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nr.h

nr.h 25 KB
文件历史 原始文件

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  1. /* CAUTION: This is the ANSI C (only) version of the Numerical Recipes
    2. 

  2.    utility file nr.h.  Do not confuse this file with the same-named
    3. 

  3.    file nr.h that is supplied in the 'misc' subdirectory.
    4. 

  4.    *That* file is the one from the book, and contains both ANSI and
    5. 

  5.    traditional K&R versions, along with #ifdef macros to select the
    6. 

  6.    correct version.  *This* file contains only ANSI C.               */
    7. 

  7. 

  8. #ifndef _NR_H_
    9. 

  9. #define _NR_H_
    10. 

  10. 

  11. #define REAL double
    12. 

  12. 

  13. 

  14. #ifndef _FCOMPLEX_DECLARE_T_
    15. 

  15. typedef struct FCOMPLEX {REAL r,i;} fcomplex;
    16. 

  16. #define _FCOMPLEX_DECLARE_T_
    17. 

  17. #endif /* _FCOMPLEX_DECLARE_T_ */
    18. 

  18. 

  19. #ifndef _ARITHCODE_DECLARE_T_
    20. 

  20. typedef struct {
    21. 

  21. 	unsigned long *ilob,*iupb,*ncumfq,jdif,nc,minint,nch,ncum,nrad;
    22. 

  22. } arithcode;
    23. 

  23. #define _ARITHCODE_DECLARE_T_
    24. 

  24. #endif /* _ARITHCODE_DECLARE_T_ */
    25. 

  25. 

  26. #ifndef _HUFFCODE_DECLARE_T_
    27. 

  27. typedef struct {
    28. 

  28. 	unsigned long *icod,*ncod,*left,*right,nch,nodemax;
    29. 

  29. } huffcode;
    30. 

  30. #define _HUFFCODE_DECLARE_T_
    31. 

  31. #endif /* _HUFFCODE_DECLARE_T_ */
    32. 

  32. 

  33. #include <stdio.h>
    34. 

  34. 

  35. void addint(double **uf, double **uc, double **res, int nf);
    36. 

  36. void airy(REAL x, REAL *ai, REAL *bi, REAL *aip, REAL *bip);
    37. 

  37. void amebsa(REAL **p, REAL y[], int ndim, REAL pb[],	REAL *yb,
    38. 

  38. 	REAL ftol, REAL (*funk)(REAL []), int *iter, REAL temptr);
    39. 

  39. void amoeba(REAL **p, REAL y[], int ndim, REAL ftol,
    40. 

  40. 	REAL (*funk)(REAL []), int *iter);
    41. 

  41. REAL amotry(REAL **p, REAL y[], REAL psum[], int ndim,
    42. 

  42. 	REAL (*funk)(REAL []), int ihi, REAL fac);
    43. 

  43. REAL amotsa(REAL **p, REAL y[], REAL psum[], int ndim, REAL pb[],
    44. 

  44. 	REAL *yb, REAL (*funk)(REAL []), int ihi, REAL *yhi, REAL fac);
    45. 

  45. void anneal(REAL x[], REAL y[], int iorder[], int ncity);
    46. 

  46. double anorm2(double **a, int n);
    47. 

  47. void arcmak(unsigned long nfreq[], unsigned long nchh, unsigned long nradd,
    48. 

  48. 	arithcode *acode);
    49. 

  49. void arcode(unsigned long *ich, unsigned char **codep, unsigned long *lcode,
    50. 

  50. 	unsigned long *lcd, int isign, arithcode *acode);
    51. 

  51. void arcsum(unsigned long iin[], unsigned long iout[], unsigned long ja,
    52. 

  52. 	int nwk, unsigned long nrad, unsigned long nc);
    53. 

  53. void asolve(unsigned long n, double b[], double x[], int itrnsp);
    54. 

  54. void atimes(unsigned long n, double x[], double r[], int itrnsp);
    55. 

  55. void avevar(REAL data[], unsigned long n, REAL *ave, REAL *var);
    56. 

  56. void balanc(REAL **a, int n);
    57. 

  57. void banbks(REAL **a, unsigned long n, int m1, int m2, REAL **al,
    58. 

  58. 	unsigned long indx[], REAL b[]);
    59. 

  59. void bandec(REAL **a, unsigned long n, int m1, int m2, REAL **al,
    60. 

  60. 	unsigned long indx[], REAL *d);
    61. 

  61. void banmul(REAL **a, unsigned long n, int m1, int m2, REAL x[], REAL b[]);
    62. 

  62. void bcucof(REAL y[], REAL y1[], REAL y2[], REAL y12[], REAL d1,
    63. 

  63. 	REAL d2, REAL **c);
    64. 

  64. void bcuint(REAL y[], REAL y1[], REAL y2[], REAL y12[],
    65. 

  65. 	REAL x1l, REAL x1u, REAL x2l, REAL x2u, REAL x1,
    66. 

  66. 	REAL x2, REAL *ansy, REAL *ansy1, REAL *ansy2);
    67. 

  67. void beschb(double x, double *gam1, double *gam2, double *gampl,
    68. 

  68. 	double *gammi);
    69. 

  69. REAL bessi(int n, REAL x);
    70. 

  70. REAL bessi0(REAL x);
    71. 

  71. REAL bessi1(REAL x);
    72. 

  72. void bessik(REAL x, REAL xnu, REAL *ri, REAL *rk, REAL *rip,
    73. 

  73. 	REAL *rkp);
    74. 

  74. REAL bessj(int n, REAL x);
    75. 

  75. REAL bessj0(REAL x);
    76. 

  76. REAL bessj1(REAL x);
    77. 

  77. void bessjy(REAL x, REAL xnu, REAL *rj, REAL *ry, REAL *rjp,
    78. 

