00001 /* cgesvxx.f -- translated by f2c (version 20061008). 00002 You must link the resulting object file with libf2c: 00003 on Microsoft Windows system, link with libf2c.lib; 00004 on Linux or Unix systems, link with .../path/to/libf2c.a -lm 00005 or, if you install libf2c.a in a standard place, with -lf2c -lm 00006 -- in that order, at the end of the command line, as in 00007 cc *.o -lf2c -lm 00008 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., 00009 00010 http://www.netlib.org/f2c/libf2c.zip 00011 */ 00012 00013 #include "f2c.h" 00014 #include "blaswrap.h" 00015 00016 /* Subroutine */ int cgesvxx_(char *fact, char *trans, integer *n, integer * 00017 nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * 00018 ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, 00019 complex *x, integer *ldx, real *rcond, real *rpvgrw, real *berr, 00020 integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, 00021 integer *nparams, real *params, complex *work, real *rwork, integer * 00022 info) 00023 { 00024 /* System generated locals */ 00025 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00026 x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00027 err_bnds_comp_dim1, err_bnds_comp_offset, i__1; 00028 real r__1, r__2; 00029 00030 /* Local variables */ 00031 integer j; 00032 extern doublereal cla_rpvgrw__(integer *, integer *, complex *, integer *, 00033 complex *, integer *); 00034 real amax; 00035 extern logical lsame_(char *, char *); 00036 real rcmin, rcmax; 00037 logical equil; 00038 extern /* Subroutine */ int claqge_(integer *, integer *, complex *, 00039 integer *, real *, real *, real *, real *, real *, char *) 00040 ; 00041 real colcnd; 00042 extern doublereal slamch_(char *); 00043 logical nofact; 00044 extern /* Subroutine */ int cgetrf_(integer *, integer *, complex *, 00045 integer *, integer *, integer *), clacpy_(char *, integer *, 00046 integer *, complex *, integer *, complex *, integer *), 00047 xerbla_(char *, integer *); 00048 real bignum; 00049 integer infequ; 00050 logical colequ; 00051 extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex 00052 *, integer *, integer *, complex *, integer *, integer *); 00053 real rowcnd; 00054 logical notran; 00055 real smlnum; 00056 logical rowequ; 00057 extern /* Subroutine */ int clascl2_(integer *, integer *, real *, 00058 complex *, integer *), cgeequb_(integer *, integer *, complex *, 00059 integer *, real *, real *, real *, real *, real *, integer *), 00060 cgerfsx_(char *, char *, integer *, integer *, complex *, integer 00061 *, complex *, integer *, integer *, real *, real *, complex *, 00062 integer *, complex *, integer *, real *, real *, integer *, real * 00063 , real *, integer *, real *, complex *, real *, integer *); 00064 00065 00066 /* -- LAPACK driver routine (version 3.2) -- */ 00067 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00068 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00069 /* -- November 2008 -- */ 00070 00071 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00072 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00073 00074 /* .. */ 00075 /* .. Scalar Arguments .. */ 00076 /* .. */ 00077 /* .. Array Arguments .. */ 00078 /* .. */ 00079 00080 /* Purpose */ 00081 /* ======= */ 00082 00083 /* CGESVXX uses the LU factorization to compute the solution to a */ 00084 /* complex system of linear equations A * X = B, where A is an */ 00085 /* N-by-N matrix and X and B are N-by-NRHS matrices. */ 00086 00087 /* If requested, both normwise and maximum componentwise error bounds */ 00088 /* are returned. CGESVXX will return a solution with a tiny */ 00089 /* guaranteed error (O(eps) where eps is the working machine */ 00090 /* precision) unless the matrix is very ill-conditioned, in which */ 00091 /* case a warning is returned. Relevant condition numbers also are */ 00092 /* calculated and returned. */ 00093 00094 /* CGESVXX accepts user-provided factorizations and equilibration */ 00095 /* factors; see the definitions of the FACT and EQUED options. */ 00096 /* Solving with refinement and using a factorization from a previous */ 00097 /* CGESVXX call will also produce a solution