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zsytri2x.c 40 kB

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  1. #include <math.h>
  2. #include <stdlib.h>
  3. #include <string.h>
  4. #include <stdio.h>
  5. #include <complex.h>
  6. #ifdef complex
  7. #undef complex
  8. #endif
  9. #ifdef I
  10. #undef I
  11. #endif
  12. #if defined(_WIN64)
  13. typedef long long BLASLONG;
  14. typedef unsigned long long BLASULONG;
  15. #else
  16. typedef long BLASLONG;
  17. typedef unsigned long BLASULONG;
  18. #endif
  19. #ifdef LAPACK_ILP64
  20. typedef BLASLONG blasint;
  21. #if defined(_WIN64)
  22. #define blasabs(x) llabs(x)
  23. #else
  24. #define blasabs(x) labs(x)
  25. #endif
  26. #else
  27. typedef int blasint;
  28. #define blasabs(x) abs(x)
  29. #endif
  30. typedef blasint integer;
  31. typedef unsigned int uinteger;
  32. typedef char *address;
  33. typedef short int shortint;
  34. typedef float real;
  35. typedef double doublereal;
  36. typedef struct { real r, i; } complex;
  37. typedef struct { doublereal r, i; } doublecomplex;
  38. #ifdef _MSC_VER
  39. static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
  40. static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
  41. static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
  42. static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
  43. #else
  44. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  46. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  47. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  48. #endif
  49. #define pCf(z) (*_pCf(z))
  50. #define pCd(z) (*_pCd(z))
  51. typedef int logical;
  52. typedef short int shortlogical;
  53. typedef char logical1;
  54. typedef char integer1;
  55. #define TRUE_ (1)
  56. #define FALSE_ (0)
  57. /* Extern is for use with -E */
  58. #ifndef Extern
  59. #define Extern extern
  60. #endif
  61. /* I/O stuff */
  62. typedef int flag;
  63. typedef int ftnlen;
  64. typedef int ftnint;
  65. /*external read, write*/
  66. typedef struct
  67. { flag cierr;
  68. ftnint ciunit;
  69. flag ciend;
  70. char *cifmt;
  71. ftnint cirec;
  72. } cilist;
  73. /*internal read, write*/
  74. typedef struct
  75. { flag icierr;
  76. char *iciunit;
  77. flag iciend;
  78. char *icifmt;
  79. ftnint icirlen;
  80. ftnint icirnum;
  81. } icilist;
  82. /*open*/
  83. typedef struct
  84. { flag oerr;
  85. ftnint ounit;
  86. char *ofnm;
  87. ftnlen ofnmlen;
  88. char *osta;
  89. char *oacc;
  90. char *ofm;
  91. ftnint orl;
  92. char *oblnk;
  93. } olist;
  94. /*close*/
  95. typedef struct
  96. { flag cerr;
  97. ftnint cunit;
  98. char *csta;
  99. } cllist;
  100. /*rewind, backspace, endfile*/
  101. typedef struct
  102. { flag aerr;
  103. ftnint aunit;
  104. } alist;
  105. /* inquire */
  106. typedef struct
  107. { flag inerr;
  108. ftnint inunit;
  109. char *infile;
  110. ftnlen infilen;
  111. ftnint *inex; /*parameters in standard's order*/
  112. ftnint *inopen;
  113. ftnint *innum;
  114. ftnint *innamed;
  115. char *inname;
  116. ftnlen innamlen;
  117. char *inacc;
  118. ftnlen inacclen;
  119. char *inseq;
  120. ftnlen inseqlen;
  121. char *indir;
  122. ftnlen indirlen;
  123. char *infmt;
  124. ftnlen infmtlen;
  125. char *inform;
  126. ftnint informlen;
  127. char *inunf;
  128. ftnlen inunflen;
  129. ftnint *inrecl;
  130. ftnint *innrec;
  131. char *inblank;
  132. ftnlen inblanklen;
  133. } inlist;
  134. #define VOID void
  135. union Multitype { /* for multiple entry points */
  136. integer1 g;
  137. shortint h;
  138. integer i;
  139. /* longint j; */
  140. real r;
  141. doublereal d;
  142. complex c;
  143. doublecomplex z;
  144. };
  145. typedef union Multitype Multitype;
  146. struct Vardesc { /* for Namelist */
  147. char *name;
  148. char *addr;
  149. ftnlen *dims;
  150. int type;
  151. };
  152. typedef struct Vardesc Vardesc;
  153. struct Namelist {
  154. char *name;
  155. Vardesc **vars;
  156. int nvars;
  157. };
  158. typedef struct Namelist Namelist;
  159. #define abs(x) ((x) >= 0 ? (x) : -(x))
  160. #define dabs(x) (fabs(x))
  161. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  162. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  163. #define dmin(a,b) (f2cmin(a,b))
  164. #define dmax(a,b) (f2cmax(a,b))
  165. #define bit_test(a,b) ((a) >> (b) & 1)
  166. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  167. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  168. #define abort_() { sig_die("Fortran abort routine called", 1); }
  169. #define c_abs(z) (cabsf(Cf(z)))
  170. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  171. #ifdef _MSC_VER
  172. #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
  173. #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/Cd(b)._Val[1]);}
  174. #else
  175. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  176. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  177. #endif
  178. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  179. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  180. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  181. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  182. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  183. #define d_abs(x) (fabs(*(x)))
  184. #define d_acos(x) (acos(*(x)))
  185. #define d_asin(x) (asin(*(x)))
  186. #define d_atan(x) (atan(*(x)))
  187. #define d_atn2(x, y) (atan2(*(x),*(y)))
