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 doublecomplex c_b1 = {1.,0.};
516 static integer c__1 = 1;
517 static integer c_n1 = -1;
518 static doublereal c_b24 = 1.;
520 /* > \brief \b ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contrib
521 ution to the reciprocal Dif-estimate. */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download ZLATDF + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatdf.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatdf.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatdf.
544 /* SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, */
547 /* INTEGER IJOB, LDZ, N */
548 /* DOUBLE PRECISION RDSCAL, RDSUM */
549 /* INTEGER IPIV( * ), JPIV( * ) */
550 /* COMPLEX*16 RHS( * ), Z( LDZ, * ) */
553 /* > \par Purpose: */
558 /* > ZLATDF computes the contribution to the reciprocal Dif-estimate */
559 /* > by solving for x in Z * x = b, where b is chosen such that the norm */
560 /* > of x is as large as possible. It is assumed that LU decomposition */
561 /* > of Z has been computed by ZGETC2. On entry RHS = f holds the */
562 /* > contribution from earlier solved sub-systems, and on return RHS = x. */
564 /* > The factorization of Z returned by ZGETC2 has the form */
565 /* > Z = P * L * U * Q, where P and Q are permutation matrices. L is lower */
566 /* > triangular with unit diagonal elements and U is upper triangular. */
572 /* > \param[in] IJOB */
574 /* > IJOB is INTEGER */
575 /* > IJOB = 2: First compute an approximative null-vector e */
576 /* > of Z using ZGECON, e is normalized and solve for */
577 /* > Zx = +-e - f with the sign giving the greater value of */
578 /* > 2-norm(x). About 5 times as expensive as Default. */
579 /* > IJOB .ne. 2: Local look ahead strategy where */
580 /* > all entries of the r.h.s. b is chosen as either +1 or */
587 /* > The number of columns of the matrix Z. */
592 /* > Z is COMPLEX*16 array, dimension (LDZ, N) */
593 /* > On entry, the LU part of the factorization of the n-by-n */
594 /* > matrix Z computed by ZGETC2: Z = P * L * U * Q */
597 /* > \param[in] LDZ */
599 /* > LDZ is INTEGER */
600 /* > The leading dimension of the array Z. LDA >= f2cmax(1, N). */
603 /* > \param[in,out] RHS */
605 /* > RHS is COMPLEX*16 array, dimension (N). */
606 /* > On entry, RHS contains contributions from other subsystems. */
607 /* > On exit, RHS contains the solution of the subsystem with */
608 /* > entries according to the value of IJOB (see above). */
611 /* > \param[in,out] RDSUM */
613 /* > RDSUM is DOUBLE PRECISION */
614 /* > On entry, the sum of squares of computed contributions to */
615 /* > the Dif-estimate under computation by ZTGSYL, where the */
616 /* > scaling factor RDSCAL (see below) has been factored out. */
617 /* > On exit, the corresponding sum of squares updated with the */
618 /* > contributions from the current sub-system. */
619 /* > If TRANS = 'T' RDSUM is not touched. */
620 /* > NOTE: RDSUM only makes sense when ZTGSY2 is called by CTGSYL. */
623 /* > \param[in,out] RDSCAL */
625 /* > RDSCAL is DOUBLE PRECISION */
626 /* > On entry, scaling factor used to prevent overflow in RDSUM. */
627 /* > On exit, RDSCAL is updated w.r.t. the current contributions */
629 /* > If TRANS = 'T', RDSCAL is not touched. */
630 /* > NOTE: RDSCAL only makes sense when ZTGSY2 is called by */
634 /* > \param[in] IPIV */
636 /* > IPIV is INTEGER array, dimension (N). */
637 /* > The pivot indices; for 1 <= i <= N, row i of the */
638 /* > matrix has been interchanged with row IPIV(i). */
641 /* > \param[in] JPIV */
643 /* > JPIV is INTEGER array, dimension (N). */
644 /* > The pivot indices; for 1 <= j <= N, column j of the */
645 /* > matrix has been interchanged with column JPIV(j). */
651 /* > \author Univ. of Tennessee */