with either O(eps) */ 00098 /* errors or warnings, but we cannot make that claim for general */ 00099 /* user-provided factorizations and equilibration factors if they */ 00100 /* differ from what CGESVXX would itself produce. */ 00101 00102 /* Description */ 00103 /* =========== */ 00104 00105 /* The following steps are performed: */ 00106 00107 /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ 00108 /* the system: */ 00109 00110 /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ 00111 /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ 00112 /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ 00113 00114 /* Whether or not the system will be equilibrated depends on the */ 00115 /* scaling of the matrix A, but if equilibration is used, A is */ 00116 /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ 00117 /* or diag(C)*B (if TRANS = 'T' or 'C'). */ 00118 00119 /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */ 00120 /* the matrix A (after equilibration if FACT = 'E') as */ 00121 00122 /* A = P * L * U, */ 00123 00124 /* where P is a permutation matrix, L is a unit lower triangular */ 00125 /* matrix, and U is upper triangular. */ 00126 00127 /* 3. If some U(i,i)=0, so that U is exactly singular, then the */ 00128 /* routine returns with INFO = i. Otherwise, the factored form of A */ 00129 /* is used to estimate the condition number of the matrix A (see */ 00130 /* argument RCOND). If the reciprocal of the condition number is less */ 00131 /* than machine precision, the routine still goes on to solve for X */ 00132 /* and compute error bounds as described below. */ 00133 00134 /* 4. The system of equations is solved for X using the factored form */ 00135 /* of A. */ 00136 00137 /* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */ 00138 /* the routine will use iterative refinement to try to get a small */ 00139 /* error and error bounds. Refinement calculates the residual to at */ 00140 /* least twice the working precision. */ 00141 00142 /* 6. If equilibration was used, the matrix X is premultiplied by */ 00143 /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ 00144 /* that it solves the original system before equilibration. */ 00145 00146 /* Arguments */ 00147 /* ========= */ 00148 00149 /* Some optional parameters are bundled in the PARAMS array. These */ 00150 /* settings determine how refinement is performed, but often the */ 00151 /* defaults are acceptable. If the defaults are acceptable, users */ 00152 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00153 /* the PARAMS argument. */ 00154 00155 /* FACT (input) CHARACTER*1 */ 00156 /* Specifies whether or not the factored form of the matrix A is */ 00157 /* supplied on entry, and if not, whether the matrix A should be */ 00158 /* equilibrated before it is factored. */ 00159 /* = 'F': On entry, AF and IPIV contain the factored form of A. */ 00160 /* If EQUED is not 'N', the matrix A has been */ 00161 /* equilibrated with scaling factors given by R and C. */ 00162 /* A, AF, and IPIV are not modified. */ 00163 /* = 'N': The matrix A will be copied to AF and factored. */ 00164 /* = 'E': The matrix A will be equilibrated if necessary, then */ 00165 /* copied to AF and factored. */ 00166 00167 /* TRANS (input) CHARACTER*1 */ 00168 /* Specifies the form of the system of equations: */ 00169 /* = 'N': A * X = B (No transpose) */ 00170 /* = 'T': A**T * X = B (Transpose) */ 00171 /* = 'C': A**H * X = B (Conjugate Transpose) */ 00172 00173 /* N (input) INTEGER */ 00174 /* The number of linear equations, i.e., the order of the */ 00175 /* matrix A. N >= 0. */ 00176 00177 /* NRHS (input) INTEGER */ 00178 /* The number of right hand sides, i.e., the number of columns */ 00179 /* of the matrices B and X. NRHS >= 0. */ 00180 00181 /* A (input/output) COMPLEX array, dimension (LDA,N) */ 00182 /* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */ 00183 /* not 'N', then A must have been equilibrated by the scaling */ 00184 /* factors in R and/or C. A is not modified if FACT = 'F' or */ 00185 /* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ 00186 00187 /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ 