14 typedef long long BLASLONG;
15 typedef unsigned long long BLASULONG;
17 typedef long BLASLONG;
18 typedef unsigned long BLASULONG;
22 typedef BLASLONG blasint;
24 #define blasabs(x) llabs(x)
26 #define blasabs(x) labs(x)
30 #define blasabs(x) abs(x)
33 typedef blasint integer;
35 typedef unsigned int uinteger;
36 typedef char *address;
37 typedef short int shortint;
39 typedef double doublereal;
40 typedef struct { real r, i; } complex;
41 typedef struct { doublereal r, i; } doublecomplex;
43 static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
44 static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
45 static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
46 static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
48 static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
49 static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
50 static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
51 static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
53 #define pCf(z) (*_pCf(z))
54 #define pCd(z) (*_pCd(z))
56 typedef short int shortlogical;
57 typedef char logical1;
58 typedef char integer1;
63 /* Extern is for use with -E */
74 /*external read, write*/
83 /*internal read, write*/
113 /*rewind, backspace, endfile*/
125 ftnint *inex; /*parameters in standard's order*/
151 union Multitype { /* for multiple entry points */
162 typedef union Multitype Multitype;
164 struct Vardesc { /* for Namelist */
170 typedef struct Vardesc Vardesc;
177 typedef struct Namelist Namelist;
179 #define abs(x) ((x) >= 0 ? (x) : -(x))
180 #define dabs(x) (fabs(x))
181 #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
182 #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
183 #define dmin(a,b) (f2cmin(a,b))
184 #define dmax(a,b) (f2cmax(a,b))
185 #define bit_test(a,b) ((a) >> (b) & 1)
186 #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
187 #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
189 #define abort_() { sig_die("Fortran abort routine called", 1); }
190 #define c_abs(z) (cabsf(Cf(z)))
191 #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
193 #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
194 #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
196 #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
197 #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
199 #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
200 #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
201 #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
202 //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
203 #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
204 #define d_abs(x) (fabs(*(x)))
205 #define d_acos(x) (acos(*(x)))
206 #define d_asin(x) (asin(*(x)))
207 #define d_atan(x) (atan(*(x)))
208 #define d_atn2(x, y) (atan2(*(x),*(y)))
209 #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
210 #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
211 #define d_cos(x) (cos(*(x)))
212 #define d_cosh(x) (cosh(*(x)))
213 #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
214 #define d_exp(x) (exp(*(x)))
215 #define d_imag(z) (cimag(Cd(z)))
216 #define r_imag(z) (cimagf(Cf(z)))
217 #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
218 #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
219 #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
220 #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
221 #define d_log(x) (log(*(x)))
222 #define d_mod(x, y) (fmod(*(x), *(y)))
223 #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
224 #define d_nint(x) u_nint(*(x))
225 #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
226 #define d_sign(a,b) u_sign(*(a),*(b))
227 #define r_sign(a,b) u_sign(*(a),*(b))
228 #define d_sin(x) (sin(*(x)))
229 #define d_sinh(x) (sinh(*(x)))
230 #define d_sqrt(x) (sqrt(*(x)))
231 #define d_tan(x) (tan(*(x)))
232 #define d_tanh(x) (tanh(*(x)))
233 #define i_abs(x) abs(*(x))
234 #define i_dnnt(x) ((integer)u_nint(*(x)))
235 #define i_len(s, n) (n)
236 #define i_nint(x) ((integer)u_nint(*(x)))
237 #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
238 #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
239 #define pow_si(B,E) spow_ui(*(B),*(E))
240 #define pow_ri(B,E) spow_ui(*(B),*(E))
241 #define pow_di(B,E) dpow_ui(*(B),*(E))
242 #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
243 #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
244 #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
245 #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
246 #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
247 #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
248 #define sig_die(s, kill) { exit(1); }
249 #define s_stop(s, n) {exit(0);}
250 static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
251 #define z_abs(z) (cabs(Cd(z)))
252 #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
253 #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
254 #define myexit_() break;
255 #define mycycle() continue;
256 #define myceiling(w) {ceil(w)}
257 #define myhuge(w) {HUGE_VAL}
258 //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
259 #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
261 /* procedure parameter types for -A and -C++ */