  78. 	REAL *ryp);
    79. 

  79. REAL bessk(int n, REAL x);
    80. 

  80. REAL bessk0(REAL x);
    81. 

  81. REAL bessk1(REAL x);
    82. 

  82. REAL bessy(int n, REAL x);
    83. 

  83. REAL bessy0(REAL x);
    84. 

  84. REAL bessy1(REAL x);
    85. 

  85. REAL beta(REAL z, REAL w);
    86. 

  86. REAL betacf(REAL a, REAL b, REAL x);
    87. 

  87. REAL betai(REAL a, REAL b, REAL x);
    88. 

  88. REAL bico(int n, int k);
    89. 

  89. void bksub(int ne, int nb, int jf, int k1, int k2, REAL ***c);
    90. 

  90. REAL bnldev(REAL pp, int n, long *idum);
    91. 

  91. REAL brent(REAL ax, REAL bx, REAL cx,
    92. 

  92. 	REAL (*f)(REAL), REAL tol, REAL *xmin);
    93. 

  93. void broydn(REAL x[], int n, int *check,
    94. 

  94. 	void (*vecfunc)(int, REAL [], REAL []));
    95. 

  95. void bsstep(REAL y[], REAL dydx[], int nv, REAL *xx, REAL htry,
    96. 

  96. 	REAL eps, REAL yscal[], REAL *hdid, REAL *hnext,
    97. 

  97. 	void (*derivs)(REAL, REAL [], REAL []));
    98. 

  98. void caldat(long julian, int *mm, int *id, int *iyyy);
    99. 

  99. void chder(REAL a, REAL b, REAL c[], REAL cder[], int n);
    100. 

  100. REAL chebev(REAL a, REAL b, REAL c[], int m, REAL x);
    101. 

  101. void chebft(REAL a, REAL b, REAL c[], int n, REAL (*func)(REAL));
    102. 

  102. void chebpc(REAL c[], REAL d[], int n);
    103. 

  103. void chint(REAL a, REAL b, REAL c[], REAL cint[], int n);
    104. 

  104. REAL chixy(REAL bang);
    105. 

  105. void choldc(REAL **a, int n, REAL p[]);
    106. 

  106. void cholsl(REAL **a, int n, REAL p[], REAL b[], REAL x[]);
    107. 

  107. void chsone(REAL bins[], REAL ebins[], int nbins, int knstrn,
    108. 

  108. 	REAL *df, REAL *chsq, REAL *prob);
    109. 

  109. void chstwo(REAL bins1[], REAL bins2[], int nbins, int knstrn,
    110. 

  110. 	REAL *df, REAL *chsq, REAL *prob);
    111. 

  111. void cisi(REAL x, REAL *ci, REAL *si);
    112. 

  112. void cntab1(int **nn, int ni, int nj, REAL *chisq,
    113. 

  113. 	REAL *df, REAL *prob, REAL *cramrv, REAL *ccc);
    114. 

  114. void cntab2(int **nn, int ni, int nj, REAL *h, REAL *hx, REAL *hy,
    115. 

  115. 	REAL *hygx, REAL *hxgy, REAL *uygx, REAL *uxgy, REAL *uxy);
    116. 

  116. void convlv(REAL data[], unsigned long n, REAL respns[], unsigned long m,
    117. 

  117. 	int isign, REAL ans[]);
    118. 

  118. void copy(double **aout, double **ain, int n);
    119. 

  119. void correl(REAL data1[], REAL data2[], unsigned long n, REAL ans[]);
    120. 

  120. void cosft(REAL y[], int n, int isign);
    121. 

  121. void cosft1(REAL y[], int n);
    122. 

  122. void cosft2(REAL y[], int n, int isign);
    123. 

  123. void covsrt(REAL **covar, int ma, int ia[], int mfit);
    124. 

  124. void crank(unsigned long n, REAL w[], REAL *s);
    125. 

  125. void cyclic(REAL a[], REAL b[], REAL c[], REAL alpha, REAL beta,
    126. 

  126. 	REAL r[], REAL x[], unsigned long n);
    127. 

  127. void daub4(REAL a[], unsigned long n, int isign);
    128. 

  128. REAL dawson(REAL x);
    129. 

  129. REAL dbrent(REAL ax, REAL bx, REAL cx,
    130. 

  130. 	REAL (*f)(REAL), REAL (*df)(REAL), REAL tol, REAL *xmin);
    131. 

  131. void ddpoly(REAL c[], int nc, REAL x, REAL pd[], int nd);
    132. 

  132. int decchk(char string[], int n, char *ch);
    133. 

  133. void derivs(REAL x, REAL y[], REAL dydx[]);
    134. 

  134. REAL df1dim(REAL x);
    135. 

  135. void dfour1(double data[], unsigned long nn, int isign);
    136. 

  136. void dfpmin(REAL p[], int n, REAL gtol, int *iter, REAL *fret,
    137. 

  137. 	REAL (*func)(REAL []), void (*dfunc)(REAL [], REAL []));
    138. 

  138. REAL dfridr(REAL (*func)(REAL), REAL x, REAL h, REAL *err);
    139. 

  139. void dftcor(REAL w, REAL delta, REAL a, REAL b, REAL endpts[],
    140. 

  140. 	REAL *corre, REAL *corim, REAL *corfac);
    141. 

  141. void dftint(REAL (*func)(REAL), REAL a, REAL b, REAL w,
    142. 

  142. 	REAL *cosint, REAL *sinint);
    143. 

  143. void difeq(int k, int k1, int k2, int jsf, int is1, int isf,
    144. 

  144. 	int indexv[], int ne, REAL **s, REAL **y);
    145. 

