00001 /* zgbsvx.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 /* Table of constant values */ 00017 00018 static integer c__1 = 1; 00019 00020 /* Subroutine */ int zgbsvx_(char *fact, char *trans, integer *n, integer *kl, 00021 integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, 00022 doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed, 00023 doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, 00024 doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr, 00025 doublereal *berr, doublecomplex *work, doublereal *rwork, integer * 00026 info) 00027 { 00028 /* System generated locals */ 00029 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 00030 x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; 00031 doublereal d__1, d__2; 00032 doublecomplex z__1; 00033 00034 /* Builtin functions */ 00035 double z_abs(doublecomplex *); 00036 00037 /* Local variables */ 00038 integer i__, j, j1, j2; 00039 doublereal amax; 00040 char norm[1]; 00041 extern logical lsame_(char *, char *); 00042 doublereal rcmin, rcmax, anorm; 00043 logical equil; 00044 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 00045 doublecomplex *, integer *); 00046 extern doublereal dlamch_(char *); 00047 doublereal colcnd; 00048 logical nofact; 00049 extern doublereal zlangb_(char *, integer *, integer *, integer *, 00050 doublecomplex *, integer *, doublereal *); 00051 extern /* Subroutine */ int xerbla_(char *, integer *), zlaqgb_( 00052 integer *, integer *, integer *, integer *, doublecomplex *, 00053 integer *, doublereal *, doublereal *, doublereal *, doublereal *, 00054 doublereal *, char *); 00055 doublereal bignum; 00056 extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer 00057 *, doublecomplex *, integer *, integer *, doublereal *, 00058 doublereal *, doublecomplex *, doublereal *, integer *); 00059 integer infequ; 00060 logical colequ; 00061 extern doublereal zlantb_(char *, char *, char *, integer *, integer *, 00062 doublecomplex *, integer *, doublereal *); 00063 doublereal rowcnd; 00064 extern /* Subroutine */ int zgbequ_(integer *, integer *, integer *, 00065 integer *, doublecomplex *, integer *, doublereal *, doublereal *, 00066 doublereal *, doublereal *, doublereal *, integer *), zgbrfs_( 00067 char *, integer *, integer *, integer *, integer *, doublecomplex 00068 *, integer *, doublecomplex *, integer *, integer *, 00069 doublecomplex *, integer *, doublecomplex *, integer *, 00070 doublereal *, doublereal *, doublecomplex *, doublereal *, 00071 integer *), zgbtrf_(integer *, integer *, integer *, 00072 integer *, doublecomplex *, integer *, integer *, integer *); 00073 logical notran; 00074 extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 00075 doublecomplex *, integer *, doublecomplex *, integer *); 00076 doublereal smlnum; 00077 extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer 00078 *, integer *, doublecomplex *, integer *, integer *, 00079 doublecomplex *, integer *, integer *); 00080 logical rowequ; 00081 doublereal rpvgrw; 00082 00083 00084 /* -- LAPACK driver routine (version 3.2) -- */ 00085 /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ 00086 /* November 2006 */ 00087 00088 /* .. Scalar Arguments .. */ 00089 /* .. */ 00090 /* .. Array Arguments .. */ 00091 /* .. */ 00092 00093 /* Purpose */ 00094 /* ======= */ 00095 00096 /* ZGBSVX uses the LU factorization to compute the solution to a complex */ 00097 /* system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */ 00098 /* where A is a band matrix of order N with KL subdiagonals and KU */ 00099 /* superdiagonals, and X and B are N-by-NRHS matrices. */ 00100 00101 /* Error bounds on the solution and a condition estimate are also */ 00102 /* provided. */ 00103 00104 /* Description */ 00105 /* =========== */ 00106 00107 /* The following steps are performed by this subroutine: */ 00108 00109 /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ 00110 /* the system: */ 00111 /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ 00112 /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ 00113 /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ 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 the */ 00120 /* matrix A (after equilibration if FACT = 'E') as */ 00121 /* A = L * U, */ 00122 /* where L is a product of permutation and unit lower triangular */ 00123 /* matrices with KL subdiagonals, and U is upper triangular with */ 00124 /* KL+KU superdiagonals. */ 00125 00126 /* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */ 00127 /* returns with INFO = i. Otherwise, the factored form of A is used */ 00128 /* to estimate the condition number of the matrix A. If the */ 00129 /* reciprocal of the condition number is less than machine precision, */ 00130 /* INFO = N+1 is returned as a warning, but the routine still goes on */ 00131 /* to solve for X and compute error bounds as described below. */ 00132 00133 /* 4. The system of equations is solved for X using the factored form */ 00134 /* of A. */ 00135 00136 /* 5. Iterative refinement is applied to improve the computed solution */ 00137 /* matrix and calculate error bounds and backward error estimates */ 00138 /* for it. */ 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 /* FACT (input) CHARACTER*1 */ 00148 /* Specifies whether or not the factored form of the matrix A is */ 00149 /* supplied on entry, and if not, whether the matrix A should be */ 00150 /* equilibrated before it is factored. */ 00151 /* = 'F': On entry, AFB and IPIV contain the factored form of */ 00152 /* A. If EQUED is not 'N', the matrix A has been */ 00153 /* equilibrated with scaling factors given by R and C. */ 00154 /* AB, AFB, and IPIV are not modified. */ 00155 /* = 'N': The matrix A will be copied to AFB and factored. */ 00156 /* = 'E': The matrix A will be equilibrated if necessary, then */ 00157 /* copied to AFB and factored. */ 00158 00159 /* TRANS (input) CHARACTER*1 */ 00160 /* Specifies the form of the system of equations. */ 00161 /* = 'N': A * X = B (No transpose) */ 00162 /* = 'T': A**T * X = B (Transpose) */ 00163 /* = 'C': A**H * X = B (Conjugate transpose) */ 00164 00165 /* N (input) INTEGER */ 00166 /* The number of linear equations, i.e., the order of the */ 00167 /* matrix A. N >= 0. */ 00168 00169 /* KL (input) INTEGER */ 00170 /* The number of subdiagonals within the band of A. KL >= 0. */ 00171 00172 /* KU (input) INTEGER */ 00173 /* The number of superdiagonals within the band of A. KU >= 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 /* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */ 00180 /* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */ 00181 /* The j-th column of A is stored in the j-th column of the */ 00182 /* array AB as follows: */ 00183 /* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */ 00184 00185 /* If FACT = 'F' and EQUED is not 'N', then A must have been */ 00186 /* equilibrated by the scaling factors in R and/or C. AB is not */ 00187 /* modified if FACT = 'F' or 'N', or if FACT = 'E' and */ 00188 /* EQUED = 'N' on exit. */ 00189 00190 /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ 00191 /* EQUED = 'R': A := diag(R) * A */ 00192 /* EQUED = 'C': A := A * diag(C) */ 00193 /* EQUED = 'B': A := diag(R) * A * diag(C). */ 00194 00195 /* LDAB (input) INTEGER */ 00196 /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ 00197 00198 /* AFB (input or output) COMPLEX*16 array, dimension (LDAFB,N) */ 00199 /* If FACT = 'F', then AFB is an input argument and on entry */ 00200 /* contains details of the LU factorization of the band matrix */ 00201 /* A, as computed by ZGBTRF. U is stored as an upper triangular */ 00202 /* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */ 00203 /* and the multipliers used during the factorization are stored */ 00204 /* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */ 