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zhetri_3x.c 39 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. #if defined(_WIN64)
  18. typedef long long BLASLONG;
  19. typedef unsigned long long BLASULONG;
  20. #else
  21. typedef long BLASLONG;
  22. typedef unsigned long BLASULONG;
  23. #endif
  24. #ifdef LAPACK_ILP64
  25. typedef BLASLONG blasint;
  26. #if defined(_WIN64)
  27. #define blasabs(x) llabs(x)
  28. #else
  29. #define blasabs(x) labs(x)
  30. #endif
  31. #else
  32. typedef int blasint;
  33. #define blasabs(x) abs(x)
  34. #endif
  35. typedef blasint integer;
  36. typedef unsigned int uinteger;
  37. typedef char *address;
  38. typedef short int shortint;
  39. typedef float real;
  40. typedef double doublereal;
  41. typedef struct { real r, i; } complex;
  42. typedef struct { doublereal r, i; } doublecomplex;
  43. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  44. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  45. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  46. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  47. #define pCf(z) (*_pCf(z))
  48. #define pCd(z) (*_pCd(z))
  49. typedef int logical;
  50. typedef short int shortlogical;
  51. typedef char logical1;
  52. typedef char integer1;
  53. #define TRUE_ (1)
  54. #define FALSE_ (0)
  55. /* Extern is for use with -E */
  56. #ifndef Extern
  57. #define Extern extern
  58. #endif
  59. /* I/O stuff */
  60. typedef int flag;
  61. typedef int ftnlen;
  62. typedef int ftnint;
  63. /*external read, write*/
  64. typedef struct
  65. { flag cierr;
  66. ftnint ciunit;
  67. flag ciend;
  68. char *cifmt;
  69. ftnint cirec;
  70. } cilist;
  71. /*internal read, write*/
  72. typedef struct
  73. { flag icierr;
  74. char *iciunit;
  75. flag iciend;
  76. char *icifmt;
  77. ftnint icirlen;
  78. ftnint icirnum;
  79. } icilist;
  80. /*open*/
  81. typedef struct
  82. { flag oerr;
  83. ftnint ounit;
  84. char *ofnm;
  85. ftnlen ofnmlen;
  86. char *osta;
  87. char *oacc;
  88. char *ofm;
  89. ftnint orl;
  90. char *oblnk;
  91. } olist;
  92. /*close*/
  93. typedef struct
  94. { flag cerr;
  95. ftnint cunit;
  96. char *csta;
  97. } cllist;
  98. /*rewind, backspace, endfile*/
  99. typedef struct
  100. { flag aerr;
  101. ftnint aunit;
  102. } alist;
  103. /* inquire */
  104. typedef struct
  105. { flag inerr;
  106. ftnint inunit;
  107. char *infile;
  108. ftnlen infilen;
  109. ftnint *inex; /*parameters in standard's order*/
  110. ftnint *inopen;
  111. ftnint *innum;
  112. ftnint *innamed;
  113. char *inname;
  114. ftnlen innamlen;
  115. char *inacc;
  116. ftnlen inacclen;
  117. char *inseq;
  118. ftnlen inseqlen;
  119. char *indir;
  120. ftnlen indirlen;
  121. char *infmt;
  122. ftnlen infmtlen;
  123. char *inform;
  124. ftnint informlen;
  125. char *inunf;
  126. ftnlen inunflen;
  127. ftnint *inrecl;
  128. ftnint *innrec;
  129. char *inblank;
  130. ftnlen inblanklen;
  131. } inlist;
  132. #define VOID void
  133. union Multitype { /* for multiple entry points */
  134. integer1 g;
  135. shortint h;
  136. integer i;
  137. /* longint j; */
  138. real r;
  139. doublereal d;
  140. complex c;
  141. doublecomplex z;
  142. };
  143. typedef union Multitype Multitype;
  144. struct Vardesc { /* for Namelist */
  145. char *name;
  146. char *addr;
  147. ftnlen *dims;
  148. int type;
  149. };
  150. typedef struct Vardesc Vardesc;
  151. struct Namelist {
  152. char *name;
  153. Vardesc **vars;
  154. int nvars;
  155. };
  156. typedef struct Namelist Namelist;
  157. #define abs(x) ((x) >= 0 ? (x) : -(x))
  158. #define dabs(x) (fabs(x))
  159. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  160. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  161. #define dmin(a,b) (f2cmin(a,b))
  162. #define dmax(a,b) (f2cmax(a,b))
  163. #define bit_test(a,b) ((a) >> (b) & 1)
  164. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  165. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  166. #define abort_() { sig_die("Fortran abort routine called", 1); }
  167. #define c_abs(z) (cabsf(Cf(z)))
  168. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  169. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  170. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  171. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  172. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  173. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  174. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  175. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  176. #define d_abs(x) (fabs(*(x)))
  177. #define d_acos(x) (acos(*(x)))
  178. #define d_asin(x) (asin(*(x)))
  179. #define d_atan(x) (atan(*(x)))
  180. #define d_atn2(x, y) (atan2(*(x),*(y)))
  181. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  182. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  183. #define d_cos(x) (cos(*(x)))
  184. #define d_cosh(x) (cosh(*(x)))
  185. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  186. #define d_exp(x) (exp(*(x)))
  187. #define d_imag(z) (cimag(Cd(z)))
  188. #define r_imag(z) (cimag(Cf(z)))
  189. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  190. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  191. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  192. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  193. #define d_log(x) (log(*(x)))
  194. #define d_mod(x, y) (fmod(*(x), *(y)))
  195. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  196. #define d_nint(x) u_nint(*(x))
  197. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  198. #define d_sign(a,b) u_sign(*(a),*(b))
  199. #define r_sign(a,b) u_sign(*(a),*(b))
