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chetrs2.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. #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 complex c_b1 = {1.f,0.f};
  381. /* > \brief \b CHETRS2 */
  382. /* =========== DOCUMENTATION =========== */
  383. /* Online html documentation available at */
  384. /* http://www.netlib.org/lapack/explore-html/ */
  385. /* > \htmlonly */
  386. /* > Download CHETRS2 + dependencies */
  387. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrs2
  388. .f"> */
  389. /* > [TGZ]</a> */
  390. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrs2
  391. .f"> */
  392. /* > [ZIP]</a> */
  393. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrs2
  394. .f"> */
  395. /* > [TXT]</a> */
  396. /* > \endhtmlonly */
  397. /* Definition: */
  398. /* =========== */
  399. /* SUBROUTINE CHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, */
  400. /* WORK, INFO ) */
  401. /* CHARACTER UPLO */
  402. /* INTEGER INFO, LDA, LDB, N, NRHS */
  403. /* INTEGER IPIV( * ) */
  404. /* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) */
  405. /* > \par Purpose: */
  406. /* ============= */
  407. /* > */
  408. /* > \verbatim */
  409. /* > */
  410. /* > CHETRS2 solves a system of linear equations A*X = B with a complex */
  411. /* > Hermitian matrix A using the factorization A = U*D*U**H or */
  412. /* > A = L*D*L**H computed by CHETRF and converted by CSYCONV. */
  413. /* > \endverbatim */
  414. /* Arguments: */
  415. /* ========== */
  416. /* > \param[in] UPLO */
  417. /* > \verbatim */
  418. /* > UPLO is CHARACTER*1 */
  419. /* > Specifies whether the details of the factorization are stored */
  420. /* > as an upper or lower triangular matrix. */
  421. /* > = 'U': Upper triangular, form is A = U*D*U**H; */
  422. /* > = 'L': Lower triangular, form is A = L*D*L**H. */
  423. /* > \endverbatim */
  424. /* > */
  425. /* > \param[in] N */
  426. /* > \verbatim */
  427. /* > N is INTEGER */
  428. /* > The order of the matrix A. N >= 0. */
  429. /* > \endverbatim */
  430. /* > */
  431. /* > \param[in] NRHS */
  432. /* > \verbatim */
  433. /* > NRHS is INTEGER */
  434. /* > The number of right hand sides, i.e., the number of columns */
  435. /* > of the matrix B. NRHS >= 0. */
  436. /* > \endverbatim */
  437. /* > */
  438. /* > \param[in] A */
  439. /* > \verbatim */
  440. /* > A is COMPLEX array, dimension (LDA,N) */
  441. /* > The block diagonal matrix D and the multipliers used to */
  442. /* > obtain the factor U or L as computed by CHETRF. */
  443. /* > \endverbatim */
  444. /* > */
  445. /* > \param[in] LDA */
  446. /* > \verbatim */
  447. /* > LDA is INTEGER */
  448. /* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
  449. /* > \endverbatim */
  450. /* > */
  451. /* > \param[in] IPIV */
  452. /* > \verbatim */
  453. /* > IPIV is INTEGER array, dimension (N) */
  454. /* > Details of the interchanges and the block structure of D */
  455. /* > as determined by CHETRF. */
  456. /* > \endverbatim */
  457. /* > */
  458. /* > \param[in,out] B */
  459. /* > \verbatim */
  460. /* > B is COMPLEX array, dimension (LDB,NRHS) */
  461. /* > On entry, the right hand side matrix B. */
