00001 /* sgesvxx.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 sgesvxx_(char *fact, char *trans, integer *n, integer * 00017 nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, 00018 char *equed, real *r__, real *c__, real *b, integer *ldb, real *x, 00019 integer *ldx, real *rcond, real *rpvgrw, real *berr, integer * 00020 n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer * 00021 nparams, real *params, real *work, integer *iwork, integer *info) 00022 { 00023 /* System generated locals */ 00024 integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 00025 x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00026 err_bnds_comp_dim1, err_bnds_comp_offset, i__1; 00027 real r__1, r__2; 00028 00029 /* Local variables */ 00030 integer j; 00031 extern doublereal sla_rpvgrw__(integer *, integer *, real *, integer *, 00032 real *, integer *); 00033 real amax; 00034 extern logical lsame_(char *, char *); 00035 real rcmin, rcmax; 00036 logical equil; 00037 real colcnd; 00038 extern doublereal slamch_(char *); 00039 logical nofact; 00040 extern /* Subroutine */ int slaqge_(integer *, integer *, real *, integer 00041 *, real *, real *, real *, real *, real *, char *), 00042 xerbla_(char *, integer *); 00043 real bignum; 00044 integer infequ; 00045 logical colequ; 00046 extern /* Subroutine */ int sgetrf_(integer *, integer *, real *, integer 00047 *, integer *, integer *), slacpy_(char *, integer *, integer *, 00048 real *, integer *, real *, integer *); 00049 real rowcnd; 00050 logical notran; 00051 extern /* Subroutine */ int sgetrs_(char *, integer *, integer *, real *, 00052 integer *, integer *, real *, integer *, integer *); 00053 real smlnum; 00054 logical rowequ; 00055 extern /* Subroutine */ int slascl2_(integer *, integer *, real *, real *, 00056 integer *), sgeequb_(integer *, integer *, real *, integer *, 00057 real *, real *, real *, real *, real *, integer *), sgerfsx_(char 00058 *, char *, integer *, integer *, real *, integer *, real *, 00059 integer *, integer *, real *, real *, real *, integer *, real *, 00060 integer *, real *, real *, integer *, real *, real *, integer *, 00061 real *, real *, integer *, integer *); 00062 00063 00064 /* -- LAPACK driver routine (version 3.2) -- */ 00065 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00066 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00067 /* -- November 2008 -- */ 00068 00069 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00070 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00071 00072 /* .. */ 00073 /* .. Scalar Arguments .. */ 00074 /* .. */ 00075 /* .. Array Arguments .. */ 00076 /* .. */ 00077 00078 /* Purpose */ 00079 /* ======= */ 00080 00081 /* SGESVXX uses the LU factorization to compute the solution to a */ 00082 /* real system of linear equations A * X = B, where A is an */ 00083 /* N-by-N matrix and X and B are N-by-NRHS matrices. */ 00084 00085 /* If requested, both normwise and maximum componentwise error bounds */ 00086 /* are returned. SGESVXX will return a solution with a tiny */ 00087 /* guaranteed error (O(eps) where eps is the working machine */ 00088 /* precision) unless the matrix is very ill-conditioned, in which */ 00089 /* case a warning is returned. Relevant condition numbers also are */ 00090 /* calculated and returned. */ 00091 00092 /* SGESVXX accepts user-provided factorizations and equilibration */ 00093 /* factors; see the definitions of the FACT and EQUED options. */ 00094 /* Solving with refinement and using a factorization from a previous */ 00095 /* SGESVXX call will also produce a solution with either O(eps) */ 00096 /* errors or warnings, but we cannot make that claim for general */ 00097 /* user-provided factorizations and equilibration factors if they */ 00098 /* differ from what SGESVXX would itself produce. */ 00099 00100 /* Description */ 00101 /* =========== */ 00102 00103 /* The following steps are performed: */ 00104 00105 /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ 00106 /* the system: */ 00107 00108 /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ 00109 /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ 00110 /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ 00111 00112 /* Whether or not the system will be equilibrated depends on the */ 00113 /* scaling of the matrix A, but if equilibration is used, A is */ 00114 /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ 00115 /* or diag(C)*B (if TRANS = 'T' or 'C'). */ 00116 00117 /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */ 00118 /* the matrix A (after equilibration if FACT = 'E') as */ 00119 00120 /* A = P * L * U, */ 00121 00122 /* where P is a permutation matrix, L is a unit lower triangular */ 00123 /* matrix, and U is upper triangular. */ 00124 00125 /* 3. If some U(i,i)=0, so that U is exactly singular, then the */ 00126 /* routine returns with INFO = i. Otherwise, the factored form of A */ 00127 /* is used to estimate the condition number of the matrix A (see */ 00128 /* argument RCOND). If the reciprocal of the condition number is less */ 00129 /* than machine precision, the routine still goes on to solve for X */ 00130 /* and compute error bounds as described below. */ 00131 00132 /* 4. The system of equations is solved for X using the factored form */ 00133 /* of A. */ 00134 00135 /* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */ 00136 /* the routine will use iterative refinement to try to get a small */ 00137 /* error and error bounds. Refinement calculates the residual to at */ 00138 /* least twice the working precision. */ 00139 00140 /* 6. If equilibration was used, the matrix X is premultiplied by */ 00141 /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ 00142 /* that it solves the original system before equilibration. */ 00143 00144 /* Arguments */ 00145 /* ========= */ 00146 00147 /* Some optional parameters are bundled in the PARAMS array. These */ 00148 /* settings determine how refinement is performed, but often the */ 00149 /* defaults are acceptable. If the defaults are acceptable, users */ 00150 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00151 /* the PARAMS argument. */ 00152 00153 /* FACT (input) CHARACTER*1 */ 00154 /* Specifies whether or not the factored form of the matrix A is */ 00155 /* supplied on entry, and if not, whether the matrix A should be */ 00156 /* equilibrated before it is factored. */ 00157 /* = 'F': On entry, AF and IPIV contain the factored form of A. */ 00158 /* If EQUED is not 'N', the matrix A has been */ 00159 /* equilibrated with scaling factors given by R and C. */ 00160 /* A, AF, and IPIV are not modified. */ 00161 /* = 'N': The matrix A will be copied to AF and factored. */ 00162 /* = 'E': The matrix A will be equilibrated if necessary, then */ 00163 /* copied to AF and factored. */ 00164 00165 /* TRANS (input) CHARACTER*1 */ 00166 /* Specifies the form of the system of equations: */ 00167 /* = 'N': A * X = B (No transpose) */ 00168 /* = 'T': A**T * X = B (Transpose) */ 00169 /* = 'C': A**H * X = B (Conjugate Transpose = Transpose) */ 00170 00171 /* N (input) INTEGER */ 00172 /* The number of linear equations, i.e., the order of the */ 00173 /* matrix A. N >= 0. */ 00174 00175 /* NRHS (input) INTEGER */ 00176 /* The number of right hand sides, i.e., the number of columns */ 00177 /* of the matrices B and X. NRHS >= 0. */ 00178 00179 /* A (input/output) REAL array, dimension (LDA,N) */ 00180 /* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */ 00181 /* not 'N', then A must have been equilibrated by the scaling */ 00182 /* factors in R and/or C. A is not modified if FACT = 'F' or */ 00183 /* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */ 00184 00185 /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ 00186 /* EQUED = 'R': A := diag(R) * A */ 00187 /* EQUED = 'C': A := A * diag(C) */ 00188 /* EQUED = 'B': A := diag(R) * A * diag(C). */ 00189 00190 /* LDA (input) INTEGER */ 00191 /* The leading dimension of the array A. LDA >= max(1,N). */ 00192 00193 /* AF (input or output) REAL array, dimension (LDAF,N) */ 00194 /* If FACT = 'F', then AF is an input argument and on entry */ 00195 /* contains the factors L and U from the factorization */ 00196 /* A = P*L*U as computed by SGETRF. If EQUED .ne. 