  188. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  189. #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
  190. #define d_cos(x) (cos(*(x)))
  191. #define d_cosh(x) (cosh(*(x)))
  192. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  193. #define d_exp(x) (exp(*(x)))
  194. #define d_imag(z) (cimag(Cd(z)))
  195. #define r_imag(z) (cimagf(Cf(z)))
  196. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  197. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  198. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  199. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  200. #define d_log(x) (log(*(x)))
  201. #define d_mod(x, y) (fmod(*(x), *(y)))
  202. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  203. #define d_nint(x) u_nint(*(x))
  204. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  205. #define d_sign(a,b) u_sign(*(a),*(b))
  206. #define r_sign(a,b) u_sign(*(a),*(b))
  207. #define d_sin(x) (sin(*(x)))
  208. #define d_sinh(x) (sinh(*(x)))
  209. #define d_sqrt(x) (sqrt(*(x)))
  210. #define d_tan(x) (tan(*(x)))
  211. #define d_tanh(x) (tanh(*(x)))
  212. #define i_abs(x) abs(*(x))
  213. #define i_dnnt(x) ((integer)u_nint(*(x)))
  214. #define i_len(s, n) (n)
  215. #define i_nint(x) ((integer)u_nint(*(x)))
  216. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  217. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  218. #define pow_si(B,E) spow_ui(*(B),*(E))
  219. #define pow_ri(B,E) spow_ui(*(B),*(E))
  220. #define pow_di(B,E) dpow_ui(*(B),*(E))
  221. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  222. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  223. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  224. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  225. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  226. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  227. #define sig_die(s, kill) { exit(1); }
  228. #define s_stop(s, n) {exit(0);}
  229. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  230. #define z_abs(z) (cabs(Cd(z)))
  231. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  232. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  233. #define myexit_() break;
  234. #define mycycle_() continue;
  235. #define myceiling_(w) {ceil(w)}
  236. #define myhuge_(w) {HUGE_VAL}
  237. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  238. #define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  239. /* procedure parameter types for -A and -C++ */
  240. #define F2C_proc_par_types 1
  241. #ifdef __cplusplus
  242. typedef logical (*L_fp)(...);
  243. #else
  244. typedef logical (*L_fp)();
  245. #endif
  246. static float spow_ui(float x, integer n) {
  247. float pow=1.0; unsigned long int u;
  248. if(n != 0) {
  249. if(n < 0) n = -n, x = 1/x;
  250. for(u = n; ; ) {
  251. if(u & 01) pow *= x;
  252. if(u >>= 1) x *= x;
  253. else break;
  254. }
  255. }
  256. return pow;
  257. }
  258. static double dpow_ui(double x, integer n) {
  259. double pow=1.0; unsigned long int u;
  260. if(n != 0) {
  261. if(n < 0) n = -n, x = 1/x;
  262. for(u = n; ; ) {
  263. if(u & 01) pow *= x;
  264. if(u >>= 1) x *= x;
  265. else break;
  266. }
  267. }
  268. return pow;
  269. }
  270. #ifdef _MSC_VER
  271. static _Fcomplex cpow_ui(complex x, integer n) {
  272. complex pow={1.0,0.0}; unsigned long int u;
  273. if(n != 0) {
  274. if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
  275. for(u = n; ; ) {
  276. if(u & 01) pow.r *= x.r, pow.i *= x.i;
  277. if(u >>= 1) x.r *= x.r, x.i *= x.i;
  278. else break;
  279. }
  280. }
  281. _Fcomplex p={pow.r, pow.i};
  282. return p;
  283. }
  284. #else
  285. static _Complex float cpow_ui(_Complex float x, integer n) {
  286. _Complex float pow=1.0; unsigned long int u;
  287. if(n != 0) {
  288. if(n < 0) n = -n, x = 1/x;
  289. for(u = n; ; ) {
  290. if(u & 01) pow *= x;
  291. if(u >>= 1) x *= x;
  292. else break;
  293. }
  294. }
  295. return pow;
  296. }
  297. #endif
  298. #ifdef _MSC_VER
  299. static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
  300. _Dcomplex pow={1.0,0.0}; unsigned long int u;
  301. if(n != 0) {
  302. if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
  303. for(u = n; ; ) {
  304. if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
  305. if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
  306. else break;
  307. }
  308. }
  309. _Dcomplex p = {pow._Val[0], pow._Val[1]};
  310. return p;
  311. }
  312. #else
  313. static _Complex double zpow_ui(_Complex double x, integer n) {
  314. _Complex double pow=1.0; unsigned long int u;
  315. if(n != 0) {
  316. if(n < 0) n = -n, x = 1/x;
  317. for(u = n; ; ) {
  318. if(u & 01) pow *= x;
  319. if(u >>= 1) x *= x;
  320. else break;
  321. }
  322. }
  323. return pow;
  324. }
  325. #endif
  326. static integer pow_ii(integer x, integer n) {
  327. integer pow; unsigned long int u;
  328. if (n <= 0) {
  329. if (n == 0 || x == 1) pow = 1;
  330. else if (x != -1) pow = x == 0 ? 1/x : 0;
  331. else n = -n;
  332. }
  333. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  334. u = n;
  335. for(pow = 1; ; ) {
  336. if(u & 01) pow *= x;
  337. if(u >>= 1) x *= x;
  338. else break;
  339. }
  340. }
  341. return pow;
  342. }
  343. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  344. {
  345. double m; integer i, mi;
  346. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  347. if (w[i-1]>m) mi=i ,m=w[i-1];