00205 /* the factored form of the equilibrated matrix A. */ 00206 00207 /* If FACT = 'N', then AFB is an output argument and on exit */ 00208 /* returns details of the LU factorization of A. */ 00209 00210 /* If FACT = 'E', then AFB is an output argument and on exit */ 00211 /* returns details of the LU factorization of the equilibrated */ 00212 /* matrix A (see the description of AB for the form of the */ 00213 /* equilibrated matrix). */ 00214 00215 /* LDAFB (input) INTEGER */ 00216 /* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */ 00217 00218 /* IPIV (input or output) INTEGER array, dimension (N) */ 00219 /* If FACT = 'F', then IPIV is an input argument and on entry */ 00220 /* contains the pivot indices from the factorization A = L*U */ 00221 /* as computed by ZGBTRF; row i of the matrix was interchanged */ 00222 /* with row IPIV(i). */ 00223 00224 /* If FACT = 'N', then IPIV is an output argument and on exit */ 00225 /* contains the pivot indices from the factorization A = L*U */ 00226 /* of the original matrix A. */ 00227 00228 /* If FACT = 'E', then IPIV is an output argument and on exit */ 00229 /* contains the pivot indices from the factorization A = L*U */ 00230 /* of the equilibrated matrix A. */ 00231 00232 /* EQUED (input or output) CHARACTER*1 */ 00233 /* Specifies the form of equilibration that was done. */ 00234 /* = 'N': No equilibration (always true if FACT = 'N'). */ 00235 /* = 'R': Row equilibration, i.e., A has been premultiplied by */ 00236 /* diag(R). */ 00237 /* = 'C': Column equilibration, i.e., A has been postmultiplied */ 00238 /* by diag(C). */ 00239 /* = 'B': Both row and column equilibration, i.e., A has been */ 00240 /* replaced by diag(R) * A * diag(C). */ 00241 /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ 00242 /* output argument. */ 00243 00244 /* R (input or output) DOUBLE PRECISION array, dimension (N) */ 00245 /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ 00246 /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ 00247 /* is not accessed. R is an input argument if FACT = 'F'; */ 00248 /* otherwise, R is an output argument. If FACT = 'F' and */ 00249 /* EQUED = 'R' or 'B', each element of R must be positive. */ 00250 00251 /* C (input or output) DOUBLE PRECISION array, dimension (N) */ 00252 /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ 00253 /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ 00254 /* is not accessed. C is an input argument if FACT = 'F'; */ 00255 /* otherwise, C is an output argument. If FACT = 'F' and */ 00256 /* EQUED = 'C' or 'B', each element of C must be positive. */ 00257 00258 /* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */ 00259 /* On entry, the right hand side matrix B. */ 00260 /* On exit, */ 00261 /* if EQUED = 'N', B is not modified; */ 00262 /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ 00263 /* diag(R)*B; */ 00264 /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ 00265 /* overwritten by diag(C)*B. */ 00266 00267 /* LDB (input) INTEGER */ 00268 /* The leading dimension of the array B. LDB >= max(1,N). */ 00269 00270 /* X (output) COMPLEX*16 array, dimension (LDX,NRHS) */ 00271 /* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */ 00272 /* to the original system of equations. Note that A and B are */ 00273 /* modified on exit if EQUED .ne. 