Annotation of rpl/lapack/lapack/zposvxx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
! 2: $ S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
! 3: $ N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP,
! 4: $ NPARAMS, PARAMS, WORK, RWORK, INFO )
! 5: *
! 6: * -- LAPACK driver 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 EQUED, FACT, UPLO
! 18: INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
! 19: $ N_ERR_BNDS
! 20: DOUBLE PRECISION RCOND, RPVGRW
! 21: * ..
! 22: * .. Array Arguments ..
! 23: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
! 24: $ WORK( * ), X( LDX, * )
! 25: DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
! 26: $ ERR_BNDS_NORM( NRHS, * ),
! 27: $ ERR_BNDS_COMP( NRHS, * )
! 28: * ..
! 29: *
! 30: * Purpose
! 31: * =======
! 32: *
! 33: * ZPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
! 34: * to compute the solution to a complex*16 system of linear equations
! 35: * A * X = B, where A is an N-by-N symmetric positive definite matrix
! 36: * and X and B are N-by-NRHS matrices.
! 37: *
! 38: * If requested, both normwise and maximum componentwise error bounds
! 39: * are returned. ZPOSVXX will return a solution with a tiny
! 40: * guaranteed error (O(eps) where eps is the working machine
! 41: * precision) unless the matrix is very ill-conditioned, in which
! 42: * case a warning is returned. Relevant condition numbers also are
! 43: * calculated and returned.
! 44: *
! 45: * ZPOSVXX accepts user-provided factorizations and equilibration
! 46: * factors; see the definitions of the FACT and EQUED options.
! 47: * Solving with refinement and using a factorization from a previous
! 48: * ZPOSVXX call will also produce a solution with either O(eps)
! 49: * errors or warnings, but we cannot make that claim for general
! 50: * user-provided factorizations and equilibration factors if they
! 51: * differ from what ZPOSVXX would itself produce.
! 52: *
! 53: * Description
! 54: * ===========
! 55: *
! 56: * The following steps are performed:
! 57: *
! 58: * 1. If FACT = 'E', double precision scaling factors are computed to equilibrate
! 59: * the system:
! 60: *
! 61: * diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
! 62: *
! 63: * Whether or not the system will be equilibrated depends on the
! 64: * scaling of the matrix A, but if equilibration is used, A is
! 65: * overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
! 66: *
! 67: * 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
! 68: * factor the matrix A (after equilibration if FACT = 'E') as
! 69: * A = U**T* U, if UPLO = 'U', or
! 70: * A = L * L**T, if UPLO = 'L',
! 71: * where U is an upper triangular matrix and L is a lower triangular
! 72: * matrix.
! 73: *
! 74: * 3. If the leading i-by-i principal minor is not positive definite,
! 75: * then the routine returns with INFO = i. Otherwise, the factored
! 76: * form of A is used to estimate the condition number of the matrix
! 77: * A (see argument RCOND). If the reciprocal of the condition number
! 78: * is less than machine precision, the routine still goes on to solve
! 79: * for X and compute error bounds as described below.
! 80: *
! 81: * 4. The system of equations is solved for X using the factored form
! 82: * of A.
! 83: *
! 84: * 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
! 85: * the routine will use iterative refinement to try to get a small
! 86: * error and error bounds. Refinement calculates the residual to at
! 87: * least twice the working precision.
! 88: *
! 89: * 6. If equilibration was used, the matrix X is premultiplied by
! 90: * diag(S) so that it solves the original system before
! 91: * equilibration.
! 92: *
! 93: * Arguments
! 94: * =========
! 95: *
! 96: * Some optional parameters are bundled in the PARAMS array. These
! 97: * settings determine how refinement is performed, but often the
! 98: * defaults are acceptable. If the defaults are acceptable, users
! 99: * can pass NPARAMS = 0 which prevents the source code from accessing
! 100: * the PARAMS argument.
! 101: *
! 102: * FACT (input) CHARACTER*1
! 103: * Specifies whether or not the factored form of the matrix A is
! 104: * supplied on entry, and if not, whether the matrix A should be
! 105: * equilibrated before it is factored.