  145. void dlinmin(REAL p[], REAL xi[], int n, REAL *fret,
    146. 

  146. 	REAL (*func)(REAL []), void (*dfunc)(REAL [], REAL[]));
    147. 

  147. double dpythag(double a, double b);
    148. 

  148. void drealft(double data[], unsigned long n, int isign);
    149. 

  149. void dsprsax(double sa[], unsigned long ija[], double x[], double b[],
    150. 

  150. 	unsigned long n);
    151. 

  151. void dsprstx(double sa[], unsigned long ija[], double x[], double b[],
    152. 

  152. 	unsigned long n);
    153. 

  153. void dsvbksb(double **u, double w[], double **v, int m, int n, double b[],
    154. 

  154. 	double x[]);
    155. 

  155. void dsvdcmp(double **a, int m, int n, double w[], double **v);
    156. 

  156. void eclass(int nf[], int n, int lista[], int listb[], int m);
    157. 

  157. void eclazz(int nf[], int n, int (*equiv)(int, int));
    158. 

  158. REAL ei(REAL x);
    159. 

  159. void eigsrt(REAL d[], REAL **v, int n);
    160. 

  160. REAL elle(REAL phi, REAL ak);
    161. 

  161. REAL ellf(REAL phi, REAL ak);
    162. 

  162. REAL ellpi(REAL phi, REAL en, REAL ak);
    163. 

  163. void elmhes(REAL **a, int n);
    164. 

  164. REAL erfcc(REAL x);
    165. 

  165. //REAL erff(REAL x);
    166. 

  166. REAL erffc(REAL x);
    167. 

  167. void eulsum(REAL *sum, REAL term, int jterm, REAL wksp[]);
    168. 

  168. REAL evlmem(REAL fdt, REAL d[], int m, REAL xms);
    169. 

  169. REAL expdev(long *idum);
    170. 

  170. REAL expint(int n, REAL x);
    171. 

  171. REAL f1(REAL x);
    172. 

  172. REAL f1dim(REAL x);
    173. 

  173. REAL f2(REAL y);
    174. 

  174. REAL f3(REAL z);
    175. 

  175. REAL factln(int n);
    176. 

  176. REAL factrl(int n);
    177. 

  177. void fasper(REAL x[], REAL y[], unsigned long n, REAL ofac, REAL hifac,
    178. 

  178. 	REAL wk1[], REAL wk2[], unsigned long nwk, unsigned long *nout,
    179. 

  179. 	unsigned long *jmax, REAL *prob);
    180. 

  180. void fdjac(int n, REAL x[], REAL fvec[], REAL **df,
    181. 

  181. 	void (*vecfunc)(int, REAL [], REAL []));
    182. 

  182. void fgauss(REAL x, REAL a[], REAL *y, REAL dyda[], int na);
    183. 

  183. void fill0(double **u, int n);
    184. 

  184. void fit(REAL x[], REAL y[], int ndata, REAL sig[], int mwt,
    185. 

  185. 	REAL *a, REAL *b, REAL *siga, REAL *sigb, REAL *chi2, REAL *q);
    186. 

  186. void fitexy(REAL x[], REAL y[], int ndat, REAL sigx[], REAL sigy[],
    187. 

  187. 	REAL *a, REAL *b, REAL *siga, REAL *sigb, REAL *chi2, REAL *q);
    188. 

  188. void fixrts(REAL d[], int m);
    189. 

  189. void fleg(REAL x, REAL pl[], int nl);
    190. 

  190. void flmoon(int n, int nph, long *jd, REAL *frac);
    191. 

  191. REAL fmin(REAL x[]);
    192. 

  192. void four1(REAL data[], unsigned long nn, int isign);
    193. 

  193. void fourew(FILE *file[5], int *na, int *nb, int *nc, int *nd);
    194. 

  194. void fourfs(FILE *file[5], unsigned long nn[], int ndim, int isign);
    195. 

  195. void fourn(REAL data[], unsigned long nn[], int ndim, int isign);
    196. 

  196. void fpoly(REAL x, REAL p[], int np);
    197. 

  197. void fred2(int n, REAL a, REAL b, REAL t[], REAL f[], REAL w[],
    198. 

  198. 	REAL (*g)(REAL), REAL (*ak)(REAL, REAL));
    199. 

  199. REAL fredin(REAL x, int n, REAL a, REAL b, REAL t[], REAL f[], REAL w[],
    200. 

  200. 	REAL (*g)(REAL), REAL (*ak)(REAL, REAL));
    201. 

  201. void frenel(REAL x, REAL *s, REAL *c);
    202. 

  202. void frprmn(REAL p[], int n, REAL ftol, int *iter, REAL *fret,
    203. 

  203. 	REAL (*func)(REAL []), void (*dfunc)(REAL [], REAL []));
    204. 

  204. void ftest(REAL data1[], unsigned long n1, REAL data2[], unsigned long n2,
    205. 

  205. 	REAL *f, REAL *prob);
    206. 

  206. REAL gamdev(int ia, long *idum);
    207. 

  207. REAL gammln(REAL xx);
    208. 

  208. REAL gammp(REAL a, REAL x);
    209. 

  209. REAL gammq(REAL a, REAL x);
    210. 

  210. REAL gasdev(long *idum);
    211. 

  211. void gaucof(int n, REAL a[], REAL b[], REAL amu0, REAL x[], REAL w[]);
    212. 

  212. void gauher(REAL x[], REAL w[], int n);
    213. 

  213. void gaujac(REAL x[], REAL w[], int n, REAL alf, REAL bet);
    214. 

  214. void gaulag(REAL x[], REAL w[], int n, REAL alf);
    215. 

  215. void gauleg(REAL x1, REAL x2, REAL x[], REAL w[], int n);
    216. 

