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 doublereal c_b11 = 0.;
516 static doublereal c_b12 = 1.;
517 static integer c__12 = 12;
518 static integer c__2 = 2;
519 static integer c__49 = 49;
521 /* > \brief \b DHSEQR */
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download DHSEQR + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dhseqr.
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dhseqr.
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dhseqr.
544 /* SUBROUTINE DHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, */
545 /* LDZ, WORK, LWORK, INFO ) */
547 /* INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N */
548 /* CHARACTER COMPZ, JOB */
549 /* DOUBLE PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ), */
553 /* > \par Purpose: */
558 /* > DHSEQR computes the eigenvalues of a Hessenberg matrix H */
559 /* > and, optionally, the matrices T and Z from the Schur decomposition */
560 /* > H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
561 /* > Schur form), and Z is the orthogonal matrix of Schur vectors. */
563 /* > Optionally Z may be postmultiplied into an input orthogonal */
564 /* > matrix Q so that this routine can give the Schur factorization */
565 /* > of a matrix A which has been reduced to the Hessenberg form H */
566 /* > by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
572 /* > \param[in] JOB */
574 /* > JOB is CHARACTER*1 */
575 /* > = 'E': compute eigenvalues only; */
576 /* > = 'S': compute eigenvalues and the Schur form T. */
579 /* > \param[in] COMPZ */
581 /* > COMPZ is CHARACTER*1 */
582 /* > = 'N': no Schur vectors are computed; */
583 /* > = 'I': Z is initialized to the unit matrix and the matrix Z */
584 /* > of Schur vectors of H is returned; */
585 /* > = 'V': Z must contain an orthogonal matrix Q on entry, and */
586 /* > the product Q*Z is returned. */
592 /* > The order of the matrix H. N >= 0. */
595 /* > \param[in] ILO */
597 /* > ILO is INTEGER */
600 /* > \param[in] IHI */
602 /* > IHI is INTEGER */
604 /* > It is assumed that H is already upper triangular in rows */
605 /* > and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
606 /* > set by a previous call to DGEBAL, and then passed to ZGEHRD */
607 /* > when the matrix output by DGEBAL is reduced to Hessenberg */
608 /* > form. Otherwise ILO and IHI should be set to 1 and N */
609 /* > respectively. If N > 0, then 1 <= ILO <= IHI <= N. */
610 /* > If N = 0, then ILO = 1 and IHI = 0. */
613 /* > \param[in,out] H */
615 /* > H is DOUBLE PRECISION array, dimension (LDH,N) */
616 /* > On entry, the upper Hessenberg matrix H. */
617 /* > On exit, if INFO = 0 and JOB = 'S', then H contains the */
618 /* > upper quasi-triangular matrix T from the Schur decomposition */
619 /* > (the Schur form); 2-by-2 diagonal blocks (corresponding to */
620 /* > complex conjugate pairs of eigenvalues) are returned in */
621 /* > standard form, with H(i,i) = H(i+1,i+1) and */
622 /* > H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and JOB = 'E', the */
623 /* > contents of H are unspecified on exit. (The output value of */
624 /* > H when INFO > 0 is given under the description of INFO */
627 /* > Unlike earlier versions of DHSEQR, this subroutine may */
628 /* > explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1 */
629 /* > or j = IHI+1, IHI+2, ... N. */
632 /* > \param[in] LDH */
634 /* > LDH is INTEGER */
635 /* > The leading dimension of the array H. LDH >= f2cmax(1,N). */
638 /* > \param[out] WR */
640 /* > WR is DOUBLE PRECISION array, dimension (N) */
643 /* > \param[out] WI */
645 /* > WI is DOUBLE PRECISION array, dimension (N) */
647 /* > The real and imaginary parts, respectively, of the computed */
648 /* > eigenvalues. If two eigenvalues are computed as a complex */
649 /* > conjugate pair, they are stored in consecutive elements of */
650 /* > WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and */
651 /* > WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in */
652 /* > the same order as on the diagonal of the Schur form returned */
