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sstein.c 24 kB

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  1. /* f2c.h -- Standard Fortran to C header file */
  2. /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
  3. - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  4. #ifndef F2C_INCLUDE
  5. #define F2C_INCLUDE
  6. #include <math.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <stdio.h>
  10. #include <complex.h>
  11. #ifdef complex
  12. #undef complex
  13. #endif
  14. #ifdef I
  15. #undef I
  16. #endif
  17. typedef int integer;
  18. typedef unsigned int uinteger;
  19. typedef char *address;
  20. typedef short int shortint;
  21. typedef float real;
  22. typedef double doublereal;
  23. typedef struct { real r, i; } complex;
  24. typedef struct { doublereal r, i; } doublecomplex;
  25. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  26. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  27. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  28. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  29. #define pCf(z) (*_pCf(z))
  30. #define pCd(z) (*_pCd(z))
  31. typedef int logical;
  32. typedef short int shortlogical;
  33. typedef char logical1;
  34. typedef char integer1;
  35. #define TRUE_ (1)
  36. #define FALSE_ (0)
  37. /* Extern is for use with -E */
  38. #ifndef Extern
  39. #define Extern extern
  40. #endif
  41. /* I/O stuff */
  42. typedef int flag;
  43. typedef int ftnlen;
  44. typedef int ftnint;
  45. /*external read, write*/
  46. typedef struct
  47. { flag cierr;
  48. ftnint ciunit;
  49. flag ciend;
  50. char *cifmt;
  51. ftnint cirec;
  52. } cilist;
  53. /*internal read, write*/
  54. typedef struct
  55. { flag icierr;
  56. char *iciunit;
  57. flag iciend;
  58. char *icifmt;
  59. ftnint icirlen;
  60. ftnint icirnum;
  61. } icilist;
  62. /*open*/
  63. typedef struct
  64. { flag oerr;
  65. ftnint ounit;
  66. char *ofnm;
  67. ftnlen ofnmlen;
  68. char *osta;
  69. char *oacc;
  70. char *ofm;
  71. ftnint orl;
  72. char *oblnk;
  73. } olist;
  74. /*close*/
  75. typedef struct
  76. { flag cerr;
  77. ftnint cunit;
  78. char *csta;
  79. } cllist;
  80. /*rewind, backspace, endfile*/
  81. typedef struct
  82. { flag aerr;
  83. ftnint aunit;
  84. } alist;
  85. /* inquire */
  86. typedef struct
  87. { flag inerr;
  88. ftnint inunit;
  89. char *infile;
  90. ftnlen infilen;
  91. ftnint *inex; /*parameters in standard's order*/
  92. ftnint *inopen;
  93. ftnint *innum;
  94. ftnint *innamed;
  95. char *inname;
  96. ftnlen innamlen;
  97. char *inacc;
  98. ftnlen inacclen;
  99. char *inseq;
  100. ftnlen inseqlen;
  101. char *indir;
  102. ftnlen indirlen;
  103. char *infmt;
  104. ftnlen infmtlen;
  105. char *inform;
  106. ftnint informlen;
  107. char *inunf;
  108. ftnlen inunflen;
  109. ftnint *inrecl;
  110. ftnint *innrec;
  111. char *inblank;
  112. ftnlen inblanklen;
  113. } inlist;
  114. #define VOID void
  115. union Multitype { /* for multiple entry points */
  116. integer1 g;
  117. shortint h;
  118. integer i;
  119. /* longint j; */
  120. real r;
  121. doublereal d;
  122. complex c;
  123. doublecomplex z;
  124. };
  125. typedef union Multitype Multitype;
  126. struct Vardesc { /* for Namelist */
  127. char *name;
  128. char *addr;
  129. ftnlen *dims;
  130. int type;
  131. };
  132. typedef struct Vardesc Vardesc;
  133. struct Namelist {
  134. char *name;
  135. Vardesc **vars;
  136. int nvars;
  137. };
  138. typedef struct Namelist Namelist;
  139. #define abs(x) ((x) >= 0 ? (x) : -(x))
  140. #define dabs(x) (fabs(x))
  141. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  142. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  143. #define dmin(a,b) (f2cmin(a,b))
  144. #define dmax(a,b) (f2cmax(a,b))
  145. #define bit_test(a,b) ((a) >> (b) & 1)
  146. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  147. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  148. #define abort_() { sig_die("Fortran abort routine called", 1); }
