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;
518 static doublereal c_b36 = 0.;
519 static doublereal c_b37 = 1.;
521 /* > \brief <b> DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matr
524 /* =========== DOCUMENTATION =========== */
526 /* Online html documentation available at */
527 /* http://www.netlib.org/lapack/explore-html/ */
530 /* > Download DGGEV + dependencies */
531 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggev.f
534 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggev.f
537 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggev.f
545 /* SUBROUTINE DGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, */
546 /* BETA, VL, LDVL, VR, LDVR, WORK, LWORK, INFO ) */
548 /* CHARACTER JOBVL, JOBVR */
549 /* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N */
550 /* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
551 /* $ B( LDB, * ), BETA( * ), VL( LDVL, * ), */
552 /* $ VR( LDVR, * ), WORK( * ) */
555 /* > \par Purpose: */
560 /* > DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B) */
561 /* > the generalized eigenvalues, and optionally, the left and/or right */
562 /* > generalized eigenvectors. */
564 /* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
565 /* > lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */
566 /* > singular. It is usually represented as the pair (alpha,beta), as */
567 /* > there is a reasonable interpretation for beta=0, and even for both */
570 /* > The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */
571 /* > of (A,B) satisfies */
573 /* > A * v(j) = lambda(j) * B * v(j). */
575 /* > The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */
576 /* > of (A,B) satisfies */
578 /* > u(j)**H * A = lambda(j) * u(j)**H * B . */
580 /* > where u(j)**H is the conjugate-transpose of u(j). */
587 /* > \param[in] JOBVL */
589 /* > JOBVL is CHARACTER*1 */
590 /* > = 'N': do not compute the left generalized eigenvectors; */
591 /* > = 'V': compute the left generalized eigenvectors. */
594 /* > \param[in] JOBVR */
596 /* > JOBVR is CHARACTER*1 */
597 /* > = 'N': do not compute the right generalized eigenvectors; */
598 /* > = 'V': compute the right generalized eigenvectors. */
604 /* > The order of the matrices A, B, VL, and VR. N >= 0. */
607 /* > \param[in,out] A */
609 /* > A is DOUBLE PRECISION array, dimension (LDA, N) */
610 /* > On entry, the matrix A in the pair (A,B). */
611 /* > On exit, A has been overwritten. */
614 /* > \param[in] LDA */
616 /* > LDA is INTEGER */
617 /* > The leading dimension of A. LDA >= f2cmax(1,N). */
620 /* > \param[in,out] B */
622 /* > B is DOUBLE PRECISION array, dimension (LDB, N) */
623 /* > On entry, the matrix B in the pair (A,B). */
624 /* > On exit, B has been overwritten. */
627 /* > \param[in] LDB */
629 /* > LDB is INTEGER */
630 /* > The leading dimension of B. LDB >= f2cmax(1,N). */
633 /* > \param[out] ALPHAR */
635 /* > ALPHAR is DOUBLE PRECISION array, dimension (N) */
638 /* > \param[out] ALPHAI */
640 /* > ALPHAI is DOUBLE PRECISION array, dimension (N) */
643 /* > \param[out] BETA */
645 /* > BETA is DOUBLE PRECISION array, dimension (N) */
646 /* > On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
647 /* > be the generalized eigenvalues. If ALPHAI(j) is zero, then */
648 /* > the j-th eigenvalue is real; if positive, then the j-th and */
649 /* > (j+1)-st eigenvalues are a complex conjugate pair, with */
650 /* > ALPHAI(j+1) negative. */
652 /* > Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
653 /* > may easily over- or underflow, and BETA(j) may even be zero. */
654 /* > Thus, the user should avoid naively computing the ratio */
655 /* > alpha/beta. However, ALPHAR and ALPHAI will be always less */
656 /* > than and usually comparable with norm(A) in magnitude, and */
657 /* > BETA always less than and usually comparable with norm(B). */
660 /* > \param[out] VL */
662 /* > VL is DOUBLE PRECISION array, dimension (LDVL,N) */
663 /* > If JOBVL = 'V', the left eigenvectors u(j) are stored one */
664 /* > after another in the columns of VL, in the same order as */
