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dstebz.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 blasint logical;
  52. typedef char logical1;
  53. typedef char integer1;
  54. #define TRUE_ (1)
  55. #define FALSE_ (0)
  56. /* Extern is for use with -E */
  57. #ifndef Extern
  58. #define Extern extern
  59. #endif
  60. /* I/O stuff */
  61. typedef int flag;
  62. typedef int ftnlen;
  63. typedef int ftnint;
  64. /*external read, write*/
  65. typedef struct
  66. { flag cierr;
  67. ftnint ciunit;
  68. flag ciend;
  69. char *cifmt;
  70. ftnint cirec;
  71. } cilist;
  72. /*internal read, write*/
  73. typedef struct
  74. { flag icierr;
  75. char *iciunit;
  76. flag iciend;
  77. char *icifmt;
  78. ftnint icirlen;
  79. ftnint icirnum;
  80. } icilist;
  81. /*open*/
  82. typedef struct
  83. { flag oerr;
  84. ftnint ounit;
  85. char *ofnm;
  86. ftnlen ofnmlen;
  87. char *osta;
  88. char *oacc;
  89. char *ofm;
  90. ftnint orl;
  91. char *oblnk;
  92. } olist;
  93. /*close*/
  94. typedef struct
  95. { flag cerr;
  96. ftnint cunit;
  97. char *csta;
  98. } cllist;
  99. /*rewind, backspace, endfile*/
  100. typedef struct
  101. { flag aerr;
  102. ftnint aunit;
  103. } alist;
  104. /* inquire */
  105. typedef struct
  106. { flag inerr;
  107. ftnint inunit;
  108. char *infile;
  109. ftnlen infilen;
  110. ftnint *inex; /*parameters in standard's order*/
  111. ftnint *inopen;
  112. ftnint *innum;
  113. ftnint *innamed;
  114. char *inname;
  115. ftnlen innamlen;
  116. char *inacc;
  117. ftnlen inacclen;
  118. char *inseq;
  119. ftnlen inseqlen;
  120. char *indir;
  121. ftnlen indirlen;
  122. char *infmt;
  123. ftnlen infmtlen;
  124. char *inform;
  125. ftnint informlen;
  126. char *inunf;
  127. ftnlen inunflen;
  128. ftnint *inrecl;
  129. ftnint *innrec;
  130. char *inblank;
  131. ftnlen inblanklen;
  132. } inlist;
  133. #define VOID void
  134. union Multitype { /* for multiple entry points */
  135. integer1 g;
  136. shortint h;
  137. integer i;
  138. /* longint j; */
  139. real r;
  140. doublereal d;
  141. complex c;
  142. doublecomplex z;
  143. };
  144. typedef union Multitype Multitype;
  145. struct Vardesc { /* for Namelist */
  146. char *name;
  147. char *addr;
  148. ftnlen *dims;
  149. int type;
  150. };
  151. typedef struct Vardesc Vardesc;
  152. struct Namelist {
  153. char *name;
  154. Vardesc **vars;
  155. int nvars;
  156. };
  157. typedef struct Namelist Namelist;
  158. #define abs(x) ((x) >= 0 ? (x) : -(x))
  159. #define dabs(x) (fabs(x))
  160. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  161. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  162. #define dmin(a,b) (f2cmin(a,b))
  163. #define dmax(a,b) (f2cmax(a,b))
  164. #define bit_test(a,b) ((a) >> (b) & 1)
  165. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  166. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  167. #define abort_() { sig_die("Fortran abort routine called", 1); }
  168. #define c_abs(z) (cabsf(Cf(z)))
  169. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  170. #ifdef _MSC_VER
  171. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  172. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
  173. #else
  174. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  175. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  176. #endif
  177. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  178. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  179. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  180. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  181. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  182. #define d_abs(x) (fabs(*(x)))
  183. #define d_acos(x) (acos(*(x)))
  184. #define d_asin(x) (asin(*(x)))
  185. #define d_atan(x) (atan(*(x)))
  186. #define d_atn2(x, y) (atan2(*(x),*(y)))
  187. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  188. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  189. #define d_cos(x) (cos(*(x)))
  190. #define d_cosh(x) (cosh(*(x)))
  191. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  192. #define d_exp(x) (exp(*(x)))
  193. #define d_imag(z) (cimag(Cd(z)))
  194. #define r_imag(z) (cimagf(Cf(z)))
  195. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  196. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  198. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define d_log(x) (log(*(x)))
  200. #define d_mod(x, y) (fmod(*(x), *(y)))
  201. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  202. #define d_nint(x) u_nint(*(x))
  203. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  204. #define d_sign(a,b) u_sign(*(a),*(b))
