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]/Cd(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 doublecomplex c_b16 = {1.,0.};
518 /* > \brief \b ZPTRFS */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download ZPTRFS + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptrfs.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptrfs.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptrfs.
541 /* SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, */
542 /* FERR, BERR, WORK, RWORK, INFO ) */
545 /* INTEGER INFO, LDB, LDX, N, NRHS */
546 /* DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ), */
548 /* COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), */
552 /* > \par Purpose: */
557 /* > ZPTRFS improves the computed solution to a system of linear */
558 /* > equations when the coefficient matrix is Hermitian positive definite */
559 /* > and tridiagonal, and provides error bounds and backward error */
560 /* > estimates for the solution. */
566 /* > \param[in] UPLO */
568 /* > UPLO is CHARACTER*1 */
569 /* > Specifies whether the superdiagonal or the subdiagonal of the */
570 /* > tridiagonal matrix A is stored and the form of the */
571 /* > factorization: */
572 /* > = 'U': E is the superdiagonal of A, and A = U**H*D*U; */
573 /* > = 'L': E is the subdiagonal of A, and A = L*D*L**H. */
574 /* > (The two forms are equivalent if A is real.) */
580 /* > The order of the matrix A. N >= 0. */
583 /* > \param[in] NRHS */
585 /* > NRHS is INTEGER */
586 /* > The number of right hand sides, i.e., the number of columns */
587 /* > of the matrix B. NRHS >= 0. */
592 /* > D is DOUBLE PRECISION array, dimension (N) */
593 /* > The n real diagonal elements of the tridiagonal matrix A. */
598 /* > E is COMPLEX*16 array, dimension (N-1) */
599 /* > The (n-1) off-diagonal elements of the tridiagonal matrix A */
603 /* > \param[in] DF */
605 /* > DF is DOUBLE PRECISION array, dimension (N) */
606 /* > The n diagonal elements of the diagonal matrix D from */
607 /* > the factorization computed by ZPTTRF. */
610 /* > \param[in] EF */
612 /* > EF is COMPLEX*16 array, dimension (N-1) */
613 /* > The (n-1) off-diagonal elements of the unit bidiagonal */
614 /* > factor U or L from the factorization computed by ZPTTRF */
620 /* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
621 /* > The right hand side matrix B. */
624 /* > \param[in] LDB */
626 /* > LDB is INTEGER */
627 /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
630 /* > \param[in,out] X */
632 /* > X is COMPLEX*16 array, dimension (LDX,NRHS) */
633 /* > On entry, the solution matrix X, as computed by ZPTTRS. */
634 /* > On exit, the improved solution matrix X. */
637 /* > \param[in] LDX */
639 /* > LDX is INTEGER */
640 /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
643 /* > \param[out] FERR */
645 /* > FERR is DOUBLE PRECISION array, dimension (NRHS) */
646 /* > The forward error bound for each solution vector */
647 /* > X(j) (the j-th column of the solution matrix X). */
648 /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
649 /* > is an estimated upper bound for the magnitude of the largest */
650 /* > element in (X(j) - XTRUE) divided by the magnitude of the */
651 /* > largest element in X(j). */
654 /* > \param[out] BERR */
656 /* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
657 /* > The componentwise relative backward error of each solution */
658 /* > vector X(j) (i.e., the smallest relative change in */
659 /* > any element of A or B that makes X(j) an exact solution). */
662 /* > \param[out] WORK */
664 /* > WORK is COMPLEX*16 array, dimension (N) */
667 /* > \param[out] RWORK */
669 /* > RWORK is DOUBLE PRECISION array, dimension (N) */
672 /* > \param[out] INFO */
674 /* > INFO is INTEGER */
675 /* > = 0: successful exit */
676 /* > < 0: if INFO = -i, the i-th argument had an illegal value */
679 /* > \par Internal Parameters: */
680 /* ========================= */
683 /* > ITMAX is the maximum number of steps of iterative refinement. */
689 /* > \author Univ. of Tennessee */
690 /* > \author Univ. of California Berkeley */
691 /* > \author Univ. of Colorado Denver */
692 /* > \author NAG Ltd. */
694 /* > \date December 2016 */
696 /* > \ingroup complex16PTcomputational */
