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;
517 /* > \brief \b SLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using th
518 e double-shift/single-shift QR algorithm. */
520 /* =========== DOCUMENTATION =========== */
522 /* Online html documentation available at */
523 /* http://www.netlib.org/lapack/explore-html/ */
526 /* > Download SLAHQR + dependencies */
527 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slahqr.
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slahqr.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slahqr.
541 /* SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, */
542 /* ILOZ, IHIZ, Z, LDZ, INFO ) */
544 /* INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N */
545 /* LOGICAL WANTT, WANTZ */
546 /* REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * ) */
549 /* > \par Purpose: */
554 /* > SLAHQR is an auxiliary routine called by SHSEQR to update the */
555 /* > eigenvalues and Schur decomposition already computed by SHSEQR, by */
556 /* > dealing with the Hessenberg submatrix in rows and columns ILO to */
563 /* > \param[in] WANTT */
565 /* > WANTT is LOGICAL */
566 /* > = .TRUE. : the full Schur form T is required; */
567 /* > = .FALSE.: only eigenvalues are required. */
570 /* > \param[in] WANTZ */
572 /* > WANTZ is LOGICAL */
573 /* > = .TRUE. : the matrix of Schur vectors Z is required; */
574 /* > = .FALSE.: Schur vectors are not required. */
580 /* > The order of the matrix H. N >= 0. */
583 /* > \param[in] ILO */
585 /* > ILO is INTEGER */
588 /* > \param[in] IHI */
590 /* > IHI is INTEGER */
591 /* > It is assumed that H is already upper quasi-triangular in */
592 /* > rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless */
593 /* > ILO = 1). SLAHQR works primarily with the Hessenberg */
594 /* > submatrix in rows and columns ILO to IHI, but applies */
595 /* > transformations to all of H if WANTT is .TRUE.. */
596 /* > 1 <= ILO <= f2cmax(1,IHI); IHI <= N. */
599 /* > \param[in,out] H */
601 /* > H is REAL array, dimension (LDH,N) */
602 /* > On entry, the upper Hessenberg matrix H. */
603 /* > On exit, if INFO is zero and if WANTT is .TRUE., H is upper */
604 /* > quasi-triangular in rows and columns ILO:IHI, with any */
605 /* > 2-by-2 diagonal blocks in standard form. If INFO is zero */
606 /* > and WANTT is .FALSE., the contents of H are unspecified on */
607 /* > exit. The output state of H if INFO is nonzero is given */
608 /* > below under the description of INFO. */
611 /* > \param[in] LDH */
613 /* > LDH is INTEGER */
614 /* > The leading dimension of the array H. LDH >= f2cmax(1,N). */
617 /* > \param[out] WR */
619 /* > WR is REAL array, dimension (N) */
622 /* > \param[out] WI */
624 /* > WI is REAL array, dimension (N) */
625 /* > The real and imaginary parts, respectively, of the computed */
626 /* > eigenvalues ILO to IHI are stored in the corresponding */
627 /* > elements of WR and WI. If two eigenvalues are computed as a */
628 /* > complex conjugate pair, they are stored in consecutive */
629 /* > elements of WR and WI, say the i-th and (i+1)th, with */
630 /* > WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the */
631 /* > eigenvalues are stored in the same order as on the diagonal */
632 /* > of the Schur form returned in H, with WR(i) = H(i,i), and, if */
633 /* > H(i:i+1,i:i+1) is a 2-by-2 diagonal block, */