  200. #define d_sin(x) (sin(*(x)))
  201. #define d_sinh(x) (sinh(*(x)))
  202. #define d_sqrt(x) (sqrt(*(x)))
  203. #define d_tan(x) (tan(*(x)))
  204. #define d_tanh(x) (tanh(*(x)))
  205. #define i_abs(x) abs(*(x))
  206. #define i_dnnt(x) ((integer)u_nint(*(x)))
  207. #define i_len(s, n) (n)
  208. #define i_nint(x) ((integer)u_nint(*(x)))
  209. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  210. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  211. #define pow_si(B,E) spow_ui(*(B),*(E))
  212. #define pow_ri(B,E) spow_ui(*(B),*(E))
  213. #define pow_di(B,E) dpow_ui(*(B),*(E))
  214. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  215. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  216. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  217. #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++ = ' '; }
  218. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  219. #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]; }
  220. #define sig_die(s, kill) { exit(1); }
  221. #define s_stop(s, n) {exit(0);}
  222. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  223. #define z_abs(z) (cabs(Cd(z)))
  224. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  225. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  226. #define myexit_() break;
  227. #define mycycle() continue;
  228. #define myceiling(w) {ceil(w)}
  229. #define myhuge(w) {HUGE_VAL}
  230. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  231. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  232. /* procedure parameter types for -A and -C++ */
  233. #define F2C_proc_par_types 1
  234. #ifdef __cplusplus
  235. typedef logical (*L_fp)(...);
  236. #else
  237. typedef logical (*L_fp)();
  238. #endif
  239. static float spow_ui(float x, integer n) {
  240. float pow=1.0; unsigned long int u;
  241. if(n != 0) {
  242. if(n < 0) n = -n, x = 1/x;
  243. for(u = n; ; ) {
  244. if(u & 01) pow *= x;
  245. if(u >>= 1) x *= x;
  246. else break;
  247. }
  248. }
  249. return pow;
  250. }
  251. static double dpow_ui(double x, integer n) {
  252. double pow=1.0; unsigned long int u;
  253. if(n != 0) {
  254. if(n < 0) n = -n, x = 1/x;
  255. for(u = n; ; ) {
  256. if(u & 01) pow *= x;
  257. if(u >>= 1) x *= x;
  258. else break;
  259. }
  260. }
  261. return pow;
  262. }
  263. static _Complex float cpow_ui(_Complex float x, integer n) {
  264. _Complex float pow=1.0; unsigned long int u;
  265. if(n != 0) {
  266. if(n < 0) n = -n, x = 1/x;
  267. for(u = n; ; ) {
  268. if(u & 01) pow *= x;
  269. if(u >>= 1) x *= x;
  270. else break;
  271. }
  272. }
  273. return pow;
  274. }
  275. static _Complex double zpow_ui(_Complex double x, integer n) {
  276. _Complex double pow=1.0; unsigned long int u;
  277. if(n != 0) {
  278. if(n < 0) n = -n, x = 1/x;
  279. for(u = n; ; ) {
  280. if(u & 01) pow *= x;
  281. if(u >>= 1) x *= x;
  282. else break;
  283. }
  284. }
  285. return pow;
  286. }
  287. static integer pow_ii(integer x, integer n) {
  288. integer pow; unsigned long int u;
  289. if (n <= 0) {
  290. if (n == 0 || x == 1) pow = 1;
  291. else if (x != -1) pow = x == 0 ? 1/x : 0;
  292. else n = -n;
  293. }
  294. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  295. u = n;
  296. for(pow = 1; ; ) {
  297. if(u & 01) pow *= x;
  298. if(u >>= 1) x *= x;
  299. else break;
  300. }
  301. }
  302. return pow;
  303. }
  304. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  305. {
  306. double m; integer i, mi;
  307. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  308. if (w[i-1]>m) mi=i ,m=w[i-1];
  309. return mi-s+1;
  310. }
  311. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  312. {
  313. float m; integer i, mi;
  314. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  315. if (w[i-1]>m) mi=i ,m=w[i-1];
  316. return mi-s+1;
  317. }
  318. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  319. integer n = *n_, incx = *incx_, incy = *incy_, i;
  320. _Complex float zdotc = 0.0;
  321. if (incx == 1 && incy == 1) {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  324. }
  325. } else {
  326. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  327. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  328. }
  329. }
  330. pCf(z) = zdotc;
  331. }
  332. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  333. integer n = *n_, incx = *incx_, incy = *incy_, i;
  334. _Complex double zdotc = 0.0;
  335. if (incx == 1 && incy == 1) {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  338. }
  339. } else {
  340. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  341. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  342. }
  343. }
  344. pCd(z) = zdotc;
  345. }
  346. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  347. integer n = *n_, incx = *incx_, incy = *incy_, i;
  348. _Complex float zdotc = 0.0;
  349. if (incx == 1 && incy == 1) {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cf(&x[i]) * Cf(&y[i]);
  352. }
  353. } else {
  354. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  355. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  356. }
  357. }
  358. pCf(z) = zdotc;
  359. }
  360. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  361. integer n = *n_, incx = *incx_, incy = *incy_, i;
  362. _Complex double zdotc = 0.0;
  363. if (incx == 1 && incy == 1) {
  364. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  365. zdotc += Cd(&x[i]) * Cd(&y[i]);
  366. }
  367. } else {
  368. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  369. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  370. }
  371. }
  372. pCd(z) = zdotc;
  373. }
  374. #endif
  375. /* -- translated by f2c (version 20000121).
