You can not select more than 25 topics Topics must start with a chinese character,a letter or number, can include dashes ('-') and can be up to 35 characters long.

ztrttf.c 28 kB

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495969798991001011021031041051061071081091101111121131141151161171181191201211221231241251261271281291301311321331341351361371381391401411421431441451461471481491501511521531541551561571581591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992002012022032042052062072082092102112122132142152162172182192202212222232242252262272282292302312322332342352362372382392402412422432442452462472482492502512522532542552562572582592602612622632642652662672682692702712722732742752762772782792802812822832842852862872882892902912922932942952962972982993003013023033043053063073083093103113123133143153163173183193203213223233243253263273283293303313323333343353363373383393403413423433443453463473483493503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014024034044054064074084094104114124134144154164174184194204214224234244254264274284294304314324334344354364374384394404414424434444454464474484494504514524534544554564574584594604614624634644654664674684694704714724734744754764774784794804814824834844854864874884894904914924934944954964974984995005015025035045055065075085095105115125135145155165175185195205215225235245255265275285295305315325335345355365375385395405415425435445455465475485495505515525535545555565575585595605615625635645655665675685695705715725735745755765775785795805815825835845855865875885895905915925935945955965975985996006016026036046056066076086096106116126136146156166176186196206216226236246256266276286296306316326336346356366376386396406416426436446456466476486496506516526536546556566576586596606616626636646656666676686696706716726736746756766776786796806816826836846856866876886896906916926936946956966976986997007017027037047057067077087097107117127137147157167177187197207217227237247257267277287297307317327337347357367377387397407417427437447457467477487497507517527537547557567577587597607617627637647657667677687697707717727737747757767777787797807817827837847857867877887897907917927937947957967977987998008018028038048058068078088098108118128138148158168178188198208218228238248258268278288298308318328338348358368378388398408418428438448458468478488498508518528538548558568578588598608618628638648658668678688698708718728738748758768778788798808818828838848858868878888898908918928938948958968978988999009019029039049059069079089099109119129139149159169179189199209219229239249259269279289299309319329339349359369379389399409419429439449459469479489499509519529539549559569579589599609619629639649659669679689699709719729739749759769779789799809819829839849859869879889899909919929939949959969979989991000100110021003100410051006
  1. /* f2c.h -- Standard Fortran to C header file */
  2. /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
  3. - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
  4. #ifndef F2C_INCLUDE
  5. #define F2C_INCLUDE
  6. #include <math.h>
  7. #include <stdlib.h>
  8. #include <string.h>
  9. #include <stdio.h>
  10. #include <complex.h>
  11. #ifdef complex
  12. #undef complex
  13. #endif
  14. #ifdef I
  15. #undef I
  16. #endif
  17. typedef int integer;
  18. typedef unsigned int uinteger;
  19. typedef char *address;
  20. typedef short int shortint;
  21. typedef float real;
  22. typedef double doublereal;
  23. typedef struct { real r, i; } complex;
  24. typedef struct { doublereal r, i; } doublecomplex;
  25. static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
  26. static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
  27. static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
  28. static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
  29. #define pCf(z) (*_pCf(z))
  30. #define pCd(z) (*_pCd(z))
  31. typedef int logical;
  32. typedef short int shortlogical;
  33. typedef char logical1;
  34. typedef char integer1;
  35. #define TRUE_ (1)
  36. #define FALSE_ (0)
  37. /* Extern is for use with -E */
  38. #ifndef Extern
  39. #define Extern extern
  40. #endif
  41. /* I/O stuff */
  42. typedef int flag;
  43. typedef int ftnlen;
  44. typedef int ftnint;
  45. /*external read, write*/
  46. typedef struct
  47. { flag cierr;
  48. ftnint ciunit;
  49. flag ciend;
  50. char *cifmt;
  51. ftnint cirec;
  52. } cilist;
  53. /*internal read, write*/
  54. typedef struct
  55. { flag icierr;
  56. char *iciunit;
  57. flag iciend;
  58. char *icifmt;
  59. ftnint icirlen;
  60. ftnint icirnum;
  61. } icilist;
  62. /*open*/
  63. typedef struct
  64. { flag oerr;
  65. ftnint ounit;
  66. char *ofnm;
  67. ftnlen ofnmlen;
  68. char *osta;
  69. char *oacc;
  70. char *ofm;
  71. ftnint orl;
  72. char *oblnk;
  73. } olist;
  74. /*close*/
  75. typedef struct
