wolffd@0: /* CAUTION: This is the ANSI C (only) version of the Numerical Recipes
wolffd@0:    utility file nr.h.  Do not confuse this file with the same-named
wolffd@0:    file nr.h that is supplied in the 'misc' subdirectory.
wolffd@0:    *That* file is the one from the book, and contains both ANSI and
wolffd@0:    traditional K&R versions, along with #ifdef macros to select the
wolffd@0:    correct version.  *This* file contains only ANSI C.               */
wolffd@0: 
wolffd@0: #ifndef _NR_H_
wolffd@0: #define _NR_H_
wolffd@0: 
wolffd@0: #ifndef _FCOMPLEX_DECLARE_T_
wolffd@0: typedef struct FCOMPLEX {float r,i;} fcomplex;
wolffd@0: #define _FCOMPLEX_DECLARE_T_
wolffd@0: #endif /* _FCOMPLEX_DECLARE_T_ */
wolffd@0: 
wolffd@0: #ifndef _ARITHCODE_DECLARE_T_
wolffd@0: typedef struct {
wolffd@0: 	unsigned long *ilob,*iupb,*ncumfq,jdif,nc,minint,nch,ncum,nrad;
wolffd@0: } arithcode;
wolffd@0: #define _ARITHCODE_DECLARE_T_
wolffd@0: #endif /* _ARITHCODE_DECLARE_T_ */
wolffd@0: 
wolffd@0: #ifndef _HUFFCODE_DECLARE_T_
wolffd@0: typedef struct {
wolffd@0: 	unsigned long *icod,*ncod,*left,*right,nch,nodemax;
wolffd@0: } huffcode;
wolffd@0: #define _HUFFCODE_DECLARE_T_
wolffd@0: #endif /* _HUFFCODE_DECLARE_T_ */
wolffd@0: 
wolffd@0: #include <stdio.h>
wolffd@0: 
wolffd@0: void addint(double **uf, double **uc, double **res, int nf);
wolffd@0: void airy(float x, float *ai, float *bi, float *aip, float *bip);
wolffd@0: void amebsa(float **p, float y[], int ndim, float pb[],	float *yb,
wolffd@0: 	float ftol, float (*funk)(float []), int *iter, float temptr);
wolffd@0: void amoeba(float **p, float y[], int ndim, float ftol,
wolffd@0: 	float (*funk)(float []), int *iter);
wolffd@0: float amotry(float **p, float y[], float psum[], int ndim,
wolffd@0: 	float (*funk)(float []), int ihi, float fac);
wolffd@0: float amotsa(float **p, float y[], float psum[], int ndim, float pb[],
wolffd@0: 	float *yb, float (*funk)(float []), int ihi, float *yhi, float fac);
wolffd@0: void anneal(float x[], float y[], int iorder[], int ncity);
wolffd@0: double anorm2(double **a, int n);
wolffd@0: void arcmak(unsigned long nfreq[], unsigned long nchh, unsigned long nradd,
wolffd@0: 	arithcode *acode);
wolffd@0: void arcode(unsigned long *ich, unsigned char **codep, unsigned long *lcode,
wolffd@0: 	unsigned long *lcd, int isign, arithcode *acode);
wolffd@0: void arcsum(unsigned long iin[], unsigned long iout[], unsigned long ja,
wolffd@0: 	int nwk, unsigned long nrad, unsigned long nc);
wolffd@0: void asolve(unsigned long n, double b[], double x[], int itrnsp);
wolffd@0: void atimes(unsigned long n, double x[], double r[], int itrnsp);
wolffd@0: void avevar(float data[], unsigned long n, float *ave, float *var);
wolffd@0: void balanc(float **a, int n);
wolffd@0: void banbks(float **a, unsigned long n, int m1, int m2, float **al,
wolffd@0: 	unsigned long indx[], float b[]);
wolffd@0: void bandec(float **a, unsigned long n, int m1, int m2, float **al,
wolffd@0: 	unsigned long indx[], float *d);
wolffd@0: void banmul(float **a, unsigned long n, int m1, int m2, float x[], float b[]);
wolffd@0: void bcucof(float y[], float y1[], float y2[], float y12[], float d1,
wolffd@0: 	float d2, float **c);
wolffd@0: void bcuint(float y[], float y1[], float y2[], float y12[],
wolffd@0: 	float x1l, float x1u, float x2l, float x2u, float x1,
wolffd@0: 	float x2, float *ansy, float *ansy1, float *ansy2);
wolffd@0: void beschb(double x, double *gam1, double *gam2, double *gampl,
wolffd@0: 	double *gammi);
wolffd@0: float bessi(int n, float x);
wolffd@0: float bessi0(float x);
wolffd@0: float bessi1(float x);
