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 /* Table of constant values */
515 static integer c__1 = 1;
516 static real c_b18 = -1.f;
517 static real c_b19 = 1.f;
518 static complex c_b26 = {1.f,0.f};
520 /* > \brief \b CGTRFS */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download CGTRFS + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtrfs.
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtrfs.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtrfs.
543 /* SUBROUTINE CGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, */
544 /* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, */
547 /* CHARACTER TRANS */
548 /* INTEGER INFO, LDB, LDX, N, NRHS */
549 /* INTEGER IPIV( * ) */
550 /* REAL BERR( * ), FERR( * ), RWORK( * ) */
551 /* COMPLEX B( LDB, * ), D( * ), DF( * ), DL( * ), */
552 /* $ DLF( * ), DU( * ), DU2( * ), DUF( * ), */
553 /* $ WORK( * ), X( LDX, * ) */
556 /* > \par Purpose: */
561 /* > CGTRFS improves the computed solution to a system of linear */
562 /* > equations when the coefficient matrix is tridiagonal, and provides */
563 /* > error bounds and backward error estimates for the solution. */
569 /* > \param[in] TRANS */
571 /* > TRANS is CHARACTER*1 */
572 /* > Specifies the form of the system of equations: */
573 /* > = 'N': A * X = B (No transpose) */
574 /* > = 'T': A**T * X = B (Transpose) */
575 /* > = 'C': A**H * X = B (Conjugate transpose) */
581 /* > The order of the matrix A. N >= 0. */
584 /* > \param[in] NRHS */
586 /* > NRHS is INTEGER */
587 /* > The number of right hand sides, i.e., the number of columns */
588 /* > of the matrix B. NRHS >= 0. */
591 /* > \param[in] DL */
593 /* > DL is COMPLEX array, dimension (N-1) */
594 /* > The (n-1) subdiagonal elements of A. */
599 /* > D is COMPLEX array, dimension (N) */
600 /* > The diagonal elements of A. */
603 /* > \param[in] DU */
605 /* > DU is COMPLEX array, dimension (N-1) */
606 /* > The (n-1) superdiagonal elements of A. */
609 /* > \param[in] DLF */
611 /* > DLF is COMPLEX array, dimension (N-1) */
612 /* > The (n-1) multipliers that define the matrix L from the */
613 /* > LU factorization of A as computed by CGTTRF. */
616 /* > \param[in] DF */
618 /* > DF is COMPLEX array, dimension (N) */
619 /* > The n diagonal elements of the upper triangular matrix U from */
620 /* > the LU factorization of A. */
623 /* > \param[in] DUF */
625 /* > DUF is COMPLEX array, dimension (N-1) */
626 /* > The (n-1) elements of the first superdiagonal of U. */
629 /* > \param[in] DU2 */
631 /* > DU2 is COMPLEX array, dimension (N-2) */
632 /* > The (n-2) elements of the second superdiagonal of U. */
635 /* > \param[in] IPIV */
637 /* > IPIV is INTEGER array, dimension (N) */
638 /* > The pivot indices; for 1 <= i <= n, row i of the matrix was */
639 /* > interchanged with row IPIV(i). IPIV(i) will always be either */
640 /* > i or i+1; IPIV(i) = i indicates a row interchange was not */
646 /* > B is COMPLEX array, dimension (LDB,NRHS) */
647 /* > The right hand side matrix B. */
650 /* > \param[in] LDB */
652 /* > LDB is INTEGER */
653 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
656 /* > \param[in,out] X */
658 /* > X is COMPLEX array, dimension (LDX,NRHS) */
659 /* > On entry, the solution matrix X, as computed by CGTTRS. */
660 /* > On exit, the improved solution matrix X. */
663 /* > \param[in] LDX */
665 /* > LDX is INTEGER */
666 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
669 /* > \param[out] FERR */
671 /* > FERR is REAL array, dimension (NRHS) */
672 /* > The estimated forward error bound for each solution vector */
673 /* > X(j) (the j-th column of the solution matrix X). */
674 /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
675 /* > is an estimated upper bound for the magnitude of the largest */
676 /* > element in (X(j) - XTRUE) divided by the magnitude of the */