  462. /* > On exit, the solution matrix X. */
  463. /* > \endverbatim */
  464. /* > */
  465. /* > \param[in] LDB */
  466. /* > \verbatim */
  467. /* > LDB is INTEGER */
  468. /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
  469. /* > \endverbatim */
  470. /* > */
  471. /* > \param[out] WORK */
  472. /* > \verbatim */
  473. /* > WORK is COMPLEX array, dimension (N) */
  474. /* > \endverbatim */
  475. /* > */
  476. /* > \param[out] INFO */
  477. /* > \verbatim */
  478. /* > INFO is INTEGER */
  479. /* > = 0: successful exit */
  480. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  481. /* > \endverbatim */
  482. /* Authors: */
  483. /* ======== */
  484. /* > \author Univ. of Tennessee */
  485. /* > \author Univ. of California Berkeley */
  486. /* > \author Univ. of Colorado Denver */
  487. /* > \author NAG Ltd. */
  488. /* > \date December 2016 */
  489. /* > \ingroup complexHEcomputational */
  490. /* ===================================================================== */
  491. /* Subroutine */ int chetrs2_(char *uplo, integer *n, integer *nrhs, complex *
  492. a, integer *lda, integer *ipiv, complex *b, integer *ldb, complex *
  493. work, integer *info)
  494. {
  495. /* System generated locals */
  496. integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
  497. complex q__1, q__2, q__3;
  498. /* Local variables */
  499. complex akm1k;
  500. integer i__, j, k;
  501. real s;
  502. extern logical lsame_(char *, char *);
  503. complex denom;
  504. integer iinfo;
  505. extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
  506. complex *, integer *), ctrsm_(char *, char *, char *, char *,
  507. integer *, integer *, complex *, complex *, integer *, complex *,
  508. integer *);
  509. logical upper;
  510. complex ak, bk;
  511. integer kp;
  512. extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
  513. *), xerbla_(char *, integer *, ftnlen);
  514. complex akm1, bkm1;
  515. extern /* Subroutine */ int csyconv_(char *, char *, integer *, complex *,
  516. integer *, integer *, complex *, integer *);
  517. /* -- LAPACK computational routine (version 3.7.0) -- */
  518. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  519. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  520. /* December 2016 */
  521. /* ===================================================================== */
  522. /* Parameter adjustments */
  523. a_dim1 = *lda;
  524. a_offset = 1 + a_dim1 * 1;
  525. a -= a_offset;
  526. --ipiv;
  527. b_dim1 = *ldb;
  528. b_offset = 1 + b_dim1 * 1;
  529. b -= b_offset;
  530. --work;
  531. /* Function Body */
  532. *info = 0;
  533. upper = lsame_(uplo, "U");
  534. if (! upper && ! lsame_(uplo, "L")) {
  535. *info = -1;
  536. } else if (*n < 0) {
  537. *info = -2;
  538. } else if (*nrhs < 0) {
  539. *info = -3;
  540. } else if (*lda < f2cmax(1,*n)) {
  541. *info = -5;
  542. } else if (*ldb < f2cmax(1,*n)) {
  543. *info = -8;
  544. }
  545. if (*info != 0) {
  546. i__1 = -(*info);
  547. xerbla_("CHETRS2", &i__1, (ftnlen)7);
  548. return 0;
  549. }
  550. /* Quick return if possible */
  551. if (*n == 0 || *nrhs == 0) {
  552. return 0;
  553. }
  554. /* Convert A */
  555. csyconv_(uplo, "C", n, &a[a_offset], lda, &ipiv[1], &work[1], &iinfo);