  205. #define r_sign(a,b) u_sign(*(a),*(b))
  206. #define d_sin(x) (sin(*(x)))
  207. #define d_sinh(x) (sinh(*(x)))
  208. #define d_sqrt(x) (sqrt(*(x)))
  209. #define d_tan(x) (tan(*(x)))
  210. #define d_tanh(x) (tanh(*(x)))
  211. #define i_abs(x) abs(*(x))
  212. #define i_dnnt(x) ((integer)u_nint(*(x)))
  213. #define i_len(s, n) (n)
  214. #define i_nint(x) ((integer)u_nint(*(x)))
  215. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  216. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  217. #define pow_si(B,E) spow_ui(*(B),*(E))
  218. #define pow_ri(B,E) spow_ui(*(B),*(E))
  219. #define pow_di(B,E) dpow_ui(*(B),*(E))
  220. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  221. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  222. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  223. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  224. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  225. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  226. #define sig_die(s, kill) { exit(1); }
  227. #define s_stop(s, n) {exit(0);}
  228. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  229. #define z_abs(z) (cabs(Cd(z)))
  230. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  231. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  232. #define myexit_() break;
  233. #define mycycle() continue;
  234. #define myceiling(w) {ceil(w)}
  235. #define myhuge(w) {HUGE_VAL}
  236. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  237. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  238. /* procedure parameter types for -A and -C++ */
  239. #ifdef __cplusplus
  240. typedef logical (*L_fp)(...);
  241. #else
  242. typedef logical (*L_fp)();
  243. #endif
  244. static float spow_ui(float x, integer n) {
  245. float pow=1.0; unsigned long int u;
  246. if(n != 0) {
  247. if(n < 0) n = -n, x = 1/x;
  248. for(u = n; ; ) {
  249. if(u & 01) pow *= x;
  250. if(u >>= 1) x *= x;
  251. else break;
  252. }
  253. }
  254. return pow;
  255. }
  256. static double dpow_ui(double x, integer n) {
  257. double pow=1.0; unsigned long int u;
  258. if(n != 0) {
  259. if(n < 0) n = -n, x = 1/x;
  260. for(u = n; ; ) {
  261. if(u & 01) pow *= x;
  262. if(u >>= 1) x *= x;
  263. else break;
  264. }
  265. }
  266. return pow;
  267. }
  268. #ifdef _MSC_VER
  269. static _Fcomplex cpow_ui(complex x, integer n) {
  270. complex pow={1.0,0.0}; unsigned long int u;
  271. if(n != 0) {
  272. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  273. for(u = n; ; ) {
  274. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  275. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  276. else break;
  277. }
  278. }
  279. _Fcomplex p={pow.r, pow.i};
  280. return p;
  281. }
  282. #else
  283. static _Complex float cpow_ui(_Complex float x, integer n) {
  284. _Complex float pow=1.0; unsigned long int u;
  285. if(n != 0) {
  286. if(n < 0) n = -n, x = 1/x;
  287. for(u = n; ; ) {
  288. if(u & 01) pow *= x;
  289. if(u >>= 1) x *= x;
  290. else break;
  291. }
  292. }
  293. return pow;
  294. }
  295. #endif
  296. #ifdef _MSC_VER
  297. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  298. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  299. if(n != 0) {
  300. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  301. for(u = n; ; ) {
  302. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  303. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  304. else break;
  305. }
  306. }
  307. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  308. return p;
  309. }
  310. #else
  311. static _Complex double zpow_ui(_Complex double x, integer n) {
  312. _Complex double pow=1.0; unsigned long int u;
  313. if(n != 0) {
  314. if(n < 0) n = -n, x = 1/x;
  315. for(u = n; ; ) {
  316. if(u & 01) pow *= x;
  317. if(u >>= 1) x *= x;
  318. else break;
  319. }
  320. }
  321. return pow;
  322. }
  323. #endif
  324. static integer pow_ii(integer x, integer n) {
  325. integer pow; unsigned long int u;
  326. if (n <= 0) {
  327. if (n == 0 || x == 1) pow = 1;
  328. else if (x != -1) pow = x == 0 ? 1/x : 0;
  329. else n = -n;
  330. }
  331. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  332. u = n;
  333. for(pow = 1; ; ) {
  334. if(u & 01) pow *= x;
  335. if(u >>= 1) x *= x;
  336. else break;
  337. }
  338. }
  339. return pow;
  340. }
  341. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  342. {
  343. double m; integer i, mi;
  344. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  345. if (w[i-1]>m) mi=i ,m=w[i-1];
  346. return mi-s+1;
  347. }
  348. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  349. {
