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ztgevc.c 44 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef blasint logical;
  52. typedef char logical1;
  53. typedef char integer1;
  54. #define TRUE_ (1)
  55. #define FALSE_ (0)
  56. /* Extern is for use with -E */
  57. #ifndef Extern
  58. #define Extern extern
  59. #endif
  60. /* I/O stuff */
  61. typedef int flag;
  62. typedef int ftnlen;
  63. typedef int ftnint;
  64. /*external read, write*/
  65. typedef struct
  66. { flag cierr;
  67. ftnint ciunit;
  68. flag ciend;
  69. char *cifmt;
  70. ftnint cirec;
  71. } cilist;
  72. /*internal read, write*/
  73. typedef struct
  74. { flag icierr;
  75. char *iciunit;
  76. flag iciend;
  77. char *icifmt;
  78. ftnint icirlen;
  79. ftnint icirnum;
  80. } icilist;
  81. /*open*/
  82. typedef struct
  83. { flag oerr;
  84. ftnint ounit;
  85. char *ofnm;
  86. ftnlen ofnmlen;
  87. char *osta;
  88. char *oacc;
  89. char *ofm;
  90. ftnint orl;
  91. char *oblnk;
  92. } olist;
  93. /*close*/
  94. typedef struct
  95. { flag cerr;
  96. ftnint cunit;
  97. char *csta;
  98. } cllist;
  99. /*rewind, backspace, endfile*/
  100. typedef struct
  101. { flag aerr;
  102. ftnint aunit;
  103. } alist;
  104. /* inquire */
  105. typedef struct
  106. { flag inerr;
  107. ftnint inunit;
  108. char *infile;
  109. ftnlen infilen;
  110. ftnint *inex; /*parameters in standard's order*/
  111. ftnint *inopen;
  112. ftnint *innum;
  113. ftnint *innamed;
  114. char *inname;
  115. ftnlen innamlen;
  116. char *inacc;
  117. ftnlen inacclen;
  118. char *inseq;
  119. ftnlen inseqlen;
  120. char *indir;
  121. ftnlen indirlen;
  122. char *infmt;
  123. ftnlen infmtlen;
  124. char *inform;
  125. ftnint informlen;
  126. char *inunf;
  127. ftnlen inunflen;
  128. ftnint *inrecl;
  129. ftnint *innrec;
  130. char *inblank;
  131. ftnlen inblanklen;
  132. } inlist;
  133. #define VOID void
  134. union Multitype { /* for multiple entry points */
  135. integer1 g;
  136. shortint h;
  137. integer i;
  138. /* longint j; */
  139. real r;
  140. doublereal d;
  141. complex c;
  142. doublecomplex z;
  143. };
  144. typedef union Multitype Multitype;
  145. struct Vardesc { /* for Namelist */
  146. char *name;
  147. char *addr;
  148. ftnlen *dims;
  149. int type;
  150. };
  151. typedef struct Vardesc Vardesc;
  152. struct Namelist {
  153. char *name;
  154. Vardesc **vars;
  155. int nvars;
  156. };
  157. typedef struct Namelist Namelist;
  158. #define abs(x) ((x) >= 0 ? (x) : -(x))
  159. #define dabs(x) (fabs(x))
  160. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  161. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  162. #define dmin(a,b) (f2cmin(a,b))
  163. #define dmax(a,b) (f2cmax(a,b))
  164. #define bit_test(a,b) ((a) >> (b) & 1)
  165. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  166. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  167. #define abort_() { sig_die("Fortran abort routine called", 1); }
  168. #define c_abs(z) (cabsf(Cf(z)))
  169. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  170. #ifdef _MSC_VER
  171. #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]);}
  172. #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]/Cd(b)._Val[1]);}
  173. #else
  174. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  175. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  176. #endif
  177. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  178. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  179. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  180. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  181. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  182. #define d_abs(x) (fabs(*(x)))
  183. #define d_acos(x) (acos(*(x)))
  184. #define d_asin(x) (asin(*(x)))
  185. #define d_atan(x) (atan(*(x)))
  186. #define d_atn2(x, y) (atan2(*(x),*(y)))
  187. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  188. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  189. #define d_cos(x) (cos(*(x)))
  190. #define d_cosh(x) (cosh(*(x)))
  191. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  192. #define d_exp(x) (exp(*(x)))
  193. #define d_imag(z) (cimag(Cd(z)))
  194. #define r_imag(z) (cimagf(Cf(z)))
  195. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  196. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  198. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define d_log(x) (log(*(x)))
  200. #define d_mod(x, y) (fmod(*(x), *(y)))
  201. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  202. #define d_nint(x) u_nint(*(x))
  203. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  204. #define d_sign(a,b) u_sign(*(a),*(b))
  205. #define r_sign(a,b) u_sign(*(a),*(b))
  206. #define d_sin(x) (sin(*(x)))
  207. #define d_sinh(x) (sinh(*(x)))
  208. #define d_sqrt(x) (sqrt(*(x)))
  209. #define d_tan(x) (tan(*(x)))
  210. #define d_tanh(x) (tanh(*(x)))
  211. #define i_abs(x) abs(*(x))
  212. #define i_dnnt(x) ((integer)u_nint(*(x)))
  213. #define i_len(s, n) (n)
  214. #define i_nint(x) ((integer)u_nint(*(x)))
  215. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  216. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  217. #define pow_si(B,E) spow_ui(*(B),*(E))
  218. #define pow_ri(B,E) spow_ui(*(B),*(E))
  219. #define pow_di(B,E) dpow_ui(*(B),*(E))
  220. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  221. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  222. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  223. #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++ = ' '; }
  224. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  225. #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]; }
  226. #define sig_die(s, kill) { exit(1); }
  227. #define s_stop(s, n) {exit(0);}
  228. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  229. #define z_abs(z) (cabs(Cd(z)))
  230. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  231. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  232. #define myexit_() break;
  233. #define mycycle_() continue;
  234. #define myceiling_(w) {ceil(w)}
  235. #define myhuge_(w) {HUGE_VAL}
  236. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  237. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  238. /* procedure parameter types for -A and -C++ */
  239. #ifdef __cplusplus
  240. typedef logical (*L_fp)(...);
  241. #else
  242. typedef logical (*L_fp)();
  243. #endif
  244. static float spow_ui(float x, integer n) {
  245. float pow=1.0; unsigned long int u;
  246. if(n != 0) {
  247. if(n < 0) n = -n, x = 1/x;
  248. for(u = n; ; ) {
  249. if(u & 01) pow *= x;
  250. if(u >>= 1) x *= x;
  251. else break;
  252. }
  253. }
  254. return pow;
  255. }
  256. static double dpow_ui(double x, integer n) {
  257. double pow=1.0; unsigned long int u;
  258. if(n != 0) {