'N', then */ 00197 /* AF is the factored form of the equilibrated matrix A. */ 00198 00199 /* If FACT = 'N', then AF is an output argument and on exit */ 00200 /* returns the factors L and U from the factorization A = P*L*U */ 00201 /* of the original matrix A. */ 00202 00203 /* If FACT = 'E', then AF is an output argument and on exit */ 00204 /* returns the factors L and U from the factorization A = P*L*U */ 00205 /* of the equilibrated matrix A (see the description of A for */ 00206 /* the form of the equilibrated matrix). */ 00207 00208 /* LDAF (input) INTEGER */ 00209 /* The leading dimension of the array AF. LDAF >= max(1,N). */ 00210 00211 /* IPIV (input or output) INTEGER array, dimension (N) */ 00212 /* If FACT = 'F', then IPIV is an input argument and on entry */ 00213 /* contains the pivot indices from the factorization A = P*L*U */ 00214 /* as computed by SGETRF; row i of the matrix was interchanged */ 00215 /* with row IPIV(i). */ 00216 00217 /* If FACT = 'N', then IPIV is an output argument and on exit */ 00218 /* contains the pivot indices from the factorization A = P*L*U */ 00219 /* of the original matrix A. */ 00220 00221 /* If FACT = 'E', then IPIV is an output argument and on exit */ 00222 /* contains the pivot indices from the factorization A = P*L*U */ 00223 /* of the equilibrated matrix A. */ 00224 00225 /* EQUED (input or output) CHARACTER*1 */ 00226 /* Specifies the form of equilibration that was done. */ 00227 /* = 'N': No equilibration (always true if FACT = 'N'). */ 00228 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00229 /* diag(R). */ 00230 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00231 /* by diag(C). */ 00232 /* = 'B': Both row and column equilibration, i.e., A has been */ 00233 /* replaced by diag(R) * A * diag(C). */ 00234 /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ 00235 /* output argument. */ 00236 00237 /* R (input or output) REAL array, dimension (N) */ 00238 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00239 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00240 /* is not accessed. R is an input argument if FACT = 'F'; */ 00241 /* otherwise, R is an output argument. If FACT = 'F' and */ 00242 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00243 /* If R is output, each element of R is a power of the radix. */ 00244 /* If R is input, each element of R should be a power of the radix */ 00245 /* to ensure a reliable solution and error estimates. Scaling by */ 00246 /* powers of the radix does not cause rounding errors unless the */ 00247 /* result underflows or overflows. Rounding errors during scaling */ 00248 /* lead to refining with a matrix that is not equivalent to the */ 00249 /* input matrix, producing error estimates that may not be */ 00250 /* reliable. */ 00251 00252 /* C (input or output) REAL array, dimension (N) */ 00253 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00254 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00255 /* is not accessed. C is an input argument if FACT = 'F'; */ 00256 /* otherwise, C is an output argument. If FACT = 'F' and */ 00257 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00258 /* If C is output, each element of C is a power of the radix. */ 00259 /* If C is input, each element of C should be a power of the radix */ 00260 /* to ensure a reliable solution and error estimates. Scaling by */ 00261 /* powers of the radix does not cause rounding errors unless the */ 00262 /* result underflows or overflows. Rounding errors during scaling */ 00263 /* lead to refining with a matrix that is not equivalent to the */ 00264 /* input matrix, producing error estimates that may not be */ 00265 /* reliable. */ 00266 00267 /* B (input/output) REAL array, dimension (LDB,NRHS) */ 00268 /* On entry, the N-by-NRHS right hand side matrix B. */ 00269 /* On exit, */ 00270 /* if EQUED = 'N', B is not modified; */ 00271 /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ 00272 /* diag(R)*B; */ 00273 /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ 00274 /* overwritten by diag(C)*B. */ 00275 00276 /* LDB (input) INTEGER */ 00277 /* The leading dimension of the array B. LDB >= max(1,N). */ 00278 00279 /* X (output) REAL array, dimension (LDX,NRHS) */ 00280 /* If INFO = 0, the N-by-NRHS solution matrix X to the original */ 00281 /* system of equations. Note that A and B are modified on exit */ 00282 /* if EQUED .ne. 