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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 int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #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]);}
  173. #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]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #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++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #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]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle_() continue;
  235. #define myceiling_(w) {ceil(w)}
  236. #define myhuge_(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static doublecomplex c_b1 = {0.,0.};
  487. static doublecomplex c_b2 = {1.,0.};
  488. static integer c__1 = 1;
  489. /* > \brief \b ZTGEVC */
  490. /* =========== DOCUMENTATION =========== */
  491. /* Online html documentation available at */
  492. /* http://www.netlib.org/lapack/explore-html/ */
  493. /* > \htmlonly */
  494. /* > Download ZTGEVC + dependencies */
  495. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgevc.
  496. f"> */
  497. /* > [TGZ]</a> */
  498. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgevc.
  499. f"> */
  500. /* > [ZIP]</a> */
  501. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgevc.
  502. f"> */
  503. /* > [TXT]</a> */
  504. /* > \endhtmlonly */
  505. /* Definition: */
  506. /* =========== */
  507. /* SUBROUTINE ZTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */
  508. /* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) */
  509. /* CHARACTER HOWMNY, SIDE */
  510. /* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */
  511. /* LOGICAL SELECT( * ) */
  512. /* DOUBLE PRECISION RWORK( * ) */
  513. /* COMPLEX*16 P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */
  514. /* $ VR( LDVR, * ), WORK( * ) */
  515. /* > \par Purpose: */
  516. /* ============= */
  517. /* > */
  518. /* > \verbatim */
  519. /* > */
  520. /* > ZTGEVC computes some or all of the right and/or left eigenvectors of */
  521. /* > a pair of complex matrices (S,P), where S and P are upper triangular. */
  522. /* > Matrix pairs of this type are produced by the generalized Schur */
  523. /* > factorization of a complex matrix pair (A,B): */
  524. /* > */
  525. /* > A = Q*S*Z**H, B = Q*P*Z**H */
  526. /* > */
  527. /* > as computed by ZGGHRD + ZHGEQZ. */
  528. /* > */
  529. /* > The right eigenvector x and the left eigenvector y of (S,P) */
  530. /* > corresponding to an eigenvalue w are defined by: */
  531. /* > */
  532. /* > S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
  533. /* > */
  534. /* > where y**H denotes the conjugate tranpose of y. */
  535. /* > The eigenvalues are not input to this routine, but are computed */
  536. /* > directly from the diagonal elements of S and P. */
  537. /* > */
  538. /* > This routine returns the matrices X and/or Y of right and left */
  539. /* > eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
  540. /* > where Z and Q are input matrices. */
  541. /* > If Q and Z are the unitary factors from the generalized Schur */
  542. /* > factorization of a matrix pair (A,B), then Z*X and Q*Y */
  543. /* > are the matrices of right and left eigenvectors of (A,B). */
  544. /* > \endverbatim */
  545. /* Arguments: */
  546. /* ========== */
  547. /* > \param[in] SIDE */
  548. /* > \verbatim */
  549. /* > SIDE is CHARACTER*1 */
  550. /* > = 'R': compute right eigenvectors only; */
  551. /* > = 'L': compute left eigenvectors only; */
  552. /* > = 'B': compute both right and left eigenvectors. */
  553. /* > \endverbatim */
  554. /* > */
  555. /* > \param[in] HOWMNY */
  556. /* > \verbatim */
  557. /* > HOWMNY is CHARACTER*1 */
  558. /* > = 'A': compute all right and/or left eigenvectors; */
  559. /* > = 'B': compute all right and/or left eigenvectors, */
  560. /* > backtransformed by the matrices in VR and/or VL; */
  561. /* > = 'S': compute selected right and/or left eigenvectors, */
  562. /* > specified by the logical array SELECT. */
  563. /* > \endverbatim */
  564. /* > */
  565. /* > \param[in] SELECT */
  566. /* > \verbatim */
