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 doublereal c_b12 = 0.;
518 static doublereal c_b13 = 1.;
519 static logical c_true = TRUE_;
521 /* > \brief \b DLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and d
522 eflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
525 /* =========== DOCUMENTATION =========== */
527 /* Online html documentation available at */
528 /* http://www.netlib.org/lapack/explore-html/ */
531 /* > Download DLAQR2 + dependencies */
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr2.
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr2.
538 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr2.
546 /* SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, */
547 /* IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, */
548 /* LDT, NV, WV, LDWV, WORK, LWORK ) */
550 /* INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, */
551 /* $ LDZ, LWORK, N, ND, NH, NS, NV, NW */
552 /* LOGICAL WANTT, WANTZ */
553 /* DOUBLE PRECISION H( LDH, * ), SI( * ), SR( * ), T( LDT, * ), */
554 /* $ V( LDV, * ), WORK( * ), WV( LDWV, * ), */
558 /* > \par Purpose: */
563 /* > DLAQR2 is identical to DLAQR3 except that it avoids */
564 /* > recursion by calling DLAHQR instead of DLAQR4. */
566 /* > Aggressive early deflation: */
568 /* > This subroutine accepts as input an upper Hessenberg matrix */
569 /* > H and performs an orthogonal similarity transformation */
570 /* > designed to detect and deflate fully converged eigenvalues from */
571 /* > a trailing principal submatrix. On output H has been over- */
572 /* > written by a new Hessenberg matrix that is a perturbation of */
573 /* > an orthogonal similarity transformation of H. It is to be */
574 /* > hoped that the final version of H has many zero subdiagonal */
581 /* > \param[in] WANTT */
583 /* > WANTT is LOGICAL */
584 /* > If .TRUE., then the Hessenberg matrix H is fully updated */
585 /* > so that the quasi-triangular Schur factor may be */
586 /* > computed (in cooperation with the calling subroutine). */
587 /* > If .FALSE., then only enough of H is updated to preserve */
588 /* > the eigenvalues. */
591 /* > \param[in] WANTZ */
593 /* > WANTZ is LOGICAL */
594 /* > If .TRUE., then the orthogonal matrix Z is updated so */
595 /* > so that the orthogonal Schur factor may be computed */
596 /* > (in cooperation with the calling subroutine). */
597 /* > If .FALSE., then Z is not referenced. */
603 /* > The order of the matrix H and (if WANTZ is .TRUE.) the */
604 /* > order of the orthogonal matrix Z. */
607 /* > \param[in] KTOP */
609 /* > KTOP is INTEGER */
610 /* > It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
611 /* > KBOT and KTOP together determine an isolated block */
612 /* > along the diagonal of the Hessenberg matrix. */
615 /* > \param[in] KBOT */
617 /* > KBOT is INTEGER */
618 /* > It is assumed without a check that either */
619 /* > KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */
620 /* > determine an isolated block along the diagonal of the */
621 /* > Hessenberg matrix. */
624 /* > \param[in] NW */
626 /* > NW is INTEGER */
627 /* > Deflation window size. 1 <= NW <= (KBOT-KTOP+1). */
630 /* > \param[in,out] H */
632 /* > H is DOUBLE PRECISION array, dimension (LDH,N) */
633 /* > On input the initial N-by-N section of H stores the */
634 /* > Hessenberg matrix undergoing aggressive early deflation. */
635 /* > On output H has been transformed by an orthogonal */
636 /* > similarity transformation, perturbed, and the returned */
637 /* > to Hessenberg form that (it is to be hoped) has some */
638 /* > zero subdiagonal entries. */
641 /* > \param[in] LDH */
643 /* > LDH is INTEGER */
