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_n1 = -1;
517 static doublereal c_b36 = 0.;
518 static doublereal c_b37 = 1.;
520 /* > \brief <b> DGEEVX 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 DGEGS + dependencies */
530 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgegs.f
533 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgegs.f
536 /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgegs.f
544 /* SUBROUTINE DGEGS( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, */
545 /* ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, */
548 /* CHARACTER JOBVSL, JOBVSR */
549 /* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N */
550 /* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
551 /* $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), */
552 /* $ VSR( LDVSR, * ), WORK( * ) */
555 /* > \par Purpose: */
560 /* > This routine is deprecated and has been replaced by routine DGGES. */
562 /* > DGEGS computes the eigenvalues, real Schur form, and, optionally, */
563 /* > left and or/right Schur vectors of a real matrix pair (A,B). */
564 /* > Given two square matrices A and B, the generalized real Schur */
565 /* > factorization has the form */
567 /* > A = Q*S*Z**T, B = Q*T*Z**T */
569 /* > where Q and Z are orthogonal matrices, T is upper triangular, and S */
570 /* > is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal */
571 /* > blocks, the 2-by-2 blocks corresponding to complex conjugate pairs */
572 /* > of eigenvalues of (A,B). The columns of Q are the left Schur vectors */
573 /* > and the columns of Z are the right Schur vectors. */
575 /* > If only the eigenvalues of (A,B) are needed, the driver routine */
576 /* > DGEGV should be used instead. See DGEGV for a description of the */
577 /* > eigenvalues of the generalized nonsymmetric eigenvalue problem */
584 /* > \param[in] JOBVSL */
586 /* > JOBVSL is CHARACTER*1 */
587 /* > = 'N': do not compute the left Schur vectors; */
588 /* > = 'V': compute the left Schur vectors (returned in VSL). */
591 /* > \param[in] JOBVSR */
593 /* > JOBVSR is CHARACTER*1 */
594 /* > = 'N': do not compute the right Schur vectors; */
595 /* > = 'V': compute the right Schur vectors (returned in VSR). */
601 /* > The order of the matrices A, B, VSL, and VSR. N >= 0. */
604 /* > \param[in,out] A */
606 /* > A is DOUBLE PRECISION array, dimension (LDA, N) */
607 /* > On entry, the matrix A. */
608 /* > On exit, the upper quasi-triangular matrix S from the */
609 /* > generalized real Schur factorization. */
612 /* > \param[in] LDA */
614 /* > LDA is INTEGER */
615 /* > The leading dimension of A. LDA >= f2cmax(1,N). */
618 /* > \param[in,out] B */
620 /* > B is DOUBLE PRECISION array, dimension (LDB, N) */
621 /* > On entry, the matrix B. */
622 /* > On exit, the upper triangular matrix T from the generalized */
623 /* > real Schur factorization. */
626 /* > \param[in] LDB */
628 /* > LDB is INTEGER */
629 /* > The leading dimension of B. LDB >= f2cmax(1,N). */
632 /* > \param[out] ALPHAR */
634 /* > ALPHAR is DOUBLE PRECISION array, dimension (N) */
635 /* > The real parts of each scalar alpha defining an eigenvalue */
639 /* > \param[out] ALPHAI */
641 /* > ALPHAI is DOUBLE PRECISION array, dimension (N) */
642 /* > The imaginary parts of each scalar alpha defining an */
643 /* > eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th */
644 /* > eigenvalue is real; if positive, then the j-th and (j+1)-st */
645 /* > eigenvalues are a complex conjugate pair, with */
646 /* > ALPHAI(j+1) = -ALPHAI(j). */
649 /* > \param[out] BETA */
651 /* > BETA is DOUBLE PRECISION array, dimension (N) */
652 /* > The scalars beta that define the eigenvalues of GNEP. */
653 /* > Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
654 /* > beta = BETA(j) represent the j-th eigenvalue of the matrix */
655 /* > pair (A,B), in one of the forms lambda = alpha/beta or */
656 /* > mu = beta/alpha. Since either lambda or mu may overflow, */
657 /* > they should not, in general, be computed. */
660 /* > \param[out] VSL */
662 /* > VSL is DOUBLE PRECISION array, dimension (LDVSL,N) */
663 /* > If JOBVSL = 'V', the matrix of left Schur vectors Q. */
664 /* > Not referenced if JOBVSL = 'N'. */
667 /* > \param[in] LDVSL */
669 /* > LDVSL is INTEGER */
670 /* > The leading dimension of the matrix VSL. LDVSL >=1, and */
671 /* > if JOBVSL = 'V', LDVSL >= N. */
674 /* > \param[out] VSR */
676 /* > VSR is DOUBLE PRECISION array, dimension (LDVSR,N) */
677 /* > If JOBVSR = 'V', the matrix of right Schur vectors Z. */
678 /* > Not referenced if JOBVSR = 'N'. */
681 /* > \param[in] LDVSR */
683 /* > LDVSR is INTEGER */
684 /* > The leading dimension of the matrix VSR. LDVSR >= 1, and */