  567. /* > SELECT is LOGICAL array, dimension (N) */
  568. /* > If HOWMNY='S', SELECT specifies the eigenvectors to be */
  569. /* > computed. The eigenvector corresponding to the j-th */
  570. /* > eigenvalue is computed if SELECT(j) = .TRUE.. */
  571. /* > Not referenced if HOWMNY = 'A' or 'B'. */
  572. /* > \endverbatim */
  573. /* > */
  574. /* > \param[in] N */
  575. /* > \verbatim */
  576. /* > N is INTEGER */
  577. /* > The order of the matrices S and P. N >= 0. */
  578. /* > \endverbatim */
  579. /* > */
  580. /* > \param[in] S */
  581. /* > \verbatim */
  582. /* > S is COMPLEX*16 array, dimension (LDS,N) */
  583. /* > The upper triangular matrix S from a generalized Schur */
  584. /* > factorization, as computed by ZHGEQZ. */
  585. /* > \endverbatim */
  586. /* > */
  587. /* > \param[in] LDS */
  588. /* > \verbatim */
  589. /* > LDS is INTEGER */
  590. /* > The leading dimension of array S. LDS >= f2cmax(1,N). */
  591. /* > \endverbatim */
  592. /* > */
  593. /* > \param[in] P */
  594. /* > \verbatim */
  595. /* > P is COMPLEX*16 array, dimension (LDP,N) */
  596. /* > The upper triangular matrix P from a generalized Schur */
  597. /* > factorization, as computed by ZHGEQZ. P must have real */
  598. /* > diagonal elements. */
  599. /* > \endverbatim */
  600. /* > */
  601. /* > \param[in] LDP */
  602. /* > \verbatim */
  603. /* > LDP is INTEGER */
  604. /* > The leading dimension of array P. LDP >= f2cmax(1,N). */
  605. /* > \endverbatim */
  606. /* > */
  607. /* > \param[in,out] VL */
  608. /* > \verbatim */
  609. /* > VL is COMPLEX*16 array, dimension (LDVL,MM) */
  610. /* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
  611. /* > contain an N-by-N matrix Q (usually the unitary matrix Q */
  612. /* > of left Schur vectors returned by ZHGEQZ). */
  613. /* > On exit, if SIDE = 'L' or 'B', VL contains: */
  614. /* > if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
  615. /* > if HOWMNY = 'B', the matrix Q*Y; */
  616. /* > if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
  617. /* > SELECT, stored consecutively in the columns of */
  618. /* > VL, in the same order as their eigenvalues. */
  619. /* > Not referenced if SIDE = 'R'. */
  620. /* > \endverbatim */
  621. /* > */
  622. /* > \param[in] LDVL */
  623. /* > \verbatim */
  624. /* > LDVL is INTEGER */
  625. /* > The leading dimension of array VL. LDVL >= 1, and if */
  626. /* > SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N. */
  627. /* > \endverbatim */
  628. /* > */
  629. /* > \param[in,out] VR */
  630. /* > \verbatim */
  631. /* > VR is COMPLEX*16 array, dimension (LDVR,MM) */
  632. /* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
  633. /* > contain an N-by-N matrix Q (usually the unitary matrix Z */
  634. /* > of right Schur vectors returned by ZHGEQZ). */
  635. /* > On exit, if SIDE = 'R' or 'B', VR contains: */
  636. /* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
  637. /* > if HOWMNY = 'B', the matrix Z*X; */
  638. /* > if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
  639. /* > SELECT, stored consecutively in the columns of */
  640. /* > VR, in the same order as their eigenvalues. */
  641. /* > Not referenced if SIDE = 'L'. */
  642. /* > \endverbatim */
  643. /* > */
  644. /* > \param[in] LDVR */
  645. /* > \verbatim */
  646. /* > LDVR is INTEGER */
  647. /* > The leading dimension of the array VR. LDVR >= 1, and if */
  648. /* > SIDE = 'R' or 'B', LDVR >= N. */
  649. /* > \endverbatim */
  650. /* > */
  651. /* > \param[in] MM */
  652. /* > \verbatim */
  653. /* > MM is INTEGER */
  654. /* > The number of columns in the arrays VL and/or VR. MM >= M. */
  655. /* > \endverbatim */
  656. /* > */
  657. /* > \param[out] M */
  658. /* > \verbatim */
  659. /* > M is INTEGER */
  660. /* > The number of columns in the arrays VL and/or VR actually */
  661. /* > used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */
  662. /* > is set to N. Each selected eigenvector occupies one column. */
  663. /* > \endverbatim */
  664. /* > */
  665. /* > \param[out] WORK */
  666. /* > \verbatim */
  667. /* > WORK is COMPLEX*16 array, dimension (2*N) */