  348. return mi-s+1;
  349. }
  350. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  351. {
  352. float m; integer i, mi;
  353. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  354. if (w[i-1]>m) mi=i ,m=w[i-1];
  355. return mi-s+1;
  356. }
  357. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  358. integer n = *n_, incx = *incx_, incy = *incy_, i;
  359. #ifdef _MSC_VER
  360. _Fcomplex zdotc = {0.0, 0.0};
  361. if (incx == 1 && incy == 1) {
  362. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  363. zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
  364. zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
  365. }
  366. } else {
  367. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  368. zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
  369. zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
  370. }
  371. }
  372. pCf(z) = zdotc;
  373. }
  374. #else
  375. _Complex float zdotc = 0.0;
  376. if (incx == 1 && incy == 1) {
  377. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  378. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  379. }
  380. } else {
  381. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  382. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  383. }
  384. }
  385. pCf(z) = zdotc;
  386. }
  387. #endif
  388. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  389. integer n = *n_, incx = *incx_, incy = *incy_, i;
  390. #ifdef _MSC_VER
  391. _Dcomplex zdotc = {0.0, 0.0};
  392. if (incx == 1 && incy == 1) {
  393. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  394. zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
  395. zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
  396. }
  397. } else {
  398. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  399. zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
  400. zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
  401. }
  402. }
  403. pCd(z) = zdotc;
  404. }
  405. #else
  406. _Complex double zdotc = 0.0;
  407. if (incx == 1 && incy == 1) {
  408. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  409. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  410. }
  411. } else {
  412. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  413. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  414. }
  415. }
  416. pCd(z) = zdotc;
  417. }
  418. #endif
  419. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  420. integer n = *n_, incx = *incx_, incy = *incy_, i;
  421. #ifdef _MSC_VER
  422. _Fcomplex zdotc = {0.0, 0.0};
  423. if (incx == 1 && incy == 1) {
  424. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  425. zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
  426. zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
  427. }
  428. } else {
  429. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  430. zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
  431. zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
  432. }
  433. }
  434. pCf(z) = zdotc;
  435. }
  436. #else
  437. _Complex float zdotc = 0.0;
  438. if (incx == 1 && incy == 1) {
  439. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  440. zdotc += Cf(&x[i]) * Cf(&y[i]);
  441. }
  442. } else {
  443. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  444. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  445. }
  446. }
  447. pCf(z) = zdotc;
  448. }
  449. #endif
  450. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  451. integer n = *n_, incx = *incx_, incy = *incy_, i;
  452. #ifdef _MSC_VER
  453. _Dcomplex zdotc = {0.0, 0.0};
  454. if (incx == 1 && incy == 1) {
  455. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  456. zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
  457. zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
  458. }
  459. } else {
  460. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  461. zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
  462. zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
  463. }
  464. }
  465. pCd(z) = zdotc;
  466. }
  467. #else
  468. _Complex double zdotc = 0.0;
  469. if (incx == 1 && incy == 1) {
  470. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  471. zdotc += Cd(&x[i]) * Cd(&y[i]);
  472. }
  473. } else {
  474. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  475. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  476. }
  477. }
  478. pCd(z) = zdotc;
  479. }
  480. #endif
  481. /* -- translated by f2c (version 20000121).
  482. You must link the resulting object file with the libraries:
  483. -lf2c -lm (in that order)
  484. */
  485. /* Table of constant values */
  486. static doublecomplex c_b1 = {1.,0.};
  487. static doublecomplex c_b2 = {0.,0.};
  488. /* > \brief \b ZSYTRI2X */
  489. /* =========== DOCUMENTATION =========== */
  490. /* Online html documentation available at */
  491. /* http://www.netlib.org/lapack/explore-html/ */
  492. /* > \htmlonly */
  493. /* > Download ZSYTRI2X + dependencies */
  494. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri2
  495. x.f"> */
  496. /* > [TGZ]</a> */
  497. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytri2
  498. x.f"> */
  499. /* > [ZIP]</a> */
  500. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytri2
  501. x.f"> */
  502. /* > [TXT]</a> */
  503. /* > \endhtmlonly */
  504. /* Definition: */
  505. /* =========== */
  506. /* SUBROUTINE ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) */
