Annotation of rpl/lapack/lapack/zporfsx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, S, B,
! 2: $ LDB, X, LDX, RCOND, BERR, N_ERR_BNDS,
! 3: $ ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS,
! 4: $ WORK, RWORK, INFO )
! 5: *
! 6: * -- LAPACK routine (version 3.2.2) --
! 7: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
! 8: * -- Jason Riedy of Univ. of California Berkeley. --
! 9: * -- June 2010 --
! 10: *
! 11: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 12: * -- Univ. of California Berkeley and NAG Ltd. --
! 13: *
! 14: IMPLICIT NONE
! 15: * ..
! 16: * .. Scalar Arguments ..
! 17: CHARACTER UPLO, EQUED
! 18: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
! 19: $ N_ERR_BNDS
! 20: DOUBLE PRECISION RCOND
! 21: * ..
! 22: * .. Array Arguments ..
! 23: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 24: $ X( LDX, * ), WORK( * )
! 25: DOUBLE PRECISION RWORK( * ), S( * ), PARAMS(*), BERR( * ),
! 26: $ ERR_BNDS_NORM( NRHS, * ),
! 27: $ ERR_BNDS_COMP( NRHS, * )
! 28: * ..
! 29: *
! 30: * Purpose
! 31: * =======
! 32: *
! 33: * ZPORFSX improves the computed solution to a system of linear
! 34: * equations when the coefficient matrix is symmetric positive
! 35: * definite, and provides error bounds and backward error estimates
! 36: * for the solution. In addition to normwise error bound, the code
! 37: * provides maximum componentwise error bound if possible. See
! 38: * comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the
! 39: * error bounds.
! 40: *
! 41: * The original system of linear equations may have been equilibrated
! 42: * before calling this routine, as described by arguments EQUED and S
! 43: * below. In this case, the solution and error bounds returned are
! 44: * for the original unequilibrated system.
! 45: *
! 46: * Arguments
! 47: * =========
! 48: *
! 49: * Some optional parameters are bundled in the PARAMS array. These
! 50: * settings determine how refinement is performed, but often the
! 51: * defaults are acceptable. If the defaults are acceptable, users
! 52: * can pass NPARAMS = 0 which prevents the source code from accessing
! 53: * the PARAMS argument.
! 54: *
! 55: * UPLO (input) CHARACTER*1
! 56: * = 'U': Upper triangle of A is stored;
! 57: * = 'L': Lower triangle of A is stored.
! 58: *
! 59: * EQUED (input) CHARACTER*1
! 60: * Specifies the form of equilibration that was done to A
! 61: * before calling this routine. This is needed to compute
! 62: * the solution and error bounds correctly.
! 63: * = 'N': No equilibration
! 64: * = 'Y': Both row and column equilibration, i.e., A has been
! 65: * replaced by diag(S) * A * diag(S).
! 66: * The right hand side B has been changed accordingly.
! 67: *
! 68: * N (input) INTEGER
! 69: * The order of the matrix A. N >= 0.
! 70: *
! 71: * NRHS (input) INTEGER
! 72: * The number of right hand sides, i.e., the number of columns
! 73: * of the matrices B and X. NRHS >= 0.
! 74: *
! 75: * A (input) COMPLEX*16 array, dimension (LDA,N)
! 76: * The symmetric matrix A. If UPLO = 'U', the leading N-by-N
! 77: * upper triangular part of A contains the upper triangular part
! 78: * of the matrix A, and the strictly lower triangular part of A
! 79: * is not referenced. If UPLO = 'L', the leading N-by-N lower
! 80: * triangular part of A contains the lower triangular part of
! 81: * the matrix A, and the strictly upper triangular part of A is
! 82: * not referenced.
! 83: *
! 84: * LDA (input) INTEGER
! 85: * The leading dimension of the array A. LDA >= max(1,N).
! 86: *
! 87: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
! 88: * The triangular factor U or L from the Cholesky factorization
! 89: * A = U**T*U or A = L*L**T, as computed by DPOTRF.
! 90: *
! 91: * LDAF (input) INTEGER
! 92: * The leading dimension of the array AF. LDAF >= max(1,N).
! 93: *
! 94: * S (input or output) DOUBLE PRECISION array, dimension (N)
! 95: * The row scale factors for A. If EQUED = 'Y', A is multiplied on
! 96: * the left and right by diag(S). S is an input argument if FACT =
! 97: * 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
! 98: * = 'Y', each element of S must be positive. If S is output, each
! 99: * element of S is a power of the radix. If S is input, each element
! 100: * of S should be a power of the radix to ensure a reliable solution
! 101: * and error estimates. Scaling by powers of the radix does not cause
! 102: * rounding errors unless the result underflows or overflows.