  259. if(n < 0) n = -n, x = 1/x;
  260. for(u = n; ; ) {
  261. if(u & 01) pow *= x;
  262. if(u >>= 1) x *= x;
  263. else break;
  264. }
  265. }
  266. return pow;
  267. }
  268. #ifdef _MSC_VER
  269. static _Fcomplex cpow_ui(complex x, integer n) {
  270. complex pow={1.0,0.0}; unsigned long int u;
  271. if(n != 0) {
  272. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  273. for(u = n; ; ) {
  274. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  275. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  276. else break;
  277. }
  278. }
  279. _Fcomplex p={pow.r, pow.i};
  280. return p;
  281. }
  282. #else
  283. static _Complex float cpow_ui(_Complex float x, integer n) {
  284. _Complex float pow=1.0; unsigned long int u;
  285. if(n != 0) {
  286. if(n < 0) n = -n, x = 1/x;
  287. for(u = n; ; ) {
  288. if(u & 01) pow *= x;
  289. if(u >>= 1) x *= x;
  290. else break;
  291. }
  292. }
  293. return pow;
  294. }
  295. #endif
  296. #ifdef _MSC_VER
  297. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  298. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  299. if(n != 0) {
  300. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  301. for(u = n; ; ) {
  302. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  303. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  304. else break;
  305. }
  306. }
  307. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  308. return p;
  309. }
  310. #else
  311. static _Complex double zpow_ui(_Complex double x, integer n) {
  312. _Complex double pow=1.0; unsigned long int u;
  313. if(n != 0) {
  314. if(n < 0) n = -n, x = 1/x;
  315. for(u = n; ; ) {
  316. if(u & 01) pow *= x;
  317. if(u >>= 1) x *= x;
  318. else break;
  319. }
  320. }
  321. return pow;
  322. }
  323. #endif
  324. static integer pow_ii(integer x, integer n) {
  325. integer pow; unsigned long int u;
  326. if (n <= 0) {
  327. if (n == 0 || x == 1) pow = 1;
  328. else if (x != -1) pow = x == 0 ? 1/x : 0;
  329. else n = -n;
  330. }
  331. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  332. u = n;
  333. for(pow = 1; ; ) {
  334. if(u & 01) pow *= x;
  335. if(u >>= 1) x *= x;
  336. else break;
  337. }
  338. }
  339. return pow;
  340. }
  341. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  342. {
  343. double m; integer i, mi;
  344. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  345. if (w[i-1]>m) mi=i ,m=w[i-1];
  346. return mi-s+1;
  347. }
  348. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  349. {
  350. float m; integer i, mi;
  351. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  352. if (w[i-1]>m) mi=i ,m=w[i-1];
  353. return mi-s+1;
  354. }
  355. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  356. integer n = *n_, incx = *incx_, incy = *incy_, i;
  357. #ifdef _MSC_VER
  358. _Fcomplex zdotc = {0.0, 0.0};
  359. if (incx == 1 && incy == 1) {
  360. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  361. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  362. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  363. }
  364. } else {
  365. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  366. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  367. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  368. }
  369. }
  370. pCf(z) = zdotc;
  371. }
  372. #else
  373. _Complex float zdotc = 0.0;
  374. if (incx == 1 && incy == 1) {
  375. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  376. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  377. }
  378. } else {
  379. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  380. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  381. }
  382. }
  383. pCf(z) = zdotc;
  384. }
  385. #endif
  386. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  387. integer n = *n_, incx = *incx_, incy = *incy_, i;
  388. #ifdef _MSC_VER
  389. _Dcomplex zdotc = {0.0, 0.0};
  390. if (incx == 1 && incy == 1) {
  391. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  392. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  393. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  394. }
  395. } else {
  396. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  397. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  398. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  399. }
  400. }
  401. pCd(z) = zdotc;
  402. }
  403. #else
  404. _Complex double zdotc = 0.0;
  405. if (incx == 1 && incy == 1) {
  406. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  407. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  408. }
  409. } else {
  410. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  411. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  412. }
  413. }
  414. pCd(z) = zdotc;
  415. }
  416. #endif
  417. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  418. integer n = *n_, incx = *incx_, incy = *incy_, i;
  419. #ifdef _MSC_VER
  420. _Fcomplex zdotc = {0.0, 0.0};
  421. if (incx == 1 && incy == 1) {
  422. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  423. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  424. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  425. }
  426. } else {
  427. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  428. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  429. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  430. }
  431. }
  432. pCf(z) = zdotc;
  433. }
  434. #else
  435. _Complex float zdotc = 0.0;
  436. if (incx == 1 && incy == 1) {
  437. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  438. zdotc += Cf(&x[i]) * Cf(&y[i]);
  439. }
  440. } else {
  441. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  442. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  443. }
  444. }
  445. pCf(z) = zdotc;
  446. }
  447. #endif
  448. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  449. integer n = *n_, incx = *incx_, incy = *incy_, i;
  450. #ifdef _MSC_VER
  451. _Dcomplex zdotc = {0.0, 0.0};
  452. if (incx == 1 && incy == 1) {
  453. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  454. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  455. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  456. }
  457. } else {
  458. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  459. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  460. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  461. }
  462. }
  463. pCd(z) = zdotc;
  464. }
  465. #else
  466. _Complex double zdotc = 0.0;
  467. if (incx == 1 && incy == 1) {
  468. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  469. zdotc += Cd(&x[i]) * Cd(&y[i]);
  470. }
  471. } else {
  472. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  473. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  474. }
  475. }
  476. pCd(z) = zdotc;
  477. }
  478. #endif
  479. /* -- translated by f2c (version 20000121).
