Annotation of rpl/lapack/lapack/zla_porfsx_extended.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLA_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: COMPLEX*16 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: * ZLA_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 ZPORFSX 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) COMPLEX*16 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) COMPLEX*16 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 ZPOTRF.
! 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) COMPLEX*16 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) COMPLEX*16 array, dimension
! 105: * (LDY,NRHS)
! 106: * On entry, the solution matrix X, as computed by ZPOTRS.
! 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 ZLA_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) COMPLEX*16 array, dimension (N)
! 220: * Workspace to hold the intermediate residual.
! 221: *
! 222: * AYB (input) DOUBLE PRECISION array, dimension (N)
! 223: * Workspace.
! 224: *
! 225: * DY (input) COMPLEX*16 PRECISION array, dimension (N)
! 226: * Workspace to hold the intermediate solution.
! 227: *
! 228: * Y_TAIL (input) COMPLEX*16 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 ZPOTRS had an illegal
! 272: * value
! 273: *
! 274: * =====================================================================
! 275: *
! 276: * .. Local Scalars ..
! 277: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE,
! 278: $ Y_PREC_STATE
! 279: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
! 280: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
! 281: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
! 282: $ EPS, HUGEVAL, INCR_THRESH
! 283: LOGICAL INCR_PREC
! 284: COMPLEX*16 ZDUM
! 285: * ..
! 286: * .. Parameters ..
! 287: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
! 288: $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
! 289: $ EXTRA_Y
! 290: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
! 291: $ CONV_STATE = 2, NOPROG_STATE = 3 )
! 292: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
! 293: $ EXTRA_Y = 2 )
! 294: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
! 295: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
! 296: INTEGER CMP_ERR_I, PIV_GROWTH_I
! 297: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
! 298: $ BERR_I = 3 )
! 299: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
! 300: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
! 301: $ PIV_GROWTH_I = 9 )
! 302: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
! 303: $ LA_LINRX_CWISE_I
! 304: PARAMETER ( LA_LINRX_ITREF_I = 1,
! 305: $ LA_LINRX_ITHRESH_I = 2 )
! 306: PARAMETER ( LA_LINRX_CWISE_I = 3 )
! 307: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
! 308: $ LA_LINRX_RCOND_I
! 309: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
! 310: PARAMETER ( LA_LINRX_RCOND_I = 3 )
! 311: * ..
! 312: * .. External Functions ..
! 313: LOGICAL LSAME
! 314: EXTERNAL ILAUPLO
! 315: INTEGER ILAUPLO
! 316: * ..
! 317: * .. External Subroutines ..
! 318: EXTERNAL ZAXPY, ZCOPY, ZPOTRS, ZHEMV, BLAS_ZHEMV_X,
! 319: $ BLAS_ZHEMV2_X, ZLA_HEAMV, ZLA_WWADDW,
! 320: $ ZLA_LIN_BERR, DLAMCH
! 321: DOUBLE PRECISION DLAMCH
! 322: * ..
! 323: * .. Intrinsic Functions ..
! 324: INTRINSIC ABS, DBLE, DIMAG, MAX, MIN
! 325: * ..
! 326: * .. Statement Functions ..
! 327: DOUBLE PRECISION CABS1
! 328: * ..
! 329: * .. Statement Function Definitions ..
! 330: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 331: * ..
! 332: * .. Executable Statements ..
! 333: *
! 334: IF (INFO.NE.0) RETURN
! 335: EPS = DLAMCH( 'Epsilon' )
! 336: HUGEVAL = DLAMCH( 'Overflow' )
! 337: * Force HUGEVAL to Inf
! 338: HUGEVAL = HUGEVAL * HUGEVAL
! 339: * Using HUGEVAL may lead to spurious underflows.