! 103: * Rounding errors during scaling lead to refining with a matrix that
! 104: * is not equivalent to the input matrix, producing error estimates
! 105: * that may not be reliable.
! 106: *
! 107: * B (input) COMPLEX*16 array, dimension (LDB,NRHS)
! 108: * The right hand side matrix B.
! 109: *
! 110: * LDB (input) INTEGER
! 111: * The leading dimension of the array B. LDB >= max(1,N).
! 112: *
! 113: * X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
! 114: * On entry, the solution matrix X, as computed by DGETRS.
! 115: * On exit, the improved solution matrix X.
! 116: *
! 117: * LDX (input) INTEGER
! 118: * The leading dimension of the array X. LDX >= max(1,N).
! 119: *
! 120: * RCOND (output) DOUBLE PRECISION
! 121: * Reciprocal scaled condition number. This is an estimate of the
! 122: * reciprocal Skeel condition number of the matrix A after
! 123: * equilibration (if done). If this is less than the machine
! 124: * precision (in particular, if it is zero), the matrix is singular
! 125: * to working precision. Note that the error may still be small even
! 126: * if this number is very small and the matrix appears ill-
! 127: * conditioned.
! 128: *
! 129: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 130: * Componentwise relative backward error. This is the
! 131: * componentwise relative backward error of each solution vector X(j)
! 132: * (i.e., the smallest relative change in any element of A or B that
! 133: * makes X(j) an exact solution).
! 134: *
! 135: * N_ERR_BNDS (input) INTEGER
! 136: * Number of error bounds to return for each right hand side
! 137: * and each type (normwise or componentwise). See ERR_BNDS_NORM and
! 138: * ERR_BNDS_COMP below.
! 139: *
! 140: * ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 141: * For each right-hand side, this array contains information about
! 142: * various error bounds and condition numbers corresponding to the
! 143: * normwise relative error, which is defined as follows:
! 144: *
! 145: * Normwise relative error in the ith solution vector:
! 146: * max_j (abs(XTRUE(j,i) - X(j,i)))
! 147: * ------------------------------
! 148: * max_j abs(X(j,i))
! 149: *
! 150: * The array is indexed by the type of error information as described
! 151: * below. There currently are up to three pieces of information
! 152: * returned.
! 153: *
! 154: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 155: * right-hand side.
! 156: *
! 157: * The second index in ERR_BNDS_NORM(:,err) contains the following
! 158: * three fields:
! 159: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 160: * reciprocal condition number is less than the threshold
! 161: * sqrt(n) * dlamch('Epsilon').
! 162: *
! 163: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 164: * almost certainly within a factor of 10 of the true error
! 165: * so long as the next entry is greater than the threshold
! 166: * sqrt(n) * dlamch('Epsilon'). This error bound should only
! 167: * be trusted if the previous boolean is true.
! 168: *
! 169: * err = 3 Reciprocal condition number: Estimated normwise
! 170: * reciprocal condition number. Compared with the threshold
! 171: * sqrt(n) * dlamch('Epsilon') to determine if the error
! 172: * estimate is "guaranteed". These reciprocal condition
! 173: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 174: * appropriately scaled matrix Z.
! 175: * Let Z = S*A, where S scales each row by a power of the
! 176: * radix so all absolute row sums of Z are approximately 1.
! 177: *
! 178: * See Lapack Working Note 165 for further details and extra
! 179: * cautions.
! 180: *
! 181: * ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 182: * For each right-hand side, this array contains information about
! 183: * various error bounds and condition numbers corresponding to the
! 184: * componentwise relative error, which is defined as follows:
! 185: *
! 186: * Componentwise relative error in the ith solution vector:
! 187: * abs(XTRUE(j,i) - X(j,i))
! 188: * max_j ----------------------
! 189: * abs(X(j,i))
! 190: *
! 191: * The array is indexed by the right-hand side i (on which the
! 192: * componentwise relative error depends), and the type of error
! 193: * information as described below. There currently are up to three
! 194: * pieces of information returned for each right-hand side. If
! 195: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 196: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 197: * the first (:,N_ERR_BNDS) entries are returned.
! 198: *
! 199: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 200: * right-hand side.