263 #define F2C_proc_par_types 1
265 typedef logical (*L_fp)(...);
267 typedef logical (*L_fp)();
270 static float spow_ui(float x, integer n) {
271 float pow=1.0; unsigned long int u;
273 if(n < 0) n = -n, x = 1/x;
282 static double dpow_ui(double x, integer n) {
283 double pow=1.0; unsigned long int u;
285 if(n < 0) n = -n, x = 1/x;
295 static _Fcomplex cpow_ui(complex x, integer n) {
296 complex pow={1.0,0.0}; unsigned long int u;
298 if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
300 if(u & 01) pow.r *= x.r, pow.i *= x.i;
301 if(u >>= 1) x.r *= x.r, x.i *= x.i;
305 _Fcomplex p={pow.r, pow.i};
309 static _Complex float cpow_ui(_Complex float x, integer n) {
310 _Complex float pow=1.0; unsigned long int u;
312 if(n < 0) n = -n, x = 1/x;
323 static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
324 _Dcomplex pow={1.0,0.0}; unsigned long int u;
326 if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
328 if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
329 if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
333 _Dcomplex p = {pow._Val[0], pow._Val[1]};
337 static _Complex double zpow_ui(_Complex double x, integer n) {
338 _Complex double pow=1.0; unsigned long int u;
340 if(n < 0) n = -n, x = 1/x;
350 static integer pow_ii(integer x, integer n) {
351 integer pow; unsigned long int u;
353 if (n == 0 || x == 1) pow = 1;
354 else if (x != -1) pow = x == 0 ? 1/x : 0;
357 if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
367 static integer dmaxloc_(double *w, integer s, integer e, integer *n)
369 double m; integer i, mi;
370 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
371 if (w[i-1]>m) mi=i ,m=w[i-1];
374 static integer smaxloc_(float *w, integer s, integer e, integer *n)
376 float m; integer i, mi;
377 for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
378 if (w[i-1]>m) mi=i ,m=w[i-1];
381 static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
382 integer n = *n_, incx = *incx_, incy = *incy_, i;
384 _Fcomplex zdotc = {0.0, 0.0};
385 if (incx == 1 && incy == 1) {
386 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
387 zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
388 zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
391 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
392 zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
393 zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
399 _Complex float zdotc = 0.0;
400 if (incx == 1 && incy == 1) {
401 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
402 zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
405 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
406 zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
412 static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
413 integer n = *n_, incx = *incx_, incy = *incy_, i;
415 _Dcomplex zdotc = {0.0, 0.0};
416 if (incx == 1 && incy == 1) {
417 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
418 zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
419 zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
422 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
423 zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
424 zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
430 _Complex double zdotc = 0.0;
431 if (incx == 1 && incy == 1) {
432 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
433 zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
436 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
437 zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
443 static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
444 integer n = *n_, incx = *incx_, incy = *incy_, i;
446 _Fcomplex zdotc = {0.0, 0.0};
447 if (incx == 1 && incy == 1) {
448 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
449 zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
450 zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
453 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
454 zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
455 zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
461 _Complex float zdotc = 0.0;
462 if (incx == 1 && incy == 1) {
463 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
464 zdotc += Cf(&x[i]) * Cf(&y[i]);
467 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
468 zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
474 static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
475 integer n = *n_, incx = *incx_, incy = *incy_, i;
477 _Dcomplex zdotc = {0.0, 0.0};
478 if (incx == 1 && incy == 1) {
479 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
480 zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
481 zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
484 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
485 zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
486 zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
492 _Complex double zdotc = 0.0;
493 if (incx == 1 && incy == 1) {
494 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
495 zdotc += Cd(&x[i]) * Cd(&y[i]);
498 for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
499 zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
505 /* -- translated by f2c (version 20000121).