  480. You must link the resulting object file with the libraries:
  481. -lf2c -lm (in that order)
  482. */
  483. /* Table of constant values */
  484. static doublecomplex c_b1 = {0.,0.};
  485. static doublecomplex c_b2 = {1.,0.};
  486. static integer c__1 = 1;
  487. /* > \brief \b ZTGEVC */
  488. /* =========== DOCUMENTATION =========== */
  489. /* Online html documentation available at */
  490. /* http://www.netlib.org/lapack/explore-html/ */
  491. /* > \htmlonly */
  492. /* > Download ZTGEVC + dependencies */
  493. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgevc.
  494. f"> */
  495. /* > [TGZ]</a> */
  496. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgevc.
  497. f"> */
  498. /* > [ZIP]</a> */
  499. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgevc.
  500. f"> */
  501. /* > [TXT]</a> */
  502. /* > \endhtmlonly */
  503. /* Definition: */
  504. /* =========== */
  505. /* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */
  506. /* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) */
  507. /* CHARACTER HOWMNY, SIDE */
  508. /* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */
  509. /* LOGICAL SELECT( * ) */
  510. /* DOUBLE PRECISION RWORK( * ) */
  511. /* COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */
  512. /* $ VR( LDVR, * ), WORK( * ) */
  513. /* > \par Purpose: */
  514. /* ============= */
  515. /* > */
  516. /* > \verbatim */
  517. /* > */
  518. /* > ZTGEVC computes some or all of the right and/or left eigenvectors of */
  519. /* > a pair of complex matrices (S,P), where S and P are upper triangular. */
  520. /* > Matrix pairs of this type are produced by the generalized Schur */
  521. /* > factorization of a complex matrix pair (A,B): */
  522. /* > */
  523. /* > A = Q*S*Z**H, B = Q*P*Z**H */
  524. /* > */
  525. /* > as computed by ZGGHRD + ZHGEQZ. */
  526. /* > */
  527. /* > The right eigenvector x and the left eigenvector y of (S,P) */
  528. /* > corresponding to an eigenvalue w are defined by: */
  529. /* > */
  530. /* > S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
  531. /* > */
  532. /* > where y**H denotes the conjugate tranpose of y. */
  533. /* > The eigenvalues are not input to this routine, but are computed */
  534. /* > directly from the diagonal elements of S and P. */
  535. /* > */
  536. /* > This routine returns the matrices X and/or Y of right and left */
  537. /* > eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
  538. /* > where Z and Q are input matrices. */
  539. /* > If Q and Z are the unitary factors from the generalized Schur */
  540. /* > factorization of a matrix pair (A,B), then Z*X and Q*Y */
  541. /* > are the matrices of right and left eigenvectors of (A,B). */
  542. /* > \endverbatim */
  543. /* Arguments: */
  544. /* ========== */
  545. /* > \param[in] SIDE */
  546. /* > \verbatim */
  547. /* > SIDE is CHARACTER*1 */
  548. /* > = 'R': compute right eigenvectors only; */
  549. /* > = 'L': compute left eigenvectors only; */
  550. /* > = 'B': compute both right and left eigenvectors. */
  551. /* > \endverbatim */
  552. /* > */
  553. /* > \param[in] HOWMNY */
  554. /* > \verbatim */
  555. /* > HOWMNY is CHARACTER*1 */
  556. /* > = 'A': compute all right and/or left eigenvectors; */
  557. /* > = 'B': compute all right and/or left eigenvectors, */
  558. /* > backtransformed by the matrices in VR and/or VL; */
  559. /* > = 'S': compute selected right and/or left eigenvectors, */
  560. /* > specified by the logical array SELECT. */
  561. /* > \endverbatim */
  562. /* > */
  563. /* > \param[in] SELECT */
  564. /* > \verbatim */
  565. /* > SELECT is LOGICAL array, dimension (N) */
  566. /* > If HOWMNY='S', SELECT specifies the eigenvectors to be */
  567. /* > computed. The eigenvector corresponding to the j-th */
  568. /* > eigenvalue is computed if SELECT(j) = .TRUE.. */
  569. /* > Not referenced if HOWMNY = 'A' or 'B'. */
  570. /* > \endverbatim */
  571. /* > */
  572. /* > \param[in] N */
  573. /* > \verbatim */
  574. /* > N is INTEGER */
  575. /* > The order of the matrices S and P. N >= 0. */
  576. /* > \endverbatim */
  577. /* > */
  578. /* > \param[in] S */
  579. /* > \verbatim */
  580. /* > S is COMPLEX*16 array, dimension (LDS,N) */
  581. /* > The upper triangular matrix S from a generalized Schur */
  582. /* > factorization, as computed by ZHGEQZ. */
  583. /* > \endverbatim */
  584. /* > */
  585. /* > \param[in] LDS */
  586. /* > \verbatim */
  587. /* > LDS is INTEGER */
  588. /* > The leading dimension of array S. LDS >= f2cmax(1,N). */
  589. /* > \endverbatim */
  590. /* > */
  591. /* > \param[in] P */
  592. /* > \verbatim */
  593. /* > P is COMPLEX*16 array, dimension (LDP,N) */
  594. /* > The upper triangular matrix P from a generalized Schur */
  595. /* > factorization, as computed by ZHGEQZ. P must have real */
  596. /* > diagonal elements. */
  597. /* > \endverbatim */
  598. /* > */
  599. /* > \param[in] LDP */
  600. /* > \verbatim */
  601. /* > LDP is INTEGER */
  602. /* > The leading dimension of array P. LDP >= f2cmax(1,N). */
  603. /* > \endverbatim */
  604. /* > */
  605. /* > \param[in,out] VL */
  606. /* > \verbatim */
  607. /* > VL is COMPLEX*16 array, dimension (LDVL,MM) */
  608. /* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
  609. /* > contain an N-by-N matrix Q (usually the unitary matrix Q */
  610. /* > of left Schur vectors returned by ZHGEQZ). */
  611. /* > On exit, if SIDE = 'L' or 'B', VL contains: */