653 /* > in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */
654 /* > diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
655 /* > WI(i+1) = -WI(i). */
658 /* > \param[in,out] Z */
660 /* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */
661 /* > If COMPZ = 'N', Z is not referenced. */
662 /* > If COMPZ = 'I', on entry Z need not be set and on exit, */
663 /* > if INFO = 0, Z contains the orthogonal matrix Z of the Schur */
664 /* > vectors of H. If COMPZ = 'V', on entry Z must contain an */
665 /* > N-by-N matrix Q, which is assumed to be equal to the unit */
666 /* > matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */
667 /* > if INFO = 0, Z contains Q*Z. */
668 /* > Normally Q is the orthogonal matrix generated by DORGHR */
669 /* > after the call to DGEHRD which formed the Hessenberg matrix */
670 /* > H. (The output value of Z when INFO > 0 is given under */
671 /* > the description of INFO below.) */
674 /* > \param[in] LDZ */
676 /* > LDZ is INTEGER */
677 /* > The leading dimension of the array Z. if COMPZ = 'I' or */
678 /* > COMPZ = 'V', then LDZ >= MAX(1,N). Otherwise, LDZ >= 1. */
681 /* > \param[out] WORK */
683 /* > WORK is DOUBLE PRECISION array, dimension (LWORK) */
684 /* > On exit, if INFO = 0, WORK(1) returns an estimate of */
685 /* > the optimal value for LWORK. */
688 /* > \param[in] LWORK */
690 /* > LWORK is INTEGER */
691 /* > The dimension of the array WORK. LWORK >= f2cmax(1,N) */
692 /* > is sufficient and delivers very good and sometimes */
693 /* > optimal performance. However, LWORK as large as 11*N */
694 /* > may be required for optimal performance. A workspace */
695 /* > query is recommended to determine the optimal workspace */
698 /* > If LWORK = -1, then DHSEQR does a workspace query. */
699 /* > In this case, DHSEQR checks the input parameters and */
700 /* > estimates the optimal workspace size for the given */
701 /* > values of N, ILO and IHI. The estimate is returned */
702 /* > in WORK(1). No error message related to LWORK is */
703 /* > issued by XERBLA. Neither H nor Z are accessed. */
706 /* > \param[out] INFO */
708 /* > INFO is INTEGER */
709 /* > = 0: successful exit */
710 /* > < 0: if INFO = -i, the i-th argument had an illegal */
712 /* > > 0: if INFO = i, DHSEQR failed to compute all of */
713 /* > the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */
714 /* > and WI contain those eigenvalues which have been */
715 /* > successfully computed. (Failures are rare.) */
717 /* > If INFO > 0 and JOB = 'E', then on exit, the */
718 /* > remaining unconverged eigenvalues are the eigen- */
719 /* > values of the upper Hessenberg matrix rows and */
720 /* > columns ILO through INFO of the final, output */
723 /* > If INFO > 0 and JOB = 'S', then on exit */
725 /* > (*) (initial value of H)*U = U*(final value of H) */
727 /* > where U is an orthogonal matrix. The final */
728 /* > value of H is upper Hessenberg and quasi-triangular */
729 /* > in rows and columns INFO+1 through IHI. */
731 /* > If INFO > 0 and COMPZ = 'V', then on exit */
733 /* > (final value of Z) = (initial value of Z)*U */
735 /* > where U is the orthogonal matrix in (*) (regard- */
736 /* > less of the value of JOB.) */
738 /* > If INFO > 0 and COMPZ = 'I', then on exit */
739 /* > (final value of Z) = U */
740 /* > where U is the orthogonal matrix in (*) (regard- */
741 /* > less of the value of JOB.) */
743 /* > If INFO > 0 and COMPZ = 'N', then Z is not */
750 /* > \author Univ. of Tennessee */
751 /* > \author Univ. of California Berkeley */
752 /* > \author Univ. of Colorado Denver */
753 /* > \author NAG Ltd. */
755 /* > \date December 2016 */
757 /* > \ingroup doubleOTHERcomputational */
759 /* > \par Contributors: */
760 /* ================== */
762 /* > Karen Braman and Ralph Byers, Department of Mathematics, */
763 /* > University of Kansas, USA */
765 /* > \par Further Details: */
766 /* ===================== */
770 /* > Default values supplied by */
771 /* > ILAENV(ISPEC,'DHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */
772 /* > It is suggested that these defaults be adjusted in order */
773 /* > to attain best performance in each particular */
774 /* > computational environment. */
776 /* > ISPEC=12: The DLAHQR vs DLAQR0 crossover point. */
777 /* > Default: 75. (Must be at least 11.) */
779 /* > ISPEC=13: Recommended deflation window size. */
780 /* > This depends on ILO, IHI and NS. NS is the */
781 /* > number of simultaneous shifts returned */
782 /* > by ILAENV(ISPEC=15). (See ISPEC=15 below.) */
783 /* > The default for (IHI-ILO+1) <= 500 is NS. */
784 /* > The default for (IHI-ILO+1) > 500 is 3*NS/2. */
786 /* > ISPEC=14: Nibble crossover point. (See IPARMQ for */
787 /* > details.) Default: 14% of deflation window */
790 /* > ISPEC=15: Number of simultaneous shifts in a multishift */
791 /* > QR iteration. */
793 /* > If IHI-ILO+1 is ... */
795 /* > greater than ...but less ... the */
796 /* > or equal to ... than default is */
798 /* > 1 30 NS = 2(+) */
799 /* > 30 60 NS = 4(+) */
800 /* > 60 150 NS = 10(+) */
801 /* > 150 590 NS = ** */
802 /* > 590 3000 NS = 64 */
803 /* > 3000 6000 NS = 128 */
804 /* > 6000 infinity NS = 256 */
806 /* > (+) By default some or all matrices of this order */
807 /* > are passed to the implicit double shift routine */
808 /* > DLAHQR and this parameter is ignored. See */
809 /* > ISPEC=12 above and comments in IPARMQ for */
812 /* > (**) The asterisks (**) indicate an ad-hoc */
813 /* > function of N increasing from 10 to 64. */
815 /* > ISPEC=16: Select structured matrix multiply. */
816 /* > If the number of simultaneous shifts (specified */
817 /* > by ISPEC=15) is less than 14, then the default */
818 /* > for ISPEC=16 is 0. Otherwise the default for */
819 /* > ISPEC=16 is 2. */
822 /* > \par References: */
823 /* ================ */
825 /* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
826 /* > Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
827 /* > Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
828 /* > 929--947, 2002. */
830 /* > K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
831 /* > Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
832 /* > of Matrix Analysis, volume 23, pages 948--973, 2002. */
834 /* ===================================================================== */
835 /* Subroutine */ int dhseqr_(char *job, char *compz, integer *n, integer *ilo,
836 integer *ihi, doublereal *h__, integer *ldh, doublereal *wr,
837 doublereal *wi, doublereal *z__, integer *ldz, doublereal *work,
838 integer *lwork, integer *info)
840 /* System generated locals */
842 integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2[2], i__3;
846 /* Local variables */
847 integer kbot, nmin, i__;
848 extern logical lsame_(char *, char *);
850 doublereal workl[49];
851 logical wantt, wantz;
852 extern /* Subroutine */ int dlaqr0_(logical *, logical *, integer *,
853 integer *, integer *, doublereal *, integer *, doublereal *,
854 doublereal *, integer *, integer *, doublereal *, integer *,
855 doublereal *, integer *, integer *);
856 doublereal hl[2401] /* was [49][49] */;
857 extern /* Subroutine */ int dlahqr_(logical *, logical *, integer *,
858 integer *, integer *, doublereal *, integer *, doublereal *,
859 doublereal *, integer *, integer *, doublereal *, integer *,
860 integer *), dlacpy_(char *, integer *, integer *, doublereal *,
861 integer *, doublereal *, integer *), dlaset_(char *,
862 integer *, integer *, doublereal *, doublereal *, doublereal *,
864 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
865 integer *, integer *, ftnlen, ftnlen);
866 extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
870 /* -- LAPACK computational routine (version 3.7.0) -- */
871 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
872 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
876 /* ===================================================================== */
879 /* ==== Matrices of order NTINY or smaller must be processed by */
880 /* . DLAHQR because of insufficient subdiagonal scratch space. */
881 /* . (This is a hard limit.) ==== */
