATMAX ) DXRATMAX = DXRAT
! 445: END IF
! 446: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
! 447: END IF
! 448:
! 449: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
! 450: $ Z_STATE = WORKING_STATE
! 451: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
! 452: $ Z_STATE = WORKING_STATE
! 453: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
! 454: IF ( DZ_Z .LE. EPS ) THEN
! 455: Z_STATE = CONV_STATE
! 456: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
! 457: Z_STATE = UNSTABLE_STATE
! 458: DZRATMAX = 0.0D+0
! 459: FINAL_DZ_Z = HUGEVAL
! 460: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
! 461: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
! 462: INCR_PREC = .TRUE.
! 463: ELSE
! 464: Z_STATE = NOPROG_STATE
! 465: END IF
! 466: ELSE
! 467: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
! 468: END IF
! 469: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
! 470: END IF
! 471:
! 472: IF ( X_STATE.NE.WORKING_STATE.AND.
! 473: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
! 474: $ GOTO 666
! 475:
! 476: IF ( INCR_PREC ) THEN
! 477: INCR_PREC = .FALSE.
! 478: Y_PREC_STATE = Y_PREC_STATE + 1
! 479: DO I = 1, N
! 480: Y_TAIL( I ) = 0.0D+0
! 481: END DO
! 482: END IF
! 483:
! 484: PREVNORMDX = NORMDX
! 485: PREV_DZ_Z = DZ_Z
! 486: *
! 487: * Update soluton.
! 488: *
! 489: IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
! 490: CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )
! 491: ELSE
! 492: CALL DLA_WWADDW( N, Y( 1, J ), Y_TAIL, DY )
! 493: END IF
! 494:
! 495: END DO
! 496: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
! 497: 666 CONTINUE
! 498: *
! 499: * Set final_* when cnt hits ithresh.
! 500: *
! 501: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
! 502: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
! 503: *
! 504: * Compute error bounds.
! 505: *
! 506: IF ( N_NORMS .GE. 1 ) THEN
! 507: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
! 508: $ FINAL_DX_X / (1 - DXRATMAX)
! 509: END IF
! 510: IF ( N_NORMS .GE. 2 ) THEN
! 511: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
! 512: $ FINAL_DZ_Z / (1 - DZRATMAX)
! 513: END IF
! 514: *
! 515: * Compute componentwise relative backward error from formula
! 516: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 517: * where abs(Z) is the componentwise absolute value of the matrix
! 518: * or vector Z.
! 519: *
! 520: * Compute residual RES = B_s - op(A_s) * Y,
! 521: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 522: *
! 523: CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
! 524: CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
! 525: $ 1 )
! 526:
! 527: DO I = 1, N
! 528: AYB( I ) = ABS( B( I, J ) )
! 529: END DO
! 530: *
! 531: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
! 532: *
! 533: CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
! 534: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
! 535:
! 536: CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
! 537: *
! 538: * End of loop for each RHS.
! 539: *
! 540: END DO
! 541: *
! 542: RETURN
! 543: END
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