  350. float m; integer i, mi;
  351. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  352. if (w[i-1]>m) mi=i ,m=w[i-1];
  353. return mi-s+1;
  354. }
  355. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  356. integer n = *n_, incx = *incx_, incy = *incy_, i;
  357. #ifdef _MSC_VER
  358. _Fcomplex zdotc = {0.0, 0.0};
  359. if (incx == 1 && incy == 1) {
  360. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  361. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  362. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  363. }
  364. } else {
  365. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  366. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  367. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  368. }
  369. }
  370. pCf(z) = zdotc;
  371. }
  372. #else
  373. _Complex float zdotc = 0.0;
  374. if (incx == 1 && incy == 1) {
  375. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  376. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  377. }
  378. } else {
  379. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  380. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  381. }
  382. }
  383. pCf(z) = zdotc;
  384. }
  385. #endif
  386. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  387. integer n = *n_, incx = *incx_, incy = *incy_, i;
  388. #ifdef _MSC_VER
  389. _Dcomplex zdotc = {0.0, 0.0};
  390. if (incx == 1 && incy == 1) {
  391. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  392. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  393. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  394. }
  395. } else {
  396. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  397. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  398. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  399. }
  400. }
  401. pCd(z) = zdotc;
  402. }
  403. #else
  404. _Complex double zdotc = 0.0;
  405. if (incx == 1 && incy == 1) {
  406. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  407. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  408. }
  409. } else {
  410. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  411. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  412. }
  413. }
  414. pCd(z) = zdotc;
  415. }
  416. #endif
  417. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  418. integer n = *n_, incx = *incx_, incy = *incy_, i;
  419. #ifdef _MSC_VER
  420. _Fcomplex zdotc = {0.0, 0.0};
  421. if (incx == 1 && incy == 1) {
  422. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  423. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  424. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  425. }
  426. } else {
  427. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  428. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  429. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  430. }
  431. }
  432. pCf(z) = zdotc;
  433. }
  434. #else
  435. _Complex float zdotc = 0.0;
  436. if (incx == 1 && incy == 1) {
  437. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  438. zdotc += Cf(&x[i]) * Cf(&y[i]);
  439. }
  440. } else {
  441. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  442. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  443. }
  444. }
  445. pCf(z) = zdotc;
  446. }
  447. #endif
  448. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  449. integer n = *n_, incx = *incx_, incy = *incy_, i;
  450. #ifdef _MSC_VER
  451. _Dcomplex zdotc = {0.0, 0.0};
  452. if (incx == 1 && incy == 1) {
  453. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  454. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  455. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  456. }
  457. } else {
  458. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  459. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  460. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  461. }
  462. }
  463. pCd(z) = zdotc;
  464. }
  465. #else
  466. _Complex double zdotc = 0.0;
  467. if (incx == 1 && incy == 1) {
  468. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  469. zdotc += Cd(&x[i]) * Cd(&y[i]);
  470. }
  471. } else {
  472. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  473. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  474. }
  475. }
  476. pCd(z) = zdotc;
  477. }
  478. #endif
  479. /* -- translated by f2c (version 20000121).
  480. You must link the resulting object file with the libraries:
  481. -lf2c -lm (in that order)
  482. */
  483. /* Table of constant values */
  484. static integer c__1 = 1;
  485. static integer c_n1 = -1;
  486. static integer c__3 = 3;
  487. static integer c__2 = 2;
  488. static integer c__0 = 0;
  489. /* > \brief \b DSTEBZ */