  76. { flag cerr;
  77. ftnint cunit;
  78. char *csta;
  79. } cllist;
  80. /*rewind, backspace, endfile*/
  81. typedef struct
  82. { flag aerr;
  83. ftnint aunit;
  84. } alist;
  85. /* inquire */
  86. typedef struct
  87. { flag inerr;
  88. ftnint inunit;
  89. char *infile;
  90. ftnlen infilen;
  91. ftnint *inex; /*parameters in standard's order*/
  92. ftnint *inopen;
  93. ftnint *innum;
  94. ftnint *innamed;
  95. char *inname;
  96. ftnlen innamlen;
  97. char *inacc;
  98. ftnlen inacclen;
  99. char *inseq;
  100. ftnlen inseqlen;
  101. char *indir;
  102. ftnlen indirlen;
  103. char *infmt;
  104. ftnlen infmtlen;
  105. char *inform;
  106. ftnint informlen;
  107. char *inunf;
  108. ftnlen inunflen;
  109. ftnint *inrecl;
  110. ftnint *innrec;
  111. char *inblank;
  112. ftnlen inblanklen;
  113. } inlist;
  114. #define VOID void
  115. union Multitype { /* for multiple entry points */
  116. integer1 g;
  117. shortint h;
  118. integer i;
  119. /* longint j; */
  120. real r;
  121. doublereal d;
  122. complex c;
  123. doublecomplex z;
  124. };
  125. typedef union Multitype Multitype;
  126. struct Vardesc { /* for Namelist */
  127. char *name;
  128. char *addr;
  129. ftnlen *dims;
  130. int type;
  131. };
  132. typedef struct Vardesc Vardesc;
  133. struct Namelist {
  134. char *name;
  135. Vardesc **vars;
  136. int nvars;
  137. };
  138. typedef struct Namelist Namelist;
  139. #define abs(x) ((x) >= 0 ? (x) : -(x))
  140. #define dabs(x) (fabs(x))
  141. #define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
  142. #define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
  143. #define dmin(a,b) (f2cmin(a,b))
  144. #define dmax(a,b) (f2cmax(a,b))
  145. #define bit_test(a,b) ((a) >> (b) & 1)
  146. #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
  147. #define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
  148. #define abort_() { sig_die("Fortran abort routine called", 1); }
  149. #define c_abs(z) (cabsf(Cf(z)))
  150. #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
  151. #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
  152. #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
  153. #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
  154. #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
  155. #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
  156. //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
  157. #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
  158. #define d_abs(x) (fabs(*(x)))
  159. #define d_acos(x) (acos(*(x)))
  160. #define d_asin(x) (asin(*(x)))
  161. #define d_atan(x) (atan(*(x)))
  162. #define d_atn2(x, y) (atan2(*(x),*(y)))
  163. #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
  164. #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
  165. #define d_cos(x) (cos(*(x)))
  166. #define d_cosh(x) (cosh(*(x)))
  167. #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
  168. #define d_exp(x) (exp(*(x)))
  169. #define d_imag(z) (cimag(Cd(z)))
  170. #define r_imag(z) (cimag(Cf(z)))
  171. #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  172. #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
  173. #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  174. #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
  175. #define d_log(x) (log(*(x)))
  176. #define d_mod(x, y) (fmod(*(x), *(y)))
  177. #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
  178. #define d_nint(x) u_nint(*(x))
  179. #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
  180. #define d_sign(a,b) u_sign(*(a),*(b))
  181. #define r_sign(a,b) u_sign(*(a),*(b))
  182. #define d_sin(x) (sin(*(x)))
  183. #define d_sinh(x) (sinh(*(x)))
  184. #define d_sqrt(x) (sqrt(*(x)))
  185. #define d_tan(x) (tan(*(x)))
  186. #define d_tanh(x) (tanh(*(x)))
  187. #define i_abs(x) abs(*(x))
  188. #define i_dnnt(x) ((integer)u_nint(*(x)))
  189. #define i_len(s, n) (n)
  190. #define i_nint(x) ((integer)u_nint(*(x)))
  191. #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
  192. #define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
  193. #define pow_si(B,E) spow_ui(*(B),*(E))
  194. #define pow_ri(B,E) spow_ui(*(B),*(E))
  195. #define pow_di(B,E) dpow_ui(*(B),*(E))
  196. #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
  197. #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
  198. #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
  199. #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
  200. #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
  201. #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
  202. #define sig_die(s, kill) { exit(1); }
  203. #define s_stop(s, n) {exit(0);}
  204. static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
  205. #define z_abs(z) (cabs(Cd(z)))
