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sstebz.c 38 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]/df(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 integer c__1 = 1;
  487. static integer c_n1 = -1;
  488. static integer c__3 = 3;
  489. static integer c__2 = 2;
  490. static integer c__0 = 0;
  491. /* > \brief \b SSTEBZ */
  492. /* =========== DOCUMENTATION =========== */
  493. /* Online html documentation available at */
  494. /* http://www.netlib.org/lapack/explore-html/ */
  495. /* > \htmlonly */
  496. /* > Download SSTEBZ + dependencies */
  497. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstebz.
  498. f"> */
  499. /* > [TGZ]</a> */
  500. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstebz.
  501. f"> */
  502. /* > [ZIP]</a> */
  503. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstebz.
  504. f"> */
  505. /* > [TXT]</a> */
  506. /* > \endhtmlonly */
  507. /* Definition: */
  508. /* =========== */
  509. /* SUBROUTINE SSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, */
  510. /* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, */
  511. /* INFO ) */
  512. /* CHARACTER ORDER, RANGE */
  513. /* INTEGER IL, INFO, IU, M, N, NSPLIT */
  514. /* REAL ABSTOL, VL, VU */
  515. /* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) */
  516. /* REAL D( * ), E( * ), W( * ), WORK( * ) */
  517. /* > \par Purpose: */
  518. /* ============= */
  519. /* > */
  520. /* > \verbatim */
  521. /* > */
  522. /* > SSTEBZ computes the eigenvalues of a symmetric tridiagonal */
  523. /* > matrix T. The user may ask for all eigenvalues, all eigenvalues */
  524. /* > in the half-open interval (VL, VU], or the IL-th through IU-th */
  525. /* > eigenvalues. */
  526. /* > */
  527. /* > To avoid overflow, the matrix must be scaled so that its */
  528. /* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
  529. */
  530. /* > accuracy, it should not be much smaller than that. */
  531. /* > */
  532. /* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
  533. /* > Matrix", Report CS41, Computer Science Dept., Stanford */
  534. /* > University, July 21, 1966. */
  535. /* > \endverbatim */
  536. /* Arguments: */
  537. /* ========== */
  538. /* > \param[in] RANGE */
  539. /* > \verbatim */
  540. /* > RANGE is CHARACTER*1 */
  541. /* > = 'A': ("All") all eigenvalues will be found. */
  542. /* > = 'V': ("Value") all eigenvalues in the half-open interval */
  543. /* > (VL, VU] will be found. */
  544. /* > = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
  545. /* > entire matrix) will be found. */
  546. /* > \endverbatim */
  547. /* > */
  548. /* > \param[in] ORDER */
  549. /* > \verbatim */
  550. /* > ORDER is CHARACTER*1 */
  551. /* > = 'B': ("By Block") the eigenvalues will be grouped by */
  552. /* > split-off block (see IBLOCK, ISPLIT) and */
  553. /* > ordered from smallest to largest within */
  554. /* > the block. */
  555. /* > = 'E': ("Entire matrix") */
  556. /* > the eigenvalues for the entire matrix */
  557. /* > will be ordered from smallest to */
  558. /* > largest. */
  559. /* > \endverbatim */
  560. /* > */
  561. /* > \param[in] N */
  562. /* > \verbatim */
  563. /* > N is INTEGER */
  564. /* > The order of the tridiagonal matrix T. N >= 0. */
  565. /* > \endverbatim */
  566. /* > */
  567. /* > \param[in] VL */
  568. /* > \verbatim */
  569. /* > VL is REAL */
  570. /* > */
  571. /* > If RANGE='V', the lower bound of the interval to */
  572. /* > be searched for eigenvalues. Eigenvalues less than or equal */
  573. /* > to VL, or greater than VU, will not be returned. VL < VU. */
