00001 /* cgbsvxx.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 cgbsvxx_(char *fact, char *trans, integer *n, integer * 00017 kl, integer *ku, integer *nrhs, complex *ab, integer *ldab, complex * 00018 afb, integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__, 00019 complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, 00020 real *rpvgrw, real *berr, integer *n_err_bnds__, real * 00021 err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * 00022 params, complex *work, real *rwork, integer *info) 00023 { 00024 /* System generated locals */ 00025 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 00026 x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, 00027 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4; 00028 real r__1, r__2; 00029 00030 /* Local variables */ 00031 integer i__, j; 00032 real amax; 00033 extern doublereal cla_gbrpvgrw__(integer *, integer *, integer *, integer 00034 *, complex *, integer *, complex *, integer *); 00035 extern logical lsame_(char *, char *); 00036 real rcmin, rcmax; 00037 logical equil; 00038 extern /* Subroutine */ int claqgb_(integer *, integer *, integer *, 00039 integer *, complex *, integer *, real *, real *, real *, real *, 00040 real *, char *); 00041 real colcnd; 00042 extern doublereal slamch_(char *); 00043 extern /* Subroutine */ int cgbtrf_(integer *, integer *, integer *, 00044 integer *, complex *, integer *, integer *, integer *); 00045 logical nofact; 00046 extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 00047 *, integer *, complex *, integer *), xerbla_(char *, 00048 integer *); 00049 real bignum; 00050 extern /* Subroutine */ int cgbtrs_(char *, integer *, integer *, integer 00051 *, integer *, complex *, integer *, integer *, complex *, integer 00052 *, integer *); 00053 integer infequ; 00054 logical colequ; 00055 real rowcnd; 00056 logical notran; 00057 real smlnum; 00058 logical rowequ; 00059 extern /* Subroutine */ int clascl2_(integer *, integer *, real *, 00060 complex *, integer *), cgbequb_(integer *, integer *, integer *, 00061 integer *, complex *, integer *, real *, real *, real *, real *, 00062 real *, integer *), cgbrfsx_(char *, char *, integer *, integer *, 00063 integer *, integer *, complex *, integer *, complex *, integer *, 00064 integer *, real *, real *, complex *, integer *, complex *, 00065 integer *, real *, real *, integer *, real *, real *, integer *, 00066 real *, complex *, real *, integer *); 00067 00068 00069 /* -- LAPACK driver routine (version 3.2) -- */ 00070 /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ 00071 /* -- Jason Riedy of Univ. of California Berkeley. -- */ 00072 /* -- November 2008 -- */ 00073 00074 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ 00075 /* -- Univ. of California Berkeley and NAG Ltd. -- */ 00076 00077 /* .. */ 00078 /* .. Scalar Arguments .. */ 00079 /* .. */ 00080 /* .. Array Arguments .. */ 00081 /* .. */ 00082 00083 /* Purpose */ 00084 /* ======= */ 00085 00086 /* CGBSVXX uses the LU factorization to compute the solution to a */ 00087 /* complex system of linear equations A * X = B, where A is an */ 00088 /* N-by-N matrix and X and B are N-by-NRHS matrices. */ 00089 00090 /* If requested, both normwise and maximum componentwise error bounds */ 00091 /* are returned. CGBSVXX will return a solution with a tiny */ 00092 /* guaranteed error (O(eps) where eps is the working machine */ 00093 /* precision) unless the matrix is very ill-conditioned, in which */ 00094 /* case a warning is returned. Relevant condition numbers also are */ 00095 /* calculated and returned. */ 00096 00097 /* CGBSVXX accepts user-provided factorizations and equilibration */ 00098 /* factors; see the definitions of the FACT and EQUED options. */ 00099 /* Solving with refinement and using a factorization from a previous */ 00100 /* CGBSVXX call will also produce a solution with either O(eps) */ 00101 /* errors or warnings, but we cannot make that claim for general */ 00102 /* user-provided factorizations and equilibration factors if they */ 00103 /* differ from what CGBSVXX would itself produce. */ 00104 00105 /* Description */ 00106 /* =========== */ 00107 00108 /* The following steps are performed: */ 00109 00110 /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ 00111 /* the system: */ 