  206. #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
  207. #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
  208. #define myexit_() break;
  209. #define mycycle() continue;
  210. #define myceiling(w) {ceil(w)}
  211. #define myhuge(w) {HUGE_VAL}
  212. //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
  213. #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
  214. /* procedure parameter types for -A and -C++ */
  215. #define F2C_proc_par_types 1
  216. #ifdef __cplusplus
  217. typedef logical (*L_fp)(...);
  218. #else
  219. typedef logical (*L_fp)();
  220. #endif
  221. static float spow_ui(float x, integer n) {
  222. float pow=1.0; unsigned long int u;
  223. if(n != 0) {
  224. if(n < 0) n = -n, x = 1/x;
  225. for(u = n; ; ) {
  226. if(u & 01) pow *= x;
  227. if(u >>= 1) x *= x;
  228. else break;
  229. }
  230. }
  231. return pow;
  232. }
  233. static double dpow_ui(double x, integer n) {
  234. double pow=1.0; unsigned long int u;
  235. if(n != 0) {
  236. if(n < 0) n = -n, x = 1/x;
  237. for(u = n; ; ) {
  238. if(u & 01) pow *= x;
  239. if(u >>= 1) x *= x;
  240. else break;
  241. }
  242. }
  243. return pow;
  244. }
  245. static _Complex float cpow_ui(_Complex float x, integer n) {
  246. _Complex float pow=1.0; unsigned long int u;
  247. if(n != 0) {
  248. if(n < 0) n = -n, x = 1/x;
  249. for(u = n; ; ) {
  250. if(u & 01) pow *= x;
  251. if(u >>= 1) x *= x;
  252. else break;
  253. }
  254. }
  255. return pow;
  256. }
  257. static _Complex double zpow_ui(_Complex double x, integer n) {
  258. _Complex double pow=1.0; unsigned long int u;
  259. if(n != 0) {
  260. if(n < 0) n = -n, x = 1/x;
  261. for(u = n; ; ) {
  262. if(u & 01) pow *= x;
  263. if(u >>= 1) x *= x;
  264. else break;
  265. }
  266. }
  267. return pow;
  268. }
  269. static integer pow_ii(integer x, integer n) {
  270. integer pow; unsigned long int u;
  271. if (n <= 0) {
  272. if (n == 0 || x == 1) pow = 1;
  273. else if (x != -1) pow = x == 0 ? 1/x : 0;
  274. else n = -n;
  275. }
  276. if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
  277. u = n;
  278. for(pow = 1; ; ) {
  279. if(u & 01) pow *= x;
  280. if(u >>= 1) x *= x;
  281. else break;
  282. }
  283. }
  284. return pow;
  285. }
  286. static integer dmaxloc_(double *w, integer s, integer e, integer *n)
  287. {
  288. double m; integer i, mi;
  289. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  290. if (w[i-1]>m) mi=i ,m=w[i-1];
  291. return mi-s+1;
  292. }
  293. static integer smaxloc_(float *w, integer s, integer e, integer *n)
  294. {
  295. float m; integer i, mi;
  296. for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
  297. if (w[i-1]>m) mi=i ,m=w[i-1];
  298. return mi-s+1;
  299. }
  300. static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  301. integer n = *n_, incx = *incx_, incy = *incy_, i;
  302. _Complex float zdotc = 0.0;
  303. if (incx == 1 && incy == 1) {
  304. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  305. zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
  306. }
  307. } else {
  308. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  309. zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
  310. }
  311. }
  312. pCf(z) = zdotc;
  313. }
  314. static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  315. integer n = *n_, incx = *incx_, incy = *incy_, i;
  316. _Complex double zdotc = 0.0;
  317. if (incx == 1 && incy == 1) {
  318. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  319. zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
  320. }
  321. } else {
  322. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  323. zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
  324. }
  325. }
  326. pCd(z) = zdotc;
  327. }
  328. static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
  329. integer n = *n_, incx = *incx_, incy = *incy_, i;
  330. _Complex float zdotc = 0.0;
  331. if (incx == 1 && incy == 1) {
  332. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  333. zdotc += Cf(&x[i]) * Cf(&y[i]);
  334. }
  335. } else {
  336. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  337. zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
  338. }
  339. }
  340. pCf(z) = zdotc;
  341. }
  342. static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
  343. integer n = *n_, incx = *incx_, incy = *incy_, i;
  344. _Complex double zdotc = 0.0;
  345. if (incx == 1 && incy == 1) {
  346. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  347. zdotc += Cd(&x[i]) * Cd(&y[i]);
  348. }
  349. } else {
  350. for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
  351. zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
  352. }
  353. }
  354. pCd(z) = zdotc;
  355. }
  356. #endif
  357. /* -- translated by f2c (version 20000121).