! 106: * = 'F': On entry, AF contains the factored form of A.
! 107: * If EQUED is not 'N', the matrix A has been
! 108: * equilibrated with scaling factors given by S.
! 109: * A and AF are not modified.
! 110: * = 'N': The matrix A will be copied to AF and factored.
! 111: * = 'E': The matrix A will be equilibrated if necessary, then
! 112: * copied to AF and factored.
! 113: *
! 114: * UPLO (input) CHARACTER*1
! 115: * = 'U': Upper triangle of A is stored;
! 116: * = 'L': Lower triangle of A is stored.
! 117: *
! 118: * N (input) INTEGER
! 119: * The number of linear equations, i.e., the order of the
! 120: * matrix A. N >= 0.
! 121: *
! 122: * NRHS (input) INTEGER
! 123: * The number of right hand sides, i.e., the number of columns
! 124: * of the matrices B and X. NRHS >= 0.
! 125: *
! 126: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 127: * On entry, the symmetric matrix A, except if FACT = 'F' and EQUED =
! 128: * 'Y', then A must contain the equilibrated matrix
! 129: * diag(S)*A*diag(S). If UPLO = 'U', the leading N-by-N upper
! 130: * triangular part of A contains the upper triangular part of the
! 131: * matrix A, and the strictly lower triangular part of A is not
! 132: * referenced. If UPLO = 'L', the leading N-by-N lower triangular
! 133: * part of A contains the lower triangular part of the matrix A, and
! 134: * the strictly upper triangular part of A is not referenced. A is
! 135: * not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED =
! 136: * 'N' on exit.
! 137: *
! 138: * On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
! 139: * diag(S)*A*diag(S).
! 140: *
! 141: * LDA (input) INTEGER
! 142: * The leading dimension of the array A. LDA >= max(1,N).
! 143: *
! 144: * AF (input or output) COMPLEX*16 array, dimension (LDAF,N)
! 145: * If FACT = 'F', then AF is an input argument and on entry
! 146: * contains the triangular factor U or L from the Cholesky
! 147: * factorization A = U**T*U or A = L*L**T, in the same storage
! 148: * format as A. If EQUED .ne. 'N', then AF is the factored
! 149: * form of the equilibrated matrix diag(S)*A*diag(S).
! 150: *
! 151: * If FACT = 'N', then AF is an output argument and on exit
! 152: * returns the triangular factor U or L from the Cholesky
! 153: * factorization A = U**T*U or A = L*L**T of the original
! 154: * matrix A.
! 155: *
! 156: * If FACT = 'E', then AF is an output argument and on exit
! 157: * returns the triangular factor U or L from the Cholesky
! 158: * factorization A = U**T*U or A = L*L**T of the equilibrated
! 159: * matrix A (see the description of A for the form of the
! 160: * equilibrated matrix).
! 161: *
! 162: * LDAF (input) INTEGER
! 163: * The leading dimension of the array AF. LDAF >= max(1,N).
! 164: *
! 165: * EQUED (input or output) CHARACTER*1
! 166: * Specifies the form of equilibration that was done.
! 167: * = 'N': No equilibration (always true if FACT = 'N').
! 168: * = 'Y': Both row and column equilibration, i.e., A has been
! 169: * replaced by diag(S) * A * diag(S).
! 170: * EQUED is an input argument if FACT = 'F'; otherwise, it is an
! 171: * output argument.
! 172: *
! 173: * S (input or output) DOUBLE PRECISION array, dimension (N)
! 174: * The row scale factors for A. If EQUED = 'Y', A is multiplied on
! 175: * the left and right by diag(S). S is an input argument if FACT =
! 176: * 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED
! 177: * = 'Y', each element of S must be positive. If S is output, each
! 178: * element of S is a power of the radix. If S is input, each element
! 179: * of S should be a power of the radix to ensure a reliable solution
! 180: * and error estimates. Scaling by powers of the radix does not cause
! 181: * rounding errors unless the result underflows or overflows.
