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claed0.c 23 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__9 = 9;
  363. static integer c__0 = 0;
  364. static integer c__2 = 2;
  365. static integer c__1 = 1;
  366. /* > \brief \b CLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced
  367. symmetric tridiagonal matrix using the divide and conquer method. */
  368. /* =========== DOCUMENTATION =========== */
  369. /* Online html documentation available at */
  370. /* http://www.netlib.org/lapack/explore-html/ */
  371. /* > \htmlonly */
  372. /* > Download CLAED0 + dependencies */
  373. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claed0.
  374. f"> */
  375. /* > [TGZ]</a> */
  376. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claed0.
  377. f"> */
  378. /* > [ZIP]</a> */
  379. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claed0.
  380. f"> */
  381. /* > [TXT]</a> */
  382. /* > \endhtmlonly */
  383. /* Definition: */
  384. /* =========== */
  385. /* SUBROUTINE CLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, */
  386. /* IWORK, INFO ) */
  387. /* INTEGER INFO, LDQ, LDQS, N, QSIZ */
  388. /* INTEGER IWORK( * ) */
  389. /* REAL D( * ), E( * ), RWORK( * ) */
  390. /* COMPLEX Q( LDQ, * ), QSTORE( LDQS, * ) */
  391. /* > \par Purpose: */
  392. /* ============= */
  393. /* > */
  394. /* > \verbatim */
  395. /* > */
  396. /* > Using the divide and conquer method, CLAED0 computes all eigenvalues */
  397. /* > of a symmetric tridiagonal matrix which is one diagonal block of */
  398. /* > those from reducing a dense or band Hermitian matrix and */
  399. /* > corresponding eigenvectors of the dense or band matrix. */
  400. /* > \endverbatim */
  401. /* Arguments: */
  402. /* ========== */
  403. /* > \param[in] QSIZ */
  404. /* > \verbatim */
  405. /* > QSIZ is INTEGER */
  406. /* > The dimension of the unitary matrix used to reduce */
  407. /* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
  408. /* > \endverbatim */
  409. /* > */
  410. /* > \param[in] N */
  411. /* > \verbatim */
  412. /* > N is INTEGER */
  413. /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
  414. /* > \endverbatim */
  415. /* > */
  416. /* > \param[in,out] D */
  417. /* > \verbatim */
  418. /* > D is REAL array, dimension (N) */
  419. /* > On entry, the diagonal elements of the tridiagonal matrix. */
  420. /* > On exit, the eigenvalues in ascending order. */
  421. /* > \endverbatim */
  422. /* > */
  423. /* > \param[in,out] E */
  424. /* > \verbatim */
  425. /* > E is REAL array, dimension (N-1) */
  426. /* > On entry, the off-diagonal elements of the tridiagonal matrix. */
  427. /* > On exit, E has been destroyed. */
  428. /* > \endverbatim */
  429. /* > */
  430. /* > \param[in,out] Q */
  431. /* > \verbatim */
  432. /* > Q is COMPLEX array, dimension (LDQ,N) */
  433. /* > On entry, Q must contain an QSIZ x N matrix whose columns */
  434. /* > unitarily orthonormal. It is a part of the unitary matrix */
  435. /* > that reduces the full dense Hermitian matrix to a */
  436. /* > (reducible) symmetric tridiagonal matrix. */
  437. /* > \endverbatim */
  438. /* > */
  439. /* > \param[in] LDQ */
  440. /* > \verbatim */
  441. /* > LDQ is INTEGER */
  442. /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N). */
  443. /* > \endverbatim */
  444. /* > */
  445. /* > \param[out] IWORK */
  446. /* > \verbatim */
  447. /* > IWORK is INTEGER array, */
  448. /* > the dimension of IWORK must be at least */
  449. /* > 6 + 6*N + 5*N*lg N */
  450. /* > ( lg( N ) = smallest integer k */
  451. /* > such that 2^k >= N ) */
  452. /* > \endverbatim */
  453. /* > */
  454. /* > \param[out] RWORK */
  455. /* > \verbatim */
  456. /* > RWORK is REAL array, */
  457. /* > dimension (1 + 3*N + 2*N*lg N + 3*N**2) */
  458. /* > ( lg( N ) = smallest integer k */
  459. /* > such that 2^k >= N ) */
  460. /* > \endverbatim */
  461. /* > */
  462. /* > \param[out] QSTORE */
  463. /* > \verbatim */
  464. /* > QSTORE is COMPLEX array, dimension (LDQS, N) */
  465. /* > Used to store parts of */
  466. /* > the eigenvector matrix when the updating matrix multiplies */
  467. /* > take place. */
  468. /* > \endverbatim */
  469. /* > */
  470. /* > \param[in] LDQS */
  471. /* > \verbatim */
  472. /* > LDQS is INTEGER */
