float (*func)(float []));void linmin_arg(float p[], float xi[], int n, float *fret,	float (*func)(float [], void*), void *arg);void lnsrch(int n, float xold[], float fold, float g[], float p[], float x[],	 float *f, float stpmax, int *check, float (*func)(float []));void load(float x1, float v[], float y[]);void load1(float x1, float v1[], float y[]);void load2(float x2, float v2[], float y[]);void locate(float xx[], unsigned long n, float x, unsigned long *j);void lop(double **out, double **u, int n);void lubksb(float **a, int n, int *indx, float b[]);void ludcmp(float **a, int n, int *indx, float *d);void machar(int *ibeta, int *it, int *irnd, int *ngrd,	int *machep, int *negep, int *iexp, int *minexp, int *maxexp,	float *eps, float *epsneg, float *xmin, float *xmax);void matadd(double **a, double **b, double **c, int n);void matsub(double **a, double **b, double **c, int n);void medfit(float x[], float y[], int ndata, float *a, float *b, float *abdev);void memcof(float data[], int n, int m, float *xms, float d[]);int metrop(float de, float t);void mgfas(double **u, int n, int maxcyc);void mglin(double **u, int n, int ncycle);float midexp(float (*funk)(float), float aa, float bb, int n);float midinf(float (*funk)(float), float aa, float bb, int n);float midpnt(float (*func)(float), float a, float b, int n);float midsql(float (*funk)(float), float aa, float bb, int n);float midsqu(float (*funk)(float), float aa, float bb, int n);void miser(float (*func)(float []), float regn[], int ndim, unsigned long npts,	float dith, float *ave, float *var);void mmid(float y[], float dydx[], int nvar, float xs, float htot,	int nstep, float yout[], void (*derivs)(float, float[], float[]));void mnbrak(float *ax, float *bx, float *cx, float *fa, float *fb,	float *fc, float (*func)(float));void mnbrak_arg(float *ax, float *bx, float *cx, float *fa, float *fb,	float *fc, float (*func)(float, void*), void *arg);void mnewt(int ntrial, float x[], int n, float tolx, float tolf);void moment(float data[], int n, float *ave, float *adev, float *sdev,	float *var, float *skew, float *curt);void mp2dfr(unsigned char a[], unsigned char s[], int n, int *m);void mpadd(unsigned char w[], unsigned char u[], unsigned char v[], int n);void mpdiv(unsigned char q[], unsigned char r[], unsigned char u[],	unsigned char v[], int n, int m);void mpinv(unsigned char u[], unsigned char v[], int n, int m);void mplsh(unsigned char u[], int n);void mpmov(unsigned char u[], unsigned char v[], int n);void mpmul(unsigned char w[], unsigned char u[], unsigned char v[], int n,	int m);void mpneg(unsigned char u[], int n);void mppi(int n);void mprove(float **a, float **alud, int n, int indx[], float b[],	float x[]);void mpsad(unsigned char w[], unsigned char u[], int n, int iv);void mpsdv(unsigned char w[], unsigned char u[], int n, int iv, int *ir);void mpsmu(unsigned char w[], unsigned char u[], int n, int iv);void mpsqrt(unsigned char w[], unsigned char u[], unsigned char v[], int n,	int m);void mpsub(int *is, unsigned char w[], unsigned char u[], unsigned char v[],	int n);void mrqcof(float x[], float y[], float sig[], int ndata, float a[],	int ia[], int ma, float **alpha, float beta[], float *chisq,	void (*funcs)(float, float [], float *, float [], int));void mrqmin(float x[], float y[], float sig[], int ndata, float a[],	int ia[], int ma, float **covar, float **alpha, float *chisq,	void (*funcs)(float, float [], float *, float [], int), float *alamda);void newt(float x[], int n, int *check,	void (*vecfunc)(int, float [], float []));void odeint(float ystart[], int nvar, float x1, float x2,	float eps, float h1, float hmin, int *nok, int *nbad,	void (*derivs)(float, float [], float []),	void (*rkqs)(float [], float [], int, float *, float, float,	float [], float *, float *, void (*)(float, float [], float [])));void orthog(int n, float anu[], float alpha[], float beta[], float a[],	float b[]);void pade(double cof[], int n, float *resid);void pccheb(float d[], float c[], int n);void pcshft(float a, float b, float d[], int n);void pearsn(float x[], float y[], unsigned long n, float *r, float *prob,	float *z);void period(float x[], float y[], int n, float ofac, float hifac,	float px[], float py[], int np, int *nout, int *jmax, float *prob);void piksr2(int n, float arr[], float brr[]);void piksrt(int n, float arr[]);void pinvs(int ie1, int ie2, int je1, int jsf, int jc1, int k,	float ***c, float **s);float plgndr(int l, int m, float x);float poidev(float xm, long *idum);void polcoe(float x[], float y[], int n, float cof[]);void polcof(float xa[], float ya[], int n, float cof[]);void poldiv(float u[], int n, float