  358. You must link the resulting object file with the libraries:
  359. -lf2c -lm (in that order)
  360. */
  361. /* > \brief \b ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full pa
  362. cked format (TF). */
  363. /* =========== DOCUMENTATION =========== */
  364. /* Online html documentation available at */
  365. /* http://www.netlib.org/lapack/explore-html/ */
  366. /* > \htmlonly */
  367. /* > Download ZTRTTF + dependencies */
  368. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrttf.
  369. f"> */
  370. /* > [TGZ]</a> */
  371. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrttf.
  372. f"> */
  373. /* > [ZIP]</a> */
  374. /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrttf.
  375. f"> */
  376. /* > [TXT]</a> */
  377. /* > \endhtmlonly */
  378. /* Definition: */
  379. /* =========== */
  380. /* SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO ) */
  381. /* CHARACTER TRANSR, UPLO */
  382. /* INTEGER INFO, N, LDA */
  383. /* COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * ) */
  384. /* > \par Purpose: */
  385. /* ============= */
  386. /* > */
  387. /* > \verbatim */
  388. /* > */
  389. /* > ZTRTTF copies a triangular matrix A from standard full format (TR) */
  390. /* > to rectangular full packed format (TF) . */
  391. /* > \endverbatim */
  392. /* Arguments: */
  393. /* ========== */
  394. /* > \param[in] TRANSR */
  395. /* > \verbatim */
  396. /* > TRANSR is CHARACTER*1 */
  397. /* > = 'N': ARF in Normal mode is wanted; */
  398. /* > = 'C': ARF in Conjugate Transpose mode is wanted; */
  399. /* > \endverbatim */
  400. /* > */
  401. /* > \param[in] UPLO */
  402. /* > \verbatim */
  403. /* > UPLO is CHARACTER*1 */
  404. /* > = 'U': A is upper triangular; */
  405. /* > = 'L': A is lower triangular. */
  406. /* > \endverbatim */
  407. /* > */
  408. /* > \param[in] N */
  409. /* > \verbatim */
  410. /* > N is INTEGER */
  411. /* > The order of the matrix A. N >= 0. */
  412. /* > \endverbatim */
  413. /* > */
  414. /* > \param[in] A */
  415. /* > \verbatim */
  416. /* > A is COMPLEX*16 array, dimension ( LDA, N ) */
  417. /* > On entry, the triangular matrix A. If UPLO = 'U', the */
  418. /* > leading N-by-N upper triangular part of the array A contains */
  419. /* > the upper triangular matrix, and the strictly lower */
  420. /* > triangular part of A is not referenced. If UPLO = 'L', the */
  421. /* > leading N-by-N lower triangular part of the array A contains */
  422. /* > the lower triangular matrix, and the strictly upper */
  423. /* > triangular part of A is not referenced. */
  424. /* > \endverbatim */
  425. /* > */
  426. /* > \param[in] LDA */
  427. /* > \verbatim */
  428. /* > LDA is INTEGER */
  429. /* > The leading dimension of the matrix A. LDA >= f2cmax(1,N). */
  430. /* > \endverbatim */
  431. /* > */
  432. /* > \param[out] ARF */
  433. /* > \verbatim */
  434. /* > ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), */
  435. /* > On exit, the upper or lower triangular matrix A stored in */
  436. /* > RFP format. For a further discussion see Notes below. */
  437. /* > \endverbatim */
  438. /* > */
  439. /* > \param[out] INFO */
  440. /* > \verbatim */
  441. /* > INFO is INTEGER */
  442. /* > = 0: successful exit */
  443. /* > < 0: if INFO = -i, the i-th argument had an illegal value */
  444. /* > \endverbatim */
  445. /* Authors: */
  446. /* ======== */
  447. /* > \author Univ. of Tennessee */
  448. /* > \author Univ. of California Berkeley */
  449. /* > \author Univ. of Colorado Denver */