wolffd@0: void bessik(float x, float xnu, float *ri, float *rk, float *rip,
wolffd@0: 	float *rkp);
wolffd@0: float bessj(int n, float x);
wolffd@0: float bessj0(float x);
wolffd@0: float bessj1(float x);
wolffd@0: void bessjy(float x, float xnu, float *rj, float *ry, float *rjp,
wolffd@0: 	float *ryp);
wolffd@0: float bessk(int n, float x);
wolffd@0: float bessk0(float x);
wolffd@0: float bessk1(float x);
wolffd@0: float bessy(int n, float x);
wolffd@0: float bessy0(float x);
wolffd@0: float bessy1(float x);
wolffd@0: float beta(float z, float w);
wolffd@0: float betacf(float a, float b, float x);
wolffd@0: float betai(float a, float b, float x);
wolffd@0: float bico(int n, int k);
wolffd@0: void bksub(int ne, int nb, int jf, int k1, int k2, float ***c);
wolffd@0: float bnldev(float pp, int n, long *idum);
wolffd@0: float brent(float ax, float bx, float cx,
wolffd@0: 	float (*f)(float), float tol, float *xmin);
wolffd@0: float brent_arg(float ax, float bx, float cx,
wolffd@0: 	float (*f)(float, void*), float tol, float *xmin, void *arg);
wolffd@0: void broydn(float x[], int n, int *check,
wolffd@0: 	void (*vecfunc)(int, float [], float []));
wolffd@0: void bsstep(float y[], float dydx[], int nv, float *xx, float htry,
wolffd@0: 	float eps, float yscal[], float *hdid, float *hnext,
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void caldat(long julian, int *mm, int *id, int *iyyy);
wolffd@0: void chder(float a, float b, float c[], float cder[], int n);
wolffd@0: float chebev(float a, float b, float c[], int m, float x);
wolffd@0: void chebft(float a, float b, float c[], int n, float (*func)(float));
wolffd@0: void chebpc(float c[], float d[], int n);
wolffd@0: void chint(float a, float b, float c[], float cint[], int n);
wolffd@0: float chixy(float bang);
wolffd@0: void choldc(float **a, int n, float p[]);
wolffd@0: void cholsl(float **a, int n, float p[], float b[], float x[]);
wolffd@0: void chsone(float bins[], float ebins[], int nbins, int knstrn,
wolffd@0: 	float *df, float *chsq, float *prob);
wolffd@0: void chstwo(float bins1[], float bins2[], int nbins, int knstrn,
wolffd@0: 	float *df, float *chsq, float *prob);
wolffd@0: void cisi(float x, float *ci, float *si);
wolffd@0: void cntab1(int **nn, int ni, int nj, float *chisq,
wolffd@0: 	float *df, float *prob, float *cramrv, float *ccc);
wolffd@0: void cntab2(int **nn, int ni, int nj, float *h, float *hx, float *hy,
wolffd@0: 	float *hygx, float *hxgy, float *uygx, float *uxgy, float *uxy);
wolffd@0: void convlv(float data[], unsigned long n, float respns[], unsigned long m,
wolffd@0: 	int isign, float ans[]);
wolffd@0: void copy(double **aout, double **ain, int n);
wolffd@0: void correl(float data1[], float data2[], unsigned long n, float ans[]);
wolffd@0: void cosft(float y[], int n, int isign);
wolffd@0: void cosft1(float y[], int n);
wolffd@0: void cosft2(float y[], int n, int isign);
wolffd@0: void covsrt(float **covar, int ma, int ia[], int mfit);
wolffd@0: void crank(unsigned long n, float w[], float *s);
wolffd@0: void cyclic(float a[], float b[], float c[], float alpha, float beta,
wolffd@0: 	float r[], float x[], unsigned long n);
wolffd@0: void daub4(float a[], unsigned long n, int isign);
wolffd@0: float dawson(float x);
wolffd@0: float dbrent(float ax, float bx, float cx,
wolffd@0: 	float (*f)(float), float (*df)(float), float tol, float *xmin);
wolffd@0: void ddpoly(float c[], int nc, float x, float pd[], int nd);
wolffd@0: int decchk(char string[], int n, char *ch);
wolffd@0: void derivs(float x, float y[], float dydx[]);
wolffd@0: float df1dim(float x);