883 /* ==== NL allocates some local workspace to help small matrices */
884 /* . through a rare DLAHQR failure. NL > NTINY = 15 is */
885 /* . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom- */
886 /* . mended. (The default value of NMIN is 75.) Using NL = 49 */
887 /* . allows up to six simultaneous shifts and a 16-by-16 */
888 /* . deflation window. ==== */
890 /* ==== Decode and check the input parameters. ==== */
892 /* Parameter adjustments */
894 h_offset = 1 + h_dim1 * 1;
899 z_offset = 1 + z_dim1 * 1;
904 wantt = lsame_(job, "S");
905 initz = lsame_(compz, "I");
906 wantz = initz || lsame_(compz, "V");
907 work[1] = (doublereal) f2cmax(1,*n);
908 lquery = *lwork == -1;
911 if (! lsame_(job, "E") && ! wantt) {
913 } else if (! lsame_(compz, "N") && ! wantz) {
917 } else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
919 } else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
921 } else if (*ldh < f2cmax(1,*n)) {
923 } else if (*ldz < 1 || wantz && *ldz < f2cmax(1,*n)) {
925 } else if (*lwork < f2cmax(1,*n) && ! lquery) {
931 /* ==== Quick return in case of invalid argument. ==== */
934 xerbla_("DHSEQR", &i__1, (ftnlen)6);
937 } else if (*n == 0) {
939 /* ==== Quick return in case N = 0; nothing to do. ==== */
945 /* ==== Quick return in case of a workspace query ==== */
947 dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[
948 1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
949 /* ==== Ensure reported workspace size is backward-compatible with */
950 /* . previous LAPACK versions. ==== */
952 d__1 = (doublereal) f2cmax(1,*n);
953 work[1] = f2cmax(d__1,work[1]);
958 /* ==== copy eigenvalues isolated by DGEBAL ==== */
961 for (i__ = 1; i__ <= i__1; ++i__) {
962 wr[i__] = h__[i__ + i__ * h_dim1];
967 for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
968 wr[i__] = h__[i__ + i__ * h_dim1];
973 /* ==== Initialize Z, if requested ==== */
976 dlaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz)
980 /* ==== Quick return if possible ==== */
983 wr[*ilo] = h__[*ilo + *ilo * h_dim1];
988 /* ==== DLAHQR/DLAQR0 crossover point ==== */
990 /* Writing concatenation */
991 i__2[0] = 1, a__1[0] = job;
992 i__2[1] = 1, a__1[1] = compz;
993 s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
994 nmin = ilaenv_(&c__12, "DHSEQR", ch__1, n, ilo, ihi, lwork, (ftnlen)6,
996 nmin = f2cmax(15,nmin);
998 /* ==== DLAQR0 for big matrices; DLAHQR for small ones ==== */
1001 dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
1002 &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork,
1006 /* ==== Small matrix ==== */
1008 dlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
1009 &wi[1], ilo, ihi, &z__[z_offset], ldz, info);
1013 /* ==== A rare DLAHQR failure! DLAQR0 sometimes succeeds */
1014 /* . when DLAHQR fails. ==== */
1020 /* ==== Larger matrices have enough subdiagonal scratch */
1021 /* . space to call DLAQR0 directly. ==== */
1023 dlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset],
1024 ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset],
1025 ldz, &work[1], lwork, info);
1029 /* ==== Tiny matrices don't have enough subdiagonal */
1030 /* . scratch space to benefit from DLAQR0. Hence, */
1031 /* . tiny matrices must be copied into a larger */
1032 /* . array before calling DLAQR0. ==== */
1034 dlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
1035 hl[*n + 1 + *n * 49 - 50] = 0.;
1037 dlaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) *
1039 dlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, &
1040 wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz,
1041 workl, &c__49, info);
1042 if (wantt || *info != 0) {
1043 dlacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh);
1049 /* ==== Clear out the trash, if necessary. ==== */
1051 if ((wantt || *info != 0) && *n > 2) {
1054 dlaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
1057 /* ==== Ensure reported workspace size is backward-compatible with */
1058 /* . previous LAPACK versions. ==== */
1061 d__1 = (doublereal) f2cmax(1,*n);
1062 work[1] = f2cmax(d__1,work[1]);
1065 /* ==== End of DHSEQR ==== */