'N', and the solution to the equilibrated system is */ 00283 /* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */ 00284 /* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */ 00285 00286 /* LDX (input) INTEGER */ 00287 /* The leading dimension of the array X. LDX >= max(1,N). */ 00288 00289 /* RCOND (output) REAL */ 00290 /* Reciprocal scaled condition number. This is an estimate of the */ 00291 /* reciprocal Skeel condition number of the matrix A after */ 00292 /* equilibration (if done). If this is less than the machine */ 00293 /* precision (in particular, if it is zero), the matrix is singular */ 00294 /* to working precision. Note that the error may still be small even */ 00295 /* if this number is very small and the matrix appears ill- */ 00296 /* conditioned. */ 00297 00298 /* RPVGRW (output) REAL */ 00299 /* Reciprocal pivot growth. On exit, this contains the reciprocal */ 00300 /* pivot growth factor norm(A)/norm(U). The "max absolute element" */ 00301 /* norm is used. If this is much less than 1, then the stability of */ 00302 /* the LU factorization of the (equilibrated) matrix A could be poor. */ 00303 /* This also means that the solution X, estimated condition numbers, */ 00304 /* and error bounds could be unreliable. If factorization fails with */ 00305 /* 0<INFO<=N, then this contains the reciprocal pivot growth factor */ 00306 /* for the leading INFO columns of A. In SGESVX, this quantity is */ 00307 /* returned in WORK(1). */ 00308 00309 /* BERR (output) REAL array, dimension (NRHS) */ 00310 /* Componentwise relative backward error. This is the */ 00311 /* componentwise relative backward error of each solution vector X(j) */ 00312 /* (i.e., the smallest relative change in any element of A or B that */ 00313 /* makes X(j) an exact solution). */ 00314 00315 /* N_ERR_BNDS (input) INTEGER */ 00316 /* Number of error bounds to return for each right hand side */ 00317 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00318 /* ERR_BNDS_COMP below. */ 00319 00320 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00321 /* For each right-hand side, this array contains information about */ 00322 /* various error bounds and condition numbers corresponding to the */ 00323 /* normwise relative error, which is defined as follows: */ 00324 00325 /* Normwise relative error in the ith solution vector: */ 00326 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00327 /* ------------------------------ */ 00328 /* max_j abs(X(j,i)) */ 00329 00330 /* The array is indexed by the type of error information as described */ 00331 /* below. There currently are up to three pieces of information */ 00332 /* returned. */ 00333 00334 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00335 /* right-hand side. */ 00336 00337 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00338 /* three fields: */ 00339 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00340 /* reciprocal condition number is less than the threshold */ 00341 /* sqrt(n) * slamch('Epsilon'). */ 00342 00343 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00344 /* almost certainly within a factor of 10 of the true error */ 00345 /* so long as the next entry is greater than the threshold */ 00346 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00347 /* be trusted if the previous boolean is true. */ 00348 00349 /* err = 3 Reciprocal condition number: Estimated normwise */ 00350 /* reciprocal condition number. Compared with the threshold */ 00351 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00352 /* estimate is "guaranteed". These reciprocal condition */ 00353 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00354 /* appropriately scaled matrix Z. */ 00355 /* Let Z = S*A, where S scales each row by a power of the */ 00356 /* radix so all absolute row sums of Z are approximately 1. */ 00357 00358 /* See Lapack Working Note 165 for further details and extra */ 00359 /* cautions. */ 00360 00361 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00362 /* For each right-hand side, this array contains information about */ 00363 /* various error bounds and condition numbers corresponding to the */ 00364 /* componentwise relative error, which is defined as follows: */ 00365 00366 /* Componentwise relative error in the ith solution vector: */ 00367 /* abs(XTRUE(j,i) - X(j,i)) */ 00368 /* max_j ---------------------- */ 00369 /* abs(X(j,i)) */ 00370 00371 /* The array is indexed by the right-hand side i (on which the */ 00372 /* componentwise relative error depends), and the type of error */ 00373 /* information as described below. There currently are up to three */ 00374 /* pieces of information returned for each right-hand side. If */ 00375 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00376 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00377 /* the first (:,N_ERR_BNDS) entries are returned. */ 00378 00379 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00380 /* right-hand side. */ 00381 00382 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00383 /* three fields: */ 00384 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00385 /* reciprocal condition number is less than the threshold */ 00386 /* sqrt(n) * slamch('Epsilon'). */ 00387 00388 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00389 /* almost certainly within a factor of 10 of the true error */ 00390 /* so long as the next entry is greater than the threshold */ 00391 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00392 /* be trusted if the previous boolean is true. */ 00393 00394 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00395 /* reciprocal condition number. Compared with the threshold */ 00396 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00397 /* estimate is "guaranteed". These reciprocal condition */ 00398 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00399 /* appropriately scaled matrix Z. */ 00400 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00401 /* current right-hand side and S scales each row of */ 00402 /* A*diag(x) by a power of the radix so all absolute row */ 00403 /* sums of Z are approximately 1. */ 00404 00405 /* See Lapack Working Note 165 for further details and extra */ 00406 /* cautions. */ 00407 00408 /* NPARAMS (input) INTEGER */ 00409 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00410 /* PARAMS array is never referenced and default values are used. */ 00411 00412 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00413 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00414 /* that entry will be filled with default value used for that */ 00415 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00416 /* are used for higher-numbered parameters. */ 00417 00418 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00419 /* refinement or not. */ 00420 /* Default: 1.0 */ 00421 /* = 0.0 : No refinement is performed, and no error bounds are */ 00422 /* computed. */ 00423 /* = 1.0 : Use the double-precision refinement algorithm, */ 00424 /* possibly with doubled-single computations if the */ 00425 /* compilation environment does not support DOUBLE */ 00426 /* PRECISION. */ 00427 /* (other values are reserved for future use) */ 00428 00429 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00430 /* computations allowed for refinement. */ 00431 /* Default: 10 */ 00432 /* Aggressive: Set to 100 to permit convergence using approximate */ 00433 /* factorizations or factorizations other than LU. If */ 00434 /* the factorization uses a technique other than */ 00435 /* Gaussian elimination, the guarantees in */ 00436 /* err_bnds_norm and err_bnds_comp may no longer be */ 00437 /* trustworthy. */ 00438 00439 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00440 /* will