698 /* ===================================================================== */
699 /* Subroutine */ int zptrfs_(char *uplo, integer *n, integer *nrhs,
700 doublereal *d__, doublecomplex *e, doublereal *df, doublecomplex *ef,
701 doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
702 doublereal *ferr, doublereal *berr, doublecomplex *work, doublereal *
703 rwork, integer *info)
705 /* System generated locals */
706 integer b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5,
708 doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
710 doublecomplex z__1, z__2, z__3;
712 /* Local variables */
713 doublereal safe1, safe2;
716 extern logical lsame_(char *, char *);
719 extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
720 doublecomplex *, integer *, doublecomplex *, integer *);
722 extern doublereal dlamch_(char *);
723 doublecomplex cx, dx, ex;
725 extern integer idamax_(integer *, doublereal *, integer *);
728 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
730 extern /* Subroutine */ int zpttrs_(char *, integer *, integer *,
731 doublereal *, doublecomplex *, doublecomplex *, integer *,
736 /* -- LAPACK computational routine (version 3.7.0) -- */
737 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
738 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
742 /* ===================================================================== */
745 /* Test the input parameters. */
747 /* Parameter adjustments */
753 b_offset = 1 + b_dim1 * 1;
756 x_offset = 1 + x_dim1 * 1;
765 upper = lsame_(uplo, "U");
766 if (! upper && ! lsame_(uplo, "L")) {
770 } else if (*nrhs < 0) {
772 } else if (*ldb < f2cmax(1,*n)) {
774 } else if (*ldx < f2cmax(1,*n)) {
779 xerbla_("ZPTRFS", &i__1, (ftnlen)6);
783 /* Quick return if possible */
785 if (*n == 0 || *nrhs == 0) {
787 for (j = 1; j <= i__1; ++j) {
795 /* NZ = maximum number of nonzero elements in each row of A, plus 1 */
798 eps = dlamch_("Epsilon");
799 safmin = dlamch_("Safe minimum");
803 /* Do for each right hand side */
806 for (j = 1; j <= i__1; ++j) {
812 /* Loop until stopping criterion is satisfied. */
814 /* Compute residual R = B - A * X. Also compute */
815 /* abs(A)*abs(x) + abs(b) for use in the backward error bound. */
819 i__2 = j * b_dim1 + 1;
820 bi.r = b[i__2].r, bi.i = b[i__2].i;
821 i__2 = j * x_dim1 + 1;
822 z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
823 dx.r = z__1.r, dx.i = z__1.i;
824 z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i;
825 work[1].r = z__1.r, work[1].i = z__1.i;
826 rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
827 abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 =
828 d_imag(&dx), abs(d__4)));
830 i__2 = j * b_dim1 + 1;
831 bi.r = b[i__2].r, bi.i = b[i__2].i;
832 i__2 = j * x_dim1 + 1;
833 z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
834 dx.r = z__1.r, dx.i = z__1.i;
835 i__2 = j * x_dim1 + 2;
836 z__1.r = e[1].r * x[i__2].r - e[1].i * x[i__2].i, z__1.i = e[
837 1].r * x[i__2].i + e[1].i * x[i__2].r;
838 ex.r = z__1.r, ex.i = z__1.i;
839 z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i;
840 z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
841 work[1].r = z__1.r, work[1].i = z__1.i;
842 i__2 = j * x_dim1 + 2;
843 rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
844 abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 =
845 d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5))
846 + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[
847 i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 +
850 for (i__ = 2; i__ <= i__2; ++i__) {
851 i__3 = i__ + j * b_dim1;
852 bi.r = b[i__3].r, bi.i = b[i__3].i;
853 d_cnjg(&z__2, &e[i__ - 1]);
854 i__3 = i__ - 1 + j * x_dim1;
855 z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i =
856 z__2.r * x[i__3].i + z__2.i * x[i__3].r;
857 cx.r = z__1.r, cx.i = z__1.i;
859 i__4 = i__ + j * x_dim1;
860 z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[
862 dx.r = z__1.r, dx.i = z__1.i;
864 i__4 = i__ + 1 + j * x_dim1;
865 z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i,
866 z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[
868 ex.r = z__1.r, ex.i = z__1.i;
870 z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i;
