LAPACK 3.3.1
Linear Algebra PACKage

zposvxx.f

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00001       SUBROUTINE ZPOSVXX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED,
00002      $                    S, B, LDB, X, LDX, RCOND, RPVGRW, BERR,
00003      $                    N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP,
00004      $                    NPARAMS, PARAMS, WORK, RWORK, INFO )
00005 *
00006 *     -- LAPACK driver routine (version 3.2.2)                          --
00007 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00008 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00009 *     -- June 2010                                                    --
00010 *
00011 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00012 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00013 *
00014       IMPLICIT NONE
00015 *     ..
00016 *     .. Scalar Arguments ..
00017       CHARACTER          EQUED, FACT, UPLO
00018       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
00019      $                   N_ERR_BNDS
00020       DOUBLE PRECISION   RCOND, RPVGRW
00021 *     ..
00022 *     .. Array Arguments ..
00023       COMPLEX*16         A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
00024      $                   WORK( * ), X( LDX, * )
00025       DOUBLE PRECISION   S( * ), PARAMS( * ), BERR( * ), RWORK( * ),
00026      $                   ERR_BNDS_NORM( NRHS, * ),
00027      $                   ERR_BNDS_COMP( NRHS, * )
00028 *     ..
00029 *
00030 *     Purpose
00031 *     =======
00032 *
00033 *     ZPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
00034 *     to compute the solution to a complex*16 system of linear equations
00035 *     A * X = B, where A is an N-by-N symmetric positive definite matrix
00036 *     and X and B are N-by-NRHS matrices.
00037 *
00038 *     If requested, both normwise and maximum componentwise error bounds
00039 *     are returned. ZPOSVXX will return a solution with a tiny
00040 *     guaranteed error (O(eps) where eps is the working machine
00041 *     precision) unless the matrix is very ill-conditioned, in which
00042 *     case a warning is returned. Relevant condition numbers also are
00043 *     calculated and returned.
00044 *
00045 *     ZPOSVXX accepts user-provided factorizations and equilibration
00046 *     factors; see the definitions of the FACT and EQUED options.
00047 *     Solving with refinement and using a factorization from a previous
00048 *     ZPOSVXX call will also produce a solution with either O(eps)
00049 *     errors or warnings, but we cannot make that claim for general
00050 *     user-provided factorizations and equilibration factors if they
00051 *     differ from what ZPOSVXX would itself produce.
00052 *
00053 *     Description
00054 *     ===========
00055 *
00056 *     The following steps are performed:
00057 *
00058 *     1. If FACT = 'E', double precision scaling factors are computed to equilibrate
00059 *     the system:
00060 *
00061 *       diag(S)*A*diag(S)     *inv(diag(S))*X = diag(S)*B
00062 *
00063 *     Whether or not the system will be equilibrated depends on the
00064 *     scaling of the matrix A, but if equilibration is used, A is
00065 *     overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
00066 *
00067 *     2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
00068 *     factor the matrix A (after equilibration if FACT = 'E') as
00069 *        A = U**T* U,  if UPLO = 'U', or
00070 *        A = L * L**T,  if UPLO = 'L',
00071 *     where U is an upper triangular matrix and L is a lower triangular
00072 *     matrix.
00073 *
00074 *     3. If the leading i-by-i principal minor is not positive definite,
00075 *     then the routine returns with INFO = i. Otherwise, the factored
00076 *     form of A is used to estimate the condition number of the matrix
00077 *     A (see argument RCOND).  If the reciprocal of the condition number
00078 *     is less than machine precision, the routine still goes on to solve
00079 *     for X and compute error bounds as described below.
00080 *
00081 *     4. The system of equations is solved for X using the factored form
00082 *     of A.
00083 *
00084 *     5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
00085 *     the routine will use iterative refinement to try to get a small
00086 *     error and error bounds.  Refinement calculates the residual to at
00087 *     least twice the working precision.
00088 *
00089 *     6. If equilibration was used, the matrix X is premultiplied by
00090 *     diag(S) so that it solves the original system before
00091 *     equilibration.