'N', and the solution to the */ 00274 /* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */ 00275 /* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */ 00276 /* and EQUED = 'R' or 'B'. */ 00277 00278 /* LDX (input) INTEGER */ 00279 /* The leading dimension of the array X. LDX >= max(1,N). */ 00280 00281 /* RCOND (output) DOUBLE PRECISION */ 00282 /* The estimate of the reciprocal condition number of the matrix */ 00283 /* A after equilibration (if done). If RCOND is less than the */ 00284 /* machine precision (in particular, if RCOND = 0), the matrix */ 00285 /* is singular to working precision. This condition is */ 00286 /* indicated by a return code of INFO > 0. */ 00287 00288 /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ 00289 /* The estimated forward error bound for each solution vector */ 00290 /* X(j) (the j-th column of the solution matrix X). */ 00291 /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ 00292 /* is an estimated upper bound for the magnitude of the largest */ 00293 /* element in (X(j) - XTRUE) divided by the magnitude of the */ 00294 /* largest element in X(j). The estimate is as reliable as */ 00295 /* the estimate for RCOND, and is almost always a slight */ 00296 /* overestimate of the true error. */ 00297 00298 /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ 00299 /* The componentwise relative backward error of each solution */ 00300 /* vector X(j) (i.e., the smallest relative change in */ 00301 /* any element of A or B that makes X(j) an exact solution). */ 00302 00303 /* WORK (workspace) COMPLEX*16 array, dimension (2*N) */ 00304 00305 /* RWORK (workspace/output) DOUBLE PRECISION array, dimension (N) */ 00306 /* On exit, RWORK(1) contains the reciprocal pivot growth */ 00307 /* factor norm(A)/norm(U). The "max absolute element" norm is */ 00308 /* used. If RWORK(1) is much less than 1, then the stability */ 00309 /* of the LU factorization of the (equilibrated) matrix A */ 00310 /* could be poor. This also means that the solution X, condition */ 00311 /* estimator RCOND, and forward error bound FERR could be */ 00312 /* unreliable. If factorization fails with 0<INFO<=N, then */ 00313 /* RWORK(1) contains the reciprocal pivot growth factor for the */ 00314 /* leading INFO columns of A. */ 00315 00316 /* INFO (output) INTEGER */ 00317 /* = 0: successful exit */ 00318 /* < 0: if INFO = -i, the i-th argument had an illegal value */ 00319 /* > 0: if INFO = i, and i is */ 00320 /* <= N: U(i,i) is exactly zero. The factorization */ 00321 /* has been completed, but the factor U is exactly */ 00322 /* singular, so the solution and error bounds */ 00323 /* could not be computed. RCOND = 0 is returned. */ 00324 /* = N+1: U is nonsingular, but RCOND is less than machine */ 00325 /* precision, meaning that the matrix is singular */ 00326 /* to working precision. Nevertheless, the */ 00327 /* solution and error bounds are computed because */ 00328 /* there are a number of situations where the */ 00329 /* computed solution can be more accurate than the */ 00330 /* value of RCOND would suggest. */ 00331 00332 /* ===================================================================== */ 00333 /* Moved setting of INFO = N+1 so INFO does not subsequently get */ 00334 /* overwritten. Sven, 17 Mar 05. */ 00335 /* ===================================================================== */ 00336 00337 /* .. Parameters .. */ 00338 /* .. */ 00339 /* .. Local Scalars .. */ 00340 /* .. */ 00341 /* .. External Functions .. */ 00342 /* .. */ 00343 /* .. External Subroutines .. */ 00344 /* .. */ 00345 /* .. Intrinsic Functions .. */ 00346 /* .. */ 00347 /* .. Executable Statements .. */ 00348 00349 /* Parameter adjustments */ 00350 ab_dim1 = *ldab; 00351 ab_offset = 1 + ab_dim1; 00352 ab -= ab_offset; 00353 afb_dim1 = *ldafb; 00354 afb_offset = 1 + afb_dim1; 00355 afb -= afb_offset; 00356 --ipiv; 00357 --r__; 00358 --c__; 00359 b_dim1 = *ldb; 00360 b_offset = 1 + b_dim1; 00361 b -= b_offset; 00362 x_dim1 = *ldx; 00363 x_offset = 1 + x_dim1; 00364 x -= x_offset; 00365 --ferr; 00366 --berr; 00367 --work; 00368 --rwork; 00369 00370 /* Function Body */ 00371 *info = 0; 00372 nofact = lsame_(fact, "N"); 00373 equil = lsame_(fact, "E"); 00374 notran = lsame_(trans, "N"); 00375 if (nofact || equil) { 00376 *(unsigned char *)equed = 'N'; 00377 rowequ = FALSE_; 00378 colequ = FALSE_; 00379 } else { 00380 rowequ = lsame_(equed, "R") || lsame_(equed, 00381 "B"); 00382 colequ = lsame_(equed, "C") || lsame_(equed, 00383 "B"); 00384 smlnum = dlamch_("Safe minimum"); 00385 bignum = 1. / smlnum; 00386 } 00387 00388 /* Test the input parameters. */ 00389 00390 if (! nofact && ! equil && ! lsame_(fact, "F")) { 00391 *info = -1; 00392 } else if (! notran && ! lsame_(trans, "T") && ! 