wolffd@0: void dfour1(double data[], unsigned long nn, int isign);
wolffd@0: void dfpmin(float p[], int n, float gtol, int *iter, float *fret,
wolffd@0: 	float (*func)(float []), void (*dfunc)(float [], float []));
wolffd@0: float dfridr(float (*func)(float), float x, float h, float *err);
wolffd@0: void dftcor(float w, float delta, float a, float b, float endpts[],
wolffd@0: 	float *corre, float *corim, float *corfac);
wolffd@0: void dftint(float (*func)(float), float a, float b, float w,
wolffd@0: 	float *cosint, float *sinint);
wolffd@0: void difeq(int k, int k1, int k2, int jsf, int is1, int isf,
wolffd@0: 	int indexv[], int ne, float **s, float **y);
wolffd@0: void dlinmin(float p[], float xi[], int n, float *fret,
wolffd@0: 	float (*func)(float []), void (*dfunc)(float [], float[]));
wolffd@0: double dpythag(double a, double b);
wolffd@0: void drealft(double data[], unsigned long n, int isign);
wolffd@0: void dsprsax(double sa[], unsigned long ija[], double x[], double b[],
wolffd@0: 	unsigned long n);
wolffd@0: void dsprstx(double sa[], unsigned long ija[], double x[], double b[],
wolffd@0: 	unsigned long n);
wolffd@0: void dsvbksb(double **u, double w[], double **v, int m, int n, double b[],
wolffd@0: 	double x[]);
wolffd@0: void dsvdcmp(double **a, int m, int n, double w[], double **v);
wolffd@0: void eclass(int nf[], int n, int lista[], int listb[], int m);
wolffd@0: void eclazz(int nf[], int n, int (*equiv)(int, int));
wolffd@0: float ei(float x);
wolffd@0: void eigsrt(float d[], float **v, int n);
wolffd@0: float elle(float phi, float ak);
wolffd@0: float ellf(float phi, float ak);
wolffd@0: float ellpi(float phi, float en, float ak);
wolffd@0: void elmhes(float **a, int n);
wolffd@0: float erfcc(float x);
wolffd@0: float erff(float x);
wolffd@0: float erffc(float x);
wolffd@0: void eulsum(float *sum, float term, int jterm, float wksp[]);
wolffd@0: float evlmem(float fdt, float d[], int m, float xms);
wolffd@0: float expdev(long *idum);
wolffd@0: float expint(int n, float x);
wolffd@0: float f1(float x);
wolffd@0: float f1dim(float x);
wolffd@0: float f1dim_arg(float x, void *arg);
wolffd@0: float f2(float y);
wolffd@0: float f3(float z);
wolffd@0: float factln(int n);
wolffd@0: float factrl(int n);
wolffd@0: void fasper(float x[], float y[], unsigned long n, float ofac, float hifac,
wolffd@0: 	float wk1[], float wk2[], unsigned long nwk, unsigned long *nout,
wolffd@0: 	unsigned long *jmax, float *prob);
wolffd@0: void fdjac(int n, float x[], float fvec[], float **df,
wolffd@0: 	void (*vecfunc)(int, float [], float []));
wolffd@0: void fgauss(float x, float a[], float *y, float dyda[], int na);
wolffd@0: void fill0(double **u, int n);
wolffd@0: void fit(float x[], float y[], int ndata, float sig[], int mwt,
wolffd@0: 	float *a, float *b, float *siga, float *sigb, float *chi2, float *q);
wolffd@0: void fitexy(float x[], float y[], int ndat, float sigx[], float sigy[],
wolffd@0: 	float *a, float *b, float *siga, float *sigb, float *chi2, float *q);
wolffd@0: void fixrts(float d[], int m);
wolffd@0: void fleg(float x, float pl[], int nl);
wolffd@0: void flmoon(int n, int nph, long *jd, float *frac);
wolffd@0: float fmin(float x[]);
wolffd@0: void four1(float data[], unsigned long nn, int isign);
wolffd@0: void fourew(FILE *file[5], int *na, int *nb, int *nc, int *nd);
wolffd@0: void fourfs(FILE *file[5], unsigned long nn[], int ndim, int isign);
wolffd@0: void fourn(float data[], unsigned long nn[], int ndim, int isign);
wolffd@0: void fpoly(float x, float p[], int np);
wolffd@0: void fred2(int n, float a, float b, float t[], float f[], float w[],