00092 *
00093 *     Arguments
00094 *     =========
00095 *
00096 *     Some optional parameters are bundled in the PARAMS array.  These
00097 *     settings determine how refinement is performed, but often the
00098 *     defaults are acceptable.  If the defaults are acceptable, users
00099 *     can pass NPARAMS = 0 which prevents the source code from accessing
00100 *     the PARAMS argument.
00101 *
00102 *     FACT    (input) CHARACTER*1
00103 *     Specifies whether or not the factored form of the matrix A is
00104 *     supplied on entry, and if not, whether the matrix A should be
00105 *     equilibrated before it is factored.
00106 *       = 'F':  On entry, AF contains the factored form of A.
00107 *               If EQUED is not 'N', the matrix A has been
00108 *               equilibrated with scaling factors given by S.
00109 *               A and AF are not modified.
00110 *       = 'N':  The matrix A will be copied to AF and factored.
00111 *       = 'E':  The matrix A will be equilibrated if necessary, then
00112 *               copied to AF and factored.
00113 *
00114 *     UPLO    (input) CHARACTER*1
00115 *       = 'U':  Upper triangle of A is stored;
00116 *       = 'L':  Lower triangle of A is stored.
00117 *
00118 *     N       (input) INTEGER
00119 *     The number of linear equations, i.e., the order of the
00120 *     matrix A.  N >= 0.
00121 *
00122 *     NRHS    (input) INTEGER
00123 *     The number of right hand sides, i.e., the number of columns
00124 *     of the matrices B and X.  NRHS >= 0.
00125 *
00126 *     A       (input/output) COMPLEX*16 array, dimension (LDA,N)
00127 *     On entry, the symmetric matrix A, except if FACT = 'F' and EQUED =
00128 *     'Y', then A must contain the equilibrated matrix
00129 *     diag(S)*A*diag(S).  If UPLO = 'U', the leading N-by-N upper
00130 *     triangular part of A contains the upper triangular part of the
00131 *     matrix A, and the strictly lower triangular part of A is not
00132 *     referenced.  If UPLO = 'L', the leading N-by-N lower triangular
00133 *     part of A contains the lower triangular part of the matrix A, and
00134 *     the strictly upper triangular part of A is not referenced.  A is
00135 *     not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED =
00136 *     'N' on exit.
00137 *
00138 *     On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
00139 *     diag(S)*A*diag(S).
00140 *
00141 *     LDA     (input) INTEGER
00142 *     The leading dimension of the array A.  LDA >= max(1,N).
00143 *
00144 *     AF      (input or output) COMPLEX*16 array, dimension (LDAF,N)
00145 *     If FACT = 'F', then AF is an input argument and on entry
00146 *     contains the triangular factor U or L from the Cholesky
00147 *     factorization A = U**T*U or A = L*L**T, in the same storage
00148 *     format as A.  If EQUED .ne. 'N', then AF is the factored
00149 *     form of the equilibrated matrix diag(S)*A*diag(S).
00150 *
00151 *     If FACT = 'N', then AF is an output argument and on exit
00152 *     returns the triangular factor U or L from the Cholesky
00153 *     factorization A = U**T*U or A = L*L**T of the original
00154 *     matrix A.
00155 *
00156 *     If FACT = 'E', then AF is an output argument and on exit
00157 *     returns the triangular factor U or L from the Cholesky
00158 *     factorization A = U**T*U or A = L*L**T of the equilibrated
00159 *     matrix A (see the description of A for the form of the
00160 *     equilibrated matrix).
00161 *
00162 *     LDAF    (input) INTEGER
00163 *     The leading dimension of the array AF.  LDAF >= max(1,N).
00164 *
00165 *     EQUED   (input or output) CHARACTER*1
00166 *     Specifies the form of equilibration that was done.
00167 *       = 'N':  No equilibration (always true if FACT = 'N').
00168 *       = 'Y':  Both row and column equilibration, i.e., A has been
00169 *               replaced by diag(S) * A * diag(S).
00170 *     EQUED is an input argument if FACT = 'F'; otherwise, it is an
00171 *     output argument.