  574. /* > Not referenced if RANGE = 'A' or 'I'. */
  575. /* > \endverbatim */
  576. /* > */
  577. /* > \param[in] VU */
  578. /* > \verbatim */
  579. /* > VU is REAL */
  580. /* > */
  581. /* > If RANGE='V', the upper bound of the interval to */
  582. /* > be searched for eigenvalues. Eigenvalues less than or equal */
  583. /* > to VL, or greater than VU, will not be returned. VL < VU. */
  584. /* > Not referenced if RANGE = 'A' or 'I'. */
  585. /* > \endverbatim */
  586. /* > */
  587. /* > \param[in] IL */
  588. /* > \verbatim */
  589. /* > IL is INTEGER */
  590. /* > */
  591. /* > If RANGE='I', the index of the */
  592. /* > smallest eigenvalue to be returned. */
  593. /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  594. /* > Not referenced if RANGE = 'A' or 'V'. */
  595. /* > \endverbatim */
  596. /* > */
  597. /* > \param[in] IU */
  598. /* > \verbatim */
  599. /* > IU is INTEGER */
  600. /* > */
  601. /* > If RANGE='I', the index of the */
  602. /* > largest eigenvalue to be returned. */
  603. /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  604. /* > Not referenced if RANGE = 'A' or 'V'. */
  605. /* > \endverbatim */
  606. /* > */
  607. /* > \param[in] ABSTOL */
  608. /* > \verbatim */
  609. /* > ABSTOL is REAL */
  610. /* > The absolute tolerance for the eigenvalues. An eigenvalue */
  611. /* > (or cluster) is considered to be located if it has been */
  612. /* > determined to lie in an interval whose width is ABSTOL or */
  613. /* > less. If ABSTOL is less than or equal to zero, then ULP*|T| */
  614. /* > will be used, where |T| means the 1-norm of T. */
  615. /* > */
  616. /* > Eigenvalues will be computed most accurately when ABSTOL is */
  617. /* > set to twice the underflow threshold 2*SLAMCH('S'), not zero. */
  618. /* > \endverbatim */
  619. /* > */
  620. /* > \param[in] D */
  621. /* > \verbatim */
  622. /* > D is REAL array, dimension (N) */
  623. /* > The n diagonal elements of the tridiagonal matrix T. */
  624. /* > \endverbatim */
  625. /* > */
  626. /* > \param[in] E */
  627. /* > \verbatim */
  628. /* > E is REAL array, dimension (N-1) */
  629. /* > The (n-1) off-diagonal elements of the tridiagonal matrix T. */
  630. /* > \endverbatim */
  631. /* > */
  632. /* > \param[out] M */
  633. /* > \verbatim */
  634. /* > M is INTEGER */
  635. /* > The actual number of eigenvalues found. 0 <= M <= N. */
  636. /* > (See also the description of INFO=2,3.) */
  637. /* > \endverbatim */
  638. /* > */
  639. /* > \param[out] NSPLIT */
  640. /* > \verbatim */
  641. /* > NSPLIT is INTEGER */
  642. /* > The number of diagonal blocks in the matrix T. */
  643. /* > 1 <= NSPLIT <= N. */
  644. /* > \endverbatim */
  645. /* > */
  646. /* > \param[out] W */
  647. /* > \verbatim */
  648. /* > W is REAL array, dimension (N) */
  649. /* > On exit, the first M elements of W will contain the */
  650. /* > eigenvalues. (SSTEBZ may use the remaining N-M elements as */
  651. /* > workspace.) */
  652. /* > \endverbatim */
  653. /* > */
  654. /* > \param[out] IBLOCK */
  655. /* > \verbatim */
  656. /* > IBLOCK is INTEGER array, dimension (N) */
  657. /* > At each row/column j where E(j) is zero or small, the */
  658. /* > matrix T is considered to split into a block diagonal */
  659. /* > matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
  660. /* > block (from 1 to the number of blocks) the eigenvalue W(i) */
  661. /* > belongs. (SSTEBZ may use the remaining N-M elements as */
  662. /* > workspace.) */
  663. /* > \endverbatim */
  664. /* > */
  665. /* > \param[out] ISPLIT */