  376. You must link the resulting object file with the libraries:
  377. -lf2c -lm (in that order)
  378. */
  379. /* Table of constant values */
  380. static doublecomplex c_b1 = {1.,0.};
  381. static doublecomplex c_b2 = {0.,0.};
  382. /* > \brief \b ZHETRI_3X */
  383. /* =========== DOCUMENTATION =========== */
  384. /* Online html documentation available at */
  385. /* http://www.netlib.org/lapack/explore-html/ */
  386. /* > \htmlonly */
  387. /* > Download ZHETRI_3X + dependencies */
  388. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetri_
  389. 3x.f"> */
  390. /* > [TGZ]</a> */
  391. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetri_
  392. 3x.f"> */
  393. /* > [ZIP]</a> */
  394. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetri_
  395. 3x.f"> */
  396. /* > [TXT]</a> */
  397. /* > \endhtmlonly */
  398. /* Definition: */
  399. /* =========== */
  400. /* SUBROUTINE ZHETRI_3X( UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO ) */
  401. /* CHARACTER UPLO */
  402. /* INTEGER INFO, LDA, N, NB */
  403. /* INTEGER IPIV( * ) */
  404. /* COMPLEX*16 A( LDA, * ), E( * ), WORK( N+NB+1, * ) */
  405. /* > \par Purpose: */
  406. /* ============= */
  407. /* > */
  408. /* > \verbatim */
  409. /* > ZHETRI_3X computes the inverse of a complex Hermitian indefinite */
  410. /* > matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK: */
  411. /* > */
  412. /* > A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), */
  413. /* > */
  414. /* > where U (or L) is unit upper (or lower) triangular matrix, */
  415. /* > U**H (or L**H) is the conjugate of U (or L), P is a permutation */
  416. /* > matrix, P**T is the transpose of P, and D is Hermitian and block */
  417. /* > diagonal with 1-by-1 and 2-by-2 diagonal blocks. */
  418. /* > */
  419. /* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
  420. /* > \endverbatim */
  421. /* Arguments: */
  422. /* ========== */
  423. /* > \param[in] UPLO */
  424. /* > \verbatim */
  425. /* > UPLO is CHARACTER*1 */
  426. /* > Specifies whether the details of the factorization are */
  427. /* > stored as an upper or lower triangular matrix. */
  428. /* > = 'U': Upper triangle of A is stored; */
  429. /* > = 'L': Lower triangle of A is stored. */
  430. /* > \endverbatim */
  431. /* > */
  432. /* > \param[in] N */
  433. /* > \verbatim */
  434. /* > N is INTEGER */
  435. /* > The order of the matrix A. N >= 0. */
  436. /* > \endverbatim */
  437. /* > */
  438. /* > \param[in,out] A */
  439. /* > \verbatim */
  440. /* > A is COMPLEX*16 array, dimension (LDA,N) */
  441. /* > On entry, diagonal of the block diagonal matrix D and */
  442. /* > factors U or L as computed by ZHETRF_RK and ZHETRF_BK: */
  443. /* > a) ONLY diagonal elements of the Hermitian block diagonal */
  444. /* > matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); */
  445. /* > (superdiagonal (or subdiagonal) elements of D */
  446. /* > should be provided on entry in array E), and */
  447. /* > b) If UPLO = 'U': factor U in the superdiagonal part of A. */
  448. /* > If UPLO = 'L': factor L in the subdiagonal part of A. */
  449. /* > */
  450. /* > On exit, if INFO = 0, the Hermitian inverse of the original */
  451. /* > matrix. */
  452. /* > If UPLO = 'U': the upper triangular part of the inverse */
  453. /* > is formed and the part of A below the diagonal is not */
  454. /* > referenced; */
  455. /* > If UPLO = 'L': the lower triangular part of the inverse */
  456. /* > is formed and the part of A above the diagonal is not */
  457. /* > referenced. */
  458. /* > \endverbatim */
  459. /* > */
  460. /* > \param[in] LDA */
  461. /* > \verbatim */
  462. /* > LDA is INTEGER */
  463. /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
  464. /* > \endverbatim */
  465. /* > */
  466. /* > \param[in] E */
  467. /* > \verbatim */
  468. /* > E is COMPLEX*16 array, dimension (N) */
  469. /* > On entry, contains the superdiagonal (or subdiagonal) */
  470. /* > elements of the Hermitian block diagonal matrix D */
  471. /* > with 1-by-1 or 2-by-2 diagonal blocks, where */
  472. /* > If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced; */
  473. /* > If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced. */
  474. /* > */
  475. /* > NOTE: For 1-by-1 diagonal block D(k), where */
  476. /* > 1 <= k <= N, the element E(k) is not referenced in both */
  477. /* > UPLO = 'U' or UPLO = 'L' cases. */
  478. /* > \endverbatim */
  479. /* > */
  480. /* > \param[in] IPIV */
  481. /* > \verbatim */
  482. /* > IPIV is INTEGER array, dimension (N) */
  483. /* > Details of the interchanges and the block structure of D */
  484. /* > as determined by ZHETRF_RK or ZHETRF_BK. */
  485. /* > \endverbatim */
  486. /* > */
  487. /* > \param[out] WORK */
  488. /* > \verbatim */
  489. /* > WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3). */
  490. /* > \endverbatim */
  491. /* > */
  492. /* > \param[in] NB */
  493. /* > \verbatim */
  494. /* > NB is INTEGER */