652 /* > \author Univ. of California Berkeley */
653 /* > \author Univ. of Colorado Denver */
654 /* > \author NAG Ltd. */
656 /* > \date June 2016 */
658 /* > \ingroup complex16OTHERauxiliary */
660 /* > \par Further Details: */
661 /* ===================== */
663 /* > This routine is a further developed implementation of algorithm */
664 /* > BSOLVE in [1] using complete pivoting in the LU factorization. */
666 /* > \par Contributors: */
667 /* ================== */
669 /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
670 /* > Umea University, S-901 87 Umea, Sweden. */
672 /* > \par References: */
673 /* ================ */
675 /* > [1] Bo Kagstrom and Lars Westin, */
676 /* > Generalized Schur Methods with Condition Estimators for */
677 /* > Solving the Generalized Sylvester Equation, IEEE Transactions */
678 /* > on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
680 /* > [2] Peter Poromaa, */
681 /* > On Efficient and Robust Estimators for the Separation */
682 /* > between two Regular Matrix Pairs with Applications in */
683 /* > Condition Estimation. Report UMINF-95.05, Department of */
684 /* > Computing Science, Umea University, S-901 87 Umea, Sweden, */
687 /* ===================================================================== */
688 /* Subroutine */ int zlatdf_(integer *ijob, integer *n, doublecomplex *z__,
689 integer *ldz, doublecomplex *rhs, doublereal *rdsum, doublereal *
690 rdscal, integer *ipiv, integer *jpiv)
692 /* System generated locals */
693 integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
694 doublecomplex z__1, z__2, z__3;
696 /* Local variables */
698 doublecomplex temp, work[8];
701 extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
702 doublecomplex *, integer *);
704 extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
705 doublecomplex *, integer *, doublecomplex *, integer *);
706 doublereal rtemp, sminu, rwork[2];
707 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
708 doublecomplex *, integer *);
710 extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *,
711 doublecomplex *, integer *, doublecomplex *, integer *), zgesc2_(
712 integer *, doublecomplex *, integer *, doublecomplex *, integer *,
713 integer *, doublereal *);
714 doublecomplex bm, bp, xm[2], xp[2];
715 extern /* Subroutine */ int zgecon_(char *, integer *, doublecomplex *,
716 integer *, doublereal *, doublereal *, doublecomplex *,
717 doublereal *, integer *);
718 extern doublereal dzasum_(integer *, doublecomplex *, integer *);
719 extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
720 doublereal *, doublereal *), zlaswp_(integer *, doublecomplex *,
721 integer *, integer *, integer *, integer *, integer *);
724 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
725 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
726 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
730 /* ===================================================================== */
733 /* Parameter adjustments */
735 z_offset = 1 + z_dim1 * 1;
744 /* Apply permutations IPIV to RHS */
747 zlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
749 /* Solve for L-part choosing RHS either to +1 or -1. */
751 z__1.r = -1., z__1.i = 0.;
752 pmone.r = z__1.r, pmone.i = z__1.i;
754 for (j = 1; j <= i__1; ++j) {
756 z__1.r = rhs[i__2].r + 1., z__1.i = rhs[i__2].i + 0.;
757 bp.r = z__1.r, bp.i = z__1.i;
759 z__1.r = rhs[i__2].r - 1., z__1.i = rhs[i__2].i + 0.;
760 bm.r = z__1.r, bm.i = z__1.i;
763 /* Lockahead for L- part RHS(1:N-1) = +-1 */
764 /* SPLUS and SMIN computed more efficiently than in BSOLVE[1]. */
767 zdotc_(&z__1, &i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
768 + j * z_dim1], &c__1);
771 zdotc_(&z__1, &i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
775 splus *= rhs[i__2].r;