! 182: * Rounding errors during scaling lead to refining with a matrix that
! 183: * is not equivalent to the input matrix, producing error estimates
! 184: * that may not be reliable.
! 185: *
! 186: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 187: * On entry, the N-by-NRHS right hand side matrix B.
! 188: * On exit,
! 189: * if EQUED = 'N', B is not modified;
! 190: * if EQUED = 'Y', B is overwritten by diag(S)*B;
! 191: *
! 192: * LDB (input) INTEGER
! 193: * The leading dimension of the array B. LDB >= max(1,N).
! 194: *
! 195: * X (output) COMPLEX*16 array, dimension (LDX,NRHS)
! 196: * If INFO = 0, the N-by-NRHS solution matrix X to the original
! 197: * system of equations. Note that A and B are modified on exit if
! 198: * EQUED .ne. 'N', and the solution to the equilibrated system is
! 199: * inv(diag(S))*X.
! 200: *
! 201: * LDX (input) INTEGER
! 202: * The leading dimension of the array X. LDX >= max(1,N).
! 203: *
! 204: * RCOND (output) DOUBLE PRECISION
! 205: * Reciprocal scaled condition number. This is an estimate of the
! 206: * reciprocal Skeel condition number of the matrix A after
! 207: * equilibration (if done). If this is less than the machine
! 208: * precision (in particular, if it is zero), the matrix is singular
! 209: * to working precision. Note that the error may still be small even
! 210: * if this number is very small and the matrix appears ill-
! 211: * conditioned.
! 212: *
! 213: * RPVGRW (output) DOUBLE PRECISION
! 214: * Reciprocal pivot growth. On exit, this contains the reciprocal
! 215: * pivot growth factor norm(A)/norm(U). The "max absolute element"
! 216: * norm is used. If this is much less than 1, then the stability of
! 217: * the LU factorization of the (equilibrated) matrix A could be poor.
! 218: * This also means that the solution X, estimated condition numbers,
! 219: * and error bounds could be unreliable. If factorization fails with
! 220: * 0<INFO<=N, then this contains the reciprocal pivot growth factor
! 221: * for the leading INFO columns of A.
! 222: *
! 223: * BERR (output) DOUBLE PRECISION array, dimension (NRHS)
! 224: * Componentwise relative backward error. This is the
! 225: * componentwise relative backward error of each solution vector X(j)
! 226: * (i.e., the smallest relative change in any element of A or B that
! 227: * makes X(j) an exact solution).
! 228: *
! 229: * N_ERR_BNDS (input) INTEGER
! 230: * Number of error bounds to return for each right hand side
! 231: * and each type (normwise or componentwise). See ERR_BNDS_NORM and
! 232: * ERR_BNDS_COMP below.
! 233: *
! 234: * ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 235: * For each right-hand side, this array contains information about
! 236: * various error bounds and condition numbers corresponding to the
! 237: * normwise relative error, which is defined as follows:
! 238: *
! 239: * Normwise relative error in the ith solution vector:
! 240: * max_j (abs(XTRUE(j,i) - X(j,i)))
! 241: * ------------------------------
! 242: * max_j abs(X(j,i))
! 243: *
! 244: * The array is indexed by the type of error information as described
! 245: * below. There currently are up to three pieces of information
! 246: * returned.
! 247: *
! 248: * The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
! 249: * right-hand side.
! 250: *
! 251: * The second index in ERR_BNDS_NORM(:,err) contains the following
! 252: * three fields:
! 253: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 254: * reciprocal condition number is less than the threshold
! 255: * sqrt(n) * dlamch('Epsilon').
! 256: *
! 257: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 258: * almost certainly within a factor of 10 of the true error
! 259: * so long as the next entry is greater than the threshold
! 260: * sqrt(n) * dlamch('Epsilon'). This error bound should only
! 261: * be trusted if the previous boolean is true.
! 262: *
! 263: * err = 3 Reciprocal condition number: Estimated normwise
! 264: * reciprocal condition number. Compared with the threshold
! 265: * sqrt(n) * dlamch('Epsilon') to determine if the error
! 266: * estimate is "guaranteed". These reciprocal condition
! 267: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 268: * appropriately scaled matrix Z.