506 You must link the resulting object file with the libraries:
507 -lf2c -lm (in that order)
513 /* > \brief <b> DGBSVXX computes the solution to system of linear equations A * X = B for GB matrices</b> */
515 /* =========== DOCUMENTATION =========== */
517 /* Online html documentation available at */
518 /* http://www.netlib.org/lapack/explore-html/ */
521 /* > Download DGBSVXX + dependencies */
522 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbsvxx
525 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbsvxx
528 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbsvxx
536 /* SUBROUTINE DGBSVXX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, */
537 /* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, */
538 /* RCOND, RPVGRW, BERR, N_ERR_BNDS, */
539 /* ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, */
540 /* WORK, IWORK, INFO ) */
542 /* CHARACTER EQUED, FACT, TRANS */
543 /* INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, NRHS, NPARAMS, */
544 /* $ N_ERR_BNDS, KL, KU */
545 /* DOUBLE PRECISION RCOND, RPVGRW */
546 /* INTEGER IPIV( * ), IWORK( * ) */
547 /* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
548 /* $ X( LDX , * ),WORK( * ) */
549 /* DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ), */
550 /* $ ERR_BNDS_NORM( NRHS, * ), */
551 /* $ ERR_BNDS_COMP( NRHS, * ) */
554 /* > \par Purpose: */
559 /* > DGBSVXX uses the LU factorization to compute the solution to a */
560 /* > double precision system of linear equations A * X = B, where A is an */
561 /* > N-by-N matrix and X and B are N-by-NRHS matrices. */
563 /* > If requested, both normwise and maximum componentwise error bounds */
564 /* > are returned. DGBSVXX will return a solution with a tiny */
565 /* > guaranteed error (O(eps) where eps is the working machine */
566 /* > precision) unless the matrix is very ill-conditioned, in which */
567 /* > case a warning is returned. Relevant condition numbers also are */
568 /* > calculated and returned. */
570 /* > DGBSVXX accepts user-provided factorizations and equilibration */
571 /* > factors; see the definitions of the FACT and EQUED options. */
572 /* > Solving with refinement and using a factorization from a previous */
573 /* > DGBSVXX call will also produce a solution with either O(eps) */
574 /* > errors or warnings, but we cannot make that claim for general */
575 /* > user-provided factorizations and equilibration factors if they */
576 /* > differ from what DGBSVXX would itself produce. */
579 /* > \par Description: */
580 /* ================= */
584 /* > The following steps are performed: */
586 /* > 1. If FACT = 'E', double precision scaling factors are computed to equilibrate */
589 /* > TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
590 /* > TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
591 /* > TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
593 /* > Whether or not the system will be equilibrated depends on the */
594 /* > scaling of the matrix A, but if equilibration is used, A is */
595 /* > overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
596 /* > or diag(C)*B (if TRANS = 'T' or 'C'). */
598 /* > 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */
599 /* > the matrix A (after equilibration if FACT = 'E') as */
601 /* > A = P * L * U, */
603 /* > where P is a permutation matrix, L is a unit lower triangular */
604 /* > matrix, and U is upper triangular. */
606 /* > 3. If some U(i,i)=0, so that U is exactly singular, then the */
607 /* > routine returns with INFO = i. Otherwise, the factored form of A */
608 /* > is used to estimate the condition number of the matrix A (see */
609 /* > argument RCOND). If the reciprocal of the condition number is less */
610 /* > than machine precision, the routine still goes on to solve for X */
611 /* > and compute error bounds as described below. */
613 /* > 4. The system of equations is solved for X using the factored form */
616 /* > 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
617 /* > the routine will use iterative refinement to try to get a small */
618 /* > error and error bounds. Refinement calculates the residual to at */
619 /* > least twice the working precision. */
621 /* > 6. If equilibration was used, the matrix X is premultiplied by */
622 /* > diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
623 /* > that it solves the original system before equilibration. */
630 /* > Some optional parameters are bundled in the PARAMS array. These */
631 /* > settings determine how refinement is performed, but often the */
632 /* > defaults are acceptable. If the defaults are acceptable, users */
633 /* > can pass NPARAMS = 0 which prevents the source code from accessing */
634 /* > the PARAMS argument. */
637 /* > \param[in] FACT */
639 /* > FACT is CHARACTER*1 */
640 /* > Specifies whether or not the factored form of the matrix A is */
641 /* > supplied on entry, and if not, whether the matrix A should be */
642 /* > equilibrated before it is factored. */
643 /* > = 'F': On entry, AF and IPIV contain the factored form of A. */
644 /* > If EQUED is not 'N', the matrix A has been */
645 /* > equilibrated with scaling factors given by R and C. */