  612. /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
  613. /* > if HOWMNY = 'B', the matrix Q*Y; */
  614. /* > if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
  615. /* > SELECT, stored consecutively in the columns of */
  616. /* > VL, in the same order as their eigenvalues. */
  617. /* > Not referenced if SIDE = 'R'. */
  618. /* > \endverbatim */
  619. /* > */
  620. /* > \param[in] LDVL */
  621. /* > \verbatim */
  622. /* > LDVL is INTEGER */
  623. /* > The leading dimension of array VL. LDVL >= 1, and if */
  624. /* > SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */
  625. /* > \endverbatim */
  626. /* > */
  627. /* > \param[in,out] VR */
  628. /* > \verbatim */
  629. /* > VR is COMPLEX*16 array, dimension (LDVR,MM) */
  630. /* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
  631. /* > contain an N-by-N matrix Q (usually the unitary matrix Z */
  632. /* > of right Schur vectors returned by ZHGEQZ). */
  633. /* > On exit, if SIDE = 'R' or 'B', VR contains: */
  634. /* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
  635. /* > if HOWMNY = 'B', the matrix Z*X; */
  636. /* > if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
  637. /* > SELECT, stored consecutively in the columns of */
  638. /* > VR, in the same order as their eigenvalues. */
  639. /* > Not referenced if SIDE = 'L'. */
  640. /* > \endverbatim */
  641. /* > */
  642. /* > \param[in] LDVR */
  643. /* > \verbatim */
  644. /* > LDVR is INTEGER */
  645. /* > The leading dimension of the array VR. LDVR >= 1, and if */
  646. /* > SIDE = 'R' or 'B', LDVR >= N. */
  647. /* > \endverbatim */
  648. /* > */
  649. /* > \param[in] MM */
  650. /* > \verbatim */
  651. /* > MM is INTEGER */
  652. /* > The number of columns in the arrays VL and/or VR. MM >= M. */
  653. /* > \endverbatim */
  654. /* > */
  655. /* > \param[out] M */
  656. /* > \verbatim */
  657. /* > M is INTEGER */
  658. /* > The number of columns in the arrays VL and/or VR actually */
  659. /* > used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */
  660. /* > is set to N. Each selected eigenvector occupies one column. */
  661. /* > \endverbatim */
  662. /* > */
  663. /* > \param[out] WORK */
  664. /* > \verbatim */
  665. /* > WORK is COMPLEX*16 array, dimension (2*N) */
  666. /* > \endverbatim */
  667. /* > */
  668. /* > \param[out] RWORK */
  669. /* > \verbatim */
  670. /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
  671. /* > \endverbatim */
  672. /* > */
  673. /* > \param[out] INFO */
  674. /* > \verbatim */
  675. /* > INFO is INTEGER */
  676. /* > = 0: successful exit. */
  677. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  678. /* > \endverbatim */
  679. /* Authors: */
  680. /* ======== */
  681. /* > \author Univ. of Tennessee */
  682. /* > \author Univ. of California Berkeley */
  683. /* > \author Univ. of Colorado Denver */
  684. /* > \author NAG Ltd. */
  685. /* > \date December 2016 */
  686. /* > \ingroup complex16GEcomputational */
  687. /* ===================================================================== */
  688. /* Subroutine */ void ztgevc_(char *side, char *howmny, logical *select,
  689. integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer
  690. *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
  691. ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork,
  692. integer *info)
  693. {
  694. /* System generated locals */
  695. integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
  696. vr_offset, i__1, i__2, i__3, i__4, i__5;
  697. doublereal d__1, d__2, d__3, d__4, d__5, d__6;
  698. doublecomplex z__1, z__2, z__3, z__4;
  699. /* Local variables */
  700. integer ibeg, ieig, iend;
  701. doublereal dmin__;
  702. integer isrc;
  703. doublereal temp;
  704. doublecomplex suma, sumb;
  705. doublereal xmax;
  706. doublecomplex d__;
  707. integer i__, j;
  708. doublereal scale;
  709. logical ilall;
  710. integer iside;
  711. doublereal sbeta;
  712. extern logical lsame_(char *, char *);
  713. doublereal small;
  714. logical compl;
  715. doublereal anorm, bnorm;
  716. logical compr;
  717. extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
  718. doublecomplex *, doublecomplex *, integer *, doublecomplex *,
  719. integer *, doublecomplex *, doublecomplex *, integer *);
  720. doublecomplex ca, cb;
  721. extern /* Subroutine */ void dlabad_(doublereal *, doublereal *);
  722. logical ilbbad;
  723. doublereal acoefa;
  724. integer je;
  725. doublereal bcoefa, acoeff;
  726. doublecomplex bcoeff;
  727. logical ilback;
  728. integer im;
  729. doublereal ascale, bscale;
  730. extern doublereal dlamch_(char *);
  731. integer jr;
  732. doublecomplex salpha;
  733. doublereal safmin;
  734. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  735. doublereal bignum;
  736. logical ilcomp;
  737. extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
  738. doublecomplex *);
  739. integer ihwmny;
  740. doublereal big;
  741. logical lsa, lsb;
  742. doublereal ulp;
  743. doublecomplex sum;
  744. /* -- LAPACK computational routine (version 3.7.0) -- */
  745. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  746. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  747. /* December 2016 */
  748. /* ===================================================================== */
  749. /* Decode and Test the input parameters */
  750. /* Parameter adjustments */
  751. --select;
  752. s_dim1 = *lds;