wolffd@0: 	float (*g)(float), float (*ak)(float, float));
wolffd@0: float fredin(float x, int n, float a, float b, float t[], float f[], float w[],
wolffd@0: 	float (*g)(float), float (*ak)(float, float));
wolffd@0: void frenel(float x, float *s, float *c);
wolffd@0: void frprmn(float p[], int n, float ftol, int *iter, float *fret,
wolffd@0: 	float (*func)(float []), void (*dfunc)(float [], float []));
wolffd@0: void frprmn_arg(float p[], int n, float ftol, int *iter, float *fret,
wolffd@0: 	float (*func)(float [], void*), void (*dfunc)(float [], float [], void*), void* arg);
wolffd@0: void ftest(float data1[], unsigned long n1, float data2[], unsigned long n2,
wolffd@0: 	float *f, float *prob);
wolffd@0: float gamdev(int ia, long *idum);
wolffd@0: float gammln(float xx);
wolffd@0: float gammp(float a, float x);
wolffd@0: float gammq(float a, float x);
wolffd@0: float gasdev(long *idum);
wolffd@0: void gaucof(int n, float a[], float b[], float amu0, float x[], float w[]);
wolffd@0: void gauher(float x[], float w[], int n);
wolffd@0: void gaujac(float x[], float w[], int n, float alf, float bet);
wolffd@0: void gaulag(float x[], float w[], int n, float alf);
wolffd@0: void gauleg(float x1, float x2, float x[], float w[], int n);
wolffd@0: void gaussj(float **a, int n, float **b, int m);
wolffd@0: void gcf(float *gammcf, float a, float x, float *gln);
wolffd@0: float golden(float ax, float bx, float cx, float (*f)(float), float tol,
wolffd@0: 	float *xmin);
wolffd@0: void gser(float *gamser, float a, float x, float *gln);
wolffd@0: void hpsel(unsigned long m, unsigned long n, float arr[], float heap[]);
wolffd@0: void hpsort(unsigned long n, float ra[]);
wolffd@0: void hqr(float **a, int n, float wr[], float wi[]);
wolffd@0: void hufapp(unsigned long index[], unsigned long nprob[], unsigned long n,
wolffd@0: 	unsigned long i);
wolffd@0: void hufdec(unsigned long *ich, unsigned char *code, unsigned long lcode,
wolffd@0: 	unsigned long *nb, huffcode *hcode);
wolffd@0: void hufenc(unsigned long ich, unsigned char **codep, unsigned long *lcode,
wolffd@0: 	unsigned long *nb, huffcode *hcode);
wolffd@0: void hufmak(unsigned long nfreq[], unsigned long nchin, unsigned long *ilong,
wolffd@0: 	unsigned long *nlong, huffcode *hcode);
wolffd@0: void hunt(float xx[], unsigned long n, float x, unsigned long *jlo);
wolffd@0: void hypdrv(float s, float yy[], float dyyds[]);
wolffd@0: fcomplex hypgeo(fcomplex a, fcomplex b, fcomplex c, fcomplex z);
wolffd@0: void hypser(fcomplex a, fcomplex b, fcomplex c, fcomplex z,
wolffd@0: 	fcomplex *series, fcomplex *deriv);
wolffd@0: unsigned short icrc(unsigned short crc, unsigned char *bufptr,
wolffd@0: 	unsigned long len, short jinit, int jrev);
wolffd@0: unsigned short icrc1(unsigned short crc, unsigned char onech);
wolffd@0: unsigned long igray(unsigned long n, int is);
wolffd@0: void iindexx(unsigned long n, long arr[], unsigned long indx[]);
wolffd@0: void indexx(unsigned long n, float arr[], unsigned long indx[]);
wolffd@0: void interp(double **uf, double **uc, int nf);
wolffd@0: int irbit1(unsigned long *iseed);
wolffd@0: int irbit2(unsigned long *iseed);
wolffd@0: void jacobi(float **a, int n, float d[], float **v, int *nrot);
wolffd@0: void jacobn(float x, float y[], float dfdx[], float **dfdy, int n);
wolffd@0: long julday(int mm, int id, int iyyy);
wolffd@0: void kendl1(float data1[], float data2[], unsigned long n, float *tau, float *z,
wolffd@0: 	float *prob);
wolffd@0: void kendl2(float **tab, int i, int j, float *tau, float *z, float *prob);
wolffd@0: void kermom(double w[], double y, int m);