871 z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i;
872 z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
873 work[i__3].r = z__1.r, work[i__3].i = z__1.i;
875 i__4 = i__ - 1 + j * x_dim1;
877 i__6 = i__ + 1 + j * x_dim1;
878 rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&
879 bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3))
880 + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * ((
881 d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[
882 i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 =
883 dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))
884 ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 =
885 d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6]
886 .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j *
887 x_dim1]), abs(d__12)));
890 i__2 = *n + j * b_dim1;
891 bi.r = b[i__2].r, bi.i = b[i__2].i;
892 d_cnjg(&z__2, &e[*n - 1]);
893 i__2 = *n - 1 + j * x_dim1;
894 z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i =
895 z__2.r * x[i__2].i + z__2.i * x[i__2].r;
896 cx.r = z__1.r, cx.i = z__1.i;
898 i__3 = *n + j * x_dim1;
899 z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3]
901 dx.r = z__1.r, dx.i = z__1.i;
903 z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i;
904 z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i;
905 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
907 i__3 = *n - 1 + j * x_dim1;
908 rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
909 abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 =
910 d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r,
911 abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]),
912 abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 =
913 d_imag(&dx), abs(d__8)));
917 i__2 = j * b_dim1 + 1;
918 bi.r = b[i__2].r, bi.i = b[i__2].i;
919 i__2 = j * x_dim1 + 1;
920 z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
921 dx.r = z__1.r, dx.i = z__1.i;
922 z__1.r = bi.r - dx.r, z__1.i = bi.i - dx.i;
923 work[1].r = z__1.r, work[1].i = z__1.i;
924 rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
925 abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 =
926 d_imag(&dx), abs(d__4)));
928 i__2 = j * b_dim1 + 1;
929 bi.r = b[i__2].r, bi.i = b[i__2].i;
930 i__2 = j * x_dim1 + 1;
931 z__1.r = d__[1] * x[i__2].r, z__1.i = d__[1] * x[i__2].i;
932 dx.r = z__1.r, dx.i = z__1.i;
933 d_cnjg(&z__2, &e[1]);
934 i__2 = j * x_dim1 + 2;
935 z__1.r = z__2.r * x[i__2].r - z__2.i * x[i__2].i, z__1.i =
936 z__2.r * x[i__2].i + z__2.i * x[i__2].r;
937 ex.r = z__1.r, ex.i = z__1.i;
938 z__2.r = bi.r - dx.r, z__2.i = bi.i - dx.i;
939 z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
940 work[1].r = z__1.r, work[1].i = z__1.i;
941 i__2 = j * x_dim1 + 2;
942 rwork[1] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
943 abs(d__2)) + ((d__3 = dx.r, abs(d__3)) + (d__4 =
944 d_imag(&dx), abs(d__4))) + ((d__5 = e[1].r, abs(d__5))
945 + (d__6 = d_imag(&e[1]), abs(d__6))) * ((d__7 = x[
946 i__2].r, abs(d__7)) + (d__8 = d_imag(&x[j * x_dim1 +
949 for (i__ = 2; i__ <= i__2; ++i__) {
950 i__3 = i__ + j * b_dim1;
951 bi.r = b[i__3].r, bi.i = b[i__3].i;
953 i__4 = i__ - 1 + j * x_dim1;
954 z__1.r = e[i__3].r * x[i__4].r - e[i__3].i * x[i__4].i,
955 z__1.i = e[i__3].r * x[i__4].i + e[i__3].i * x[
957 cx.r = z__1.r, cx.i = z__1.i;
959 i__4 = i__ + j * x_dim1;
960 z__1.r = d__[i__3] * x[i__4].r, z__1.i = d__[i__3] * x[
962 dx.r = z__1.r, dx.i = z__1.i;
963 d_cnjg(&z__2, &e[i__]);
964 i__3 = i__ + 1 + j * x_dim1;
965 z__1.r = z__2.r * x[i__3].r - z__2.i * x[i__3].i, z__1.i =
966 z__2.r * x[i__3].i + z__2.i * x[i__3].r;
967 ex.r = z__1.r, ex.i = z__1.i;
969 z__3.r = bi.r - cx.r, z__3.i = bi.i - cx.i;
970 z__2.r = z__3.r - dx.r, z__2.i = z__3.i - dx.i;
971 z__1.r = z__2.r - ex.r, z__1.i = z__2.i - ex.i;
972 work[i__3].r = z__1.r, work[i__3].i = z__1.i;
974 i__4 = i__ - 1 + j * x_dim1;
976 i__6 = i__ + 1 + j * x_dim1;
977 rwork[i__] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&
978 bi), abs(d__2)) + ((d__3 = e[i__3].r, abs(d__3))
979 + (d__4 = d_imag(&e[i__ - 1]), abs(d__4))) * ((
980 d__5 = x[i__4].r, abs(d__5)) + (d__6 = d_imag(&x[
981 i__ - 1 + j * x_dim1]), abs(d__6))) + ((d__7 =
982 dx.r, abs(d__7)) + (d__8 = d_imag(&dx), abs(d__8))