646 /* > A, AF, and IPIV are not modified. */
647 /* > = 'N': The matrix A will be copied to AF and factored. */
648 /* > = 'E': The matrix A will be equilibrated if necessary, then */
649 /* > copied to AF and factored. */
652 /* > \param[in] TRANS */
654 /* > TRANS is CHARACTER*1 */
655 /* > Specifies the form of the system of equations: */
656 /* > = 'N': A * X = B (No transpose) */
657 /* > = 'T': A**T * X = B (Transpose) */
658 /* > = 'C': A**H * X = B (Conjugate Transpose = Transpose) */
664 /* > The number of linear equations, i.e., the order of the */
665 /* > matrix A. N >= 0. */
668 /* > \param[in] KL */
670 /* > KL is INTEGER */
671 /* > The number of subdiagonals within the band of A. KL >= 0. */
674 /* > \param[in] KU */
676 /* > KU is INTEGER */
677 /* > The number of superdiagonals within the band of A. KU >= 0. */
680 /* > \param[in] NRHS */
682 /* > NRHS is INTEGER */
683 /* > The number of right hand sides, i.e., the number of columns */
684 /* > of the matrices B and X. NRHS >= 0. */
687 /* > \param[in,out] AB */
689 /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
690 /* > On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
691 /* > The j-th column of A is stored in the j-th column of the */
692 /* > array AB as follows: */
693 /* > AB(KU+1+i-j,j) = A(i,j) for f2cmax(1,j-KU)<=i<=f2cmin(N,j+kl) */
695 /* > If FACT = 'F' and EQUED is not 'N', then AB must have been */
696 /* > equilibrated by the scaling factors in R and/or C. AB is not */
697 /* > modified if FACT = 'F' or 'N', or if FACT = 'E' and */
698 /* > EQUED = 'N' on exit. */
700 /* > On exit, if EQUED .ne. 'N', A is scaled as follows: */
701 /* > EQUED = 'R': A := diag(R) * A */
702 /* > EQUED = 'C': A := A * diag(C) */
703 /* > EQUED = 'B': A := diag(R) * A * diag(C). */
706 /* > \param[in] LDAB */
708 /* > LDAB is INTEGER */
709 /* > The leading dimension of the array AB. LDAB >= KL+KU+1. */
712 /* > \param[in,out] AFB */
714 /* > AFB is DOUBLE PRECISION array, dimension (LDAFB,N) */
715 /* > If FACT = 'F', then AFB is an input argument and on entry */
716 /* > contains details of the LU factorization of the band matrix */
717 /* > A, as computed by DGBTRF. U is stored as an upper triangular */
718 /* > band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */
719 /* > and the multipliers used during the factorization are stored */
720 /* > in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */
721 /* > the factored form of the equilibrated matrix A. */
723 /* > If FACT = 'N', then AF is an output argument and on exit */
724 /* > returns the factors L and U from the factorization A = P*L*U */
725 /* > of the original matrix A. */
727 /* > If FACT = 'E', then AF is an output argument and on exit */
728 /* > returns the factors L and U from the factorization A = P*L*U */
729 /* > of the equilibrated matrix A (see the description of A for */
730 /* > the form of the equilibrated matrix). */
733 /* > \param[in] LDAFB */
735 /* > LDAFB is INTEGER */
736 /* > The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
739 /* > \param[in,out] IPIV */
741 /* > IPIV is INTEGER array, dimension (N) */
742 /* > If FACT = 'F', then IPIV is an input argument and on entry */
743 /* > contains the pivot indices from the factorization A = P*L*U */
744 /* > as computed by DGETRF; row i of the matrix was interchanged */
745 /* > with row IPIV(i). */
747 /* > If FACT = 'N', then IPIV is an output argument and on exit */
748 /* > contains the pivot indices from the factorization A = P*L*U */
749 /* > of the original matrix A. */
751 /* > If FACT = 'E', then IPIV is an output argument and on exit */
752 /* > contains the pivot indices from the factorization A = P*L*U */
753 /* > of the equilibrated matrix A. */
756 /* > \param[in,out] EQUED */
758 /* > EQUED is CHARACTER*1 */
759 /* > Specifies the form of equilibration that was done. */
760 /* > = 'N': No equilibration (always true if FACT = 'N'). */
761 /* > = 'R': Row equilibration, i.e., A has been premultiplied by */
763 /* > = 'C': Column equilibration, i.e., A has been postmultiplied */
765 /* > = 'B': Both row and column equilibration, i.e., A has been */
766 /* > replaced by diag(R) * A * diag(C). */
767 /* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */
768 /* > output argument. */
771 /* > \param[in,out] R */
773 /* > R is DOUBLE PRECISION array, dimension (N) */
774 /* > The row scale factors for A. If EQUED = 'R' or 'B', A is */
775 /* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
776 /* > is not accessed. R is an input argument if FACT = 'F'; */
777 /* > otherwise, R is an output argument. If FACT = 'F' and */
778 /* > EQUED = 'R' or 'B', each element of R must be positive. */
779 /* > If R is output, each element of R is a power of the radix. */
780 /* > If R is input, each element of R should be a power of the radix */
781 /* > to ensure a reliable solution and error estimates. Scaling by */
782 /* > powers of the radix does not cause rounding errors unless the */
783 /* > result underflows or overflows. Rounding errors during scaling */
784 /* > lead to refining with a matrix that is not equivalent to the */
785 /* > input matrix, producing error estimates that may not be */