644 /* > Leading dimension of H just as declared in the calling */
645 /* > subroutine. N <= LDH */
648 /* > \param[in] ILOZ */
650 /* > ILOZ is INTEGER */
653 /* > \param[in] IHIZ */
655 /* > IHIZ is INTEGER */
656 /* > Specify the rows of Z to which transformations must be */
657 /* > applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. */
660 /* > \param[in,out] Z */
662 /* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */
663 /* > IF WANTZ is .TRUE., then on output, the orthogonal */
664 /* > similarity transformation mentioned above has been */
665 /* > accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. */
666 /* > If WANTZ is .FALSE., then Z is unreferenced. */
669 /* > \param[in] LDZ */
671 /* > LDZ is INTEGER */
672 /* > The leading dimension of Z just as declared in the */
673 /* > calling subroutine. 1 <= LDZ. */
676 /* > \param[out] NS */
678 /* > NS is INTEGER */
679 /* > The number of unconverged (ie approximate) eigenvalues */
680 /* > returned in SR and SI that may be used as shifts by the */
681 /* > calling subroutine. */
684 /* > \param[out] ND */
686 /* > ND is INTEGER */
687 /* > The number of converged eigenvalues uncovered by this */
691 /* > \param[out] SR */
693 /* > SR is DOUBLE PRECISION array, dimension (KBOT) */
696 /* > \param[out] SI */
698 /* > SI is DOUBLE PRECISION array, dimension (KBOT) */
699 /* > On output, the real and imaginary parts of approximate */
700 /* > eigenvalues that may be used for shifts are stored in */
701 /* > SR(KBOT-ND-NS+1) through SR(KBOT-ND) and */
702 /* > SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively. */
703 /* > The real and imaginary parts of converged eigenvalues */
704 /* > are stored in SR(KBOT-ND+1) through SR(KBOT) and */
705 /* > SI(KBOT-ND+1) through SI(KBOT), respectively. */
708 /* > \param[out] V */
710 /* > V is DOUBLE PRECISION array, dimension (LDV,NW) */
711 /* > An NW-by-NW work array. */
714 /* > \param[in] LDV */
716 /* > LDV is INTEGER */
717 /* > The leading dimension of V just as declared in the */
718 /* > calling subroutine. NW <= LDV */
721 /* > \param[in] NH */
723 /* > NH is INTEGER */
724 /* > The number of columns of T. NH >= NW. */
727 /* > \param[out] T */
729 /* > T is DOUBLE PRECISION array, dimension (LDT,NW) */
732 /* > \param[in] LDT */
734 /* > LDT is INTEGER */
735 /* > The leading dimension of T just as declared in the */
736 /* > calling subroutine. NW <= LDT */
739 /* > \param[in] NV */
741 /* > NV is INTEGER */
742 /* > The number of rows of work array WV available for */
743 /* > workspace. NV >= NW. */
746 /* > \param[out] WV */
748 /* > WV is DOUBLE PRECISION array, dimension (LDWV,NW) */
751 /* > \param[in] LDWV */
753 /* > LDWV is INTEGER */
754 /* > The leading dimension of W just as declared in the */
755 /* > calling subroutine. NW <= LDV */
758 /* > \param[out] WORK */
760 /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */
761 /* > On exit, WORK(1) is set to an estimate of the optimal value */
762 /* > of LWORK for the given values of N, NW, KTOP and KBOT. */
765 /* > \param[in] LWORK */
767 /* > LWORK is INTEGER */
768 /* > The dimension of the work array WORK. LWORK = 2*NW */
769 /* > suffices, but greater efficiency may result from larger */
770 /* > values of LWORK. */
772 /* > If LWORK = -1, then a workspace query is assumed; DLAQR2 */
773 /* > only estimates the optimal workspace size for the given */
774 /* > values of N, NW, KTOP and KBOT. The estimate is returned */
775 /* > in WORK(1). No error message related to LWORK is issued */
776 /* > by XERBLA. Neither H nor Z are accessed. */
782 /* > \author Univ. of Tennessee */
783 /* > \author Univ. of California Berkeley */
784 /* > \author Univ. of Colorado Denver */