  450. /* > \author NAG Ltd. */
  451. /* > \date December 2016 */
  452. /* > \ingroup complex16OTHERcomputational */
  453. /* > \par Further Details: */
  454. /* ===================== */
  455. /* > */
  456. /* > \verbatim */
  457. /* > */
  458. /* > We first consider Standard Packed Format when N is even. */
  459. /* > We give an example where N = 6. */
  460. /* > */
  461. /* > AP is Upper AP is Lower */
  462. /* > */
  463. /* > 00 01 02 03 04 05 00 */
  464. /* > 11 12 13 14 15 10 11 */
  465. /* > 22 23 24 25 20 21 22 */
  466. /* > 33 34 35 30 31 32 33 */
  467. /* > 44 45 40 41 42 43 44 */
  468. /* > 55 50 51 52 53 54 55 */
  469. /* > */
  470. /* > */
  471. /* > Let TRANSR = 'N'. RFP holds AP as follows: */
  472. /* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
  473. /* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
  474. /* > conjugate-transpose of the first three columns of AP upper. */
  475. /* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
  476. /* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
  477. /* > conjugate-transpose of the last three columns of AP lower. */
  478. /* > To denote conjugate we place -- above the element. This covers the */
  479. /* > case N even and TRANSR = 'N'. */
  480. /* > */
  481. /* > RFP A RFP A */
  482. /* > */
  483. /* > -- -- -- */
  484. /* > 03 04 05 33 43 53 */
  485. /* > -- -- */
  486. /* > 13 14 15 00 44 54 */
  487. /* > -- */
  488. /* > 23 24 25 10 11 55 */
  489. /* > */
  490. /* > 33 34 35 20 21 22 */
  491. /* > -- */
  492. /* > 00 44 45 30 31 32 */
  493. /* > -- -- */
  494. /* > 01 11 55 40 41 42 */
  495. /* > -- -- -- */
  496. /* > 02 12 22 50 51 52 */
  497. /* > */
  498. /* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
  499. /* > transpose of RFP A above. One therefore gets: */
  500. /* > */
  501. /* > */
  502. /* > RFP A RFP A */
  503. /* > */
  504. /* > -- -- -- -- -- -- -- -- -- -- */
  505. /* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
  506. /* > -- -- -- -- -- -- -- -- -- -- */
  507. /* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
  508. /* > -- -- -- -- -- -- -- -- -- -- */
  509. /* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
  510. /* > */
  511. /* > */
  512. /* > We next consider Standard Packed Format when N is odd. */
  513. /* > We give an example where N = 5. */
  514. /* > */
  515. /* > AP is Upper AP is Lower */
  516. /* > */
  517. /* > 00 01 02 03 04 00 */
  518. /* > 11 12 13 14 10 11 */
  519. /* > 22 23 24 20 21 22 */
  520. /* > 33 34 30 31 32 33 */
  521. /* > 44 40 41 42 43 44 */
  522. /* > */
  523. /* > */
  524. /* > Let TRANSR = 'N'. RFP holds AP as follows: */
  525. /* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
  526. /* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
  527. /* > conjugate-transpose of the first two columns of AP upper. */
  528. /* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
  529. /* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
  530. /* > conjugate-transpose of the last two columns of AP lower. */
  531. /* > To denote conjugate we place -- above the element. This covers the */
  532. /* > case N odd and TRANSR = 'N'. */
  533. /* > */
  534. /* > RFP A RFP A */
  535. /* > */
  536. /* > -- -- */
  537. /* > 02 03 04 00 33 43 */
  538. /* > -- */
  539. /* > 12 13 14 10 11 44 */
  540. /* > */
  541. /* > 22 23 24 20 21 22 */
  542. /* > -- */
  543. /* > 00 33 34 30 31 32 */
  544. /* > -- -- */
  545. /* > 01 11 44 40 41 42 */
  546. /* > */
  547. /* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