! 201: *
! 202: * The second index in ERR_BNDS_COMP(:,err) contains the following
! 203: * three fields:
! 204: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 205: * reciprocal condition number is less than the threshold
! 206: * sqrt(n) * dlamch('Epsilon').
! 207: *
! 208: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 209: * almost certainly within a factor of 10 of the true error
! 210: * so long as the next entry is greater than the threshold
! 211: * sqrt(n) * dlamch('Epsilon'). This error bound should only
! 212: * be trusted if the previous boolean is true.
! 213: *
! 214: * err = 3 Reciprocal condition number: Estimated componentwise
! 215: * reciprocal condition number. Compared with the threshold
! 216: * sqrt(n) * dlamch('Epsilon') to determine if the error
! 217: * estimate is "guaranteed". These reciprocal condition
! 218: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 219: * appropriately scaled matrix Z.
! 220: * Let Z = S*(A*diag(x)), where x is the solution for the
! 221: * current right-hand side and S scales each row of
! 222: * A*diag(x) by a power of the radix so all absolute row
! 223: * sums of Z are approximately 1.
! 224: *
! 225: * See Lapack Working Note 165 for further details and extra
! 226: * cautions.
! 227: *
! 228: * NPARAMS (input) INTEGER
! 229: * Specifies the number of parameters set in PARAMS. If .LE. 0, the
! 230: * PARAMS array is never referenced and default values are used.
! 231: *
! 232: * PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS
! 233: * Specifies algorithm parameters. If an entry is .LT. 0.0, then
! 234: * that entry will be filled with default value used for that
! 235: * parameter. Only positions up to NPARAMS are accessed; defaults
! 236: * are used for higher-numbered parameters.
! 237: *
! 238: * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
! 239: * refinement or not.
! 240: * Default: 1.0D+0
! 241: * = 0.0 : No refinement is performed, and no error bounds are
! 242: * computed.
! 243: * = 1.0 : Use the double-precision refinement algorithm,
! 244: * possibly with doubled-single computations if the
! 245: * compilation environment does not support DOUBLE
! 246: * PRECISION.
! 247: * (other values are reserved for future use)
! 248: *
! 249: * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
! 250: * computations allowed for refinement.
! 251: * Default: 10
! 252: * Aggressive: Set to 100 to permit convergence using approximate
! 253: * factorizations or factorizations other than LU. If
! 254: * the factorization uses a technique other than
! 255: * Gaussian elimination, the guarantees in
! 256: * err_bnds_norm and err_bnds_comp may no longer be
! 257: * trustworthy.
! 258: *
! 259: * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
! 260: * will attempt to find a solution with small componentwise
! 261: * relative error in the double-precision algorithm. Positive
! 262: * is true, 0.0 is false.
! 263: * Default: 1.0 (attempt componentwise convergence)
! 264: *
! 265: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 266: *
! 267: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 268: *
! 269: * INFO (output) INTEGER
! 270: * = 0: Successful exit. The solution to every right-hand side is
! 271: * guaranteed.
! 272: * < 0: If INFO = -i, the i-th argument had an illegal value
! 273: * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
! 274: * has been completed, but the factor U is exactly singular, so
! 275: * the solution and error bounds could not be computed. RCOND = 0
! 276: * is returned.
! 277: * = N+J: The solution corresponding to the Jth right-hand side is
! 278: * not guaranteed. The solutions corresponding to other right-
! 279: * hand sides K with K > J may not be guaranteed as well, but
! 280: * only the first such right-hand side is reported. If a small
! 281: * componentwise error is not requested (PARAMS(3) = 0.0) then
! 282: * the Jth right-hand side is the first with a normwise error
! 283: * bound that is not guaranteed (the smallest J such
! 284: * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
! 285: * the Jth right-hand side is the first with either a normwise or
! 286: * componentwise error bound that is not guaranteed (the smallest
! 287: * J such that either ERR_BNDS_NORM(J,1) = 0.0 or
! 288: * ERR_BNDS_COMP(J,1) = 0.0). See the definition of
! 289: * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
! 290: * about all of the right-hand sides check ERR_BNDS_NORM or
! 291: * ERR_BNDS_COMP.
! 292: *
! 293: * ==================================================================
! 294: *
! 295: * .. Parameters ..