  149. #define c_abs(z) (cabsf(Cf(z)))
  150. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  151. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  152. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  153. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  154. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  155. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  156. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  157. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  158. #define d_abs(x) (fabs(*(x)))
  159. #define d_acos(x) (acos(*(x)))
  160. #define d_asin(x) (asin(*(x)))
  161. #define d_atan(x) (atan(*(x)))
  162. #define d_atn2(x, y) (atan2(*(x),*(y)))
  163. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  164. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  165. #define d_cos(x) (cos(*(x)))
  166. #define d_cosh(x) (cosh(*(x)))
  167. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  168. #define d_exp(x) (exp(*(x)))
  169. #define d_imag(z) (cimag(Cd(z)))
  170. #define r_imag(z) (cimag(Cf(z)))
  171. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  172. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  173. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  174. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  175. #define d_log(x) (log(*(x)))
  176. #define d_mod(x, y) (fmod(*(x), *(y)))
  177. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  178. #define d_nint(x) u_nint(*(x))
  179. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  180. #define d_sign(a,b) u_sign(*(a),*(b))
  181. #define r_sign(a,b) u_sign(*(a),*(b))
  182. #define d_sin(x) (sin(*(x)))
  183. #define d_sinh(x) (sinh(*(x)))
  184. #define d_sqrt(x) (sqrt(*(x)))
  185. #define d_tan(x) (tan(*(x)))
  186. #define d_tanh(x) (tanh(*(x)))
  187. #define i_abs(x) abs(*(x))
  188. #define i_dnnt(x) ((integer)u_nint(*(x)))
  189. #define i_len(s, n) (n)
  190. #define i_nint(x) ((integer)u_nint(*(x)))
  191. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  192. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  193. #define pow_si(B,E) spow_ui(*(B),*(E))
  194. #define pow_ri(B,E) spow_ui(*(B),*(E))
  195. #define pow_di(B,E) dpow_ui(*(B),*(E))
  196. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  197. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  198. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  199. #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++ = ' '; }
  200. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  201. #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]; }
  202. #define sig_die(s, kill) { exit(1); }
  203. #define s_stop(s, n) {exit(0);}
  204. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  205. #define z_abs(z) (cabs(Cd(z)))
  206. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  207. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  208. #define myexit_() break;
  209. #define mycycle() continue;
  210. #define myceiling(w) {ceil(w)}
  211. #define myhuge(w) {HUGE_VAL}
  212. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  213. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  214. /* procedure parameter types for -A and -C++ */
  215. #define F2C_proc_par_types 1
  216. #ifdef __cplusplus
  217. typedef logical (*L_fp)(...);
  218. #else
  219. typedef logical (*L_fp)();
  220. #endif
  221. static float spow_ui(float x, integer n) {
  222. float pow=1.0; unsigned long int u;
  223. if(n != 0) {
  224. if(n < 0) n = -n, x = 1/x;
  225. for(u = n; ; ) {
  226. if(u & 01) pow *= x;
  227. if(u >>= 1) x *= x;
  228. else break;
  229. }
  230. }
  231. return pow;
  232. }
  233. static double dpow_ui(double x, integer n) {
  234. double pow=1.0; unsigned long int u;
  235. if(n != 0) {
  236. if(n < 0) n = -n, x = 1/x;
  237. for(u = n; ; ) {
  238. if(u & 01) pow *= x;
  239. if(u >>= 1) x *= x;
  240. else break;
  241. }
  242. }
  243. return pow;
  244. }
  245. static _Complex float cpow_ui(_Complex float x, integer n) {