634 /* > WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i). */
637 /* > \param[in] ILOZ */
639 /* > ILOZ is INTEGER */
642 /* > \param[in] IHIZ */
644 /* > IHIZ is INTEGER */
645 /* > Specify the rows of Z to which transformations must be */
646 /* > applied if WANTZ is .TRUE.. */
647 /* > 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. */
650 /* > \param[in,out] Z */
652 /* > Z is REAL array, dimension (LDZ,N) */
653 /* > If WANTZ is .TRUE., on entry Z must contain the current */
654 /* > matrix Z of transformations accumulated by SHSEQR, and on */
655 /* > exit Z has been updated; transformations are applied only to */
656 /* > the submatrix Z(ILOZ:IHIZ,ILO:IHI). */
657 /* > If WANTZ is .FALSE., Z is not referenced. */
660 /* > \param[in] LDZ */
662 /* > LDZ is INTEGER */
663 /* > The leading dimension of the array Z. LDZ >= f2cmax(1,N). */
666 /* > \param[out] INFO */
668 /* > INFO is INTEGER */
669 /* > = 0: successful exit */
670 /* > > 0: If INFO = i, SLAHQR failed to compute all the */
671 /* > eigenvalues ILO to IHI in a total of 30 iterations */
672 /* > per eigenvalue; elements i+1:ihi of WR and WI */
673 /* > contain those eigenvalues which have been */
674 /* > successfully computed. */
676 /* > If INFO > 0 and WANTT is .FALSE., then on exit, */
677 /* > the remaining unconverged eigenvalues are the */
678 /* > eigenvalues of the upper Hessenberg matrix rows */
679 /* > and columns ILO through INFO of the final, output */
682 /* > If INFO > 0 and WANTT is .TRUE., then on exit */
683 /* > (*) (initial value of H)*U = U*(final value of H) */
684 /* > where U is an orthogonal matrix. The final */
685 /* > value of H is upper Hessenberg and triangular in */
686 /* > rows and columns INFO+1 through IHI. */
688 /* > If INFO > 0 and WANTZ is .TRUE., then on exit */
689 /* > (final value of Z) = (initial value of Z)*U */
690 /* > where U is the orthogonal matrix in (*) */
691 /* > (regardless of the value of WANTT.) */
697 /* > \author Univ. of Tennessee */
698 /* > \author Univ. of California Berkeley */
699 /* > \author Univ. of Colorado Denver */
700 /* > \author NAG Ltd. */
702 /* > \date December 2016 */
704 /* > \ingroup realOTHERauxiliary */
706 /* > \par Further Details: */
707 /* ===================== */
711 /* > 02-96 Based on modifications by */
712 /* > David Day, Sandia National Laboratory, USA */
714 /* > 12-04 Further modifications by */
715 /* > Ralph Byers, University of Kansas, USA */
716 /* > This is a modified version of SLAHQR from LAPACK version 3.0. */
717 /* > It is (1) more robust against overflow and underflow and */
718 /* > (2) adopts the more conservative Ahues & Tisseur stopping */
719 /* > criterion (LAWN 122, 1997). */
722 /* ===================================================================== */
723 /* Subroutine */ int slahqr_(logical *wantt, logical *wantz, integer *n,
724 integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real *
725 wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *
728 /* System generated locals */
729 integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
730 real r__1, r__2, r__3, r__4;
732 /* Local variables */
733 extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
734 integer *, real *, real *);
735 integer i__, j, k, l, m;
737 integer itmax, i1, i2;
738 extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