wolffd@0: void ks2d1s(float x1[], float y1[], unsigned long n1,
wolffd@0: 	void (*quadvl)(float, float, float *, float *, float *, float *),
wolffd@0: 	float *d1, float *prob);
wolffd@0: void ks2d2s(float x1[], float y1[], unsigned long n1, float x2[], float y2[],
wolffd@0: 	unsigned long n2, float *d, float *prob);
wolffd@0: void ksone(float data[], unsigned long n, float (*func)(float), float *d,
wolffd@0: 	float *prob);
wolffd@0: void kstwo(float data1[], unsigned long n1, float data2[], unsigned long n2,
wolffd@0: 	float *d, float *prob);
wolffd@0: void laguer(fcomplex a[], int m, fcomplex *x, int *its);
wolffd@0: void lfit(float x[], float y[], float sig[], int ndat, float a[], int ia[],
wolffd@0: 	int ma, float **covar, float *chisq, void (*funcs)(float, float [], int));
wolffd@0: void linbcg(unsigned long n, double b[], double x[], int itol, double tol,
wolffd@0: 	 int itmax, int *iter, double *err);
wolffd@0: void linmin(float p[], float xi[], int n, float *fret,
wolffd@0: 	float (*func)(float []));
wolffd@0: void linmin_arg(float p[], float xi[], int n, float *fret,
wolffd@0: 	float (*func)(float [], void*), void *arg);
wolffd@0: void lnsrch(int n, float xold[], float fold, float g[], float p[], float x[],
wolffd@0: 	 float *f, float stpmax, int *check, float (*func)(float []));
wolffd@0: void load(float x1, float v[], float y[]);
wolffd@0: void load1(float x1, float v1[], float y[]);
wolffd@0: void load2(float x2, float v2[], float y[]);
wolffd@0: void locate(float xx[], unsigned long n, float x, unsigned long *j);
wolffd@0: void lop(double **out, double **u, int n);
wolffd@0: void lubksb(float **a, int n, int *indx, float b[]);
wolffd@0: void ludcmp(float **a, int n, int *indx, float *d);
wolffd@0: void machar(int *ibeta, int *it, int *irnd, int *ngrd,
wolffd@0: 	int *machep, int *negep, int *iexp, int *minexp, int *maxexp,
wolffd@0: 	float *eps, float *epsneg, float *xmin, float *xmax);
wolffd@0: void matadd(double **a, double **b, double **c, int n);
wolffd@0: void matsub(double **a, double **b, double **c, int n);
wolffd@0: void medfit(float x[], float y[], int ndata, float *a, float *b, float *abdev);
wolffd@0: void memcof(float data[], int n, int m, float *xms, float d[]);
wolffd@0: int metrop(float de, float t);
wolffd@0: void mgfas(double **u, int n, int maxcyc);
wolffd@0: void mglin(double **u, int n, int ncycle);
wolffd@0: float midexp(float (*funk)(float), float aa, float bb, int n);
wolffd@0: float midinf(float (*funk)(float), float aa, float bb, int n);
wolffd@0: float midpnt(float (*func)(float), float a, float b, int n);
wolffd@0: float midsql(float (*funk)(float), float aa, float bb, int n);
wolffd@0: float midsqu(float (*funk)(float), float aa, float bb, int n);
wolffd@0: void miser(float (*func)(float []), float regn[], int ndim, unsigned long npts,
wolffd@0: 	float dith, float *ave, float *var);
wolffd@0: void mmid(float y[], float dydx[], int nvar, float xs, float htot,
wolffd@0: 	int nstep, float yout[], void (*derivs)(float, float[], float[]));
wolffd@0: void mnbrak(float *ax, float *bx, float *cx, float *fa, float *fb,
wolffd@0: 	float *fc, float (*func)(float));
wolffd@0: void mnbrak_arg(float *ax, float *bx, float *cx, float *fa, float *fb,
wolffd@0: 	float *fc, float (*func)(float, void*), void *arg);
wolffd@0: void mnewt(int ntrial, float x[], int n, float tolx, float tolf);
wolffd@0: void moment(float data[], int n, float *ave, float *adev, float *sdev,
wolffd@0: 	float *var, float *skew, float *curt);
wolffd@0: void mp2dfr(unsigned char a[], unsigned char s[], int n, int *m);
