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 integer c_n1 = -1;
517 static real c_b23 = 1.f;
518 static real c_b37 = -1.f;
520 /* > \brief \b SLATDF 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 SLATDF + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slatdf.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slatdf.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slatdf.
544 /* SUBROUTINE SLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, */
547 /* INTEGER IJOB, LDZ, N */
548 /* REAL RDSCAL, RDSUM */
549 /* INTEGER IPIV( * ), JPIV( * ) */
550 /* REAL RHS( * ), Z( LDZ, * ) */
553 /* > \par Purpose: */
558 /* > SLATDF uses the LU factorization of the n-by-n matrix Z computed by */
559 /* > SGETC2 and computes a contribution to the reciprocal Dif-estimate */
560 /* > by solving Z * x = b for x, and choosing the r.h.s. b such that */
561 /* > the norm of x is as large as possible. On entry RHS = b holds the */
562 /* > contribution from earlier solved sub-systems, and on return RHS = x. */
564 /* > The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q, */
565 /* > where P and Q are permutation matrices. L is lower triangular with */
566 /* > 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 SGECON, e is normalized and solve for */
577 /* > Zx = +-e - f with the sign giving the greater value */
578 /* > of 2-norm(x). About 5 times as expensive as Default. */
579 /* > IJOB .ne. 2: Local look ahead strategy where all entries of */
580 /* > the r.h.s. b is chosen as either +1 or -1 (Default). */
586 /* > The number of columns of the matrix Z. */
591 /* > Z is REAL array, dimension (LDZ, N) */
592 /* > On entry, the LU part of the factorization of the n-by-n */
593 /* > matrix Z computed by SGETC2: Z = P * L * U * Q */
596 /* > \param[in] LDZ */
598 /* > LDZ is INTEGER */
599 /* > The leading dimension of the array Z. LDA >= f2cmax(1, N). */
602 /* > \param[in,out] RHS */
604 /* > RHS is REAL array, dimension N. */
605 /* > On entry, RHS contains contributions from other subsystems. */
606 /* > On exit, RHS contains the solution of the subsystem with */
607 /* > entries according to the value of IJOB (see above). */
610 /* > \param[in,out] RDSUM */
612 /* > RDSUM is REAL */
613 /* > On entry, the sum of squares of computed contributions to */
614 /* > the Dif-estimate under computation by STGSYL, where the */
615 /* > scaling factor RDSCAL (see below) has been factored out. */
616 /* > On exit, the corresponding sum of squares updated with the */
617 /* > contributions from the current sub-system. */
618 /* > If TRANS = 'T' RDSUM is not touched. */
619 /* > NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL. */
622 /* > \param[in,out] RDSCAL */
624 /* > RDSCAL is REAL */
625 /* > On entry, scaling factor used to prevent overflow in RDSUM. */
626 /* > On exit, RDSCAL is updated w.r.t. the current contributions */
628 /* > If TRANS = 'T', RDSCAL is not touched. */
629 /* > NOTE: RDSCAL only makes sense when STGSY2 is called by */
633 /* > \param[in] IPIV */
635 /* > IPIV is INTEGER array, dimension (N). */
636 /* > The pivot indices; for 1 <= i <= N, row i of the */
637 /* > matrix has been interchanged with row IPIV(i). */
640 /* > \param[in] JPIV */
642 /* > JPIV is INTEGER array, dimension (N). */
643 /* > The pivot indices; for 1 <= j <= N, column j of the */
644 /* > matrix has been interchanged with column JPIV(j). */
650 /* > \author Univ. of Tennessee */
651 /* > \author Univ. of California Berkeley */
652 /* > \author Univ. of Colorado Denver */
653 /* > \author NAG Ltd. */
655 /* > \date June 2016 */
657 /* > \ingroup realOTHERauxiliary */
659 /* > \par Further Details: */
660 /* ===================== */
662 /* > This routine is a further developed implementation of algorithm */
663 /* > BSOLVE in [1] using complete pivoting in the LU factorization. */
665 /* > \par Contributors: */
666 /* ================== */
668 /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
669 /* > Umea University, S-901 87 Umea, Sweden. */
671 /* > \par References: */
672 /* ================ */
677 /* > [1] Bo Kagstrom and Lars Westin, */
678 /* > Generalized Schur Methods with Condition Estimators for */
679 /* > Solving the Generalized Sylvester Equation, IEEE Transactions */
680 /* > on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
