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__0 = 0;
517 static integer c_n1 = -1;
519 /* > \brief <b> ZGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f
520 or GE matrices</b> */
522 /* =========== DOCUMENTATION =========== */
524 /* Online html documentation available at */
525 /* http://www.netlib.org/lapack/explore-html/ */
528 /* > Download ZGEES + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgees.f
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgees.f
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgees.f
543 /* SUBROUTINE ZGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, */
544 /* LDVS, WORK, LWORK, RWORK, BWORK, INFO ) */
546 /* CHARACTER JOBVS, SORT */
547 /* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM */
548 /* LOGICAL BWORK( * ) */
549 /* DOUBLE PRECISION RWORK( * ) */
550 /* COMPLEX*16 A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) */
552 /* EXTERNAL SELECT */
555 /* > \par Purpose: */
560 /* > ZGEES computes for an N-by-N complex nonsymmetric matrix A, the */
561 /* > eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
562 /* > vectors Z. This gives the Schur factorization A = Z*T*(Z**H). */
564 /* > Optionally, it also orders the eigenvalues on the diagonal of the */
565 /* > Schur form so that selected eigenvalues are at the top left. */
566 /* > The leading columns of Z then form an orthonormal basis for the */
567 /* > invariant subspace corresponding to the selected eigenvalues. */
569 /* > A complex matrix is in Schur form if it is upper triangular. */
575 /* > \param[in] JOBVS */
577 /* > JOBVS is CHARACTER*1 */
578 /* > = 'N': Schur vectors are not computed; */
579 /* > = 'V': Schur vectors are computed. */
582 /* > \param[in] SORT */
584 /* > SORT is CHARACTER*1 */
585 /* > Specifies whether or not to order the eigenvalues on the */
586 /* > diagonal of the Schur form. */
587 /* > = 'N': Eigenvalues are not ordered: */
588 /* > = 'S': Eigenvalues are ordered (see SELECT). */
591 /* > \param[in] SELECT */
593 /* > SELECT is a LOGICAL FUNCTION of one COMPLEX*16 argument */
594 /* > SELECT must be declared EXTERNAL in the calling subroutine. */
595 /* > If SORT = 'S', SELECT is used to select eigenvalues to order */
596 /* > to the top left of the Schur form. */
597 /* > IF SORT = 'N', SELECT is not referenced. */
598 /* > The eigenvalue W(j) is selected if SELECT(W(j)) is true. */
604 /* > The order of the matrix A. N >= 0. */
607 /* > \param[in,out] A */
609 /* > A is COMPLEX*16 array, dimension (LDA,N) */
610 /* > On entry, the N-by-N matrix A. */
611 /* > On exit, A has been overwritten by its Schur form T. */
614 /* > \param[in] LDA */
616 /* > LDA is INTEGER */
617 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
620 /* > \param[out] SDIM */
622 /* > SDIM is INTEGER */
623 /* > If SORT = 'N', SDIM = 0. */
624 /* > If SORT = 'S', SDIM = number of eigenvalues for which */
625 /* > SELECT is true. */
628 /* > \param[out] W */
630 /* > W is COMPLEX*16 array, dimension (N) */
631 /* > W contains the computed eigenvalues, in the same order that */
632 /* > they appear on the diagonal of the output Schur form T. */
635 /* > \param[out] VS */
637 /* > VS is COMPLEX*16 array, dimension (LDVS,N) */
638 /* > If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
640 /* > If JOBVS = 'N', VS is not referenced. */
643 /* > \param[in] LDVS */
645 /* > LDVS is INTEGER */
646 /* > The leading dimension of the array VS. LDVS >= 1; if */
647 /* > JOBVS = 'V', LDVS >= N. */
650 /* > \param[out] WORK */
652 /* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
653 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
656 /* > \param[in] LWORK */
658 /* > LWORK is INTEGER */
659 /* > The dimension of the array WORK. LWORK >= f2cmax(1,2*N). */
660 /* > For good performance, LWORK must generally be larger. */
662 /* > If LWORK = -1, then a workspace query is assumed; the routine */
663 /* > only calculates the optimal size of the WORK array, returns */
664 /* > this value as the first entry of the WORK array, and no error */
665 /* > message related to LWORK is issued by XERBLA. */
668 /* > \param[out] RWORK */
670 /* > RWORK is DOUBLE PRECISION array, dimension (N) */
673 /* > \param[out] BWORK */
675 /* > BWORK is LOGICAL array, dimension (N) */
676 /* > Not referenced if SORT = 'N'. */
679 /* > \param[out] INFO */
681 /* > INFO is INTEGER */
682 /* > = 0: successful exit */
683 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
684 /* > > 0: if INFO = i, and i is */
685 /* > <= N: the QR algorithm failed to compute all the */
686 /* > eigenvalues; elements 1:ILO-1 and i+1:N of W */
687 /* > contain those eigenvalues which have converged; */
688 /* > if JOBVS = 'V', VS contains the matrix which */
689 /* > reduces A to its partially converged Schur form. */
690 /* > = N+1: the eigenvalues could not be reordered because */
691 /* > some eigenvalues were too close to separate (the */
692 /* > problem is very ill-conditioned); */
693 /* > = N+2: after reordering, roundoff changed values of */
694 /* > some complex eigenvalues so that leading */
695 /* > eigenvalues in the Schur form no longer satisfy */
696 /* > SELECT = .TRUE.. This could also be caused by */
697 /* > underflow due to scaling. */
703 /* > \author Univ. of Tennessee */
704 /* > \author Univ. of California Berkeley */
705 /* > \author Univ. of Colorado Denver */
706 /* > \author NAG Ltd. */
708 /* > \date December 2016 */
710 /* > \ingroup complex16GEeigen */
712 /* ===================================================================== */
713 /* Subroutine */ int zgees_(char *jobvs, char *sort, L_fp select, integer *n,
714 doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w,
715 doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork,
716 doublereal *rwork, logical *bwork, integer *info)
718 /* System generated locals */
719 integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;
721 /* Local variables */