  753. s_offset = 1 + s_dim1 * 1;
  754. s -= s_offset;
  755. p_dim1 = *ldp;
  756. p_offset = 1 + p_dim1 * 1;
  757. p -= p_offset;
  758. vl_dim1 = *ldvl;
  759. vl_offset = 1 + vl_dim1 * 1;
  760. vl -= vl_offset;
  761. vr_dim1 = *ldvr;
  762. vr_offset = 1 + vr_dim1 * 1;
  763. vr -= vr_offset;
  764. --work;
  765. --rwork;
  766. /* Function Body */
  767. if (lsame_(howmny, "A")) {
  768. ihwmny = 1;
  769. ilall = TRUE_;
  770. ilback = FALSE_;
  771. } else if (lsame_(howmny, "S")) {
  772. ihwmny = 2;
  773. ilall = FALSE_;
  774. ilback = FALSE_;
  775. } else if (lsame_(howmny, "B")) {
  776. ihwmny = 3;
  777. ilall = TRUE_;
  778. ilback = TRUE_;
  779. } else {
  780. ihwmny = -1;
  781. }
  782. if (lsame_(side, "R")) {
  783. iside = 1;
  784. compl = FALSE_;
  785. compr = TRUE_;
  786. } else if (lsame_(side, "L")) {
  787. iside = 2;
  788. compl = TRUE_;
  789. compr = FALSE_;
  790. } else if (lsame_(side, "B")) {
  791. iside = 3;
  792. compl = TRUE_;
  793. compr = TRUE_;
  794. } else {
  795. iside = -1;
  796. }
  797. *info = 0;
  798. if (iside < 0) {
  799. *info = -1;
  800. } else if (ihwmny < 0) {
  801. *info = -2;
  802. } else if (*n < 0) {
  803. *info = -4;
  804. } else if (*lds < f2cmax(1,*n)) {
  805. *info = -6;
  806. } else if (*ldp < f2cmax(1,*n)) {
  807. *info = -8;
  808. }
  809. if (*info != 0) {
  810. i__1 = -(*info);
  811. xerbla_("ZTGEVC", &i__1, (ftnlen)6);
  812. return;
  813. }
  814. /* Count the number of eigenvectors */
  815. if (! ilall) {
  816. im = 0;
  817. i__1 = *n;
  818. for (j = 1; j <= i__1; ++j) {
  819. if (select[j]) {
  820. ++im;
  821. }
  822. /* L10: */
  823. }
  824. } else {
  825. im = *n;
  826. }
  827. /* Check diagonal of B */
  828. ilbbad = FALSE_;
  829. i__1 = *n;
  830. for (j = 1; j <= i__1; ++j) {
  831. if (d_imag(&p[j + j * p_dim1]) != 0.) {
  832. ilbbad = TRUE_;
  833. }
  834. /* L20: */
  835. }
  836. if (ilbbad) {
  837. *info = -7;
  838. } else if (compl && *ldvl < *n || *ldvl < 1) {
  839. *info = -10;
  840. } else if (compr && *ldvr < *n || *ldvr < 1) {
  841. *info = -12;
  842. } else if (*mm < im) {
  843. *info = -13;
  844. }
  845. if (*info != 0) {
  846. i__1 = -(*info);
  847. xerbla_("ZTGEVC", &i__1, (ftnlen)6);
  848. return;
  849. }
  850. /* Quick return if possible */
  851. *m = im;
  852. if (*n == 0) {
  853. return;
  854. }
  855. /* Machine Constants */
  856. safmin = dlamch_("Safe minimum");
  857. big = 1. / safmin;
  858. dlabad_(&safmin, &big);
  859. ulp = dlamch_("Epsilon") * dlamch_("Base");
  860. small = safmin * *n / ulp;
  861. big = 1. / small;
  862. bignum = 1. / (safmin * *n);
  863. /* Compute the 1-norm of each column of the strictly upper triangular */
  864. /* part of A and B to check for possible overflow in the triangular */
  865. /* solver. */
  866. i__1 = s_dim1 + 1;
  867. anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]),
  868. abs(d__2));
  869. i__1 = p_dim1 + 1;
  870. bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]),
  871. abs(d__2));
  872. rwork[1] = 0.;
  873. rwork[*n + 1] = 0.;
  874. i__1 = *n;
  875. for (j = 2; j <= i__1; ++j) {
  876. rwork[j] = 0.;
  877. rwork[*n + j] = 0.;
  878. i__2 = j - 1;
  879. for (i__ = 1; i__ <= i__2; ++i__) {
  880. i__3 = i__ + j * s_dim1;
  881. rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__
  882. + j * s_dim1]), abs(d__2));
  883. i__3 = i__ + j * p_dim1;
  884. rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(&
  885. p[i__ + j * p_dim1]), abs(d__2));
  886. /* L30: */
  887. }
  888. /* Computing MAX */
  889. i__2 = j + j * s_dim1;
  890. d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + (
  891. d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2)));
  892. anorm = f2cmax(d__3,d__4);
  893. /* Computing MAX */
  894. i__2 = j + j * p_dim1;
  895. d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) +
  896. (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2)));
  897. bnorm = f2cmax(d__3,d__4);
  898. /* L40: */
  899. }
  900. ascale = 1. / f2cmax(anorm,safmin);
  901. bscale = 1. / f2cmax(bnorm,safmin);
  902. /* Left eigenvectors */
  903. if (compl) {
  904. ieig = 0;
  905. /* Main loop over eigenvalues */
  906. i__1 = *n;
  907. for (je = 1; je <= i__1; ++je) {
  908. if (ilall) {
  909. ilcomp = TRUE_;
  910. } else {
  911. ilcomp = select[je];
  912. }
  913. if (ilcomp) {
  914. ++ieig;
  915. i__2 = je + je * s_dim1;
  916. i__3 = je + je * p_dim1;
  917. if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
  918. * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r,
  919. abs(d__1)) <= safmin) {
  920. /* Singular matrix pencil -- return unit eigenvector */
  921. i__2 = *n;
  922. for (jr = 1; jr <= i__2; ++jr) {
  923. i__3 = jr + ieig * vl_dim1;
  924. vl[i__3].r = 0., vl[i__3].i = 0.;
  925. /* L50: */
  926. }
  927. i__2 = ieig + ieig * vl_dim1;
  928. vl[i__2].r = 1., vl[i__2].i = 0.;
  929. goto L140;
  930. }
  931. /* Non-singular eigenvalue: */
  932. /* Compute coefficients a and b in */
  933. /* H */
  934. /* y ( a A - b B ) = 0 */
  935. /* Computing MAX */
  936. i__2 = je + je * s_dim1;
  937. i__3 = je + je * p_dim1;
  938. d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je
  939. + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
  940. p[i__3].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
  941. temp = 1. / f2cmax(d__4,safmin);
  942. i__2 = je + je * s_dim1;
  943. z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i;