682 /* > [2] Peter Poromaa, */
683 /* > On Efficient and Robust Estimators for the Separation */
684 /* > between two Regular Matrix Pairs with Applications in */
685 /* > Condition Estimation. Report IMINF-95.05, Departement of */
686 /* > Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
689 /* ===================================================================== */
690 /* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer *
691 ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer *
694 /* System generated locals */
695 integer z_dim1, z_offset, i__1, i__2;
698 /* Local variables */
701 extern real sdot_(integer *, real *, integer *, real *, integer *);
704 extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
706 extern real sasum_(integer *, real *, integer *);
709 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
710 integer *), saxpy_(integer *, real *, real *, integer *, real *,
713 extern /* Subroutine */ int sgesc2_(integer *, real *, integer *, real *,
714 integer *, integer *, real *);
715 real bm, bp, xm[8], xp[8];
716 extern /* Subroutine */ int sgecon_(char *, integer *, real *, integer *,
717 real *, real *, real *, integer *, integer *), slassq_(
718 integer *, real *, integer *, real *, real *), slaswp_(integer *,
719 real *, integer *, integer *, integer *, integer *, integer *);
722 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
723 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
724 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
728 /* ===================================================================== */
731 /* Parameter adjustments */
733 z_offset = 1 + z_dim1 * 1;
742 /* Apply permutations IPIV to RHS */
745 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
747 /* Solve for L-part choosing RHS either to +1 or -1. */
752 for (j = 1; j <= i__1; ++j) {
757 /* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
758 /* SMIN computed more efficiently than in BSOLVE [1]. */
761 splus += sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
762 + j * z_dim1], &c__1);
764 sminu = sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
769 } else if (sminu > splus) {
773 /* In this case the updating sums are equal and we can */
774 /* choose RHS(J) +1 or -1. The first time this happens */
775 /* we choose -1, thereafter +1. This is a simple way to */
776 /* get good estimates of matrices like Byers well-known */
777 /* example (see [1]). (Not done in BSOLVE.) */
783 /* Compute the remaining r.h.s. */
787 saxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
793 /* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
794 /* in BSOLVE and will hopefully give us a better estimate because */
795 /* any ill-conditioning of the original matrix is transferred to U */
796 /* and not to L. U(N, N) is an approximation to sigma_min(LU). */
799 scopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
800 xp[*n - 1] = rhs[*n] + 1.f;
804 for (i__ = *n; i__ >= 1; --i__) {
805 temp = 1.f / z__[i__ + i__ * z_dim1];
809 for (k = i__ + 1; k <= i__1; ++k) {
810 xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
811 rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
814 splus += (r__1 = xp[i__ - 1], abs(r__1));
815 sminu += (r__1 = rhs[i__], abs(r__1));
819 scopy_(n, xp, &c__1, &rhs[1], &c__1);
822 /* Apply the permutations JPIV to the computed solution (RHS) */
825 slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
827 /* Compute the sum of squares */
829 slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
833 /* IJOB = 2, Compute approximate nullvector XM of Z */
835 sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
837 scopy_(n, &work[*n], &c__1, xm, &c__1);
842 slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
843 temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1));
844 sscal_(n, &temp, xm, &c__1);
845 scopy_(n, xm, &c__1, xp, &c__1);
846 saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
847 saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
848 sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
849 sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
850 if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1)) {
851 scopy_(n, xp, &c__1, &rhs[1], &c__1);
854 /* Compute the sum of squares */
856 slassq_(n, &rhs[1], &c__1, rdscal, rdsum);