00188 /* EQUED = 'R': A := diag(R) * A */ 00189 /* EQUED = 'C': A := A * diag(C) */ 00190 /* EQUED = 'B': A := diag(R) * A * diag(C). */ 00191 00192 /* LDA (input) INTEGER */ 00193 /* The leading dimension of the array A. LDA >= max(1,N). */ 00194 00195 /* AF (input or output) COMPLEX array, dimension (LDAF,N) */ 00196 /* If FACT = 'F', then AF is an input argument and on entry */ 00197 /* contains the factors L and U from the factorization */ 00198 /* A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then */ 00199 /* AF is the factored form of the equilibrated matrix A. */ 00200 00201 /* If FACT = 'N', then AF is an output argument and on exit */ 00202 /* returns the factors L and U from the factorization A = P*L*U */ 00203 /* of the original matrix A. */ 00204 00205 /* If FACT = 'E', then AF is an output argument and on exit */ 00206 /* returns the factors L and U from the factorization A = P*L*U */ 00207 /* of the equilibrated matrix A (see the description of A for */ 00208 /* the form of the equilibrated matrix). */ 00209 00210 /* LDAF (input) INTEGER */ 00211 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00212 00213 /* IPIV (input or output) INTEGER array, dimension (N) */ 00214 /* If FACT = 'F', then IPIV is an input argument and on entry */ 00215 /* contains the pivot indices from the factorization A = P*L*U */ 00216 /* as computed by CGETRF; row i of the matrix was interchanged */ 00217 /* with row IPIV(i). */ 00218 00219 /* If FACT = 'N', then IPIV is an output argument and on exit */ 00220 /* contains the pivot indices from the factorization A = P*L*U */ 00221 /* of the original matrix A. */ 00222 00223 /* If FACT = 'E', then IPIV is an output argument and on exit */ 00224 /* contains the pivot indices from the factorization A = P*L*U */ 00225 /* of the equilibrated matrix A. */ 00226 00227 /* EQUED (input or output) CHARACTER*1 */ 00228 /* Specifies the form of equilibration that was done. */ 00229 /* = 'N': No equilibration (always true if FACT = 'N'). */ 00230 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00231 /* diag(R). */ 00232 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00233 /* by diag(C). */ 00234 /* = 'B': Both row and column equilibration, i.e., A has been */ 00235 /* replaced by diag(R) * A * diag(C). */ 00236 /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ 00237 /* output argument. */ 00238 00239 /* R (input or output) REAL array, dimension (N) */ 00240 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00241 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00242 /* is not accessed. R is an input argument if FACT = 'F'; */ 00243 /* otherwise, R is an output argument. If FACT = 'F' and */ 00244 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00245 /* If R is output, each element of R is a power of the radix. */ 00246 /* If R is input, each element of R should be a power of the radix */ 00247 /* to ensure a reliable solution and error estimates. Scaling by */ 00248 /* powers of the radix does not cause rounding errors unless the */ 00249 /* result underflows or overflows. Rounding errors during scaling */ 00250 /* lead to refining with a matrix that is not equivalent to the */ 00251 /* input matrix, producing error estimates that may not be */ 00252 /* reliable. */ 00253 00254 /* C (input or output) REAL array, dimension (N) */ 00255 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00256 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00257 /* is not accessed. C is an input argument if FACT = 'F'; */ 00258 /* otherwise, C is an output argument. If FACT = 'F' and */ 00259 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00260 /* If C is output, each element of C is a power of the radix. */ 00261 /* If C is input, each element of C should be a power of the radix */ 00262 /* to ensure a reliable solution and error estimates. Scaling by */ 00263 /* powers of the radix does not cause rounding errors unless the */ 00264 /* result underflows or overflows. Rounding errors during scaling */ 00265 /* lead to refining with a matrix that is not equivalent to the */ 00266 /* input matrix, producing error estimates that may not be */ 00267 /* reliable. */ 00268 00269 /* B (input/output) COMPLEX array, dimension (LDB,NRHS) */ 00270 /* On entry, the N-by-NRHS right hand side matrix B. */ 00271 /* On exit, */ 00272 /* if EQUED = 'N', B is not modified; */ 00273 /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ 00274 /* diag(R)*B; */ 00275 /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ 00276 /* overwritten by diag(C)*B. */ 00277 00278 /* LDB (input) INTEGER */ 00279 /* The leading dimension of the array B. LDB >= max(1,N). */ 00280 00281 /* X (output) COMPLEX array, dimension (LDX,NRHS) */ 00282 /* If INFO = 0, the N-by-NRHS solution matrix X to the original */ 00283 /* system of equations. Note that A and B are modified on exit */ 00284 /* if EQUED .ne. 'N', and the solution to the equilibrated system is */ 00285 /* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */ 00286 /* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */ 00287 00288 /* LDX (input) INTEGER */ 00289 /* The leading dimension of the array X. LDX >= max(1,N). */ 00290 00291 /* RCOND (output) REAL */ 00292 /* Reciprocal scaled condition number. This is an estimate of the */ 00293 /* reciprocal Skeel condition number of the matrix A after */ 00294 /* equilibration (if done). If this is less than the machine */ 00295 /* precision (in particular, if it is zero), the matrix is singular */ 00296 /* to working precision. Note that the error may still be small even */ 00297 /* if this number is very small and the matrix appears ill- */ 00298 /* conditioned. */ 00299 00300 /* RPVGRW (output) REAL */ 00301 /* Reciprocal pivot growth. On exit, this contains the reciprocal */ 00302 /* pivot growth factor norm(A)/norm(U). The "max absolute element" */ 00303 /* norm is used. If this is much less than 1, then the stability of */ 00304 /* the LU factorization of the (equilibrated) matrix A could be poor. */ 00305 /* This also means that the solution X, estimated condition numbers, */ 00306 /* and error bounds could be unreliable. If factorization fails with */ 00307 /* 0<INFO<=N, then this contains the reciprocal pivot growth factor */ 00308 /* for the leading INFO columns of A. In CGESVX, this quantity is */ 00309 /* returned in WORK(1). */ 00310 00311 /* BERR (output) REAL array, dimension (NRHS) */ 00312 /* Componentwise relative backward error. This is the */ 00313 /* componentwise relative backward error of each solution vector X(j) */ 00314 /* (i.e., the smallest relative change in any element of A or B that */ 00315 /* makes X(j) an exact solution). */ 00316 00317 /* N_ERR_BNDS (input) INTEGER */ 00318 /* Number of error bounds to return for each right hand side */ 00319 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00320 /* ERR_BNDS_COMP below. */ 00321 00322 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00323 /* For each right-hand side, this array contains information about */ 00324 /* various error bounds and condition numbers corresponding to the */ 00325 /* normwise relative error, which is defined as follows: */ 00326 00327 /* Normwise relative error in the ith solution vector: */ 00328 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00329 /* ------------------------------ */ 00330 /* max_j abs(X(j,i)) */ 00331 00332 /* The array is indexed by the type of error information as described */ 00333 /* below. There currently are up to three pieces of information */ 00334 /* returned. */ 00335 00336 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00337 /* right-hand side. */ 00338 00339 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00340 /* three fields: */ 00341 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00342 /* reciprocal condition number is less than the threshold */ 00343 /* sqrt(n) * slamch('Epsilon'). */ 00344 00345 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00346 /* almost certainly within a factor of 10 of the true error */ 00347 /* so long as the next entry is greater than the threshold */ 00348 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00349 /* be trusted if the previous boolean is true. */ 00350 00351 /* err = 3 Reciprocal condition number: Estimated normwise */ 00352 /* reciprocal condition number. Compared with the threshold */ 00353 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00354 /* estimate is "guaranteed". These reciprocal condition */ 00355 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00356 /* appropriately scaled matrix Z. */ 00357 /* Let Z = S*A, where S scales each row by a power of the */ 00358 /* radix so all absolute row sums of Z are approximately 1. */ 00359 00360 /* See Lapack Working Note 165 for further details and extra */ 00361 /* cautions. */ 00362 00363 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00364 /* For each right-hand side, this array contains information about */ 00365 /* various error bounds and condition numbers corresponding to the */ 00366 /* componentwise relative error, which is defined as follows: */ 00367 00368 /* Componentwise relative error in the ith solution vector: */ 00369 /* abs(XTRUE(j,i) - X(j,i)) */ 00370 /* max_j ---------------------- */ 00371 /* abs(X(j,i)) */ 00372 00373 /* The array is indexed by the right-hand side i (on which the */ 00374 /* componentwise relative error depends), and the type of error */ 00375 /* information as described below. There currently are up to three */ 00376 /* pieces of information returned for each right-hand side. If */ 00377 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00378 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00379 /* the first (:,N_ERR_BNDS) entries are returned. */ 00380 00381 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00382 /* right-hand side. */ 00383 00384 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00385 /* three fields: */ 00386 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00387 /* reciprocal condition number is less than the threshold */ 00388 /* sqrt(n) * slamch('Epsilon'). */ 00389 00390 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00391 /* almost certainly within a factor of 10 of the true error */ 00392 /* so long as the next entry is greater than the threshold */ 00393 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00394 /* be trusted if the previous boolean is true. */ 00395 00396 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00397 /* reciprocal condition number. Compared with the threshold */ 00398 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00399 /* estimate is "guaranteed". These reciprocal condition */ 00400 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00401 /* appropriately scaled matrix Z. */ 00402 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00403 /* current right-hand side and S scales each row of */ 00404 /* A*diag(x) by a power of the radix so all absolute row */ 00405 /* sums of Z are approximately 1. */ 00406 00407 /* See Lapack Working Note 165 for further details and extra */ 00408 /* cautions. */ 00409 00410 /* NPARAMS (input) INTEGER */ 00411 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00412 /* PARAMS array is never referenced and default values are used. */ 00413 00414 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00415 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00416 /* that entry will be filled with default value used for that */ 00417 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00418 /* are used for higher-numbered parameters. */ 00419 00420 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00421 /* refinement or not. */ 00422 /* Default: 1.0 */ 00423 /* = 0.0 : No refinement is performed, and no error bounds are */ 00424 /* computed. */ 00425 /* = 1.0 : Use the double-precision refinement algorithm, */ 00426 /* possibly with doubled-single computations if the */ 00427 /* compilation environment does not support DOUBLE */ 00428 /* PRECISION. */ 00429 /* (other values are reserved for future use) */ 00430 00431 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00432 /* computations allowed for refinement. */ 00433 /* Default: 10 */ 00434 /* Aggressive: Set to 100 to permit convergence using approximate */ 00435 /* factorizations or factorizations other than LU. If */ 00436 /* the factorization uses a technique other than */ 00437 /* Gaussian elimination, the guarantees in */ 00438 /* err_bnds_norm and err_bnds_comp may no longer be */ 00439 /* trustworthy. */ 00440 00441 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00442 /* will attempt to find a solution with small componentwise */ 00443 /* relative error in the double-precision algorithm. Positive */ 00444 /* is true, 0.0 is false. */ 00445 /* Default: 1.0 (attempt componentwise convergence) */ 00446 00447 /* WORK (workspace) COMPLEX array, dimension (2*N) */ 00448 00449 /* RWORK (workspace) REAL array, dimension (3*N) */ 00450 00451 /* INFO (output) INTEGER */ 00452 /* = 0: Successful exit. The solution to every right-hand side is */ 00453 /* guaranteed. */ 00454 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00455 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00456 /* has been completed, but the factor U is exactly singular, so */ 00457 /* the solution and error bounds could not be computed. RCOND = 0 */ 00458 /* is returned. */ 00459 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00460 /* not guaranteed. The solutions corresponding to other right- */ 00461 /* hand sides K with K > J may not be guaranteed as well, but */ 00462 /* only the first such right-hand side is reported. If a small */ 00463 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00464 /* the Jth right-hand side is the first with a normwise error */ 00465 /* bound that is not guaranteed (the smallest J such */ 00466 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00467 /* the Jth right-hand side is the first with either a normwise or */ 00468 /* componentwise error bound that is not guaranteed (the smallest */ 00469 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00470 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00471 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00472 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00473 /* ERR_BNDS_COMP. */ 00474 00475 /* ================================================================== */ 00476 00477 /* .. Parameters .. */ 00478 /* .. */ 00479 /* .. Local Scalars .. */ 00480 /* .. */ 00481 /* .. External Functions .. */ 00482 /* .. */ 00483 /* .. External Subroutines .. */ 00484 /* .. */ 00485 /* .. Intrinsic Functions .. */ 00486 /* .. */ 00487 /* .. Executable Statements .. */ 00488 00489 /* Parameter adjustments */ 00490 err_bnds_comp_dim1 = *nrhs; 00491 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00492 err_bnds_comp__ -= err_bnds_comp_offset; 00493 err_bnds_norm_dim1 = *nrhs; 00494 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00495 err_bnds_norm__ -= err_bnds_norm_offset; 00496 a_dim1 = *lda; 00497 a_offset = 1 + a_dim1; 00498 a -= a_offset; 00499 af_dim1 = *ldaf; 00500 af_offset = 1 + af_dim1; 00501 af -= af_offset; 00502 --ipiv; 00503 --r__; 00504 --c__; 00505 b_dim1 = *ldb; 00506 b_offset = 1 + b_dim1; 00507 b -= b_offset; 00508 x_dim1 = *ldx; 00509 x_offset = 1 + x_dim1; 00510 x -= x_offset; 00511 --berr; 00512 --params; 00513 --work; 00514 --rwork; 00515 00516 /* Function Body */ 00517 *info = 0; 00518 nofact = lsame_(fact, "N"); 00519 equil = lsame_(fact, "E"); 00520 notran = lsame_(trans, "N"); 00521 smlnum = slamch_("Safe minimum"); 00522 bignum = 1.f / smlnum; 00523 if (nofact || equil) { 00524 *(unsigned char *)equed = 'N'; 00525 rowequ = FALSE_; 00526 colequ = FALSE_; 00527 } else { 00528 rowequ = lsame_(equed, "R") || lsame_(equed, 00529 "B"); 00530 colequ = lsame_(equed, "C") || lsame_(equed, 00531 "B"); 00532 } 00533 00534 /* Default is failure. If an input parameter is wrong or */ 00535 /* factorization fails, make everything look horrible. Only the */ 00536 /* pivot growth is set here, the rest is initialized in CGERFSX. */ 00537 00538 *rpvgrw = 0.f; 00539 00540 /* Test the input parameters. PARAMS is not tested until CGERFSX. */ 00541 00542 if (! nofact && ! equil && ! lsame_(fact, "F")) { 00543 *info = -1; 00544 } else if (! notran && ! lsame_(trans, "T") && ! 