  944. z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
  945. salpha.r = z__1.r, salpha.i = z__1.i;
  946. i__2 = je + je * p_dim1;
  947. sbeta = temp * p[i__2].r * bscale;
  948. acoeff = sbeta * ascale;
  949. z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
  950. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  951. /* Scale to avoid underflow */
  952. lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
  953. lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
  954. abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
  955. + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
  956. scale = 1.;
  957. if (lsa) {
  958. scale = small / abs(sbeta) * f2cmin(anorm,big);
  959. }
  960. if (lsb) {
  961. /* Computing MAX */
  962. d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
  963. + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
  964. bnorm,big);
  965. scale = f2cmax(d__3,d__4);
  966. }
  967. if (lsa || lsb) {
  968. /* Computing MIN */
  969. /* Computing MAX */
  970. d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
  971. d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
  972. d_imag(&bcoeff), abs(d__2));
  973. d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
  974. scale = f2cmin(d__3,d__4);
  975. if (lsa) {
  976. acoeff = ascale * (scale * sbeta);
  977. } else {
  978. acoeff = scale * acoeff;
  979. }
  980. if (lsb) {
  981. z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
  982. z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
  983. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  984. } else {
  985. z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
  986. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  987. }
  988. }
  989. acoefa = abs(acoeff);
  990. bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
  991. bcoeff), abs(d__2));
  992. xmax = 1.;
  993. i__2 = *n;
  994. for (jr = 1; jr <= i__2; ++jr) {
  995. i__3 = jr;
  996. work[i__3].r = 0., work[i__3].i = 0.;
  997. /* L60: */
  998. }
  999. i__2 = je;
  1000. work[i__2].r = 1., work[i__2].i = 0.;
  1001. /* Computing MAX */
  1002. d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
  1003. d__1 = f2cmax(d__1,d__2);
  1004. dmin__ = f2cmax(d__1,safmin);
  1005. /* H */
  1006. /* Triangular solve of (a A - b B) y = 0 */
  1007. /* H */
  1008. /* (rowwise in (a A - b B) , or columnwise in a A - b B) */
  1009. i__2 = *n;
  1010. for (j = je + 1; j <= i__2; ++j) {
  1011. /* Compute */
  1012. /* j-1 */
  1013. /* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
  1014. /* k=je */
  1015. /* (Scale if necessary) */
  1016. temp = 1. / xmax;
  1017. if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum *
  1018. temp) {
  1019. i__3 = j - 1;
  1020. for (jr = je; jr <= i__3; ++jr) {
  1021. i__4 = jr;
  1022. i__5 = jr;
  1023. z__1.r = temp * work[i__5].r, z__1.i = temp *
  1024. work[i__5].i;
  1025. work[i__4].r = z__1.r, work[i__4].i = z__1.i;
  1026. /* L70: */
  1027. }
  1028. xmax = 1.;
  1029. }
  1030. suma.r = 0., suma.i = 0.;
  1031. sumb.r = 0., sumb.i = 0.;
  1032. i__3 = j - 1;
  1033. for (jr = je; jr <= i__3; ++jr) {
  1034. d_cnjg(&z__3, &s[jr + j * s_dim1]);
  1035. i__4 = jr;
  1036. z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
  1037. .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
  1038. work[i__4].r;
  1039. z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i;
  1040. suma.r = z__1.r, suma.i = z__1.i;
  1041. d_cnjg(&z__3, &p[jr + j * p_dim1]);
  1042. i__4 = jr;
  1043. z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
  1044. .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
  1045. work[i__4].r;
  1046. z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i;
  1047. sumb.r = z__1.r, sumb.i = z__1.i;
  1048. /* L80: */
  1049. }
  1050. z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i;
  1051. d_cnjg(&z__4, &bcoeff);
  1052. z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i =
  1053. z__4.r * sumb.i + z__4.i * sumb.r;
  1054. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1055. sum.r = z__1.r, sum.i = z__1.i;
  1056. /* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
  1057. /* with scaling and perturbation of the denominator */
  1058. i__3 = j + j * s_dim1;
  1059. z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i;
  1060. i__4 = j + j * p_dim1;
  1061. z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
  1062. z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
  1063. .r;
  1064. z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
  1065. d_cnjg(&z__1, &z__2);
  1066. d__.r = z__1.r, d__.i = z__1.i;
  1067. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1068. d__2)) <= dmin__) {
  1069. z__1.r = dmin__, z__1.i = 0.;
  1070. d__.r = z__1.r, d__.i = z__1.i;
  1071. }
  1072. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1073. d__2)) < 1.) {
  1074. if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum),
  1075. abs(d__2)) >= bignum * ((d__3 = d__.r, abs(
  1076. d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) {
  1077. temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 =
  1078. d_imag(&sum), abs(d__2)));
  1079. i__3 = j - 1;
  1080. for (jr = je; jr <= i__3; ++jr) {
  1081. i__4 = jr;
  1082. i__5 = jr;
  1083. z__1.r = temp * work[i__5].r, z__1.i = temp *
  1084. work[i__5].i;
  1085. work[i__4].r = z__1.r, work[i__4].i = z__1.i;
  1086. /* L90: */
  1087. }
  1088. xmax = temp * xmax;
  1089. z__1.r = temp * sum.r, z__1.i = temp * sum.i;
