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 complex c_b1 = {0.f,0.f};
516 static complex c_b2 = {1.f,0.f};
517 static integer c__1 = 1;
518 static integer c_n1 = -1;
520 /* > \brief <b> CGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
523 /* =========== DOCUMENTATION =========== */
525 /* Online html documentation available at */
526 /* http://www.netlib.org/lapack/explore-html/ */
529 /* > Download CGEGS + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgegs.f
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgegs.f
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgegs.f
544 /* SUBROUTINE CGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA, */
545 /* VSL, LDVSL, VSR, LDVSR, WORK, LWORK, RWORK, */
548 /* CHARACTER JOBVSL, JOBVSR */
549 /* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N */
550 /* REAL RWORK( * ) */
551 /* COMPLEX A( LDA, * ), ALPHA( * ), B( LDB, * ), */
552 /* $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), */
556 /* > \par Purpose: */
561 /* > This routine is deprecated and has been replaced by routine CGGES. */
563 /* > CGEGS computes the eigenvalues, Schur form, and, optionally, the */
564 /* > left and or/right Schur vectors of a complex matrix pair (A,B). */
565 /* > Given two square matrices A and B, the generalized Schur */
566 /* > factorization has the form */
568 /* > A = Q*S*Z**H, B = Q*T*Z**H */
570 /* > where Q and Z are unitary matrices and S and T are upper triangular. */
571 /* > The columns of Q are the left Schur vectors */
572 /* > and the columns of Z are the right Schur vectors. */
574 /* > If only the eigenvalues of (A,B) are needed, the driver routine */
575 /* > CGEGV should be used instead. See CGEGV for a description of the */
576 /* > eigenvalues of the generalized nonsymmetric eigenvalue problem */
583 /* > \param[in] JOBVSL */
585 /* > JOBVSL is CHARACTER*1 */
586 /* > = 'N': do not compute the left Schur vectors; */
587 /* > = 'V': compute the left Schur vectors (returned in VSL). */
590 /* > \param[in] JOBVSR */
592 /* > JOBVSR is CHARACTER*1 */
593 /* > = 'N': do not compute the right Schur vectors; */
594 /* > = 'V': compute the right Schur vectors (returned in VSR). */
600 /* > The order of the matrices A, B, VSL, and VSR. N >= 0. */
603 /* > \param[in,out] A */
605 /* > A is COMPLEX array, dimension (LDA, N) */
606 /* > On entry, the matrix A. */
607 /* > On exit, the upper triangular matrix S from the generalized */
608 /* > Schur factorization. */
611 /* > \param[in] LDA */
613 /* > LDA is INTEGER */
614 /* > The leading dimension of A. LDA >= f2cmax(1,N). */
617 /* > \param[in,out] B */
619 /* > B is COMPLEX array, dimension (LDB, N) */
620 /* > On entry, the matrix B. */
621 /* > On exit, the upper triangular matrix T from the generalized */
622 /* > Schur factorization. */
625 /* > \param[in] LDB */
627 /* > LDB is INTEGER */
628 /* > The leading dimension of B. LDB >= f2cmax(1,N). */
631 /* > \param[out] ALPHA */
633 /* > ALPHA is COMPLEX array, dimension (N) */
634 /* > The complex scalars alpha that define the eigenvalues of */
635 /* > GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur */
639 /* > \param[out] BETA */
641 /* > BETA is COMPLEX array, dimension (N) */
642 /* > The non-negative real scalars beta that define the */
643 /* > eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element */
644 /* > of the triangular factor T. */
646 /* > Together, the quantities alpha = ALPHA(j) and beta = BETA(j) */
647 /* > represent the j-th eigenvalue of the matrix pair (A,B), in */
648 /* > one of the forms lambda = alpha/beta or mu = beta/alpha. */
649 /* > Since either lambda or mu may overflow, they should not, */
650 /* > in general, be computed. */
653 /* > \param[out] VSL */
655 /* > VSL is COMPLEX array, dimension (LDVSL,N) */
656 /* > If JOBVSL = 'V', the matrix of left Schur vectors Q. */
657 /* > Not referenced if JOBVSL = 'N'. */
660 /* > \param[in] LDVSL */
662 /* > LDVSL is INTEGER */
663 /* > The leading dimension of the matrix VSL. LDVSL >= 1, and */
664 /* > if JOBVSL = 'V', LDVSL >= N. */
667 /* > \param[out] VSR */
669 /* > VSR is COMPLEX array, dimension (LDVSR,N) */
670 /* > If JOBVSR = 'V', the matrix of right Schur vectors Z. */
671 /* > Not referenced if JOBVSR = 'N'. */
674 /* > \param[in] LDVSR */
676 /* > LDVSR is INTEGER */
677 /* > The leading dimension of the matrix VSR. LDVSR >= 1, and */
678 /* > if JOBVSR = 'V', LDVSR >= N. */
681 /* > \param[out] WORK */