789 /* > \param[in,out] C */
791 /* > C is DOUBLE PRECISION array, dimension (N) */
792 /* > The column scale factors for A. If EQUED = 'C' or 'B', A is */
793 /* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
794 /* > is not accessed. C is an input argument if FACT = 'F'; */
795 /* > otherwise, C is an output argument. If FACT = 'F' and */
796 /* > EQUED = 'C' or 'B', each element of C must be positive. */
797 /* > If C is output, each element of C is a power of the radix. */
798 /* > If C is input, each element of C should be a power of the radix */
799 /* > to ensure a reliable solution and error estimates. Scaling by */
800 /* > powers of the radix does not cause rounding errors unless the */
801 /* > result underflows or overflows. Rounding errors during scaling */
802 /* > lead to refining with a matrix that is not equivalent to the */
803 /* > input matrix, producing error estimates that may not be */
807 /* > \param[in,out] B */
809 /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
810 /* > On entry, the N-by-NRHS right hand side matrix B. */
812 /* > if EQUED = 'N', B is not modified; */
813 /* > if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
815 /* > if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
816 /* > overwritten by diag(C)*B. */
819 /* > \param[in] LDB */
821 /* > LDB is INTEGER */
822 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
825 /* > \param[out] X */
827 /* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
828 /* > If INFO = 0, the N-by-NRHS solution matrix X to the original */
829 /* > system of equations. Note that A and B are modified on exit */
830 /* > if EQUED .ne. 'N', and the solution to the equilibrated system is */
831 /* > inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */
832 /* > inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */
835 /* > \param[in] LDX */
837 /* > LDX is INTEGER */
838 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
841 /* > \param[out] RCOND */
843 /* > RCOND is DOUBLE PRECISION */
844 /* > Reciprocal scaled condition number. This is an estimate of the */
845 /* > reciprocal Skeel condition number of the matrix A after */
846 /* > equilibration (if done). If this is less than the machine */
847 /* > precision (in particular, if it is zero), the matrix is singular */
848 /* > to working precision. Note that the error may still be small even */
849 /* > if this number is very small and the matrix appears ill- */
853 /* > \param[out] RPVGRW */
855 /* > RPVGRW is DOUBLE PRECISION */
856 /* > Reciprocal pivot growth. On exit, this contains the reciprocal */
857 /* > pivot growth factor norm(A)/norm(U). The "f2cmax absolute element" */
858 /* > norm is used. If this is much less than 1, then the stability of */
859 /* > the LU factorization of the (equilibrated) matrix A could be poor. */
860 /* > This also means that the solution X, estimated condition numbers, */
861 /* > and error bounds could be unreliable. If factorization fails with */
862 /* > 0<INFO<=N, then this contains the reciprocal pivot growth factor */
863 /* > for the leading INFO columns of A. In DGESVX, this quantity is */
864 /* > returned in WORK(1). */
867 /* > \param[out] BERR */
869 /* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
870 /* > Componentwise relative backward error. This is the */
871 /* > componentwise relative backward error of each solution vector X(j) */
872 /* > (i.e., the smallest relative change in any element of A or B that */
873 /* > makes X(j) an exact solution). */
876 /* > \param[in] N_ERR_BNDS */
878 /* > N_ERR_BNDS is INTEGER */
879 /* > Number of error bounds to return for each right hand side */
880 /* > and each type (normwise or componentwise). See ERR_BNDS_NORM and */
881 /* > ERR_BNDS_COMP below. */
884 /* > \param[out] ERR_BNDS_NORM */
886 /* > ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
887 /* > For each right-hand side, this array contains information about */
888 /* > various error bounds and condition numbers corresponding to the */
889 /* > normwise relative error, which is defined as follows: */
891 /* > Normwise relative error in the ith solution vector: */
892 /* > max_j (abs(XTRUE(j,i) - X(j,i))) */
893 /* > ------------------------------ */
894 /* > max_j abs(X(j,i)) */
896 /* > The array is indexed by the type of error information as described */
897 /* > below. There currently are up to three pieces of information */
900 /* > The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
901 /* > right-hand side. */
903 /* > The second index in ERR_BNDS_NORM(:,err) contains the following */
904 /* > three fields: */
905 /* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
906 /* > reciprocal condition number is less than the threshold */
907 /* > sqrt(n) * dlamch('Epsilon'). */
909 /* > err = 2 "Guaranteed" error bound: The estimated forward error, */
910 /* > almost certainly within a factor of 10 of the true error */
911 /* > so long as the next entry is greater than the threshold */
912 /* > sqrt(n) * dlamch('Epsilon'). This error bound should only */
913 /* > be trusted if the previous boolean is true. */