685 /* > if JOBVSR = 'V', LDVSR >= N. */
688 /* > \param[out] WORK */
690 /* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
691 /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
694 /* > \param[in] LWORK */
696 /* > LWORK is INTEGER */
697 /* > The dimension of the array WORK. LWORK >= f2cmax(1,4*N). */
698 /* > For good performance, LWORK must generally be larger. */
699 /* > To compute the optimal value of LWORK, call ILAENV to get */
700 /* > blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: */
701 /* > NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR */
702 /* > The optimal LWORK is 2*N + N*(NB+1). */
704 /* > If LWORK = -1, then a workspace query is assumed; the routine */
705 /* > only calculates the optimal size of the WORK array, returns */
706 /* > this value as the first entry of the WORK array, and no error */
707 /* > message related to LWORK is issued by XERBLA. */
710 /* > \param[out] INFO */
712 /* > INFO is INTEGER */
713 /* > = 0: successful exit */
714 /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
716 /* > The QZ iteration failed. (A,B) are not in Schur */
717 /* > form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
718 /* > be correct for j=INFO+1,...,N. */
719 /* > > N: errors that usually indicate LAPACK problems: */
720 /* > =N+1: error return from DGGBAL */
721 /* > =N+2: error return from DGEQRF */
722 /* > =N+3: error return from DORMQR */
723 /* > =N+4: error return from DORGQR */
724 /* > =N+5: error return from DGGHRD */
725 /* > =N+6: error return from DHGEQZ (other than failed */
727 /* > =N+7: error return from DGGBAK (computing VSL) */
728 /* > =N+8: error return from DGGBAK (computing VSR) */
729 /* > =N+9: error return from DLASCL (various places) */
735 /* > \author Univ. of Tennessee */
736 /* > \author Univ. of California Berkeley */
737 /* > \author Univ. of Colorado Denver */
738 /* > \author NAG Ltd. */
740 /* > \date December 2016 */
742 /* > \ingroup doubleGEeigen */
744 /* ===================================================================== */
745 /* Subroutine */ int dgegs_(char *jobvsl, char *jobvsr, integer *n,
746 doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
747 alphar, doublereal *alphai, doublereal *beta, doublereal *vsl,
748 integer *ldvsl, doublereal *vsr, integer *ldvsr, doublereal *work,
749 integer *lwork, integer *info)
751 /* System generated locals */
752 integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
753 vsr_dim1, vsr_offset, i__1, i__2;
755 /* Local variables */
756 doublereal anrm, bnrm;
758 extern logical lsame_(char *, char *);
759 integer ileft, iinfo, icols;
764 extern /* Subroutine */ int dggbak_(char *, char *, integer *, integer *,
765 integer *, doublereal *, doublereal *, integer *, doublereal *,
766 integer *, integer *);
768 extern /* Subroutine */ int dggbal_(char *, integer *, doublereal *,
769 integer *, doublereal *, integer *, integer *, integer *,
770 doublereal *, doublereal *, doublereal *, integer *);
771 extern doublereal dlamch_(char *), dlange_(char *, integer *,
772 integer *, doublereal *, integer *, doublereal *);
773 extern /* Subroutine */ int dgghrd_(char *, char *, integer *, integer *,
774 integer *, doublereal *, integer *, doublereal *, integer *,
775 doublereal *, integer *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal
776 *, doublereal *, integer *, integer *, doublereal *, integer *,
778 logical ilascl, ilbscl;
779 extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
780 integer *, doublereal *, doublereal *, integer *, integer *),
781 dlacpy_(char *, integer *, integer *, doublereal *, integer *,
782 doublereal *, integer *);
784 extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
785 doublereal *, doublereal *, doublereal *, integer *),
786 xerbla_(char *, integer *);
787 extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
788 integer *, integer *, ftnlen, ftnlen);
790 extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *,
791 integer *, integer *, doublereal *, integer *, doublereal *,
792 integer *, doublereal *, doublereal *, doublereal *, doublereal *,
793 integer *, doublereal *, integer *, doublereal *, integer *,
795 integer ijobvl, iright, ijobvr;
796 extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *,
797 doublereal *, integer *, doublereal *, doublereal *, integer *,
800 integer lwkmin, nb1, nb2, nb3;
802 extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
803 integer *, doublereal *, integer *, doublereal *, doublereal *,
804 integer *, doublereal *, integer *, integer *);
812 /* -- LAPACK driver routine (version 3.7.0) -- */
813 /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