665 /* > their eigenvalues. If the j-th eigenvalue is real, then */
666 /* > u(j) = VL(:,j), the j-th column of VL. If the j-th and */
667 /* > (j+1)-th eigenvalues form a complex conjugate pair, then */
668 /* > u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
669 /* > Each eigenvector is scaled so the largest component has */
670 /* > abs(real part)+abs(imag. part)=1. */
671 /* > Not referenced if JOBVL = 'N'. */
674 /* > \param[in] LDVL */
676 /* > LDVL is INTEGER */
677 /* > The leading dimension of the matrix VL. LDVL >= 1, and */
678 /* > if JOBVL = 'V', LDVL >= N. */
681 /* > \param[out] VR */
683 /* > VR is DOUBLE PRECISION array, dimension (LDVR,N) */
684 /* > If JOBVR = 'V', the right eigenvectors v(j) are stored one */
685 /* > after another in the columns of VR, in the same order as */
686 /* > their eigenvalues. If the j-th eigenvalue is real, then */
687 /* > v(j) = VR(:,j), the j-th column of VR. If the j-th and */
688 /* > (j+1)-th eigenvalues form a complex conjugate pair, then */
689 /* > v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
690 /* > Each eigenvector is scaled so the largest component has */
691 /* > abs(real part)+abs(imag. part)=1. */
692 /* > Not referenced if JOBVR = 'N'. */
695 /* > \param[in] LDVR */
697 /* > LDVR is INTEGER */
698 /* > The leading dimension of the matrix VR. LDVR >= 1, and */
699 /* > if JOBVR = 'V', LDVR >= N. */
702 /* > \param[out] WORK */
704 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
705 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
708 /* > \param[in] LWORK */
710 /* > LWORK is INTEGER */
711 /* > The dimension of the array WORK. LWORK >= f2cmax(1,8*N). */
712 /* > For good performance, LWORK must generally be larger. */
714 /* > If LWORK = -1, then a workspace query is assumed; the routine */
715 /* > only calculates the optimal size of the WORK array, returns */
716 /* > this value as the first entry of the WORK array, and no error */
717 /* > message related to LWORK is issued by XERBLA. */
720 /* > \param[out] INFO */
722 /* > INFO is INTEGER */
723 /* > = 0: successful exit */
724 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
726 /* > The QZ iteration failed. No eigenvectors have been */
727 /* > calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
728 /* > should be correct for j=INFO+1,...,N. */
729 /* > > N: =N+1: other than QZ iteration failed in DHGEQZ. */
730 /* > =N+2: error return from DTGEVC. */
736 /* > \author Univ. of Tennessee */
737 /* > \author Univ. of California Berkeley */
738 /* > \author Univ. of Colorado Denver */
739 /* > \author NAG Ltd. */
741 /* > \date April 2012 */
743 /* > \ingroup doubleGEeigen */
745 /* ===================================================================== */
746 /* Subroutine */ int dggev_(char *jobvl, char *jobvr, integer *n, doublereal *
747 a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar,
748 doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl,
749 doublereal *vr, integer *ldvr, doublereal *work, integer *lwork,
752 /* System generated locals */
753 integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
754 vr_offset, i__1, i__2;
755 doublereal d__1, d__2, d__3, d__4;
757 /* Local variables */
758 doublereal anrm, bnrm;
763 extern logical lsame_(char *, char *);
764 integer ileft, icols, irows;
765 extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
767 extern /* Subroutine */ int dggbak_(char *, char *, integer *, integer *,
768 integer *, doublereal *, doublereal *, integer *, doublereal *,
769 integer *, integer *), dggbal_(char *, integer *,
770 doublereal *, integer *, doublereal *, integer *, integer *,
771 integer *, doublereal *, doublereal *, doublereal *, integer *);
773 extern doublereal dlamch_(char *), dlange_(char *, integer *,
774 integer *, doublereal *, integer *, doublereal *);
776 extern /* Subroutine */ int dgghrd_(char *, char *, integer *, integer *,
777 integer *, doublereal *, integer *, doublereal *, integer *,
778 doublereal *, integer *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal
779 *, doublereal *, integer *, integer *, doublereal *, integer *,
781 logical ilascl, ilbscl;