915 /* > err = 3 Reciprocal condition number: Estimated normwise */
916 /* > reciprocal condition number. Compared with the threshold */
917 /* > sqrt(n) * dlamch('Epsilon') to determine if the error */
918 /* > estimate is "guaranteed". These reciprocal condition */
919 /* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
920 /* > appropriately scaled matrix Z. */
921 /* > Let Z = S*A, where S scales each row by a power of the */
922 /* > radix so all absolute row sums of Z are approximately 1. */
924 /* > See Lapack Working Note 165 for further details and extra */
928 /* > \param[out] ERR_BNDS_COMP */
930 /* > ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
931 /* > For each right-hand side, this array contains information about */
932 /* > various error bounds and condition numbers corresponding to the */
933 /* > componentwise relative error, which is defined as follows: */
935 /* > Componentwise relative error in the ith solution vector: */
936 /* > abs(XTRUE(j,i) - X(j,i)) */
937 /* > max_j ---------------------- */
940 /* > The array is indexed by the right-hand side i (on which the */
941 /* > componentwise relative error depends), and the type of error */
942 /* > information as described below. There currently are up to three */
943 /* > pieces of information returned for each right-hand side. If */
944 /* > componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
945 /* > ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most */
946 /* > the first (:,N_ERR_BNDS) entries are returned. */
948 /* > The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
949 /* > right-hand side. */
951 /* > The second index in ERR_BNDS_COMP(:,err) contains the following */
952 /* > three fields: */
953 /* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
954 /* > reciprocal condition number is less than the threshold */
955 /* > sqrt(n) * dlamch('Epsilon'). */
957 /* > err = 2 "Guaranteed" error bound: The estimated forward error, */
958 /* > almost certainly within a factor of 10 of the true error */
959 /* > so long as the next entry is greater than the threshold */
960 /* > sqrt(n) * dlamch('Epsilon'). This error bound should only */
961 /* > be trusted if the previous boolean is true. */
963 /* > err = 3 Reciprocal condition number: Estimated componentwise */
964 /* > reciprocal condition number. Compared with the threshold */
965 /* > sqrt(n) * dlamch('Epsilon') to determine if the error */
966 /* > estimate is "guaranteed". These reciprocal condition */
967 /* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
968 /* > appropriately scaled matrix Z. */
969 /* > Let Z = S*(A*diag(x)), where x is the solution for the */
970 /* > current right-hand side and S scales each row of */
971 /* > A*diag(x) by a power of the radix so all absolute row */
972 /* > sums of Z are approximately 1. */
974 /* > See Lapack Working Note 165 for further details and extra */
978 /* > \param[in] NPARAMS */
980 /* > NPARAMS is INTEGER */
981 /* > Specifies the number of parameters set in PARAMS. If <= 0, the */
982 /* > PARAMS array is never referenced and default values are used. */
985 /* > \param[in,out] PARAMS */
987 /* > PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) */
988 /* > Specifies algorithm parameters. If an entry is < 0.0, then */
989 /* > that entry will be filled with default value used for that */
990 /* > parameter. Only positions up to NPARAMS are accessed; defaults */
991 /* > are used for higher-numbered parameters. */
993 /* > PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
994 /* > refinement or not. */
995 /* > Default: 1.0D+0 */
996 /* > = 0.0: No refinement is performed, and no error bounds are */
998 /* > = 1.0: Use the extra-precise refinement algorithm. */
999 /* > (other values are reserved for future use) */
1001 /* > PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
1002 /* > computations allowed for refinement. */
1004 /* > Aggressive: Set to 100 to permit convergence using approximate */
1005 /* > factorizations or factorizations other than LU. If */
1006 /* > the factorization uses a technique other than */
1007 /* > Gaussian elimination, the guarantees in */
1008 /* > err_bnds_norm and err_bnds_comp may no longer be */
1009 /* > trustworthy. */
1011 /* > PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
1012 /* > will attempt to find a solution with small componentwise */
1013 /* > relative error in the double-precision algorithm. Positive */
1014 /* > is true, 0.0 is false. */
1015 /* > Default: 1.0 (attempt componentwise convergence) */
1016 /* > \endverbatim */
1018 /* > \param[out] WORK */
1020 /* > WORK is DOUBLE PRECISION array, dimension (4*N) */
1021 /* > \endverbatim */
1023 /* > \param[out] IWORK */
1025 /* > IWORK is INTEGER array, dimension (N) */
1026 /* > \endverbatim */
1028 /* > \param[out] INFO */
1030 /* > INFO is INTEGER */
1031 /* > = 0: Successful exit. The solution to every right-hand side is */
1033 /* > < 0: If INFO = -i, the i-th argument had an illegal value */
1034 /* > > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
1035 /* > has been completed, but the factor U is exactly singular, so */
1036 /* > the solution and error bounds could not be computed. RCOND = 0 */