  548. /* > transpose of RFP A above. One therefore gets: */
  549. /* > */
  550. /* > */
  551. /* > RFP A RFP A */
  552. /* > */
  553. /* > -- -- -- -- -- -- -- -- -- */
  554. /* > 02 12 22 00 01 00 10 20 30 40 50 */
  555. /* > -- -- -- -- -- -- -- -- -- */
  556. /* > 03 13 23 33 11 33 11 21 31 41 51 */
  557. /* > -- -- -- -- -- -- -- -- -- */
  558. /* > 04 14 24 34 44 43 44 22 32 42 52 */
  559. /* > \endverbatim */
  560. /* > */
  561. /* ===================================================================== */
  562. /* Subroutine */ int ztrttf_(char *transr, char *uplo, integer *n,
  563. doublecomplex *a, integer *lda, doublecomplex *arf, integer *info)
  564. {
  565. /* System generated locals */
  566. integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
  567. doublecomplex z__1;
  568. /* Local variables */
  569. integer np1x2, i__, j, k, l;
  570. logical normaltransr;
  571. extern logical lsame_(char *, char *);
  572. logical lower;
  573. integer n1, n2, ij, nt;
  574. extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
  575. logical nisodd;
  576. integer nx2;
  577. /* -- LAPACK computational routine (version 3.7.0) -- */
  578. /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
  579. /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  580. /* December 2016 */
  581. /* ===================================================================== */
  582. /* Test the input parameters. */
  583. /* Parameter adjustments */
  584. a_dim1 = *lda - 1 - 0 + 1;
  585. a_offset = 0 + a_dim1 * 0;
  586. a -= a_offset;
  587. /* Function Body */
  588. *info = 0;
  589. normaltransr = lsame_(transr, "N");
  590. lower = lsame_(uplo, "L");
  591. if (! normaltransr && ! lsame_(transr, "C")) {
  592. *info = -1;
  593. } else if (! lower && ! lsame_(uplo, "U")) {
  594. *info = -2;
  595. } else if (*n < 0) {
  596. *info = -3;
  597. } else if (*lda < f2cmax(1,*n)) {
  598. *info = -5;
  599. }
  600. if (*info != 0) {
  601. i__1 = -(*info);
  602. xerbla_("ZTRTTF", &i__1, (ftnlen)6);
  603. return 0;
  604. }
  605. /* Quick return if possible */
  606. if (*n <= 1) {
  607. if (*n == 1) {
  608. if (normaltransr) {
  609. arf[0].r = a[0].r, arf[0].i = a[0].i;
  610. } else {
  611. d_cnjg(&z__1, a);
  612. arf[0].r = z__1.r, arf[0].i = z__1.i;
  613. }
  614. }
  615. return 0;
  616. }
  617. /* Size of array ARF(1:2,0:nt-1) */
  618. nt = *n * (*n + 1) / 2;
  619. /* set N1 and N2 depending on LOWER: for N even N1=N2=K */
  620. if (lower) {
  621. n2 = *n / 2;
  622. n1 = *n - n2;
  623. } else {
  624. n1 = *n / 2;
  625. n2 = *n - n1;
  626. }
  627. /* If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2. */
  628. /* If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is */
  629. /* N--by--(N+1)/2. */
  630. if (*n % 2 == 0) {
  631. k = *n / 2;
  632. nisodd = FALSE_;
  633. if (! lower) {
  634. np1x2 = *n + *n + 2;
  635. }
  636. } else {
  637. nisodd = TRUE_;
  638. if (! lower) {
  639. nx2 = *n + *n;
  640. }
  641. }
  642. if (nisodd) {
  643. /* N is odd */
  644. if (normaltransr) {
  645. /* N is odd and TRANSR = 'N' */
  646. if (lower) {
  647. /* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
  648. /* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
  649. /* T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n */
  650. ij = 0;
  651. i__1 = n2;
  652. for (j = 0; j <= i__1; ++j) {
  653. i__2 = n2 + j;
  654. for (i__ = n1; i__ <= i__2; ++i__) {
  655. i__3 = ij;
  656. d_cnjg(&z__1, &a[n2 + j + i__ * a_dim1]);