  666. /* > \verbatim */
  667. /* > ISPLIT is INTEGER array, dimension (N) */
  668. /* > The splitting points, at which T breaks up into submatrices. */
  669. /* > The first submatrix consists of rows/columns 1 to ISPLIT(1), */
  670. /* > the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
  671. /* > etc., and the NSPLIT-th consists of rows/columns */
  672. /* > ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
  673. /* > (Only the first NSPLIT elements will actually be used, but */
  674. /* > since the user cannot know a priori what value NSPLIT will */
  675. /* > have, N words must be reserved for ISPLIT.) */
  676. /* > \endverbatim */
  677. /* > */
  678. /* > \param[out] WORK */
  679. /* > \verbatim */
  680. /* > WORK is REAL array, dimension (4*N) */
  681. /* > \endverbatim */
  682. /* > */
  683. /* > \param[out] IWORK */
  684. /* > \verbatim */
  685. /* > IWORK is INTEGER array, dimension (3*N) */
  686. /* > \endverbatim */
  687. /* > */
  688. /* > \param[out] INFO */
  689. /* > \verbatim */
  690. /* > INFO is INTEGER */
  691. /* > = 0: successful exit */
  692. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  693. /* > > 0: some or all of the eigenvalues failed to converge or */
  694. /* > were not computed: */
  695. /* > =1 or 3: Bisection failed to converge for some */
  696. /* > eigenvalues; these eigenvalues are flagged by a */
  697. /* > negative block number. The effect is that the */
  698. /* > eigenvalues may not be as accurate as the */
  699. /* > absolute and relative tolerances. This is */
  700. /* > generally caused by unexpectedly inaccurate */
  701. /* > arithmetic. */
  702. /* > =2 or 3: RANGE='I' only: Not all of the eigenvalues */
  703. /* > IL:IU were found. */
  704. /* > Effect: M < IU+1-IL */
  705. /* > Cause: non-monotonic arithmetic, causing the */
  706. /* > Sturm sequence to be non-monotonic. */
  707. /* > Cure: recalculate, using RANGE='A', and pick */
  708. /* > out eigenvalues IL:IU. In some cases, */
  709. /* > increasing the PARAMETER "FUDGE" may */
  710. /* > make things work. */
  711. /* > = 4: RANGE='I', and the Gershgorin interval */
  712. /* > initially used was too small. No eigenvalues */
  713. /* > were computed. */
  714. /* > Probable cause: your machine has sloppy */
  715. /* > floating-point arithmetic. */
  716. /* > Cure: Increase the PARAMETER "FUDGE", */
  717. /* > recompile, and try again. */
  718. /* > \endverbatim */
  719. /* > \par Internal Parameters: */
  720. /* ========================= */
  721. /* > */
  722. /* > \verbatim */
  723. /* > RELFAC REAL, default = 2.0e0 */
  724. /* > The relative tolerance. An interval (a,b] lies within */
  725. /* > "relative tolerance" if b-a < RELFAC*ulp*f2cmax(|a|,|b|), */
  726. /* > where "ulp" is the machine precision (distance from 1 to */
  727. /* > the next larger floating point number.) */
  728. /* > */
  729. /* > FUDGE REAL, default = 2 */
  730. /* > A "fudge factor" to widen the Gershgorin intervals. Ideally, */
  731. /* > a value of 1 should work, but on machines with sloppy */
  732. /* > arithmetic, this needs to be larger. The default for */
  733. /* > publicly released versions should be large enough to handle */
  734. /* > the worst machine around. Note that this has no effect */
  735. /* > on accuracy of the solution. */
  736. /* > \endverbatim */
  737. /* Authors: */
  738. /* ======== */
  739. /* > \author Univ. of Tennessee */
  740. /* > \author Univ. of California Berkeley */
  741. /* > \author Univ. of Colorado Denver */
  742. /* > \author NAG Ltd. */
  743. /* > \date June 2016 */
  744. /* > \ingroup auxOTHERcomputational */