782 extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
783 integer *, doublereal *, doublereal *, integer *, integer *),
784 dlacpy_(char *, integer *, integer *, doublereal *, integer *,
785 doublereal *, integer *), dlaset_(char *, integer *,
786 integer *, doublereal *, doublereal *, doublereal *, integer *), dtgevc_(char *, char *, logical *, integer *, doublereal
787 *, integer *, doublereal *, integer *, doublereal *, integer *,
788 doublereal *, integer *, integer *, integer *, doublereal *,
793 extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *,
794 integer *, integer *, doublereal *, integer *, doublereal *,
795 integer *, doublereal *, doublereal *, doublereal *, doublereal *,
796 integer *, doublereal *, integer *, doublereal *, integer *,
797 integer *), xerbla_(char *, integer *, ftnlen);
798 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
799 integer *, integer *, ftnlen, ftnlen);
800 integer ijobvl, iright, ijobvr;
801 extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *,
802 doublereal *, integer *, doublereal *, doublereal *, integer *,
804 doublereal anrmto, bnrmto;
805 extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
806 integer *, doublereal *, integer *, doublereal *, doublereal *,
807 integer *, doublereal *, integer *, integer *);
808 integer minwrk, maxwrk;
816 /* -- LAPACK driver routine (version 3.7.0) -- */
817 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
818 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
822 /* ===================================================================== */
825 /* Decode the input arguments */
827 /* Parameter adjustments */
829 a_offset = 1 + a_dim1 * 1;
832 b_offset = 1 + b_dim1 * 1;
838 vl_offset = 1 + vl_dim1 * 1;
841 vr_offset = 1 + vr_dim1 * 1;
846 if (lsame_(jobvl, "N")) {
849 } else if (lsame_(jobvl, "V")) {
857 if (lsame_(jobvr, "N")) {
860 } else if (lsame_(jobvr, "V")) {
869 /* Test the input arguments */
872 lquery = *lwork == -1;
875 } else if (ijobvr <= 0) {
879 } else if (*lda < f2cmax(1,*n)) {
881 } else if (*ldb < f2cmax(1,*n)) {
883 } else if (*ldvl < 1 || ilvl && *ldvl < *n) {
885 } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
889 /* Compute workspace */
890 /* (Note: Comments in the code beginning "Workspace:" describe the */
891 /* minimal amount of workspace needed at that point in the code, */
892 /* as well as the preferred amount for good performance. */
893 /* NB refers to the optimal block size for the immediately */
894 /* following subroutine, as returned by ILAENV. The workspace is */
895 /* computed assuming ILO = 1 and IHI = N, the worst case.) */
899 i__1 = 1, i__2 = *n << 3;
900 minwrk = f2cmax(i__1,i__2);
902 i__1 = 1, i__2 = *n * (ilaenv_(&c__1, "DGEQRF", " ", n, &c__1, n, &
903 c__0, (ftnlen)6, (ftnlen)1) + 7);
904 maxwrk = f2cmax(i__1,i__2);
906 i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "DORMQR", " ", n, &c__1, n,
907 &c__0, (ftnlen)6, (ftnlen)1) + 7);
908 maxwrk = f2cmax(i__1,i__2);
911 i__1 = maxwrk, i__2 = *n * (ilaenv_(&c__1, "DORGQR", " ", n, &
912 c__1, n, &c_n1, (ftnlen)6, (ftnlen)1) + 7);
913 maxwrk = f2cmax(i__1,i__2);
915 work[1] = (doublereal) maxwrk;
917 if (*lwork < minwrk && ! lquery) {
924 xerbla_("DGGEV ", &i__1, (ftnlen)6);
930 /* Quick return if possible */
936 /* Get machine constants */
939 smlnum = dlamch_("S");
940 bignum = 1. / smlnum;
941 dlabad_(&smlnum, &bignum);
942 smlnum = sqrt(smlnum) / eps;
943 bignum = 1. / smlnum;
945 /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
947 anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
949 if (anrm > 0. && anrm < smlnum) {
952 } else if (anrm > bignum) {
957 dlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
961 /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
963 bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
965 if (bnrm > 0. && bnrm < smlnum) {
968 } else if (bnrm > bignum) {
973 dlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
977 /* Permute the matrices A, B to isolate eigenvalues if possible */
978 /* (Workspace: need 6*N) */
983 dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