724 integer ierr, itau, iwrk, i__;
726 integer icond, ieval;
727 extern logical lsame_(char *, char *);
728 extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
729 doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
731 extern doublereal dlamch_(char *);
733 extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
734 integer *, doublereal *, integer *, doublecomplex *, integer *,
735 integer *), zgebal_(char *, integer *,
736 doublecomplex *, integer *, integer *, integer *, doublereal *,
737 integer *), xerbla_(char *, integer *, ftnlen);
738 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
739 integer *, integer *, ftnlen, ftnlen);
740 extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
741 integer *, doublereal *);
743 extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
744 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
745 integer *, integer *), zlascl_(char *, integer *, integer *,
746 doublereal *, doublereal *, integer *, integer *, doublecomplex *,
747 integer *, integer *), zlacpy_(char *, integer *,
748 integer *, doublecomplex *, integer *, doublecomplex *, integer *);
749 integer minwrk, maxwrk;
751 extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
752 integer *, doublecomplex *, integer *, doublecomplex *,
753 doublecomplex *, integer *, doublecomplex *, integer *, integer *);
755 extern /* Subroutine */ int zunghr_(integer *, integer *, integer *,
756 doublecomplex *, integer *, doublecomplex *, doublecomplex *,
757 integer *, integer *);
758 logical wantst, lquery, wantvs;
759 extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *,
760 doublecomplex *, integer *, doublecomplex *, integer *,
761 doublecomplex *, integer *, doublereal *, doublereal *,
762 doublecomplex *, integer *, integer *);
764 doublereal dum[1], eps, sep;
767 /* -- LAPACK driver routine (version 3.7.0) -- */
768 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
769 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
773 /* ===================================================================== */
776 /* Test the input arguments */
778 /* Parameter adjustments */
780 a_offset = 1 + a_dim1 * 1;
784 vs_offset = 1 + vs_dim1 * 1;
792 lquery = *lwork == -1;
793 wantvs = lsame_(jobvs, "V");
794 wantst = lsame_(sort, "S");
795 if (! wantvs && ! lsame_(jobvs, "N")) {
797 } else if (! wantst && ! lsame_(sort, "N")) {
801 } else if (*lda < f2cmax(1,*n)) {
803 } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
807 /* Compute workspace */
808 /* (Note: Comments in the code beginning "Workspace:" describe the */
809 /* minimal amount of workspace needed at that point in the code, */
810 /* as well as the preferred amount for good performance. */
811 /* CWorkspace refers to complex workspace, and RWorkspace to real */
812 /* workspace. NB refers to the optimal block size for the */
813 /* immediately following subroutine, as returned by ILAENV. */
814 /* HSWORK refers to the workspace preferred by ZHSEQR, as */
815 /* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
816 /* the worst case.) */
823 maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &
824 c__0, (ftnlen)6, (ftnlen)1);
827 zhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
828 vs_offset], ldvs, &work[1], &c_n1, &ieval);
829 hswork = (integer) work[1].r;
832 maxwrk = f2cmax(maxwrk,hswork);
835 i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
836 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
837 maxwrk = f2cmax(i__1,i__2);
838 maxwrk = f2cmax(maxwrk,hswork);
841 work[1].r = (doublereal) maxwrk, work[1].i = 0.;
843 if (*lwork < minwrk && ! lquery) {
850 xerbla_("ZGEES ", &i__1, (ftnlen)6);
856 /* Quick return if possible */
863 /* Get machine constants */
866 smlnum = dlamch_("S");
867 bignum = 1. / smlnum;
868 dlabad_(&smlnum, &bignum);
869 smlnum = sqrt(smlnum) / eps;
870 bignum = 1. / smlnum;
872 /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
874 anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
876 if (anrm > 0. && anrm < smlnum) {
879 } else if (anrm > bignum) {
884 zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
888 /* Permute the matrix to make it more nearly triangular */
889 /* (CWorkspace: none) */
890 /* (RWorkspace: need N) */
893 zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
895 /* Reduce to upper Hessenberg form */
896 /* (CWorkspace: need 2*N, prefer N+N*NB) */
897 /* (RWorkspace: none) */
901 i__1 = *lwork - iwrk + 1;
902 zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
907 /* Copy Householder vectors to VS */
909 zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
912 /* Generate unitary matrix in VS */
913 /* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
914 /* (RWorkspace: none) */
916 i__1 = *lwork - iwrk + 1;
917 zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
923 /* Perform QR iteration, accumulating Schur vectors in VS if desired */
924 /* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
925 /* (RWorkspace: none) */
928 i__1 = *lwork - iwrk + 1;
929 zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
930 vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
935 /* Sort eigenvalues if desired */
937 if (wantst && *info == 0) {
939 zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
943 for (i__ = 1; i__ <= i__1; ++i__) {
944 bwork[i__] = (*select)(&w[i__]);
948 /* Reorder eigenvalues and transform Schur vectors */
949 /* (CWorkspace: none) */
950 /* (RWorkspace: none) */
952 i__1 = *lwork - iwrk + 1;
953 ztrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
954 ldvs, &w[1], sdim, &s, &sep, &work[iwrk], &i__1, &icond);
960 /* (CWorkspace: none) */
961 /* (RWorkspace: need N) */
963 zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset],
969 /* Undo scaling for the Schur form of A */
971 zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
974 zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
977 work[1].r = (doublereal) maxwrk, work[1].i = 0.;