  668. /* > \endverbatim */
  669. /* > */
  670. /* > \param[out] RWORK */
  671. /* > \verbatim */
  672. /* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
  673. /* > \endverbatim */
  674. /* > */
  675. /* > \param[out] INFO */
  676. /* > \verbatim */
  677. /* > INFO is INTEGER */
  678. /* > = 0: successful exit. */
  679. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  680. /* > \endverbatim */
  681. /* Authors: */
  682. /* ======== */
  683. /* > \author Univ. of Tennessee */
  684. /* > \author Univ. of California Berkeley */
  685. /* > \author Univ. of Colorado Denver */
  686. /* > \author NAG Ltd. */
  687. /* > \date December 2016 */
  688. /* > \ingroup complex16GEcomputational */
  689. /* ===================================================================== */
  690. /* Subroutine */ int ztgevc_(char *side, char *howmny, logical *select,
  691. integer *n, doublecomplex *s, integer *lds, doublecomplex *p, integer
  692. *ldp, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *
  693. ldvr, integer *mm, integer *m, doublecomplex *work, doublereal *rwork,
  694. integer *info)
  695. {
  696. /* System generated locals */
  697. integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
  698. vr_offset, i__1, i__2, i__3, i__4, i__5;
  699. doublereal d__1, d__2, d__3, d__4, d__5, d__6;
  700. doublecomplex z__1, z__2, z__3, z__4;
  701. /* Local variables */
  702. integer ibeg, ieig, iend;
  703. doublereal dmin__;
  704. integer isrc;
  705. doublereal temp;
  706. doublecomplex suma, sumb;
  707. doublereal xmax;
  708. doublecomplex d__;
  709. integer i__, j;
  710. doublereal scale;
  711. logical ilall;
  712. integer iside;
  713. doublereal sbeta;
  714. extern logical lsame_(char *, char *);
  715. doublereal small;
  716. logical compl;
  717. doublereal anorm, bnorm;
  718. logical compr;
  719. extern /* Subroutine */ int zgemv_(char *, integer *, integer *,
  720. doublecomplex *, doublecomplex *, integer *, doublecomplex *,
  721. integer *, doublecomplex *, doublecomplex *, integer *);
  722. doublecomplex ca, cb;
  723. extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
  724. logical ilbbad;
  725. doublereal acoefa;
  726. integer je;
  727. doublereal bcoefa, acoeff;
  728. doublecomplex bcoeff;
  729. logical ilback;
  730. integer im;
  731. doublereal ascale, bscale;
  732. extern doublereal dlamch_(char *);
  733. integer jr;
  734. doublecomplex salpha;
  735. doublereal safmin;
  736. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  737. doublereal bignum;
  738. logical ilcomp;
  739. extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
  740. doublecomplex *);
  741. integer ihwmny;
  742. doublereal big;
  743. logical lsa, lsb;
  744. doublereal ulp;
  745. doublecomplex sum;
  746. /* -- LAPACK computational routine (version 3.7.0) -- */
  747. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  748. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  749. /* December 2016 */
  750. /* ===================================================================== */
  751. /* Decode and Test the input parameters */
  752. /* Parameter adjustments */
  753. --select;
  754. s_dim1 = *lds;
  755. s_offset = 1 + s_dim1 * 1;
  756. s -= s_offset;
  757. p_dim1 = *ldp;
  758. p_offset = 1 + p_dim1 * 1;
  759. p -= p_offset;
  760. vl_dim1 = *ldvl;
  761. vl_offset = 1 + vl_dim1 * 1;
  762. vl -= vl_offset;
  763. vr_dim1 = *ldvr;
  764. vr_offset = 1 + vr_dim1 * 1;
  765. vr -= vr_offset;
  766. --work;
  767. --rwork;
  768. /* Function Body */
  769. if (lsame_(howmny, "A")) {
  770. ihwmny = 1;
  771. ilall = TRUE_;
  772. ilback = FALSE_;
  773. } else if (lsame_(howmny, "S")) {
  774. ihwmny = 2;
  775. ilall = FALSE_;
  776. ilback = FALSE_;
  777. } else if (lsame_(howmny, "B")) {
  778. ihwmny = 3;
  779. ilall = TRUE_;
  780. ilback = TRUE_;
  781. } else {
  782. ihwmny = -1;
  783. }
  784. if (lsame_(side, "R")) {
  785. iside = 1;
  786. compl = FALSE_;
  787. compr = TRUE_;
  788. } else if (lsame_(side, "L")) {
  789. iside = 2;
  790. compl = TRUE_;
  791. compr = FALSE_;
  792. } else if (lsame_(side, "B")) {
  793. iside = 3;
  794. compl = TRUE_;
  795. compr = TRUE_;