740 real t1, t2, t3, v2, v3, aa, ab, ba, bb;
741 extern /* Subroutine */ int slanv2_(real *, real *, real *, real *, real *
742 , real *, real *, real *, real *, real *);
743 real h11, h12, h21, h22, cs;
745 extern /* Subroutine */ int slabad_(real *, real *);
749 extern real slamch_(char *);
752 extern /* Subroutine */ int slarfg_(integer *, real *, real *, integer *,
754 real safmax, rtdisc, smlnum, det, h21s;
756 real ulp, sum, tst, rt1i, rt2i, rt1r, rt2r;
759 /* -- LAPACK auxiliary routine (version 3.7.0) -- */
760 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
761 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
765 /* ========================================================= */
768 /* Parameter adjustments */
770 h_offset = 1 + h_dim1 * 1;
775 z_offset = 1 + z_dim1 * 1;
781 /* Quick return if possible */
787 wr[*ilo] = h__[*ilo + *ilo * h_dim1];
792 /* ==== clear out the trash ==== */
794 for (j = *ilo; j <= i__1; ++j) {
795 h__[j + 2 + j * h_dim1] = 0.f;
796 h__[j + 3 + j * h_dim1] = 0.f;
799 if (*ilo <= *ihi - 2) {
800 h__[*ihi + (*ihi - 2) * h_dim1] = 0.f;
803 nh = *ihi - *ilo + 1;
804 nz = *ihiz - *iloz + 1;
806 /* Set machine-dependent constants for the stopping criterion. */
808 safmin = slamch_("SAFE MINIMUM");
809 safmax = 1.f / safmin;
810 slabad_(&safmin, &safmax);
811 ulp = slamch_("PRECISION");
812 smlnum = safmin * ((real) nh / ulp);
814 /* I1 and I2 are the indices of the first row and last column of H */
815 /* to which transformations must be applied. If eigenvalues only are */
816 /* being computed, I1 and I2 are set inside the main loop. */
823 /* ITMAX is the total number of QR iterations allowed. */
825 itmax = f2cmax(10,nh) * 30;
827 /* The main loop begins here. I is the loop index and decreases from */
828 /* IHI to ILO in steps of 1 or 2. Each iteration of the loop works */
829 /* with the active submatrix in rows and columns L to I. */
830 /* Eigenvalues I+1 to IHI have already converged. Either L = ILO or */
831 /* H(L,L-1) is negligible so that the matrix splits. */
840 /* Perform QR iterations on rows and columns ILO to I until a */
841 /* submatrix of order 1 or 2 splits off at the bottom because a */
842 /* subdiagonal element has become negligible. */
845 for (its = 0; its <= i__1; ++its) {
847 /* Look for a single small subdiagonal element. */
850 for (k = i__; k >= i__2; --k) {
851 if ((r__1 = h__[k + (k - 1) * h_dim1], abs(r__1)) <= smlnum) {
854 tst = (r__1 = h__[k - 1 + (k - 1) * h_dim1], abs(r__1)) + (r__2 =
855 h__[k + k * h_dim1], abs(r__2));
858 tst += (r__1 = h__[k - 1 + (k - 2) * h_dim1], abs(r__1));
861 tst += (r__1 = h__[k + 1 + k * h_dim1], abs(r__1));
864 /* ==== The following is a conservative small subdiagonal */
865 /* . deflation criterion due to Ahues & Tisseur (LAWN 122, */
866 /* . 1997). It has better mathematical foundation and */
867 /* . improves accuracy in some cases. ==== */
868 if ((r__1 = h__[k + (k - 1) * h_dim1], abs(r__1)) <= ulp * tst) {
870 r__3 = (r__1 = h__[k + (k - 1) * h_dim1], abs(r__1)), r__4 = (
871 r__2 = h__[k - 1 + k * h_dim1], abs(r__2));
872 ab = f2cmax(r__3,r__4);
874 r__3 = (r__1 = h__[k + (k - 1) * h_dim1], abs(r__1)), r__4 = (
875 r__2 = h__[k - 1 + k * h_dim1], abs(r__2));
876 ba = f2cmin(r__3,r__4);
878 r__3 = (r__1 = h__[k + k * h_dim1], abs(r__1)), r__4 = (r__2 =