00172 *
00173 *     S       (input or output) DOUBLE PRECISION array, dimension (N)
00174 *     The row scale factors for A.  If EQUED = 'Y', A is multiplied on
00175 *     the left and right by diag(S).  S is an input argument if FACT =
00176 *     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
00177 *     = 'Y', each element of S must be positive.  If S is output, each
00178 *     element of S is a power of the radix. If S is input, each element
00179 *     of S should be a power of the radix to ensure a reliable solution
00180 *     and error estimates. Scaling by powers of the radix does not cause
00181 *     rounding errors unless the result underflows or overflows.
00182 *     Rounding errors during scaling lead to refining with a matrix that
00183 *     is not equivalent to the input matrix, producing error estimates
00184 *     that may not be reliable.
00185 *
00186 *     B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00187 *     On entry, the N-by-NRHS right hand side matrix B.
00188 *     On exit,
00189 *     if EQUED = 'N', B is not modified;
00190 *     if EQUED = 'Y', B is overwritten by diag(S)*B;
00191 *
00192 *     LDB     (input) INTEGER
00193 *     The leading dimension of the array B.  LDB >= max(1,N).
00194 *
00195 *     X       (output) COMPLEX*16 array, dimension (LDX,NRHS)
00196 *     If INFO = 0, the N-by-NRHS solution matrix X to the original
00197 *     system of equations.  Note that A and B are modified on exit if
00198 *     EQUED .ne. 'N', and the solution to the equilibrated system is
00199 *     inv(diag(S))*X.
00200 *
00201 *     LDX     (input) INTEGER
00202 *     The leading dimension of the array X.  LDX >= max(1,N).
00203 *
00204 *     RCOND   (output) DOUBLE PRECISION
00205 *     Reciprocal scaled condition number.  This is an estimate of the
00206 *     reciprocal Skeel condition number of the matrix A after
00207 *     equilibration (if done).  If this is less than the machine
00208 *     precision (in particular, if it is zero), the matrix is singular
00209 *     to working precision.  Note that the error may still be small even
00210 *     if this number is very small and the matrix appears ill-
00211 *     conditioned.
00212 *
00213 *     RPVGRW  (output) DOUBLE PRECISION
00214 *     Reciprocal pivot growth.  On exit, this contains the reciprocal
00215 *     pivot growth factor norm(A)/norm(U). The "max absolute element"
00216 *     norm is used.  If this is much less than 1, then the stability of
00217 *     the LU factorization of the (equilibrated) matrix A could be poor.
00218 *     This also means that the solution X, estimated condition numbers,
00219 *     and error bounds could be unreliable. If factorization fails with
00220 *     0<INFO<=N, then this contains the reciprocal pivot growth factor
00221 *     for the leading INFO columns of A.
00222 *
00223 *     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
00224 *     Componentwise relative backward error.  This is the
00225 *     componentwise relative backward error of each solution vector X(j)
00226 *     (i.e., the smallest relative change in any element of A or B that
00227 *     makes X(j) an exact solution).
00228 *
00229 *     N_ERR_BNDS (input) INTEGER
00230 *     Number of error bounds to return for each right hand side
00231 *     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
00232 *     ERR_BNDS_COMP below.
00233 *
00234 *     ERR_BNDS_NORM  (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
00235 *     For each right-hand side, this array contains information about
00236 *     various error bounds and condition numbers corresponding to the
00237 *     normwise relative error, which is defined as follows:
00238 *
00239 *     Normwise relative error in the ith solution vector:
00240 *             max_j (abs(XTRUE(j,i) - X(j,i)))
00241 *            ------------------------------
00242 *                  max_j abs(X(j,i))
00243 *
00244 *     The array is indexed by the type of error information as described
00245 *     below. There currently are up to three pieces of information
00246 *     returned.
00247 *
00248 *     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
00249 *     right-hand side.
00250 *
00251 *     The second index in ERR_BNDS_NORM(:,err) contains the following
00252 *     three fields:
00253 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00254 *              reciprocal condition number is less than the threshold
00255 *              sqrt(n) * dlamch('Epsilon').
00256 *
00257 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00258 *              almost certainly within a factor of 10 of the true error
00259 *              so long as the next entry is greater than the threshold
00260 *              sqrt(n) * dlamch('Epsilon'). This error bound should only
00261 *              be trusted if the previous boolean is true.