00112 00113 /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ 00114 /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ 00115 /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ 00116 00117 /* Whether or not the system will be equilibrated depends on the */ 00118 /* scaling of the matrix A, but if equilibration is used, A is */ 00119 /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ 00120 /* or diag(C)*B (if TRANS = 'T' or 'C'). */ 00121 00122 /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */ 00123 /* the matrix A (after equilibration if FACT = 'E') as */ 00124 00125 /* A = P * L * U, */ 00126 00127 /* where P is a permutation matrix, L is a unit lower triangular */ 00128 /* matrix, and U is upper triangular. */ 00129 00130 /* 3. If some U(i,i)=0, so that U is exactly singular, then the */ 00131 /* routine returns with INFO = i. Otherwise, the factored form of A */ 00132 /* is used to estimate the condition number of the matrix A (see */ 00133 /* argument RCOND). If the reciprocal of the condition number is less */ 00134 /* than machine precision, the routine still goes on to solve for X */ 00135 /* and compute error bounds as described below. */ 00136 00137 /* 4. The system of equations is solved for X using the factored form */ 00138 /* of A. */ 00139 00140 /* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */ 00141 /* the routine will use iterative refinement to try to get a small */ 00142 /* error and error bounds. Refinement calculates the residual to at */ 00143 /* least twice the working precision. */ 00144 00145 /* 6. If equilibration was used, the matrix X is premultiplied by */ 00146 /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ 00147 /* that it solves the original system before equilibration. */ 00148 00149 /* Arguments */ 00150 /* ========= */ 00151 00152 /* Some optional parameters are bundled in the PARAMS array. These */ 00153 /* settings determine how refinement is performed, but often the */ 00154 /* defaults are acceptable. If the defaults are acceptable, users */ 00155 /* can pass NPARAMS = 0 which prevents the source code from accessing */ 00156 /* the PARAMS argument. */ 00157 00158 /* FACT (input) CHARACTER*1 */ 00159 /* Specifies whether or not the factored form of the matrix A is */ 00160 /* supplied on entry, and if not, whether the matrix A should be */ 00161 /* equilibrated before it is factored. */ 00162 /* = 'F': On entry, AF and IPIV contain the factored form of A. */ 00163 /* If EQUED is not 'N', the matrix A has been */ 00164 /* equilibrated with scaling factors given by R and C. */ 00165 /* A, AF, and IPIV are not modified. */ 00166 /* = 'N': The matrix A will be copied to AF and factored. */ 00167 /* = 'E': The matrix A will be equilibrated if necessary, then */ 00168 /* copied to AF and factored. */ 00169 00170 /* TRANS (input) CHARACTER*1 */ 00171 /* Specifies the form of the system of equations: */ 00172 /* = 'N': A * X = B (No transpose) */ 00173 /* = 'T': A**T * X = B (Transpose) */ 00174 /* = 'C': A**H * X = B (Conjugate Transpose = Transpose) */ 00175 00176 /* N (input) INTEGER */ 00177 /* The number of linear equations, i.e., the order of the */ 00178 /* matrix A. N >= 0. */ 00179 00180 /* KL (input) INTEGER */ 00181 /* The number of subdiagonals within the band of A. KL >= 0. */ 00182 00183 /* KU (input) INTEGER */ 00184 /* The number of superdiagonals within the band of A. KU >= 0. */ 00185 00186 /* NRHS (input) INTEGER */ 00187 /* The number of right hand sides, i.e., the number of columns */ 00188 /* of the matrices B and X. NRHS >= 0. */ 00189 00190 /* AB (input/output) REAL array, dimension (LDAB,N) */ 00191 /* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */ 00192 /* The j-th column of A is stored in the j-th column of the */ 00193 /* array AB as follows: */ 00194 /* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */ 00195 00196 /* If FACT = 'F' and EQUED is not 'N', then AB must have been */ 00197 /* equilibrated by the scaling factors in R and/or C. AB is not */ 00198 /* modified if FACT = 'F' or 'N', or if FACT = 'E' and */ 00199 /* EQUED = 'N' on exit. */ 00200 00201 /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ 00202 /* EQUED = 'R': A := diag(R) * A */ 00203 /* EQUED = 'C': A := A * diag(C) */ 00204 /* EQUED = 'B': A := diag(R) * A * diag(C). */ 00205 00206 /* LDAB (input) INTEGER */ 00207 /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ 00208 00209 /* AFB (input or output) REAL array, dimension (LDAFB,N) */ 00210 /* If FACT = 'F', then AFB is an input argument and on entry */ 00211 /* contains details of the LU factorization of the band matrix */ 00212 /* A, as computed by CGBTRF. U is stored as an upper triangular */ 00213 /* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */ 00214 /* and the multipliers used during the factorization are stored */ 00215 /* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */ 00216 /* the factored form of the equilibrated matrix A. */ 00217 00218 /* If FACT = 'N', then AF is an output argument and on exit */ 00219 /* returns the factors L and U from the factorization A = P*L*U */ 00220 /* of the original matrix A. */ 00221 00222 /* If FACT = 'E', then AF is an output argument and on exit */ 00223 /* returns the factors L and U from the factorization A = P*L*U */ 00224 /* of the equilibrated matrix A (see the description of A for */ 00225 /* the form of the equilibrated matrix). */ 00226 00227 /* LDAFB (input) INTEGER */ 00228 /* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */ 00229 00230 /* IPIV (input or output) INTEGER array, dimension (N) */ 00231 /* If FACT = 'F', then IPIV is an input argument and on entry */ 00232 /* contains the pivot indices from the factorization A = P*L*U */ 00233 /* as computed by SGETRF; row i of the matrix was interchanged */ 00234 /* with row IPIV(i). */ 00235 00236 /* If FACT = 'N', then IPIV is an output argument and on exit */ 00237 /* contains the pivot indices from the factorization A = P*L*U */ 00238 /* of the original matrix A. */ 00239 00240 /* If FACT = 'E', then IPIV is an output argument and on exit */ 00241 /* contains the pivot indices from the factorization A = P*L*U */ 00242 /* of the equilibrated matrix A. */ 00243 00244 /* EQUED (input or output) CHARACTER*1 */ 00245 /* Specifies the form of equilibration that was done. */ 00246 /* = 'N': No equilibration (always true if FACT = 'N'). */ 00247 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00248 /* diag(R). */ 00249 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00250 /* by diag(C). */ 00251 /* = 'B': Both row and column equilibration, i.e., A has been */ 00252 /* replaced by diag(R) * A * diag(C). */ 00253 /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ 00254 /* output argument. */ 00255 00256 /* R (input or output) REAL array, dimension (N) */ 00257 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00258 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00259 /* is not accessed. R is an input argument if FACT = 'F'; */ 00260 /* otherwise, R is an output argument. If FACT = 'F' and */ 00261 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00262 /* If R is output, each element of R is a power of the radix. */ 00263 /* If R is input, each element of R should be a power of the radix */ 00264 /* to ensure a reliable solution and error estimates. Scaling by */ 00265 /* powers of the radix does not cause rounding errors unless the */ 00266 /* result underflows or overflows. Rounding errors during scaling */ 00267 /* lead to refining with a matrix that is not equivalent to the */ 00268 /* input matrix, producing error estimates that may not be */ 00269 /* reliable. */ 00270 00271 /* C (input or output) REAL array, dimension (N) */ 00272 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00273 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00274 /* is not accessed. C is an input argument if FACT = 'F'; */ 00275 /* otherwise, C is an output argument. If FACT = 'F' and */ 00276 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00277 /* If C is output, each element of C is a power of the radix. */ 00278 /* If C is input, each element of C should be a power of the radix */ 00279 /* to ensure a reliable solution and error estimates. Scaling by */ 00280 /* powers of the radix does not cause rounding errors unless the */ 00281 /* result underflows or overflows. Rounding errors during scaling */ 00282 /* lead to refining with a matrix that is not equivalent to the */ 00283 /* input matrix, producing error estimates that may not be */ 00284 /* reliable. */ 00285 00286 /* B (input/output) REAL