v[], int nv, float q[], float r[]);void polin2(float x1a[], float x2a[], float **ya, int m, int n,	float x1, float x2, float *y, float *dy);void polint(float xa[], float ya[], int n, float x, float *y, float *dy);void powell(float p[], float **xi, int n, float ftol, int *iter, float *fret,	float (*func)(float []));void predic(float data[], int ndata, float d[], int m, float future[], int nfut);float probks(float alam);void psdes(unsigned long *lword, unsigned long *irword);void pwt(float a[], unsigned long n, int isign);void pwtset(int n);float pythag(float a, float b);void pzextr(int iest, float xest, float yest[], float yz[], float dy[],	int nv);float qgaus(float (*func)(float), float a, float b);void qrdcmp(float **a, int n, float *c, float *d, int *sing);float qromb(float (*func)(float), float a, float b);float qromo(float (*func)(float), float a, float b,	float (*choose)(float (*)(float), float, float, int));void qroot(float p[], int n, float *b, float *c, float eps);void qrsolv(float **a, int n, float c[], float d[], float b[]);void qrupdt(float **r, float **qt, int n, float u[], float v[]);float qsimp(float (*func)(float), float a, float b);float qtrap(float (*func)(float), float a, float b);float quad3d(float (*func)(float, float, float), float x1, float x2);void quadct(float x, float y, float xx[], float yy[], unsigned long nn,	float *fa, float *fb, float *fc, float *fd);void quadmx(float **a, int n);void quadvl(float x, float y, float *fa, float *fb, float *fc, float *fd);float ran0(long *idum);float ran1(long *idum);float ran2(long *idum);float ran3(long *idum);float ran4(long *idum);void rank(unsigned long n, unsigned long indx[], unsigned long irank[]);void ranpt(float pt[], float regn[], int n);void ratint(float xa[], float ya[], int n, float x, float *y, float *dy);void ratlsq(double (*fn)(double), double a, double b, int mm, int kk,	double cof[], double *dev);double ratval(double x, double cof[], int mm, int kk);float rc(float x, float y);float rd(float x, float y, float z);void realft(float data[], unsigned long n, int isign);void rebin(float rc, int nd, float r[], float xin[], float xi[]);void red(int iz1, int iz2, int jz1, int jz2, int jm1, int jm2, int jmf,	int ic1, int jc1, int jcf, int kc, float ***c, float **s);void relax(double **u, double **rhs, int n);void relax2(double **u, double **rhs, int n);void resid(double **res, double **u, double **rhs, int n);float revcst(float x[], float y[], int iorder[], int ncity, int n[]);void reverse(int iorder[], int ncity, int n[]);float rf(float x, float y, float z);float rj(float x, float y, float z, float p);void rk4(float y[], float dydx[], int n, float x, float h, float yout[],	void (*derivs)(float, float [], float []));void rkck(float y[], float dydx[], int n, float x, float h,	float yout[], float yerr[], void (*derivs)(float, float [], float []));void rkdumb(float vstart[], int nvar, float x1, float x2, int nstep,	void (*derivs)(float, float [], float []));void rkqs(float y[], float dydx[], int n, float *x,	float htry, float eps, float yscal[], float *hdid, float *hnext,	void (*derivs)(float, float [], float []));void rlft3(float ***data, float **speq, unsigned long nn1,	unsigned long nn2, unsigned long nn3, int isign);float rofunc(float b);void rotate(float **r, float **qt, int n, int i, float a, float b);void rsolv(float **a, int n, float d[], float b[]);void rstrct(double **uc, double **uf, int nc);float rtbis(float (*func)(float), float x1, float x2, float xacc);float rtflsp(float (*func)(float), float x1, float x2, float xacc);float rtnewt(void (*funcd)(float, float *, float *), float x1, float x2,	float xacc);float rtsafe(void (*funcd)(float, float *, float *), float x1, float x2,	float xacc);float rtsec(float (*func)(float), float x1, float x2, float xacc);void rzextr(int iest, float xest, float yest[], float yz[], float dy[], int nv);void savgol(float c[], int np, int nl, int nr, int ld, int m);void score(float xf, float y[], float f[]);void scrsho(float (*fx)(float));float select(unsigned long k, unsigned long n, float arr[]);float selip(unsigned long k, unsigned long n, float arr[]);void shell(unsigned long n, float a[]);void shoot(int n, float v[], float f[]);void shootf(int n, float v[], float f[]);void simp1(float **a, int mm, int ll[], int nll, int iabf, int *kp,	float *bmax);void simp2(float **a, int n, int l2[], int nl2, int *ip, int kp, float *q1);void simp3(float **a, int i1, int k1, int ip, int kp);void simplx(float **a, int m, int n, int m1, int m2, int m3, int *icase,	int izrov[], int iposv[]);void simpr(float y[], float dydx[], float dfdx[], float **dfdy,	int