  796. } else {
  797. iside = -1;
  798. }
  799. *info = 0;
  800. if (iside < 0) {
  801. *info = -1;
  802. } else if (ihwmny < 0) {
  803. *info = -2;
  804. } else if (*n < 0) {
  805. *info = -4;
  806. } else if (*lds < f2cmax(1,*n)) {
  807. *info = -6;
  808. } else if (*ldp < f2cmax(1,*n)) {
  809. *info = -8;
  810. }
  811. if (*info != 0) {
  812. i__1 = -(*info);
  813. xerbla_("ZTGEVC", &i__1, (ftnlen)6);
  814. return 0;
  815. }
  816. /* Count the number of eigenvectors */
  817. if (! ilall) {
  818. im = 0;
  819. i__1 = *n;
  820. for (j = 1; j <= i__1; ++j) {
  821. if (select[j]) {
  822. ++im;
  823. }
  824. /* L10: */
  825. }
  826. } else {
  827. im = *n;
  828. }
  829. /* Check diagonal of B */
  830. ilbbad = FALSE_;
  831. i__1 = *n;
  832. for (j = 1; j <= i__1; ++j) {
  833. if (d_imag(&p[j + j * p_dim1]) != 0.) {
  834. ilbbad = TRUE_;
  835. }
  836. /* L20: */
  837. }
  838. if (ilbbad) {
  839. *info = -7;
  840. } else if (compl && *ldvl < *n || *ldvl < 1) {
  841. *info = -10;
  842. } else if (compr && *ldvr < *n || *ldvr < 1) {
  843. *info = -12;
  844. } else if (*mm < im) {
  845. *info = -13;
  846. }
  847. if (*info != 0) {
  848. i__1 = -(*info);
  849. xerbla_("ZTGEVC", &i__1, (ftnlen)6);
  850. return 0;
  851. }
  852. /* Quick return if possible */
  853. *m = im;
  854. if (*n == 0) {
  855. return 0;
  856. }
  857. /* Machine Constants */
  858. safmin = dlamch_("Safe minimum");
  859. big = 1. / safmin;
  860. dlabad_(&safmin, &big);
  861. ulp = dlamch_("Epsilon") * dlamch_("Base");
  862. small = safmin * *n / ulp;
  863. big = 1. / small;
  864. bignum = 1. / (safmin * *n);
  865. /* Compute the 1-norm of each column of the strictly upper triangular */
  866. /* part of A and B to check for possible overflow in the triangular */
  867. /* solver. */
  868. i__1 = s_dim1 + 1;
  869. anorm = (d__1 = s[i__1].r, abs(d__1)) + (d__2 = d_imag(&s[s_dim1 + 1]),
  870. abs(d__2));
  871. i__1 = p_dim1 + 1;
  872. bnorm = (d__1 = p[i__1].r, abs(d__1)) + (d__2 = d_imag(&p[p_dim1 + 1]),
  873. abs(d__2));
  874. rwork[1] = 0.;
  875. rwork[*n + 1] = 0.;
  876. i__1 = *n;
  877. for (j = 2; j <= i__1; ++j) {
  878. rwork[j] = 0.;
  879. rwork[*n + j] = 0.;
  880. i__2 = j - 1;
  881. for (i__ = 1; i__ <= i__2; ++i__) {
  882. i__3 = i__ + j * s_dim1;
  883. rwork[j] += (d__1 = s[i__3].r, abs(d__1)) + (d__2 = d_imag(&s[i__
  884. + j * s_dim1]), abs(d__2));
  885. i__3 = i__ + j * p_dim1;
  886. rwork[*n + j] += (d__1 = p[i__3].r, abs(d__1)) + (d__2 = d_imag(&
  887. p[i__ + j * p_dim1]), abs(d__2));
  888. /* L30: */
  889. }
  890. /* Computing MAX */
  891. i__2 = j + j * s_dim1;
  892. d__3 = anorm, d__4 = rwork[j] + ((d__1 = s[i__2].r, abs(d__1)) + (
  893. d__2 = d_imag(&s[j + j * s_dim1]), abs(d__2)));
  894. anorm = f2cmax(d__3,d__4);
  895. /* Computing MAX */
  896. i__2 = j + j * p_dim1;
  897. d__3 = bnorm, d__4 = rwork[*n + j] + ((d__1 = p[i__2].r, abs(d__1)) +
  898. (d__2 = d_imag(&p[j + j * p_dim1]), abs(d__2)));
  899. bnorm = f2cmax(d__3,d__4);
  900. /* L40: */
  901. }
  902. ascale = 1. / f2cmax(anorm,safmin);
  903. bscale = 1. / f2cmax(bnorm,safmin);
  904. /* Left eigenvectors */
  905. if (compl) {
  906. ieig = 0;
  907. /* Main loop over eigenvalues */
  908. i__1 = *n;
  909. for (je = 1; je <= i__1; ++je) {
  910. if (ilall) {
  911. ilcomp = TRUE_;
  912. } else {
  913. ilcomp = select[je];
  914. }
  915. if (ilcomp) {
  916. ++ieig;
  917. i__2 = je + je * s_dim1;
  918. i__3 = je + je * p_dim1;
  919. if ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
  920. * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__3].r,
  921. abs(d__1)) <= safmin) {
  922. /* Singular matrix pencil -- return unit eigenvector */
  923. i__2 = *n;
  924. for (jr = 1; jr <= i__2; ++jr) {
  925. i__3 = jr + ieig * vl_dim1;
  926. vl[i__3].r = 0., vl[i__3].i = 0.;
  927. /* L50: */
  928. }
  929. i__2 = ieig + ieig * vl_dim1;
  930. vl[i__2].r = 1., vl[i__2].i = 0.;
  931. goto L140;
  932. }
  933. /* Non-singular eigenvalue: */
  934. /* Compute coefficients a and b in */
  935. /* H */
  936. /* y ( a A - b B ) = 0 */
  937. /* Computing MAX */
  938. i__2 = je + je * s_dim1;