  556. if (upper) {
  557. /* Solve A*X = B, where A = U*D*U**H. */
  558. /* P**T * B */
  559. k = *n;
  560. while(k >= 1) {
  561. if (ipiv[k] > 0) {
  562. /* 1 x 1 diagonal block */
  563. /* Interchange rows K and IPIV(K). */
  564. kp = ipiv[k];
  565. if (kp != k) {
  566. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  567. }
  568. --k;
  569. } else {
  570. /* 2 x 2 diagonal block */
  571. /* Interchange rows K-1 and -IPIV(K). */
  572. kp = -ipiv[k];
  573. if (kp == -ipiv[k - 1]) {
  574. cswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1],
  575. ldb);
  576. }
  577. k += -2;
  578. }
  579. }
  580. /* Compute (U \P**T * B) -> B [ (U \P**T * B) ] */
  581. ctrsm_("L", "U", "N", "U", n, nrhs, &c_b1, &a[a_offset], lda, &b[
  582. b_offset], ldb);
  583. /* Compute D \ B -> B [ D \ (U \P**T * B) ] */
  584. i__ = *n;
  585. while(i__ >= 1) {
  586. if (ipiv[i__] > 0) {
  587. i__1 = i__ + i__ * a_dim1;
  588. s = 1.f / a[i__1].r;
  589. csscal_(nrhs, &s, &b[i__ + b_dim1], ldb);
  590. } else if (i__ > 1) {
  591. if (ipiv[i__ - 1] == ipiv[i__]) {
  592. i__1 = i__;
  593. akm1k.r = work[i__1].r, akm1k.i = work[i__1].i;
  594. c_div(&q__1, &a[i__ - 1 + (i__ - 1) * a_dim1], &akm1k);
  595. akm1.r = q__1.r, akm1.i = q__1.i;
  596. r_cnjg(&q__2, &akm1k);
  597. c_div(&q__1, &a[i__ + i__ * a_dim1], &q__2);
  598. ak.r = q__1.r, ak.i = q__1.i;
  599. q__2.r = akm1.r * ak.r - akm1.i * ak.i, q__2.i = akm1.r *
  600. ak.i + akm1.i * ak.r;
  601. q__1.r = q__2.r - 1.f, q__1.i = q__2.i + 0.f;
  602. denom.r = q__1.r, denom.i = q__1.i;
  603. i__1 = *nrhs;
  604. for (j = 1; j <= i__1; ++j) {
  605. c_div(&q__1, &b[i__ - 1 + j * b_dim1], &akm1k);
  606. bkm1.r = q__1.r, bkm1.i = q__1.i;
  607. r_cnjg(&q__2, &akm1k);
  608. c_div(&q__1, &b[i__ + j * b_dim1], &q__2);
  609. bk.r = q__1.r, bk.i = q__1.i;
  610. i__2 = i__ - 1 + j * b_dim1;
  611. q__3.r = ak.r * bkm1.r - ak.i * bkm1.i, q__3.i = ak.r
  612. * bkm1.i + ak.i * bkm1.r;
  613. q__2.r = q__3.r - bk.r, q__2.i = q__3.i - bk.i;
  614. c_div(&q__1, &q__2, &denom);
  615. b[i__2].r = q__1.r, b[i__2].i = q__1.i;
  616. i__2 = i__ + j * b_dim1;
  617. q__3.r = akm1.r * bk.r - akm1.i * bk.i, q__3.i =
  618. akm1.r * bk.i + akm1.i * bk.r;
  619. q__2.r = q__3.r - bkm1.r, q__2.i = q__3.i - bkm1.i;
  620. c_div(&q__1, &q__2, &denom);
  621. b[i__2].r = q__1.r, b[i__2].i = q__1.i;
  622. /* L15: */
  623. }
  624. --i__;
  625. }
  626. }
  627. --i__;
  628. }
  629. /* Compute (U**H \ B) -> B [ U**H \ (D \ (U \P**T * B) ) ] */
  630. ctrsm_("L", "U", "C", "U", n, nrhs, &c_b1, &a[a_offset], lda, &b[
  631. b_offset], ldb);
  632. /* P * B [ P * (U**H \ (D \ (U \P**T * B) )) ] */
  633. k = 1;
  634. while(k <= *n) {
  635. if (ipiv[k] > 0) {
  636. /* 1 x 1 diagonal block */
  637. /* Interchange rows K and IPIV(K). */
  638. kp = ipiv[k];
  639. if (kp != k) {
  640. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  641. }
  642. ++k;
  643. } else {
  644. /* 2 x 2 diagonal block */
  645. /* Interchange rows K-1 and -IPIV(K). */
  646. kp = -ipiv[k];
  647. if (k < *n && kp == -ipiv[k + 1]) {
  648. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  649. }
  650. k += 2;
  651. }
  652. }
  653. } else {
  654. /* Solve A*X = B, where A = L*D*L**H. */