  216. void gaussj(REAL **a, int n, REAL **b, int m);
    217. 

  217. void gcf(REAL *gammcf, REAL a, REAL x, REAL *gln);
    218. 

  218. REAL golden(REAL ax, REAL bx, REAL cx, REAL (*f)(REAL), REAL tol,
    219. 

  219. 	REAL *xmin);
    220. 

  220. void gser(REAL *gamser, REAL a, REAL x, REAL *gln);
    221. 

  221. void hpsel(unsigned long m, unsigned long n, REAL arr[], REAL heap[]);
    222. 

  222. void hpsort(unsigned long n, REAL ra[]);
    223. 

  223. void hqr(REAL **a, int n, REAL wr[], REAL wi[]);
    224. 

  224. void hufapp(unsigned long index[], unsigned long nprob[], unsigned long n,
    225. 

  225. 	unsigned long i);
    226. 

  226. void hufdec(unsigned long *ich, unsigned char *code, unsigned long lcode,
    227. 

  227. 	unsigned long *nb, huffcode *hcode);
    228. 

  228. void hufenc(unsigned long ich, unsigned char **codep, unsigned long *lcode,
    229. 

  229. 	unsigned long *nb, huffcode *hcode);
    230. 

  230. void hufmak(unsigned long nfreq[], unsigned long nchin, unsigned long *ilong,
    231. 

  231. 	unsigned long *nlong, huffcode *hcode);
    232. 

  232. void hunt(REAL xx[], unsigned long n, REAL x, unsigned long *jlo);
    233. 

  233. void hypdrv(REAL s, REAL yy[], REAL dyyds[]);
    234. 

  234. fcomplex hypgeo(fcomplex a, fcomplex b, fcomplex c, fcomplex z);
    235. 

  235. void hypser(fcomplex a, fcomplex b, fcomplex c, fcomplex z,
    236. 

  236. 	fcomplex *series, fcomplex *deriv);
    237. 

  237. unsigned short icrc(unsigned short crc, unsigned char *bufptr,
    238. 

  238. 	unsigned long len, short jinit, int jrev);
    239. 

  239. unsigned short icrc1(unsigned short crc, unsigned char onech);
    240. 

  240. unsigned long igray(unsigned long n, int is);
    241. 

  241. void iindexx(unsigned long n, long arr[], unsigned long indx[]);
    242. 

  242. void indexx(unsigned long n, REAL arr[], unsigned long indx[]);
    243. 

  243. void interp(double **uf, double **uc, int nf);
    244. 

  244. int irbit1(unsigned long *iseed);
    245. 

  245. int irbit2(unsigned long *iseed);
    246. 

  246. void jacobi(REAL **a, int n, REAL d[], REAL **v, int *nrot);
    247. 

  247. void jacobn(REAL x, REAL y[], REAL dfdx[], REAL **dfdy, int n);
    248. 

  248. long julday(int mm, int id, int iyyy);
    249. 

  249. void kendl1(REAL data1[], REAL data2[], unsigned long n, REAL *tau, REAL *z,
    250. 

  250. 	REAL *prob);
    251. 

  251. void kendl2(REAL **tab, int i, int j, REAL *tau, REAL *z, REAL *prob);
    252. 

  252. void kermom(double w[], double y, int m);
    253. 

  253. void ks2d1s(REAL x1[], REAL y1[], unsigned long n1,
    254. 

  254. 	void (*quadvl)(REAL, REAL, REAL *, REAL *, REAL *, REAL *),
    255. 

  255. 	REAL *d1, REAL *prob);
    256. 

  256. void ks2d2s(REAL x1[], REAL y1[], unsigned long n1, REAL x2[], REAL y2[],
    257. 

  257. 	unsigned long n2, REAL *d, REAL *prob);
    258. 

  258. void ksone(REAL data[], unsigned long n, REAL (*func)(REAL), REAL *d,
    259. 

  259. 	REAL *prob);
    260. 

  260. void kstwo(REAL data1[], unsigned long n1, REAL data2[], unsigned long n2,
    261. 

  261. 	REAL *d, REAL *prob);
    262. 

  262. void laguer(fcomplex a[], int m, fcomplex *x, int *its);
    263. 

  263. void lfit(REAL x[], REAL y[], REAL sig[], int ndat, REAL a[], int ia[],
    264. 

  264. 	int ma, REAL **covar, REAL *chisq, void (*funcs)(REAL, REAL [], int));
    265. 

  265. void linbcg(unsigned long n, double b[], double x[], int itol, double tol,
    266. 

  266. 	 int itmax, int *iter, double *err);
    267. 

  267. void linmin(REAL p[], REAL xi[], int n, REAL *fret,
    268. 

  268. 	REAL (*func)(REAL []));
    269. 

  269. void lnsrch(int n, REAL xold[], REAL fold, REAL g[], REAL p[], REAL x[],
    270. 

  270. 	 REAL *f, REAL stpmax, int *check, REAL (*func)(REAL []));
    271. 

  271. void load(REAL x1, REAL v[], REAL y[]);
    272. 

  272. void load1(REAL x1, REAL v1[], REAL y[]);
    273. 

  273. void load2(REAL x2, REAL v2[], REAL y[]);
    274. 

  274. void locate(REAL xx[], unsigned long n, REAL x, unsigned long *j);
    275. 

  275. void lop(double **out, double **u, int n);
    276. 

  276. void lubksb(REAL **a, int n, int *indx, REAL b[]);
    277. 

  277. void ludcmp(REAL **a, int n, int *indx, REAL *d);
    278. 

  278. void machar(int *ibeta, int *it, int *irnd, int *ngrd,
    279. 