677 /* > largest element in X(j). The estimate is as reliable as */
678 /* > the estimate for RCOND, and is almost always a slight */
679 /* > overestimate of the true error. */
682 /* > \param[out] BERR */
684 /* > BERR is REAL array, dimension (NRHS) */
685 /* > The componentwise relative backward error of each solution */
686 /* > vector X(j) (i.e., the smallest relative change in */
687 /* > any element of A or B that makes X(j) an exact solution). */
690 /* > \param[out] WORK */
692 /* > WORK is COMPLEX array, dimension (2*N) */
695 /* > \param[out] RWORK */
697 /* > RWORK is REAL array, dimension (N) */
700 /* > \param[out] INFO */
702 /* > INFO is INTEGER */
703 /* > = 0: successful exit */
704 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
707 /* > \par Internal Parameters: */
708 /* ========================= */
711 /* > ITMAX is the maximum number of steps of iterative refinement. */
717 /* > \author Univ. of Tennessee */
718 /* > \author Univ. of California Berkeley */
719 /* > \author Univ. of Colorado Denver */
720 /* > \author NAG Ltd. */
722 /* > \date December 2016 */
724 /* > \ingroup complexGTcomputational */
726 /* ===================================================================== */
727 /* Subroutine */ int cgtrfs_(char *trans, integer *n, integer *nrhs, complex *
728 dl, complex *d__, complex *du, complex *dlf, complex *df, complex *
729 duf, complex *du2, integer *ipiv, complex *b, integer *ldb, complex *
730 x, integer *ldx, real *ferr, real *berr, complex *work, real *rwork,
733 /* System generated locals */
734 integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5,
735 i__6, i__7, i__8, i__9;
736 real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10, r__11,
740 /* Local variables */
745 extern logical lsame_(char *, char *);
747 extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
748 complex *, integer *), caxpy_(integer *, complex *, complex *,
749 integer *, complex *, integer *);
751 extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
752 *, integer *, integer *), clagtm_(char *, integer *, integer *,
753 real *, complex *, complex *, complex *, complex *, integer *,
754 real *, complex *, integer *);
756 extern real slamch_(char *);
758 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
761 extern /* Subroutine */ int cgttrs_(char *, integer *, integer *, complex
762 *, complex *, complex *, complex *, integer *, complex *, integer
768 /* -- LAPACK computational routine (version 3.7.0) -- */
769 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
770 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
774 /* ===================================================================== */
777 /* Test the input parameters. */
779 /* Parameter adjustments */
789 b_offset = 1 + b_dim1 * 1;
792 x_offset = 1 + x_dim1 * 1;
801 notran = lsame_(trans, "N");
802 if (! notran && ! lsame_(trans, "T") && ! lsame_(
807 } else if (*nrhs < 0) {
809 } else if (*ldb < f2cmax(1,*n)) {
811 } else if (*ldx < f2cmax(1,*n)) {
816 xerbla_("CGTRFS", &i__1, (ftnlen)6);
820 /* Quick return if possible */
822 if (*n == 0 || *nrhs == 0) {
824 for (j = 1; j <= i__1; ++j) {
833 *(unsigned char *)transn = 'N';
834 *(unsigned char *)transt = 'C';
836 *(unsigned char *)transn = 'C';
837 *(unsigned char *)transt = 'N';
840 /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
843 eps = slamch_("Epsilon");
844 safmin = slamch_("Safe minimum");
848 /* Do for each right hand side */
851 for (j = 1; j <= i__1; ++j) {
857 /* Loop until stopping criterion is satisfied. */
859 /* Compute residual R = B - op(A) * X, */
860 /* where op(A) = A, A**T, or A**H, depending on TRANS. */
862 ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
863 clagtm_(trans, n, &c__1, &c_b18, &dl[1], &d__[1], &du[1], &x[j *
864 x_dim1 + 1], ldx, &c_b19, &work[1], n);
866 /* Compute abs(op(A))*abs(x) + abs(b) for use in the backward */