! 269: * Let Z = S*A, where S scales each row by a power of the
! 270: * radix so all absolute row sums of Z are approximately 1.
! 271: *
! 272: * See Lapack Working Note 165 for further details and extra
! 273: * cautions.
! 274: *
! 275: * ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
! 276: * For each right-hand side, this array contains information about
! 277: * various error bounds and condition numbers corresponding to the
! 278: * componentwise relative error, which is defined as follows:
! 279: *
! 280: * Componentwise relative error in the ith solution vector:
! 281: * abs(XTRUE(j,i) - X(j,i))
! 282: * max_j ----------------------
! 283: * abs(X(j,i))
! 284: *
! 285: * The array is indexed by the right-hand side i (on which the
! 286: * componentwise relative error depends), and the type of error
! 287: * information as described below. There currently are up to three
! 288: * pieces of information returned for each right-hand side. If
! 289: * componentwise accuracy is not requested (PARAMS(3) = 0.0), then
! 290: * ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most
! 291: * the first (:,N_ERR_BNDS) entries are returned.
! 292: *
! 293: * The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
! 294: * right-hand side.
! 295: *
! 296: * The second index in ERR_BNDS_COMP(:,err) contains the following
! 297: * three fields:
! 298: * err = 1 "Trust/don't trust" boolean. Trust the answer if the
! 299: * reciprocal condition number is less than the threshold
! 300: * sqrt(n) * dlamch('Epsilon').
! 301: *
! 302: * err = 2 "Guaranteed" error bound: The estimated forward error,
! 303: * almost certainly within a factor of 10 of the true error
! 304: * so long as the next entry is greater than the threshold
! 305: * sqrt(n) * dlamch('Epsilon'). This error bound should only
! 306: * be trusted if the previous boolean is true.
! 307: *
! 308: * err = 3 Reciprocal condition number: Estimated componentwise
! 309: * reciprocal condition number. Compared with the threshold
! 310: * sqrt(n) * dlamch('Epsilon') to determine if the error
! 311: * estimate is "guaranteed". These reciprocal condition
! 312: * numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
! 313: * appropriately scaled matrix Z.
! 314: * Let Z = S*(A*diag(x)), where x is the solution for the
! 315: * current right-hand side and S scales each row of
! 316: * A*diag(x) by a power of the radix so all absolute row
! 317: * sums of Z are approximately 1.
! 318: *
! 319: * See Lapack Working Note 165 for further details and extra
! 320: * cautions.
! 321: *
! 322: * NPARAMS (input) INTEGER
! 323: * Specifies the number of parameters set in PARAMS. If .LE. 0, the
! 324: * PARAMS array is never referenced and default values are used.
! 325: *
! 326: * PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS
! 327: * Specifies algorithm parameters. If an entry is .LT. 0.0, then
! 328: * that entry will be filled with default value used for that
! 329: * parameter. Only positions up to NPARAMS are accessed; defaults
! 330: * are used for higher-numbered parameters.
! 331: *
! 332: * PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
! 333: * refinement or not.
! 334: * Default: 1.0D+0
! 335: * = 0.0 : No refinement is performed, and no error bounds are
! 336: * computed.
! 337: * = 1.0 : Use the extra-precise refinement algorithm.
! 338: * (other values are reserved for future use)
! 339: *
! 340: * PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
! 341: * computations allowed for refinement.
! 342: * Default: 10
! 343: * Aggressive: Set to 100 to permit convergence using approximate
! 344: * factorizations or factorizations other than LU. If
! 345: * the factorization uses a technique other than
! 346: * Gaussian elimination, the guarantees in
! 347: * err_bnds_norm and err_bnds_comp may no longer be
! 348: * trustworthy.
! 349: *
! 350: * PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
! 351: * will attempt to find a solution with small componentwise
! 352: * relative error in the double-precision algorithm. Positive
! 353: * is true, 0.0 is false.