array, dimension (LDB,NRHS) */ 00287 /* On entry, the N-by-NRHS right hand side matrix B. */ 00288 /* On exit, */ 00289 /* if EQUED = 'N', B is not modified; */ 00290 /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ 00291 /* diag(R)*B; */ 00292 /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ 00293 /* overwritten by diag(C)*B. */ 00294 00295 /* LDB (input) INTEGER */ 00296 /* The leading dimension of the array B. LDB >= max(1,N). */ 00297 00298 /* X (output) REAL array, dimension (LDX,NRHS) */ 00299 /* If INFO = 0, the N-by-NRHS solution matrix X to the original */ 00300 /* system of equations. Note that A and B are modified on exit */ 00301 /* if EQUED .ne. 'N', and the solution to the equilibrated system is */ 00302 /* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */ 00303 /* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */ 00304 00305 /* LDX (input) INTEGER */ 00306 /* The leading dimension of the array X. LDX >= max(1,N). */ 00307 00308 /* RCOND (output) REAL */ 00309 /* Reciprocal scaled condition number. This is an estimate of the */ 00310 /* reciprocal Skeel condition number of the matrix A after */ 00311 /* equilibration (if done). If this is less than the machine */ 00312 /* precision (in particular, if it is zero), the matrix is singular */ 00313 /* to working precision. Note that the error may still be small even */ 00314 /* if this number is very small and the matrix appears ill- */ 00315 /* conditioned. */ 00316 00317 /* RPVGRW (output) REAL */ 00318 /* Reciprocal pivot growth. On exit, this contains the reciprocal */ 00319 /* pivot growth factor norm(A)/norm(U). The "max absolute element" */ 00320 /* norm is used. If this is much less than 1, then the stability of */ 00321 /* the LU factorization of the (equilibrated) matrix A could be poor. */ 00322 /* This also means that the solution X, estimated condition numbers, */ 00323 /* and error bounds could be unreliable. If factorization fails with */ 00324 /* 0<INFO<=N, then this contains the reciprocal pivot growth factor */ 00325 /* for the leading INFO columns of A. In SGESVX, this quantity is */ 00326 /* returned in WORK(1). */ 00327 00328 /* BERR (output) REAL array, dimension (NRHS) */ 00329 /* Componentwise relative backward error. This is the */ 00330 /* componentwise relative backward error of each solution vector X(j) */ 00331 /* (i.e., the smallest relative change in any element of A or B that */ 00332 /* makes X(j) an exact solution). */ 00333 00334 /* N_ERR_BNDS (input) INTEGER */ 00335 /* Number of error bounds to return for each right hand side */ 00336 /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ 00337 /* ERR_BNDS_COMP below. */ 00338 00339 /* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00340 /* For each right-hand side, this array contains information about */ 00341 /* various error bounds and condition numbers corresponding to the */ 00342 /* normwise relative error, which is defined as follows: */ 00343 00344 /* Normwise relative error in the ith solution vector: */ 00345 /* max_j (abs(XTRUE(j,i) - X(j,i))) */ 00346 /* ------------------------------ */ 00347 /* max_j abs(X(j,i)) */ 00348 00349 /* The array is indexed by the type of error information as described */ 00350 /* below. There currently are up to three pieces of information */ 00351 /* returned. */ 00352 00353 /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ 00354 /* right-hand side. */ 00355 00356 /* The second index in ERR_BNDS_NORM(:,err) contains the following */ 00357 /* three fields: */ 00358 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00359 /* reciprocal condition number is less than the threshold */ 00360 /* sqrt(n) * slamch('Epsilon'). */ 00361 00362 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00363 /* almost certainly within a factor of 10 of the true error */ 00364 /* so long as the next entry is greater than the threshold */ 00365 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00366 /* be trusted if the previous boolean is true. */ 00367 00368 /* err = 3 Reciprocal condition number: Estimated normwise */ 00369 /* reciprocal condition number. Compared with the threshold */ 00370 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00371 /* estimate is "guaranteed". These reciprocal condition */ 00372 