  490. /* =========== DOCUMENTATION =========== */
  491. /* Online html documentation available at */
  492. /* http://www.netlib.org/lapack/explore-html/ */
  493. /* > \htmlonly */
  494. /* > Download DSTEBZ + dependencies */
  495. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstebz.
  496. f"> */
  497. /* > [TGZ]</a> */
  498. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstebz.
  499. f"> */
  500. /* > [ZIP]</a> */
  501. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstebz.
  502. f"> */
  503. /* > [TXT]</a> */
  504. /* > \endhtmlonly */
  505. /* Definition: */
  506. /* =========== */
  507. /* SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, */
  508. /* M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, */
  509. /* INFO ) */
  510. /* CHARACTER ORDER, RANGE */
  511. /* INTEGER IL, INFO, IU, M, N, NSPLIT */
  512. /* DOUBLE PRECISION ABSTOL, VL, VU */
  513. /* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) */
  514. /* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) */
  515. /* > \par Purpose: */
  516. /* ============= */
  517. /* > */
  518. /* > \verbatim */
  519. /* > */
  520. /* > DSTEBZ computes the eigenvalues of a symmetric tridiagonal */
  521. /* > matrix T. The user may ask for all eigenvalues, all eigenvalues */
  522. /* > in the half-open interval (VL, VU], or the IL-th through IU-th */
  523. /* > eigenvalues. */
  524. /* > */
  525. /* > To avoid overflow, the matrix must be scaled so that its */
  526. /* > largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
  527. */
  528. /* > accuracy, it should not be much smaller than that. */
  529. /* > */
  530. /* > See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
  531. /* > Matrix", Report CS41, Computer Science Dept., Stanford */
  532. /* > University, July 21, 1966. */
  533. /* > \endverbatim */
  534. /* Arguments: */
  535. /* ========== */
  536. /* > \param[in] RANGE */
  537. /* > \verbatim */
  538. /* > RANGE is CHARACTER*1 */
  539. /* > = 'A': ("All") all eigenvalues will be found. */
  540. /* > = 'V': ("Value") all eigenvalues in the half-open interval */
  541. /* > (VL, VU] will be found. */
  542. /* > = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
  543. /* > entire matrix) will be found. */
  544. /* > \endverbatim */
  545. /* > */
  546. /* > \param[in] ORDER */
  547. /* > \verbatim */
  548. /* > ORDER is CHARACTER*1 */
  549. /* > = 'B': ("By Block") the eigenvalues will be grouped by */
  550. /* > split-off block (see IBLOCK, ISPLIT) and */
  551. /* > ordered from smallest to largest within */
  552. /* > the block. */
  553. /* > = 'E': ("Entire matrix") */
  554. /* > the eigenvalues for the entire matrix */
  555. /* > will be ordered from smallest to */
  556. /* > largest. */
  557. /* > \endverbatim */
  558. /* > */
  559. /* > \param[in] N */
  560. /* > \verbatim */
  561. /* > N is INTEGER */
  562. /* > The order of the tridiagonal matrix T. N >= 0. */
  563. /* > \endverbatim */
  564. /* > */
  565. /* > \param[in] VL */
  566. /* > \verbatim */
  567. /* > VL is DOUBLE PRECISION */
  568. /* > */
  569. /* > If RANGE='V', the lower bound of the interval to */
  570. /* > be searched for eigenvalues. Eigenvalues less than or equal */
  571. /* > to VL, or greater than VU, will not be returned. VL < VU. */
  572. /* > Not referenced if RANGE = 'A' or 'I'. */
  573. /* > \endverbatim */
  574. /* > */
  575. /* > \param[in] VU */
  576. /* > \verbatim */
  577. /* > VU is DOUBLE PRECISION */
  578. /* > */
  579. /* > If RANGE='V', the upper bound of the interval to */
  580. /* > be searched for eigenvalues. Eigenvalues less than or equal */
  581. /* > to VL, or greater than VU, will not be returned. VL < VU. */
  582. /* > Not referenced if RANGE = 'A' or 'I'. */
  583. /* > \endverbatim */
  584. /* > */
  585. /* > \param[in] IL */
  586. /* > \verbatim */
  587. /* > IL is INTEGER */
  588. /* > */
  589. /* > If RANGE='I', the index of the */
  590. /* > smallest eigenvalue to be returned. */
  591. /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  592. /* > Not referenced if RANGE = 'A' or 'V'. */
  593. /* > \endverbatim */
  594. /* > */
  595. /* > \param[in] IU */
  596. /* > \verbatim */
  597. /* > IU is INTEGER */
  598. /* > */
  599. /* > If RANGE='I', the index of the */
  600. /* > largest eigenvalue to be returned. */
  601. /* > 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
  602. /* > Not referenced if RANGE = 'A' or 'V'. */
  603. /* > \endverbatim */
  604. /* > */
  605. /* > \param[in] ABSTOL */
  606. /* > \verbatim */
  607. /* > ABSTOL is DOUBLE PRECISION */
  608. /* > The absolute tolerance for the eigenvalues. An eigenvalue */