  745. /* ===================================================================== */
  746. /* Subroutine */ void sstebz_(char *range, char *order, integer *n, real *vl,
  747. real *vu, integer *il, integer *iu, real *abstol, real *d__, real *e,
  748. integer *m, integer *nsplit, real *w, integer *iblock, integer *
  749. isplit, real *work, integer *iwork, integer *info)
  750. {
  751. /* System generated locals */
  752. integer i__1, i__2, i__3;
  753. real r__1, r__2, r__3, r__4, r__5;
  754. /* Local variables */
  755. integer iend, ioff, iout, itmp1, j, jdisc;
  756. extern logical lsame_(char *, char *);
  757. integer iinfo;
  758. real atoli;
  759. integer iwoff;
  760. real bnorm;
  761. integer itmax;
  762. real wkill, rtoli, tnorm;
  763. integer ib, jb, ie, je, nb;
  764. real gl;
  765. integer im, in, ibegin;
  766. real gu;
  767. integer iw;
  768. real wl;
  769. integer irange, idiscl;
  770. extern real slamch_(char *);
  771. real safemn, wu;
  772. integer idumma[1];
  773. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  774. integer *, integer *, ftnlen, ftnlen);
  775. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  776. integer idiscu;
  777. extern /* Subroutine */ void slaebz_(integer *, integer *, integer *,
  778. integer *, integer *, integer *, real *, real *, real *, real *,
  779. real *, real *, integer *, real *, real *, integer *, integer *,
  780. real *, integer *, integer *);
  781. integer iorder;
  782. logical ncnvrg;
  783. real pivmin;
  784. logical toofew;
  785. integer nwl;
  786. real ulp, wlu, wul;
  787. integer nwu;
  788. real tmp1, tmp2;
  789. /* -- LAPACK computational routine (version 3.7.0) -- */
  790. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  791. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  792. /* June 2016 */
  793. /* ===================================================================== */
  794. /* Parameter adjustments */
  795. --iwork;
  796. --work;
  797. --isplit;
  798. --iblock;
  799. --w;
  800. --e;
  801. --d__;
  802. /* Function Body */
  803. *info = 0;
  804. /* Decode RANGE */
  805. if (lsame_(range, "A")) {
  806. irange = 1;
  807. } else if (lsame_(range, "V")) {
  808. irange = 2;
  809. } else if (lsame_(range, "I")) {
  810. irange = 3;
  811. } else {
  812. irange = 0;
  813. }
  814. /* Decode ORDER */
  815. if (lsame_(order, "B")) {
  816. iorder = 2;
  817. } else if (lsame_(order, "E")) {
  818. iorder = 1;
  819. } else {
  820. iorder = 0;
  821. }
  822. /* Check for Errors */
  823. if (irange <= 0) {
  824. *info = -1;
  825. } else if (iorder <= 0) {
  826. *info = -2;
  827. } else if (*n < 0) {
  828. *info = -3;
  829. } else if (irange == 2) {
  830. if (*vl >= *vu) {
  831. *info = -5;
  832. }
  833. } else if (irange == 3 && (*il < 1 || *il > f2cmax(1,*n))) {
  834. *info = -6;
  835. } else if (irange == 3 && (*iu < f2cmin(*n,*il) || *iu > *n)) {
  836. *info = -7;
  837. }
  838. if (*info != 0) {
  839. i__1 = -(*info);
  840. xerbla_("SSTEBZ", &i__1, (ftnlen)6);
  841. return;
  842. }
  843. /* Initialize error flags */
  844. *info = 0;
  845. ncnvrg = FALSE_;
  846. toofew = FALSE_;
  847. /* Quick return if possible */
  848. *m = 0;
  849. if (*n == 0) {
  850. return;
  851. }
  852. /* Simplifications: */
  853. if (irange == 3 && *il == 1 && *iu == *n) {
  854. irange = 1;
  855. }
  856. /* Get machine constants */
  857. /* NB is the minimum vector length for vector bisection, or 0 */
  858. /* if only scalar is to be done. */
  859. safemn = slamch_("S");
  860. ulp = slamch_("P");
  861. rtoli = ulp * 2.f;