683 /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
684 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
687 /* > \param[in] LWORK */
689 /* > LWORK is INTEGER */
690 /* > The dimension of the array WORK. LWORK >= f2cmax(1,2*N). */
691 /* > For good performance, LWORK must generally be larger. */
692 /* > To compute the optimal value of LWORK, call ILAENV to get */
693 /* > blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: */
694 /* > NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; */
695 /* > the optimal LWORK is N*(NB+1). */
697 /* > If LWORK = -1, then a workspace query is assumed; the routine */
698 /* > only calculates the optimal size of the WORK array, returns */
699 /* > this value as the first entry of the WORK array, and no error */
700 /* > message related to LWORK is issued by XERBLA. */
703 /* > \param[out] RWORK */
705 /* > RWORK is REAL array, dimension (3*N) */
708 /* > \param[out] INFO */
710 /* > INFO is INTEGER */
711 /* > = 0: successful exit */
712 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
714 /* > The QZ iteration failed. (A,B) are not in Schur */
715 /* > form, but ALPHA(j) and BETA(j) should be correct for */
716 /* > j=INFO+1,...,N. */
717 /* > > N: errors that usually indicate LAPACK problems: */
718 /* > =N+1: error return from CGGBAL */
719 /* > =N+2: error return from CGEQRF */
720 /* > =N+3: error return from CUNMQR */
721 /* > =N+4: error return from CUNGQR */
722 /* > =N+5: error return from CGGHRD */
723 /* > =N+6: error return from CHGEQZ (other than failed */
725 /* > =N+7: error return from CGGBAK (computing VSL) */
726 /* > =N+8: error return from CGGBAK (computing VSR) */
727 /* > =N+9: error return from CLASCL (various places) */
733 /* > \author Univ. of Tennessee */
734 /* > \author Univ. of California Berkeley */
735 /* > \author Univ. of Colorado Denver */
736 /* > \author NAG Ltd. */
738 /* > \date December 2016 */
740 /* > \ingroup complexGEeigen */
742 /* ===================================================================== */
743 /* Subroutine */ int cgegs_(char *jobvsl, char *jobvsr, integer *n, complex *
744 a, integer *lda, complex *b, integer *ldb, complex *alpha, complex *
745 beta, complex *vsl, integer *ldvsl, complex *vsr, integer *ldvsr,
746 complex *work, integer *lwork, real *rwork, integer *info)
748 /* System generated locals */
749 integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
750 vsr_dim1, vsr_offset, i__1, i__2, i__3;
752 /* Local variables */
755 extern logical lsame_(char *, char *);
756 integer ileft, iinfo, icols;
761 extern /* Subroutine */ int cggbak_(char *, char *, integer *, integer *,
762 integer *, real *, real *, integer *, complex *, integer *,
763 integer *), cggbal_(char *, integer *, complex *,
764 integer *, complex *, integer *, integer *, integer *, real *,
765 real *, real *, integer *);
767 extern real clange_(char *, integer *, integer *, complex *, integer *,
769 extern /* Subroutine */ int cgghrd_(char *, char *, integer *, integer *,
770 integer *, complex *, integer *, complex *, integer *, complex *,
771 integer *, complex *, integer *, integer *),
772 clascl_(char *, integer *, integer *, real *, real *, integer *,
773 integer *, complex *, integer *, integer *);
774 logical ilascl, ilbscl;
775 extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *,
776 integer *, complex *, complex *, integer *, integer *);
777 extern real slamch_(char *);
778 extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
779 *, integer *, complex *, integer *), claset_(char *,
780 integer *, integer *, complex *, complex *, complex *, integer *);
782 extern /* Subroutine */ int xerbla_(char *, integer *);
783 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
784 integer *, integer *, ftnlen, ftnlen);
786 extern /* Subroutine */ int chgeqz_(char *, char *, char *, integer *,
787 integer *, integer *, complex *, integer *, complex *, integer *,
788 complex *, complex *, complex *, integer *, complex *, integer *,
789 complex *, integer *, real *, integer *);
790 integer ijobvl, iright, ijobvr;
792 integer lwkmin, nb1, nb2, nb3;
794 extern /* Subroutine */ int cungqr_(integer *, integer *, integer *,
795 complex *, integer *, complex *, complex *, integer *, integer *),
796 cunmqr_(char *, char *, integer *, integer *, integer *, complex
797 *, integer *, complex *, complex *, integer *, complex *, integer
800 integer irwork, lwkopt;
806 /* -- LAPACK driver routine (version 3.7.0) -- */
807 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