  609. /* > (or cluster) is considered to be located if it has been */
  610. /* > determined to lie in an interval whose width is ABSTOL or */
  611. /* > less. If ABSTOL is less than or equal to zero, then ULP*|T| */
  612. /* > will be used, where |T| means the 1-norm of T. */
  613. /* > */
  614. /* > Eigenvalues will be computed most accurately when ABSTOL is */
  615. /* > set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
  616. /* > \endverbatim */
  617. /* > */
  618. /* > \param[in] D */
  619. /* > \verbatim */
  620. /* > D is DOUBLE PRECISION array, dimension (N) */
  621. /* > The n diagonal elements of the tridiagonal matrix T. */
  622. /* > \endverbatim */
  623. /* > */
  624. /* > \param[in] E */
  625. /* > \verbatim */
  626. /* > E is DOUBLE PRECISION array, dimension (N-1) */
  627. /* > The (n-1) off-diagonal elements of the tridiagonal matrix T. */
  628. /* > \endverbatim */
  629. /* > */
  630. /* > \param[out] M */
  631. /* > \verbatim */
  632. /* > M is INTEGER */
  633. /* > The actual number of eigenvalues found. 0 <= M <= N. */
  634. /* > (See also the description of INFO=2,3.) */
  635. /* > \endverbatim */
  636. /* > */
  637. /* > \param[out] NSPLIT */
  638. /* > \verbatim */
  639. /* > NSPLIT is INTEGER */
  640. /* > The number of diagonal blocks in the matrix T. */
  641. /* > 1 <= NSPLIT <= N. */
  642. /* > \endverbatim */
  643. /* > */
  644. /* > \param[out] W */
  645. /* > \verbatim */
  646. /* > W is DOUBLE PRECISION array, dimension (N) */
  647. /* > On exit, the first M elements of W will contain the */
  648. /* > eigenvalues. (DSTEBZ may use the remaining N-M elements as */
  649. /* > workspace.) */
  650. /* > \endverbatim */
  651. /* > */
  652. /* > \param[out] IBLOCK */
  653. /* > \verbatim */
  654. /* > IBLOCK is INTEGER array, dimension (N) */
  655. /* > At each row/column j where E(j) is zero or small, the */
  656. /* > matrix T is considered to split into a block diagonal */
  657. /* > matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
  658. /* > block (from 1 to the number of blocks) the eigenvalue W(i) */
  659. /* > belongs. (DSTEBZ may use the remaining N-M elements as */
  660. /* > workspace.) */
  661. /* > \endverbatim */
  662. /* > */
  663. /* > \param[out] ISPLIT */
  664. /* > \verbatim */
  665. /* > ISPLIT is INTEGER array, dimension (N) */
  666. /* > The splitting points, at which T breaks up into submatrices. */
  667. /* > The first submatrix consists of rows/columns 1 to ISPLIT(1), */
  668. /* > the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
  669. /* > etc., and the NSPLIT-th consists of rows/columns */
  670. /* > ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
  671. /* > (Only the first NSPLIT elements will actually be used, but */
  672. /* > since the user cannot know a priori what value NSPLIT will */
  673. /* > have, N words must be reserved for ISPLIT.) */
  674. /* > \endverbatim */
  675. /* > */
  676. /* > \param[out] WORK */
  677. /* > \verbatim */
  678. /* > WORK is DOUBLE PRECISION array, dimension (4*N) */
  679. /* > \endverbatim */
  680. /* > */
  681. /* > \param[out] IWORK */
  682. /* > \verbatim */
  683. /* > IWORK is INTEGER array, dimension (3*N) */
  684. /* > \endverbatim */
  685. /* > */
  686. /* > \param[out] INFO */
  687. /* > \verbatim */
  688. /* > INFO is INTEGER */
  689. /* > = 0: successful exit */
  690. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  691. /* > > 0: some or all of the eigenvalues failed to converge or */
  692. /* > were not computed: */
  693. /* > =1 or 3: Bisection failed to converge for some */
  694. /* > eigenvalues; these eigenvalues are flagged by a */
  695. /* > negative block number. The effect is that the */
  696. /* > eigenvalues may not be as accurate as the */
  697. /* > absolute and relative tolerances. This is */
  698. /* > generally caused by unexpectedly inaccurate */
  699. /* > arithmetic. */
  700. /* > =2 or 3: RANGE='I' only: Not all of the eigenvalues */
  701. /* > IL:IU were found. */
  702. /* > Effect: M < IU+1-IL */
  703. /* > Cause: non-monotonic arithmetic, causing the */
  704. /* > Sturm sequence to be non-monotonic. */
  705. /* > Cure: recalculate, using RANGE='A', and pick */
  706. /* > out eigenvalues IL:IU. In some cases, */
  707. /* > increasing the PARAMETER "FUDGE" may */
  708. /* > make things work. */
  709. /* > = 4: RANGE='I', and the Gershgorin interval */
  710. /* > initially used was too small. No eigenvalues */
  711. /* > were computed. */
  712. /* > Probable cause: your machine has sloppy */
  713. /* > floating-point arithmetic. */