814 /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
818 /* ===================================================================== */
821 /* Decode the input arguments */
823 /* Parameter adjustments */
825 a_offset = 1 + a_dim1 * 1;
828 b_offset = 1 + b_dim1 * 1;
834 vsl_offset = 1 + vsl_dim1 * 1;
837 vsr_offset = 1 + vsr_dim1 * 1;
842 if (lsame_(jobvsl, "N")) {
845 } else if (lsame_(jobvsl, "V")) {
853 if (lsame_(jobvsr, "N")) {
856 } else if (lsame_(jobvsr, "V")) {
864 /* Test the input arguments */
868 lwkmin = f2cmax(i__1,1);
870 work[1] = (doublereal) lwkopt;
871 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 (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
885 } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
887 } else if (*lwork < lwkmin && ! lquery) {
892 nb1 = ilaenv_(&c__1, "DGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
894 nb2 = ilaenv_(&c__1, "DORMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
896 nb3 = ilaenv_(&c__1, "DORGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
899 i__1 = f2cmax(nb1,nb2);
900 nb = f2cmax(i__1,nb3);
901 lopt = (*n << 1) + *n * (nb + 1);
902 work[1] = (doublereal) lopt;
907 xerbla_("DGEGS ", &i__1);
913 /* Quick return if possible */
919 /* Get machine constants */
921 eps = dlamch_("E") * dlamch_("B");
922 safmin = dlamch_("S");
923 smlnum = *n * safmin / eps;
924 bignum = 1. / smlnum;
926 /* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
928 anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
930 if (anrm > 0. && anrm < smlnum) {
933 } else if (anrm > bignum) {
939 dlascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
947 /* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
949 bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
951 if (bnrm > 0. && bnrm < smlnum) {
954 } else if (bnrm > bignum) {
960 dlascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
968 /* Permute the matrix to make it more nearly triangular */
969 /* Workspace layout: (2*N words -- "work..." not actually used) */
970 /* left_permutation, right_permutation, work... */
975 dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
976 ileft], &work[iright], &work[iwork], &iinfo);
982 /* Reduce B to triangular form, and initialize VSL and/or VSR */
983 /* Workspace layout: ("work..." must have at least N words) */
984 /* left_permutation, right_permutation, tau, work... */
986 irows = ihi + 1 - ilo;
987 icols = *n + 1 - ilo;
989 iwork = itau + irows;
990 i__1 = *lwork + 1 - iwork;
991 dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
992 iwork], &i__1, &iinfo);
995 i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
996 lwkopt = f2cmax(i__1,i__2);
1003 i__1 = *lwork + 1 - iwork;
1004 dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
1005 work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
1009 i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
1010 lwkopt = f2cmax(i__1,i__2);
1018 dlaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
1021 dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo
1022 + 1 + ilo * vsl_dim1], ldvsl);
1023 i__1 = *lwork + 1 - iwork;
1024 dorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
1025 work[itau], &work[iwork], &i__1, &iinfo);
1028 i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
1029 lwkopt = f2cmax(i__1,i__2);
1038 dlaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
1041 /* Reduce to generalized Hessenberg form */
1043 dgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
1044 ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo);
1050 /* Perform QZ algorithm, computing Schur vectors if desired */
1051 /* Workspace layout: ("work..." must have at least 1 word) */
1052 /* left_permutation, right_permutation, work... */
1055 i__1 = *lwork + 1 - iwork;
1056 dhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
1057 b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
1058 , ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo);
1061 i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
1062 lwkopt = f2cmax(i__1,i__2);
1065 if (iinfo > 0 && iinfo <= *n) {
1067 } else if (iinfo > *n && iinfo <= *n << 1) {
1075 /* Apply permutation to VSL and VSR */
1078 dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
1079 vsl_offset], ldvsl, &iinfo);
1086 dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
1087 vsr_offset], ldvsr, &iinfo);
1097 dlascl_("H", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
1103 dlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
1109 dlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
1118 dlascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
1124 dlascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
1133 work[1] = (doublereal) lwkopt;