1037 /* > is returned. */
1038 /* > = N+J: The solution corresponding to the Jth right-hand side is */
1039 /* > not guaranteed. The solutions corresponding to other right- */
1040 /* > hand sides K with K > J may not be guaranteed as well, but */
1041 /* > only the first such right-hand side is reported. If a small */
1042 /* > componentwise error is not requested (PARAMS(3) = 0.0) then */
1043 /* > the Jth right-hand side is the first with a normwise error */
1044 /* > bound that is not guaranteed (the smallest J such */
1045 /* > that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
1046 /* > the Jth right-hand side is the first with either a normwise or */
1047 /* > componentwise error bound that is not guaranteed (the smallest */
1048 /* > J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
1049 /* > ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
1050 /* > ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
1051 /* > about all of the right-hand sides check ERR_BNDS_NORM or */
1052 /* > ERR_BNDS_COMP. */
1053 /* > \endverbatim */
1058 /* > \author Univ. of Tennessee */
1059 /* > \author Univ. of California Berkeley */
1060 /* > \author Univ. of Colorado Denver */
1061 /* > \author NAG Ltd. */
1063 /* > \date April 2012 */
1065 /* > \ingroup doubleGBsolve */
1067 /* ===================================================================== */
1068 /* Subroutine */ int dgbsvxx_(char *fact, char *trans, integer *n, integer *
1069 kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab,
1070 doublereal *afb, integer *ldafb, integer *ipiv, char *equed,
1071 doublereal *r__, doublereal *c__, doublereal *b, integer *ldb,
1072 doublereal *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw,
1073 doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__,
1074 doublereal *err_bnds_comp__, integer *nparams, doublereal *params,
1075 doublereal *work, integer *iwork, integer *info)
1077 /* System generated locals */
1078 integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
1079 x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
1080 err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2;
1081 doublereal d__1, d__2;
1083 /* Local variables */
1085 extern doublereal dla_gbrpvgrw_(integer *, integer *, integer *, integer
1086 *, doublereal *, integer *, doublereal *, integer *);
1088 extern logical lsame_(char *, char *);
1089 doublereal rcmin, rcmax;
1091 extern doublereal dlamch_(char *);
1092 extern /* Subroutine */ int dlaqgb_(integer *, integer *, integer *,
1093 integer *, doublereal *, integer *, doublereal *, doublereal *,
1094 doublereal *, doublereal *, doublereal *, char *);
1096 extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *,
1097 integer *, doublereal *, integer *, integer *, integer *);
1099 extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
1100 doublereal *, integer *, doublereal *, integer *),
1101 xerbla_(char *, integer *, ftnlen);
1103 extern /* Subroutine */ int dgbtrs_(char *, integer *, integer *, integer
1104 *, integer *, doublereal *, integer *, integer *, doublereal *,
1105 integer *, integer *);
1112 extern /* Subroutine */ int dlascl2_(integer *, integer *, doublereal *,
1113 doublereal *, integer *), dgbequb_(integer *, integer *, integer *
1114 , integer *, doublereal *, integer *, doublereal *, doublereal *,
1115 doublereal *, doublereal *, doublereal *, integer *), dgbrfsx_(
1116 char *, char *, integer *, integer *, integer *, integer *,
1117 doublereal *, integer *, doublereal *, integer *, integer *,
1118 doublereal *, doublereal *, doublereal *, integer *, doublereal *,
1119 integer *, doublereal *, doublereal *, integer *, doublereal *,
1120 doublereal *, integer *, doublereal *, doublereal *, integer *,
1124 /* -- LAPACK driver routine (version 3.7.0) -- */
1125 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
1126 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
1130 /* ================================================================== */
1133 /* Parameter adjustments */
1134 err_bnds_comp_dim1 = *nrhs;
1135 err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1;
1136 err_bnds_comp__ -= err_bnds_comp_offset;
1137 err_bnds_norm_dim1 = *nrhs;
1138 err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1;
1139 err_bnds_norm__ -= err_bnds_norm_offset;
1141 ab_offset = 1 + ab_dim1 * 1;
1144 afb_offset = 1 + afb_dim1 * 1;
1150 b_offset = 1 + b_dim1 * 1;
1153 x_offset = 1 + x_dim1 * 1;
1162 nofact = lsame_(fact, "N");
1163 equil = lsame_(fact, "E");
1164 notran = lsame_(trans, "N");
1165 smlnum = dlamch_("Safe minimum");
1166 bignum = 1. / smlnum;
1167 if (nofact || equil) {
1168 *(unsigned char *)equed = 'N';
1172 rowequ = lsame_(equed, "R") || lsame_(equed,
1174 colequ = lsame_(equed, "C") || lsame_(equed,
1178 /* Default is failure. If an input parameter is wrong or */
1179 /* factorization fails, make everything look horrible. Only the */
1180 /* pivot growth is set here, the rest is initialized in DGBRFSX. */
1184 /* Test the input parameters. PARAMS is not tested until DGBRFSX. */
1186 if (! nofact && ! equil && ! lsame_(fact, "F")) {
1188 } else if (! notran && ! lsame_(trans, "T") && !