785 /* > \author NAG Ltd. */
787 /* > \date June 2017 */
789 /* > \ingroup doubleOTHERauxiliary */
791 /* > \par Contributors: */
792 /* ================== */
794 /* > Karen Braman and Ralph Byers, Department of Mathematics, */
795 /* > University of Kansas, USA */
797 /* ===================================================================== */
798 /* Subroutine */ int dlaqr2_(logical *wantt, logical *wantz, integer *n,
799 integer *ktop, integer *kbot, integer *nw, doublereal *h__, integer *
800 ldh, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz,
801 integer *ns, integer *nd, doublereal *sr, doublereal *si, doublereal *
802 v, integer *ldv, integer *nh, doublereal *t, integer *ldt, integer *
803 nv, doublereal *wv, integer *ldwv, doublereal *work, integer *lwork)
805 /* System generated locals */
806 integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
807 wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
808 doublereal d__1, d__2, d__3, d__4, d__5, d__6;
810 /* Local variables */
812 integer kend, kcol, info, ifst, ilst, ltop, krow, i__, j, k;
814 extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
815 doublereal *, integer *, doublereal *, doublereal *, integer *,
816 doublereal *), dgemm_(char *, char *, integer *, integer *
817 , integer *, doublereal *, doublereal *, integer *, doublereal *,
818 integer *, doublereal *, doublereal *, integer *);
820 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
821 doublereal *, integer *);
822 integer infqr, kwtop;
823 extern /* Subroutine */ int dlanv2_(doublereal *, doublereal *,
824 doublereal *, doublereal *, doublereal *, doublereal *,
825 doublereal *, doublereal *, doublereal *, doublereal *);
826 doublereal aa, bb, cc;
827 extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
829 extern doublereal dlamch_(char *);
830 extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
831 doublereal *, integer *, doublereal *, doublereal *, integer *,
832 integer *), dlarfg_(integer *, doublereal *, doublereal *,
833 integer *, doublereal *);
836 extern /* Subroutine */ int dlahqr_(logical *, logical *, integer *,
837 integer *, integer *, doublereal *, integer *, doublereal *,
838 doublereal *, integer *, integer *, doublereal *, integer *,
839 integer *), dlacpy_(char *, integer *, integer *, doublereal *,
840 integer *, doublereal *, integer *);
841 doublereal safmin, safmax;
842 extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
843 doublereal *, doublereal *, doublereal *, integer *),
844 dtrexc_(char *, integer *, doublereal *, integer *, doublereal *,
845 integer *, integer *, integer *, doublereal *, integer *),
846 dormhr_(char *, char *, integer *, integer *, integer *, integer
847 *, doublereal *, integer *, doublereal *, doublereal *, integer *,
848 doublereal *, integer *, integer *);
852 doublereal evi, evk, foo;
858 /* -- LAPACK auxiliary routine (version 3.7.1) -- */
859 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
860 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
864 /* ================================================================ */
866 /* ==== Estimate optimal workspace. ==== */
868 /* Parameter adjustments */
870 h_offset = 1 + h_dim1 * 1;
873 z_offset = 1 + z_dim1 * 1;
878 v_offset = 1 + v_dim1 * 1;
881 t_offset = 1 + t_dim1 * 1;
884 wv_offset = 1 + wv_dim1 * 1;
890 i__1 = *nw, i__2 = *kbot - *ktop + 1;
891 jw = f2cmin(i__1,i__2);
896 /* ==== Workspace query call to DGEHRD ==== */
899 dgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
901 lwk1 = (integer) work[1];
903 /* ==== Workspace query call to DORMHR ==== */
906 dormhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1],
907 &v[v_offset], ldv, &work[1], &c_n1, &info);