  862. nb = ilaenv_(&c__1, "SSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
  863. ftnlen)1);
  864. if (nb <= 1) {
  865. nb = 0;
  866. }
  867. /* Special Case when N=1 */
  868. if (*n == 1) {
  869. *nsplit = 1;
  870. isplit[1] = 1;
  871. if (irange == 2 && (*vl >= d__[1] || *vu < d__[1])) {
  872. *m = 0;
  873. } else {
  874. w[1] = d__[1];
  875. iblock[1] = 1;
  876. *m = 1;
  877. }
  878. return;
  879. }
  880. /* Compute Splitting Points */
  881. *nsplit = 1;
  882. work[*n] = 0.f;
  883. pivmin = 1.f;
  884. i__1 = *n;
  885. for (j = 2; j <= i__1; ++j) {
  886. /* Computing 2nd power */
  887. r__1 = e[j - 1];
  888. tmp1 = r__1 * r__1;
  889. /* Computing 2nd power */
  890. r__2 = ulp;
  891. if ((r__1 = d__[j] * d__[j - 1], abs(r__1)) * (r__2 * r__2) + safemn
  892. > tmp1) {
  893. isplit[*nsplit] = j - 1;
  894. ++(*nsplit);
  895. work[j - 1] = 0.f;
  896. } else {
  897. work[j - 1] = tmp1;
  898. pivmin = f2cmax(pivmin,tmp1);
  899. }
  900. /* L10: */
  901. }
  902. isplit[*nsplit] = *n;
  903. pivmin *= safemn;
  904. /* Compute Interval and ATOLI */
  905. if (irange == 3) {
  906. /* RANGE='I': Compute the interval containing eigenvalues */
  907. /* IL through IU. */
  908. /* Compute Gershgorin interval for entire (split) matrix */
  909. /* and use it as the initial interval */
  910. gu = d__[1];
  911. gl = d__[1];
  912. tmp1 = 0.f;
  913. i__1 = *n - 1;
  914. for (j = 1; j <= i__1; ++j) {
  915. tmp2 = sqrt(work[j]);
  916. /* Computing MAX */
  917. r__1 = gu, r__2 = d__[j] + tmp1 + tmp2;
  918. gu = f2cmax(r__1,r__2);
  919. /* Computing MIN */
  920. r__1 = gl, r__2 = d__[j] - tmp1 - tmp2;
  921. gl = f2cmin(r__1,r__2);
  922. tmp1 = tmp2;
  923. /* L20: */
  924. }
  925. /* Computing MAX */
  926. r__1 = gu, r__2 = d__[*n] + tmp1;
  927. gu = f2cmax(r__1,r__2);
  928. /* Computing MIN */
  929. r__1 = gl, r__2 = d__[*n] - tmp1;
  930. gl = f2cmin(r__1,r__2);
  931. /* Computing MAX */
  932. r__1 = abs(gl), r__2 = abs(gu);
  933. tnorm = f2cmax(r__1,r__2);
  934. gl = gl - tnorm * 2.1f * ulp * *n - pivmin * 4.2000000000000002f;
  935. gu = gu + tnorm * 2.1f * ulp * *n + pivmin * 2.1f;
  936. /* Compute Iteration parameters */
  937. itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.f)) +
  938. 2;
  939. if (*abstol <= 0.f) {
  940. atoli = ulp * tnorm;
  941. } else {
  942. atoli = *abstol;
  943. }
  944. work[*n + 1] = gl;
  945. work[*n + 2] = gl;
  946. work[*n + 3] = gu;
  947. work[*n + 4] = gu;
  948. work[*n + 5] = gl;
  949. work[*n + 6] = gu;
  950. iwork[1] = -1;
  951. iwork[2] = -1;
  952. iwork[3] = *n + 1;
  953. iwork[4] = *n + 1;
  954. iwork[5] = *il - 1;
  955. iwork[6] = *iu;
  956. slaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
  957. &d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
  958. + 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
  959. if (iwork[6] == *iu) {
  960. wl = work[*n + 1];
  961. wlu = work[*n + 3];
  962. nwl = iwork[1];
  963. wu = work[*n + 4];
  964. wul = work[*n + 2];
  965. nwu = iwork[4];
  966. } else {
  967. wl = work[*n + 2];
  968. wlu = work[*n + 4];
  969. nwl = iwork[2];
  970. wu = work[*n + 3];
  971. wul = work[*n + 1];
  972. nwu = iwork[3];
  973. }
  974. if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
  975. *info = 4;
  976. return;
  977. }
  978. } else {
  979. /* RANGE='A' or 'V' -- Set ATOLI */
  980. /* Computing MAX */
  981. r__3 = abs(d__[1]) + abs(e[1]), r__4 = (r__1 = d__[*n], abs(r__1)) + (
  982. r__2 = e[*n - 1], abs(r__2));
  983. tnorm = f2cmax(r__3,r__4);
  984. i__1 = *n - 1;
  985. for (j = 2; j <= i__1; ++j) {
  986. /* Computing MAX */