1189 lsame_(trans, "C")) {
1191 } else if (*n < 0) {
1193 } else if (*kl < 0) {
1195 } else if (*ku < 0) {
1197 } else if (*nrhs < 0) {
1199 } else if (*ldab < *kl + *ku + 1) {
1201 } else if (*ldafb < (*kl << 1) + *ku + 1) {
1203 } else if (lsame_(fact, "F") && ! (rowequ || colequ
1204 || lsame_(equed, "N"))) {
1211 for (j = 1; j <= i__1; ++j) {
1213 d__1 = rcmin, d__2 = r__[j];
1214 rcmin = f2cmin(d__1,d__2);
1216 d__1 = rcmax, d__2 = r__[j];
1217 rcmax = f2cmax(d__1,d__2);
1222 } else if (*n > 0) {
1223 rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
1228 if (colequ && *info == 0) {
1232 for (j = 1; j <= i__1; ++j) {
1234 d__1 = rcmin, d__2 = c__[j];
1235 rcmin = f2cmin(d__1,d__2);
1237 d__1 = rcmax, d__2 = c__[j];
1238 rcmax = f2cmax(d__1,d__2);
1243 } else if (*n > 0) {
1244 colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
1250 if (*ldb < f2cmax(1,*n)) {
1252 } else if (*ldx < f2cmax(1,*n)) {
1260 xerbla_("DGBSVXX", &i__1, (ftnlen)7);
1266 /* Compute row and column scalings to equilibrate the matrix A. */
1268 dgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
1269 rowcnd, &colcnd, &amax, &infequ);
1272 /* Equilibrate the matrix. */
1274 dlaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
1275 rowcnd, &colcnd, &amax, equed);
1276 rowequ = lsame_(equed, "R") || lsame_(equed,
1278 colequ = lsame_(equed, "C") || lsame_(equed,
1282 /* If the scaling factors are not applied, set them to 1.0. */
1286 for (j = 1; j <= i__1; ++j) {
1292 for (j = 1; j <= i__1; ++j) {
1298 /* Scale the right hand side. */
1302 dlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
1306 dlascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
1310 if (nofact || equil) {
1312 /* Compute the LU factorization of A. */
1315 for (j = 1; j <= i__1; ++j) {
1316 i__2 = (*kl << 1) + *ku + 1;
1317 for (i__ = *kl + 1; i__ <= i__2; ++i__) {
1318 afb[i__ + j * afb_dim1] = ab[i__ - *kl + j * ab_dim1];
1323 dgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info);
1325 /* Return if INFO is non-zero. */
1329 /* Pivot in column INFO is exactly 0 */
1330 /* Compute the reciprocal pivot growth factor of the */
1331 /* leading rank-deficient INFO columns of A. */
1333 *rpvgrw = dla_gbrpvgrw_(n, kl, ku, info, &ab[ab_offset], ldab, &
1334 afb[afb_offset], ldafb);
1339 /* Compute the reciprocal pivot growth factor RPVGRW. */
1341 *rpvgrw = dla_gbrpvgrw_(n, kl, ku, n, &ab[ab_offset], ldab, &afb[
1342 afb_offset], ldafb);
1344 /* Compute the solution matrix X. */
1346 dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
1347 dgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &ipiv[1], &x[
1348 x_offset], ldx, info);
1350 /* Use iterative refinement to improve the computed solution and */
1351 /* compute error bounds and backward error estimates for it. */
1353 dgbrfsx_(trans, equed, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[
1354 afb_offset], ldafb, &ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb,
1355 &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &
1356 err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[
1357 err_bnds_comp_offset], nparams, ¶ms[1], &work[1], &iwork[1],
1360 /* Scale solutions. */
1362 if (colequ && notran) {
1363 dlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
1364 } else if (rowequ && ! notran) {
1365 dlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
1370 /* End of DGBSVXX */