  246. _Complex float pow=1.0; unsigned long int u;
  247. if(n != 0) {
  248. if(n < 0) n = -n, x = 1/x;
  249. for(u = n; ; ) {
  250. if(u & 01) pow *= x;
  251. if(u >>= 1) x *= x;
  252. else break;
  253. }
  254. }
  255. return pow;
  256. }
  257. static _Complex double zpow_ui(_Complex double x, integer n) {
  258. _Complex double pow=1.0; unsigned long int u;
  259. if(n != 0) {
  260. if(n < 0) n = -n, x = 1/x;
  261. for(u = n; ; ) {
  262. if(u & 01) pow *= x;
  263. if(u >>= 1) x *= x;
  264. else break;
  265. }
  266. }
  267. return pow;
  268. }
  269. static integer pow_ii(integer x, integer n) {
  270. integer pow; unsigned long int u;
  271. if (n <= 0) {
  272. if (n == 0 || x == 1) pow = 1;
  273. else if (x != -1) pow = x == 0 ? 1/x : 0;
  274. else n = -n;
  275. }
  276. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  277. u = n;
  278. for(pow = 1; ; ) {
  279. if(u & 01) pow *= x;
  280. if(u >>= 1) x *= x;
  281. else break;
  282. }
  283. }
  284. return pow;
  285. }
  286. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  287. {
  288. double m; integer i, mi;
  289. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  290. if (w[i-1]>m) mi=i ,m=w[i-1];
  291. return mi-s+1;
  292. }
  293. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  294. {
  295. float m; integer i, mi;
  296. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  297. if (w[i-1]>m) mi=i ,m=w[i-1];
  298. return mi-s+1;
  299. }
  300. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  301. integer n = *n_, incx = *incx_, incy = *incy_, i;
  302. _Complex float zdotc = 0.0;
  303. if (incx == 1 && incy == 1) {
  304. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  305. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  306. }
  307. } else {
  308. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  309. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  310. }
  311. }
  312. pCf(z) = zdotc;
  313. }
  314. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  315. integer n = *n_, incx = *incx_, incy = *incy_, i;
  316. _Complex double zdotc = 0.0;
  317. if (incx == 1 && incy == 1) {
  318. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  319. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  320. }
  321. } else {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  324. }
  325. }
  326. pCd(z) = zdotc;
  327. }
  328. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  329. integer n = *n_, incx = *incx_, incy = *incy_, i;
  330. _Complex float zdotc = 0.0;
  331. if (incx == 1 && incy == 1) {
  332. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  333. zdotc += Cf(&x[i]) * Cf(&y[i]);
  334. }
  335. } else {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  338. }
  339. }
  340. pCf(z) = zdotc;
  341. }
  342. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  343. integer n = *n_, incx = *incx_, incy = *incy_, i;
  344. _Complex double zdotc = 0.0;
  345. if (incx == 1 && incy == 1) {
  346. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  347. zdotc += Cd(&x[i]) * Cd(&y[i]);
  348. }
  349. } else {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  352. }
  353. }
  354. pCd(z) = zdotc;
  355. }
  356. #endif
  357. /* -- translated by f2c (version 20000121).
  358. You must link the resulting object file with the libraries:
  359. -lf2c -lm (in that order)
  360. */
  361. /* Table of constant values */
  362. static integer c__2 = 2;
  363. static integer c__1 = 1;
  364. static integer c_n1 = -1;
  365. /* > \brief \b SSTEIN */
  366. /* =========== DOCUMENTATION =========== */
  367. /* Online html documentation available at */
  368. /* http://www.netlib.org/lapack/explore-html/ */
  369. /* > \htmlonly */
  370. /* > Download SSTEIN + dependencies */
  371. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstein.
  372. f"> */
  373. /* > [TGZ]</a> */
  374. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstein.
  375. f"> */
  376. /* > [ZIP]</a> */
  377. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstein.