  1090. sum.r = z__1.r, sum.i = z__1.i;
  1091. }
  1092. }
  1093. i__3 = j;
  1094. z__2.r = -sum.r, z__2.i = -sum.i;
  1095. zladiv_(&z__1, &z__2, &d__);
  1096. work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  1097. /* Computing MAX */
  1098. i__3 = j;
  1099. d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
  1100. d__2 = d_imag(&work[j]), abs(d__2));
  1101. xmax = f2cmax(d__3,d__4);
  1102. /* L100: */
  1103. }
  1104. /* Back transform eigenvector if HOWMNY='B'. */
  1105. if (ilback) {
  1106. i__2 = *n + 1 - je;
  1107. zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl,
  1108. &work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
  1109. isrc = 2;
  1110. ibeg = 1;
  1111. } else {
  1112. isrc = 1;
  1113. ibeg = je;
  1114. }
  1115. /* Copy and scale eigenvector into column of VL */
  1116. xmax = 0.;
  1117. i__2 = *n;
  1118. for (jr = ibeg; jr <= i__2; ++jr) {
  1119. /* Computing MAX */
  1120. i__3 = (isrc - 1) * *n + jr;
  1121. d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
  1122. d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
  1123. d__2));
  1124. xmax = f2cmax(d__3,d__4);
  1125. /* L110: */
  1126. }
  1127. if (xmax > safmin) {
  1128. temp = 1. / xmax;
  1129. i__2 = *n;
  1130. for (jr = ibeg; jr <= i__2; ++jr) {
  1131. i__3 = jr + ieig * vl_dim1;
  1132. i__4 = (isrc - 1) * *n + jr;
  1133. z__1.r = temp * work[i__4].r, z__1.i = temp * work[
  1134. i__4].i;
  1135. vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
  1136. /* L120: */
  1137. }
  1138. } else {
  1139. ibeg = *n + 1;
  1140. }
  1141. i__2 = ibeg - 1;
  1142. for (jr = 1; jr <= i__2; ++jr) {
  1143. i__3 = jr + ieig * vl_dim1;
  1144. vl[i__3].r = 0., vl[i__3].i = 0.;
  1145. /* L130: */
  1146. }
  1147. }
  1148. L140:
  1149. ;
  1150. }
  1151. }
  1152. /* Right eigenvectors */
  1153. if (compr) {
  1154. ieig = im + 1;
  1155. /* Main loop over eigenvalues */
  1156. for (je = *n; je >= 1; --je) {
  1157. if (ilall) {
  1158. ilcomp = TRUE_;
  1159. } else {
  1160. ilcomp = select[je];
  1161. }
  1162. if (ilcomp) {
  1163. --ieig;
  1164. i__1 = je + je * s_dim1;
  1165. i__2 = je + je * p_dim1;
  1166. if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
  1167. * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r,
  1168. abs(d__1)) <= safmin) {
  1169. /* Singular matrix pencil -- return unit eigenvector */
  1170. i__1 = *n;
  1171. for (jr = 1; jr <= i__1; ++jr) {
  1172. i__2 = jr + ieig * vr_dim1;
  1173. vr[i__2].r = 0., vr[i__2].i = 0.;
  1174. /* L150: */
  1175. }
  1176. i__1 = ieig + ieig * vr_dim1;
  1177. vr[i__1].r = 1., vr[i__1].i = 0.;
  1178. goto L250;
  1179. }
  1180. /* Non-singular eigenvalue: */
  1181. /* Compute coefficients a and b in */
  1182. /* ( a A - b B ) x = 0 */
  1183. /* Computing MAX */
  1184. i__1 = je + je * s_dim1;
  1185. i__2 = je + je * p_dim1;
  1186. d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je
  1187. + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
  1188. p[i__2].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
  1189. temp = 1. / f2cmax(d__4,safmin);
  1190. i__1 = je + je * s_dim1;
  1191. z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i;
  1192. z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
  1193. salpha.r = z__1.r, salpha.i = z__1.i;
  1194. i__1 = je + je * p_dim1;
  1195. sbeta = temp * p[i__1].r * bscale;
  1196. acoeff = sbeta * ascale;
  1197. z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
  1198. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1199. /* Scale to avoid underflow */
  1200. lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
  1201. lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
  1202. abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
  1203. + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
  1204. scale = 1.;
  1205. if (lsa) {
  1206. scale = small / abs(sbeta) * f2cmin(anorm,big);
  1207. }
  1208. if (lsb) {
  1209. /* Computing MAX */
  1210. d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
  1211. + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
  1212. bnorm,big);
  1213. scale = f2cmax(d__3,d__4);
  1214. }
  1215. if (lsa || lsb) {
  1216. /* Computing MIN */
  1217. /* Computing MAX */
  1218. d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
  1219. d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
  1220. d_imag(&bcoeff), abs(d__2));
  1221. d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
  1222. scale = f2cmin(d__3,d__4);
  1223. if (lsa) {
  1224. acoeff = ascale * (scale * sbeta);
  1225. } else {
  1226. acoeff = scale * acoeff;
  1227. }
  1228. if (lsb) {
  1229. z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
  1230. z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
  1231. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1232. } else {
  1233. z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
  1234. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1235. }
  1236. }
  1237. acoefa = abs(acoeff);
  1238. bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
  1239. bcoeff), abs(d__2));
  1240. xmax = 1.;
  1241. i__1 = *n;
  1242. for (jr = 1; jr <= i__1; ++jr) {
  1243. i__2 = jr;
  1244. work[i__2].r = 0., work[i__2].i = 0.;
  1245. /* L160: */
  1246. }
  1247. i__1 = je;
  1248. work[i__1].r = 1., work[i__1].i = 0.;
  1249. /* Computing MAX */
  1250. d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