  507. /* CHARACTER UPLO */
  508. /* INTEGER INFO, LDA, N, NB */
  509. /* INTEGER IPIV( * ) */
  510. /* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* ) */
  511. /* > \par Purpose: */
  512. /* ============= */
  513. /* > */
  514. /* > \verbatim */
  515. /* > */
  516. /* > ZSYTRI2X computes the inverse of a complex symmetric indefinite matrix */
  517. /* > A using the factorization A = U*D*U**T or A = L*D*L**T computed by */
  518. /* > ZSYTRF. */
  519. /* > \endverbatim */
  520. /* Arguments: */
  521. /* ========== */
  522. /* > \param[in] UPLO */
  523. /* > \verbatim */
  524. /* > UPLO is CHARACTER*1 */
  525. /* > Specifies whether the details of the factorization are stored */
  526. /* > as an upper or lower triangular matrix. */
  527. /* > = 'U': Upper triangular, form is A = U*D*U**T; */
  528. /* > = 'L': Lower triangular, form is A = L*D*L**T. */
  529. /* > \endverbatim */
  530. /* > */
  531. /* > \param[in] N */
  532. /* > \verbatim */
  533. /* > N is INTEGER */
  534. /* > The order of the matrix A. N >= 0. */
  535. /* > \endverbatim */
  536. /* > */
  537. /* > \param[in,out] A */
  538. /* > \verbatim */
  539. /* > A is COMPLEX*16 array, dimension (LDA,N) */
  540. /* > On entry, the NNB diagonal matrix D and the multipliers */
  541. /* > used to obtain the factor U or L as computed by ZSYTRF. */
  542. /* > */
  543. /* > On exit, if INFO = 0, the (symmetric) inverse of the original */
  544. /* > matrix. If UPLO = 'U', the upper triangular part of the */
  545. /* > inverse is formed and the part of A below the diagonal is not */
  546. /* > referenced; if UPLO = 'L' the lower triangular part of the */
  547. /* > inverse is formed and the part of A above the diagonal is */
  548. /* > not referenced. */
  549. /* > \endverbatim */
  550. /* > */
  551. /* > \param[in] LDA */
  552. /* > \verbatim */
  553. /* > LDA is INTEGER */
  554. /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
  555. /* > \endverbatim */
  556. /* > */
  557. /* > \param[in] IPIV */
  558. /* > \verbatim */
  559. /* > IPIV is INTEGER array, dimension (N) */
  560. /* > Details of the interchanges and the NNB structure of D */
  561. /* > as determined by ZSYTRF. */
  562. /* > \endverbatim */
  563. /* > */
  564. /* > \param[out] WORK */
  565. /* > \verbatim */
  566. /* > WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3) */
  567. /* > \endverbatim */
  568. /* > */
  569. /* > \param[in] NB */
  570. /* > \verbatim */
  571. /* > NB is INTEGER */
  572. /* > Block size */
  573. /* > \endverbatim */
  574. /* > */
  575. /* > \param[out] INFO */
  576. /* > \verbatim */
  577. /* > INFO is INTEGER */
  578. /* > = 0: successful exit */
  579. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  580. /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
  581. /* > inverse could not be computed. */
  582. /* > \endverbatim */
  583. /* Authors: */
  584. /* ======== */
  585. /* > \author Univ. of Tennessee */
  586. /* > \author Univ. of California Berkeley */
  587. /* > \author Univ. of Colorado Denver */
  588. /* > \author NAG Ltd. */
  589. /* > \date June 2017 */
  590. /* > \ingroup complex16SYcomputational */
  591. /* ===================================================================== */
  592. /* Subroutine */ void zsytri2x_(char *uplo, integer *n, doublecomplex *a,
  593. integer *lda, integer *ipiv, doublecomplex *work, integer *nb,
  594. integer *info)
  595. {
  596. /* System generated locals */
  597. integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4,
  598. i__5, i__6;
  599. doublecomplex z__1, z__2, z__3;
  600. /* Local variables */
  601. integer invd;
  602. doublecomplex akkp1, d__;
  603. integer i__, j, k;
  604. extern /* Subroutine */ void zsyswapr_(char *, integer *, doublecomplex *,
  605. integer *, integer *, integer *);
  606. doublecomplex t;
  607. extern logical lsame_(char *, char *);
  608. integer iinfo;
  609. extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
  610. integer *, doublecomplex *, doublecomplex *, integer *,
  611. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  612. integer *);
  613. integer count;
  614. logical upper;
  615. extern /* Subroutine */ void ztrmm_(char *, char *, char *, char *,
  616. integer *, integer *, doublecomplex *, doublecomplex *, integer *,
  617. doublecomplex *, integer *);
  618. doublecomplex ak, u01_i_j__;
  619. integer u11;
  620. doublecomplex u11_i_j__;
  621. integer ip;
  622. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  623. extern int ztrtri_(
  624. char *, char *, integer *, doublecomplex *, integer *, integer *);
  625. integer nnb, cut;
  626. doublecomplex akp1, u01_ip1_j__, u11_ip1_j__;
  627. extern /* Subroutine */ void zsyconv_(char *, char *, integer *,
  628. doublecomplex *, integer *, integer *, doublecomplex *, integer *);
  629. /* -- LAPACK computational routine (version 3.7.1) -- */
  630. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  631. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  632. /* June 2017 */
  633. /* ===================================================================== */
  634. /* Test the input parameters. */
  635. /* Parameter adjustments */
  636. a_dim1 = *lda;
  637. a_offset = 1 + a_dim1 * 1;
  638. a -= a_offset;
  639. --ipiv;
  640. work_dim1 = *n + *nb + 1;
  641. work_offset = 1 + work_dim1 * 1;
  642. work -= work_offset;
  643. /* Function Body */
  644. *info = 0;
