Annotation of rpl/lapack/lapack/zla_syrfsx_extended.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLA_SYRFSX_EXTENDED( PREC_TYPE, UPLO, N, NRHS, A, LDA,
! 2: $ AF, LDAF, IPIV, COLEQU, C, B, LDB,
! 3: $ Y, 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: INTEGER IPIV( * )
! 28: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 29: $ Y( LDY, * ), RES( * ), DY( * ), Y_TAIL( * )
! 30: DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ),
! 31: $ ERR_BNDS_NORM( NRHS, * ),
! 32: $ ERR_BNDS_COMP( NRHS, * )
! 33: * ..
! 34: *
! 35: * Purpose
! 36: * =======
! 37: *
! 38: * ZLA_SYRFSX_EXTENDED improves the computed solution to a system of
! 39: * linear equations by performing extra-precise iterative refinement
! 40: * and provides error bounds and backward error estimates for the solution.
! 41: * This subroutine is called by ZSYRFSX to perform iterative refinement.
! 42: * In addition to normwise error bound, the code provides maximum
! 43: * componentwise error bound if possible. See comments for ERR_BNDS_NORM
! 44: * and ERR_BNDS_COMP for details of the error bounds. Note that this
! 45: * subroutine is only resonsible for setting the second fields of
! 46: * ERR_BNDS_NORM and ERR_BNDS_COMP.
! 47: *
! 48: * Arguments
! 49: * =========
! 50: *
! 51: * PREC_TYPE (input) INTEGER
! 52: * Specifies the intermediate precision to be used in refinement.
! 53: * The value is defined by ILAPREC(P) where P is a CHARACTER and
! 54: * P = 'S': Single
! 55: * = 'D': Double
! 56: * = 'I': Indigenous
! 57: * = 'X', 'E': Extra
! 58: *
! 59: * UPLO (input) CHARACTER*1
! 60: * = 'U': Upper triangle of A is stored;
! 61: * = 'L': Lower triangle of A is stored.
! 62: *
! 63: * N (input) INTEGER
! 64: * The number of linear equations, i.e., the order of the
! 65: * matrix A. N >= 0.
! 66: *
! 67: * NRHS (input) INTEGER
! 68: * The number of right-hand-sides, i.e., the number of columns of the
! 69: * matrix B.
! 70: *
! 71: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 72: * On entry, the N-by-N matrix A.
! 73: *
! 74: * LDA (input) INTEGER
! 75: * The leading dimension of the array A. LDA >= max(1,N).
! 76: *
! 77: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 78: * The block diagonal matrix D and the multipliers used to
! 79: * obtain the factor U or L as computed by ZSYTRF.
! 80: *
! 81: * LDAF (input) INTEGER
! 82: * The leading dimension of the array AF. LDAF >= max(1,N).
! 83: *
! 84: * IPIV (input) INTEGER array, dimension (N)
! 85: * Details of the interchanges and the block structure of D
! 86: * as determined by ZSYTRF.
! 87: *
! 88: * COLEQU (input) LOGICAL
! 89: * If .TRUE. then column equilibration was done to A before calling
! 90: * this routine. This is needed to compute the solution and error
! 91: * bounds correctly.
! 92: *
! 93: * C (input) DOUBLE PRECISION array, dimension (N)
! 94: * The column scale factors for A. If COLEQU = .FALSE., C
! 95: * is not accessed. If C is input, each element of C should be a power
! 96: * of the radix to ensure a reliable solution and error estimates.
! 97: * Scaling by powers of the radix does not cause rounding errors unless
! 98: * the result underflows or overflows. Rounding errors during scaling
! 99: * lead to refining with a matrix that is not equivalent to the
! 100: * input matrix, producing error estimates that may not be
! 101: * reliable.
! 102: *
! 103: * B (input) COMPLEX*16 array, dimension (LDB,NRHS)
! 104: * The right-hand-side matrix B.
! 105: *
! 106: * LDB (input) INTEGER
! 107: * The leading dimension of the array B. LDB >= max(1,N).
! 108: *
! 109: * Y (input/output) COMPLEX*16 array, dimension
! 110: * (LDY,NRHS)
! 111: * On entry, the solution matrix X, as computed by ZSYTRS.
