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> DGEES 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 DGEES + dependencies */
529 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgees.f
532 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgees.f
535 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgees.f
543 /* SUBROUTINE DGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, */
544 /* VS, LDVS, WORK, LWORK, BWORK, INFO ) */
546 /* CHARACTER JOBVS, SORT */
547 /* INTEGER INFO, LDA, LDVS, LWORK, N, SDIM */
548 /* LOGICAL BWORK( * ) */
549 /* DOUBLE PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ), */
552 /* EXTERNAL SELECT */
555 /* > \par Purpose: */
560 /* > DGEES computes for an N-by-N real nonsymmetric matrix A, the */
561 /* > eigenvalues, the real Schur form T, and, optionally, the matrix of */
562 /* > Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). */
564 /* > Optionally, it also orders the eigenvalues on the diagonal of the */
565 /* > real 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 matrix is in real Schur form if it is upper quasi-triangular with */
570 /* > 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the */
575 /* > where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */
581 /* > \param[in] JOBVS */
583 /* > JOBVS is CHARACTER*1 */
584 /* > = 'N': Schur vectors are not computed; */
585 /* > = 'V': Schur vectors are computed. */
588 /* > \param[in] SORT */
590 /* > SORT is CHARACTER*1 */
591 /* > Specifies whether or not to order the eigenvalues on the */
592 /* > diagonal of the Schur form. */
593 /* > = 'N': Eigenvalues are not ordered; */
594 /* > = 'S': Eigenvalues are ordered (see SELECT). */
597 /* > \param[in] SELECT */
599 /* > SELECT is a LOGICAL FUNCTION of two DOUBLE PRECISION arguments */
600 /* > SELECT must be declared EXTERNAL in the calling subroutine. */
601 /* > If SORT = 'S', SELECT is used to select eigenvalues to sort */
602 /* > to the top left of the Schur form. */
603 /* > If SORT = 'N', SELECT is not referenced. */
604 /* > An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */
605 /* > SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex */
606 /* > conjugate pair of eigenvalues is selected, then both complex */
607 /* > eigenvalues are selected. */
608 /* > Note that a selected complex eigenvalue may no longer */
609 /* > satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */
610 /* > ordering may change the value of complex eigenvalues */
611 /* > (especially if the eigenvalue is ill-conditioned); in this */
612 /* > case INFO is set to N+2 (see INFO below). */
618 /* > The order of the matrix A. N >= 0. */
621 /* > \param[in,out] A */
623 /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
624 /* > On entry, the N-by-N matrix A. */
625 /* > On exit, A has been overwritten by its real Schur form T. */
628 /* > \param[in] LDA */
630 /* > LDA is INTEGER */
631 /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
634 /* > \param[out] SDIM */
636 /* > SDIM is INTEGER */
637 /* > If SORT = 'N', SDIM = 0. */
638 /* > If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
639 /* > for which SELECT is true. (Complex conjugate */
640 /* > pairs for which SELECT is true for either */
641 /* > eigenvalue count as 2.) */
644 /* > \param[out] WR */
646 /* > WR is DOUBLE PRECISION array, dimension (N) */
649 /* > \param[out] WI */
651 /* > WI is DOUBLE PRECISION array, dimension (N) */
652 /* > WR and WI contain the real and imaginary parts, */
653 /* > respectively, of the computed eigenvalues in the same order */
654 /* > that they appear on the diagonal of the output Schur form T. */
655 /* > Complex conjugate pairs of eigenvalues will appear */
656 /* > consecutively with the eigenvalue having the positive */
657 /* > imaginary part first. */
660 /* > \param[out] VS */
662 /* > VS is DOUBLE PRECISION array, dimension (LDVS,N) */
663 /* > If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur */
665 /* > If JOBVS = 'N', VS is not referenced. */
668 /* > \param[in] LDVS */
670 /* > LDVS is INTEGER */
671 /* > The leading dimension of the array VS. LDVS >= 1; if */
672 /* > JOBVS = 'V', LDVS >= N. */
675 /* > \param[out] WORK */
677 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
678 /* > On exit, if INFO = 0, WORK(1) contains the optimal LWORK. */
681 /* > \param[in] LWORK */
683 /* > LWORK is INTEGER */
684 /* > The dimension of the array WORK. LWORK >= f2cmax(1,3*N). */
685 /* > For good performance, LWORK must generally be larger. */
687 /* > If LWORK = -1, then a workspace query is assumed; the routine */
688 /* > only calculates the optimal size of the WORK array, returns */