  645. upper = lsame_(uplo, "U");
  646. if (! upper && ! lsame_(uplo, "L")) {
  647. *info = -1;
  648. } else if (*n < 0) {
  649. *info = -2;
  650. } else if (*lda < f2cmax(1,*n)) {
  651. *info = -4;
  652. }
  653. /* Quick return if possible */
  654. if (*info != 0) {
  655. i__1 = -(*info);
  656. xerbla_("ZSYTRI2X", &i__1, (ftnlen)8);
  657. return;
  658. }
  659. if (*n == 0) {
  660. return;
  661. }
  662. /* Convert A */
  663. /* Workspace got Non-diag elements of D */
  664. zsyconv_(uplo, "C", n, &a[a_offset], lda, &ipiv[1], &work[work_offset], &
  665. iinfo);
  666. /* Check that the diagonal matrix D is nonsingular. */
  667. if (upper) {
  668. /* Upper triangular storage: examine D from bottom to top */
  669. for (*info = *n; *info >= 1; --(*info)) {
  670. i__1 = *info + *info * a_dim1;
  671. if (ipiv[*info] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
  672. return;
  673. }
  674. }
  675. } else {
  676. /* Lower triangular storage: examine D from top to bottom. */
  677. i__1 = *n;
  678. for (*info = 1; *info <= i__1; ++(*info)) {
  679. i__2 = *info + *info * a_dim1;
  680. if (ipiv[*info] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
  681. return;
  682. }
  683. }
  684. }
  685. *info = 0;
  686. /* Splitting Workspace */
  687. /* U01 is a block (N,NB+1) */
  688. /* The first element of U01 is in WORK(1,1) */
  689. /* U11 is a block (NB+1,NB+1) */
  690. /* The first element of U11 is in WORK(N+1,1) */
  691. u11 = *n;
  692. /* INVD is a block (N,2) */
  693. /* The first element of INVD is in WORK(1,INVD) */
  694. invd = *nb + 2;
  695. if (upper) {
  696. /* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
  697. ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
  698. /* inv(D) and inv(D)*inv(U) */
  699. k = 1;
  700. while(k <= *n) {
  701. if (ipiv[k] > 0) {
  702. /* 1 x 1 diagonal NNB */
  703. i__1 = k + invd * work_dim1;
  704. z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
  705. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  706. i__1 = k + (invd + 1) * work_dim1;
  707. work[i__1].r = 0., work[i__1].i = 0.;
  708. ++k;
  709. } else {
  710. /* 2 x 2 diagonal NNB */
  711. i__1 = k + 1 + work_dim1;
  712. t.r = work[i__1].r, t.i = work[i__1].i;
  713. z_div(&z__1, &a[k + k * a_dim1], &t);
  714. ak.r = z__1.r, ak.i = z__1.i;
  715. z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &t);
  716. akp1.r = z__1.r, akp1.i = z__1.i;
  717. z_div(&z__1, &work[k + 1 + work_dim1], &t);
  718. akkp1.r = z__1.r, akkp1.i = z__1.i;
  719. z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r *
  720. akp1.i + ak.i * akp1.r;
  721. z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
  722. z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i +
  723. t.i * z__2.r;
  724. d__.r = z__1.r, d__.i = z__1.i;
  725. i__1 = k + invd * work_dim1;
  726. z_div(&z__1, &akp1, &d__);
  727. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  728. i__1 = k + 1 + (invd + 1) * work_dim1;
  729. z_div(&z__1, &ak, &d__);
  730. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  731. i__1 = k + (invd + 1) * work_dim1;
  732. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  733. z_div(&z__1, &z__2, &d__);
  734. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  735. i__1 = k + 1 + invd * work_dim1;
  736. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  737. z_div(&z__1, &z__2, &d__);
  738. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  739. k += 2;
  740. }
  741. }
  742. /* inv(U**T) = (inv(U))**T */
  743. /* inv(U**T)*inv(D)*inv(U) */
  744. cut = *n;
  745. while(cut > 0) {
  746. nnb = *nb;
  747. if (cut <= nnb) {
  748. nnb = cut;
  749. } else {
  750. count = 0;
  751. /* count negative elements, */
  752. i__1 = cut;
  753. for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
  754. if (ipiv[i__] < 0) {
  755. ++count;
  756. }
  757. }
  758. /* need a even number for a clear cut */
  759. if (count % 2 == 1) {
  760. ++nnb;
  761. }
  762. }
  763. cut -= nnb;
  764. /* U01 Block */
  765. i__1 = cut;
  766. for (i__ = 1; i__ <= i__1; ++i__) {
  767. i__2 = nnb;
  768. for (j = 1; j <= i__2; ++j) {
  769. i__3 = i__ + j * work_dim1;
  770. i__4 = i__ + (cut + j) * a_dim1;
  771. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  772. }
  773. }
  774. /* U11 Block */
  775. i__1 = nnb;
  776. for (i__ = 1; i__ <= i__1; ++i__) {
  777. i__2 = u11 + i__ + i__ * work_dim1;
  778. work[i__2].r = 1., work[i__2].i = 0.;
  779. i__2 = i__ - 1;
  780. for (j = 1; j <= i__2; ++j) {
  781. i__3 = u11 + i__ + j * work_dim1;
  782. work[i__3].r = 0., work[i__3].i = 0.;
  783. }
  784. i__2 = nnb;
  785. for (j = i__ + 1; j <= i__2; ++j) {
  786. i__3 = u11 + i__ + j * work_dim1;
  787. i__4 = cut + i__ + (cut + j) * a_dim1;
  788. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  789. }
  790. }
  791. /* invD*U01 */
  792. i__ = 1;
  793. while(i__ <= cut) {
  794. if (ipiv[i__] > 0) {
  795. i__1 = nnb;
  796. for (j = 1; j <= i__1; ++j) {
  797. i__2 = i__ + j * work_dim1;
  798. i__3 = i__ + invd * work_dim1;
  799. i__4 = i__ + j * work_dim1;
  800. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  801. work[i__4].i, z__1.i = work[i__3].r * work[
  802. i__4].i + work[i__3].i * work[i__4].r;
  803. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  804. }
  805. ++i__;
  806. } else {
  807. i__1 = nnb;
  808. for (j = 1; j <= i__1; ++j) {
  809. i__2 = i__ + j * work_dim1;