  279. 	int *machep, int *negep, int *iexp, int *minexp, int *maxexp,
    280. 

  280. 	REAL *eps, REAL *epsneg, REAL *xmin, REAL *xmax);
    281. 

  281. void matadd(double **a, double **b, double **c, int n);
    282. 

  282. void matsub(double **a, double **b, double **c, int n);
    283. 

  283. void medfit(REAL x[], REAL y[], int ndata, REAL *a, REAL *b, REAL *abdev);
    284. 

  284. void memcof(REAL data[], int n, int m, REAL *xms, REAL d[]);
    285. 

  285. int metrop(REAL de, REAL t);
    286. 

  286. void mgfas(double **u, int n, int maxcyc);
    287. 

  287. void mglin(double **u, int n, int ncycle);
    288. 

  288. REAL midexp(REAL (*funk)(REAL), REAL aa, REAL bb, int n);
    289. 

  289. REAL midinf(REAL (*funk)(REAL), REAL aa, REAL bb, int n);
    290. 

  290. REAL midpnt(REAL (*func)(REAL), REAL a, REAL b, int n);
    291. 

  291. REAL midsql(REAL (*funk)(REAL), REAL aa, REAL bb, int n);
    292. 

  292. REAL midsqu(REAL (*funk)(REAL), REAL aa, REAL bb, int n);
    293. 

  293. void miser(REAL (*func)(REAL []), REAL regn[], int ndim, unsigned long npts,
    294. 

  294. 	REAL dith, REAL *ave, REAL *var);
    295. 

  295. void mmid(REAL y[], REAL dydx[], int nvar, REAL xs, REAL htot,
    296. 

  296. 	int nstep, REAL yout[], void (*derivs)(REAL, REAL[], REAL[]));
    297. 

  297. void mnbrak(REAL *ax, REAL *bx, REAL *cx, REAL *fa, REAL *fb,
    298. 

  298. 	REAL *fc, REAL (*func)(REAL));
    299. 

  299. void mnewt(int ntrial, REAL x[], int n, REAL tolx, REAL tolf);
    300. 

  300. void moment(REAL data[], int n, REAL *ave, REAL *adev, REAL *sdev,
    301. 

  301. 	REAL *var, REAL *skew, REAL *curt);
    302. 

  302. void mp2dfr(unsigned char a[], unsigned char s[], int n, int *m);
    303. 

  303. void mpadd(unsigned char w[], unsigned char u[], unsigned char v[], int n);
    304. 

  304. void mpdiv(unsigned char q[], unsigned char r[], unsigned char u[],
    305. 

  305. 	unsigned char v[], int n, int m);
    306. 

  306. void mpinv(unsigned char u[], unsigned char v[], int n, int m);
    307. 

  307. void mplsh(unsigned char u[], int n);
    308. 

  308. void mpmov(unsigned char u[], unsigned char v[], int n);
    309. 

  309. void mpmul(unsigned char w[], unsigned char u[], unsigned char v[], int n,
    310. 

  310. 	int m);
    311. 

  311. void mpneg(unsigned char u[], int n);
    312. 

  312. void mppi(int n);
    313. 

  313. void mprove(REAL **a, REAL **alud, int n, int indx[], REAL b[],
    314. 

  314. 	REAL x[]);
    315. 

  315. void mpsad(unsigned char w[], unsigned char u[], int n, int iv);
    316. 

  316. void mpsdv(unsigned char w[], unsigned char u[], int n, int iv, int *ir);
    317. 

  317. void mpsmu(unsigned char w[], unsigned char u[], int n, int iv);
    318. 

  318. void mpsqrt(unsigned char w[], unsigned char u[], unsigned char v[], int n,
    319. 

  319. 	int m);
    320. 

  320. void mpsub(int *is, unsigned char w[], unsigned char u[], unsigned char v[],
    321. 

  321. 	int n);
    322. 

  322. void mrqcof(REAL x[], REAL y[], REAL sig[], int ndata, REAL a[],
    323. 

  323. 	int ia[], int ma, REAL **alpha, REAL beta[], REAL *chisq,
    324. 

  324. 	void (*funcs)(REAL, REAL [], REAL *, REAL [], int));
    325. 

  325. void mrqmin(REAL x[], REAL y[], REAL sig[], int ndata, REAL a[],
    326. 

  326. 	int ia[], int ma, REAL **covar, REAL **alpha, REAL *chisq,
    327. 

  327. 	void (*funcs)(REAL, REAL [], REAL *, REAL [], int), REAL *alamda);
    328. 

  328. void newt(REAL x[], int n, int *check,
    329. 

  329. 	void (*vecfunc)(int, REAL [], REAL []));
    330. 

  330. void odeint(REAL ystart[], int nvar, REAL x1, REAL x2,
    331. 

  331. 	REAL eps, REAL h1, REAL hmin, int *nok, int *nbad,
    332. 

  332. 	void (*derivs)(REAL, REAL [], REAL []),
    333. 

  333. 	void (*rkqs)(REAL [], REAL [], int, REAL *, REAL, REAL,
    334. 

  334. 	REAL [], REAL *, REAL *, void (*)(REAL, REAL [], REAL [])));
    335. 

  335. void orthog(int n, REAL anu[], REAL alpha[], REAL beta[], REAL a[],
    336. 

  336. 	REAL b[]);
    337. 

  337. void pade(double cof[], int n, REAL *resid);
    338. 

  338. void pccheb(REAL d[], REAL c[], int n);
    339. 

  339. void pcshft(REAL a, REAL b, REAL d[], int n);
    340. 

  340. void pearsn(REAL x[], REAL y[], unsigned long n, REAL *r, REAL *prob,
    341. 