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00373 /* appropriately scaled matrix Z. */ 00374 /* Let Z = S*A, where S scales each row by a power of the */ 00375 /* radix so all absolute row sums of Z are approximately 1. */ 00376 00377 /* See Lapack Working Note 165 for further details and extra */ 00378 /* cautions. */ 00379 00380 /* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */ 00381 /* For each right-hand side, this array contains information about */ 00382 /* various error bounds and condition numbers corresponding to the */ 00383 /* componentwise relative error, which is defined as follows: */ 00384 00385 /* Componentwise relative error in the ith solution vector: */ 00386 /* abs(XTRUE(j,i) - X(j,i)) */ 00387 /* max_j ---------------------- */ 00388 /* abs(X(j,i)) */ 00389 00390 /* The array is indexed by the right-hand side i (on which the */ 00391 /* componentwise relative error depends), and the type of error */ 00392 /* information as described below. There currently are up to three */ 00393 /* pieces of information returned for each right-hand side. If */ 00394 /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ 00395 /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ 00396 /* the first (:,N_ERR_BNDS) entries are returned. */ 00397 00398 /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ 00399 /* right-hand side. */ 00400 00401 /* The second index in ERR_BNDS_COMP(:,err) contains the following */ 00402 /* three fields: */ 00403 /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ 00404 /* reciprocal condition number is less than the threshold */ 00405 /* sqrt(n) * slamch('Epsilon'). */ 00406 00407 /* err = 2 "Guaranteed" error bound: The estimated forward error, */ 00408 /* almost certainly within a factor of 10 of the true error */ 00409 /* so long as the next entry is greater than the threshold */ 00410 /* sqrt(n) * slamch('Epsilon'). This error bound should only */ 00411 /* be trusted if the previous boolean is true. */ 00412 00413 /* err = 3 Reciprocal condition number: Estimated componentwise */ 00414 /* reciprocal condition number. Compared with the threshold */ 00415 /* sqrt(n) * slamch('Epsilon') to determine if the error */ 00416 /* estimate is "guaranteed". These reciprocal condition */ 00417 /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ 00418 /* appropriately scaled matrix Z. */ 00419 /* Let Z = S*(A*diag(x)), where x is the solution for the */ 00420 /* current right-hand side and S scales each row of */ 00421 /* A*diag(x) by a power of the radix so all absolute row */ 00422 /* sums of Z are approximately 1. */ 00423 00424 /* See Lapack Working Note 165 for further details and extra */ 00425 /* cautions. */ 00426 00427 /* NPARAMS (input) INTEGER */ 00428 /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ 00429 /* PARAMS array is never referenced and default values are used. */ 00430 00431 /* PARAMS (input / output) REAL array, dimension NPARAMS */ 00432 /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ 00433 /* that entry will be filled with default value used for that */ 00434 /* parameter. Only positions up to NPARAMS are accessed; defaults */ 00435 /* are used for higher-numbered parameters. */ 00436 00437 /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ 00438 /* refinement or not. */ 00439 /* Default: 1.0 */ 00440 /* = 0.0 : No refinement is performed, and no error bounds are */ 00441 /* computed. */ 00442 /* = 1.0 : Use the double-precision refinement algorithm, */ 00443 /* possibly with doubled-single computations if the */ 00444 /* compilation environment does not support DOUBLE */ 00445 /* PRECISION. */ 00446 /* (other values are reserved for future use) */ 00447 00448 /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ 00449 /* computations allowed for refinement. */ 00450 /* Default: 10 */ 00451 /* Aggressive: Set to 100 to permit convergence using approximate */ 00452 /* factorizations or factorizations other than LU. If */ 00453 /* the factorization uses a technique other than */ 00454 /* Gaussian elimination, the guarantees in */ 00455 /* err_bnds_norm and err_bnds_comp may no longer be */ 00456 /* trustworthy. */ 00457 00458 /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ 00459 /* will attempt to find a solution with small componentwise */ 