! 112: * On exit, the improved solution matrix Y.
! 113: *
! 114: * LDY (input) INTEGER
! 115: * The leading dimension of the array Y. LDY >= max(1,N).
! 116: *
! 117: * BERR_OUT (output) DOUBLE PRECISION array, dimension (NRHS)
! 118: * On exit, BERR_OUT(j) contains the componentwise relative backward
! 119: * error for right-hand-side j from the formula
! 120: * max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 121: * where abs(Z) is the componentwise absolute value of the matrix
! 122: * or vector Z. This is computed by ZLA_LIN_BERR.
! 123: *
! 124: * N_NORMS (input) INTEGER
! 125: * Determines which error bounds to return (see ERR_BNDS_NORM
! 126: * and ERR_BNDS_COMP).
! 127: * If N_NORMS >= 1 return normwise error bounds.
! 128: * If N_NORMS >= 2 return componentwise error bounds.
! 129: *
! 130: * ERR_BNDS_NORM (input/output) DOUBLE PRECISION array, dimension
! 131: * (NRHS, N_ERR_BNDS)
! 132: * For each right-hand side, this array contains information about
! 133: * various error bounds and condition numbers corresponding to the
! 134: * normwise relative error, which is defined as follows:
! 135: *
! 136: * Normwise relative error in the ith solution vector:
! 137: * max_j (abs(XTRUE(j,i) - X(j,i)))
! 138: * ------------------------------
! 139: * max_j abs(X(j,i))
! 140: *
! 141: * The array is indexed by the type of error information as described
! 142: * below. There currently are up to three pieces of information
! 143: * returned.
! 144: *
! 145: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 146: * right-hand side.
! 147: *
! 148: * The second index in ERR_BNDS_NORM(:,err) contains the following
! 149: * three fields:
! 150: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 151: * reciprocal condition number is less than the threshold
! 152: * sqrt(n) * slamch('Epsilon').
! 153: *
! 154: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 155: * almost certainly within a factor of 10 of the true error
! 156: * so long as the next entry is greater than the threshold
! 157: * sqrt(n) * slamch('Epsilon'). This error bound should only
! 158: * be trusted if the previous boolean is true.
! 159: *
! 160: * err = 3 Reciprocal condition number: Estimated normwise
! 161: * reciprocal condition number. Compared with the threshold
! 162: * sqrt(n) * slamch('Epsilon') to determine if the error
! 163: * estimate is "guaranteed". These reciprocal condition
! 164: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 165: * appropriately scaled matrix Z.
! 166: * Let Z = S*A, where S scales each row by a power of the
! 167: * radix so all absolute row sums of Z are approximately 1.
! 168: *
! 169: * This subroutine is only responsible for setting the second field
! 170: * above.
! 171: * See Lapack Working Note 165 for further details and extra
! 172: * cautions.
! 173: *
! 174: * ERR_BNDS_COMP (input/output) DOUBLE PRECISION array, dimension
! 175: * (NRHS, N_ERR_BNDS)
! 176: * For each right-hand side, this array contains information about
! 177: * various error bounds and condition numbers corresponding to the
! 178: * componentwise relative error, which is defined as follows:
! 179: *
! 180: * Componentwise relative error in the ith solution vector:
! 181: * abs(XTRUE(j,i) - X(j,i))
! 182: * max_j ----------------------
! 183: * abs(X(j,i))
! 184: *
! 185: * The array is indexed by the right-hand side i (on which the
! 186: * componentwise relative error depends), and the type of error
! 187: * information as described below. There currently are up to three
! 188: * pieces of information returned for each right-hand side. If
! 189: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 190: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 191: * the first (:,N_ERR_BNDS) entries are returned.
! 192: *
! 193: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 194: * right-hand side.
! 195: *
! 196: * The second index in ERR_BNDS_COMP(:,err) contains the following
! 197: * three fields:
! 198: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 199: * reciprocal condition number is less than the threshold
! 200: * sqrt(n) * slamch('Epsilon').
! 201: *
! 202: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 203: * almost certainly within a factor of 10 of the true error
! 204: * so long as the next entry is greater than the threshold
! 205: * sqrt(n) * slamch('Epsilon'). This error bound should only
! 206: * be trusted if the previous boolean is true.