00262 *
00263 *     err = 3  Reciprocal condition number: Estimated normwise
00264 *              reciprocal condition number.  Compared with the threshold
00265 *              sqrt(n) * dlamch('Epsilon') to determine if the error
00266 *              estimate is "guaranteed". These reciprocal condition
00267 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00268 *              appropriately scaled matrix Z.
00269 *              Let Z = S*A, where S scales each row by a power of the
00270 *              radix so all absolute row sums of Z are approximately 1.
00271 *
00272 *     See Lapack Working Note 165 for further details and extra
00273 *     cautions.
00274 *
00275 *     ERR_BNDS_COMP  (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
00276 *     For each right-hand side, this array contains information about
00277 *     various error bounds and condition numbers corresponding to the
00278 *     componentwise relative error, which is defined as follows:
00279 *
00280 *     Componentwise relative error in the ith solution vector:
00281 *                    abs(XTRUE(j,i) - X(j,i))
00282 *             max_j ----------------------
00283 *                         abs(X(j,i))
00284 *
00285 *     The array is indexed by the right-hand side i (on which the
00286 *     componentwise relative error depends), and the type of error
00287 *     information as described below. There currently are up to three
00288 *     pieces of information returned for each right-hand side. If
00289 *     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
00290 *     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
00291 *     the first (:,N_ERR_BNDS) entries are returned.
00292 *
00293 *     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
00294 *     right-hand side.
00295 *
00296 *     The second index in ERR_BNDS_COMP(:,err) contains the following
00297 *     three fields:
00298 *     err = 1 "Trust/don't trust" boolean. Trust the answer if the
00299 *              reciprocal condition number is less than the threshold
00300 *              sqrt(n) * dlamch('Epsilon').
00301 *
00302 *     err = 2 "Guaranteed" error bound: The estimated forward error,
00303 *              almost certainly within a factor of 10 of the true error
00304 *              so long as the next entry is greater than the threshold
00305 *              sqrt(n) * dlamch('Epsilon'). This error bound should only
00306 *              be trusted if the previous boolean is true.
00307 *
00308 *     err = 3  Reciprocal condition number: Estimated componentwise
00309 *              reciprocal condition number.  Compared with the threshold
00310 *              sqrt(n) * dlamch('Epsilon') to determine if the error
00311 *              estimate is "guaranteed". These reciprocal condition
00312 *              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
00313 *              appropriately scaled matrix Z.
00314 *              Let Z = S*(A*diag(x)), where x is the solution for the
00315 *              current right-hand side and S scales each row of
00316 *              A*diag(x) by a power of the radix so all absolute row
00317 *              sums of Z are approximately 1.
00318 *
00319 *     See Lapack Working Note 165 for further details and extra
00320 *     cautions.
00321 *
00322 *     NPARAMS (input) INTEGER
00323 *     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
00324 *     PARAMS array is never referenced and default values are used.
00325 *
00326 *     PARAMS  (input / output) DOUBLE PRECISION array, dimension NPARAMS
00327 *     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
00328 *     that entry will be filled with default value used for that
00329 *     parameter.  Only positions up to NPARAMS are accessed; defaults
00330 *     are used for higher-numbered parameters.
00331 *
00332 *       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
00333 *            refinement or not.
00334 *         Default: 1.0D+0
00335 *            = 0.0 : No refinement is performed, and no error bounds are
00336 *                    computed.
00337 *            = 1.0 : Use the extra-precise refinement algorithm.
00338 *              (other values are reserved for future use)
00339 *
00340 *       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
00341 *            computations allowed for refinement.
00342 *         Default: 10
00343 *         Aggressive: Set to 100 to permit convergence using approximate
00344 *                     factorizations or factorizations other than LU. If
00345 *                     the factorization uses a technique other than
00346 *                     Gaussian elimination, the guarantees in
00347 *                     err_bnds_norm and err_bnds_comp may no longer be
00348 *                     trustworthy.
00349 *
00350 *       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
00351 *            will attempt to find a solution with small componentwise
00352 *            relative error in the double-precision algorithm.  Positive
00353 *            is true, 0.0 is false.