  714. /* > Cure: Increase the PARAMETER "FUDGE", */
  715. /* > recompile, and try again. */
  716. /* > \endverbatim */
  717. /* > \par Internal Parameters: */
  718. /* ========================= */
  719. /* > */
  720. /* > \verbatim */
  721. /* > RELFAC DOUBLE PRECISION, default = 2.0e0 */
  722. /* > The relative tolerance. An interval (a,b] lies within */
  723. /* > "relative tolerance" if b-a < RELFAC*ulp*f2cmax(|a|,|b|), */
  724. /* > where "ulp" is the machine precision (distance from 1 to */
  725. /* > the next larger floating point number.) */
  726. /* > */
  727. /* > FUDGE DOUBLE PRECISION, default = 2 */
  728. /* > A "fudge factor" to widen the Gershgorin intervals. Ideally, */
  729. /* > a value of 1 should work, but on machines with sloppy */
  730. /* > arithmetic, this needs to be larger. The default for */
  731. /* > publicly released versions should be large enough to handle */
  732. /* > the worst machine around. Note that this has no effect */
  733. /* > on accuracy of the solution. */
  734. /* > \endverbatim */
  735. /* Authors: */
  736. /* ======== */
  737. /* > \author Univ. of Tennessee */
  738. /* > \author Univ. of California Berkeley */
  739. /* > \author Univ. of Colorado Denver */
  740. /* > \author NAG Ltd. */
  741. /* > \date June 2016 */
  742. /* > \ingroup auxOTHERcomputational */
  743. /* ===================================================================== */
  744. /* Subroutine */ void dstebz_(char *range, char *order, integer *n, doublereal
  745. *vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
  746. doublereal *d__, doublereal *e, integer *m, integer *nsplit,
  747. doublereal *w, integer *iblock, integer *isplit, doublereal *work,
  748. integer *iwork, integer *info)
  749. {
  750. /* System generated locals */
  751. integer i__1, i__2, i__3;
  752. doublereal d__1, d__2, d__3, d__4, d__5;
  753. /* Local variables */
  754. integer iend, ioff, iout, itmp1, j, jdisc;
  755. extern logical lsame_(char *, char *);
  756. integer iinfo;
  757. doublereal atoli;
  758. integer iwoff;
  759. doublereal bnorm;
  760. integer itmax;
  761. doublereal wkill, rtoli, tnorm;
  762. integer ib, jb, ie, je, nb;
  763. doublereal gl;
  764. integer im, in;
  765. extern doublereal dlamch_(char *);
  766. integer ibegin;
  767. doublereal gu;
  768. integer iw;
  769. extern /* Subroutine */ void dlaebz_(integer *, integer *, integer *,
  770. integer *, integer *, integer *, doublereal *, doublereal *,
  771. doublereal *, doublereal *, doublereal *, doublereal *, integer *,
  772. doublereal *, doublereal *, integer *, integer *, doublereal *,
  773. integer *, integer *);
  774. doublereal wl;
  775. integer irange, idiscl;
  776. doublereal safemn, wu;
  777. integer idumma[1];
  778. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  779. integer *, integer *, ftnlen, ftnlen);
  780. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  781. integer idiscu, iorder;
  782. logical ncnvrg;
  783. doublereal pivmin;
  784. logical toofew;
  785. integer nwl;
  786. doublereal ulp, wlu, wul;
  787. integer nwu;
  788. doublereal 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_("DSTEBZ", &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 = dlamch_("S");
  860. ulp = dlamch_("P");
  861. rtoli = ulp * 2.;
  862. nb = ilaenv_(&c__1, "DSTEBZ", " ", 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.;
  883. pivmin = 1.;
  884. i__1 = *n;
  885. for (j = 2; j <= i__1; ++j) {
  886. /* Computing 2nd power */
  887. d__1 = e[j - 1];
  888. tmp1 = d__1 * d__1;
  889. /* Computing 2nd power */
  890. d__2 = ulp;
  891. if ((d__1 = d__[j] * d__[j - 1], abs(d__1)) * (d__2 * d__2) + safemn
  892. > tmp1) {
  893. isplit[*nsplit] = j - 1;
  894. ++(*nsplit);
  895. work[j - 1] = 0.;
  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.;
  913. i__1 = *n - 1;
  914. for (j = 1; j <= i__1; ++j) {
  915. tmp2 = sqrt(work[j]);
  916. /* Computing MAX */
  917. d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
  918. gu = f2cmax(d__1,d__2);
  919. /* Computing MIN */
  920. d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
  921. gl = f2cmin(d__1,d__2);
  922. tmp1 = tmp2;
  923. /* L20: */
  924. }
  925. /* Computing MAX */
  926. d__1 = gu, d__2 = d__[*n] + tmp1;
  927. gu = f2cmax(d__1,d__2);
  928. /* Computing MIN */
  929. d__1 = gl, d__2 = d__[*n] - tmp1;
  930. gl = f2cmin(d__1,d__2);
  931. /* Computing MAX */
  932. d__1 = abs(gl), d__2 = abs(gu);
  933. tnorm = f2cmax(d__1,d__2);
  934. gl = gl - tnorm * 2.1 * ulp * *n - pivmin * 4.2000000000000002;
  935. gu = gu + tnorm * 2.1 * ulp * *n + pivmin * 2.1;
  936. /* Compute Iteration parameters */