879 h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1],
881 aa = f2cmax(r__3,r__4);
883 r__3 = (r__1 = h__[k + k * h_dim1], abs(r__1)), r__4 = (r__2 =
884 h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1],
886 bb = f2cmin(r__3,r__4);
889 r__1 = smlnum, r__2 = ulp * (bb * (aa / s));
890 if (ba * (ab / s) <= f2cmax(r__1,r__2)) {
900 /* H(L,L-1) is negligible */
902 h__[l + (l - 1) * h_dim1] = 0.f;
905 /* Exit from loop if a submatrix of order 1 or 2 has split off. */
911 /* Now the active submatrix is in rows and columns L to I. If */
912 /* eigenvalues only are being computed, only the active submatrix */
913 /* need be transformed. */
922 /* Exceptional shift. */
924 s = (r__1 = h__[l + 1 + l * h_dim1], abs(r__1)) + (r__2 = h__[l +
925 2 + (l + 1) * h_dim1], abs(r__2));
926 h11 = s * .75f + h__[l + l * h_dim1];
930 } else if (its == 20) {
932 /* Exceptional shift. */
934 s = (r__1 = h__[i__ + (i__ - 1) * h_dim1], abs(r__1)) + (r__2 =
935 h__[i__ - 1 + (i__ - 2) * h_dim1], abs(r__2));
936 h11 = s * .75f + h__[i__ + i__ * h_dim1];
942 /* Prepare to use Francis' double shift */
943 /* (i.e. 2nd degree generalized Rayleigh quotient) */
945 h11 = h__[i__ - 1 + (i__ - 1) * h_dim1];
946 h21 = h__[i__ + (i__ - 1) * h_dim1];
947 h12 = h__[i__ - 1 + i__ * h_dim1];
948 h22 = h__[i__ + i__ * h_dim1];
950 s = abs(h11) + abs(h12) + abs(h21) + abs(h22);
961 tr = (h11 + h22) / 2.f;
962 det = (h11 - tr) * (h22 - tr) - h12 * h21;
963 rtdisc = sqrt((abs(det)));
966 /* ==== complex conjugate shifts ==== */
974 /* ==== real shifts (use only one of them) ==== */
978 if ((r__1 = rt1r - h22, abs(r__1)) <= (r__2 = rt2r - h22, abs(
991 /* Look for two consecutive small subdiagonal elements. */
994 for (m = i__ - 2; m >= i__2; --m) {
995 /* Determine the effect of starting the double-shift QR */
996 /* iteration at row M, and see if this would make H(M,M-1) */
997 /* negligible. (The following uses scaling to avoid */
998 /* overflows and most underflows.) */
1000 h21s = h__[m + 1 + m * h_dim1];
1001 s = (r__1 = h__[m + m * h_dim1] - rt2r, abs(r__1)) + abs(rt2i) +
1003 h21s = h__[m + 1 + m * h_dim1] / s;
1004 v[0] = h21s * h__[m + (m + 1) * h_dim1] + (h__[m + m * h_dim1] -
1005 rt1r) * ((h__[m + m * h_dim1] - rt2r) / s) - rt1i * (rt2i
1007 v[1] = h21s * (h__[m + m * h_dim1] + h__[m + 1 + (m + 1) * h_dim1]
1009 v[2] = h21s * h__[m + 2 + (m + 1) * h_dim1];
1010 s = abs(v[0]) + abs(v[1]) + abs(v[2]);
1017 if ((r__1 = h__[m + (m - 1) * h_dim1], abs(r__1)) * (abs(v[1]) +
1018 abs(v[2])) <= ulp * abs(v[0]) * ((r__2 = h__[m - 1 + (m -
1019 1) * h_dim1], abs(r__2)) + (r__3 = h__[m + m * h_dim1],
1020 abs(r__3)) + (r__4 = h__[m + 1 + (m + 1) * h_dim1], abs(
1028 /* Double-shift QR step */
1031 for (k = m; k <= i__2; ++k) {
1033 /* The first iteration of this loop determines a reflection G */
1034 /* from the vector V and applies it from left and right to H, */
1035 /* thus creating a nonzero bulge below the subdiagonal. */
1037 /* Each subsequent iteration determines a reflection G to */
1038 /* restore the Hessenberg form in the (K-1)th column, and thus */
1039 /* chases the bulge one step toward the bottom of the active */
1040 /* submatrix. NR is the order of G. */
1043 i__3 = 3, i__4 = i__ - k + 1;
1044 nr = f2cmin(i__3,i__4);
1046 scopy_(&nr, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
1048 slarfg_(&nr, v, &v[1], &c__1, &t1);