00460 /* relative error in the double-precision algorithm. Positive */ 00461 /* is true, 0.0 is false. */ 00462 /* Default: 1.0 (attempt componentwise convergence) */ 00463 00464 /* WORK (workspace) REAL array, dimension (4*N) */ 00465 00466 /* IWORK (workspace) INTEGER array, dimension (N) */ 00467 00468 /* INFO (output) INTEGER */ 00469 /* = 0: Successful exit. The solution to every right-hand side is */ 00470 /* guaranteed. */ 00471 /* < 0: If INFO = -i, the i-th argument had an illegal value */ 00472 /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ 00473 /* has been completed, but the factor U is exactly singular, so */ 00474 /* the solution and error bounds could not be computed. RCOND = 0 */ 00475 /* is returned. */ 00476 /* = N+J: The solution corresponding to the Jth right-hand side is */ 00477 /* not guaranteed. The solutions corresponding to other right- */ 00478 /* hand sides K with K > J may not be guaranteed as well, but */ 00479 /* only the first such right-hand side is reported. If a small */ 00480 /* componentwise error is not requested (PARAMS(3) = 0.0) then */ 00481 /* the Jth right-hand side is the first with a normwise error */ 00482 /* bound that is not guaranteed (the smallest J such */ 00483 /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ 00484 /* the Jth right-hand side is the first with either a normwise or */ 00485 /* componentwise error bound that is not guaranteed (the smallest */ 00486 /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ 00487 /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ 00488 /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ 00489 /* about all of the right-hand sides check ERR_BNDS_NORM or */ 00490 /* ERR_BNDS_COMP. */ 00491 00492 /* ================================================================== */ 00493 00494 /* .. Parameters .. */ 00495 /* .. */ 00496 /* .. Local Scalars .. */ 00497 /* .. */ 00498 /* .. External Functions .. */ 00499 /* .. */ 00500 /* .. External Subroutines .. */ 00501 /* .. */ 00502 /* .. Intrinsic Functions .. */ 00503 /* .. */ 00504 /* .. Executable Statements .. */ 00505 00506 /* Parameter adjustments */ 00507 err_bnds_comp_dim1 = *nrhs; 00508 err_bnds_comp_offset = 1 + err_bnds_comp_dim1; 00509 err_bnds_comp__ -= err_bnds_comp_offset; 00510 err_bnds_norm_dim1 = *nrhs; 00511 err_bnds_norm_offset = 1 + err_bnds_norm_dim1; 00512 err_bnds_norm__ -= err_bnds_norm_offset; 00513 ab_dim1 = *ldab; 00514 ab_offset = 1 + ab_dim1; 00515 ab -= ab_offset; 00516 afb_dim1 = *ldafb; 00517 afb_offset = 1 + afb_dim1; 00518 afb -= afb_offset; 00519 --ipiv; 00520 --r__; 00521 --c__; 00522 b_dim1 = *ldb; 00523 b_offset = 1 + b_dim1; 00524 b -= b_offset; 00525 x_dim1 = *ldx; 00526 x_offset = 1 + x_dim1; 00527 x -= x_offset; 00528 --berr; 00529 --params; 00530 --work; 00531 --rwork; 00532 00533 /* Function Body */ 00534 *info = 0; 00535 nofact = lsame_(fact, "N"); 00536 equil = lsame_(fact, "E"); 00537 notran = lsame_(trans, "N"); 00538 smlnum = slamch_("Safe minimum"); 00539 bignum = 1.f / smlnum; 00540 if (nofact || equil) { 00541 *(unsigned char *)equed = 'N'; 00542 rowequ = FALSE_; 00543 colequ = FALSE_; 00544 } else { 00545 rowequ = lsame_(equed, "R") || lsame_(equed, 00546 "B"); 00547 colequ = lsame_(equed, "C") || lsame_(equed, 00548 "B"); 00549 } 00550 00551 /* Default is failure. If an input parameter is wrong or */ 00552 /* factorization fails, make everything look horrible. Only the */ 00553 /* pivot growth is set here, the rest is initialized in CGBRFSX. */ 00554 00555 *rpvgrw = 0.f; 00556 00557 /* Test the input parameters. PARAMS is not tested until SGERFSX. */ 00558 00559 if (! nofact && ! equil && ! lsame_(fact, "F")) { 00560 *info = -1; 00561 } else if (! notran && ! lsame_(trans, "T") && ! 