  341. 	REAL *z);
    342. 

  342. void period(REAL x[], REAL y[], int n, REAL ofac, REAL hifac,
    343. 

  343. 	REAL px[], REAL py[], int np, int *nout, int *jmax, REAL *prob);
    344. 

  344. void piksr2(int n, REAL arr[], REAL brr[]);
    345. 

  345. void piksrt(int n, REAL arr[]);
    346. 

  346. void pinvs(int ie1, int ie2, int je1, int jsf, int jc1, int k,
    347. 

  347. 	REAL ***c, REAL **s);
    348. 

  348. REAL plgndr(int l, int m, REAL x);
    349. 

  349. REAL poidev(REAL xm, long *idum);
    350. 

  350. void polcoe(REAL x[], REAL y[], int n, REAL cof[]);
    351. 

  351. void polcof(REAL xa[], REAL ya[], int n, REAL cof[]);
    352. 

  352. void poldiv(REAL u[], int n, REAL v[], int nv, REAL q[], REAL r[]);
    353. 

  353. void polin2(REAL x1a[], REAL x2a[], REAL **ya, int m, int n,
    354. 

  354. 	REAL x1, REAL x2, REAL *y, REAL *dy);
    355. 

  355. void polint(REAL xa[], REAL ya[], int n, REAL x, REAL *y, REAL *dy);
    356. 

  356. void powell(REAL p[], REAL **xi, int n, REAL ftol, int *iter, REAL *fret,
    357. 

  357. 	REAL (*func)(REAL []));
    358. 

  358. void predic(REAL data[], int ndata, REAL d[], int m, REAL future[], int nfut);
    359. 

  359. REAL probks(REAL alam);
    360. 

  360. void psdes(unsigned long *lword, unsigned long *irword);
    361. 

  361. void pwt(REAL a[], unsigned long n, int isign);
    362. 

  362. void pwtset(int n);
    363. 

  363. REAL pythag(REAL a, REAL b);
    364. 

  364. void pzextr(int iest, REAL xest, REAL yest[], REAL yz[], REAL dy[],
    365. 

  365. 	int nv);
    366. 

  366. REAL qgaus(REAL (*func)(REAL), REAL a, REAL b);
    367. 

  367. void qrdcmp(REAL **a, int n, REAL *c, REAL *d, int *sing);
    368. 

  368. REAL qromb(REAL (*func)(REAL), REAL a, REAL b);
    369. 

  369. REAL qromo(REAL (*func)(REAL), REAL a, REAL b,
    370. 

  370. 	REAL (*choose)(REAL (*)(REAL), REAL, REAL, int));
    371. 

  371. void qroot(REAL p[], int n, REAL *b, REAL *c, REAL eps);
    372. 

  372. void qrsolv(REAL **a, int n, REAL c[], REAL d[], REAL b[]);
    373. 

  373. void qrupdt(REAL **r, REAL **qt, int n, REAL u[], REAL v[]);
    374. 

  374. REAL qsimp(REAL (*func)(REAL), REAL a, REAL b);
    375. 

  375. REAL qtrap(REAL (*func)(REAL), REAL a, REAL b);
    376. 

  376. REAL quad3d(REAL (*func)(REAL, REAL, REAL), REAL x1, REAL x2);
    377. 

  377. void quadct(REAL x, REAL y, REAL xx[], REAL yy[], unsigned long nn,
    378. 

  378. 	REAL *fa, REAL *fb, REAL *fc, REAL *fd);
    379. 

  379. void quadmx(REAL **a, int n);
    380. 

  380. void quadvl(REAL x, REAL y, REAL *fa, REAL *fb, REAL *fc, REAL *fd);
    381. 

  381. REAL ran0(long *idum);
    382. 

  382. REAL ran1(long *idum);
    383. 

  383. REAL ran2(long *idum);
    384. 

  384. REAL ran3(long *idum);
    385. 

  385. REAL ran4(long *idum);
    386. 

  386. void rank(unsigned long n, unsigned long indx[], unsigned long irank[]);
    387. 

  387. void ranpt(REAL pt[], REAL regn[], int n);
    388. 

  388. void ratint(REAL xa[], REAL ya[], int n, REAL x, REAL *y, REAL *dy);
    389. 

  389. void ratlsq(double (*fn)(double), double a, double b, int mm, int kk,
    390. 

  390. 	double cof[], double *dev);
    391. 

  391. double ratval(double x, double cof[], int mm, int kk);
    392. 

  392. REAL rc(REAL x, REAL y);
    393. 

  393. REAL rd(REAL x, REAL y, REAL z);
    394. 

  394. void realft(REAL data[], unsigned long n, int isign);
    395. 

  395. void rebin(REAL rc, int nd, REAL r[], REAL xin[], REAL xi[]);
    396. 

  396. void red(int iz1, int iz2, int jz1, int jz2, int jm1, int jm2, int jmf,
    397. 

  397. 	int ic1, int jc1, int jcf, int kc, REAL ***c, REAL **s);
    398. 

  398. void relax(double **u, double **rhs, int n);
    399. 

  399. void relax2(double **u, double **rhs, int n);
    400. 

  400. void resid(double **res, double **u, double **rhs, int n);
    401. 

  401. REAL revcst(REAL x[], REAL y[], int iorder[], int ncity, int n[]);
    402. 

  402. void reverse(int iorder[], int ncity, int n[]);
    403. 

  403. REAL rf(REAL x, REAL y, REAL z);
    404. 

  404. REAL rj(REAL x, REAL y, REAL z, REAL p);
    405. 

  405. void rk4(REAL y[], REAL dydx[], int n, REAL x, REAL h, REAL yout[],
    406. 

  406. 	void (*derivs)(REAL, REAL [], REAL []));
    407. 