! 207: *
! 208: * err = 3 Reciprocal condition number: Estimated componentwise
! 209: * reciprocal condition number. Compared with the threshold
! 210: * sqrt(n) * slamch('Epsilon') to determine if the error
! 211: * estimate is "guaranteed". These reciprocal condition
! 212: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 213: * appropriately scaled matrix Z.
! 214: * Let Z = S*(A*diag(x)), where x is the solution for the
! 215: * current right-hand side and S scales each row of
! 216: * A*diag(x) by a power of the radix so all absolute row
! 217: * sums of Z are approximately 1.
! 218: *
! 219: * This subroutine is only responsible for setting the second field
! 220: * above.
! 221: * See Lapack Working Note 165 for further details and extra
! 222: * cautions.
! 223: *
! 224: * RES (input) COMPLEX*16 array, dimension (N)
! 225: * Workspace to hold the intermediate residual.
! 226: *
! 227: * AYB (input) DOUBLE PRECISION array, dimension (N)
! 228: * Workspace.
! 229: *
! 230: * DY (input) COMPLEX*16 array, dimension (N)
! 231: * Workspace to hold the intermediate solution.
! 232: *
! 233: * Y_TAIL (input) COMPLEX*16 array, dimension (N)
! 234: * Workspace to hold the trailing bits of the intermediate solution.
! 235: *
! 236: * RCOND (input) DOUBLE PRECISION
! 237: * Reciprocal scaled condition number. This is an estimate of the
! 238: * reciprocal Skeel condition number of the matrix A after
! 239: * equilibration (if done). If this is less than the machine
! 240: * precision (in particular, if it is zero), the matrix is singular
! 241: * to working precision. Note that the error may still be small even
! 242: * if this number is very small and the matrix appears ill-
! 243: * conditioned.
! 244: *
! 245: * ITHRESH (input) INTEGER
! 246: * The maximum number of residual computations allowed for
! 247: * refinement. The default is 10. For 'aggressive' set to 100 to
! 248: * permit convergence using approximate factorizations or
! 249: * factorizations other than LU. If the factorization uses a
! 250: * technique other than Gaussian elimination, the guarantees in
! 251: * ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.
! 252: *
! 253: * RTHRESH (input) DOUBLE PRECISION
! 254: * Determines when to stop refinement if the error estimate stops
! 255: * decreasing. Refinement will stop when the next solution no longer
! 256: * satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
! 257: * the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
! 258: * default value is 0.5. For 'aggressive' set to 0.9 to permit
! 259: * convergence on extremely ill-conditioned matrices. See LAWN 165
! 260: * for more details.
! 261: *
! 262: * DZ_UB (input) DOUBLE PRECISION
! 263: * Determines when to start considering componentwise convergence.
! 264: * Componentwise convergence is only considered after each component
! 265: * of the solution Y is stable, which we definte as the relative
! 266: * change in each component being less than DZ_UB. The default value
! 267: * is 0.25, requiring the first bit to be stable. See LAWN 165 for
! 268: * more details.
! 269: *
! 270: * IGNORE_CWISE (input) LOGICAL
! 271: * If .TRUE. then ignore componentwise convergence. Default value
! 272: * is .FALSE..
! 273: *
! 274: * INFO (output) INTEGER
! 275: * = 0: Successful exit.
! 276: * < 0: if INFO = -i, the ith argument to ZSYTRS had an illegal
! 277: * value
! 278: *
! 279: * =====================================================================
! 280: *
! 281: * .. Local Scalars ..
! 282: INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE,
! 283: $ Y_PREC_STATE
! 284: DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT,
! 285: $ DZRAT, PREVNORMDX, PREV_DZ_Z, DXRATMAX,
! 286: $ DZRATMAX, DX_X, DZ_Z, FINAL_DX_X, FINAL_DZ_Z,
! 287: $ EPS, HUGEVAL, INCR_THRESH
! 288: LOGICAL INCR_PREC
! 289: COMPLEX*16 ZDUM
! 290: * ..
! 291: * .. Parameters ..