  657. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  658. ++ij;
  659. }
  660. i__2 = *n - 1;
  661. for (i__ = j; i__ <= i__2; ++i__) {
  662. i__3 = ij;
  663. i__4 = i__ + j * a_dim1;
  664. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  665. ++ij;
  666. }
  667. }
  668. } else {
  669. /* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
  670. /* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
  671. /* T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n */
  672. ij = nt - *n;
  673. i__1 = n1;
  674. for (j = *n - 1; j >= i__1; --j) {
  675. i__2 = j;
  676. for (i__ = 0; i__ <= i__2; ++i__) {
  677. i__3 = ij;
  678. i__4 = i__ + j * a_dim1;
  679. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  680. ++ij;
  681. }
  682. i__2 = n1 - 1;
  683. for (l = j - n1; l <= i__2; ++l) {
  684. i__3 = ij;
  685. d_cnjg(&z__1, &a[j - n1 + l * a_dim1]);
  686. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  687. ++ij;
  688. }
  689. ij -= nx2;
  690. }
  691. }
  692. } else {
  693. /* N is odd and TRANSR = 'C' */
  694. if (lower) {
  695. /* SRPA for LOWER, TRANSPOSE and N is odd */
  696. /* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
  697. /* T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1 */
  698. ij = 0;
  699. i__1 = n2 - 1;
  700. for (j = 0; j <= i__1; ++j) {
  701. i__2 = j;
  702. for (i__ = 0; i__ <= i__2; ++i__) {
  703. i__3 = ij;
  704. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  705. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  706. ++ij;
  707. }
  708. i__2 = *n - 1;
  709. for (i__ = n1 + j; i__ <= i__2; ++i__) {
  710. i__3 = ij;
  711. i__4 = i__ + (n1 + j) * a_dim1;
  712. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  713. ++ij;
  714. }
  715. }
  716. i__1 = *n - 1;
  717. for (j = n2; j <= i__1; ++j) {
  718. i__2 = n1 - 1;
  719. for (i__ = 0; i__ <= i__2; ++i__) {
  720. i__3 = ij;
  721. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  722. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  723. ++ij;
  724. }
  725. }
  726. } else {
  727. /* SRPA for UPPER, TRANSPOSE and N is odd */
  728. /* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
  729. /* T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2 */
  730. ij = 0;
  731. i__1 = n1;
  732. for (j = 0; j <= i__1; ++j) {
  733. i__2 = *n - 1;
  734. for (i__ = n1; i__ <= i__2; ++i__) {
  735. i__3 = ij;
  736. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  737. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  738. ++ij;
  739. }
  740. }
  741. i__1 = n1 - 1;
  742. for (j = 0; j <= i__1; ++j) {
  743. i__2 = j;
  744. for (i__ = 0; i__ <= i__2; ++i__) {
  745. i__3 = ij;
  746. i__4 = i__ + j * a_dim1;
  747. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  748. ++ij;
  749. }
  750. i__2 = *n - 1;
  751. for (l = n2 + j; l <= i__2; ++l) {
  752. i__3 = ij;
  753. d_cnjg(&z__1, &a[n2 + j + l * a_dim1]);
  754. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  755. ++ij;
  756. }
  757. }
  758. }
  759. }
  760. } else {
  761. /* N is even */
  762. if (normaltransr) {
  763. /* N is even and TRANSR = 'N' */
  764. if (lower) {
  765. /* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
  766. /* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
  767. /* T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1 */
  768. ij = 0;
  769. i__1 = k - 1;
  770. for (j = 0; j <= i__1; ++j) {
  771. i__2 = k + j;
  772. for (i__ = k; i__ <= i__2; ++i__) {
  773. i__3 = ij;
  774. d_cnjg(&z__1, &a[k + j + i__ * a_dim1]);