  407. void rkck(REAL y[], REAL dydx[], int n, REAL x, REAL h,
    408. 

  408. 	REAL yout[], REAL yerr[], void (*derivs)(REAL, REAL [], REAL []));
    409. 

  409. void rkdumb(REAL vstart[], int nvar, REAL x1, REAL x2, int nstep,
    410. 

  410. 	void (*derivs)(REAL, REAL [], REAL []));
    411. 

  411. void rkqs(REAL y[], REAL dydx[], int n, REAL *x,
    412. 

  412. 	REAL htry, REAL eps, REAL yscal[], REAL *hdid, REAL *hnext,
    413. 

  413. 	void (*derivs)(REAL, REAL [], REAL []));
    414. 

  414. void rlft3(REAL ***data, REAL **speq, unsigned long nn1,
    415. 

  415. 	unsigned long nn2, unsigned long nn3, int isign);
    416. 

  416. REAL rofunc(REAL b);
    417. 

  417. void rotate(REAL **r, REAL **qt, int n, int i, REAL a, REAL b);
    418. 

  418. void rsolv(REAL **a, int n, REAL d[], REAL b[]);
    419. 

  419. void rstrct(double **uc, double **uf, int nc);
    420. 

  420. REAL rtbis(REAL (*func)(REAL), REAL x1, REAL x2, REAL xacc);
    421. 

  421. REAL rtflsp(REAL (*func)(REAL), REAL x1, REAL x2, REAL xacc);
    422. 

  422. REAL rtnewt(void (*funcd)(REAL, REAL *, REAL *), REAL x1, REAL x2,
    423. 

  423. 	REAL xacc);
    424. 

  424. REAL rtsafe(void (*funcd)(REAL, REAL *, REAL *), REAL x1, REAL x2,
    425. 

  425. 	REAL xacc);
    426. 

  426. REAL rtsec(REAL (*func)(REAL), REAL x1, REAL x2, REAL xacc);
    427. 

  427. void rzextr(int iest, REAL xest, REAL yest[], REAL yz[], REAL dy[], int nv);
    428. 

  428. void savgol(REAL c[], int np, int nl, int nr, int ld, int m);
    429. 

  429. void score(REAL xf, REAL y[], REAL f[]);
    430. 

  430. void scrsho(REAL (*fx)(REAL));
    431. 

  431. REAL select_(unsigned long k, unsigned long n, REAL arr[]);
    432. 

  432. REAL selip(unsigned long k, unsigned long n, REAL arr[]);
    433. 

  433. void shell(unsigned long n, REAL a[]);
    434. 

  434. void shoot(int n, REAL v[], REAL f[]);
    435. 

  435. void shootf(int n, REAL v[], REAL f[]);
    436. 

  436. void simp1(REAL **a, int mm, int ll[], int nll, int iabf, int *kp,
    437. 

  437. 	REAL *bmax);
    438. 

  438. void simp2(REAL **a, int n, int l2[], int nl2, int *ip, int kp, REAL *q1);
    439. 

  439. void simp3(REAL **a, int i1, int k1, int ip, int kp);
    440. 

  440. void simplx(REAL **a, int m, int n, int m1, int m2, int m3, int *icase,
    441. 

  441. 	int izrov[], int iposv[]);
    442. 

  442. void simpr(REAL y[], REAL dydx[], REAL dfdx[], REAL **dfdy,
    443. 

  443. 	int n, REAL xs, REAL htot, int nstep, REAL yout[],
    444. 

  444. 	void (*derivs)(REAL, REAL [], REAL []));
    445. 

  445. void sinft(REAL y[], int n);
    446. 

  446. void slvsm2(double **u, double **rhs);
    447. 

  447. void slvsml(double **u, double **rhs);
    448. 

  448. void sncndn(REAL uu, REAL emmc, REAL *sn, REAL *cn, REAL *dn);
    449. 

  449. double snrm(unsigned long n, double sx[], int itol);
    450. 

  450. void sobseq(int *n, REAL x[]);
    451. 

  451. void solvde(int itmax, REAL conv, REAL slowc, REAL scalv[],
    452. 

  452. 	int indexv[], int ne, int nb, int m, REAL **y, REAL ***c, REAL **s);
    453. 

  453. void sor(double **a, double **b, double **c, double **d, double **e,
    454. 

  454. 	double **f, double **u, int jmax, double rjac);
    455. 

  455. void sort(unsigned long n, REAL arr[]);
    456. 

  456. void sort2(unsigned long n, REAL arr[], REAL brr[]);
    457. 

  457. void sort3(unsigned long n, REAL ra[], REAL rb[], REAL rc[]);
    458. 

  458. void spctrm(FILE *fp, REAL p[], int m, int k, int ovrlap);
    459. 

  459. void spear(REAL data1[], REAL data2[], unsigned long n, REAL *d, REAL *zd,
    460. 

  460. 	REAL *probd, REAL *rs, REAL *probrs);
    461. 

  461. void sphbes(int n, REAL x, REAL *sj, REAL *sy, REAL *sjp, REAL *syp);
    462. 

  462. void splie2(REAL x1a[], REAL x2a[], REAL **ya, int m, int n, REAL **y2a);
    463. 

  463. void splin2(REAL x1a[], REAL x2a[], REAL **ya, REAL **y2a, int m, int n,
    464. 

  464. 	REAL x1, REAL x2, REAL *y);
    465. 

  465. void spline(REAL x[], REAL y[], int n, REAL yp1, REAL ypn, REAL y2[]);
    466. 

  466. void splint(REAL xa[], REAL ya[], REAL y2a[], int n, REAL x, REAL *y);
    467. 

  467. void spread(REAL y, REAL yy[], unsigned long n, REAL x, int m);
    468. 