  1251. d__1 = f2cmax(d__1,d__2);
  1252. dmin__ = f2cmax(d__1,safmin);
  1253. /* Triangular solve of (a A - b B) x = 0 (columnwise) */
  1254. /* WORK(1:j-1) contains sums w, */
  1255. /* WORK(j+1:JE) contains x */
  1256. i__1 = je - 1;
  1257. for (jr = 1; jr <= i__1; ++jr) {
  1258. i__2 = jr;
  1259. i__3 = jr + je * s_dim1;
  1260. z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i;
  1261. i__4 = jr + je * p_dim1;
  1262. z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
  1263. z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
  1264. .r;
  1265. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1266. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1267. /* L170: */
  1268. }
  1269. i__1 = je;
  1270. work[i__1].r = 1., work[i__1].i = 0.;
  1271. for (j = je - 1; j >= 1; --j) {
  1272. /* Form x(j) := - w(j) / d */
  1273. /* with scaling and perturbation of the denominator */
  1274. i__1 = j + j * s_dim1;
  1275. z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i;
  1276. i__2 = j + j * p_dim1;
  1277. z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i,
  1278. z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
  1279. .r;
  1280. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1281. d__.r = z__1.r, d__.i = z__1.i;
  1282. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1283. d__2)) <= dmin__) {
  1284. z__1.r = dmin__, z__1.i = 0.;
  1285. d__.r = z__1.r, d__.i = z__1.i;
  1286. }
  1287. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1288. d__2)) < 1.) {
  1289. i__1 = j;
  1290. if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
  1291. &work[j]), abs(d__2)) >= bignum * ((d__3 =
  1292. d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
  1293. d__4)))) {
  1294. i__1 = j;
  1295. temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
  1296. d__2 = d_imag(&work[j]), abs(d__2)));
  1297. i__1 = je;
  1298. for (jr = 1; jr <= i__1; ++jr) {
  1299. i__2 = jr;
  1300. i__3 = jr;
  1301. z__1.r = temp * work[i__3].r, z__1.i = temp *
  1302. work[i__3].i;
  1303. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1304. /* L180: */
  1305. }
  1306. }
  1307. }
  1308. i__1 = j;
  1309. i__2 = j;
  1310. z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
  1311. zladiv_(&z__1, &z__2, &d__);
  1312. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1313. if (j > 1) {
  1314. /* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
  1315. i__1 = j;
  1316. if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
  1317. &work[j]), abs(d__2)) > 1.) {
  1318. i__1 = j;
  1319. temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
  1320. d__2 = d_imag(&work[j]), abs(d__2)));
  1321. if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >=
  1322. bignum * temp) {
  1323. i__1 = je;
  1324. for (jr = 1; jr <= i__1; ++jr) {
  1325. i__2 = jr;
  1326. i__3 = jr;
  1327. z__1.r = temp * work[i__3].r, z__1.i =
  1328. temp * work[i__3].i;
  1329. work[i__2].r = z__1.r, work[i__2].i =
  1330. z__1.i;
  1331. /* L190: */
  1332. }
  1333. }
  1334. }
  1335. i__1 = j;
  1336. z__1.r = acoeff * work[i__1].r, z__1.i = acoeff *
  1337. work[i__1].i;
  1338. ca.r = z__1.r, ca.i = z__1.i;
  1339. i__1 = j;
  1340. z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
  1341. i__1].i, z__1.i = bcoeff.r * work[i__1].i +
  1342. bcoeff.i * work[i__1].r;
  1343. cb.r = z__1.r, cb.i = z__1.i;
  1344. i__1 = j - 1;
  1345. for (jr = 1; jr <= i__1; ++jr) {
  1346. i__2 = jr;
  1347. i__3 = jr;
  1348. i__4 = jr + j * s_dim1;
  1349. z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i,
  1350. z__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
  1351. .r;
  1352. z__2.r = work[i__3].r + z__3.r, z__2.i = work[
  1353. i__3].i + z__3.i;
  1354. i__5 = jr + j * p_dim1;
  1355. z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i,
  1356. z__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
  1357. .r;
  1358. z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
  1359. z__4.i;
  1360. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1361. /* L200: */
  1362. }
  1363. }
  1364. /* L210: */
  1365. }
  1366. /* Back transform eigenvector if HOWMNY='B'. */
  1367. if (ilback) {
  1368. zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
  1369. &c__1, &c_b1, &work[*n + 1], &c__1);
  1370. isrc = 2;
  1371. iend = *n;
  1372. } else {
  1373. isrc = 1;
  1374. iend = je;
  1375. }
  1376. /* Copy and scale eigenvector into column of VR */
  1377. xmax = 0.;
  1378. i__1 = iend;
  1379. for (jr = 1; jr <= i__1; ++jr) {
  1380. /* Computing MAX */
  1381. i__2 = (isrc - 1) * *n + jr;
  1382. d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
  1383. d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
  1384. d__2));
  1385. xmax = f2cmax(d__3,d__4);
  1386. /* L220: */
  1387. }
  1388. if (xmax > safmin) {
  1389. temp = 1. / xmax;
  1390. i__1 = iend;
  1391. for (jr = 1; jr <= i__1; ++jr) {
  1392. i__2 = jr + ieig * vr_dim1;
  1393. i__3 = (isrc - 1) * *n + jr;
  1394. z__1.r = temp * work[i__3].r, z__1.i = temp * work[
  1395. i__3].i;
  1396. vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
  1397. /* L230: */
  1398. }
  1399. } else {
  1400. iend = 0;
  1401. }
  1402. i__1 = *n;
  1403. for (jr = iend + 1; jr <= i__1; ++jr) {
  1404. i__2 = jr + ieig * vr_dim1;
  1405. vr[i__2].r = 0., vr[i__2].i = 0.;
  1406. /* L240: */
  1407. }
  1408. }
  1409. L250:
  1410. ;
  1411. }
  1412. }
  1413. return;
  1414. /* End of ZTGEVC */
  1415. } /* ztgevc_ */