  378. f"> */
  379. /* > [TXT]</a> */
  380. /* > \endhtmlonly */
  381. /* Definition: */
  382. /* =========== */
  383. /* SUBROUTINE SSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, */
  384. /* IWORK, IFAIL, INFO ) */
  385. /* INTEGER INFO, LDZ, M, N */
  386. /* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), */
  387. /* $ IWORK( * ) */
  388. /* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) */
  389. /* > \par Purpose: */
  390. /* ============= */
  391. /* > */
  392. /* > \verbatim */
  393. /* > */
  394. /* > SSTEIN computes the eigenvectors of a real symmetric tridiagonal */
  395. /* > matrix T corresponding to specified eigenvalues, using inverse */
  396. /* > iteration. */
  397. /* > */
  398. /* > The maximum number of iterations allowed for each eigenvector is */
  399. /* > specified by an internal parameter MAXITS (currently set to 5). */
  400. /* > \endverbatim */
  401. /* Arguments: */
  402. /* ========== */
  403. /* > \param[in] N */
  404. /* > \verbatim */
  405. /* > N is INTEGER */
  406. /* > The order of the matrix. N >= 0. */
  407. /* > \endverbatim */
  408. /* > */
  409. /* > \param[in] D */
  410. /* > \verbatim */
  411. /* > D is REAL array, dimension (N) */
  412. /* > The n diagonal elements of the tridiagonal matrix T. */
  413. /* > \endverbatim */
  414. /* > */
  415. /* > \param[in] E */
  416. /* > \verbatim */
  417. /* > E is REAL array, dimension (N-1) */
  418. /* > The (n-1) subdiagonal elements of the tridiagonal matrix */
  419. /* > T, in elements 1 to N-1. */
  420. /* > \endverbatim */
  421. /* > */
  422. /* > \param[in] M */
  423. /* > \verbatim */
  424. /* > M is INTEGER */
  425. /* > The number of eigenvectors to be found. 0 <= M <= N. */
  426. /* > \endverbatim */
  427. /* > */
  428. /* > \param[in] W */
  429. /* > \verbatim */
  430. /* > W is REAL array, dimension (N) */
  431. /* > The first M elements of W contain the eigenvalues for */
  432. /* > which eigenvectors are to be computed. The eigenvalues */
  433. /* > should be grouped by split-off block and ordered from */
  434. /* > smallest to largest within the block. ( The output array */
  435. /* > W from SSTEBZ with ORDER = 'B' is expected here. ) */
  436. /* > \endverbatim */
  437. /* > */
  438. /* > \param[in] IBLOCK */
  439. /* > \verbatim */
  440. /* > IBLOCK is INTEGER array, dimension (N) */
  441. /* > The submatrix indices associated with the corresponding */
  442. /* > eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */
  443. /* > the first submatrix from the top, =2 if W(i) belongs to */
  444. /* > the second submatrix, etc. ( The output array IBLOCK */
  445. /* > from SSTEBZ is expected here. ) */
  446. /* > \endverbatim */
  447. /* > */
  448. /* > \param[in] ISPLIT */
  449. /* > \verbatim */
  450. /* > ISPLIT is INTEGER array, dimension (N) */
  451. /* > The splitting points, at which T breaks up into submatrices. */
  452. /* > The first submatrix consists of rows/columns 1 to */
  453. /* > ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
  454. /* > through ISPLIT( 2 ), etc. */
  455. /* > ( The output array ISPLIT from SSTEBZ is expected here. ) */
  456. /* > \endverbatim */
  457. /* > */
  458. /* > \param[out] Z */
  459. /* > \verbatim */
  460. /* > Z is REAL array, dimension (LDZ, M) */
  461. /* > The computed eigenvectors. The eigenvector associated */
  462. /* > with the eigenvalue W(i) is stored in the i-th column of */
  463. /* > Z. Any vector which fails to converge is set to its current */