908 lwk2 = (integer) work[1];
910 /* ==== Optimal workspace ==== */
912 lwkopt = jw + f2cmax(lwk1,lwk2);
915 /* ==== Quick return in case of workspace query. ==== */
918 work[1] = (doublereal) lwkopt;
922 /* ==== Nothing to do ... */
923 /* ... for an empty active block ... ==== */
930 /* ... nor for an empty deflation window. ==== */
935 /* ==== Machine constants ==== */
937 safmin = dlamch_("SAFE MINIMUM");
938 safmax = 1. / safmin;
939 dlabad_(&safmin, &safmax);
940 ulp = dlamch_("PRECISION");
941 smlnum = safmin * ((doublereal) (*n) / ulp);
943 /* ==== Setup deflation window ==== */
946 i__1 = *nw, i__2 = *kbot - *ktop + 1;
947 jw = f2cmin(i__1,i__2);
948 kwtop = *kbot - jw + 1;
949 if (kwtop == *ktop) {
952 s = h__[kwtop + (kwtop - 1) * h_dim1];
955 if (*kbot == kwtop) {
957 /* ==== 1-by-1 deflation window: not much to do ==== */
959 sr[kwtop] = h__[kwtop + kwtop * h_dim1];
964 d__2 = smlnum, d__3 = ulp * (d__1 = h__[kwtop + kwtop * h_dim1], abs(
966 if (abs(s) <= f2cmax(d__2,d__3)) {
970 h__[kwtop + (kwtop - 1) * h_dim1] = 0.;
977 /* ==== Convert to spike-triangular form. (In case of a */
978 /* . rare QR failure, this routine continues to do */
979 /* . aggressive early deflation using that part of */
980 /* . the deflation window that converged using INFQR */
981 /* . here and there to keep track.) ==== */
983 dlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
988 dcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
991 dlaset_("A", &jw, &jw, &c_b12, &c_b13, &v[v_offset], ldv);
992 dlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop],
993 &si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
995 /* ==== DTREXC needs a clean margin near the diagonal ==== */
998 for (j = 1; j <= i__1; ++j) {
999 t[j + 2 + j * t_dim1] = 0.;
1000 t[j + 3 + j * t_dim1] = 0.;
1004 t[jw + (jw - 2) * t_dim1] = 0.;
1007 /* ==== Deflation detection loop ==== */
1016 bulge = t[*ns + (*ns - 1) * t_dim1] != 0.;
1019 /* ==== Small spike tip test for deflation ==== */
1023 /* ==== Real eigenvalue ==== */
1025 foo = (d__1 = t[*ns + *ns * t_dim1], abs(d__1));
1030 d__2 = smlnum, d__3 = ulp * foo;
1031 if ((d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)) <= f2cmax(d__2,d__3))
1034 /* ==== Deflatable ==== */
1039 /* ==== Undeflatable. Move it up out of the way. */
1040 /* . (DTREXC can not fail in this case.) ==== */
1043 dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
1044 &ilst, &work[1], &info);
1049 /* ==== Complex conjugate pair ==== */
1051 foo = (d__3 = t[*ns + *ns * t_dim1], abs(d__3)) + sqrt((d__1 = t[*
1052 ns + (*ns - 1) * t_dim1], abs(d__1))) * sqrt((d__2 = t[*
1053 ns - 1 + *ns * t_dim1], abs(d__2)));
1058 d__3 = (d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)), d__4 = (d__2 =
1059 s * v[(*ns - 1) * v_dim1 + 1], abs(d__2));
1061 d__5 = smlnum, d__6 = ulp * foo;
1062 if (f2cmax(d__3,d__4) <= f2cmax(d__5,d__6)) {
1064 /* ==== Deflatable ==== */
1069 /* ==== Undeflatable. Move them up out of the way. */
1070 /* . Fortunately, DTREXC does the right thing with */
1071 /* . ILST in case of a rare exchange failure. ==== */
1074 dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
1075 &ilst, &work[1], &info);
1080 /* ==== End deflation detection loop ==== */
1085 /* ==== Return to Hessenberg form ==== */
1093 /* ==== sorting diagonal blocks of T improves accuracy for */
1094 /* . graded matrices. Bubble sort deals well with */
1095 /* . exchange failures. ==== */
1109 } else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
1117 evi = (d__1 = t[i__ + i__ * t_dim1], abs(d__1));
1119 evi = (d__3 = t[i__ + i__ * t_dim1], abs(d__3)) + sqrt((d__1 =
1120 t[i__ + 1 + i__ * t_dim1], abs(d__1))) * sqrt((d__2 =