  810. u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
  811. .i;
  812. i__2 = i__ + 1 + j * work_dim1;
  813. u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
  814. i__2].i;
  815. i__2 = i__ + j * work_dim1;
  816. i__3 = i__ + invd * work_dim1;
  817. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  818. u01_i_j__.i, z__2.i = work[i__3].r *
  819. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  820. i__4 = i__ + (invd + 1) * work_dim1;
  821. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  822. u01_ip1_j__.i, z__3.i = work[i__4].r *
  823. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  824. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  825. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  826. i__2 = i__ + 1 + j * work_dim1;
  827. i__3 = i__ + 1 + invd * work_dim1;
  828. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  829. u01_i_j__.i, z__2.i = work[i__3].r *
  830. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  831. i__4 = i__ + 1 + (invd + 1) * work_dim1;
  832. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  833. u01_ip1_j__.i, z__3.i = work[i__4].r *
  834. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  835. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  836. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  837. }
  838. i__ += 2;
  839. }
  840. }
  841. /* invD1*U11 */
  842. i__ = 1;
  843. while(i__ <= nnb) {
  844. if (ipiv[cut + i__] > 0) {
  845. i__1 = nnb;
  846. for (j = i__; j <= i__1; ++j) {
  847. i__2 = u11 + i__ + j * work_dim1;
  848. i__3 = cut + i__ + invd * work_dim1;
  849. i__4 = u11 + i__ + j * work_dim1;
  850. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  851. work[i__4].i, z__1.i = work[i__3].r * work[
  852. i__4].i + work[i__3].i * work[i__4].r;
  853. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  854. }
  855. ++i__;
  856. } else {
  857. i__1 = nnb;
  858. for (j = i__; j <= i__1; ++j) {
  859. i__2 = u11 + i__ + j * work_dim1;
  860. u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
  861. .i;
  862. i__2 = u11 + i__ + 1 + j * work_dim1;
  863. u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
  864. i__2].i;
  865. i__2 = u11 + i__ + j * work_dim1;
  866. i__3 = cut + i__ + invd * work_dim1;
  867. i__4 = u11 + i__ + j * work_dim1;
  868. z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
  869. work[i__4].i, z__2.i = work[i__3].r * work[
  870. i__4].i + work[i__3].i * work[i__4].r;
  871. i__5 = cut + i__ + (invd + 1) * work_dim1;
  872. i__6 = u11 + i__ + 1 + j * work_dim1;
  873. z__3.r = work[i__5].r * work[i__6].r - work[i__5].i *
  874. work[i__6].i, z__3.i = work[i__5].r * work[
  875. i__6].i + work[i__5].i * work[i__6].r;
  876. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  877. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  878. i__2 = u11 + i__ + 1 + j * work_dim1;
  879. i__3 = cut + i__ + 1 + invd * work_dim1;
  880. z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
  881. u11_i_j__.i, z__2.i = work[i__3].r *
  882. u11_i_j__.i + work[i__3].i * u11_i_j__.r;
  883. i__4 = cut + i__ + 1 + (invd + 1) * work_dim1;
  884. z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
  885. u11_ip1_j__.i, z__3.i = work[i__4].r *
  886. u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
  887. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  888. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  889. }
  890. i__ += 2;
  891. }
  892. }
  893. /* U11**T*invD1*U11->U11 */
  894. i__1 = *n + *nb + 1;
  895. ztrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut +
  896. 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
  897. i__1 = nnb;
  898. for (i__ = 1; i__ <= i__1; ++i__) {
  899. i__2 = nnb;
  900. for (j = i__; j <= i__2; ++j) {
  901. i__3 = cut + i__ + (cut + j) * a_dim1;
  902. i__4 = u11 + i__ + j * work_dim1;
  903. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  904. }
  905. }
  906. /* U01**T*invD*U01->A(CUT+I,CUT+J) */
  907. i__1 = *n + *nb + 1;
  908. i__2 = *n + *nb + 1;
  909. zgemm_("T", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 +
  910. 1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1
  911. + work_dim1], &i__2);
  912. /* U11 = U11**T*invD1*U11 + U01**T*invD*U01 */
  913. i__1 = nnb;
  914. for (i__ = 1; i__ <= i__1; ++i__) {
  915. i__2 = nnb;
  916. for (j = i__; j <= i__2; ++j) {
  917. i__3 = cut + i__ + (cut + j) * a_dim1;
  918. i__4 = cut + i__ + (cut + j) * a_dim1;
  919. i__5 = u11 + i__ + j * work_dim1;
  920. z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i +
  921. work[i__5].i;
  922. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  923. }
  924. }
  925. /* U01 = U00**T*invD0*U01 */
  926. i__1 = *n + *nb + 1;
  927. ztrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b1, &a[a_offset], lda,
  928. &work[work_offset], &i__1);
  929. /* Update U01 */
  930. i__1 = cut;
  931. for (i__ = 1; i__ <= i__1; ++i__) {
  932. i__2 = nnb;
  933. for (j = 1; j <= i__2; ++j) {
  934. i__3 = i__ + (cut + j) * a_dim1;
  935. i__4 = i__ + j * work_dim1;
  936. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  937. }
  938. }
  939. /* Next Block */
  940. }
  941. /* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
  942. i__ = 1;
  943. while(i__ <= *n) {
  944. if (ipiv[i__] > 0) {
  945. ip = ipiv[i__];
  946. if (i__ < ip) {
  947. zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
  948. }
  949. if (i__ > ip) {