! 292: INTEGER UNSTABLE_STATE, WORKING_STATE, CONV_STATE,
! 293: $ NOPROG_STATE, BASE_RESIDUAL, EXTRA_RESIDUAL,
! 294: $ EXTRA_Y
! 295: PARAMETER ( UNSTABLE_STATE = 0, WORKING_STATE = 1,
! 296: $ CONV_STATE = 2, NOPROG_STATE = 3 )
! 297: PARAMETER ( BASE_RESIDUAL = 0, EXTRA_RESIDUAL = 1,
! 298: $ EXTRA_Y = 2 )
! 299: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
! 300: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
! 301: INTEGER CMP_ERR_I, PIV_GROWTH_I
! 302: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
! 303: $ BERR_I = 3 )
! 304: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
! 305: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
! 306: $ PIV_GROWTH_I = 9 )
! 307: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
! 308: $ LA_LINRX_CWISE_I
! 309: PARAMETER ( LA_LINRX_ITREF_I = 1,
! 310: $ LA_LINRX_ITHRESH_I = 2 )
! 311: PARAMETER ( LA_LINRX_CWISE_I = 3 )
! 312: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
! 313: $ LA_LINRX_RCOND_I
! 314: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
! 315: PARAMETER ( LA_LINRX_RCOND_I = 3 )
! 316: * ..
! 317: * .. External Functions ..
! 318: LOGICAL LSAME
! 319: EXTERNAL ILAUPLO
! 320: INTEGER ILAUPLO
! 321: * ..
! 322: * .. External Subroutines ..
! 323: EXTERNAL ZAXPY, ZCOPY, ZSYTRS, ZSYMV, BLAS_ZSYMV_X,
! 324: $ BLAS_ZSYMV2_X, ZLA_SYAMV, ZLA_WWADDW,
! 325: $ ZLA_LIN_BERR
! 326: DOUBLE PRECISION DLAMCH
! 327: * ..
! 328: * .. Intrinsic Functions ..
! 329: INTRINSIC ABS, REAL, DIMAG, MAX, MIN
! 330: * ..
! 331: * .. Statement Functions ..
! 332: DOUBLE PRECISION CABS1
! 333: * ..
! 334: * .. Statement Function Definitions ..
! 335: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
! 336: * ..
! 337: * .. Executable Statements ..
! 338: *
! 339: IF ( INFO.NE.0 ) RETURN
! 340: EPS = DLAMCH( 'Epsilon' )
! 341: HUGEVAL = DLAMCH( 'Overflow' )
! 342: * Force HUGEVAL to Inf
! 343: HUGEVAL = HUGEVAL * HUGEVAL
! 344: * Using HUGEVAL may lead to spurious underflows.
! 345: INCR_THRESH = DBLE( N ) * EPS
! 346:
! 347: IF ( LSAME ( UPLO, 'L' ) ) THEN
! 348: UPLO2 = ILAUPLO( 'L' )
! 349: ELSE
! 350: UPLO2 = ILAUPLO( 'U' )
! 351: ENDIF
! 352:
! 353: DO J = 1, NRHS
! 354: Y_PREC_STATE = EXTRA_RESIDUAL
! 355: IF ( Y_PREC_STATE .EQ. EXTRA_Y ) THEN
! 356: DO I = 1, N
! 357: Y_TAIL( I ) = 0.0D+0
! 358: END DO
! 359: END IF
! 360:
! 361: DXRAT = 0.0D+0
! 362: DXRATMAX = 0.0D+0
! 363: DZRAT = 0.0D+0
! 364: DZRATMAX = 0.0D+0
! 365: FINAL_DX_X = HUGEVAL
! 366: FINAL_DZ_Z = HUGEVAL
! 367: PREVNORMDX = HUGEVAL
! 368: PREV_DZ_Z = HUGEVAL
! 369: DZ_Z = HUGEVAL
! 370: DX_X = HUGEVAL
! 371:
! 372: X_STATE = WORKING_STATE
! 373: Z_STATE = UNSTABLE_STATE
! 374: INCR_PREC = .FALSE.