  937. itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.)) + 2;
  938. if (*abstol <= 0.) {
  939. atoli = ulp * tnorm;
  940. } else {
  941. atoli = *abstol;
  942. }
  943. work[*n + 1] = gl;
  944. work[*n + 2] = gl;
  945. work[*n + 3] = gu;
  946. work[*n + 4] = gu;
  947. work[*n + 5] = gl;
  948. work[*n + 6] = gu;
  949. iwork[1] = -1;
  950. iwork[2] = -1;
  951. iwork[3] = *n + 1;
  952. iwork[4] = *n + 1;
  953. iwork[5] = *il - 1;
  954. iwork[6] = *iu;
  955. dlaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
  956. &d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
  957. + 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
  958. if (iwork[6] == *iu) {
  959. wl = work[*n + 1];
  960. wlu = work[*n + 3];
  961. nwl = iwork[1];
  962. wu = work[*n + 4];
  963. wul = work[*n + 2];
  964. nwu = iwork[4];
  965. } else {
  966. wl = work[*n + 2];
  967. wlu = work[*n + 4];
  968. nwl = iwork[2];
  969. wu = work[*n + 3];
  970. wul = work[*n + 1];
  971. nwu = iwork[3];
  972. }
  973. if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
  974. *info = 4;
  975. return;
  976. }
  977. } else {
  978. /* RANGE='A' or 'V' -- Set ATOLI */
  979. /* Computing MAX */
  980. d__3 = abs(d__[1]) + abs(e[1]), d__4 = (d__1 = d__[*n], abs(d__1)) + (
  981. d__2 = e[*n - 1], abs(d__2));
  982. tnorm = f2cmax(d__3,d__4);
  983. i__1 = *n - 1;
  984. for (j = 2; j <= i__1; ++j) {
  985. /* Computing MAX */
  986. d__4 = tnorm, d__5 = (d__1 = d__[j], abs(d__1)) + (d__2 = e[j - 1]
  987. , abs(d__2)) + (d__3 = e[j], abs(d__3));
  988. tnorm = f2cmax(d__4,d__5);
  989. /* L30: */
  990. }
  991. if (*abstol <= 0.) {
  992. atoli = ulp * tnorm;
  993. } else {
  994. atoli = *abstol;
  995. }
  996. if (irange == 2) {
  997. wl = *vl;
  998. wu = *vu;
  999. } else {
  1000. wl = 0.;
  1001. wu = 0.;
  1002. }
  1003. }
  1004. /* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. */
  1005. /* NWL accumulates the number of eigenvalues .le. WL, */
  1006. /* NWU accumulates the number of eigenvalues .le. WU */
  1007. *m = 0;
  1008. iend = 0;
  1009. *info = 0;
  1010. nwl = 0;
  1011. nwu = 0;
  1012. i__1 = *nsplit;
  1013. for (jb = 1; jb <= i__1; ++jb) {
  1014. ioff = iend;
  1015. ibegin = ioff + 1;
  1016. iend = isplit[jb];
  1017. in = iend - ioff;
  1018. if (in == 1) {
  1019. /* Special Case -- IN=1 */
  1020. if (irange == 1 || wl >= d__[ibegin] - pivmin) {
  1021. ++nwl;
  1022. }
  1023. if (irange == 1 || wu >= d__[ibegin] - pivmin) {
  1024. ++nwu;
  1025. }
  1026. if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
  1027. - pivmin) {
  1028. ++(*m);
  1029. w[*m] = d__[ibegin];
  1030. iblock[*m] = jb;
  1031. }
  1032. } else {
  1033. /* General Case -- IN > 1 */
  1034. /* Compute Gershgorin Interval */
  1035. /* and use it as the initial interval */
  1036. gu = d__[ibegin];
  1037. gl = d__[ibegin];
  1038. tmp1 = 0.;
  1039. i__2 = iend - 1;
  1040. for (j = ibegin; j <= i__2; ++j) {
  1041. tmp2 = (d__1 = e[j], abs(d__1));
  1042. /* Computing MAX */
  1043. d__1 = gu, d__2 = d__[j] + tmp1 + tmp2;
  1044. gu = f2cmax(d__1,d__2);
  1045. /* Computing MIN */
  1046. d__1 = gl, d__2 = d__[j] - tmp1 - tmp2;
  1047. gl = f2cmin(d__1,d__2);
  1048. tmp1 = tmp2;
  1049. /* L40: */
  1050. }
  1051. /* Computing MAX */
  1052. d__1 = gu, d__2 = d__[iend] + tmp1;
  1053. gu = f2cmax(d__1,d__2);
  1054. /* Computing MIN */
  1055. d__1 = gl, d__2 = d__[iend] - tmp1;
  1056. gl = f2cmin(d__1,d__2);
  1057. /* Computing MAX */
  1058. d__1 = abs(gl), d__2 = abs(gu);
  1059. bnorm = f2cmax(d__1,d__2);
  1060. gl = gl - bnorm * 2.1 * ulp * in - pivmin * 2.1;
  1061. gu = gu + bnorm * 2.1 * ulp * in + pivmin * 2.1;
  1062. /* Compute ATOLI for the current submatrix */
  1063. if (*abstol <= 0.) {
  1064. /* Computing MAX */
  1065. d__1 = abs(gl), d__2 = abs(gu);
  1066. atoli = ulp * f2cmax(d__1,d__2);
  1067. } else {
  1068. atoli = *abstol;
  1069. }
  1070. if (irange > 1) {
  1071. if (gu < wl) {
  1072. nwl += in;
  1073. nwu += in;
  1074. goto L70;
  1075. }
  1076. gl = f2cmax(gl,wl);
  1077. gu = f2cmin(gu,wu);
  1078. if (gl >= gu) {
  1079. goto L70;
  1080. }
  1081. }
  1082. /* Set Up Initial Interval */
  1083. work[*n + 1] = gl;
  1084. work[*n + in + 1] = gu;
  1085. dlaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
  1086. pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
  1087. work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
  1088. w[*m + 1], &iblock[*m + 1], &iinfo);
  1089. nwl += iwork[1];
  1090. nwu += iwork[in + 1];
  1091. iwoff = *m - iwork[1];
  1092. /* Compute Eigenvalues */
  1093. itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(2.)