871 i__2 = j * b_dim1 + 1;
872 i__3 = j * x_dim1 + 1;
873 rwork[1] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
874 j * b_dim1 + 1]), abs(r__2)) + ((r__3 = d__[1].r, abs(
875 r__3)) + (r__4 = r_imag(&d__[1]), abs(r__4))) * ((
876 r__5 = x[i__3].r, abs(r__5)) + (r__6 = r_imag(&x[j *
877 x_dim1 + 1]), abs(r__6)));
879 i__2 = j * b_dim1 + 1;
880 i__3 = j * x_dim1 + 1;
881 i__4 = j * x_dim1 + 2;
882 rwork[1] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
883 j * b_dim1 + 1]), abs(r__2)) + ((r__3 = d__[1].r, abs(
884 r__3)) + (r__4 = r_imag(&d__[1]), abs(r__4))) * ((
885 r__5 = x[i__3].r, abs(r__5)) + (r__6 = r_imag(&x[j *
886 x_dim1 + 1]), abs(r__6))) + ((r__7 = du[1].r, abs(
887 r__7)) + (r__8 = r_imag(&du[1]), abs(r__8))) * ((r__9
888 = x[i__4].r, abs(r__9)) + (r__10 = r_imag(&x[j *
889 x_dim1 + 2]), abs(r__10)));
891 for (i__ = 2; i__ <= i__2; ++i__) {
892 i__3 = i__ + j * b_dim1;
894 i__5 = i__ - 1 + j * x_dim1;
896 i__7 = i__ + j * x_dim1;
898 i__9 = i__ + 1 + j * x_dim1;
899 rwork[i__] = (r__1 = b[i__3].r, abs(r__1)) + (r__2 =
900 r_imag(&b[i__ + j * b_dim1]), abs(r__2)) + ((r__3
901 = dl[i__4].r, abs(r__3)) + (r__4 = r_imag(&dl[i__
902 - 1]), abs(r__4))) * ((r__5 = x[i__5].r, abs(r__5)
903 ) + (r__6 = r_imag(&x[i__ - 1 + j * x_dim1]), abs(
904 r__6))) + ((r__7 = d__[i__6].r, abs(r__7)) + (
905 r__8 = r_imag(&d__[i__]), abs(r__8))) * ((r__9 =
906 x[i__7].r, abs(r__9)) + (r__10 = r_imag(&x[i__ +
907 j * x_dim1]), abs(r__10))) + ((r__11 = du[i__8].r,
908 abs(r__11)) + (r__12 = r_imag(&du[i__]), abs(
909 r__12))) * ((r__13 = x[i__9].r, abs(r__13)) + (
910 r__14 = r_imag(&x[i__ + 1 + j * x_dim1]), abs(
914 i__2 = *n + j * b_dim1;
916 i__4 = *n - 1 + j * x_dim1;
918 i__6 = *n + j * x_dim1;
919 rwork[*n] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
920 *n + j * b_dim1]), abs(r__2)) + ((r__3 = dl[i__3].r,
921 abs(r__3)) + (r__4 = r_imag(&dl[*n - 1]), abs(r__4)))
922 * ((r__5 = x[i__4].r, abs(r__5)) + (r__6 = r_imag(&x[*
923 n - 1 + j * x_dim1]), abs(r__6))) + ((r__7 = d__[i__5]
924 .r, abs(r__7)) + (r__8 = r_imag(&d__[*n]), abs(r__8)))
925 * ((r__9 = x[i__6].r, abs(r__9)) + (r__10 = r_imag(&
926 x[*n + j * x_dim1]), abs(r__10)));
930 i__2 = j * b_dim1 + 1;
931 i__3 = j * x_dim1 + 1;
932 rwork[1] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
933 j * b_dim1 + 1]), abs(r__2)) + ((r__3 = d__[1].r, abs(
934 r__3)) + (r__4 = r_imag(&d__[1]), abs(r__4))) * ((
935 r__5 = x[i__3].r, abs(r__5)) + (r__6 = r_imag(&x[j *
936 x_dim1 + 1]), abs(r__6)));
938 i__2 = j * b_dim1 + 1;
939 i__3 = j * x_dim1 + 1;
940 i__4 = j * x_dim1 + 2;
941 rwork[1] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
942 j * b_dim1 + 1]), abs(r__2)) + ((r__3 = d__[1].r, abs(
943 r__3)) + (r__4 = r_imag(&d__[1]), abs(r__4))) * ((
944 r__5 = x[i__3].r, abs(r__5)) + (r__6 = r_imag(&x[j *
945 x_dim1 + 1]), abs(r__6))) + ((r__7 = dl[1].r, abs(
946 r__7)) + (r__8 = r_imag(&dl[1]), abs(r__8))) * ((r__9
947 = x[i__4].r, abs(r__9)) + (r__10 = r_imag(&x[j *
948 x_dim1 + 2]), abs(r__10)));
950 for (i__ = 2; i__ <= i__2; ++i__) {
951 i__3 = i__ + j * b_dim1;
953 i__5 = i__ - 1 + j * x_dim1;
955 i__7 = i__ + j * x_dim1;
957 i__9 = i__ + 1 + j * x_dim1;
958 rwork[i__] = (r__1 = b[i__3].r, abs(r__1)) + (r__2 =
959 r_imag(&b[i__ + j * b_dim1]), abs(r__2)) + ((r__3
960 = du[i__4].r, abs(r__3)) + (r__4 = r_imag(&du[i__
961 - 1]), abs(r__4))) * ((r__5 = x[i__5].r, abs(r__5)
962 ) + (r__6 = r_imag(&x[i__ - 1 + j * x_dim1]), abs(
963 r__6))) + ((r__7 = d__[i__6].r, abs(r__7)) + (
964 r__8 = r_imag(&d__[i__]), abs(r__8))) * ((r__9 =
965 x[i__7].r, abs(r__9)) + (r__10 = r_imag(&x[i__ +
966 j * x_dim1]), abs(r__10))) + ((r__11 = dl[i__8].r,
967 abs(r__11)) + (r__12 = r_imag(&dl[i__]), abs(
968 r__12))) * ((r__13 = x[i__9].r, abs(r__13)) + (
969 r__14 = r_imag(&x[i__ + 1 + j * x_dim1]), abs(
973 i__2 = *n + j * b_dim1;
975 i__4 = *n - 1 + j * x_dim1;