  495. /* > Block size. */
  496. /* > \endverbatim */
  497. /* > */
  498. /* > \param[out] INFO */
  499. /* > \verbatim */
  500. /* > INFO is INTEGER */
  501. /* > = 0: successful exit */
  502. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  503. /* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
  504. /* > inverse could not be computed. */
  505. /* > \endverbatim */
  506. /* Authors: */
  507. /* ======== */
  508. /* > \author Univ. of Tennessee */
  509. /* > \author Univ. of California Berkeley */
  510. /* > \author Univ. of Colorado Denver */
  511. /* > \author NAG Ltd. */
  512. /* > \date June 2017 */
  513. /* > \ingroup complex16HEcomputational */
  514. /* > \par Contributors: */
  515. /* ================== */
  516. /* > \verbatim */
  517. /* > */
  518. /* > June 2017, Igor Kozachenko, */
  519. /* > Computer Science Division, */
  520. /* > University of California, Berkeley */
  521. /* > */
  522. /* > \endverbatim */
  523. /* ===================================================================== */
  524. /* Subroutine */ int zhetri_3x_(char *uplo, integer *n, doublecomplex *a,
  525. integer *lda, doublecomplex *e, integer *ipiv, doublecomplex *work,
  526. integer *nb, integer *info)
  527. {
  528. /* System generated locals */
  529. integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4,
  530. i__5, i__6;
  531. doublereal d__1;
  532. doublecomplex z__1, z__2, z__3;
  533. /* Local variables */
  534. integer invd;
  535. doublecomplex akkp1;
  536. extern /* Subroutine */ int zheswapr_(char *, integer *, doublecomplex *,
  537. integer *, integer *, integer *);
  538. doublecomplex d__;
  539. integer i__, j, k;
  540. doublereal t;
  541. extern logical lsame_(char *, char *);
  542. extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
  543. integer *, doublecomplex *, doublecomplex *, integer *,
  544. doublecomplex *, integer *, doublecomplex *, doublecomplex *,
  545. integer *);
  546. logical upper;
  547. extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
  548. integer *, integer *, doublecomplex *, doublecomplex *, integer *,
  549. doublecomplex *, integer *);
  550. doublereal ak;
  551. doublecomplex u01_i_j__;
  552. integer u11;
  553. doublecomplex u11_i_j__;
  554. integer ip;
  555. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  556. integer icount;
  557. extern /* Subroutine */ int ztrtri_(char *, char *, integer *,
  558. doublecomplex *, integer *, integer *);
  559. integer nnb, cut;
  560. doublereal akp1;
  561. doublecomplex u01_ip1_j__, u11_ip1_j__;
  562. /* -- LAPACK computational routine (version 3.7.1) -- */
  563. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  564. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  565. /* June 2017 */
  566. /* ===================================================================== */
  567. /* Test the input parameters. */
  568. /* Parameter adjustments */
  569. a_dim1 = *lda;
  570. a_offset = 1 + a_dim1 * 1;
  571. a -= a_offset;
  572. --e;
  573. --ipiv;
  574. work_dim1 = *n + *nb + 1;
  575. work_offset = 1 + work_dim1 * 1;
  576. work -= work_offset;
  577. /* Function Body */
  578. *info = 0;
  579. upper = lsame_(uplo, "U");
  580. if (! upper && ! lsame_(uplo, "L")) {
  581. *info = -1;
  582. } else if (*n < 0) {
  583. *info = -2;
  584. } else if (*lda < f2cmax(1,*n)) {
  585. *info = -4;
  586. }
  587. /* Quick return if possible */
  588. if (*info != 0) {
  589. i__1 = -(*info);
  590. xerbla_("ZHETRI_3X", &i__1, (ftnlen)9);
  591. return 0;
  592. }
  593. if (*n == 0) {
  594. return 0;
  595. }
  596. /* Workspace got Non-diag elements of D */
  597. i__1 = *n;
  598. for (k = 1; k <= i__1; ++k) {
  599. i__2 = k + work_dim1;
  600. i__3 = k;
  601. work[i__2].r = e[i__3].r, work[i__2].i = e[i__3].i;
  602. }
  603. /* Check that the diagonal matrix D is nonsingular. */
  604. if (upper) {
  605. /* Upper triangular storage: examine D from bottom to top */
  606. for (*info = *n; *info >= 1; --(*info)) {
  607. i__1 = *info + *info * a_dim1;
  608. if (ipiv[*info] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
  609. return 0;
  610. }
  611. }
  612. } else {
  613. /* Lower triangular storage: examine D from top to bottom. */
  614. i__1 = *n;
  615. for (*info = 1; *info <= i__1; ++(*info)) {
  616. i__2 = *info + *info * a_dim1;
  617. if (ipiv[*info] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
  618. return 0;
  619. }
  620. }
  621. }
  622. *info = 0;
  623. /* Splitting Workspace */
  624. /* U01 is a block ( N, NB+1 ) */
  625. /* The first element of U01 is in WORK( 1, 1 ) */
  626. /* U11 is a block ( NB+1, NB+1 ) */
  627. /* The first element of U11 is in WORK( N+1, 1 ) */
  628. u11 = *n;
  629. /* INVD is a block ( N, 2 ) */
  630. /* The first element of INVD is in WORK( 1, INVD ) */
  631. invd = *nb + 2;
  632. if (upper) {
  633. /* Begin Upper */
  634. /* invA = P * inv(U**H) * inv(D) * inv(U) * P**T. */
  635. ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
  636. /* inv(D) and inv(D) * inv(U) */