! 296: DOUBLE PRECISION ZERO, ONE
! 297: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 298: DOUBLE PRECISION ITREF_DEFAULT, ITHRESH_DEFAULT
! 299: DOUBLE PRECISION COMPONENTWISE_DEFAULT, RTHRESH_DEFAULT
! 300: DOUBLE PRECISION DZTHRESH_DEFAULT
! 301: PARAMETER ( ITREF_DEFAULT = 1.0D+0 )
! 302: PARAMETER ( ITHRESH_DEFAULT = 10.0D+0 )
! 303: PARAMETER ( COMPONENTWISE_DEFAULT = 1.0D+0 )
! 304: PARAMETER ( RTHRESH_DEFAULT = 0.5D+0 )
! 305: PARAMETER ( DZTHRESH_DEFAULT = 0.25D+0 )
! 306: INTEGER LA_LINRX_ITREF_I, LA_LINRX_ITHRESH_I,
! 307: $ LA_LINRX_CWISE_I
! 308: PARAMETER ( LA_LINRX_ITREF_I = 1,
! 309: $ LA_LINRX_ITHRESH_I = 2 )
! 310: PARAMETER ( LA_LINRX_CWISE_I = 3 )
! 311: INTEGER LA_LINRX_TRUST_I, LA_LINRX_ERR_I,
! 312: $ LA_LINRX_RCOND_I
! 313: PARAMETER ( LA_LINRX_TRUST_I = 1, LA_LINRX_ERR_I = 2 )
! 314: PARAMETER ( LA_LINRX_RCOND_I = 3 )
! 315: * ..
! 316: * .. Local Scalars ..
! 317: CHARACTER(1) NORM
! 318: LOGICAL RCEQU
! 319: INTEGER J, PREC_TYPE, REF_TYPE
! 320: INTEGER N_NORMS
! 321: DOUBLE PRECISION ANORM, RCOND_TMP
! 322: DOUBLE PRECISION ILLRCOND_THRESH, ERR_LBND, CWISE_WRONG
! 323: LOGICAL IGNORE_CWISE
! 324: INTEGER ITHRESH
! 325: DOUBLE PRECISION RTHRESH, UNSTABLE_THRESH
! 326: * ..
! 327: * .. External Subroutines ..
! 328: EXTERNAL XERBLA, ZPOCON, ZLA_PORFSX_EXTENDED
! 329: * ..
! 330: * .. Intrinsic Functions ..
! 331: INTRINSIC MAX, SQRT, TRANSFER
! 332: * ..
! 333: * .. External Functions ..
! 334: EXTERNAL LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC
! 335: EXTERNAL DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
! 336: DOUBLE PRECISION DLAMCH, ZLANHE, ZLA_PORCOND_X, ZLA_PORCOND_C
! 337: LOGICAL LSAME
! 338: INTEGER BLAS_FPINFO_X
! 339: INTEGER ILATRANS, ILAPREC
! 340: * ..
! 341: * .. Executable Statements ..
! 342: *
! 343: * Check the input parameters.
! 344: *
! 345: INFO = 0
! 346: REF_TYPE = INT( ITREF_DEFAULT )
! 347: IF ( NPARAMS .GE. LA_LINRX_ITREF_I ) THEN
! 348: IF ( PARAMS( LA_LINRX_ITREF_I ) .LT. 0.0D+0 ) THEN
! 349: PARAMS( LA_LINRX_ITREF_I ) = ITREF_DEFAULT
! 350: ELSE
! 351: REF_TYPE = PARAMS( LA_LINRX_ITREF_I )
! 352: END IF
! 353: END IF
! 354: *
! 355: * Set default parameters.