attempt to find a solution with small componentwise */ 00441 /* relative error in the double-precision algorithm. Positive */ 00442 /* is true, 0.0 is false. */ 00443 /* Default: 1.0 (attempt componentwise convergence) */ 00444 00445 /* WORK (workspace) REAL array, dimension (4*N) */ 00446 00447 /* IWORK (workspace) INTEGER array, dimension (N) */ 00448 00449 /* INFO (output) INTEGER */ 00450 /* = 0: Successful exit. The solution to every right-hand side is */ 00451 /* guaranteed. */ 00452 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00453 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00454 /* has been completed, but the factor U is exactly singular, so */ 00455 /* the solution and error bounds could not be computed. RCOND = 0 */ 00456 /* is returned. */ 00457 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00458 /* not guaranteed. The solutions corresponding to other right- */ 00459 /* hand sides K with K > J may not be guaranteed as well, but */ 00460 /* only the first such right-hand side is reported. If a small */ 00461 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00462 /* the Jth right-hand side is the first with a normwise error */ 00463 /* bound that is not guaranteed (the smallest J such */ 00464 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00465 /* the Jth right-hand side is the first with either a normwise or */ 00466 /* componentwise error bound that is not guaranteed (the smallest */ 00467 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00468 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00469 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00470 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00471 /* ERR_BNDS_COMP. */ 00472 00473 /* ================================================================== */ 00474 00475 /* .. Parameters .. */ 00476 /* .. */ 00477 /* .. Local Scalars .. */ 00478 /* .. */ 00479 /* .. External Functions .. */ 00480 /* .. */ 00481 /* .. External Subroutines .. */ 00482 /* .. */ 00483 /* .. Intrinsic Functions .. */ 00484 /* .. */ 00485 /* .. Executable Statements .. */ 00486 00487 /* Parameter adjustments */ 00488 err_bnds_comp_dim1 = *nrhs; 00489 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00490 err_bnds_comp__ -= err_bnds_comp_offset; 00491 err_bnds_norm_dim1 = *nrhs; 00492 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00493 err_bnds_norm__ -= err_bnds_norm_offset; 00494 a_dim1 = *lda; 00495 a_offset = 1 + a_dim1; 00496 a -= a_offset; 00497 af_dim1 = *ldaf; 00498 af_offset = 1 + af_dim1; 00499 af -= af_offset; 00500 --ipiv; 00501 --r__; 00502 --c__; 00503 b_dim1 = *ldb; 00504 b_offset = 1 + b_dim1; 00505 b -= b_offset; 00506 x_dim1 = *ldx; 00507 x_offset = 1 + x_dim1; 00508 x -= x_offset; 00509 --berr; 00510 --params; 00511 --work; 00512 --iwork; 00513 00514 /* Function Body */ 00515 *info = 0; 00516 nofact = lsame_(fact, "N"); 00517 equil = lsame_(fact, "E"); 00518 notran = lsame_(trans, "N"); 00519 smlnum = slamch_("Safe minimum"); 00520 bignum = 1.f / smlnum; 00521 if (nofact || equil) { 00522 *(unsigned char *)equed = 'N'; 00523 rowequ = FALSE_; 00524 colequ = FALSE_; 00525 } else { 00526 rowequ = lsame_(equed, "R") || lsame_(equed, 00527 "B"); 00528 colequ = lsame_(equed, "C") || lsame_(equed, 00529 "B"); 00530 } 00531 00532 /* Default is failure. If an input parameter is wrong or */ 00533 /* factorization fails, make everything look horrible. Only the */ 00534 /* pivot growth is set here, the rest is initialized in SGERFSX. */ 00535 00536 *rpvgrw = 0.f; 00537 00538 /* Test the input parameters. PARAMS is not tested until SGERFSX. */ 00539 00540 if (! nofact && ! equil && ! lsame_(fact, "F")) { 00541 *info = -1; 00542 } else if (! notran && ! lsame_(trans, "T") && ! 