977 i__6 = *n + j * x_dim1;
978 rwork[*n] = (r__1 = b[i__2].r, abs(r__1)) + (r__2 = r_imag(&b[
979 *n + j * b_dim1]), abs(r__2)) + ((r__3 = du[i__3].r,
980 abs(r__3)) + (r__4 = r_imag(&du[*n - 1]), abs(r__4)))
981 * ((r__5 = x[i__4].r, abs(r__5)) + (r__6 = r_imag(&x[*
982 n - 1 + j * x_dim1]), abs(r__6))) + ((r__7 = d__[i__5]
983 .r, abs(r__7)) + (r__8 = r_imag(&d__[*n]), abs(r__8)))
984 * ((r__9 = x[i__6].r, abs(r__9)) + (r__10 = r_imag(&
985 x[*n + j * x_dim1]), abs(r__10)));
989 /* Compute componentwise relative backward error from formula */
991 /* f2cmax(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
993 /* where abs(Z) is the componentwise absolute value of the matrix */
994 /* or vector Z. If the i-th component of the denominator is less */
995 /* than SAFE2, then SAFE1 is added to the i-th components of the */
996 /* numerator and denominator before dividing. */
1000 for (i__ = 1; i__ <= i__2; ++i__) {
1001 if (rwork[i__] > safe2) {
1004 r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 =
1005 r_imag(&work[i__]), abs(r__2))) / rwork[i__];
1006 s = f2cmax(r__3,r__4);
1010 r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 =
1011 r_imag(&work[i__]), abs(r__2)) + safe1) / (rwork[i__]
1013 s = f2cmax(r__3,r__4);
1019 /* Test stopping criterion. Continue iterating if */
1020 /* 1) The residual BERR(J) is larger than machine epsilon, and */
1021 /* 2) BERR(J) decreased by at least a factor of 2 during the */
1022 /* last iteration, and */
1023 /* 3) At most ITMAX iterations tried. */
1025 if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
1027 /* Update solution and try again. */
1029 cgttrs_(trans, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[
1030 1], &work[1], n, info);
1031 caxpy_(n, &c_b26, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
1037 /* Bound error from formula */
1039 /* norm(X - XTRUE) / norm(X) .le. FERR = */
1040 /* norm( abs(inv(op(A)))* */
1041 /* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
1044 /* norm(Z) is the magnitude of the largest component of Z */
1045 /* inv(op(A)) is the inverse of op(A) */
1046 /* abs(Z) is the componentwise absolute value of the matrix or */
1048 /* NZ is the maximum number of nonzeros in any row of A, plus 1 */
1049 /* EPS is machine epsilon */
1051 /* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
1052 /* is incremented by SAFE1 if the i-th component of */
1053 /* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
1055 /* Use CLACN2 to estimate the infinity-norm of the matrix */
1056 /* inv(op(A)) * diag(W), */
1057 /* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
1060 for (i__ = 1; i__ <= i__2; ++i__) {
1061 if (rwork[i__] > safe2) {
1063 rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 =
1064 r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
1068 rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 =
1069 r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
1077 clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
1081 /* Multiply by diag(W)*inv(op(A)**H). */
1083 cgttrs_(transt, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &
1084 ipiv[1], &work[1], n, info);
1086 for (i__ = 1; i__ <= i__2; ++i__) {
1090 q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
1092 work[i__3].r = q__1.r, work[i__3].i = q__1.i;
1097 /* Multiply by inv(op(A))*diag(W). */
1100 for (i__ = 1; i__ <= i__2; ++i__) {
1104 q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
1106 work[i__3].r = q__1.r, work[i__3].i = q__1.i;
1109 cgttrs_(transn, n, &c__1, &dlf[1], &df[1], &duf[1], &du2[1], &
1110 ipiv[1], &work[1], n, info);
1115 /* Normalize error. */
1119 for (i__ = 1; i__ <= i__2; ++i__) {
1121 i__3 = i__ + j * x_dim1;
1122 r__3 = lstres, r__4 = (r__1 = x[i__3].r, abs(r__1)) + (r__2 =
1123 r_imag(&x[i__ + j * x_dim1]), abs(r__2));
1124 lstres = f2cmax(r__3,r__4);
1127 if (lstres != 0.f) {