  987. r__4 = tnorm, r__5 = (r__1 = d__[j], abs(r__1)) + (r__2 = e[j - 1]
  988. , abs(r__2)) + (r__3 = e[j], abs(r__3));
  989. tnorm = f2cmax(r__4,r__5);
  990. /* L30: */
  991. }
  992. if (*abstol <= 0.f) {
  993. atoli = ulp * tnorm;
  994. } else {
  995. atoli = *abstol;
  996. }
  997. if (irange == 2) {
  998. wl = *vl;
  999. wu = *vu;
  1000. } else {
  1001. wl = 0.f;
  1002. wu = 0.f;
  1003. }
  1004. }
  1005. /* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. */
  1006. /* NWL accumulates the number of eigenvalues .le. WL, */
  1007. /* NWU accumulates the number of eigenvalues .le. WU */
  1008. *m = 0;
  1009. iend = 0;
  1010. *info = 0;
  1011. nwl = 0;
  1012. nwu = 0;
  1013. i__1 = *nsplit;
  1014. for (jb = 1; jb <= i__1; ++jb) {
  1015. ioff = iend;
  1016. ibegin = ioff + 1;
  1017. iend = isplit[jb];
  1018. in = iend - ioff;
  1019. if (in == 1) {
  1020. /* Special Case -- IN=1 */
  1021. if (irange == 1 || wl >= d__[ibegin] - pivmin) {
  1022. ++nwl;
  1023. }
  1024. if (irange == 1 || wu >= d__[ibegin] - pivmin) {
  1025. ++nwu;
  1026. }
  1027. if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
  1028. - pivmin) {
  1029. ++(*m);
  1030. w[*m] = d__[ibegin];
  1031. iblock[*m] = jb;
  1032. }
  1033. } else {
  1034. /* General Case -- IN > 1 */
  1035. /* Compute Gershgorin Interval */
  1036. /* and use it as the initial interval */
  1037. gu = d__[ibegin];
  1038. gl = d__[ibegin];
  1039. tmp1 = 0.f;
  1040. i__2 = iend - 1;
  1041. for (j = ibegin; j <= i__2; ++j) {
  1042. tmp2 = (r__1 = e[j], abs(r__1));
  1043. /* Computing MAX */
  1044. r__1 = gu, r__2 = d__[j] + tmp1 + tmp2;
  1045. gu = f2cmax(r__1,r__2);
  1046. /* Computing MIN */
  1047. r__1 = gl, r__2 = d__[j] - tmp1 - tmp2;
  1048. gl = f2cmin(r__1,r__2);
  1049. tmp1 = tmp2;
  1050. /* L40: */
  1051. }
  1052. /* Computing MAX */
  1053. r__1 = gu, r__2 = d__[iend] + tmp1;
  1054. gu = f2cmax(r__1,r__2);
  1055. /* Computing MIN */
  1056. r__1 = gl, r__2 = d__[iend] - tmp1;
  1057. gl = f2cmin(r__1,r__2);
  1058. /* Computing MAX */
  1059. r__1 = abs(gl), r__2 = abs(gu);
  1060. bnorm = f2cmax(r__1,r__2);
  1061. gl = gl - bnorm * 2.1f * ulp * in - pivmin * 2.1f;
  1062. gu = gu + bnorm * 2.1f * ulp * in + pivmin * 2.1f;
  1063. /* Compute ATOLI for the current submatrix */
  1064. if (*abstol <= 0.f) {
  1065. /* Computing MAX */
  1066. r__1 = abs(gl), r__2 = abs(gu);
  1067. atoli = ulp * f2cmax(r__1,r__2);
  1068. } else {
  1069. atoli = *abstol;
  1070. }
  1071. if (irange > 1) {
  1072. if (gu < wl) {
  1073. nwl += in;
  1074. nwu += in;
  1075. goto L70;
  1076. }
  1077. gl = f2cmax(gl,wl);
  1078. gu = f2cmin(gu,wu);
  1079. if (gl >= gu) {
  1080. goto L70;
  1081. }
  1082. }
  1083. /* Set Up Initial Interval */
  1084. work[*n + 1] = gl;
  1085. work[*n + in + 1] = gu;
  1086. slaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
  1087. pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
  1088. work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
  1089. w[*m + 1], &iblock[*m + 1], &iinfo);
  1090. nwl += iwork[1];
  1091. nwu += iwork[in + 1];
  1092. iwoff = *m - iwork[1];
  1093. /* Compute Eigenvalues */
  1094. itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(
  1095. 2.f)) + 2;
  1096. slaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
  1097. pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
  1098. work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
  1099. &w[*m + 1], &iblock[*m + 1], &iinfo);
  1100. /* Copy Eigenvalues Into W and IBLOCK */
  1101. /* Use -JB for block number for unconverged eigenvalues. */