! 354: * Default: 1.0 (attempt componentwise convergence)
! 355: *
! 356: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
! 357: *
! 358: * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 359: *
! 360: * INFO (output) INTEGER
! 361: * = 0: Successful exit. The solution to every right-hand side is
! 362: * guaranteed.
! 363: * < 0: If INFO = -i, the i-th argument had an illegal value
! 364: * > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization
! 365: * has been completed, but the factor U is exactly singular, so
! 366: * the solution and error bounds could not be computed. RCOND = 0
! 367: * is returned.
! 368: * = N+J: The solution corresponding to the Jth right-hand side is
! 369: * not guaranteed. The solutions corresponding to other right-
! 370: * hand sides K with K > J may not be guaranteed as well, but
! 371: * only the first such right-hand side is reported. If a small
! 372: * componentwise error is not requested (PARAMS(3) = 0.0) then
! 373: * the Jth right-hand side is the first with a normwise error
! 374: * bound that is not guaranteed (the smallest J such
! 375: * that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
! 376: * the Jth right-hand side is the first with either a normwise or
! 377: * componentwise error bound that is not guaranteed (the smallest
! 378: * J such that either ERR_BNDS_NORM(J,1) = 0.0 or
! 379: * ERR_BNDS_COMP(J,1) = 0.0). See the definition of
! 380: * ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
! 381: * about all of the right-hand sides check ERR_BNDS_NORM or
! 382: * ERR_BNDS_COMP.
! 383: *
! 384: * ==================================================================
! 385: *
! 386: * .. Parameters ..
! 387: DOUBLE PRECISION ZERO, ONE
! 388: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 389: INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
! 390: INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
! 391: INTEGER CMP_ERR_I, PIV_GROWTH_I
! 392: PARAMETER ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
! 393: $ BERR_I = 3 )
! 394: PARAMETER ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
! 395: PARAMETER ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
! 396: $ PIV_GROWTH_I = 9 )
! 397: * ..
! 398: * .. Local Scalars ..
! 399: LOGICAL EQUIL, NOFACT, RCEQU
! 400: INTEGER INFEQU, J
! 401: DOUBLE PRECISION AMAX, BIGNUM, SMIN, SMAX, SCOND, SMLNUM
! 402: * ..
! 403: * .. External Functions ..
! 404: EXTERNAL LSAME, DLAMCH, ZLA_PORPVGRW
! 405: LOGICAL LSAME
! 406: DOUBLE PRECISION DLAMCH, ZLA_PORPVGRW
! 407: * ..
! 408: * .. External Subroutines ..
! 409: EXTERNAL ZPOCON, ZPOEQUB, ZPOTRF, ZPOTRS, ZLACPY,
! 410: $ ZLAQHE, XERBLA, ZLASCL2, ZPORFSX
! 411: * ..
! 412: * .. Intrinsic Functions ..
! 413: INTRINSIC MAX, MIN
! 414: * ..
! 415: * .. Executable Statements ..
! 416: *
! 417: INFO = 0
! 418: NOFACT = LSAME( FACT, 'N' )
! 419: EQUIL = LSAME( FACT, 'E' )
! 420: SMLNUM = DLAMCH( 'Safe minimum' )
! 421: BIGNUM = ONE / SMLNUM
! 422: IF( NOFACT .OR. EQUIL ) THEN
! 423: EQUED = 'N'
! 424: RCEQU = .FALSE.
! 425: ELSE
! 426: RCEQU = LSAME( EQUED, 'Y' )
! 427: ENDIF
! 428: *
! 429: * Default is failure. If an input parameter is wrong or
! 430: * factorization fails, make everything look horrible. Only the
! 431: * pivot growth is set here, the rest is initialized in ZPORFSX.
! 432: *
! 433: RPVGRW = ZERO
! 434: *
! 435: * Test the input parameters. PARAMS is not tested until ZPORFSX.
! 436: *
! 437: IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.
! 438: $ LSAME( FACT, 'F' ) ) THEN
! 439: INFO = -1
! 440: ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND.