00543 lsame_(trans, "C")) { 00544 *info = -2; 00545 } else if (*n < 0) { 00546 *info = -3; 00547 } else if (*nrhs < 0) { 00548 *info = -4; 00549 } else if (*lda < max(1,*n)) { 00550 *info = -6; 00551 } else if (*ldaf < max(1,*n)) { 00552 *info = -8; 00553 } else if (lsame_(fact, "F") && ! (rowequ || colequ 00554 || lsame_(equed, "N"))) { 00555 *info = -10; 00556 } else { 00557 if (rowequ) { 00558 rcmin = bignum; 00559 rcmax = 0.f; 00560 i__1 = *n; 00561 for (j = 1; j <= i__1; ++j) { 00562 /* Computing MIN */ 00563 r__1 = rcmin, r__2 = r__[j]; 00564 rcmin = dmin(r__1,r__2); 00565 /* Computing MAX */ 00566 r__1 = rcmax, r__2 = r__[j]; 00567 rcmax = dmax(r__1,r__2); 00568 /* L10: */ 00569 } 00570 if (rcmin <= 0.f) { 00571 *info = -11; 00572 } else if (*n > 0) { 00573 rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00574 } else { 00575 rowcnd = 1.f; 00576 } 00577 } 00578 if (colequ && *info == 0) { 00579 rcmin = bignum; 00580 rcmax = 0.f; 00581 i__1 = *n; 00582 for (j = 1; j <= i__1; ++j) { 00583 /* Computing MIN */ 00584 r__1 = rcmin, r__2 = c__[j]; 00585 rcmin = dmin(r__1,r__2); 00586 /* Computing MAX */ 00587 r__1 = rcmax, r__2 = c__[j]; 00588 rcmax = dmax(r__1,r__2); 00589 /* L20: */ 00590 } 00591 if (rcmin <= 0.f) { 00592 *info = -12; 00593 } else if (*n > 0) { 00594 colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00595 } else { 00596 colcnd = 1.f; 00597 } 00598 } 00599 if (*info == 0) { 00600 if (*ldb < max(1,*n)) { 00601 *info = -14; 00602 } else if (*ldx < max(1,*n)) { 00603 *info = -16; 00604 } 00605 } 00606 } 00607 00608 if (*info != 0) { 00609 i__1 = -(*info); 00610 xerbla_("SGESVXX", &i__1); 00611 return 0; 00612 } 00613 00614 if (equil) { 00615 00616 /* Compute row and column scalings to equilibrate the matrix A. */ 00617 00618 sgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, 00619 &amax, &infequ); 00620 if (infequ == 0) { 00621 00622 /* Equilibrate the matrix. */ 00623 00624 slaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & 00625 colcnd, &amax, equed); 00626 rowequ = lsame_(equed, "R") || lsame_(equed, 00627 "B"); 00628 colequ = lsame_(equed, "C") || lsame_(equed, 00629 "B"); 00630 } 00631 00632 /* If the scaling factors are not applied, set them to 1.0. */ 00633 00634 if (! rowequ) { 00635 i__1 = *n; 00636 for (j = 1; j <= i__1; ++j) { 00637 r__[j] = 1.f; 00638 } 00639 } 00640 if (! colequ) { 00641 i__1 = *n; 00642 for (j = 1; j <= i__1; ++j) { 00643 c__[j] = 1.f; 00644 } 00645 } 00646 } 00647 00648 /* Scale the right-hand side. */ 00649 00650 if (notran) { 00651 if (rowequ) { 00652 slascl2_(n, nrhs, &r__[1], &b[b_offset], ldb); 00653 } 00654 } else { 00655 if (colequ) { 00656 slascl2_(n, nrhs, &c__[1], &b[b_offset], ldb); 00657 } 00658 } 00659 00660 if (nofact || equil) { 00661 00662 /* Compute the LU factorization of A. */ 00663 00664 slacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf); 00665 sgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info); 00666 00667 /* Return if INFO is non-zero. */ 00668 00669 if (*info > 0) { 00670 00671 /* Pivot in column INFO is exactly 0 */ 00672 /* Compute the reciprocal pivot growth factor of the */ 00673 /* leading rank-deficient INFO columns of A. */ 00674 00675 *rpvgrw = sla_rpvgrw__(n, info, &a[a_offset], lda, &af[af_offset], 00676 ldaf); 00677 return 0; 00678 } 00679 } 00680 00681 /* Compute the reciprocal pivot growth factor RPVGRW. */ 00682 00683 *rpvgrw = sla_rpvgrw__(n, n, &a[a_offset], lda, &af[af_offset], ldaf); 00684 00685 /* Compute the solution matrix X. */ 00686 00687 slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); 00688 sgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, 00689 info); 00690 00691 /* Use iterative refinement to improve the computed solution and */ 00692 /* compute error bounds and backward error estimates for it. */ 00693 00694 sgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & 00695 ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx, 00696 rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[ 00697 err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], 00698 nparams, ¶ms[1], &work[1], &iwork[1], info); 00699 00700 /* Scale solutions. */ 00701 00702 if (colequ && notran) { 00703 slascl2_(n, nrhs, &c__[1], &x[x_offset], ldx); 00704 } else if (rowequ && ! notran) { 00705 slascl2_(n, nrhs, &r__[1], &x[x_offset], ldx); 00706 } 00707 00708 return 0; 00709 00710 /* End of SGESVXX */ 00711 } /* sgesvxx_ */