00393 lsame_(trans, "C")) { 00394 *info = -2; 00395 } else if (*n < 0) { 00396 *info = -3; 00397 } else if (*kl < 0) { 00398 *info = -4; 00399 } else if (*ku < 0) { 00400 *info = -5; 00401 } else if (*nrhs < 0) { 00402 *info = -6; 00403 } else if (*ldab < *kl + *ku + 1) { 00404 *info = -8; 00405 } else if (*ldafb < (*kl << 1) + *ku + 1) { 00406 *info = -10; 00407 } else if (lsame_(fact, "F") && ! (rowequ || colequ 00408 || lsame_(equed, "N"))) { 00409 *info = -12; 00410 } else { 00411 if (rowequ) { 00412 rcmin = bignum; 00413 rcmax = 0.; 00414 i__1 = *n; 00415 for (j = 1; j <= i__1; ++j) { 00416 /* Computing MIN */ 00417 d__1 = rcmin, d__2 = r__[j]; 00418 rcmin = min(d__1,d__2); 00419 /* Computing MAX */ 00420 d__1 = rcmax, d__2 = r__[j]; 00421 rcmax = max(d__1,d__2); 00422 /* L10: */ 00423 } 00424 if (rcmin <= 0.) { 00425 *info = -13; 00426 } else if (*n > 0) { 00427 rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); 00428 } else { 00429 rowcnd = 1.; 00430 } 00431 } 00432 if (colequ && *info == 0) { 00433 rcmin = bignum; 00434 rcmax = 0.; 00435 i__1 = *n; 00436 for (j = 1; j <= i__1; ++j) { 00437 /* Computing MIN */ 00438 d__1 = rcmin, d__2 = c__[j]; 00439 rcmin = min(d__1,d__2); 00440 /* Computing MAX */ 00441 d__1 = rcmax, d__2 = c__[j]; 00442 rcmax = max(d__1,d__2); 00443 /* L20: */ 00444 } 00445 if (rcmin <= 0.) { 00446 *info = -14; 00447 } else if (*n > 0) { 00448 colcnd = max(rcmin,smlnum) / min(rcmax,bignum); 00449 } else { 00450 colcnd = 1.; 00451 } 00452 } 00453 if (*info == 0) { 00454 if (*ldb < max(1,*n)) { 00455 *info = -16; 00456 } else if (*ldx < max(1,*n)) { 00457 *info = -18; 00458 } 00459 } 00460 } 00461 00462 if (*info != 0) { 00463 i__1 = -(*info); 00464 xerbla_("ZGBSVX", &i__1); 00465 return 0; 00466 } 00467 00468 if (equil) { 00469 00470 /* Compute row and column scalings to equilibrate the matrix A. */ 00471 00472 zgbequ_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &rowcnd, 00473 &colcnd, &amax, &infequ); 00474 if (infequ == 0) { 00475 00476 /* Equilibrate the matrix. */ 00477 00478 zlaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & 00479 rowcnd, &colcnd, &amax, equed); 00480 rowequ = lsame_(equed, "R") || lsame_(equed, 00481 "B"); 00482 colequ = lsame_(equed, "C") || lsame_(equed, 00483 "B"); 00484 } 00485 } 00486 00487 /* Scale the right hand side. */ 00488 00489 if (notran) { 00490 if (rowequ) { 00491 i__1 = *nrhs; 00492 for (j = 1; j <= i__1; ++j) { 00493 i__2 = *n; 00494 for (i__ = 1; i__ <= i__2; ++i__) { 00495 i__3 = i__ + j * b_dim1; 00496 i__4 = i__; 00497 i__5 = i__ + j * b_dim1; 00498 z__1.r = r__[i__4] * b[i__5].r, z__1.i = r__[i__4] * b[ 00499 i__5].i; 00500 b[i__3].r = z__1.r, b[i__3].i = z__1.i; 00501 /* L30: */ 00502 } 00503 /* L40: */ 00504 } 00505 } 00506 } else if (colequ) { 00507 i__1 = *nrhs; 00508 for (j = 1; j <= i__1; ++j) { 00509 i__2 = *n; 00510 for (i__ = 1; i__ <= i__2; ++i__) { 00511 i__3 = i__ + j * b_dim1; 00512 i__4 = i__; 00513 i__5 = i__ + j * b_dim1; 00514 z__1.r = c__[i__4] * b[i__5].r, z__1.i = c__[i__4] * b[i__5] 00515 .i; 00516 b[i__3].r = z__1.r, b[i__3].i = z__1.i; 00517 /* L50: */ 00518 } 00519 /* L60: */ 00520 } 00521 } 00522 00523 if (nofact || equil) { 00524 00525 /* Compute the LU factorization of the band matrix A. */ 00526 00527 i__1 = *n; 00528 for (j = 1; j <= i__1; ++j) { 00529 /* Computing MAX */ 00530 i__2 = j - *ku; 00531 j1 = max(i__2,1); 00532 /* Computing MIN */ 00533 i__2 = j + *kl; 00534 j2 = min(i__2,*n); 00535 i__2 = j2 - j1 + 1; 00536 zcopy_(&i__2, &ab[*ku + 1 - j + j1 + j * ab_dim1], &c__1, &afb[* 00537 kl + *ku + 1 - j + j1 + j * afb_dim1], &c__1); 00538 /* L70: */ 00539 } 00540 00541 zgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info); 00542 00543 /* Return if INFO is non-zero. */ 00544 00545 if (*info > 0) { 00546 00547 /* Compute the reciprocal pivot growth factor of the */ 00548 /* leading rank-deficient INFO columns of A. */ 00549 00550 anorm = 0.; 00551 i__1 = *info; 00552 for (j = 1; j <= i__1; ++j) { 00553 /* Computing MAX */ 00554 i__2 = *ku + 2 - j; 00555 /* Computing MIN */ 00556 i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1; 00557 i__3 = min(i__4,i__5); 00558 for (i__ = max(i__2,1); i__ <= i__3; ++i__) { 00559 /* Computing MAX */ 00560 d__1 = anorm, d__2 = z_abs(&ab[i__ + j * ab_dim1]); 00561 anorm = max(d__1,d__2); 00562 /* L80: */ 00563 } 00564 /* L90: */ 00565 } 00566 /* Computing MIN */ 00567 i__3 = *info - 1, i__2 = *kl + *ku; 00568 i__1 = min(i__3,i__2); 00569 /* Computing MAX */ 00570 i__4 = 1, i__5 = *kl + *ku + 2 - *info; 00571 rpvgrw = zlantb_("M", "U", "N", info, &i__1, &afb[max(i__4, i__5) 00572 + afb_dim1], ldafb, &rwork[1]); 00573 if (rpvgrw == 0.) { 00574 rpvgrw = 1.; 00575 } else { 00576 rpvgrw = anorm / rpvgrw; 00577 } 00578 rwork[1] = rpvgrw; 00579 *rcond = 0.; 00580 return 0; 00581 } 00582 } 00583 00584 /* Compute the norm of the matrix A and the */ 00585 /* reciprocal pivot growth factor RPVGRW. */ 00586 00587 if (notran) { 00588 *(unsigned char *)norm = '1'; 00589 } else { 00590 *(unsigned char *)norm = 'I'; 00591 } 00592 anorm = zlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &rwork[1]); 00593 i__1 = *kl + *ku; 00594 rpvgrw = zlantb_("M", "U", "N", n, &i__1, &afb[afb_offset], ldafb, &rwork[ 00595 1]); 00596 if (rpvgrw == 0.) { 00597 rpvgrw = 1.; 00598 } else { 00599 rpvgrw = zlangb_("M", n, kl, ku, &ab[ab_offset], ldab, &rwork[1]) / rpvgrw; 00600 } 00601 00602 /* Compute the reciprocal of the condition number of A. */ 00603 00604 zgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond, 00605 &work[1], &rwork[1], info); 00606 00607 /* Compute the solution matrix X. */ 00608 00609 zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); 00610 zgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &ipiv[1], &x[ 00611 x_offset], ldx, info); 00612 00613 /* Use iterative refinement to improve the computed solution and */ 00614 /* compute error bounds and backward error estimates for it. */ 00615 00616 zgbrfs_(trans, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], 00617 ldafb, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], & 00618 berr[1], &work[1], &rwork[1], info); 00619 00620 /* Transform the solution matrix X to a solution of the original */ 00621 /* system. */ 00622 00623 if (notran) { 00624 if (colequ) { 00625 i__1 = *nrhs; 00626 for (j = 1; j <= i__1; ++j) { 00627 i__3 = *n; 00628 for (i__ = 1; i__ <= i__3; ++i__) { 00629 i__2 = i__ + j * x_dim1; 00630 i__4 = i__; 00631 i__5 = i__ + j * x_dim1; 00632 z__1.r = c__[i__4] * x[i__5].r, z__1.i = c__[i__4] * x[ 00633 i__5].i; 00634 x[i__2].r = z__1.r, x[i__2].i = z__1.i; 00635 /* L100: */ 00636 } 00637 /* L110: */ 00638 } 00639 i__1 = *nrhs; 00640 for (j = 1; j <= i__1; ++j) { 00641 ferr[j] /= colcnd; 00642 /* L120: */ 00643 } 00644 } 00645 } else if (rowequ) { 00646 i__1 = *nrhs; 00647 for (j = 1; j <= i__1; ++j) { 00648 i__3 = *n; 00649 for (i__ = 1; i__ <= i__3; ++i__) { 00650 i__2 = i__ + j * x_dim1; 00651 i__4 = i__; 00652 i__5 = i__ + j * x_dim1; 00653 z__1.r = r__[i__4] * x[i__5].r, z__1.i = r__[i__4] * x[i__5] 00654 .i; 00655 x[i__2].r = z__1.r, x[i__2].i = z__1.i; 00656 /* L130: */ 00657 } 00658 /* L140: */ 00659 } 00660 i__1 = *nrhs; 00661 for (j = 1; j <= i__1; ++j) { 00662 ferr[j] /= rowcnd; 00663 /* L150: */ 00664 } 00665 } 00666 00667 /* Set INFO = N+1 if the matrix is singular to working precision. */ 00668 00669 if (*rcond < dlamch_("Epsilon")) { 00670 *info = *n + 1; 00671 } 00672 00673 rwork[1] = rpvgrw; 00674 return 0; 00675 00676 /* End of ZGBSVX */ 00677 00678 } /* zgbsvx_ */