! 340: INCR_THRESH = DBLE(N) * EPS
! 341:
! 342: IF (LSAME (UPLO, 'L')) THEN
! 343: UPLO2 = ILAUPLO( 'L' )
! 344: ELSE
! 345: UPLO2 = ILAUPLO( 'U' )
! 346: ENDIF
! 347:
! 348: DO J = 1, NRHS
! 349: Y_PREC_STATE = EXTRA_RESIDUAL
! 350: IF (Y_PREC_STATE .EQ. EXTRA_Y) THEN
! 351: DO I = 1, N
! 352: Y_TAIL( I ) = 0.0D+0
! 353: END DO
! 354: END IF
! 355:
! 356: DXRAT = 0.0D+0
! 357: DXRATMAX = 0.0D+0
! 358: DZRAT = 0.0D+0
! 359: DZRATMAX = 0.0D+0
! 360: FINAL_DX_X = HUGEVAL
! 361: FINAL_DZ_Z = HUGEVAL
! 362: PREVNORMDX = HUGEVAL
! 363: PREV_DZ_Z = HUGEVAL
! 364: DZ_Z = HUGEVAL
! 365: DX_X = HUGEVAL
! 366:
! 367: X_STATE = WORKING_STATE
! 368: Z_STATE = UNSTABLE_STATE
! 369: INCR_PREC = .FALSE.
! 370:
! 371: DO CNT = 1, ITHRESH
! 372: *
! 373: * Compute residual RES = B_s - op(A_s) * Y,
! 374: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 375: *
! 376: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
! 377: IF (Y_PREC_STATE .EQ. BASE_RESIDUAL) THEN
! 378: CALL ZHEMV(UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
! 379: $ DCMPLX(1.0D+0), RES, 1)
! 380: ELSE IF (Y_PREC_STATE .EQ. EXTRA_RESIDUAL) THEN
! 381: CALL BLAS_ZHEMV_X(UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
! 382: $ Y( 1, J ), 1, DCMPLX(1.0D+0), RES, 1, PREC_TYPE)
! 383: ELSE
! 384: CALL BLAS_ZHEMV2_X(UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
! 385: $ Y(1, J), Y_TAIL, 1, DCMPLX(1.0D+0), RES, 1,
! 386: $ PREC_TYPE)
! 387: END IF
! 388:
! 389: ! XXX: RES is no longer needed.
! 390: CALL ZCOPY( N, RES, 1, DY, 1 )
! 391: CALL ZPOTRS( UPLO, N, 1, AF, LDAF, DY, N, INFO)
! 392: *
! 393: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
! 394: *
! 395: NORMX = 0.0D+0
! 396: NORMY = 0.0D+0
! 397: NORMDX = 0.0D+0
! 398: DZ_Z = 0.0D+0
! 399: YMIN = HUGEVAL
! 400:
! 401: DO I = 1, N
! 402: YK = CABS1(Y(I, J))
! 403: DYK = CABS1(DY(I))
! 404:
! 405: IF (YK .NE. 0.0D+0) THEN
! 406: DZ_Z = MAX( DZ_Z, DYK / YK )
! 407: ELSE IF (DYK .NE. 0.0D+0) THEN
! 408: DZ_Z = HUGEVAL
! 409: END IF
! 410:
! 411: YMIN = MIN( YMIN, YK )
! 412:
! 413: NORMY = MAX( NORMY, YK )
! 414:
! 415: IF ( COLEQU ) THEN
! 416: NORMX = MAX(NORMX, YK * C(I))
! 417: NORMDX = MAX(NORMDX, DYK * C(I))
! 418: ELSE
! 419: NORMX = NORMY
! 420: NORMDX = MAX(NORMDX, DYK)
! 421: END IF
! 422: END DO
! 423:
! 424: IF (NORMX .NE. 0.0D+0) THEN
! 425: DX_X = NORMDX / NORMX
! 426: ELSE IF (NORMDX .EQ. 0.0D+0) THEN
! 427: DX_X = 0.0D+0
! 428: ELSE
! 429: DX_X = HUGEVAL
! 430: END IF
! 431:
! 432: DXRAT = NORMDX / PREVNORMDX
! 433: DZRAT = DZ_Z / PREV_DZ_Z
! 434: *
! 435: * Check termination criteria.
! 436: *
! 437: IF (YMIN*RCOND .LT. INCR_THRESH*NORMY
! 438: $ .AND. Y_PREC_STATE .LT. EXTRA_Y)
! 439: $ INCR_PREC = .TRUE.
! 440:
! 441: IF (X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH)
! 442: $ X_STATE = WORKING_STATE
! 443: IF (X_STATE .EQ. WORKING_STATE) THEN
! 444: IF (DX_X .LE. EPS) THEN
! 445: X_STATE = CONV_STATE
! 446: ELSE IF (DXRAT .GT. RTHRESH) THEN
! 447: IF (Y_PREC_STATE .NE. EXTRA_Y) THEN
! 448: INCR_PREC = .TRUE.