  1094. ) + 2;
  1095. dlaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
  1096. pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
  1097. work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
  1098. &w[*m + 1], &iblock[*m + 1], &iinfo);
  1099. /* Copy Eigenvalues Into W and IBLOCK */
  1100. /* Use -JB for block number for unconverged eigenvalues. */
  1101. i__2 = iout;
  1102. for (j = 1; j <= i__2; ++j) {
  1103. tmp1 = (work[j + *n] + work[j + in + *n]) * .5;
  1104. /* Flag non-convergence. */
  1105. if (j > iout - iinfo) {
  1106. ncnvrg = TRUE_;
  1107. ib = -jb;
  1108. } else {
  1109. ib = jb;
  1110. }
  1111. i__3 = iwork[j + in] + iwoff;
  1112. for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
  1113. w[je] = tmp1;
  1114. iblock[je] = ib;
  1115. /* L50: */
  1116. }
  1117. /* L60: */
  1118. }
  1119. *m += im;
  1120. }
  1121. L70:
  1122. ;
  1123. }
  1124. /* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
  1125. /* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
  1126. if (irange == 3) {
  1127. im = 0;
  1128. idiscl = *il - 1 - nwl;
  1129. idiscu = nwu - *iu;
  1130. if (idiscl > 0 || idiscu > 0) {
  1131. i__1 = *m;
  1132. for (je = 1; je <= i__1; ++je) {
  1133. if (w[je] <= wlu && idiscl > 0) {
  1134. --idiscl;
  1135. } else if (w[je] >= wul && idiscu > 0) {
  1136. --idiscu;
  1137. } else {
  1138. ++im;
  1139. w[im] = w[je];
  1140. iblock[im] = iblock[je];
  1141. }
  1142. /* L80: */
  1143. }
  1144. *m = im;
  1145. }
  1146. if (idiscl > 0 || idiscu > 0) {
  1147. /* Code to deal with effects of bad arithmetic: */
  1148. /* Some low eigenvalues to be discarded are not in (WL,WLU], */
  1149. /* or high eigenvalues to be discarded are not in (WUL,WU] */
  1150. /* so just kill off the smallest IDISCL/largest IDISCU */
  1151. /* eigenvalues, by simply finding the smallest/largest */
  1152. /* eigenvalue(s). */
  1153. /* (If N(w) is monotone non-decreasing, this should never */
  1154. /* happen.) */
  1155. if (idiscl > 0) {
  1156. wkill = wu;
  1157. i__1 = idiscl;
  1158. for (jdisc = 1; jdisc <= i__1; ++jdisc) {
  1159. iw = 0;
  1160. i__2 = *m;
  1161. for (je = 1; je <= i__2; ++je) {
  1162. if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
  1163. iw = je;
  1164. wkill = w[je];
  1165. }
  1166. /* L90: */
  1167. }
  1168. iblock[iw] = 0;
  1169. /* L100: */
  1170. }
  1171. }
  1172. if (idiscu > 0) {
  1173. wkill = wl;
  1174. i__1 = idiscu;
  1175. for (jdisc = 1; jdisc <= i__1; ++jdisc) {
  1176. iw = 0;
  1177. i__2 = *m;
  1178. for (je = 1; je <= i__2; ++je) {
  1179. if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
  1180. iw = je;
  1181. wkill = w[je];
  1182. }
  1183. /* L110: */
  1184. }
  1185. iblock[iw] = 0;
  1186. /* L120: */
  1187. }
  1188. }
  1189. im = 0;
  1190. i__1 = *m;
  1191. for (je = 1; je <= i__1; ++je) {
  1192. if (iblock[je] != 0) {
  1193. ++im;
  1194. w[im] = w[je];
  1195. iblock[im] = iblock[je];
  1196. }
  1197. /* L130: */
  1198. }
  1199. *m = im;
  1200. }
  1201. if (idiscl < 0 || idiscu < 0) {
  1202. toofew = TRUE_;
  1203. }
  1204. }
  1205. /* If ORDER='B', do nothing -- the eigenvalues are already sorted */
  1206. /* by block. */
  1207. /* If ORDER='E', sort the eigenvalues from smallest to largest */
  1208. if (iorder == 1 && *nsplit > 1) {
  1209. i__1 = *m - 1;
  1210. for (je = 1; je <= i__1; ++je) {
  1211. ie = 0;
  1212. tmp1 = w[je];
  1213. i__2 = *m;
  1214. for (j = je + 1; j <= i__2; ++j) {
  1215. if (w[j] < tmp1) {
  1216. ie = j;
  1217. tmp1 = w[j];
  1218. }
  1219. /* L140: */
  1220. }
  1221. if (ie != 0) {
  1222. itmp1 = iblock[ie];
  1223. w[ie] = w[je];
  1224. iblock[ie] = iblock[je];
  1225. w[je] = tmp1;
  1226. iblock[je] = itmp1;
  1227. }
  1228. /* L150: */
  1229. }
  1230. }
  1231. *info = 0;
  1232. if (ncnvrg) {
  1233. ++(*info);
  1234. }
  1235. if (toofew) {
  1236. *info += 2;
  1237. }
  1238. return;
  1239. /* End of DSTEBZ */
  1240. } /* dstebz_ */