  473. /* > The leading dimension of the array QSTORE. */
  474. /* > LDQS >= f2cmax(1,N). */
  475. /* > \endverbatim */
  476. /* > */
  477. /* > \param[out] INFO */
  478. /* > \verbatim */
  479. /* > INFO is INTEGER */
  480. /* > = 0: successful exit. */
  481. /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  482. /* > > 0: The algorithm failed to compute an eigenvalue while */
  483. /* > working on the submatrix lying in rows and columns */
  484. /* > INFO/(N+1) through mod(INFO,N+1). */
  485. /* > \endverbatim */
  486. /* Authors: */
  487. /* ======== */
  488. /* > \author Univ. of Tennessee */
  489. /* > \author Univ. of California Berkeley */
  490. /* > \author Univ. of Colorado Denver */
  491. /* > \author NAG Ltd. */
  492. /* > \date December 2016 */
  493. /* > \ingroup complexOTHERcomputational */
  494. /* ===================================================================== */
  495. /* Subroutine */ int claed0_(integer *qsiz, integer *n, real *d__, real *e,
  496. complex *q, integer *ldq, complex *qstore, integer *ldqs, real *rwork,
  497. integer *iwork, integer *info)
  498. {
  499. /* System generated locals */
  500. integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
  501. real r__1;
  502. /* Local variables */
  503. real temp;
  504. integer curr, i__, j, k, iperm;
  505. extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
  506. complex *, integer *);
  507. integer indxq, iwrem;
  508. extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
  509. integer *);
  510. integer iqptr;
  511. extern /* Subroutine */ int claed7_(integer *, integer *, integer *,
  512. integer *, integer *, integer *, real *, complex *, integer *,
  513. real *, integer *, real *, integer *, integer *, integer *,
  514. integer *, integer *, real *, complex *, real *, integer *,
  515. integer *);
  516. integer tlvls, ll, iq;
  517. extern /* Subroutine */ int clacrm_(integer *, integer *, complex *,
  518. integer *, real *, integer *, complex *, integer *, real *);
  519. integer igivcl;
  520. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  521. extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
  522. integer *, integer *, ftnlen, ftnlen);
  523. integer igivnm, submat, curprb, subpbs, igivpt, curlvl, matsiz, iprmpt,
  524. smlsiz;
  525. extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *,
  526. real *, integer *, real *, integer *);
  527. integer lgn, msd2, smm1, spm1, spm2;
  528. /* -- LAPACK computational routine (version 3.7.0) -- */
  529. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  530. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  531. /* December 2016 */
  532. /* ===================================================================== */
  533. /* Warning: N could be as big as QSIZ! */
  534. /* Test the input parameters. */
  535. /* Parameter adjustments */
  536. --d__;
  537. --e;
  538. q_dim1 = *ldq;
  539. q_offset = 1 + q_dim1 * 1;
  540. q -= q_offset;
  541. qstore_dim1 = *ldqs;
  542. qstore_offset = 1 + qstore_dim1 * 1;
  543. qstore -= qstore_offset;
  544. --rwork;
  545. --iwork;
  546. /* Function Body */
  547. *info = 0;
  548. /* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN */
  549. /* INFO = -1 */
  550. /* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */
  551. /* $ THEN */
  552. if (*qsiz < f2cmax(0,*n)) {
  553. *info = -1;
  554. } else if (*n < 0) {
  555. *info = -2;
  556. } else if (*ldq < f2cmax(1,*n)) {
  557. *info = -6;
  558. } else if (*ldqs < f2cmax(1,*n)) {
  559. *info = -8;
  560. }
  561. if (*info != 0) {
  562. i__1 = -(*info);
  563. xerbla_("CLAED0", &i__1, (ftnlen)6);
  564. return 0;
  565. }
  566. /* Quick return if possible */
  567. if (*n == 0) {
  568. return 0;
  569. }
  570. smlsiz = ilaenv_(&c__9, "CLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
  571. ftnlen)6, (ftnlen)1);
  572. /* Determine the size and placement of the submatrices, and save in */
  573. /* the leading elements of IWORK. */
  574. iwork[1] = *n;
  575. subpbs = 1;
  576. tlvls = 0;
  577. L10:
  578. if (iwork[subpbs] > smlsiz) {
  579. for (j = subpbs; j >= 1; --j) {
  580. iwork[j * 2] = (iwork[j] + 1) / 2;
  581. iwork[(j << 1) - 1] = iwork[j] / 2;
  582. /* L20: */
  583. }
  584. ++tlvls;
  585. subpbs <<= 1;
  586. goto L10;
  587. }
  588. i__1 = subpbs;
  589. for (j = 2; j <= i__1; ++j) {