! 375:
! 376: DO CNT = 1, ITHRESH
! 377: *
! 378: * Compute residual RES = B_s - op(A_s) * Y,
! 379: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 380: *
! 381: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
! 382: IF ( Y_PREC_STATE .EQ. BASE_RESIDUAL ) THEN
! 383: CALL ZSYMV( UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
! 384: $ DCMPLX(1.0D+0), RES, 1 )
! 385: ELSE IF ( Y_PREC_STATE .EQ. EXTRA_RESIDUAL ) THEN
! 386: CALL BLAS_ZSYMV_X( UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
! 387: $ Y( 1, J ), 1, DCMPLX(1.0D+0), RES, 1, PREC_TYPE )
! 388: ELSE
! 389: CALL BLAS_ZSYMV2_X(UPLO2, N, DCMPLX(-1.0D+0), A, LDA,
! 390: $ Y(1, J), Y_TAIL, 1, DCMPLX(1.0D+0), RES, 1,
! 391: $ PREC_TYPE)
! 392: END IF
! 393:
! 394: ! XXX: RES is no longer needed.
! 395: CALL ZCOPY( N, RES, 1, DY, 1 )
! 396: CALL ZSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
! 397: *
! 398: * Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT.
! 399: *
! 400: NORMX = 0.0D+0
! 401: NORMY = 0.0D+0
! 402: NORMDX = 0.0D+0
! 403: DZ_Z = 0.0D+0
! 404: YMIN = HUGEVAL
! 405:
! 406: DO I = 1, N
! 407: YK = CABS1( Y( I, J ) )
! 408: DYK = CABS1( DY( I ) )
! 409:
! 410: IF ( YK .NE. 0.0D+0 ) THEN
! 411: DZ_Z = MAX( DZ_Z, DYK / YK )
! 412: ELSE IF ( DYK .NE. 0.0D+0 ) THEN
! 413: DZ_Z = HUGEVAL
! 414: END IF
! 415:
! 416: YMIN = MIN( YMIN, YK )
! 417:
! 418: NORMY = MAX( NORMY, YK )
! 419:
! 420: IF ( COLEQU ) THEN
! 421: NORMX = MAX( NORMX, YK * C( I ) )
! 422: NORMDX = MAX( NORMDX, DYK * C( I ) )
! 423: ELSE
! 424: NORMX = NORMY
! 425: NORMDX = MAX( NORMDX, DYK )
! 426: END IF
! 427: END DO
! 428:
! 429: IF ( NORMX .NE. 0.0D+0 ) THEN
! 430: DX_X = NORMDX / NORMX
! 431: ELSE IF ( NORMDX .EQ. 0.0D+0 ) THEN
! 432: DX_X = 0.0D+0
! 433: ELSE
! 434: DX_X = HUGEVAL
! 435: END IF
! 436:
! 437: DXRAT = NORMDX / PREVNORMDX
! 438: DZRAT = DZ_Z / PREV_DZ_Z
! 439: *
! 440: * Check termination criteria.
! 441: *
! 442: IF ( YMIN*RCOND .LT. INCR_THRESH*NORMY
! 443: $ .AND. Y_PREC_STATE .LT. EXTRA_Y )
! 444: $ INCR_PREC = .TRUE.
! 445:
! 446: IF ( X_STATE .EQ. NOPROG_STATE .AND. DXRAT .LE. RTHRESH )
! 447: $ X_STATE = WORKING_STATE
! 448: IF ( X_STATE .EQ. WORKING_STATE ) THEN
! 449: IF ( DX_X .LE. EPS ) THEN
! 450: X_STATE = CONV_STATE
! 451: ELSE IF ( DXRAT .GT. RTHRESH ) THEN
! 452: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
! 453: INCR_PREC = .TRUE.