00354 *         Default: 1.0 (attempt componentwise convergence)
00355 *
00356 *     WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00357 *
00358 *     RWORK   (workspace) DOUBLE PRECISION array, dimension (2*N)
00359 *
00360 *     INFO    (output) INTEGER
00361 *       = 0:  Successful exit. The solution to every right-hand side is
00362 *         guaranteed.
00363 *       < 0:  If INFO = -i, the i-th argument had an illegal value
00364 *       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
00365 *         has been completed, but the factor U is exactly singular, so
00366 *         the solution and error bounds could not be computed. RCOND = 0
00367 *         is returned.
00368 *       = N+J: The solution corresponding to the Jth right-hand side is
00369 *         not guaranteed. The solutions corresponding to other right-
00370 *         hand sides K with K > J may not be guaranteed as well, but
00371 *         only the first such right-hand side is reported. If a small
00372 *         componentwise error is not requested (PARAMS(3) = 0.0) then
00373 *         the Jth right-hand side is the first with a normwise error
00374 *         bound that is not guaranteed (the smallest J such
00375 *         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
00376 *         the Jth right-hand side is the first with either a normwise or
00377 *         componentwise error bound that is not guaranteed (the smallest
00378 *         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
00379 *         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
00380 *         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
00381 *         about all of the right-hand sides check ERR_BNDS_NORM or
00382 *         ERR_BNDS_COMP.
00383 *
00384 *     ==================================================================
00385 *
00386 *     .. Parameters ..
00387       DOUBLE PRECISION   ZERO, ONE
00388       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00389       INTEGER            FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
00390       INTEGER            RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
00391       INTEGER            CMP_ERR_I, PIV_GROWTH_I
00392       PARAMETER          ( FINAL_NRM_ERR_I = 1, FINAL_CMP_ERR_I = 2,
00393      $                   BERR_I = 3 )
00394       PARAMETER          ( RCOND_I = 4, NRM_RCOND_I = 5, NRM_ERR_I = 6 )
00395       PARAMETER          ( CMP_RCOND_I = 7, CMP_ERR_I = 8,
00396      $                   PIV_GROWTH_I = 9 )
00397 *     ..
00398 *     .. Local Scalars ..
00399       LOGICAL            EQUIL, NOFACT, RCEQU
00400       INTEGER            INFEQU, J
00401       DOUBLE PRECISION   AMAX, BIGNUM, SMIN, SMAX, SCOND, SMLNUM
00402 *     ..
00403 *     .. External Functions ..
00404       EXTERNAL           LSAME, DLAMCH, ZLA_PORPVGRW
00405       LOGICAL            LSAME
00406       DOUBLE PRECISION   DLAMCH, ZLA_PORPVGRW
00407 *     ..
00408 *     .. External Subroutines ..
00409       EXTERNAL           ZPOCON, ZPOEQUB, ZPOTRF, ZPOTRS, ZLACPY,
00410      $                   ZLAQHE, XERBLA, ZLASCL2, ZPORFSX
00411 *     ..
00412 *     .. Intrinsic Functions ..
00413       INTRINSIC          MAX, MIN
00414 *     ..
00415 *     .. Executable Statements ..
00416 *
00417       INFO = 0
00418       NOFACT = LSAME( FACT, 'N' )
00419       EQUIL = LSAME( FACT, 'E' )
00420       SMLNUM = DLAMCH( 'Safe minimum' )
00421       BIGNUM = ONE / SMLNUM
00422       IF( NOFACT .OR. EQUIL ) THEN
00423          EQUED = 'N'
00424          RCEQU = .FALSE.
00425       ELSE
00426          RCEQU = LSAME( EQUED, 'Y' )
00427       ENDIF
00428 *
00429 *     Default is failure.  If an input parameter is wrong or
00430 *     factorization fails, make everything look horrible.  Only the
00431 *     pivot growth is set here, the rest is initialized in ZPORFSX.
00432 *
00433       RPVGRW = ZERO
00434 *
00435 *     Test the input parameters.  PARAMS is not tested until ZPORFSX.
00436 *
00437       IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND. .NOT.
00438      $     LSAME( FACT, 'F' ) ) THEN
00439          INFO = -1
00440       ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND.