  1102. i__2 = iout;
  1103. for (j = 1; j <= i__2; ++j) {
  1104. tmp1 = (work[j + *n] + work[j + in + *n]) * .5f;
  1105. /* Flag non-convergence. */
  1106. if (j > iout - iinfo) {
  1107. ncnvrg = TRUE_;
  1108. ib = -jb;
  1109. } else {
  1110. ib = jb;
  1111. }
  1112. i__3 = iwork[j + in] + iwoff;
  1113. for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
  1114. w[je] = tmp1;
  1115. iblock[je] = ib;
  1116. /* L50: */
  1117. }
  1118. /* L60: */
  1119. }
  1120. *m += im;
  1121. }
  1122. L70:
  1123. ;
  1124. }
  1125. /* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
  1126. /* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
  1127. if (irange == 3) {
  1128. im = 0;
  1129. idiscl = *il - 1 - nwl;
  1130. idiscu = nwu - *iu;
  1131. if (idiscl > 0 || idiscu > 0) {
  1132. i__1 = *m;
  1133. for (je = 1; je <= i__1; ++je) {
  1134. if (w[je] <= wlu && idiscl > 0) {
  1135. --idiscl;
  1136. } else if (w[je] >= wul && idiscu > 0) {
  1137. --idiscu;
  1138. } else {
  1139. ++im;
  1140. w[im] = w[je];
  1141. iblock[im] = iblock[je];
  1142. }
  1143. /* L80: */
  1144. }
  1145. *m = im;
  1146. }
  1147. if (idiscl > 0 || idiscu > 0) {
  1148. /* Code to deal with effects of bad arithmetic: */
  1149. /* Some low eigenvalues to be discarded are not in (WL,WLU], */
  1150. /* or high eigenvalues to be discarded are not in (WUL,WU] */
  1151. /* so just kill off the smallest IDISCL/largest IDISCU */
  1152. /* eigenvalues, by simply finding the smallest/largest */
  1153. /* eigenvalue(s). */
  1154. /* (If N(w) is monotone non-decreasing, this should never */
  1155. /* happen.) */
  1156. if (idiscl > 0) {
  1157. wkill = wu;
  1158. i__1 = idiscl;
  1159. for (jdisc = 1; jdisc <= i__1; ++jdisc) {
  1160. iw = 0;
  1161. i__2 = *m;
  1162. for (je = 1; je <= i__2; ++je) {
  1163. if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
  1164. iw = je;
  1165. wkill = w[je];
  1166. }
  1167. /* L90: */
  1168. }
  1169. iblock[iw] = 0;
  1170. /* L100: */
  1171. }
  1172. }
  1173. if (idiscu > 0) {
  1174. wkill = wl;
  1175. i__1 = idiscu;
  1176. for (jdisc = 1; jdisc <= i__1; ++jdisc) {
  1177. iw = 0;
  1178. i__2 = *m;
  1179. for (je = 1; je <= i__2; ++je) {
  1180. if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
  1181. iw = je;
  1182. wkill = w[je];
  1183. }
  1184. /* L110: */
  1185. }
  1186. iblock[iw] = 0;
  1187. /* L120: */
  1188. }
  1189. }
  1190. im = 0;
  1191. i__1 = *m;
  1192. for (je = 1; je <= i__1; ++je) {
  1193. if (iblock[je] != 0) {
  1194. ++im;
  1195. w[im] = w[je];
  1196. iblock[im] = iblock[je];
  1197. }
  1198. /* L130: */
  1199. }
  1200. *m = im;
  1201. }
  1202. if (idiscl < 0 || idiscu < 0) {
  1203. toofew = TRUE_;
  1204. }
  1205. }
  1206. /* If ORDER='B', do nothing -- the eigenvalues are already sorted */
  1207. /* by block. */
  1208. /* If ORDER='E', sort the eigenvalues from smallest to largest */
  1209. if (iorder == 1 && *nsplit > 1) {
  1210. i__1 = *m - 1;
  1211. for (je = 1; je <= i__1; ++je) {
  1212. ie = 0;
  1213. tmp1 = w[je];
  1214. i__2 = *m;
  1215. for (j = je + 1; j <= i__2; ++j) {
  1216. if (w[j] < tmp1) {
  1217. ie = j;
  1218. tmp1 = w[j];
  1219. }
  1220. /* L140: */
  1221. }
  1222. if (ie != 0) {
  1223. itmp1 = iblock[ie];
  1224. w[ie] = w[je];
  1225. iblock[ie] = iblock[je];
  1226. w[je] = tmp1;
  1227. iblock[je] = itmp1;
  1228. }
  1229. /* L150: */
  1230. }
  1231. }
  1232. *info = 0;
  1233. if (ncnvrg) {
  1234. ++(*info);
  1235. }
  1236. if (toofew) {
  1237. *info += 2;
  1238. }
  1239. return;
  1240. /* End of SSTEBZ */
  1241. } /* sstebz_ */