wolffd@0: void mpadd(unsigned char w[], unsigned char u[], unsigned char v[], int n);
wolffd@0: void mpdiv(unsigned char q[], unsigned char r[], unsigned char u[],
wolffd@0: 	unsigned char v[], int n, int m);
wolffd@0: void mpinv(unsigned char u[], unsigned char v[], int n, int m);
wolffd@0: void mplsh(unsigned char u[], int n);
wolffd@0: void mpmov(unsigned char u[], unsigned char v[], int n);
wolffd@0: void mpmul(unsigned char w[], unsigned char u[], unsigned char v[], int n,
wolffd@0: 	int m);
wolffd@0: void mpneg(unsigned char u[], int n);
wolffd@0: void mppi(int n);
wolffd@0: void mprove(float **a, float **alud, int n, int indx[], float b[],
wolffd@0: 	float x[]);
wolffd@0: void mpsad(unsigned char w[], unsigned char u[], int n, int iv);
wolffd@0: void mpsdv(unsigned char w[], unsigned char u[], int n, int iv, int *ir);
wolffd@0: void mpsmu(unsigned char w[], unsigned char u[], int n, int iv);
wolffd@0: void mpsqrt(unsigned char w[], unsigned char u[], unsigned char v[], int n,
wolffd@0: 	int m);
wolffd@0: void mpsub(int *is, unsigned char w[], unsigned char u[], unsigned char v[],
wolffd@0: 	int n);
wolffd@0: void mrqcof(float x[], float y[], float sig[], int ndata, float a[],
wolffd@0: 	int ia[], int ma, float **alpha, float beta[], float *chisq,
wolffd@0: 	void (*funcs)(float, float [], float *, float [], int));
wolffd@0: void mrqmin(float x[], float y[], float sig[], int ndata, float a[],
wolffd@0: 	int ia[], int ma, float **covar, float **alpha, float *chisq,
wolffd@0: 	void (*funcs)(float, float [], float *, float [], int), float *alamda);
wolffd@0: void newt(float x[], int n, int *check,
wolffd@0: 	void (*vecfunc)(int, float [], float []));
wolffd@0: void odeint(float ystart[], int nvar, float x1, float x2,
wolffd@0: 	float eps, float h1, float hmin, int *nok, int *nbad,
wolffd@0: 	void (*derivs)(float, float [], float []),
wolffd@0: 	void (*rkqs)(float [], float [], int, float *, float, float,
wolffd@0: 	float [], float *, float *, void (*)(float, float [], float [])));
wolffd@0: void orthog(int n, float anu[], float alpha[], float beta[], float a[],
wolffd@0: 	float b[]);
wolffd@0: void pade(double cof[], int n, float *resid);
wolffd@0: void pccheb(float d[], float c[], int n);
wolffd@0: void pcshft(float a, float b, float d[], int n);
wolffd@0: void pearsn(float x[], float y[], unsigned long n, float *r, float *prob,
wolffd@0: 	float *z);
wolffd@0: void period(float x[], float y[], int n, float ofac, float hifac,
wolffd@0: 	float px[], float py[], int np, int *nout, int *jmax, float *prob);
wolffd@0: void piksr2(int n, float arr[], float brr[]);
wolffd@0: void piksrt(int n, float arr[]);
wolffd@0: void pinvs(int ie1, int ie2, int je1, int jsf, int jc1, int k,
wolffd@0: 	float ***c, float **s);
wolffd@0: float plgndr(int l, int m, float x);
wolffd@0: float poidev(float xm, long *idum);
wolffd@0: void polcoe(float x[], float y[], int n, float cof[]);
wolffd@0: void polcof(float xa[], float ya[], int n, float cof[]);
wolffd@0: void poldiv(float u[], int n, float v[], int nv, float q[], float r[]);
wolffd@0: void polin2(float x1a[], float x2a[], float **ya, int m, int n,
wolffd@0: 	float x1, float x2, float *y, float *dy);
wolffd@0: void polint(float xa[], float ya[], int n, float x, float *y, float *dy);
wolffd@0: void powell(float p[], float **xi, int n, float ftol, int *iter, float *fret,
wolffd@0: 	float (*func)(float []));
wolffd@0: void predic(float data[], int ndata, float d[], int m, float future[], int nfut);
wolffd@0: float probks(float alam);
wolffd@0: void psdes(unsigned long *lword, unsigned long *irword);
wolffd@0: void pwt(float a[], unsigned long n, int isign);