  464. /* > iterate after MAXITS iterations. */
  465. /* > \endverbatim */
  466. /* > */
  467. /* > \param[in] LDZ */
  468. /* > \verbatim */
  469. /* > LDZ is INTEGER */
  470. /* > The leading dimension of the array Z. LDZ >= f2cmax(1,N). */
  471. /* > \endverbatim */
  472. /* > */
  473. /* > \param[out] WORK */
  474. /* > \verbatim */
  475. /* > WORK is REAL array, dimension (5*N) */
  476. /* > \endverbatim */
  477. /* > */
  478. /* > \param[out] IWORK */
  479. /* > \verbatim */
  480. /* > IWORK is INTEGER array, dimension (N) */
  481. /* > \endverbatim */
  482. /* > */
  483. /* > \param[out] IFAIL */
  484. /* > \verbatim */
  485. /* > IFAIL is INTEGER array, dimension (M) */
  486. /* > On normal exit, all elements of IFAIL are zero. */
  487. /* > If one or more eigenvectors fail to converge after */
  488. /* > MAXITS iterations, then their indices are stored in */
  489. /* > array IFAIL. */
  490. /* > \endverbatim */
  491. /* > */
  492. /* > \param[out] INFO */
  493. /* > \verbatim */
  494. /* > INFO is INTEGER */
  495. /* > = 0: successful exit. */
  496. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  497. /* > > 0: if INFO = i, then i eigenvectors failed to converge */
  498. /* > in MAXITS iterations. Their indices are stored in */
  499. /* > array IFAIL. */
  500. /* > \endverbatim */
  501. /* > \par Internal Parameters: */
  502. /* ========================= */
  503. /* > */
  504. /* > \verbatim */
  505. /* > MAXITS INTEGER, default = 5 */
  506. /* > The maximum number of iterations performed. */
  507. /* > */
  508. /* > EXTRA INTEGER, default = 2 */
  509. /* > The number of iterations performed after norm growth */
  510. /* > criterion is satisfied, should be at least 1. */
  511. /* > \endverbatim */
  512. /* Authors: */
  513. /* ======== */
  514. /* > \author Univ. of Tennessee */
  515. /* > \author Univ. of California Berkeley */
  516. /* > \author Univ. of Colorado Denver */
  517. /* > \author NAG Ltd. */
  518. /* > \date December 2016 */
  519. /* > \ingroup realOTHERcomputational */
  520. /* ===================================================================== */
  521. /* Subroutine */ int sstein_(integer *n, real *d__, real *e, integer *m, real
  522. *w, integer *iblock, integer *isplit, real *z__, integer *ldz, real *
  523. work, integer *iwork, integer *ifail, integer *info)
  524. {
  525. /* System generated locals */
  526. integer z_dim1, z_offset, i__1, i__2, i__3;
  527. real r__1, r__2, r__3, r__4, r__5;
  528. /* Local variables */
  529. integer jblk, nblk, jmax;
  530. extern real sdot_(integer *, real *, integer *, real *, integer *),
  531. snrm2_(integer *, real *, integer *);
  532. integer i__, j, iseed[4], gpind, iinfo;
  533. extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
  534. integer b1, j1;
  535. extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
  536. integer *);
  537. real ortol;
  538. extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
  539. real *, integer *);
  540. integer indrv1, indrv2, indrv3, indrv4, indrv5, bn;
  541. real xj;
  542. extern real slamch_(char *);
  543. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slagtf_(
  544. integer *, real *, real *, real *, real *, real *, real *,
  545. integer *, integer *);
  546. integer nrmchk;
  547. extern integer isamax_(integer *, real *, integer *);
  548. extern /* Subroutine */ int slagts_(integer *, integer *, real *, real *,
  549. real *, real *, integer *, real *, real *, integer *);
  550. integer blksiz;
  551. real onenrm, pertol;