  468. void sprsax(REAL sa[], unsigned long ija[], REAL x[], REAL b[],
    469. 

  469. 	unsigned long n);
    470. 

  470. void sprsin(REAL **a, int n, REAL thresh, unsigned long nmax, REAL sa[],
    471. 

  471. 	unsigned long ija[]);
    472. 

  472. void sprspm(REAL sa[], unsigned long ija[], REAL sb[], unsigned long ijb[],
    473. 

  473. 	REAL sc[], unsigned long ijc[]);
    474. 

  474. void sprstm(REAL sa[], unsigned long ija[], REAL sb[], unsigned long ijb[],
    475. 

  475. 	REAL thresh, unsigned long nmax, REAL sc[], unsigned long ijc[]);
    476. 

  476. void sprstp(REAL sa[], unsigned long ija[], REAL sb[], unsigned long ijb[]);
    477. 

  477. void sprstx(REAL sa[], unsigned long ija[], REAL x[], REAL b[],
    478. 

  478. 	unsigned long n);
    479. 

  479. void stifbs(REAL y[], REAL dydx[], int nv, REAL *xx,
    480. 

  480. 	REAL htry, REAL eps, REAL yscal[], REAL *hdid, REAL *hnext,
    481. 

  481. 	void (*derivs)(REAL, REAL [], REAL []));
    482. 

  482. void stiff(REAL y[], REAL dydx[], int n, REAL *x,
    483. 

  483. 	REAL htry, REAL eps, REAL yscal[], REAL *hdid, REAL *hnext,
    484. 

  484. 	void (*derivs)(REAL, REAL [], REAL []));
    485. 

  485. void stoerm(REAL y[], REAL d2y[], int nv, REAL xs,
    486. 

  486. 	REAL htot, int nstep, REAL yout[],
    487. 

  487. 	void (*derivs)(REAL, REAL [], REAL []));
    488. 

  488. void svbksb(REAL **u, REAL w[], REAL **v, int m, int n, REAL b[],
    489. 

  489. 	REAL x[]);
    490. 

  490. void svdcmp(REAL **a, int m, int n, REAL w[], REAL **v);
    491. 

  491. void svdfit(REAL x[], REAL y[], REAL sig[], int ndata, REAL a[],
    492. 

  492. 	int ma, REAL **u, REAL **v, REAL w[], REAL *chisq,
    493. 

  493. 	void (*funcs)(REAL, REAL [], int));
    494. 

  494. void svdvar(REAL **v, int ma, REAL w[], REAL **cvm);
    495. 

  495. void toeplz(REAL r[], REAL x[], REAL y[], int n);
    496. 

  496. void tptest(REAL data1[], REAL data2[], unsigned long n, REAL *t, REAL *prob);
    497. 

  497. void tqli(REAL d[], REAL e[], int n, REAL **z);
    498. 

  498. REAL trapzd(REAL (*func)(REAL), REAL a, REAL b, int n);
    499. 

  499. void tred2(REAL **a, int n, REAL d[], REAL e[]);
    500. 

  500. void tridag(REAL a[], REAL b[], REAL c[], REAL r[], REAL u[],
    501. 

  501. 	unsigned long n);
    502. 

  502. REAL trncst(REAL x[], REAL y[], int iorder[], int ncity, int n[]);
    503. 

  503. void trnspt(int iorder[], int ncity, int n[]);
    504. 

  504. void ttest(REAL data1[], unsigned long n1, REAL data2[], unsigned long n2,
    505. 

  505. 	REAL *t, REAL *prob);
    506. 

  506. void tutest(REAL data1[], unsigned long n1, REAL data2[], unsigned long n2,
    507. 

  507. 	REAL *t, REAL *prob);
    508. 

  508. void twofft(REAL data1[], REAL data2[], REAL fft1[], REAL fft2[],
    509. 

  509. 	unsigned long n);
    510. 

  510. void vander(double x[], double w[], double q[], int n);
    511. 

  511. void vegas(REAL regn[], int ndim, REAL (*fxn)(REAL [], REAL), int init,
    512. 

  512. 	unsigned long ncall, int itmx, int nprn, REAL *tgral, REAL *sd,
    513. 

  513. 	REAL *chi2a);
    514. 

  514. void voltra(int n, int m, REAL t0, REAL h, REAL *t, REAL **f,
    515. 

  515. 	REAL (*g)(int, REAL), REAL (*ak)(int, int, REAL, REAL));
    516. 

  516. void wt1(REAL a[], unsigned long n, int isign,
    517. 

  517. 	void (*wtstep)(REAL [], unsigned long, int));
    518. 

  518. void wtn(REAL a[], unsigned long nn[], int ndim, int isign,
    519. 

  519. 	void (*wtstep)(REAL [], unsigned long, int));
    520. 

  520. void wwghts(REAL wghts[], int n, REAL h,
    521. 

  521. 	void (*kermom)(double [], double ,int));
    522. 

  522. int zbrac(REAL (*func)(REAL), REAL *x1, REAL *x2);
    523. 

  523. void zbrak(REAL (*fx)(REAL), REAL x1, REAL x2, int n, REAL xb1[],
    524. 

  524. 	REAL xb2[], int *nb);
    525. 

  525. REAL zbrent(REAL (*func)(REAL), REAL x1, REAL x2, REAL tol);
    526. 

  526. void zrhqr(REAL a[], int m, REAL rtr[], REAL rti[]);
    527. 

  527. REAL zriddr(REAL (*func)(REAL), REAL x1, REAL x2, REAL xacc);
    528. 

  528. void zroots(fcomplex a[], int m, fcomplex roots[], int polish);
    529. 

  529. 

  530. #endif /* _NR_H_ */
    531. 

  531.