wolffd@0: void pwtset(int n);
wolffd@0: float pythag(float a, float b);
wolffd@0: void pzextr(int iest, float xest, float yest[], float yz[], float dy[],
wolffd@0: 	int nv);
wolffd@0: float qgaus(float (*func)(float), float a, float b);
wolffd@0: void qrdcmp(float **a, int n, float *c, float *d, int *sing);
wolffd@0: float qromb(float (*func)(float), float a, float b);
wolffd@0: float qromo(float (*func)(float), float a, float b,
wolffd@0: 	float (*choose)(float (*)(float), float, float, int));
wolffd@0: void qroot(float p[], int n, float *b, float *c, float eps);
wolffd@0: void qrsolv(float **a, int n, float c[], float d[], float b[]);
wolffd@0: void qrupdt(float **r, float **qt, int n, float u[], float v[]);
wolffd@0: float qsimp(float (*func)(float), float a, float b);
wolffd@0: float qtrap(float (*func)(float), float a, float b);
wolffd@0: float quad3d(float (*func)(float, float, float), float x1, float x2);
wolffd@0: void quadct(float x, float y, float xx[], float yy[], unsigned long nn,
wolffd@0: 	float *fa, float *fb, float *fc, float *fd);
wolffd@0: void quadmx(float **a, int n);
wolffd@0: void quadvl(float x, float y, float *fa, float *fb, float *fc, float *fd);
wolffd@0: float ran0(long *idum);
wolffd@0: float ran1(long *idum);
wolffd@0: float ran2(long *idum);
wolffd@0: float ran3(long *idum);
wolffd@0: float ran4(long *idum);
wolffd@0: void rank(unsigned long n, unsigned long indx[], unsigned long irank[]);
wolffd@0: void ranpt(float pt[], float regn[], int n);
wolffd@0: void ratint(float xa[], float ya[], int n, float x, float *y, float *dy);
wolffd@0: void ratlsq(double (*fn)(double), double a, double b, int mm, int kk,
wolffd@0: 	double cof[], double *dev);
wolffd@0: double ratval(double x, double cof[], int mm, int kk);
wolffd@0: float rc(float x, float y);
wolffd@0: float rd(float x, float y, float z);
wolffd@0: void realft(float data[], unsigned long n, int isign);
wolffd@0: void rebin(float rc, int nd, float r[], float xin[], float xi[]);
wolffd@0: void red(int iz1, int iz2, int jz1, int jz2, int jm1, int jm2, int jmf,
wolffd@0: 	int ic1, int jc1, int jcf, int kc, float ***c, float **s);
wolffd@0: void relax(double **u, double **rhs, int n);
wolffd@0: void relax2(double **u, double **rhs, int n);
wolffd@0: void resid(double **res, double **u, double **rhs, int n);
wolffd@0: float revcst(float x[], float y[], int iorder[], int ncity, int n[]);
wolffd@0: void reverse(int iorder[], int ncity, int n[]);
wolffd@0: float rf(float x, float y, float z);
wolffd@0: float rj(float x, float y, float z, float p);
wolffd@0: void rk4(float y[], float dydx[], int n, float x, float h, float yout[],
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void rkck(float y[], float dydx[], int n, float x, float h,
wolffd@0: 	float yout[], float yerr[], void (*derivs)(float, float [], float []));
wolffd@0: void rkdumb(float vstart[], int nvar, float x1, float x2, int nstep,
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void rkqs(float y[], float dydx[], int n, float *x,
wolffd@0: 	float htry, float eps, float yscal[], float *hdid, float *hnext,
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void rlft3(float ***data, float **speq, unsigned long nn1,
wolffd@0: 	unsigned long nn2, unsigned long nn3, int isign);
wolffd@0: float rofunc(float b);
wolffd@0: void rotate(float **r, float **qt, int n, int i, float a, float b);
wolffd@0: void rsolv(float **a, int n, float d[], float b[]);
wolffd@0: void rstrct(double **uc, double **uf, int nc);
wolffd@0: float rtbis(float (*func)(float), float x1, float x2, float xacc);