  950. zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
  951. }
  952. } else {
  953. ip = -ipiv[i__];
  954. ++i__;
  955. if (i__ - 1 < ip) {
  956. i__1 = i__ - 1;
  957. zsyswapr_(uplo, n, &a[a_offset], lda, &i__1, &ip);
  958. }
  959. if (i__ - 1 > ip) {
  960. i__1 = i__ - 1;
  961. zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__1);
  962. }
  963. }
  964. ++i__;
  965. }
  966. } else {
  967. /* LOWER... */
  968. /* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
  969. ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
  970. /* inv(D) and inv(D)*inv(U) */
  971. k = *n;
  972. while(k >= 1) {
  973. if (ipiv[k] > 0) {
  974. /* 1 x 1 diagonal NNB */
  975. i__1 = k + invd * work_dim1;
  976. z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
  977. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  978. i__1 = k + (invd + 1) * work_dim1;
  979. work[i__1].r = 0., work[i__1].i = 0.;
  980. --k;
  981. } else {
  982. /* 2 x 2 diagonal NNB */
  983. i__1 = k - 1 + work_dim1;
  984. t.r = work[i__1].r, t.i = work[i__1].i;
  985. z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &t);
  986. ak.r = z__1.r, ak.i = z__1.i;
  987. z_div(&z__1, &a[k + k * a_dim1], &t);
  988. akp1.r = z__1.r, akp1.i = z__1.i;
  989. z_div(&z__1, &work[k - 1 + work_dim1], &t);
  990. akkp1.r = z__1.r, akkp1.i = z__1.i;
  991. z__3.r = ak.r * akp1.r - ak.i * akp1.i, z__3.i = ak.r *
  992. akp1.i + ak.i * akp1.r;
  993. z__2.r = z__3.r - 1., z__2.i = z__3.i + 0.;
  994. z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r * z__2.i +
  995. t.i * z__2.r;
  996. d__.r = z__1.r, d__.i = z__1.i;
  997. i__1 = k - 1 + invd * work_dim1;
  998. z_div(&z__1, &akp1, &d__);
  999. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1000. i__1 = k + invd * work_dim1;
  1001. z_div(&z__1, &ak, &d__);
  1002. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1003. i__1 = k + (invd + 1) * work_dim1;
  1004. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  1005. z_div(&z__1, &z__2, &d__);
  1006. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1007. i__1 = k - 1 + (invd + 1) * work_dim1;
  1008. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  1009. z_div(&z__1, &z__2, &d__);
  1010. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  1011. k += -2;
  1012. }
  1013. }
  1014. /* inv(U**T) = (inv(U))**T */
  1015. /* inv(U**T)*inv(D)*inv(U) */
  1016. cut = 0;
  1017. while(cut < *n) {
  1018. nnb = *nb;
  1019. if (cut + nnb >= *n) {
  1020. nnb = *n - cut;
  1021. } else {
  1022. count = 0;
  1023. /* count negative elements, */
  1024. i__1 = cut + nnb;
  1025. for (i__ = cut + 1; i__ <= i__1; ++i__) {
  1026. if (ipiv[i__] < 0) {
  1027. ++count;
  1028. }
  1029. }
  1030. /* need a even number for a clear cut */
  1031. if (count % 2 == 1) {
  1032. ++nnb;
  1033. }
  1034. }
  1035. /* L21 Block */
  1036. i__1 = *n - cut - nnb;
  1037. for (i__ = 1; i__ <= i__1; ++i__) {
  1038. i__2 = nnb;
  1039. for (j = 1; j <= i__2; ++j) {
  1040. i__3 = i__ + j * work_dim1;
  1041. i__4 = cut + nnb + i__ + (cut + j) * a_dim1;
  1042. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  1043. }
  1044. }
  1045. /* L11 Block */
  1046. i__1 = nnb;
  1047. for (i__ = 1; i__ <= i__1; ++i__) {
  1048. i__2 = u11 + i__ + i__ * work_dim1;
  1049. work[i__2].r = 1., work[i__2].i = 0.;
  1050. i__2 = nnb;
  1051. for (j = i__ + 1; j <= i__2; ++j) {
  1052. i__3 = u11 + i__ + j * work_dim1;
  1053. work[i__3].r = 0., work[i__3].i = 0.;
  1054. }
  1055. i__2 = i__ - 1;
  1056. for (j = 1; j <= i__2; ++j) {
  1057. i__3 = u11 + i__ + j * work_dim1;
  1058. i__4 = cut + i__ + (cut + j) * a_dim1;
  1059. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  1060. }
  1061. }
  1062. /* invD*L21 */
  1063. i__ = *n - cut - nnb;
  1064. while(i__ >= 1) {
  1065. if (ipiv[cut + nnb + i__] > 0) {
  1066. i__1 = nnb;
  1067. for (j = 1; j <= i__1; ++j) {
  1068. i__2 = i__ + j * work_dim1;
  1069. i__3 = cut + nnb + i__ + invd * work_dim1;
  1070. i__4 = i__ + j * work_dim1;
  1071. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1072. work[i__4].i, z__1.i = work[i__3].r * work[
  1073. i__4].i + work[i__3].i * work[i__4].r;
  1074. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1075. }
  1076. --i__;
  1077. } else {
  1078. i__1 = nnb;
  1079. for (j = 1; j <= i__1; ++j) {
  1080. i__2 = i__ + j * work_dim1;
  1081. u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
  1082. .i;
  1083. i__2 = i__ - 1 + j * work_dim1;
  1084. u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
  1085. i__2].i;
  1086. i__2 = i__ + j * work_dim1;
  1087. i__3 = cut + nnb + i__ + invd * work_dim1;
  1088. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  1089. u01_i_j__.i, z__2.i = work[i__3].r *
  1090. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  1091. i__4 = cut + nnb + i__ + (invd + 1) * work_dim1;
  1092. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  1093. u01_ip1_j__.i, z__3.i = work[i__4].r *
  1094. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  1095. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1096. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1097. i__2 = i__ - 1 + j * work_dim1;
  1098. i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1;
  1099. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  1100. u01_i_j__.i, z__2.i = work[i__3].r *
  1101. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  1102. i__4 = cut + nnb + i__ - 1 + invd * work_dim1;