! 441: $ .NOT.LSAME( UPLO, 'L' ) ) THEN
! 442: INFO = -2
! 443: ELSE IF( N.LT.0 ) THEN
! 444: INFO = -3
! 445: ELSE IF( NRHS.LT.0 ) THEN
! 446: INFO = -4
! 447: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 448: INFO = -6
! 449: ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
! 450: INFO = -8
! 451: ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
! 452: $ ( RCEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
! 453: INFO = -9
! 454: ELSE
! 455: IF ( RCEQU ) THEN
! 456: SMIN = BIGNUM
! 457: SMAX = ZERO
! 458: DO 10 J = 1, N
! 459: SMIN = MIN( SMIN, S( J ) )
! 460: SMAX = MAX( SMAX, S( J ) )
! 461: 10 CONTINUE
! 462: IF( SMIN.LE.ZERO ) THEN
! 463: INFO = -10
! 464: ELSE IF( N.GT.0 ) THEN
! 465: SCOND = MAX( SMIN, SMLNUM ) / MIN( SMAX, BIGNUM )
! 466: ELSE
! 467: SCOND = ONE
! 468: END IF
! 469: END IF
! 470: IF( INFO.EQ.0 ) THEN
! 471: IF( LDB.LT.MAX( 1, N ) ) THEN
! 472: INFO = -12
! 473: ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
! 474: INFO = -14
! 475: END IF
! 476: END IF
! 477: END IF
! 478: *
! 479: IF( INFO.NE.0 ) THEN
! 480: CALL XERBLA( 'ZPOSVXX', -INFO )
! 481: RETURN
! 482: END IF
! 483: *
! 484: IF( EQUIL ) THEN
! 485: *
! 486: * Compute row and column scalings to equilibrate the matrix A.
! 487: *
! 488: CALL ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFEQU )
! 489: IF( INFEQU.EQ.0 ) THEN
! 490: *
! 491: * Equilibrate the matrix.
! 492: *
! 493: CALL ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
! 494: RCEQU = LSAME( EQUED, 'Y' )
! 495: END IF
! 496: END IF
! 497: *
! 498: * Scale the right-hand side.
! 499: *
! 500: IF( RCEQU ) CALL ZLASCL2( N, NRHS, S, B, LDB )
! 501: *
! 502: IF( NOFACT .OR. EQUIL ) THEN
! 503: *
! 504: * Compute the Cholesky factorization of A.
! 505: *
! 506: CALL ZLACPY( UPLO, N, N, A, LDA, AF, LDAF )
! 507: CALL ZPOTRF( UPLO, N, AF, LDAF, INFO )
! 508: *
! 509: * Return if INFO is non-zero.
! 510: *
! 511: IF( INFO.GT.0 ) THEN
! 512: *
! 513: * Pivot in column INFO is exactly 0
! 514: * Compute the reciprocal pivot growth factor of the
! 515: * leading rank-deficient INFO columns of A.
! 516: *
! 517: RPVGRW = ZLA_PORPVGRW( UPLO, N, A, LDA, AF, LDAF, RWORK )
! 518: RETURN
! 519: END IF
! 520: END IF
! 521: *
! 522: * Compute the reciprocal pivot growth factor RPVGRW.
! 523: *
! 524: RPVGRW = ZLA_PORPVGRW( UPLO, N, A, LDA, AF, LDAF, RWORK )
! 525: *
! 526: * Compute the solution matrix X.
! 527: *
! 528: CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
! 529: CALL ZPOTRS( UPLO, N, NRHS, AF, LDAF, X, LDX, INFO )
! 530: *
! 531: * Use iterative refinement to improve the computed solution and
! 532: * compute error bounds and backward error estimates for it.
! 533: *
! 534: CALL ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF,
! 535: $ S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, ERR_BNDS_NORM,
! 536: $ ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK, INFO )
! 537:
! 538: *
! 539: * Scale solutions.
! 540: *
! 541: IF ( RCEQU ) THEN
! 542: CALL ZLASCL2( N, NRHS, S, X, LDX )
! 543: END IF
! 544: *
! 545: RETURN
! 546: *
! 547: * End of ZPOSVXX
! 548: *
! 549: END
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