1050 h__[k + (k - 1) * h_dim1] = v[0];
1051 h__[k + 1 + (k - 1) * h_dim1] = 0.f;
1053 h__[k + 2 + (k - 1) * h_dim1] = 0.f;
1056 /* ==== Use the following instead of */
1057 /* . H( K, K-1 ) = -H( K, K-1 ) to */
1058 /* . avoid a bug when v(2) and v(3) */
1059 /* . underflow. ==== */
1060 h__[k + (k - 1) * h_dim1] *= 1.f - t1;
1068 /* Apply G from the left to transform the rows of the matrix */
1069 /* in columns K to I2. */
1072 for (j = k; j <= i__3; ++j) {
1073 sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1]
1074 + v3 * h__[k + 2 + j * h_dim1];
1075 h__[k + j * h_dim1] -= sum * t1;
1076 h__[k + 1 + j * h_dim1] -= sum * t2;
1077 h__[k + 2 + j * h_dim1] -= sum * t3;
1081 /* Apply G from the right to transform the columns of the */
1082 /* matrix in rows I1 to f2cmin(K+3,I). */
1086 i__3 = f2cmin(i__4,i__);
1087 for (j = i1; j <= i__3; ++j) {
1088 sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]
1089 + v3 * h__[j + (k + 2) * h_dim1];
1090 h__[j + k * h_dim1] -= sum * t1;
1091 h__[j + (k + 1) * h_dim1] -= sum * t2;
1092 h__[j + (k + 2) * h_dim1] -= sum * t3;
1098 /* Accumulate transformations in the matrix Z */
1101 for (j = *iloz; j <= i__3; ++j) {
1102 sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) *
1103 z_dim1] + v3 * z__[j + (k + 2) * z_dim1];
1104 z__[j + k * z_dim1] -= sum * t1;
1105 z__[j + (k + 1) * z_dim1] -= sum * t2;
1106 z__[j + (k + 2) * z_dim1] -= sum * t3;
1110 } else if (nr == 2) {
1112 /* Apply G from the left to transform the rows of the matrix */
1113 /* in columns K to I2. */
1116 for (j = k; j <= i__3; ++j) {
1117 sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1];
1118 h__[k + j * h_dim1] -= sum * t1;
1119 h__[k + 1 + j * h_dim1] -= sum * t2;
1123 /* Apply G from the right to transform the columns of the */
1124 /* matrix in rows I1 to f2cmin(K+3,I). */
1127 for (j = i1; j <= i__3; ++j) {
1128 sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]
1130 h__[j + k * h_dim1] -= sum * t1;
1131 h__[j + (k + 1) * h_dim1] -= sum * t2;
1137 /* Accumulate transformations in the matrix Z */
1140 for (j = *iloz; j <= i__3; ++j) {
1141 sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) *
1143 z__[j + k * z_dim1] -= sum * t1;
1144 z__[j + (k + 1) * z_dim1] -= sum * t2;
1155 /* Failure to converge in remaining number of iterations */
1164 /* H(I,I-1) is negligible: one eigenvalue has converged. */
1166 wr[i__] = h__[i__ + i__ * h_dim1];
1168 } else if (l == i__ - 1) {
1170 /* H(I-1,I-2) is negligible: a pair of eigenvalues have converged. */
1172 /* Transform the 2-by-2 submatrix to standard Schur form, */
1173 /* and compute and store the eigenvalues. */
1175 slanv2_(&h__[i__ - 1 + (i__ - 1) * h_dim1], &h__[i__ - 1 + i__ *
1176 h_dim1], &h__[i__ + (i__ - 1) * h_dim1], &h__[i__ + i__ *
1177 h_dim1], &wr[i__ - 1], &wi[i__ - 1], &wr[i__], &wi[i__], &cs,
1182 /* Apply the transformation to the rest of H. */
1186 srot_(&i__1, &h__[i__ - 1 + (i__ + 1) * h_dim1], ldh, &h__[
1187 i__ + (i__ + 1) * h_dim1], ldh, &cs, &sn);
1189 i__1 = i__ - i1 - 1;
1190 srot_(&i__1, &h__[i1 + (i__ - 1) * h_dim1], &c__1, &h__[i1 + i__ *
1191 h_dim1], &c__1, &cs, &sn);
1195 /* Apply the transformation to Z. */
1197 srot_(&nz, &z__[*iloz + (i__ - 1) * z_dim1], &c__1, &z__[*iloz +
1198 i__ * z_dim1], &c__1, &cs, &sn);
1202 /* return to start of the main loop with new value of I. */