n, float xs, float htot, int nstep, float yout[],	void (*derivs)(float, float [], float []));void sinft(float y[], int n);void slvsm2(double **u, double **rhs);void slvsml(double **u, double **rhs);void sncndn(float uu, float emmc, float *sn, float *cn, float *dn);double snrm(unsigned long n, double sx[], int itol);void sobseq(int *n, float x[]);void solvde(int itmax, float conv, float slowc, float scalv[],	int indexv[], int ne, int nb, int m, float **y, float ***c, float **s);void sor(double **a, double **b, double **c, double **d, double **e,	double **f, double **u, int jmax, double rjac);void sort(unsigned long n, float arr[]);void sort2(unsigned long n, float arr[], float brr[]);void sort3(unsigned long n, float ra[], float rb[], float rc[]);void spctrm(FILE *fp, float p[], int m, int k, int ovrlap);void spear(float data1[], float data2[], unsigned long n, float *d, float *zd,	float *probd, float *rs, float *probrs);void sphbes(int n, float x, float *sj, float *sy, float *sjp, float *syp);void splie2(float x1a[], float x2a[], float **ya, int m, int n, float **y2a);void splin2(float x1a[], float x2a[], float **ya, float **y2a, int m, int n,	float x1, float x2, float *y);void spline(float x[], float y[], int n, float yp1, float ypn, float y2[]);void splint(float xa[], float ya[], float y2a[], int n, float x, float *y);void spread(float y, float yy[], unsigned long n, float x, int m);void sprsax(float sa[], unsigned long ija[], float x[], float b[],	unsigned long n);void sprsin(float **a, int n, float thresh, unsigned long nmax, float sa[],	unsigned long ija[]);void sprspm(float sa[], unsigned long ija[], float sb[], unsigned long ijb[],	float sc[], unsigned long ijc[]);void sprstm(float sa[], unsigned long ija[], float sb[], unsigned long ijb[],	float thresh, unsigned long nmax, float sc[], unsigned long ijc[]);void sprstp(float sa[], unsigned long ija[], float sb[], unsigned long ijb[]);void sprstx(float sa[], unsigned long ija[], float x[], float b[],	unsigned long n);void stifbs(float y[], float dydx[], int nv, float *xx,	float htry, float eps, float yscal[], float *hdid, float *hnext,	void (*derivs)(float, float [], float []));void stiff(float y[], float dydx[], int n, float *x,	float htry, float eps, float yscal[], float *hdid, float *hnext,	void (*derivs)(float, float [], float []));void stoerm(float y[], float d2y[], int nv, float xs,	float htot, int nstep, float yout[],	void (*derivs)(float, float [], float []));void svbksb(float **u, float w[], float **v, int m, int n, float b[],	float x[]);void svdcmp(float **a, int m, int n, float w[], float **v);void svdfit(float x[], float y[], float sig[], int ndata, float a[],	int ma, float **u, float **v, float w[], float *chisq,	void (*funcs)(float, float [], int));void svdvar(float **v, int ma, float w[], float **cvm);void toeplz(float r[], float x[], float y[], int n);void tptest(float data1[], float data2[], unsigned long n, float *t, float *prob);void tqli(float d[], float e[], int n, float **z);float trapzd(float (*func)(float), float a, float b, int n);void tred2(float **a, int n, float d[], float e[]);void tridag(float a[], float b[], float c[], float r[], float u[],	unsigned long n);float trncst(float x[], float y[], int iorder[], int ncity, int n[]);void trnspt(int iorder[], int ncity, int n[]);void ttest(float data1[], unsigned long n1, float data2[], unsigned long n2,	float *t, float *prob);void tutest(float data1[], unsigned long n1, float data2[], unsigned long n2,	float *t, float *prob);void twofft(float data1[], float data2[], float fft1[], float fft2[],	unsigned long n);void vander(double x[], double w[], double q[], int n);void vegas(float regn[], int ndim, float (*fxn)(float [], float), int init,	unsigned long ncall, int itmx, int nprn, float *tgral, float *sd,	float *chi2a);void voltra(int n, int m, float t0, float h, float *t, float **f,	float (*g)(int, float), float (*ak)(int, int, float, float));void wt1(float a[], unsigned long n, int isign,	void (*wtstep)(float [], unsigned long, int));void wtn(float a[], unsigned long nn[], int ndim, int isign,	void (*wtstep)(float [], unsigned long, int));void wwghts(float wghts[], int n, float h,	void (*kermom)(double [], double ,int));int zbrac(float (*func)(float), float *x1, float *x2);void zbrak(float (*fx)(float), float x1, float x2, int n, float xb1[],	float xb2[], int *nb);float zbrent(float (*func)(float), float x1, float x2, float tol);void zrhqr(float a[], int m, float rtr[], float rti[]);float zriddr(float (*func)(float), float x1, float x2, float xacc);void zroots(fcomplex a[], int m, fcomplex roots[], int polish);#endif /* _NR_H_ */