  637. k = 1;
  638. while(k <= *n) {
  639. if (ipiv[k] > 0) {
  640. /* 1 x 1 diagonal NNB */
  641. i__1 = k + invd * work_dim1;
  642. i__2 = k + k * a_dim1;
  643. d__1 = 1. / a[i__2].r;
  644. work[i__1].r = d__1, work[i__1].i = 0.;
  645. i__1 = k + (invd + 1) * work_dim1;
  646. work[i__1].r = 0., work[i__1].i = 0.;
  647. } else {
  648. /* 2 x 2 diagonal NNB */
  649. t = z_abs(&work[k + 1 + work_dim1]);
  650. i__1 = k + k * a_dim1;
  651. ak = a[i__1].r / t;
  652. i__1 = k + 1 + (k + 1) * a_dim1;
  653. akp1 = a[i__1].r / t;
  654. i__1 = k + 1 + work_dim1;
  655. z__1.r = work[i__1].r / t, z__1.i = work[i__1].i / t;
  656. akkp1.r = z__1.r, akkp1.i = z__1.i;
  657. d__1 = ak * akp1;
  658. z__2.r = d__1 - 1., z__2.i = 0.;
  659. z__1.r = t * z__2.r, z__1.i = t * z__2.i;
  660. d__.r = z__1.r, d__.i = z__1.i;
  661. i__1 = k + invd * work_dim1;
  662. z__2.r = akp1, z__2.i = 0.;
  663. z_div(&z__1, &z__2, &d__);
  664. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  665. i__1 = k + 1 + (invd + 1) * work_dim1;
  666. z__2.r = ak, z__2.i = 0.;
  667. z_div(&z__1, &z__2, &d__);
  668. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  669. i__1 = k + (invd + 1) * work_dim1;
  670. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  671. z_div(&z__1, &z__2, &d__);
  672. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  673. i__1 = k + 1 + invd * work_dim1;
  674. d_cnjg(&z__1, &work[k + (invd + 1) * work_dim1]);
  675. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  676. ++k;
  677. }
  678. ++k;
  679. }
  680. /* inv(U**H) = (inv(U))**H */
  681. /* inv(U**H) * inv(D) * inv(U) */
  682. cut = *n;
  683. while(cut > 0) {
  684. nnb = *nb;
  685. if (cut <= nnb) {
  686. nnb = cut;
  687. } else {
  688. icount = 0;
  689. /* count negative elements, */
  690. i__1 = cut;
  691. for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
  692. if (ipiv[i__] < 0) {
  693. ++icount;
  694. }
  695. }
  696. /* need a even number for a clear cut */
  697. if (icount % 2 == 1) {
  698. ++nnb;
  699. }
  700. }
  701. cut -= nnb;
  702. /* U01 Block */
  703. i__1 = cut;
  704. for (i__ = 1; i__ <= i__1; ++i__) {
  705. i__2 = nnb;
  706. for (j = 1; j <= i__2; ++j) {
  707. i__3 = i__ + j * work_dim1;
  708. i__4 = i__ + (cut + j) * a_dim1;
  709. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  710. }
  711. }
  712. /* U11 Block */
  713. i__1 = nnb;
  714. for (i__ = 1; i__ <= i__1; ++i__) {
  715. i__2 = u11 + i__ + i__ * work_dim1;
  716. work[i__2].r = 1., work[i__2].i = 0.;
  717. i__2 = i__ - 1;
  718. for (j = 1; j <= i__2; ++j) {
  719. i__3 = u11 + i__ + j * work_dim1;
  720. work[i__3].r = 0., work[i__3].i = 0.;
  721. }
  722. i__2 = nnb;
  723. for (j = i__ + 1; j <= i__2; ++j) {
  724. i__3 = u11 + i__ + j * work_dim1;
  725. i__4 = cut + i__ + (cut + j) * a_dim1;
  726. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  727. }
  728. }
  729. /* invD * U01 */
  730. i__ = 1;
  731. while(i__ <= cut) {
  732. if (ipiv[i__] > 0) {
  733. i__1 = nnb;
  734. for (j = 1; j <= i__1; ++j) {
  735. i__2 = i__ + j * work_dim1;
  736. i__3 = i__ + invd * work_dim1;
  737. i__4 = i__ + j * work_dim1;
  738. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  739. work[i__4].i, z__1.i = work[i__3].r * work[
  740. i__4].i + work[i__3].i * work[i__4].r;
  741. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  742. }
  743. } else {
  744. i__1 = nnb;
  745. for (j = 1; j <= i__1; ++j) {
  746. i__2 = i__ + j * work_dim1;
  747. u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
  748. .i;
  749. i__2 = i__ + 1 + j * work_dim1;
  750. u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
  751. i__2].i;
  752. i__2 = i__ + j * work_dim1;
  753. i__3 = i__ + invd * work_dim1;
  754. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  755. u01_i_j__.i, z__2.i = work[i__3].r *
  756. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  757. i__4 = i__ + (invd + 1) * work_dim1;
  758. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  759. u01_ip1_j__.i, z__3.i = work[i__4].r *
  760. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  761. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  762. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  763. i__2 = i__ + 1 + j * work_dim1;
  764. i__3 = i__ + 1 + invd * work_dim1;
  765. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  766. u01_i_j__.i, z__2.i = work[i__3].r *
  767. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  768. i__4 = i__ + 1 + (invd + 1) * work_dim1;
  769. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  770. u01_ip1_j__.i, z__3.i = work[i__4].r *
  771. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  772. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  773. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  774. }
  775. ++i__;
  776. }
  777. ++i__;
  778. }
  779. /* invD1 * U11 */
  780. i__ = 1;
  781. while(i__ <= nnb) {
  782. if (ipiv[cut + i__] > 0) {
  783. i__1 = nnb;
  784. for (j = i__; j <= i__1; ++j) {