00441      $         .NOT.LSAME( UPLO, 'L' ) ) THEN
00442          INFO = -2
00443       ELSE IF( N.LT.0 ) THEN
00444          INFO = -3
00445       ELSE IF( NRHS.LT.0 ) THEN
00446          INFO = -4
00447       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00448          INFO = -6
00449       ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN
00450          INFO = -8
00451       ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
00452      $        ( RCEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
00453          INFO = -9
00454       ELSE
00455          IF ( RCEQU ) THEN
00456             SMIN = BIGNUM
00457             SMAX = ZERO
00458             DO 10 J = 1, N
00459                SMIN = MIN( SMIN, S( J ) )
00460                SMAX = MAX( SMAX, S( J ) )
00461  10         CONTINUE
00462             IF( SMIN.LE.ZERO ) THEN
00463                INFO = -10
00464             ELSE IF( N.GT.0 ) THEN
00465                SCOND = MAX( SMIN, SMLNUM ) / MIN( SMAX, BIGNUM )
00466             ELSE
00467                SCOND = ONE
00468             END IF
00469          END IF
00470          IF( INFO.EQ.0 ) THEN
00471             IF( LDB.LT.MAX( 1, N ) ) THEN
00472                INFO = -12
00473             ELSE IF( LDX.LT.MAX( 1, N ) ) THEN
00474                INFO = -14
00475             END IF
00476          END IF
00477       END IF
00478 *
00479       IF( INFO.NE.0 ) THEN
00480          CALL XERBLA( 'ZPOSVXX', -INFO )
00481          RETURN
00482       END IF
00483 *
00484       IF( EQUIL ) THEN
00485 *
00486 *     Compute row and column scalings to equilibrate the matrix A.
00487 *
00488          CALL ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFEQU )
00489          IF( INFEQU.EQ.0 ) THEN
00490 *
00491 *     Equilibrate the matrix.
00492 *
00493             CALL ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
00494             RCEQU = LSAME( EQUED, 'Y' )
00495          END IF
00496       END IF
00497 *
00498 *     Scale the right-hand side.
00499 *
00500       IF( RCEQU ) CALL ZLASCL2( N, NRHS, S, B, LDB )
00501 *
00502       IF( NOFACT .OR. EQUIL ) THEN
00503 *
00504 *        Compute the Cholesky factorization of A.
00505 *
00506          CALL ZLACPY( UPLO, N, N, A, LDA, AF, LDAF )
00507          CALL ZPOTRF( UPLO, N, AF, LDAF, INFO )
00508 *
00509 *        Return if INFO is non-zero.
00510 *
00511          IF( INFO.GT.0 ) THEN
00512 *
00513 *           Pivot in column INFO is exactly 0
00514 *           Compute the reciprocal pivot growth factor of the
00515 *           leading rank-deficient INFO columns of A.
00516 *
00517             RPVGRW = ZLA_PORPVGRW( UPLO, N, A, LDA, AF, LDAF, RWORK )
00518             RETURN
00519          END IF
00520       END IF
00521 *
00522 *     Compute the reciprocal pivot growth factor RPVGRW.
00523 *
00524       RPVGRW = ZLA_PORPVGRW( UPLO, N, A, LDA, AF, LDAF, RWORK )
00525 *
00526 *     Compute the solution matrix X.
00527 *
00528       CALL ZLACPY( 'Full', N, NRHS, B, LDB, X, LDX )
00529       CALL ZPOTRS( UPLO, N, NRHS, AF, LDAF, X, LDX, INFO )
00530 *
00531 *     Use iterative refinement to improve the computed solution and
00532 *     compute error bounds and backward error estimates for it.
00533 *
00534       CALL ZPORFSX( UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF,
00535      $     S, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, ERR_BNDS_NORM,
00536      $     ERR_BNDS_COMP,  NPARAMS, PARAMS, WORK, RWORK, INFO )
00537 
00538 *
00539 *     Scale solutions.
00540 *
00541       IF ( RCEQU ) THEN
00542          CALL ZLASCL2( N, NRHS, S, X, LDX )
00543       END IF
00544 *
00545       RETURN
00546 *
00547 *     End of ZPOSVXX
00548 *
00549       END
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