00562 lsame_(trans, "C")) { 00563 *info = -2; 00564 } else if (*n < 0) { 00565 *info = -3; 00566 } else if (*kl < 0) { 00567 *info = -4; 00568 } else if (*ku < 0) { 00569 *info = -5; 00570 } else if (*nrhs < 0) { 00571 *info = -6; 00572 } else if (*ldab < *kl + *ku + 1) { 00573 *info = -8; 00574 } else if (*ldafb < (*kl << 1) + *ku + 1) { 00575 *info = -10; 00576 } else if (lsame_(fact, "F") && ! (rowequ || colequ 00577 || lsame_(equed, "N"))) { 00578 *info = -12; 00579 } else { 00580 if (rowequ) { 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 = r__[j]; 00587 rcmin = dmin(r__1,r__2); 00588 /* Computing MAX */ 00589 r__1 = rcmax, r__2 = r__[j]; 00590 rcmax = dmax(r__1,r__2); 00591 /* L10: */ 00592 } 00593 if (rcmin <= 0.f) { 00594 *info = -13; 00595 } else if (*n > 0) { 00596 rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00597 } else { 00598 rowcnd = 1.f; 00599 } 00600 } 00601 if (colequ && *info == 0) { 00602 rcmin = bignum; 00603 rcmax = 0.f; 00604 i__1 = *n; 00605 for (j = 1; j <= i__1; ++j) { 00606 /* Computing MIN */ 00607 r__1 = rcmin, r__2 = c__[j]; 00608 rcmin = dmin(r__1,r__2); 00609 /* Computing MAX */ 00610 r__1 = rcmax, r__2 = c__[j]; 00611 rcmax = dmax(r__1,r__2); 00612 /* L20: */ 00613 } 00614 if (rcmin <= 0.f) { 00615 *info = -14; 00616 } else if (*n > 0) { 00617 colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); 00618 } else { 00619 colcnd = 1.f; 00620 } 00621 } 00622 if (*info == 0) { 00623 if (*ldb < max(1,*n)) { 00624 *info = -15; 00625 } else if (*ldx < max(1,*n)) { 00626 *info = -16; 00627 } 00628 } 00629 } 00630 00631 if (*info != 0) { 00632 i__1 = -(*info); 00633 xerbla_("CGBSVXX", &i__1); 00634 return 0; 00635 } 00636 00637 if (equil) { 00638 00639 /* Compute row and column scalings to equilibrate the matrix A. */ 00640 00641 cgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & 00642 rowcnd, &colcnd, &amax, &infequ); 00643 if (infequ == 0) { 00644 00645 /* Equilibrate the matrix. */ 00646 00647 claqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & 00648 rowcnd, &colcnd, &amax, equed); 00649 rowequ = lsame_(equed, "R") || lsame_(equed, 00650 "B"); 00651 colequ = lsame_(equed, "C") || lsame_(equed, 00652 "B"); 00653 } 00654 00655 /* If the scaling factors are not applied, set them to 1.0. */ 00656 00657 if (! rowequ) { 00658 i__1 = *n; 00659 for (j = 1; j <= i__1; ++j) { 00660 r__[j] = 1.f; 00661 } 00662 } 00663 if (! colequ) { 00664 i__1 = *n; 00665 for (j = 1; j <= i__1; ++j) { 00666 c__[j] = 1.f; 00667 } 00668 } 00669 } 00670 00671 /* Scale the right-hand side. */ 00672 00673 if (notran) { 00674 if (rowequ) { 00675 clascl2_(n, nrhs, &r__[1], &b[b_offset], ldb); 00676 } 00677 } else { 00678 if (colequ) { 00679 clascl2_(n, nrhs, &c__[1], &b[b_offset], ldb); 00680 } 00681 } 00682 00683 if (nofact || equil) { 00684 00685 /* Compute the LU factorization of A. */ 00686 00687 i__1 = *n; 00688 for (j = 1; j <= i__1; ++j) { 00689 i__2 = (*kl << 1) + *ku + 1; 00690 for (i__ = *kl + 1; i__ <= i__2; ++i__) { 00691 i__3 = i__ + j * afb_dim1; 00692 i__4 = i__ - *kl + j * ab_dim1; 00693 afb[i__3].r = ab[i__4].r, afb[i__3].i = ab[i__4].i; 00694 /* L30: */ 00695 } 00696 /* L40: */ 00697 } 00698 cgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info); 00699 00700 /* Return if INFO is non-zero. */ 00701 00702 if (*info > 0) { 00703 00704 /* Pivot in column INFO is exactly 0 */ 00705 /* Compute the reciprocal pivot growth factor of the */ 00706 /* leading rank-deficient INFO columns of A. */ 00707 00708 *rpvgrw = cla_gbrpvgrw__(n, kl, ku, info, &ab[ab_offset], ldab, & 00709 afb[afb_offset], ldafb); 00710 return 0; 00711 } 00712 } 00713 00714 /* Compute the reciprocal pivot growth factor RPVGRW. */ 00715 00716 *rpvgrw = cla_gbrpvgrw__(n, kl, ku, n, &ab[ab_offset], ldab, &afb[ 00717 afb_offset], ldafb); 00718 00719 /* Compute the solution matrix X. */ 00720 00721 clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); 00722 cgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &ipiv[1], &x[ 00723 x_offset], ldx, info); 00724 00725 /* Use iterative refinement to improve the computed solution and */ 00726 /* compute error bounds and backward error estimates for it. */ 00727 00728 cgbrfsx_(trans, equed, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[ 00729 afb_offset], ldafb, &ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, 00730 &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, & 00731 err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ 00732 err_bnds_comp_offset], nparams, ¶ms[1], &work[1], &rwork[1], 00733 info); 00734 00735 /* Scale solutions. */ 00736 00737 if (colequ && notran) { 00738 clascl2_(n, nrhs, &c__[1], &x[x_offset], ldx); 00739 } else if (rowequ && ! notran) { 00740 clascl2_(n, nrhs, &r__[1], &x[x_offset], ldx); 00741 } 00742 00743 return 0; 00744 00745 /* End of CGBSVXX */ 00746 00747 } /* cgbsvxx_ */