  775. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  776. ++ij;
  777. }
  778. i__2 = *n - 1;
  779. for (i__ = j; i__ <= i__2; ++i__) {
  780. i__3 = ij;
  781. i__4 = i__ + j * a_dim1;
  782. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  783. ++ij;
  784. }
  785. }
  786. } else {
  787. /* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
  788. /* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) */
  789. /* T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1 */
  790. ij = nt - *n - 1;
  791. i__1 = k;
  792. for (j = *n - 1; j >= i__1; --j) {
  793. i__2 = j;
  794. for (i__ = 0; i__ <= i__2; ++i__) {
  795. i__3 = ij;
  796. i__4 = i__ + j * a_dim1;
  797. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  798. ++ij;
  799. }
  800. i__2 = k - 1;
  801. for (l = j - k; l <= i__2; ++l) {
  802. i__3 = ij;
  803. d_cnjg(&z__1, &a[j - k + l * a_dim1]);
  804. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  805. ++ij;
  806. }
  807. ij -= np1x2;
  808. }
  809. }
  810. } else {
  811. /* N is even and TRANSR = 'C' */
  812. if (lower) {
  813. /* SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B) */
  814. /* T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) : */
  815. /* T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k */
  816. ij = 0;
  817. j = k;
  818. i__1 = *n - 1;
  819. for (i__ = k; i__ <= i__1; ++i__) {
  820. i__2 = ij;
  821. i__3 = i__ + j * a_dim1;
  822. arf[i__2].r = a[i__3].r, arf[i__2].i = a[i__3].i;
  823. ++ij;
  824. }
  825. i__1 = k - 2;
  826. for (j = 0; j <= i__1; ++j) {
  827. i__2 = j;
  828. for (i__ = 0; i__ <= i__2; ++i__) {
  829. i__3 = ij;
  830. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  831. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  832. ++ij;
  833. }
  834. i__2 = *n - 1;
  835. for (i__ = k + 1 + j; i__ <= i__2; ++i__) {
  836. i__3 = ij;
  837. i__4 = i__ + (k + 1 + j) * a_dim1;
  838. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  839. ++ij;
  840. }
  841. }
  842. i__1 = *n - 1;
  843. for (j = k - 1; j <= i__1; ++j) {
  844. i__2 = k - 1;
  845. for (i__ = 0; i__ <= i__2; ++i__) {
  846. i__3 = ij;
  847. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  848. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  849. ++ij;
  850. }
  851. }
  852. } else {
  853. /* SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B) */
  854. /* T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0) */
  855. /* T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k */
  856. ij = 0;
  857. i__1 = k;
  858. for (j = 0; j <= i__1; ++j) {
  859. i__2 = *n - 1;
  860. for (i__ = k; i__ <= i__2; ++i__) {
  861. i__3 = ij;
  862. d_cnjg(&z__1, &a[j + i__ * a_dim1]);
  863. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  864. ++ij;
  865. }
  866. }
  867. i__1 = k - 2;
  868. for (j = 0; j <= i__1; ++j) {
  869. i__2 = j;
  870. for (i__ = 0; i__ <= i__2; ++i__) {
  871. i__3 = ij;
  872. i__4 = i__ + j * a_dim1;
  873. arf[i__3].r = a[i__4].r, arf[i__3].i = a[i__4].i;
  874. ++ij;
  875. }
  876. i__2 = *n - 1;
  877. for (l = k + 1 + j; l <= i__2; ++l) {
  878. i__3 = ij;
  879. d_cnjg(&z__1, &a[k + 1 + j + l * a_dim1]);
  880. arf[i__3].r = z__1.r, arf[i__3].i = z__1.i;
  881. ++ij;
  882. }
  883. }
  884. /* Note that here J = K-1 */
  885. i__1 = j;
  886. for (i__ = 0; i__ <= i__1; ++i__) {
  887. i__2 = ij;
  888. i__3 = i__ + j * a_dim1;
  889. arf[i__2].r = a[i__3].r, arf[i__2].i = a[i__3].i;
  890. ++ij;
  891. }
  892. }
  893. }
  894. }
  895. return 0;
  896. /* End of ZTRTTF */
  897. } /* ztrttf_ */