  939. i__3 = je + je * p_dim1;
  940. d__4 = ((d__2 = s[i__2].r, abs(d__2)) + (d__3 = d_imag(&s[je
  941. + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
  942. p[i__3].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
  943. temp = 1. / f2cmax(d__4,safmin);
  944. i__2 = je + je * s_dim1;
  945. z__2.r = temp * s[i__2].r, z__2.i = temp * s[i__2].i;
  946. z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
  947. salpha.r = z__1.r, salpha.i = z__1.i;
  948. i__2 = je + je * p_dim1;
  949. sbeta = temp * p[i__2].r * bscale;
  950. acoeff = sbeta * ascale;
  951. z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
  952. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  953. /* Scale to avoid underflow */
  954. lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
  955. lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
  956. abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
  957. + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
  958. scale = 1.;
  959. if (lsa) {
  960. scale = small / abs(sbeta) * f2cmin(anorm,big);
  961. }
  962. if (lsb) {
  963. /* Computing MAX */
  964. d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
  965. + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
  966. bnorm,big);
  967. scale = f2cmax(d__3,d__4);
  968. }
  969. if (lsa || lsb) {
  970. /* Computing MIN */
  971. /* Computing MAX */
  972. d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
  973. d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
  974. d_imag(&bcoeff), abs(d__2));
  975. d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
  976. scale = f2cmin(d__3,d__4);
  977. if (lsa) {
  978. acoeff = ascale * (scale * sbeta);
  979. } else {
  980. acoeff = scale * acoeff;
  981. }
  982. if (lsb) {
  983. z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
  984. z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
  985. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  986. } else {
  987. z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
  988. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  989. }
  990. }
  991. acoefa = abs(acoeff);
  992. bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
  993. bcoeff), abs(d__2));
  994. xmax = 1.;
  995. i__2 = *n;
  996. for (jr = 1; jr <= i__2; ++jr) {
  997. i__3 = jr;
  998. work[i__3].r = 0., work[i__3].i = 0.;
  999. /* L60: */
  1000. }
  1001. i__2 = je;
  1002. work[i__2].r = 1., work[i__2].i = 0.;
  1003. /* Computing MAX */
  1004. d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
  1005. d__1 = f2cmax(d__1,d__2);
  1006. dmin__ = f2cmax(d__1,safmin);
  1007. /* H */
  1008. /* Triangular solve of (a A - b B) y = 0 */
  1009. /* H */
  1010. /* (rowwise in (a A - b B) , or columnwise in a A - b B) */
  1011. i__2 = *n;
  1012. for (j = je + 1; j <= i__2; ++j) {
  1013. /* Compute */
  1014. /* j-1 */
  1015. /* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
  1016. /* k=je */
  1017. /* (Scale if necessary) */
  1018. temp = 1. / xmax;
  1019. if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum *
  1020. temp) {
  1021. i__3 = j - 1;
  1022. for (jr = je; jr <= i__3; ++jr) {
  1023. i__4 = jr;
  1024. i__5 = jr;
  1025. z__1.r = temp * work[i__5].r, z__1.i = temp *
  1026. work[i__5].i;
  1027. work[i__4].r = z__1.r, work[i__4].i = z__1.i;
  1028. /* L70: */
  1029. }
  1030. xmax = 1.;
  1031. }
  1032. suma.r = 0., suma.i = 0.;
  1033. sumb.r = 0., sumb.i = 0.;
  1034. i__3 = j - 1;
  1035. for (jr = je; jr <= i__3; ++jr) {
  1036. d_cnjg(&z__3, &s[jr + j * s_dim1]);
  1037. i__4 = jr;
  1038. z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
  1039. .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
  1040. work[i__4].r;
  1041. z__1.r = suma.r + z__2.r, z__1.i = suma.i + z__2.i;
  1042. suma.r = z__1.r, suma.i = z__1.i;
  1043. d_cnjg(&z__3, &p[jr + j * p_dim1]);
  1044. i__4 = jr;
  1045. z__2.r = z__3.r * work[i__4].r - z__3.i * work[i__4]
  1046. .i, z__2.i = z__3.r * work[i__4].i + z__3.i *
  1047. work[i__4].r;
  1048. z__1.r = sumb.r + z__2.r, z__1.i = sumb.i + z__2.i;
  1049. sumb.r = z__1.r, sumb.i = z__1.i;
  1050. /* L80: */
  1051. }