  785. i__2 = u11 + i__ + j * work_dim1;
  786. i__3 = cut + i__ + invd * work_dim1;
  787. i__4 = u11 + i__ + j * work_dim1;
  788. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  789. work[i__4].i, z__1.i = work[i__3].r * work[
  790. i__4].i + work[i__3].i * work[i__4].r;
  791. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  792. }
  793. } else {
  794. i__1 = nnb;
  795. for (j = i__; j <= i__1; ++j) {
  796. i__2 = u11 + i__ + j * work_dim1;
  797. u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
  798. .i;
  799. i__2 = u11 + i__ + 1 + j * work_dim1;
  800. u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
  801. i__2].i;
  802. i__2 = u11 + i__ + j * work_dim1;
  803. i__3 = cut + i__ + invd * work_dim1;
  804. i__4 = u11 + i__ + j * work_dim1;
  805. z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
  806. work[i__4].i, z__2.i = work[i__3].r * work[
  807. i__4].i + work[i__3].i * work[i__4].r;
  808. i__5 = cut + i__ + (invd + 1) * work_dim1;
  809. i__6 = u11 + i__ + 1 + j * work_dim1;
  810. z__3.r = work[i__5].r * work[i__6].r - work[i__5].i *
  811. work[i__6].i, z__3.i = work[i__5].r * work[
  812. i__6].i + work[i__5].i * work[i__6].r;
  813. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  814. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  815. i__2 = u11 + i__ + 1 + j * work_dim1;
  816. i__3 = cut + i__ + 1 + invd * work_dim1;
  817. z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
  818. u11_i_j__.i, z__2.i = work[i__3].r *
  819. u11_i_j__.i + work[i__3].i * u11_i_j__.r;
  820. i__4 = cut + i__ + 1 + (invd + 1) * work_dim1;
  821. z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
  822. u11_ip1_j__.i, z__3.i = work[i__4].r *
  823. u11_ip1_j__.i + work[i__4].i * u11_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. }
  827. ++i__;
  828. }
  829. ++i__;
  830. }
  831. /* U11**H * invD1 * U11 -> U11 */
  832. i__1 = *n + *nb + 1;
  833. ztrmm_("L", "U", "C", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut +
  834. 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
  835. i__1 = nnb;
  836. for (i__ = 1; i__ <= i__1; ++i__) {
  837. i__2 = nnb;
  838. for (j = i__; j <= i__2; ++j) {
  839. i__3 = cut + i__ + (cut + j) * a_dim1;
  840. i__4 = u11 + i__ + j * work_dim1;
  841. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  842. }
  843. }
  844. /* U01**H * invD * U01 -> A( CUT+I, CUT+J ) */
  845. i__1 = *n + *nb + 1;
  846. i__2 = *n + *nb + 1;
  847. zgemm_("C", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 +
  848. 1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1
  849. + work_dim1], &i__2);
  850. /* U11 = U11**H * invD1 * U11 + U01**H * invD * U01 */
  851. i__1 = nnb;
  852. for (i__ = 1; i__ <= i__1; ++i__) {
  853. i__2 = nnb;
  854. for (j = i__; j <= i__2; ++j) {
  855. i__3 = cut + i__ + (cut + j) * a_dim1;
  856. i__4 = cut + i__ + (cut + j) * a_dim1;
  857. i__5 = u11 + i__ + j * work_dim1;
  858. z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i +
  859. work[i__5].i;
  860. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  861. }
  862. }
  863. /* U01 = U00**H * invD0 * U01 */
  864. i__1 = *n + *nb + 1;
  865. ztrmm_("L", uplo, "C", "U", &cut, &nnb, &c_b1, &a[a_offset], lda,
  866. &work[work_offset], &i__1);
  867. /* Update U01 */
  868. i__1 = cut;
  869. for (i__ = 1; i__ <= i__1; ++i__) {
  870. i__2 = nnb;
  871. for (j = 1; j <= i__2; ++j) {
  872. i__3 = i__ + (cut + j) * a_dim1;
  873. i__4 = i__ + j * work_dim1;
  874. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  875. }
  876. }
  877. /* Next Block */
  878. }
  879. /* Apply PERMUTATIONS P and P**T: */
  880. /* P * inv(U**H) * inv(D) * inv(U) * P**T. */
  881. /* Interchange rows and columns I and IPIV(I) in reverse order */
  882. /* from the formation order of IPIV vector for Upper case. */
  883. /* ( We can use a loop over IPIV with increment 1, */
  884. /* since the ABS value of IPIV(I) represents the row (column) */
  885. /* index of the interchange with row (column) i in both 1x1 */
  886. /* and 2x2 pivot cases, i.e. we don't need separate code branches */
  887. /* for 1x1 and 2x2 pivot cases ) */
  888. i__1 = *n;
  889. for (i__ = 1; i__ <= i__1; ++i__) {
  890. ip = (i__2 = ipiv[i__], abs(i__2));
  891. if (ip != i__) {
  892. if (i__ < ip) {
  893. zheswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
  894. }
  895. if (i__ > ip) {
  896. zheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
  897. }
  898. }
  899. }
  900. } else {
  901. /* Begin Lower */
  902. /* inv A = P * inv(L**H) * inv(D) * inv(L) * P**T. */
  903. ztrtri_(uplo, "U", n, &a[a_offset], lda, info);
  904. /* inv(D) and inv(D) * inv(L) */
  905. k = *n;
  906. while(k >= 1) {
  907. if (ipiv[k] > 0) {
  908. /* 1 x 1 diagonal NNB */
  909. i__1 = k + invd * work_dim1;
  910. i__2 = k + k * a_dim1;
  911. d__1 = 1. / a[i__2].r;
  912. work[i__1].r = d__1, work[i__1].i = 0.;
  913. i__1 = k + (invd + 1) * work_dim1;
  914. work[i__1].r = 0., work[i__1].i = 0.;
  915. } else {