! 356: *
! 357: ILLRCOND_THRESH = DBLE( N ) * DLAMCH( 'Epsilon' )
! 358: ITHRESH = INT( ITHRESH_DEFAULT )
! 359: RTHRESH = RTHRESH_DEFAULT
! 360: UNSTABLE_THRESH = DZTHRESH_DEFAULT
! 361: IGNORE_CWISE = COMPONENTWISE_DEFAULT .EQ. 0.0D+0
! 362: *
! 363: IF ( NPARAMS.GE.LA_LINRX_ITHRESH_I ) THEN
! 364: IF ( PARAMS(LA_LINRX_ITHRESH_I ).LT.0.0D+0 ) THEN
! 365: PARAMS( LA_LINRX_ITHRESH_I ) = ITHRESH
! 366: ELSE
! 367: ITHRESH = INT( PARAMS( LA_LINRX_ITHRESH_I ) )
! 368: END IF
! 369: END IF
! 370: IF ( NPARAMS.GE.LA_LINRX_CWISE_I ) THEN
! 371: IF ( PARAMS(LA_LINRX_CWISE_I ).LT.0.0D+0 ) THEN
! 372: IF ( IGNORE_CWISE ) THEN
! 373: PARAMS( LA_LINRX_CWISE_I ) = 0.0D+0
! 374: ELSE
! 375: PARAMS( LA_LINRX_CWISE_I ) = 1.0D+0
! 376: END IF
! 377: ELSE
! 378: IGNORE_CWISE = PARAMS( LA_LINRX_CWISE_I ) .EQ. 0.0D+0
! 379: END IF
! 380: END IF
! 381: IF ( REF_TYPE .EQ. 0 .OR. N_ERR_BNDS .EQ. 0 ) THEN
! 382: N_NORMS = 0
! 383: ELSE IF ( IGNORE_CWISE ) THEN
! 384: N_NORMS = 1
! 385: ELSE
! 386: N_NORMS = 2
! 387: END IF
! 388: *
! 389: RCEQU = LSAME( EQUED, 'Y' )
! 390: *
! 391: * Test input parameters.
! 392: *
! 393: IF (.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 394: INFO = -1
! 395: ELSE IF( .NOT.RCEQU .AND. .NOT.LSAME( EQUED, 'N' ) ) THEN
! 396: INFO = -2
! 397: ELSE IF( N.LT.0 ) THEN
! 398: INFO = -3
! 399: ELSE IF( NRHS.LT.0 ) THEN
! 400: INFO = -4
! 401: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 402: INFO = -6
! 403: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
! 404: INFO = -8
! 405: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 406: INFO = -11
! 407: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
! 408: INFO = -13
! 409: END IF
! 410: IF( INFO.NE.0 ) THEN
! 411: CALL XERBLA( 'ZPORFSX', -INFO )
! 412: RETURN
! 413: END IF
! 414: *
! 415: * Quick return if possible.
! 416: *
! 417: IF( N.EQ.0 .OR. NRHS.EQ.0 ) THEN
! 418: RCOND = 1.0D+0
! 419: DO J = 1, NRHS
! 420: BERR( J ) = 0.0D+0
! 421: IF ( N_ERR_BNDS .GE. 1 ) THEN
! 422: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 423: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 424: END IF
! 425: IF ( N_ERR_BNDS .GE. 2 ) THEN
! 426: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 0.0D+0
! 427: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 0.0D+0
! 428: END IF
! 429: IF ( N_ERR_BNDS .GE. 3 ) THEN
! 430: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 1.0D+0
! 431: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 1.0D+0
! 432: END IF
! 433: END DO
! 434: RETURN
! 435: END IF
! 436: *
! 437: * Default to failure.
! 438: *
! 439: RCOND = 0.0D+0
! 440: DO J = 1, NRHS
! 441: BERR( J ) = 1.0D+0
! 442: IF ( N_ERR_BNDS .GE. 1 ) THEN
! 443: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 444: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 445: END IF
! 446: IF ( N_ERR_BNDS .GE. 2 ) THEN
! 447: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
! 448: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
! 449: END IF
! 450: IF ( N_ERR_BNDS .GE. 3 ) THEN
! 451: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = 0.0D+0
! 452: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = 0.0D+0
! 453: END IF
! 454: END DO
! 455: *
! 456: * Compute the norm of A and the reciprocal of the condition
! 457: * number of A.
! 458: *
! 459: NORM = 'I'
! 460: ANORM = ZLANHE( NORM, UPLO, N, A, LDA, RWORK )
! 461: CALL ZPOCON( UPLO, N, AF, LDAF, ANORM, RCOND, WORK, RWORK,
! 462: $ INFO )
! 463: *
! 464: * Perform refinement on each right-hand side
! 465: *
! 466: IF ( REF_TYPE .NE. 0 ) THEN
! 467:
! 468: PREC_TYPE = ILAPREC( 'E' )
! 469:
! 470: CALL ZLA_PORFSX_EXTENDED( PREC_TYPE, UPLO, N,
! 471: $ NRHS, A, LDA, AF, LDAF, RCEQU, S, B,
! 472: $ LDB, X, LDX, BERR, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP,
! 473: $ WORK, RWORK, WORK(N+1),
! 474: $ TRANSFER (RWORK(1:2*N), (/ (ZERO, ZERO) /), N), RCOND,
! 475: $ ITHRESH, RTHRESH, UNSTABLE_THRESH, IGNORE_CWISE,
! 476: $ INFO )
! 477: END IF
! 478:
! 479: ERR_LBND = MAX( 10.0D+0, SQRT( DBLE( N ) ) ) * DLAMCH( 'Epsilon' )
! 480: IF ( N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 1 ) THEN
! 481: *
! 482: * Compute scaled normwise condition number cond(A*C).