  1052. z__2.r = acoeff * suma.r, z__2.i = acoeff * suma.i;
  1053. d_cnjg(&z__4, &bcoeff);
  1054. z__3.r = z__4.r * sumb.r - z__4.i * sumb.i, z__3.i =
  1055. z__4.r * sumb.i + z__4.i * sumb.r;
  1056. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1057. sum.r = z__1.r, sum.i = z__1.i;
  1058. /* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
  1059. /* with scaling and perturbation of the denominator */
  1060. i__3 = j + j * s_dim1;
  1061. z__3.r = acoeff * s[i__3].r, z__3.i = acoeff * s[i__3].i;
  1062. i__4 = j + j * p_dim1;
  1063. z__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
  1064. z__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
  1065. .r;
  1066. z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
  1067. d_cnjg(&z__1, &z__2);
  1068. d__.r = z__1.r, d__.i = z__1.i;
  1069. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1070. d__2)) <= dmin__) {
  1071. z__1.r = dmin__, z__1.i = 0.;
  1072. d__.r = z__1.r, d__.i = z__1.i;
  1073. }
  1074. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1075. d__2)) < 1.) {
  1076. if ((d__1 = sum.r, abs(d__1)) + (d__2 = d_imag(&sum),
  1077. abs(d__2)) >= bignum * ((d__3 = d__.r, abs(
  1078. d__3)) + (d__4 = d_imag(&d__), abs(d__4)))) {
  1079. temp = 1. / ((d__1 = sum.r, abs(d__1)) + (d__2 =
  1080. d_imag(&sum), abs(d__2)));
  1081. i__3 = j - 1;
  1082. for (jr = je; jr <= i__3; ++jr) {
  1083. i__4 = jr;
  1084. i__5 = jr;
  1085. z__1.r = temp * work[i__5].r, z__1.i = temp *
  1086. work[i__5].i;
  1087. work[i__4].r = z__1.r, work[i__4].i = z__1.i;
  1088. /* L90: */
  1089. }
  1090. xmax = temp * xmax;
  1091. z__1.r = temp * sum.r, z__1.i = temp * sum.i;
  1092. sum.r = z__1.r, sum.i = z__1.i;
  1093. }
  1094. }
  1095. i__3 = j;
  1096. z__2.r = -sum.r, z__2.i = -sum.i;
  1097. zladiv_(&z__1, &z__2, &d__);
  1098. work[i__3].r = z__1.r, work[i__3].i = z__1.i;
  1099. /* Computing MAX */
  1100. i__3 = j;
  1101. d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
  1102. d__2 = d_imag(&work[j]), abs(d__2));
  1103. xmax = f2cmax(d__3,d__4);
  1104. /* L100: */
  1105. }
  1106. /* Back transform eigenvector if HOWMNY='B'. */
  1107. if (ilback) {
  1108. i__2 = *n + 1 - je;
  1109. zgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl,
  1110. &work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
  1111. isrc = 2;
  1112. ibeg = 1;
  1113. } else {
  1114. isrc = 1;
  1115. ibeg = je;
  1116. }
  1117. /* Copy and scale eigenvector into column of VL */
  1118. xmax = 0.;
  1119. i__2 = *n;
  1120. for (jr = ibeg; jr <= i__2; ++jr) {
  1121. /* Computing MAX */
  1122. i__3 = (isrc - 1) * *n + jr;
  1123. d__3 = xmax, d__4 = (d__1 = work[i__3].r, abs(d__1)) + (
  1124. d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
  1125. d__2));
  1126. xmax = f2cmax(d__3,d__4);
  1127. /* L110: */
  1128. }
  1129. if (xmax > safmin) {
  1130. temp = 1. / xmax;
  1131. i__2 = *n;
  1132. for (jr = ibeg; jr <= i__2; ++jr) {
  1133. i__3 = jr + ieig * vl_dim1;
  1134. i__4 = (isrc - 1) * *n + jr;
  1135. z__1.r = temp * work[i__4].r, z__1.i = temp * work[
  1136. i__4].i;
  1137. vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
  1138. /* L120: */
  1139. }
  1140. } else {
  1141. ibeg = *n + 1;
  1142. }
  1143. i__2 = ibeg - 1;
  1144. for (jr = 1; jr <= i__2; ++jr) {
  1145. i__3 = jr + ieig * vl_dim1;
  1146. vl[i__3].r = 0., vl[i__3].i = 0.;
  1147. /* L130: */
  1148. }
  1149. }
  1150. L140:
  1151. ;
  1152. }
  1153. }
  1154. /* Right eigenvectors */
  1155. if (compr) {
  1156. ieig = im + 1;
  1157. /* Main loop over eigenvalues */
  1158. for (je = *n; je >= 1; --je) {
  1159. if (ilall) {
  1160. ilcomp = TRUE_;
  1161. } else {
  1162. ilcomp = select[je];
  1163. }
  1164. if (ilcomp) {
  1165. --ieig;
  1166. i__1 = je + je * s_dim1;
  1167. i__2 = je + je * p_dim1;
  1168. if ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je + je
  1169. * s_dim1]), abs(d__3)) <= safmin && (d__1 = p[i__2].r,
  1170. abs(d__1)) <= safmin) {
  1171. /* Singular matrix pencil -- return unit eigenvector */
  1172. i__1 = *n;
  1173. for (jr = 1; jr <= i__1; ++jr) {
  1174. i__2 = jr + ieig * vr_dim1;
  1175. vr[i__2].r = 0., vr[i__2].i = 0.;
  1176. /* L150: */