  916. /* 2 x 2 diagonal NNB */
  917. t = z_abs(&work[k - 1 + work_dim1]);
  918. i__1 = k - 1 + (k - 1) * a_dim1;
  919. ak = a[i__1].r / t;
  920. i__1 = k + k * a_dim1;
  921. akp1 = a[i__1].r / t;
  922. i__1 = k - 1 + work_dim1;
  923. z__1.r = work[i__1].r / t, z__1.i = work[i__1].i / t;
  924. akkp1.r = z__1.r, akkp1.i = z__1.i;
  925. d__1 = ak * akp1;
  926. z__2.r = d__1 - 1., z__2.i = 0.;
  927. z__1.r = t * z__2.r, z__1.i = t * z__2.i;
  928. d__.r = z__1.r, d__.i = z__1.i;
  929. i__1 = k - 1 + invd * work_dim1;
  930. z__2.r = akp1, z__2.i = 0.;
  931. z_div(&z__1, &z__2, &d__);
  932. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  933. i__1 = k + invd * work_dim1;
  934. z__2.r = ak, z__2.i = 0.;
  935. z_div(&z__1, &z__2, &d__);
  936. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  937. i__1 = k + (invd + 1) * work_dim1;
  938. z__2.r = -akkp1.r, z__2.i = -akkp1.i;
  939. z_div(&z__1, &z__2, &d__);
  940. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  941. i__1 = k - 1 + (invd + 1) * work_dim1;
  942. d_cnjg(&z__1, &work[k + (invd + 1) * work_dim1]);
  943. work[i__1].r = z__1.r, work[i__1].i = z__1.i;
  944. --k;
  945. }
  946. --k;
  947. }
  948. /* inv(L**H) = (inv(L))**H */
  949. /* inv(L**H) * inv(D) * inv(L) */
  950. cut = 0;
  951. while(cut < *n) {
  952. nnb = *nb;
  953. if (cut + nnb > *n) {
  954. nnb = *n - cut;
  955. } else {
  956. icount = 0;
  957. /* count negative elements, */
  958. i__1 = cut + nnb;
  959. for (i__ = cut + 1; i__ <= i__1; ++i__) {
  960. if (ipiv[i__] < 0) {
  961. ++icount;
  962. }
  963. }
  964. /* need a even number for a clear cut */
  965. if (icount % 2 == 1) {
  966. ++nnb;
  967. }
  968. }
  969. /* L21 Block */
  970. i__1 = *n - cut - nnb;
  971. for (i__ = 1; i__ <= i__1; ++i__) {
  972. i__2 = nnb;
  973. for (j = 1; j <= i__2; ++j) {
  974. i__3 = i__ + j * work_dim1;
  975. i__4 = cut + nnb + i__ + (cut + j) * a_dim1;
  976. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  977. }
  978. }
  979. /* L11 Block */
  980. i__1 = nnb;
  981. for (i__ = 1; i__ <= i__1; ++i__) {
  982. i__2 = u11 + i__ + i__ * work_dim1;
  983. work[i__2].r = 1., work[i__2].i = 0.;
  984. i__2 = nnb;
  985. for (j = i__ + 1; j <= i__2; ++j) {
  986. i__3 = u11 + i__ + j * work_dim1;
  987. work[i__3].r = 0., work[i__3].i = 0.;
  988. }
  989. i__2 = i__ - 1;
  990. for (j = 1; j <= i__2; ++j) {
  991. i__3 = u11 + i__ + j * work_dim1;
  992. i__4 = cut + i__ + (cut + j) * a_dim1;
  993. work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
  994. }
  995. }
  996. /* invD*L21 */
  997. i__ = *n - cut - nnb;
  998. while(i__ >= 1) {
  999. if (ipiv[cut + nnb + i__] > 0) {
  1000. i__1 = nnb;
  1001. for (j = 1; j <= i__1; ++j) {
  1002. i__2 = i__ + j * work_dim1;
  1003. i__3 = cut + nnb + i__ + invd * work_dim1;
  1004. i__4 = i__ + j * work_dim1;
  1005. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1006. work[i__4].i, z__1.i = work[i__3].r * work[
  1007. i__4].i + work[i__3].i * work[i__4].r;
  1008. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1009. }
  1010. } else {
  1011. i__1 = nnb;
  1012. for (j = 1; j <= i__1; ++j) {
  1013. i__2 = i__ + j * work_dim1;
  1014. u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
  1015. .i;
  1016. i__2 = i__ - 1 + j * work_dim1;
  1017. u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
  1018. i__2].i;
  1019. i__2 = i__ + j * work_dim1;
  1020. i__3 = cut + nnb + i__ + invd * work_dim1;
  1021. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  1022. u01_i_j__.i, z__2.i = work[i__3].r *
  1023. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  1024. i__4 = cut + nnb + i__ + (invd + 1) * work_dim1;
  1025. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  1026. u01_ip1_j__.i, z__3.i = work[i__4].r *
  1027. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  1028. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1029. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1030. i__2 = i__ - 1 + j * work_dim1;
  1031. i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1;
  1032. z__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
  1033. u01_i_j__.i, z__2.i = work[i__3].r *
  1034. u01_i_j__.i + work[i__3].i * u01_i_j__.r;
  1035. i__4 = cut + nnb + i__ - 1 + invd * work_dim1;
  1036. z__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
  1037. u01_ip1_j__.i, z__3.i = work[i__4].r *
  1038. u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
  1039. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1040. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1041. }
  1042. --i__;
  1043. }
  1044. --i__;
  1045. }
  1046. /* invD1*L11 */
  1047. i__ = nnb;
  1048. while(i__ >= 1) {
  1049. if (ipiv[cut + i__] > 0) {
  1050. i__1 = nnb;
  1051. for (j = 1; j <= i__1; ++j) {
  1052. i__2 = u11 + i__ + j * work_dim1;
  1053. i__3 = cut + i__ + invd * work_dim1;
  1054. i__4 = u11 + i__ + j * work_dim1;
  1055. z__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1056. work[i__4].i, z__1.i = work[i__3].r * work[