! 483: *
! 484: IF ( RCEQU ) THEN
! 485: RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
! 486: $ S, .TRUE., INFO, WORK, RWORK )
! 487: ELSE
! 488: RCOND_TMP = ZLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF,
! 489: $ S, .FALSE., INFO, WORK, RWORK )
! 490: END IF
! 491: DO J = 1, NRHS
! 492: *
! 493: * Cap the error at 1.0.
! 494: *
! 495: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
! 496: $ .AND. ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
! 497: $ ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
! 498: *
! 499: * Threshold the error (see LAWN).
! 500: *
! 501: IF ( RCOND_TMP .LT. ILLRCOND_THRESH ) THEN
! 502: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = 1.0D+0
! 503: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 0.0D+0
! 504: IF ( INFO .LE. N ) INFO = N + J
! 505: ELSE IF ( ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) .LT. ERR_LBND )
! 506: $ THEN
! 507: ERR_BNDS_NORM( J, LA_LINRX_ERR_I ) = ERR_LBND
! 508: ERR_BNDS_NORM( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 509: END IF
! 510: *
! 511: * Save the condition number.
! 512: *
! 513: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
! 514: ERR_BNDS_NORM( J, LA_LINRX_RCOND_I ) = RCOND_TMP
! 515: END IF
! 516:
! 517: END DO
! 518: END IF
! 519:
! 520: IF (N_ERR_BNDS .GE. 1 .AND. N_NORMS .GE. 2) THEN
! 521: *
! 522: * Compute componentwise condition number cond(A*diag(Y(:,J))) for
! 523: * each right-hand side using the current solution as an estimate of
! 524: * the true solution. If the componentwise error estimate is too
! 525: * large, then the solution is a lousy estimate of truth and the
! 526: * estimated RCOND may be too optimistic. To avoid misleading users,
! 527: * the inverse condition number is set to 0.0 when the estimated
! 528: * cwise error is at least CWISE_WRONG.
! 529: *
! 530: CWISE_WRONG = SQRT( DLAMCH( 'Epsilon' ) )
! 531: DO J = 1, NRHS
! 532: IF (ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .LT. CWISE_WRONG )
! 533: $ THEN
! 534: RCOND_TMP = ZLA_PORCOND_X( UPLO, N, A, LDA, AF, LDAF,
! 535: $ X(1,J), INFO, WORK, RWORK )
! 536: ELSE
! 537: RCOND_TMP = 0.0D+0
! 538: END IF
! 539: *
! 540: * Cap the error at 1.0.
! 541: *
! 542: IF ( N_ERR_BNDS .GE. LA_LINRX_ERR_I
! 543: $ .AND. ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) .GT. 1.0D+0 )
! 544: $ ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
! 545: *
! 546: * Threshold the error (see LAWN).
! 547: *
! 548: IF (RCOND_TMP .LT. ILLRCOND_THRESH) THEN
! 549: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = 1.0D+0
! 550: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 0.0D+0
! 551: IF ( PARAMS( LA_LINRX_CWISE_I ) .EQ. 1.0D+0
! 552: $ .AND. INFO.LT.N + J ) INFO = N + J
! 553: ELSE IF ( ERR_BNDS_COMP( J, LA_LINRX_ERR_I )
! 554: $ .LT. ERR_LBND ) THEN
! 555: ERR_BNDS_COMP( J, LA_LINRX_ERR_I ) = ERR_LBND
! 556: ERR_BNDS_COMP( J, LA_LINRX_TRUST_I ) = 1.0D+0
! 557: END IF
! 558: *
! 559: * Save the condition number.
! 560: *
! 561: IF ( N_ERR_BNDS .GE. LA_LINRX_RCOND_I ) THEN
! 562: ERR_BNDS_COMP( J, LA_LINRX_RCOND_I ) = RCOND_TMP
! 563: END IF
! 564:
! 565: END DO
! 566: END IF
! 567: *
! 568: RETURN
! 569: *
! 570: * End of ZPORFSX
! 571: *
! 572: END
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