984 ileft], &work[iright], &work[iwrk], &ierr);
986 /* Reduce B to triangular form (QR decomposition of B) */
987 /* (Workspace: need N, prefer N*NB) */
989 irows = ihi + 1 - ilo;
991 icols = *n + 1 - ilo;
997 i__1 = *lwork + 1 - iwrk;
998 dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
999 iwrk], &i__1, &ierr);
1001 /* Apply the orthogonal transformation to matrix A */
1002 /* (Workspace: need N, prefer N*NB) */
1004 i__1 = *lwork + 1 - iwrk;
1005 dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
1006 work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
1010 /* (Workspace: need N, prefer N*NB) */
1013 dlaset_("Full", n, n, &c_b36, &c_b37, &vl[vl_offset], ldvl)
1018 dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
1019 ilo + 1 + ilo * vl_dim1], ldvl);
1021 i__1 = *lwork + 1 - iwrk;
1022 dorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
1023 itau], &work[iwrk], &i__1, &ierr);
1029 dlaset_("Full", n, n, &c_b36, &c_b37, &vr[vr_offset], ldvr)
1033 /* Reduce to generalized Hessenberg form */
1034 /* (Workspace: none needed) */
1038 /* Eigenvectors requested -- work on whole matrix. */
1040 dgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
1041 ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
1043 dgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda,
1044 &b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
1045 vr_offset], ldvr, &ierr);
1048 /* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
1049 /* Schur forms and Schur vectors) */
1050 /* (Workspace: need N) */
1054 *(unsigned char *)chtemp = 'S';
1056 *(unsigned char *)chtemp = 'E';
1058 i__1 = *lwork + 1 - iwrk;
1059 dhgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
1060 b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
1061 ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &ierr);
1063 if (ierr > 0 && ierr <= *n) {
1065 } else if (ierr > *n && ierr <= *n << 1) {
1073 /* Compute Eigenvectors */
1074 /* (Workspace: need 6*N) */
1079 *(unsigned char *)chtemp = 'B';
1081 *(unsigned char *)chtemp = 'L';
1084 *(unsigned char *)chtemp = 'R';
1086 dtgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
1087 &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
1094 /* Undo balancing on VL and VR and normalization */
1095 /* (Workspace: none needed) */
1098 dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
1099 vl[vl_offset], ldvl, &ierr);
1101 for (jc = 1; jc <= i__1; ++jc) {
1102 if (alphai[jc] < 0.) {
1106 if (alphai[jc] == 0.) {
1108 for (jr = 1; jr <= i__2; ++jr) {
1110 d__2 = temp, d__3 = (d__1 = vl[jr + jc * vl_dim1],
1112 temp = f2cmax(d__2,d__3);
1117 for (jr = 1; jr <= i__2; ++jr) {
1119 d__3 = temp, d__4 = (d__1 = vl[jr + jc * vl_dim1],
1120 abs(d__1)) + (d__2 = vl[jr + (jc + 1) *
1121 vl_dim1], abs(d__2));
1122 temp = f2cmax(d__3,d__4);
1126 if (temp < smlnum) {
1130 if (alphai[jc] == 0.) {
1132 for (jr = 1; jr <= i__2; ++jr) {
1133 vl[jr + jc * vl_dim1] *= temp;
1138 for (jr = 1; jr <= i__2; ++jr) {
1139 vl[jr + jc * vl_dim1] *= temp;
1140 vl[jr + (jc + 1) * vl_dim1] *= temp;
1149 dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
1150 vr[vr_offset], ldvr, &ierr);
1152 for (jc = 1; jc <= i__1; ++jc) {
1153 if (alphai[jc] < 0.) {
1157 if (alphai[jc] == 0.) {
1159 for (jr = 1; jr <= i__2; ++jr) {
1161 d__2 = temp, d__3 = (d__1 = vr[jr + jc * vr_dim1],
1163 temp = f2cmax(d__2,d__3);
1168 for (jr = 1; jr <= i__2; ++jr) {
1170 d__3 = temp, d__4 = (d__1 = vr[jr + jc * vr_dim1],
1171 abs(d__1)) + (d__2 = vr[jr + (jc + 1) *
1172 vr_dim1], abs(d__2));
1173 temp = f2cmax(d__3,d__4);
1177 if (temp < smlnum) {
1181 if (alphai[jc] == 0.) {
1183 for (jr = 1; jr <= i__2; ++jr) {
1184 vr[jr + jc * vr_dim1] *= temp;
1189 for (jr = 1; jr <= i__2; ++jr) {
1190 vr[jr + jc * vr_dim1] *= temp;
1191 vr[jr + (jc + 1) * vr_dim1] *= temp;
1200 /* End of eigenvector calculation */
1204 /* Undo scaling if necessary */
1209 dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
1211 dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
1216 dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
1220 work[1] = (doublereal) maxwrk;