778 rhs[i__2].r = bp.r, rhs[i__2].i = bp.i;
779 } else if (sminu > splus) {
781 rhs[i__2].r = bm.r, rhs[i__2].i = bm.i;
784 /* In this case the updating sums are equal and we can */
785 /* choose RHS(J) +1 or -1. The first time this happens we */
786 /* choose -1, thereafter +1. This is a simple way to get */
787 /* good estimates of matrices like Byers well-known example */
788 /* (see [1]). (Not done in BSOLVE.) */
792 z__1.r = rhs[i__3].r + pmone.r, z__1.i = rhs[i__3].i +
794 rhs[i__2].r = z__1.r, rhs[i__2].i = z__1.i;
795 pmone.r = 1., pmone.i = 0.;
798 /* Compute the remaining r.h.s. */
801 z__1.r = -rhs[i__2].r, z__1.i = -rhs[i__2].i;
802 temp.r = z__1.r, temp.i = z__1.i;
804 zaxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
809 /* Solve for U- part, lockahead for RHS(N) = +-1. This is not done */
810 /* In BSOLVE and will hopefully give us a better estimate because */
811 /* any ill-conditioning of the original matrix is transferred to U */
812 /* and not to L. U(N, N) is an approximation to sigma_min(LU). */
815 zcopy_(&i__1, &rhs[1], &c__1, work, &c__1);
818 z__1.r = rhs[i__2].r + 1., z__1.i = rhs[i__2].i + 0.;
819 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
822 z__1.r = rhs[i__2].r - 1., z__1.i = rhs[i__2].i + 0.;
823 rhs[i__1].r = z__1.r, rhs[i__1].i = z__1.i;
826 for (i__ = *n; i__ >= 1; --i__) {
827 z_div(&z__1, &c_b1, &z__[i__ + i__ * z_dim1]);
828 temp.r = z__1.r, temp.i = z__1.i;
831 z__1.r = work[i__2].r * temp.r - work[i__2].i * temp.i, z__1.i =
832 work[i__2].r * temp.i + work[i__2].i * temp.r;
833 work[i__1].r = z__1.r, work[i__1].i = z__1.i;
836 z__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, z__1.i =
837 rhs[i__2].r * temp.i + rhs[i__2].i * temp.r;
838 rhs[i__1].r = z__1.r, rhs[i__1].i = z__1.i;
840 for (k = i__ + 1; k <= i__1; ++k) {
844 i__5 = i__ + k * z_dim1;
845 z__3.r = z__[i__5].r * temp.r - z__[i__5].i * temp.i, z__3.i =
846 z__[i__5].r * temp.i + z__[i__5].i * temp.r;
847 z__2.r = work[i__4].r * z__3.r - work[i__4].i * z__3.i,
848 z__2.i = work[i__4].r * z__3.i + work[i__4].i *
850 z__1.r = work[i__3].r - z__2.r, z__1.i = work[i__3].i -
852 work[i__2].r = z__1.r, work[i__2].i = z__1.i;
856 i__5 = i__ + k * z_dim1;
857 z__3.r = z__[i__5].r * temp.r - z__[i__5].i * temp.i, z__3.i =
858 z__[i__5].r * temp.i + z__[i__5].i * temp.r;
859 z__2.r = rhs[i__4].r * z__3.r - rhs[i__4].i * z__3.i, z__2.i =
860 rhs[i__4].r * z__3.i + rhs[i__4].i * z__3.r;
861 z__1.r = rhs[i__3].r - z__2.r, z__1.i = rhs[i__3].i - z__2.i;
862 rhs[i__2].r = z__1.r, rhs[i__2].i = z__1.i;
865 splus += z_abs(&work[i__ - 1]);
866 sminu += z_abs(&rhs[i__]);
870 zcopy_(n, work, &c__1, &rhs[1], &c__1);
873 /* Apply the permutations JPIV to the computed solution (RHS) */
876 zlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
878 /* Compute the sum of squares */
880 zlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
886 /* Compute approximate nullvector XM of Z */
888 zgecon_("I", n, &z__[z_offset], ldz, &c_b24, &rtemp, work, rwork, &info);
889 zcopy_(n, &work[*n], &c__1, xm, &c__1);
894 zlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
895 zdotc_(&z__3, n, xm, &c__1, xm, &c__1);
896 z_sqrt(&z__2, &z__3);
897 z_div(&z__1, &c_b1, &z__2);
898 temp.r = z__1.r, temp.i = z__1.i;
899 zscal_(n, &temp, xm, &c__1);
900 zcopy_(n, xm, &c__1, xp, &c__1);
901 zaxpy_(n, &c_b1, &rhs[1], &c__1, xp, &c__1);
902 z__1.r = -1., z__1.i = 0.;
903 zaxpy_(n, &z__1, xm, &c__1, &rhs[1], &c__1);
904 zgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &scale);
905 zgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &scale);
906 if (dzasum_(n, xp, &c__1) > dzasum_(n, &rhs[1], &c__1)) {
907 zcopy_(n, xp, &c__1, &rhs[1], &c__1);
910 /* Compute the sum of squares */
912 zlassq_(n, &rhs[1], &c__1, rdscal, rdsum);