  1177. }
  1178. i__1 = ieig + ieig * vr_dim1;
  1179. vr[i__1].r = 1., vr[i__1].i = 0.;
  1180. goto L250;
  1181. }
  1182. /* Non-singular eigenvalue: */
  1183. /* Compute coefficients a and b in */
  1184. /* ( a A - b B ) x = 0 */
  1185. /* Computing MAX */
  1186. i__1 = je + je * s_dim1;
  1187. i__2 = je + je * p_dim1;
  1188. d__4 = ((d__2 = s[i__1].r, abs(d__2)) + (d__3 = d_imag(&s[je
  1189. + je * s_dim1]), abs(d__3))) * ascale, d__5 = (d__1 =
  1190. p[i__2].r, abs(d__1)) * bscale, d__4 = f2cmax(d__4,d__5);
  1191. temp = 1. / f2cmax(d__4,safmin);
  1192. i__1 = je + je * s_dim1;
  1193. z__2.r = temp * s[i__1].r, z__2.i = temp * s[i__1].i;
  1194. z__1.r = ascale * z__2.r, z__1.i = ascale * z__2.i;
  1195. salpha.r = z__1.r, salpha.i = z__1.i;
  1196. i__1 = je + je * p_dim1;
  1197. sbeta = temp * p[i__1].r * bscale;
  1198. acoeff = sbeta * ascale;
  1199. z__1.r = bscale * salpha.r, z__1.i = bscale * salpha.i;
  1200. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1201. /* Scale to avoid underflow */
  1202. lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
  1203. lsb = (d__1 = salpha.r, abs(d__1)) + (d__2 = d_imag(&salpha),
  1204. abs(d__2)) >= safmin && (d__3 = bcoeff.r, abs(d__3))
  1205. + (d__4 = d_imag(&bcoeff), abs(d__4)) < small;
  1206. scale = 1.;
  1207. if (lsa) {
  1208. scale = small / abs(sbeta) * f2cmin(anorm,big);
  1209. }
  1210. if (lsb) {
  1211. /* Computing MAX */
  1212. d__3 = scale, d__4 = small / ((d__1 = salpha.r, abs(d__1))
  1213. + (d__2 = d_imag(&salpha), abs(d__2))) * f2cmin(
  1214. bnorm,big);
  1215. scale = f2cmax(d__3,d__4);
  1216. }
  1217. if (lsa || lsb) {
  1218. /* Computing MIN */
  1219. /* Computing MAX */
  1220. d__5 = 1., d__6 = abs(acoeff), d__5 = f2cmax(d__5,d__6),
  1221. d__6 = (d__1 = bcoeff.r, abs(d__1)) + (d__2 =
  1222. d_imag(&bcoeff), abs(d__2));
  1223. d__3 = scale, d__4 = 1. / (safmin * f2cmax(d__5,d__6));
  1224. scale = f2cmin(d__3,d__4);
  1225. if (lsa) {
  1226. acoeff = ascale * (scale * sbeta);
  1227. } else {
  1228. acoeff = scale * acoeff;
  1229. }
  1230. if (lsb) {
  1231. z__2.r = scale * salpha.r, z__2.i = scale * salpha.i;
  1232. z__1.r = bscale * z__2.r, z__1.i = bscale * z__2.i;
  1233. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1234. } else {
  1235. z__1.r = scale * bcoeff.r, z__1.i = scale * bcoeff.i;
  1236. bcoeff.r = z__1.r, bcoeff.i = z__1.i;
  1237. }
  1238. }
  1239. acoefa = abs(acoeff);
  1240. bcoefa = (d__1 = bcoeff.r, abs(d__1)) + (d__2 = d_imag(&
  1241. bcoeff), abs(d__2));
  1242. xmax = 1.;
  1243. i__1 = *n;
  1244. for (jr = 1; jr <= i__1; ++jr) {
  1245. i__2 = jr;
  1246. work[i__2].r = 0., work[i__2].i = 0.;
  1247. /* L160: */
  1248. }
  1249. i__1 = je;
  1250. work[i__1].r = 1., work[i__1].i = 0.;
  1251. /* Computing MAX */
  1252. d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm,
  1253. d__1 = f2cmax(d__1,d__2);
  1254. dmin__ = f2cmax(d__1,safmin);
  1255. /* Triangular solve of (a A - b B) x = 0 (columnwise) */
  1256. /* WORK(1:j-1) contains sums w, */
  1257. /* WORK(j+1:JE) contains x */
  1258. i__1 = je - 1;
  1259. for (jr = 1; jr <= i__1; ++jr) {
  1260. i__2 = jr;
  1261. i__3 = jr + je * s_dim1;
  1262. z__2.r = acoeff * s[i__3].r, z__2.i = acoeff * s[i__3].i;
  1263. i__4 = jr + je * p_dim1;
  1264. z__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
  1265. z__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
  1266. .r;
  1267. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1268. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1269. /* L170: */
  1270. }
  1271. i__1 = je;
  1272. work[i__1].r = 1., work[i__1].i = 0.;
  1273. for (j = je - 1; j >= 1; --j) {
  1274. /* Form x(j) := - w(j) / d */
  1275. /* with scaling and perturbation of the denominator */
  1276. i__1 = j + j * s_dim1;
  1277. z__2.r = acoeff * s[i__1].r, z__2.i = acoeff * s[i__1].i;
  1278. i__2 = j + j * p_dim1;
  1279. z__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i,
  1280. z__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
  1281. .r;
  1282. z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
  1283. d__.r = z__1.r, d__.i = z__1.i;