983 ) + ((d__9 = e[i__5].r, abs(d__9)) + (d__10 =
984 d_imag(&e[i__]), abs(d__10))) * ((d__11 = x[i__6]
985 .r, abs(d__11)) + (d__12 = d_imag(&x[i__ + 1 + j *
986 x_dim1]), abs(d__12)));
989 i__2 = *n + j * b_dim1;
990 bi.r = b[i__2].r, bi.i = b[i__2].i;
992 i__3 = *n - 1 + j * x_dim1;
993 z__1.r = e[i__2].r * x[i__3].r - e[i__2].i * x[i__3].i,
994 z__1.i = e[i__2].r * x[i__3].i + e[i__2].i * x[i__3]
996 cx.r = z__1.r, cx.i = z__1.i;
998 i__3 = *n + j * x_dim1;
999 z__1.r = d__[i__2] * x[i__3].r, z__1.i = d__[i__2] * x[i__3]
1001 dx.r = z__1.r, dx.i = z__1.i;
1003 z__2.r = bi.r - cx.r, z__2.i = bi.i - cx.i;
1004 z__1.r = z__2.r - dx.r, z__1.i = z__2.i - dx.i;
1005 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
1007 i__3 = *n - 1 + j * x_dim1;
1008 rwork[*n] = (d__1 = bi.r, abs(d__1)) + (d__2 = d_imag(&bi),
1009 abs(d__2)) + ((d__3 = e[i__2].r, abs(d__3)) + (d__4 =
1010 d_imag(&e[*n - 1]), abs(d__4))) * ((d__5 = x[i__3].r,
1011 abs(d__5)) + (d__6 = d_imag(&x[*n - 1 + j * x_dim1]),
1012 abs(d__6))) + ((d__7 = dx.r, abs(d__7)) + (d__8 =
1013 d_imag(&dx), abs(d__8)));
1017 /* Compute componentwise relative backward error from formula */
1019 /* f2cmax(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) ) */
1021 /* where abs(Z) is the componentwise absolute value of the matrix */
1022 /* or vector Z. If the i-th component of the denominator is less */
1023 /* than SAFE2, then SAFE1 is added to the i-th components of the */
1024 /* numerator and denominator before dividing. */
1028 for (i__ = 1; i__ <= i__2; ++i__) {
1029 if (rwork[i__] > safe2) {
1032 d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
1033 d_imag(&work[i__]), abs(d__2))) / rwork[i__];
1034 s = f2cmax(d__3,d__4);
1038 d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
1039 d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__]
1041 s = f2cmax(d__3,d__4);
1047 /* Test stopping criterion. Continue iterating if */
1048 /* 1) The residual BERR(J) is larger than machine epsilon, and */
1049 /* 2) BERR(J) decreased by at least a factor of 2 during the */
1050 /* last iteration, and */
1051 /* 3) At most ITMAX iterations tried. */
1053 if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
1055 /* Update solution and try again. */
1057 zpttrs_(uplo, n, &c__1, &df[1], &ef[1], &work[1], n, info);
1058 zaxpy_(n, &c_b16, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
1064 /* Bound error from formula */
1066 /* norm(X - XTRUE) / norm(X) .le. FERR = */
1067 /* norm( abs(inv(A))* */
1068 /* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
1071 /* norm(Z) is the magnitude of the largest component of Z */
1072 /* inv(A) is the inverse of A */
1073 /* abs(Z) is the componentwise absolute value of the matrix or */
1075 /* NZ is the maximum number of nonzeros in any row of A, plus 1 */
1076 /* EPS is machine epsilon */
1078 /* The i-th component of abs(R)+NZ*EPS*(abs(A)*abs(X)+abs(B)) */
1079 /* is incremented by SAFE1 if the i-th component of */
1080 /* abs(A)*abs(X) + abs(B) is less than SAFE2. */
1083 for (i__ = 1; i__ <= i__2; ++i__) {
1084 if (rwork[i__] > safe2) {
1086 rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
1087 d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
1091 rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
1092 d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
1097 ix = idamax_(n, &rwork[1], &c__1);
1098 ferr[j] = rwork[ix];
1100 /* Estimate the norm of inv(A). */
1102 /* Solve M(A) * x = e, where M(A) = (m(i,j)) is given by */
1104 /* m(i,j) = abs(A(i,j)), i = j, */
1105 /* m(i,j) = -abs(A(i,j)), i .ne. j, */
1107 /* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**H. */
1109 /* Solve M(L) * x = e. */
1113 for (i__ = 2; i__ <= i__2; ++i__) {
1114 rwork[i__] = rwork[i__ - 1] * z_abs(&ef[i__ - 1]) + 1.;
1118 /* Solve D * M(L)**H * x = b. */
1120 rwork[*n] /= df[*n];
1121 for (i__ = *n - 1; i__ >= 1; --i__) {
1122 rwork[i__] = rwork[i__] / df[i__] + rwork[i__ + 1] * z_abs(&ef[
1127 /* Compute norm(inv(A)) = f2cmax(x(i)), 1<=i<=n. */
1129 ix = idamax_(n, &rwork[1], &c__1);
1130 ferr[j] *= (d__1 = rwork[ix], abs(d__1));
1132 /* Normalize error. */
1136 for (i__ = 1; i__ <= i__2; ++i__) {
1138 d__1 = lstres, d__2 = z_abs(&x[i__ + j * x_dim1]);
1139 lstres = f2cmax(d__1,d__2);