689 /* > this value as the first entry of the WORK array, and no error */
690 /* > message related to LWORK is issued by XERBLA. */
693 /* > \param[out] BWORK */
695 /* > BWORK is LOGICAL array, dimension (N) */
696 /* > Not referenced if SORT = 'N'. */
699 /* > \param[out] INFO */
701 /* > INFO is INTEGER */
702 /* > = 0: successful exit */
703 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
704 /* > > 0: if INFO = i, and i is */
705 /* > <= N: the QR algorithm failed to compute all the */
706 /* > eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI */
707 /* > contain those eigenvalues which have converged; if */
708 /* > JOBVS = 'V', VS contains the matrix which reduces A */
709 /* > to its partially converged Schur form. */
710 /* > = N+1: the eigenvalues could not be reordered because some */
711 /* > eigenvalues were too close to separate (the problem */
712 /* > is very ill-conditioned); */
713 /* > = N+2: after reordering, roundoff changed values of some */
714 /* > complex eigenvalues so that leading eigenvalues in */
715 /* > the Schur form no longer satisfy SELECT=.TRUE. This */
716 /* > could also be caused by underflow due to scaling. */
722 /* > \author Univ. of Tennessee */
723 /* > \author Univ. of California Berkeley */
724 /* > \author Univ. of Colorado Denver */
725 /* > \author NAG Ltd. */
727 /* > \date December 2016 */
729 /* > \ingroup doubleGEeigen */
731 /* ===================================================================== */
732 /* Subroutine */ int dgees_(char *jobvs, char *sort, L_fp select, integer *n,
733 doublereal *a, integer *lda, integer *sdim, doublereal *wr,
734 doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work,
735 integer *lwork, logical *bwork, integer *info)
737 /* System generated locals */
738 integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;
740 /* Local variables */
743 integer idum[1], ierr, itau, iwrk, inxt, i__;
745 integer icond, ieval;
746 extern logical lsame_(char *, char *);
747 extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
748 doublereal *, integer *), dswap_(integer *, doublereal *, integer
749 *, doublereal *, integer *);
752 extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebak_(
753 char *, char *, integer *, integer *, integer *, doublereal *,
754 integer *, doublereal *, integer *, integer *),
755 dgebal_(char *, integer *, doublereal *, integer *, integer *,
756 integer *, doublereal *, integer *);
757 logical lst2sl, scalea;
760 extern doublereal dlamch_(char *), dlange_(char *, integer *,
761 integer *, doublereal *, integer *, doublereal *);
762 extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
763 doublereal *, integer *, doublereal *, doublereal *, integer *,
764 integer *), dlascl_(char *, integer *, integer *, doublereal *,
765 doublereal *, integer *, integer *, doublereal *, integer *,
766 integer *), dlacpy_(char *, integer *, integer *,
767 doublereal *, integer *, doublereal *, integer *),
768 xerbla_(char *, integer *, ftnlen);
769 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
770 integer *, integer *, ftnlen, ftnlen);
772 extern /* Subroutine */ int dorghr_(integer *, integer *, integer *,
773 doublereal *, integer *, doublereal *, doublereal *, integer *,
774 integer *), dhseqr_(char *, char *, integer *, integer *, integer
775 *, doublereal *, integer *, doublereal *, doublereal *,
776 doublereal *, integer *, doublereal *, integer *, integer *), dtrsen_(char *, char *, logical *, integer *,
777 doublereal *, integer *, doublereal *, integer *, doublereal *,
778 doublereal *, integer *, doublereal *, doublereal *, doublereal *,
779 integer *, integer *, integer *, integer *);
781 integer minwrk, maxwrk;
784 logical wantst, lquery, wantvs;
786 doublereal dum[1], eps, sep;
789 /* -- LAPACK driver routine (version 3.7.0) -- */
790 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
791 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
795 /* ===================================================================== */
798 /* Test the input arguments */
800 /* Parameter adjustments */
802 a_offset = 1 + a_dim1 * 1;
807 vs_offset = 1 + vs_dim1 * 1;
814 lquery = *lwork == -1;
815 wantvs = lsame_(jobvs, "V");
816 wantst = lsame_(sort, "S");
817 if (! wantvs && ! lsame_(jobvs, "N")) {
819 } else if (! wantst && ! lsame_(sort, "N")) {
823 } else if (*lda < f2cmax(1,*n)) {
825 } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
829 /* Compute workspace */
830 /* (Note: Comments in the code beginning "Workspace:" describe the */
831 /* minimal amount of workspace needed at that point in the code, */