  590. iwork[j] += iwork[j - 1];
  591. /* L30: */
  592. }
  593. /* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */
  594. /* using rank-1 modifications (cuts). */
  595. spm1 = subpbs - 1;
  596. i__1 = spm1;
  597. for (i__ = 1; i__ <= i__1; ++i__) {
  598. submat = iwork[i__] + 1;
  599. smm1 = submat - 1;
  600. d__[smm1] -= (r__1 = e[smm1], abs(r__1));
  601. d__[submat] -= (r__1 = e[smm1], abs(r__1));
  602. /* L40: */
  603. }
  604. indxq = (*n << 2) + 3;
  605. /* Set up workspaces for eigenvalues only/accumulate new vectors */
  606. /* routine */
  607. temp = log((real) (*n)) / log(2.f);
  608. lgn = (integer) temp;
  609. if (pow_ii(&c__2, &lgn) < *n) {
  610. ++lgn;
  611. }
  612. if (pow_ii(&c__2, &lgn) < *n) {
  613. ++lgn;
  614. }
  615. iprmpt = indxq + *n + 1;
  616. iperm = iprmpt + *n * lgn;
  617. iqptr = iperm + *n * lgn;
  618. igivpt = iqptr + *n + 2;
  619. igivcl = igivpt + *n * lgn;
  620. igivnm = 1;
  621. iq = igivnm + (*n << 1) * lgn;
  622. /* Computing 2nd power */
  623. i__1 = *n;
  624. iwrem = iq + i__1 * i__1 + 1;
  625. /* Initialize pointers */
  626. i__1 = subpbs;
  627. for (i__ = 0; i__ <= i__1; ++i__) {
  628. iwork[iprmpt + i__] = 1;
  629. iwork[igivpt + i__] = 1;
  630. /* L50: */
  631. }
  632. iwork[iqptr] = 1;
  633. /* Solve each submatrix eigenproblem at the bottom of the divide and */
  634. /* conquer tree. */
  635. curr = 0;
  636. i__1 = spm1;
  637. for (i__ = 0; i__ <= i__1; ++i__) {
  638. if (i__ == 0) {
  639. submat = 1;
  640. matsiz = iwork[1];
  641. } else {
  642. submat = iwork[i__] + 1;
  643. matsiz = iwork[i__ + 1] - iwork[i__];
  644. }
  645. ll = iq - 1 + iwork[iqptr + curr];
  646. ssteqr_("I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &
  647. rwork[1], info);
  648. clacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], &
  649. matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem]
  650. );
  651. /* Computing 2nd power */
  652. i__2 = matsiz;
  653. iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
  654. ++curr;
  655. if (*info > 0) {
  656. *info = submat * (*n + 1) + submat + matsiz - 1;
  657. return 0;
  658. }
  659. k = 1;
  660. i__2 = iwork[i__ + 1];
  661. for (j = submat; j <= i__2; ++j) {
  662. iwork[indxq + j] = k;
  663. ++k;
  664. /* L60: */
  665. }
  666. /* L70: */
  667. }
  668. /* Successively merge eigensystems of adjacent submatrices */
  669. /* into eigensystem for the corresponding larger matrix. */
  670. /* while ( SUBPBS > 1 ) */
  671. curlvl = 1;
  672. L80:
  673. if (subpbs > 1) {
  674. spm2 = subpbs - 2;
  675. i__1 = spm2;
  676. for (i__ = 0; i__ <= i__1; i__ += 2) {
  677. if (i__ == 0) {
  678. submat = 1;
  679. matsiz = iwork[2];
  680. msd2 = iwork[1];
  681. curprb = 0;
  682. } else {
  683. submat = iwork[i__] + 1;
  684. matsiz = iwork[i__ + 2] - iwork[i__];
  685. msd2 = matsiz / 2;
  686. ++curprb;
  687. }
  688. /* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */
  689. /* into an eigensystem of size MATSIZ. CLAED7 handles the case */
  690. /* when the eigenvectors of a full or band Hermitian matrix (which */
  691. /* was reduced to tridiagonal form) are desired. */
  692. /* I am free to use Q as a valuable working space until Loop 150. */
  693. claed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[
  694. submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[
  695. submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], &
  696. iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[
  697. igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat *
  698. q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info);
  699. if (*info > 0) {
  700. *info = submat * (*n + 1) + submat + matsiz - 1;
  701. return 0;
  702. }
  703. iwork[i__ / 2 + 1] = iwork[i__ + 2];
  704. /* L90: */
  705. }
  706. subpbs /= 2;
  707. ++curlvl;
  708. goto L80;
  709. }
  710. /* end while */
  711. /* Re-merge the eigenvalues/vectors which were deflated at the final */
  712. /* merge step. */
  713. i__1 = *n;
  714. for (i__ = 1; i__ <= i__1; ++i__) {
  715. j = iwork[indxq + i__];
  716. rwork[i__] = d__[j];
  717. ccopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1]
  718. , &c__1);
  719. /* L100: */
  720. }
  721. scopy_(n, &rwork[1], &c__1, &d__[1], &c__1);
  722. return 0;
  723. /* End of CLAED0 */
  724. } /* claed0_ */