  1103. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  1104. u01_ip1_j__.i, z__3.i = work[i__4].r *
  1105. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  1106. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1107. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1108. }
  1109. i__ += -2;
  1110. }
  1111. }
  1112. /* invD1*L11 */
  1113. i__ = nnb;
  1114. while(i__ >= 1) {
  1115. if (ipiv[cut + i__] > 0) {
  1116. i__1 = nnb;
  1117. for (j = 1; j <= i__1; ++j) {
  1118. i__2 = u11 + i__ + j * work_dim1;
  1119. i__3 = cut + i__ + invd * work_dim1;
  1120. i__4 = u11 + i__ + j * work_dim1;
  1121. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1122. work[i__4].i, z__1.i = work[i__3].r * work[
  1123. i__4].i + work[i__3].i * work[i__4].r;
  1124. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1125. }
  1126. --i__;
  1127. } else {
  1128. i__1 = nnb;
  1129. for (j = 1; j <= i__1; ++j) {
  1130. i__2 = u11 + i__ + j * work_dim1;
  1131. u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
  1132. .i;
  1133. i__2 = u11 + i__ - 1 + j * work_dim1;
  1134. u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
  1135. i__2].i;
  1136. i__2 = u11 + i__ + j * work_dim1;
  1137. i__3 = cut + i__ + invd * work_dim1;
  1138. i__4 = u11 + i__ + j * work_dim1;
  1139. z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1140. work[i__4].i, z__2.i = work[i__3].r * work[
  1141. i__4].i + work[i__3].i * work[i__4].r;
  1142. i__5 = cut + i__ + (invd + 1) * work_dim1;
  1143. z__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i *
  1144. u11_ip1_j__.i, z__3.i = work[i__5].r *
  1145. u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r;
  1146. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1147. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1148. i__2 = u11 + i__ - 1 + j * work_dim1;
  1149. i__3 = cut + i__ - 1 + (invd + 1) * work_dim1;
  1150. z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
  1151. u11_i_j__.i, z__2.i = work[i__3].r *
  1152. u11_i_j__.i + work[i__3].i * u11_i_j__.r;
  1153. i__4 = cut + i__ - 1 + invd * work_dim1;
  1154. z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
  1155. u11_ip1_j__.i, z__3.i = work[i__4].r *
  1156. u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
  1157. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1158. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1159. }
  1160. i__ += -2;
  1161. }
  1162. }
  1163. /* L11**T*invD1*L11->L11 */
  1164. i__1 = *n + *nb + 1;
  1165. ztrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut
  1166. + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
  1167. i__1 = nnb;
  1168. for (i__ = 1; i__ <= i__1; ++i__) {
  1169. i__2 = i__;
  1170. for (j = 1; j <= i__2; ++j) {
  1171. i__3 = cut + i__ + (cut + j) * a_dim1;
  1172. i__4 = u11 + i__ + j * work_dim1;
  1173. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1174. }
  1175. }
  1176. if (cut + nnb < *n) {
  1177. /* L21**T*invD2*L21->A(CUT+I,CUT+J) */
  1178. i__1 = *n - nnb - cut;
  1179. i__2 = *n + *nb + 1;
  1180. i__3 = *n + *nb + 1;
  1181. zgemm_("T", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 +
  1182. (cut + 1) * a_dim1], lda, &work[work_offset], &i__2, &
  1183. c_b2, &work[u11 + 1 + work_dim1], &i__3);
  1184. /* L11 = L11**T*invD1*L11 + U01**T*invD*U01 */
  1185. i__1 = nnb;
  1186. for (i__ = 1; i__ <= i__1; ++i__) {
  1187. i__2 = i__;
  1188. for (j = 1; j <= i__2; ++j) {
  1189. i__3 = cut + i__ + (cut + j) * a_dim1;
  1190. i__4 = cut + i__ + (cut + j) * a_dim1;
  1191. i__5 = u11 + i__ + j * work_dim1;
  1192. z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i
  1193. + work[i__5].i;
  1194. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  1195. }
  1196. }
  1197. /* U01 = L22**T*invD2*L21 */
  1198. i__1 = *n - nnb - cut;
  1199. i__2 = *n + *nb + 1;
  1200. ztrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b1, &a[cut + nnb
  1201. + 1 + (cut + nnb + 1) * a_dim1], lda, &work[
  1202. work_offset], &i__2);
  1203. /* Update L21 */
  1204. i__1 = *n - cut - nnb;
  1205. for (i__ = 1; i__ <= i__1; ++i__) {
  1206. i__2 = nnb;
  1207. for (j = 1; j <= i__2; ++j) {
  1208. i__3 = cut + nnb + i__ + (cut + j) * a_dim1;
  1209. i__4 = i__ + j * work_dim1;
  1210. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1211. }
  1212. }
  1213. } else {
  1214. /* L11 = L11**T*invD1*L11 */
  1215. i__1 = nnb;
  1216. for (i__ = 1; i__ <= i__1; ++i__) {
  1217. i__2 = i__;
  1218. for (j = 1; j <= i__2; ++j) {
  1219. i__3 = cut + i__ + (cut + j) * a_dim1;
  1220. i__4 = u11 + i__ + j * work_dim1;
  1221. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1222. }
  1223. }
  1224. }
  1225. /* Next Block */
  1226. cut += nnb;
  1227. }
  1228. /* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
  1229. i__ = *n;
  1230. while(i__ >= 1) {
  1231. if (ipiv[i__] > 0) {
  1232. ip = ipiv[i__];
  1233. if (i__ < ip) {
  1234. zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
  1235. }
  1236. if (i__ > ip) {
  1237. zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
  1238. }
  1239. } else {
  1240. ip = -ipiv[i__];
  1241. if (i__ < ip) {
  1242. zsyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
  1243. }
  1244. if (i__ > ip) {
  1245. zsyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
  1246. }
  1247. --i__;
  1248. }
  1249. --i__;
  1250. }
  1251. }
  1252. return;
  1253. /* End of ZSYTRI2X */
  1254. } /* zsytri2x_ */