808 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
812 /* ===================================================================== */
815 /* Decode the input arguments */
817 /* Parameter adjustments */
819 a_offset = 1 + a_dim1 * 1;
822 b_offset = 1 + b_dim1 * 1;
827 vsl_offset = 1 + vsl_dim1 * 1;
830 vsr_offset = 1 + vsr_dim1 * 1;
836 if (lsame_(jobvsl, "N")) {
839 } else if (lsame_(jobvsl, "V")) {
847 if (lsame_(jobvsr, "N")) {
850 } else if (lsame_(jobvsr, "V")) {
858 /* Test the input arguments */
862 lwkmin = f2cmax(i__1,1);
864 work[1].r = (real) lwkopt, work[1].i = 0.f;
865 lquery = *lwork == -1;
869 } else if (ijobvr <= 0) {
873 } else if (*lda < f2cmax(1,*n)) {
875 } else if (*ldb < f2cmax(1,*n)) {
877 } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
879 } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
881 } else if (*lwork < lwkmin && ! lquery) {
886 nb1 = ilaenv_(&c__1, "CGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
888 nb2 = ilaenv_(&c__1, "CUNMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
890 nb3 = ilaenv_(&c__1, "CUNGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
893 i__1 = f2cmax(nb1,nb2);
894 nb = f2cmax(i__1,nb3);
895 lopt = *n * (nb + 1);
896 work[1].r = (real) lopt, work[1].i = 0.f;
901 xerbla_("CGEGS ", &i__1);
907 /* Quick return if possible */
913 /* Get machine constants */
915 eps = slamch_("E") * slamch_("B");
916 safmin = slamch_("S");
917 smlnum = *n * safmin / eps;
918 bignum = 1.f / smlnum;
920 /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
922 anrm = clange_("M", n, n, &a[a_offset], lda, &rwork[1]);
924 if (anrm > 0.f && anrm < smlnum) {
927 } else if (anrm > bignum) {
933 clascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
941 /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
943 bnrm = clange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
945 if (bnrm > 0.f && bnrm < smlnum) {
948 } else if (bnrm > bignum) {
954 clascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
962 /* Permute the matrix to make it more nearly triangular */
966 irwork = iright + *n;
968 cggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
969 ileft], &rwork[iright], &rwork[irwork], &iinfo);
975 /* Reduce B to triangular form, and initialize VSL and/or VSR */
977 irows = ihi + 1 - ilo;
978 icols = *n + 1 - ilo;
980 iwork = itau + irows;
981 i__1 = *lwork + 1 - iwork;
982 cgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
983 iwork], &i__1, &iinfo);
987 i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
988 lwkopt = f2cmax(i__1,i__2);
995 i__1 = *lwork + 1 - iwork;
996 cunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
997 work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
1002 i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
1003 lwkopt = f2cmax(i__1,i__2);
1011 claset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
1014 clacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo
1015 + 1 + ilo * vsl_dim1], ldvsl);
1016 i__1 = *lwork + 1 - iwork;
1017 cungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
1018 work[itau], &work[iwork], &i__1, &iinfo);
1022 i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
1023 lwkopt = f2cmax(i__1,i__2);
1032 claset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
1035 /* Reduce to generalized Hessenberg form */
1037 cgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
1038 ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
1044 /* Perform QZ algorithm, computing Schur vectors if desired */
1047 i__1 = *lwork + 1 - iwork;
1048 chgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
1049 b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
1050 vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &rwork[irwork], &
1055 i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
1056 lwkopt = f2cmax(i__1,i__2);
1059 if (iinfo > 0 && iinfo <= *n) {
1061 } else if (iinfo > *n && iinfo <= *n << 1) {
1069 /* Apply permutation to VSL and VSR */
1072 cggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
1073 vsl[vsl_offset], ldvsl, &iinfo);
1080 cggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
1081 vsr[vsr_offset], ldvsr, &iinfo);
1091 clascl_("U", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
1097 clascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
1106 clascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
1112 clascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
1121 work[1].r = (real) lwkopt, work[1].i = 0.f;