  552. extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real
  553. *);
  554. real stpcrt, scl, eps, ctr, sep, nrm, tol;
  555. integer its;
  556. real xjm, eps1;
  557. /* -- LAPACK computational routine (version 3.7.0) -- */
  558. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  559. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  560. /* December 2016 */
  561. /* ===================================================================== */
  562. /* Test the input parameters. */
  563. /* Parameter adjustments */
  564. --d__;
  565. --e;
  566. --w;
  567. --iblock;
  568. --isplit;
  569. z_dim1 = *ldz;
  570. z_offset = 1 + z_dim1 * 1;
  571. z__ -= z_offset;
  572. --work;
  573. --iwork;
  574. --ifail;
  575. /* Function Body */
  576. *info = 0;
  577. i__1 = *m;
  578. for (i__ = 1; i__ <= i__1; ++i__) {
  579. ifail[i__] = 0;
  580. /* L10: */
  581. }
  582. if (*n < 0) {
  583. *info = -1;
  584. } else if (*m < 0 || *m > *n) {
  585. *info = -4;
  586. } else if (*ldz < f2cmax(1,*n)) {
  587. *info = -9;
  588. } else {
  589. i__1 = *m;
  590. for (j = 2; j <= i__1; ++j) {
  591. if (iblock[j] < iblock[j - 1]) {
  592. *info = -6;
  593. goto L30;
  594. }
  595. if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
  596. *info = -5;
  597. goto L30;
  598. }
  599. /* L20: */
  600. }
  601. L30:
  602. ;
  603. }
  604. if (*info != 0) {
  605. i__1 = -(*info);
  606. xerbla_("SSTEIN", &i__1, (ftnlen)6);
  607. return 0;
  608. }
  609. /* Quick return if possible */
  610. if (*n == 0 || *m == 0) {
  611. return 0;
  612. } else if (*n == 1) {
  613. z__[z_dim1 + 1] = 1.f;
  614. return 0;
  615. }
  616. /* Get machine constants. */
  617. eps = slamch_("Precision");
  618. /* Initialize seed for random number generator SLARNV. */
  619. for (i__ = 1; i__ <= 4; ++i__) {
  620. iseed[i__ - 1] = 1;
  621. /* L40: */
  622. }
  623. /* Initialize pointers. */
  624. indrv1 = 0;
  625. indrv2 = indrv1 + *n;
  626. indrv3 = indrv2 + *n;
  627. indrv4 = indrv3 + *n;
  628. indrv5 = indrv4 + *n;
  629. /* Compute eigenvectors of matrix blocks. */
  630. j1 = 1;
  631. i__1 = iblock[*m];
  632. for (nblk = 1; nblk <= i__1; ++nblk) {
  633. /* Find starting and ending indices of block nblk. */
  634. if (nblk == 1) {
  635. b1 = 1;
  636. } else {
  637. b1 = isplit[nblk - 1] + 1;
  638. }
  639. bn = isplit[nblk];
  640. blksiz = bn - b1 + 1;
  641. if (blksiz == 1) {
  642. goto L60;
  643. }
  644. gpind = j1;
  645. /* Compute reorthogonalization criterion and stopping criterion. */
  646. onenrm = (r__1 = d__[b1], abs(r__1)) + (r__2 = e[b1], abs(r__2));
  647. /* Computing MAX */
  648. r__3 = onenrm, r__4 = (r__1 = d__[bn], abs(r__1)) + (r__2 = e[bn - 1],
  649. abs(r__2));
  650. onenrm = f2cmax(r__3,r__4);
  651. i__2 = bn - 1;
  652. for (i__ = b1 + 1; i__ <= i__2; ++i__) {
  653. /* Computing MAX */
  654. r__4 = onenrm, r__5 = (r__1 = d__[i__], abs(r__1)) + (r__2 = e[
  655. i__ - 1], abs(r__2)) + (r__3 = e[i__], abs(r__3));
  656. onenrm = f2cmax(r__4,r__5);
  657. /* L50: */
  658. }
  659. ortol = onenrm * .001f;
  660. stpcrt = sqrt(.1f / blksiz);
  661. /* Loop through eigenvalues of block nblk. */
  662. L60:
  663. jblk = 0;
  664. i__2 = *m;
  665. for (j = j1; j <= i__2; ++j) {
  666. if (iblock[j] != nblk) {
  667. j1 = j;
  668. goto L160;
  669. }
  670. ++jblk;
  671. xj = w[j];
  672. /* Skip all the work if the block size is one. */
  673. if (blksiz == 1) {
  674. work[indrv1 + 1] = 1.f;
  675. goto L120;
  676. }
  677. /* If eigenvalues j and j-1 are too close, add a relatively */