  1284. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1285. d__2)) <= dmin__) {
  1286. z__1.r = dmin__, z__1.i = 0.;
  1287. d__.r = z__1.r, d__.i = z__1.i;
  1288. }
  1289. if ((d__1 = d__.r, abs(d__1)) + (d__2 = d_imag(&d__), abs(
  1290. d__2)) < 1.) {
  1291. i__1 = j;
  1292. if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
  1293. &work[j]), abs(d__2)) >= bignum * ((d__3 =
  1294. d__.r, abs(d__3)) + (d__4 = d_imag(&d__), abs(
  1295. d__4)))) {
  1296. i__1 = j;
  1297. temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
  1298. d__2 = d_imag(&work[j]), abs(d__2)));
  1299. i__1 = je;
  1300. for (jr = 1; jr <= i__1; ++jr) {
  1301. i__2 = jr;
  1302. i__3 = jr;
  1303. z__1.r = temp * work[i__3].r, z__1.i = temp *
  1304. work[i__3].i;
  1305. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1306. /* L180: */
  1307. }
  1308. }
  1309. }
  1310. i__1 = j;
  1311. i__2 = j;
  1312. z__2.r = -work[i__2].r, z__2.i = -work[i__2].i;
  1313. zladiv_(&z__1, &z__2, &d__);
  1314. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1315. if (j > 1) {
  1316. /* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
  1317. i__1 = j;
  1318. if ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(
  1319. &work[j]), abs(d__2)) > 1.) {
  1320. i__1 = j;
  1321. temp = 1. / ((d__1 = work[i__1].r, abs(d__1)) + (
  1322. d__2 = d_imag(&work[j]), abs(d__2)));
  1323. if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >=
  1324. bignum * temp) {
  1325. i__1 = je;
  1326. for (jr = 1; jr <= i__1; ++jr) {
  1327. i__2 = jr;
  1328. i__3 = jr;
  1329. z__1.r = temp * work[i__3].r, z__1.i =
  1330. temp * work[i__3].i;
  1331. work[i__2].r = z__1.r, work[i__2].i =
  1332. z__1.i;
  1333. /* L190: */
  1334. }
  1335. }
  1336. }
  1337. i__1 = j;
  1338. z__1.r = acoeff * work[i__1].r, z__1.i = acoeff *
  1339. work[i__1].i;
  1340. ca.r = z__1.r, ca.i = z__1.i;
  1341. i__1 = j;
  1342. z__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
  1343. i__1].i, z__1.i = bcoeff.r * work[i__1].i +
  1344. bcoeff.i * work[i__1].r;
  1345. cb.r = z__1.r, cb.i = z__1.i;
  1346. i__1 = j - 1;
  1347. for (jr = 1; jr <= i__1; ++jr) {
  1348. i__2 = jr;
  1349. i__3 = jr;
  1350. i__4 = jr + j * s_dim1;
  1351. z__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i,
  1352. z__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
  1353. .r;
  1354. z__2.r = work[i__3].r + z__3.r, z__2.i = work[
  1355. i__3].i + z__3.i;
  1356. i__5 = jr + j * p_dim1;
  1357. z__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i,
  1358. z__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
  1359. .r;
  1360. z__1.r = z__2.r - z__4.r, z__1.i = z__2.i -
  1361. z__4.i;
  1362. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1363. /* L200: */
  1364. }
  1365. }
  1366. /* L210: */
  1367. }
  1368. /* Back transform eigenvector if HOWMNY='B'. */
  1369. if (ilback) {
  1370. zgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
  1371. &c__1, &c_b1, &work[*n + 1], &c__1);
  1372. isrc = 2;
  1373. iend = *n;
  1374. } else {
  1375. isrc = 1;
  1376. iend = je;
  1377. }
  1378. /* Copy and scale eigenvector into column of VR */
  1379. xmax = 0.;
  1380. i__1 = iend;
  1381. for (jr = 1; jr <= i__1; ++jr) {
  1382. /* Computing MAX */
  1383. i__2 = (isrc - 1) * *n + jr;
  1384. d__3 = xmax, d__4 = (d__1 = work[i__2].r, abs(d__1)) + (
  1385. d__2 = d_imag(&work[(isrc - 1) * *n + jr]), abs(
  1386. d__2));
  1387. xmax = f2cmax(d__3,d__4);
  1388. /* L220: */
  1389. }
  1390. if (xmax > safmin) {
  1391. temp = 1. / xmax;
  1392. i__1 = iend;
  1393. for (jr = 1; jr <= i__1; ++jr) {
  1394. i__2 = jr + ieig * vr_dim1;
  1395. i__3 = (isrc - 1) * *n + jr;
  1396. z__1.r = temp * work[i__3].r, z__1.i = temp * work[
  1397. i__3].i;
  1398. vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
  1399. /* L230: */
  1400. }
  1401. } else {
  1402. iend = 0;
  1403. }
  1404. i__1 = *n;
  1405. for (jr = iend + 1; jr <= i__1; ++jr) {
  1406. i__2 = jr + ieig * vr_dim1;
  1407. vr[i__2].r = 0., vr[i__2].i = 0.;
  1408. /* L240: */
  1409. }
  1410. }
  1411. L250:
  1412. ;
  1413. }
  1414. }
  1415. return 0;
  1416. /* End of ZTGEVC */
  1417. } /* ztgevc_ */