! 449: ELSE
! 450: X_STATE = NOPROG_STATE
! 451: END IF
! 452: ELSE
! 453: IF (DXRAT .GT. DXRATMAX) DXRATMAX = DXRAT
! 454: END IF
! 455: IF (X_STATE .GT. WORKING_STATE) FINAL_DX_X = DX_X
! 456: END IF
! 457:
! 458: IF (Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB)
! 459: $ Z_STATE = WORKING_STATE
! 460: IF (Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH)
! 461: $ Z_STATE = WORKING_STATE
! 462: IF (Z_STATE .EQ. WORKING_STATE) THEN
! 463: IF (DZ_Z .LE. EPS) THEN
! 464: Z_STATE = CONV_STATE
! 465: ELSE IF (DZ_Z .GT. DZ_UB) THEN
! 466: Z_STATE = UNSTABLE_STATE
! 467: DZRATMAX = 0.0D+0
! 468: FINAL_DZ_Z = HUGEVAL
! 469: ELSE IF (DZRAT .GT. RTHRESH) THEN
! 470: IF (Y_PREC_STATE .NE. EXTRA_Y) THEN
! 471: INCR_PREC = .TRUE.
! 472: ELSE
! 473: Z_STATE = NOPROG_STATE
! 474: END IF
! 475: ELSE
! 476: IF (DZRAT .GT. DZRATMAX) DZRATMAX = DZRAT
! 477: END IF
! 478: IF (Z_STATE .GT. WORKING_STATE) FINAL_DZ_Z = DZ_Z
! 479: END IF
! 480:
! 481: IF ( X_STATE.NE.WORKING_STATE.AND.
! 482: $ (IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE) )
! 483: $ GOTO 666
! 484:
! 485: IF (INCR_PREC) THEN
! 486: INCR_PREC = .FALSE.
! 487: Y_PREC_STATE = Y_PREC_STATE + 1
! 488: DO I = 1, N
! 489: Y_TAIL( I ) = 0.0D+0
! 490: END DO
! 491: END IF
! 492:
! 493: PREVNORMDX = NORMDX
! 494: PREV_DZ_Z = DZ_Z
! 495: *
! 496: * Update soluton.
! 497: *
! 498: IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
! 499: CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
! 500: ELSE
! 501: CALL ZLA_WWADDW(N, Y(1,J), Y_TAIL, DY)
! 502: END IF
! 503:
! 504: END DO
! 505: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
! 506: 666 CONTINUE
! 507: *
! 508: * Set final_* when cnt hits ithresh.
! 509: *
! 510: IF (X_STATE .EQ. WORKING_STATE) FINAL_DX_X = DX_X
! 511: IF (Z_STATE .EQ. WORKING_STATE) FINAL_DZ_Z = DZ_Z
! 512: *
! 513: * Compute error bounds.
! 514: *
! 515: IF (N_NORMS .GE. 1) THEN
! 516: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
! 517: $ FINAL_DX_X / (1 - DXRATMAX)
! 518: END IF
! 519: IF (N_NORMS .GE. 2) THEN
! 520: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
! 521: $ FINAL_DZ_Z / (1 - DZRATMAX)
! 522: END IF
! 523: *
! 524: * Compute componentwise relative backward error from formula
! 525: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 526: * where abs(Z) is the componentwise absolute value of the matrix
! 527: * or vector Z.
! 528: *
! 529: * Compute residual RES = B_s - op(A_s) * Y,
! 530: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 531: *
! 532: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
! 533: CALL ZHEMV(UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
! 534: $ DCMPLX(1.0D+0), RES, 1)
! 535:
! 536: DO I = 1, N
! 537: AYB( I ) = CABS1( B( I, J ) )
! 538: END DO
! 539: *
! 540: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
! 541: *
! 542: CALL ZLA_HEAMV (UPLO2, N, 1.0D+0,
! 543: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1)
! 544:
! 545: CALL ZLA_LIN_BERR (N, N, 1, RES, AYB, BERR_OUT(J))
! 546: *
! 547: * End of loop for each RHS.
! 548: *
! 549: END DO
! 550: *
! 551: RETURN
! 552: END
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