  678. /* small perturbation. */
  679. if (jblk > 1) {
  680. eps1 = (r__1 = eps * xj, abs(r__1));
  681. pertol = eps1 * 10.f;
  682. sep = xj - xjm;
  683. if (sep < pertol) {
  684. xj = xjm + pertol;
  685. }
  686. }
  687. its = 0;
  688. nrmchk = 0;
  689. /* Get random starting vector. */
  690. slarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);
  691. /* Copy the matrix T so it won't be destroyed in factorization. */
  692. scopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
  693. i__3 = blksiz - 1;
  694. scopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
  695. i__3 = blksiz - 1;
  696. scopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);
  697. /* Compute LU factors with partial pivoting ( PT = LU ) */
  698. tol = 0.f;
  699. slagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
  700. indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);
  701. /* Update iteration count. */
  702. L70:
  703. ++its;
  704. if (its > 5) {
  705. goto L100;
  706. }
  707. /* Normalize and scale the righthand side vector Pb. */
  708. jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
  709. /* Computing MAX */
  710. r__3 = eps, r__4 = (r__1 = work[indrv4 + blksiz], abs(r__1));
  711. scl = blksiz * onenrm * f2cmax(r__3,r__4) / (r__2 = work[indrv1 +
  712. jmax], abs(r__2));
  713. sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
  714. /* Solve the system LU = Pb. */
  715. slagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
  716. work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
  717. indrv1 + 1], &tol, &iinfo);
  718. /* Reorthogonalize by modified Gram-Schmidt if eigenvalues are */
  719. /* close enough. */
  720. if (jblk == 1) {
  721. goto L90;
  722. }
  723. if ((r__1 = xj - xjm, abs(r__1)) > ortol) {
  724. gpind = j;
  725. }
  726. if (gpind != j) {
  727. i__3 = j - 1;
  728. for (i__ = gpind; i__ <= i__3; ++i__) {
  729. ctr = -sdot_(&blksiz, &work[indrv1 + 1], &c__1, &z__[b1 +
  730. i__ * z_dim1], &c__1);
  731. saxpy_(&blksiz, &ctr, &z__[b1 + i__ * z_dim1], &c__1, &
  732. work[indrv1 + 1], &c__1);
  733. /* L80: */
  734. }
  735. }
  736. /* Check the infinity norm of the iterate. */
  737. L90:
  738. jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
  739. nrm = (r__1 = work[indrv1 + jmax], abs(r__1));
  740. /* Continue for additional iterations after norm reaches */
  741. /* stopping criterion. */
  742. if (nrm < stpcrt) {
  743. goto L70;
  744. }
  745. ++nrmchk;
  746. if (nrmchk < 3) {
  747. goto L70;
  748. }
  749. goto L110;
  750. /* If stopping criterion was not satisfied, update info and */
  751. /* store eigenvector number in array ifail. */
  752. L100:
  753. ++(*info);
  754. ifail[*info] = j;
  755. /* Accept iterate as jth eigenvector. */
  756. L110:
  757. scl = 1.f / snrm2_(&blksiz, &work[indrv1 + 1], &c__1);
  758. jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
  759. if (work[indrv1 + jmax] < 0.f) {
  760. scl = -scl;
  761. }
  762. sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
  763. L120:
  764. i__3 = *n;
  765. for (i__ = 1; i__ <= i__3; ++i__) {
  766. z__[i__ + j * z_dim1] = 0.f;
  767. /* L130: */
  768. }
  769. i__3 = blksiz;
  770. for (i__ = 1; i__ <= i__3; ++i__) {
  771. z__[b1 + i__ - 1 + j * z_dim1] = work[indrv1 + i__];
  772. /* L140: */
  773. }
  774. /* Save the shift to check eigenvalue spacing at next */
  775. /* iteration. */
  776. xjm = xj;
  777. /* L150: */
  778. }
  779. L160:
  780. ;
  781. }
  782. return 0;
  783. /* End of SSTEIN */
  784. } /* sstein_ */