1121 t[i__ + (i__ + 1) * t_dim1], abs(d__2)));
1125 evk = (d__1 = t[k + k * t_dim1], abs(d__1));
1126 } else if (t[k + 1 + k * t_dim1] == 0.) {
1127 evk = (d__1 = t[k + k * t_dim1], abs(d__1));
1129 evk = (d__3 = t[k + k * t_dim1], abs(d__3)) + sqrt((d__1 = t[
1130 k + 1 + k * t_dim1], abs(d__1))) * sqrt((d__2 = t[k +
1131 (k + 1) * t_dim1], abs(d__2)));
1140 dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
1141 &ilst, &work[1], &info);
1150 } else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
1162 /* ==== Restore shift/eigenvalue array from T ==== */
1166 if (i__ >= infqr + 1) {
1167 if (i__ == infqr + 1) {
1168 sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
1169 si[kwtop + i__ - 1] = 0.;
1171 } else if (t[i__ + (i__ - 1) * t_dim1] == 0.) {
1172 sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
1173 si[kwtop + i__ - 1] = 0.;
1176 aa = t[i__ - 1 + (i__ - 1) * t_dim1];
1177 cc = t[i__ + (i__ - 1) * t_dim1];
1178 bb = t[i__ - 1 + i__ * t_dim1];
1179 dd = t[i__ + i__ * t_dim1];
1180 dlanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__
1181 - 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, &
1188 if (*ns < jw || s == 0.) {
1189 if (*ns > 1 && s != 0.) {
1191 /* ==== Reflect spike back into lower triangle ==== */
1193 dcopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
1195 dlarfg_(ns, &beta, &work[2], &c__1, &tau);
1200 dlaset_("L", &i__1, &i__2, &c_b12, &c_b12, &t[t_dim1 + 3], ldt);
1202 dlarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, &
1204 dlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
1206 dlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
1210 dgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
1214 /* ==== Copy updated reduced window into place ==== */
1217 h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
1219 dlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
1224 dcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
1227 /* ==== Accumulate orthogonal matrix in order update */
1228 /* . H and Z, if requested. ==== */
1230 if (*ns > 1 && s != 0.) {
1232 dormhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1],
1233 &v[v_offset], ldv, &work[jw + 1], &i__1, &info);
1236 /* ==== Update vertical slab in H ==== */
1245 for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
1248 i__3 = *nv, i__4 = kwtop - krow;
1249 kln = f2cmin(i__3,i__4);
1250 dgemm_("N", "N", &kln, &jw, &jw, &c_b13, &h__[krow + kwtop *
1251 h_dim1], ldh, &v[v_offset], ldv, &c_b12, &wv[wv_offset],
1253 dlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
1258 /* ==== Update horizontal slab in H ==== */
1263 for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
1266 i__3 = *nh, i__4 = *n - kcol + 1;
1267 kln = f2cmin(i__3,i__4);
1268 dgemm_("C", "N", &jw, &kln, &jw, &c_b13, &v[v_offset], ldv, &
1269 h__[kwtop + kcol * h_dim1], ldh, &c_b12, &t[t_offset],
1271 dlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
1277 /* ==== Update vertical slab in Z ==== */
1282 for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
1285 i__3 = *nv, i__4 = *ihiz - krow + 1;
1286 kln = f2cmin(i__3,i__4);
1287 dgemm_("N", "N", &kln, &jw, &jw, &c_b13, &z__[krow + kwtop *
1288 z_dim1], ldz, &v[v_offset], ldv, &c_b12, &wv[
1290 dlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
1291 kwtop * z_dim1], ldz);
1297 /* ==== Return the number of deflations ... ==== */
1301 /* ==== ... and the number of shifts. (Subtracting */
1302 /* . INFQR from the spike length takes care */
1303 /* . of the case of a rare QR failure while */
1304 /* . calculating eigenvalues of the deflation */
1305 /* . window.) ==== */
1309 /* ==== Return optimal workspace. ==== */
1311 work[1] = (doublereal) lwkopt;
1313 /* ==== End of DLAQR2 ==== */