832 /* as well as the preferred amount for good performance. */
833 /* NB refers to the optimal block size for the immediately */
834 /* following subroutine, as returned by ILAENV. */
835 /* HSWORK refers to the workspace preferred by DHSEQR, as */
836 /* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
837 /* the worst case.) */
844 maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1,
845 n, &c__0, (ftnlen)6, (ftnlen)1);
848 dhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1]
849 , &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
850 hswork = (integer) work[1];
854 i__1 = maxwrk, i__2 = *n + hswork;
855 maxwrk = f2cmax(i__1,i__2);
858 i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
859 "DORGHR", " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)
861 maxwrk = f2cmax(i__1,i__2);
863 i__1 = maxwrk, i__2 = *n + hswork;
864 maxwrk = f2cmax(i__1,i__2);
867 work[1] = (doublereal) maxwrk;
869 if (*lwork < minwrk && ! lquery) {
876 xerbla_("DGEES ", &i__1, (ftnlen)6);
882 /* Quick return if possible */
889 /* Get machine constants */
892 smlnum = dlamch_("S");
893 bignum = 1. / smlnum;
894 dlabad_(&smlnum, &bignum);
895 smlnum = sqrt(smlnum) / eps;
896 bignum = 1. / smlnum;
898 /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
900 anrm = dlange_("M", n, n, &a[a_offset], lda, dum);
902 if (anrm > 0. && anrm < smlnum) {
905 } else if (anrm > bignum) {
910 dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
914 /* Permute the matrix to make it more nearly triangular */
915 /* (Workspace: need N) */
918 dgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
920 /* Reduce to upper Hessenberg form */
921 /* (Workspace: need 3*N, prefer 2*N+N*NB) */
925 i__1 = *lwork - iwrk + 1;
926 dgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
931 /* Copy Householder vectors to VS */
933 dlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
936 /* Generate orthogonal matrix in VS */
937 /* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
939 i__1 = *lwork - iwrk + 1;
940 dorghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
946 /* Perform QR iteration, accumulating Schur vectors in VS if desired */
947 /* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
950 i__1 = *lwork - iwrk + 1;
951 dhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &vs[
952 vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
957 /* Sort eigenvalues if desired */
959 if (wantst && *info == 0) {
961 dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, &
963 dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, &
967 for (i__ = 1; i__ <= i__1; ++i__) {
968 bwork[i__] = (*select)(&wr[i__], &wi[i__]);
972 /* Reorder eigenvalues and transform Schur vectors */
973 /* (Workspace: none needed) */
975 i__1 = *lwork - iwrk + 1;
976 dtrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
977 ldvs, &wr[1], &wi[1], sdim, &s, &sep, &work[iwrk], &i__1,
978 idum, &c__1, &icond);
987 /* (Workspace: need N) */
989 dgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs,
995 /* Undo scaling for the Schur form of A */
997 dlascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
1000 dcopy_(n, &a[a_offset], &i__1, &wr[1], &c__1);
1001 if (cscale == smlnum) {
1003 /* If scaling back towards underflow, adjust WI if an */
1004 /* offdiagonal element of a 2-by-2 block in the Schur form */
1013 i__2 = f2cmax(i__3,1);
1014 dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[
1016 } else if (wantst) {
1025 for (i__ = i1; i__ <= i__1; ++i__) {
1029 if (wi[i__] == 0.) {
1032 if (a[i__ + 1 + i__ * a_dim1] == 0.) {
1035 } else if (a[i__ + 1 + i__ * a_dim1] != 0. && a[i__ + (
1036 i__ + 1) * a_dim1] == 0.) {
1041 dswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[(
1042 i__ + 1) * a_dim1 + 1], &c__1);
1045 i__2 = *n - i__ - 1;
1046 dswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, &
1047 a[i__ + 1 + (i__ + 2) * a_dim1], lda);
1050 dswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__
1051 + 1) * vs_dim1 + 1], &c__1);
1053 a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ *
1055 a[i__ + 1 + i__ * a_dim1] = 0.;
1064 /* Undo scaling for the imaginary part of the eigenvalues */
1069 i__2 = f2cmax(i__3,1);
1070 dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval +
1074 if (wantst && *info == 0) {
1076 /* Check if reordering successful */
1083 for (i__ = 1; i__ <= i__1; ++i__) {
1084 cursl = (*select)(&wr[i__], &wi[i__]);
1085 if (wi[i__] == 0.) {
1090 if (cursl && ! lastsl) {
1096 /* Last eigenvalue of conjugate pair */
1098 cursl = cursl || lastsl;
1104 if (cursl && ! lst2sl) {
1109 /* First eigenvalue of conjugate pair */
1120 work[1] = (doublereal) maxwrk;