  1057. i__4].i + work[i__3].i * work[i__4].r;
  1058. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1059. }
  1060. } else {
  1061. i__1 = nnb;
  1062. for (j = 1; j <= i__1; ++j) {
  1063. i__2 = u11 + i__ + j * work_dim1;
  1064. u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
  1065. .i;
  1066. i__2 = u11 + i__ - 1 + j * work_dim1;
  1067. u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
  1068. i__2].i;
  1069. i__2 = u11 + i__ + j * work_dim1;
  1070. i__3 = cut + i__ + invd * work_dim1;
  1071. i__4 = u11 + i__ + j * work_dim1;
  1072. z__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
  1073. work[i__4].i, z__2.i = work[i__3].r * work[
  1074. i__4].i + work[i__3].i * work[i__4].r;
  1075. i__5 = cut + i__ + (invd + 1) * work_dim1;
  1076. z__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i *
  1077. u11_ip1_j__.i, z__3.i = work[i__5].r *
  1078. u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r;
  1079. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1080. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1081. i__2 = u11 + i__ - 1 + j * work_dim1;
  1082. i__3 = cut + i__ - 1 + (invd + 1) * work_dim1;
  1083. z__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
  1084. u11_i_j__.i, z__2.i = work[i__3].r *
  1085. u11_i_j__.i + work[i__3].i * u11_i_j__.r;
  1086. i__4 = cut + i__ - 1 + invd * work_dim1;
  1087. z__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
  1088. u11_ip1_j__.i, z__3.i = work[i__4].r *
  1089. u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
  1090. z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
  1091. work[i__2].r = z__1.r, work[i__2].i = z__1.i;
  1092. }
  1093. --i__;
  1094. }
  1095. --i__;
  1096. }
  1097. /* L11**H * invD1 * L11 -> L11 */
  1098. i__1 = *n + *nb + 1;
  1099. ztrmm_("L", uplo, "C", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut
  1100. + 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
  1101. i__1 = nnb;
  1102. for (i__ = 1; i__ <= i__1; ++i__) {
  1103. i__2 = i__;
  1104. for (j = 1; j <= i__2; ++j) {
  1105. i__3 = cut + i__ + (cut + j) * a_dim1;
  1106. i__4 = u11 + i__ + j * work_dim1;
  1107. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1108. }
  1109. }
  1110. if (cut + nnb < *n) {
  1111. /* L21**H * invD2*L21 -> A( CUT+I, CUT+J ) */
  1112. i__1 = *n - nnb - cut;
  1113. i__2 = *n + *nb + 1;
  1114. i__3 = *n + *nb + 1;
  1115. zgemm_("C", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 +
  1116. (cut + 1) * a_dim1], lda, &work[work_offset], &i__2, &
  1117. c_b2, &work[u11 + 1 + work_dim1], &i__3);
  1118. /* L11 = L11**H * invD1 * L11 + U01**H * invD * U01 */
  1119. i__1 = nnb;
  1120. for (i__ = 1; i__ <= i__1; ++i__) {
  1121. i__2 = i__;
  1122. for (j = 1; j <= i__2; ++j) {
  1123. i__3 = cut + i__ + (cut + j) * a_dim1;
  1124. i__4 = cut + i__ + (cut + j) * a_dim1;
  1125. i__5 = u11 + i__ + j * work_dim1;
  1126. z__1.r = a[i__4].r + work[i__5].r, z__1.i = a[i__4].i
  1127. + work[i__5].i;
  1128. a[i__3].r = z__1.r, a[i__3].i = z__1.i;
  1129. }
  1130. }
  1131. /* L01 = L22**H * invD2 * L21 */
  1132. i__1 = *n - nnb - cut;
  1133. i__2 = *n + *nb + 1;
  1134. ztrmm_("L", uplo, "C", "U", &i__1, &nnb, &c_b1, &a[cut + nnb
  1135. + 1 + (cut + nnb + 1) * a_dim1], lda, &work[
  1136. work_offset], &i__2);
  1137. /* Update L21 */
  1138. i__1 = *n - cut - nnb;
  1139. for (i__ = 1; i__ <= i__1; ++i__) {
  1140. i__2 = nnb;
  1141. for (j = 1; j <= i__2; ++j) {
  1142. i__3 = cut + nnb + i__ + (cut + j) * a_dim1;
  1143. i__4 = i__ + j * work_dim1;
  1144. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1145. }
  1146. }
  1147. } else {
  1148. /* L11 = L11**H * invD1 * L11 */
  1149. i__1 = nnb;
  1150. for (i__ = 1; i__ <= i__1; ++i__) {
  1151. i__2 = i__;
  1152. for (j = 1; j <= i__2; ++j) {
  1153. i__3 = cut + i__ + (cut + j) * a_dim1;
  1154. i__4 = u11 + i__ + j * work_dim1;
  1155. a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
  1156. }
  1157. }
  1158. }
  1159. /* Next Block */
  1160. cut += nnb;
  1161. }
  1162. /* Apply PERMUTATIONS P and P**T: */
  1163. /* P * inv(L**H) * inv(D) * inv(L) * P**T. */
  1164. /* Interchange rows and columns I and IPIV(I) in reverse order */
  1165. /* from the formation order of IPIV vector for Lower case. */
  1166. /* ( We can use a loop over IPIV with increment -1, */
  1167. /* since the ABS value of IPIV(I) represents the row (column) */
  1168. /* index of the interchange with row (column) i in both 1x1 */
  1169. /* and 2x2 pivot cases, i.e. we don't need separate code branches */
  1170. /* for 1x1 and 2x2 pivot cases ) */
  1171. for (i__ = *n; i__ >= 1; --i__) {
  1172. ip = (i__1 = ipiv[i__], abs(i__1));
  1173. if (ip != i__) {
  1174. if (i__ < ip) {
  1175. zheswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
  1176. }
  1177. if (i__ > ip) {
  1178. zheswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
  1179. }
  1180. }
  1181. }
  1182. }
  1183. return 0;
  1184. /* End of ZHETRI_3X */
  1185. } /* zhetri_3x__ */