! 454: ELSE
! 455: X_STATE = NOPROG_STATE
! 456: END IF
! 457: ELSE
! 458: IF (DXRAT .GT. DXRATMAX) DXRATMAX = DXRAT
! 459: END IF
! 460: IF ( X_STATE .GT. WORKING_STATE ) FINAL_DX_X = DX_X
! 461: END IF
! 462:
! 463: IF ( Z_STATE .EQ. UNSTABLE_STATE .AND. DZ_Z .LE. DZ_UB )
! 464: $ Z_STATE = WORKING_STATE
! 465: IF ( Z_STATE .EQ. NOPROG_STATE .AND. DZRAT .LE. RTHRESH )
! 466: $ Z_STATE = WORKING_STATE
! 467: IF ( Z_STATE .EQ. WORKING_STATE ) THEN
! 468: IF ( DZ_Z .LE. EPS ) THEN
! 469: Z_STATE = CONV_STATE
! 470: ELSE IF ( DZ_Z .GT. DZ_UB ) THEN
! 471: Z_STATE = UNSTABLE_STATE
! 472: DZRATMAX = 0.0D+0
! 473: FINAL_DZ_Z = HUGEVAL
! 474: ELSE IF ( DZRAT .GT. RTHRESH ) THEN
! 475: IF ( Y_PREC_STATE .NE. EXTRA_Y ) THEN
! 476: INCR_PREC = .TRUE.
! 477: ELSE
! 478: Z_STATE = NOPROG_STATE
! 479: END IF
! 480: ELSE
! 481: IF ( DZRAT .GT. DZRATMAX ) DZRATMAX = DZRAT
! 482: END IF
! 483: IF ( Z_STATE .GT. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
! 484: END IF
! 485:
! 486: IF ( X_STATE.NE.WORKING_STATE.AND.
! 487: $ ( IGNORE_CWISE.OR.Z_STATE.NE.WORKING_STATE ) )
! 488: $ GOTO 666
! 489:
! 490: IF ( INCR_PREC ) THEN
! 491: INCR_PREC = .FALSE.
! 492: Y_PREC_STATE = Y_PREC_STATE + 1
! 493: DO I = 1, N
! 494: Y_TAIL( I ) = 0.0D+0
! 495: END DO
! 496: END IF
! 497:
! 498: PREVNORMDX = NORMDX
! 499: PREV_DZ_Z = DZ_Z
! 500: *
! 501: * Update soluton.
! 502: *
! 503: IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
! 504: CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )
! 505: ELSE
! 506: CALL ZLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
! 507: END IF
! 508:
! 509: END DO
! 510: * Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT.
! 511: 666 CONTINUE
! 512: *
! 513: * Set final_* when cnt hits ithresh.
! 514: *
! 515: IF ( X_STATE .EQ. WORKING_STATE ) FINAL_DX_X = DX_X
! 516: IF ( Z_STATE .EQ. WORKING_STATE ) FINAL_DZ_Z = DZ_Z
! 517: *
! 518: * Compute error bounds.
! 519: *
! 520: IF ( N_NORMS .GE. 1 ) THEN
! 521: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) =
! 522: $ FINAL_DX_X / (1 - DXRATMAX)
! 523: END IF
! 524: IF ( N_NORMS .GE. 2 ) THEN
! 525: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) =
! 526: $ FINAL_DZ_Z / (1 - DZRATMAX)
! 527: END IF
! 528: *
! 529: * Compute componentwise relative backward error from formula
! 530: * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
! 531: * where abs(Z) is the componentwise absolute value of the matrix
! 532: * or vector Z.
! 533: *
! 534: * Compute residual RES = B_s - op(A_s) * Y,
! 535: * op(A) = A, A**T, or A**H depending on TRANS (and type).
! 536: *
! 537: CALL ZCOPY( N, B( 1, J ), 1, RES, 1 )
! 538: CALL ZSYMV( UPLO, N, DCMPLX(-1.0D+0), A, LDA, Y(1,J), 1,
! 539: $ DCMPLX(1.0D+0), RES, 1 )
! 540:
! 541: DO I = 1, N
! 542: AYB( I ) = CABS1( B( I, J ) )
! 543: END DO
! 544: *
! 545: * Compute abs(op(A_s))*abs(Y) + abs(B_s).
! 546: *
! 547: CALL ZLA_SYAMV ( UPLO2, N, 1.0D+0,
! 548: $ A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
! 549:
! 550: CALL ZLA_LIN_BERR ( N, N, 1, RES, AYB, BERR_OUT( J ) )
! 551: *
! 552: * End of loop for each RHS.
! 553: *
! 554: END DO
! 555: *
! 556: RETURN
! 557: END
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