00545 lsame_(trans, "C")) { 00546 *info = -2; 00547 } else if (*n < 0) { 00548 *info = -3; 00549 } else if (*nrhs < 0) { 00550 *info = -4; 00551 } else if (*lda < max(1,*n)) { 00552 *info = -6; 00553 } else if (*ldaf < max(1,*n)) { 00554 *info = -8; 00555 } else if (lsame_(fact, "F") && ! (rowequ || colequ 00556 || lsame_(equed, "N"))) { 00557 *info = -10; 00558 } else { 00559 if (rowequ) { 00560 rcmin = bignum; 00561 rcmax = 0.f; 00562 i__1 = *n; 00563 for (j = 1; j <= i__1; ++j) { 00564 /* Computing MIN */ 00565 r__1 = rcmin, r__2 = r__[j]; 00566 rcmin = dmin(r__1,r__2); 00567 /* Computing MAX */ 00568 r__1 = rcmax, r__2 = r__[j]; 00569 rcmax = dmax(r__1,r__2); 00570 /* L10: */ 00571 } 00572 if (rcmin <= 0.f) { 00573 *info = -11; 00574 } else if (*n > 0) { 00575 rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00576 } else { 00577 rowcnd = 1.f; 00578 } 00579 } 00580 if (colequ && *info == 0) { 00581 rcmin = bignum; 00582 rcmax = 0.f; 00583 i__1 = *n; 00584 for (j = 1; j <= i__1; ++j) { 00585 /* Computing MIN */ 00586 r__1 = rcmin, r__2 = c__[j]; 00587 rcmin = dmin(r__1,r__2); 00588 /* Computing MAX */ 00589 r__1 = rcmax, r__2 = c__[j]; 00590 rcmax = dmax(r__1,r__2); 00591 /* L20: */ 00592 } 00593 if (rcmin <= 0.f) { 00594 *info = -12; 00595 } else if (*n > 0) { 00596 colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00597 } else { 00598 colcnd = 1.f; 00599 } 00600 } 00601 if (*info == 0) { 00602 if (*ldb < max(1,*n)) { 00603 *info = -14; 00604 } else if (*ldx < max(1,*n)) { 00605 *info = -16; 00606 } 00607 } 00608 } 00609 00610 if (*info != 0) { 00611 i__1 = -(*info); 00612 xerbla_("CGESVXX", &i__1); 00613 return 0; 00614 } 00615 00616 if (equil) { 00617 00618 /* Compute row and column scalings to equilibrate the matrix A. */ 00619 00620 cgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, 00621 &amax, &infequ); 00622 if (infequ == 0) { 00623 00624 /* Equilibrate the matrix. */ 00625 00626 claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & 00627 colcnd, &amax, equed); 00628 rowequ = lsame_(equed, "R") || lsame_(equed, 00629 "B"); 00630 colequ = lsame_(equed, "C") || lsame_(equed, 00631 "B"); 00632 } 00633 00634 /* If the scaling factors are not applied, set them to 1.0. */ 00635 00636 if (! rowequ) { 00637 i__1 = *n; 00638 for (j = 1; j <= i__1; ++j) { 00639 r__[j] = 1.f; 00640 } 00641 } 00642 if (! colequ) { 00643 i__1 = *n; 00644 for (j = 1; j <= i__1; ++j) { 00645 c__[j] = 1.f; 00646 } 00647 } 00648 } 00649 00650 /* Scale the right-hand side. */ 00651 00652 if (notran) { 00653 if (rowequ) { 00654 clascl2_(n, nrhs, &r__[1], &b[b_offset], ldb); 00655 } 00656 } else { 00657 if (colequ) { 00658 clascl2_(n, nrhs, &c__[1], &b[b_offset], ldb); 00659 } 00660 } 00661 00662 if (nofact || equil) { 00663 00664 /* Compute the LU factorization of A. */ 00665 00666 clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); 00667 cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); 00668 00669 /* Return if INFO is non-zero. */ 00670 00671 if (*info > 0) { 00672 00673 /* Pivot in column INFO is exactly 0 */ 00674 /* Compute the reciprocal pivot growth factor of the */ 00675 /* leading rank-deficient INFO columns of A. */ 00676 00677 *rpvgrw = cla_rpvgrw__(n, info, &a[a_offset], lda, &af[af_offset], 00678 ldaf); 00679 return 0; 00680 } 00681 } 00682 00683 /* Compute the reciprocal pivot growth factor RPVGRW. */ 00684 00685 *rpvgrw = cla_rpvgrw__(n, n, &a[a_offset], lda, &af[af_offset], ldaf); 00686 00687 /* Compute the solution matrix X. */ 00688 00689 clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); 00690 cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, 00691 info); 00692 00693 /* Use iterative refinement to improve the computed solution and */ 00694 /* compute error bounds and backward error estimates for it. */ 00695 00696 cgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & 00697 ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx, 00698 rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[ 00699 err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], 00700 nparams, ¶ms[1], &work[1], &rwork[1], info); 00701 00702 /* Scale solutions. */ 00703 00704 if (colequ && notran) { 00705 clascl2_(n, nrhs, &c__[1], &x[x_offset], ldx); 00706 } else if (rowequ && ! notran) { 00707 clascl2_(n, nrhs, &r__[1], &x[x_offset], ldx); 00708 } 00709 00710 return 0; 00711 00712 /* End of CGESVXX */ 00713 00714 } /* cgesvxx_ */