  655. /* P**T * B */
  656. k = 1;
  657. while(k <= *n) {
  658. if (ipiv[k] > 0) {
  659. /* 1 x 1 diagonal block */
  660. /* Interchange rows K and IPIV(K). */
  661. kp = ipiv[k];
  662. if (kp != k) {
  663. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  664. }
  665. ++k;
  666. } else {
  667. /* 2 x 2 diagonal block */
  668. /* Interchange rows K and -IPIV(K+1). */
  669. kp = -ipiv[k + 1];
  670. if (kp == -ipiv[k]) {
  671. cswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1],
  672. ldb);
  673. }
  674. k += 2;
  675. }
  676. }
  677. /* Compute (L \P**T * B) -> B [ (L \P**T * B) ] */
  678. ctrsm_("L", "L", "N", "U", n, nrhs, &c_b1, &a[a_offset], lda, &b[
  679. b_offset], ldb);
  680. /* Compute D \ B -> B [ D \ (L \P**T * B) ] */
  681. i__ = 1;
  682. while(i__ <= *n) {
  683. if (ipiv[i__] > 0) {
  684. i__1 = i__ + i__ * a_dim1;
  685. s = 1.f / a[i__1].r;
  686. csscal_(nrhs, &s, &b[i__ + b_dim1], ldb);
  687. } else {
  688. i__1 = i__;
  689. akm1k.r = work[i__1].r, akm1k.i = work[i__1].i;
  690. r_cnjg(&q__2, &akm1k);
  691. c_div(&q__1, &a[i__ + i__ * a_dim1], &q__2);
  692. akm1.r = q__1.r, akm1.i = q__1.i;
  693. c_div(&q__1, &a[i__ + 1 + (i__ + 1) * a_dim1], &akm1k);
  694. ak.r = q__1.r, ak.i = q__1.i;
  695. q__2.r = akm1.r * ak.r - akm1.i * ak.i, q__2.i = akm1.r *
  696. ak.i + akm1.i * ak.r;
  697. q__1.r = q__2.r - 1.f, q__1.i = q__2.i + 0.f;
  698. denom.r = q__1.r, denom.i = q__1.i;
  699. i__1 = *nrhs;
  700. for (j = 1; j <= i__1; ++j) {
  701. r_cnjg(&q__2, &akm1k);
  702. c_div(&q__1, &b[i__ + j * b_dim1], &q__2);
  703. bkm1.r = q__1.r, bkm1.i = q__1.i;
  704. c_div(&q__1, &b[i__ + 1 + j * b_dim1], &akm1k);
  705. bk.r = q__1.r, bk.i = q__1.i;
  706. i__2 = i__ + j * b_dim1;
  707. q__3.r = ak.r * bkm1.r - ak.i * bkm1.i, q__3.i = ak.r *
  708. bkm1.i + ak.i * bkm1.r;
  709. q__2.r = q__3.r - bk.r, q__2.i = q__3.i - bk.i;
  710. c_div(&q__1, &q__2, &denom);
  711. b[i__2].r = q__1.r, b[i__2].i = q__1.i;
  712. i__2 = i__ + 1 + j * b_dim1;
  713. q__3.r = akm1.r * bk.r - akm1.i * bk.i, q__3.i = akm1.r *
  714. bk.i + akm1.i * bk.r;
  715. q__2.r = q__3.r - bkm1.r, q__2.i = q__3.i - bkm1.i;
  716. c_div(&q__1, &q__2, &denom);
  717. b[i__2].r = q__1.r, b[i__2].i = q__1.i;
  718. /* L25: */
  719. }
  720. ++i__;
  721. }
  722. ++i__;
  723. }
  724. /* Compute (L**H \ B) -> B [ L**H \ (D \ (L \P**T * B) ) ] */
  725. ctrsm_("L", "L", "C", "U", n, nrhs, &c_b1, &a[a_offset], lda, &b[
  726. b_offset], ldb);
  727. /* P * B [ P * (L**H \ (D \ (L \P**T * B) )) ] */
  728. k = *n;
  729. while(k >= 1) {
  730. if (ipiv[k] > 0) {
  731. /* 1 x 1 diagonal block */
  732. /* Interchange rows K and IPIV(K). */
  733. kp = ipiv[k];
  734. if (kp != k) {
  735. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  736. }
  737. --k;
  738. } else {
  739. /* 2 x 2 diagonal block */
  740. /* Interchange rows K-1 and -IPIV(K). */
  741. kp = -ipiv[k];
  742. if (k > 1 && kp == -ipiv[k - 1]) {
  743. cswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
  744. }
  745. k += -2;
  746. }
  747. }
  748. }
  749. /* Revert A */
  750. csyconv_(uplo, "R", n, &a[a_offset], lda, &ipiv[1], &work[1], &iinfo);
  751. return 0;
  752. /* End of CHETRS2 */
  753. } /* chetrs2_ */