wolffd@0: float rtflsp(float (*func)(float), float x1, float x2, float xacc);
wolffd@0: float rtnewt(void (*funcd)(float, float *, float *), float x1, float x2,
wolffd@0: 	float xacc);
wolffd@0: float rtsafe(void (*funcd)(float, float *, float *), float x1, float x2,
wolffd@0: 	float xacc);
wolffd@0: float rtsec(float (*func)(float), float x1, float x2, float xacc);
wolffd@0: void rzextr(int iest, float xest, float yest[], float yz[], float dy[], int nv);
wolffd@0: void savgol(float c[], int np, int nl, int nr, int ld, int m);
wolffd@0: void score(float xf, float y[], float f[]);
wolffd@0: void scrsho(float (*fx)(float));
wolffd@0: float select(unsigned long k, unsigned long n, float arr[]);
wolffd@0: float selip(unsigned long k, unsigned long n, float arr[]);
wolffd@0: void shell(unsigned long n, float a[]);
wolffd@0: void shoot(int n, float v[], float f[]);
wolffd@0: void shootf(int n, float v[], float f[]);
wolffd@0: void simp1(float **a, int mm, int ll[], int nll, int iabf, int *kp,
wolffd@0: 	float *bmax);
wolffd@0: void simp2(float **a, int n, int l2[], int nl2, int *ip, int kp, float *q1);
wolffd@0: void simp3(float **a, int i1, int k1, int ip, int kp);
wolffd@0: void simplx(float **a, int m, int n, int m1, int m2, int m3, int *icase,
wolffd@0: 	int izrov[], int iposv[]);
wolffd@0: void simpr(float y[], float dydx[], float dfdx[], float **dfdy,
wolffd@0: 	int n, float xs, float htot, int nstep, float yout[],
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void sinft(float y[], int n);
wolffd@0: void slvsm2(double **u, double **rhs);
wolffd@0: void slvsml(double **u, double **rhs);
wolffd@0: void sncndn(float uu, float emmc, float *sn, float *cn, float *dn);
wolffd@0: double snrm(unsigned long n, double sx[], int itol);
wolffd@0: void sobseq(int *n, float x[]);
wolffd@0: void solvde(int itmax, float conv, float slowc, float scalv[],
wolffd@0: 	int indexv[], int ne, int nb, int m, float **y, float ***c, float **s);
wolffd@0: void sor(double **a, double **b, double **c, double **d, double **e,
wolffd@0: 	double **f, double **u, int jmax, double rjac);
wolffd@0: void sort(unsigned long n, float arr[]);
wolffd@0: void sort2(unsigned long n, float arr[], float brr[]);
wolffd@0: void sort3(unsigned long n, float ra[], float rb[], float rc[]);
wolffd@0: void spctrm(FILE *fp, float p[], int m, int k, int ovrlap);
wolffd@0: void spear(float data1[], float data2[], unsigned long n, float *d, float *zd,
wolffd@0: 	float *probd, float *rs, float *probrs);
wolffd@0: void sphbes(int n, float x, float *sj, float *sy, float *sjp, float *syp);
wolffd@0: void splie2(float x1a[], float x2a[], float **ya, int m, int n, float **y2a);
wolffd@0: void splin2(float x1a[], float x2a[], float **ya, float **y2a, int m, int n,
wolffd@0: 	float x1, float x2, float *y);
wolffd@0: void spline(float x[], float y[], int n, float yp1, float ypn, float y2[]);
wolffd@0: void splint(float xa[], float ya[], float y2a[], int n, float x, float *y);
wolffd@0: void spread(float y, float yy[], unsigned long n, float x, int m);
wolffd@0: void sprsax(float sa[], unsigned long ija[], float x[], float b[],
wolffd@0: 	unsigned long n);
wolffd@0: void sprsin(float **a, int n, float thresh, unsigned long nmax, float sa[],
wolffd@0: 	unsigned long ija[]);
wolffd@0: void sprspm(float sa[], unsigned long ija[], float sb[], unsigned long ijb[],
wolffd@0: 	float sc[], unsigned long ijc[]);
wolffd@0: void sprstm(float sa[], unsigned long ija[], float sb[], unsigned long ijb[],
wolffd@0: 	float thresh, unsigned long nmax, float sc[], unsigned long ijc[]);
wolffd@0: void sprstp(float sa[], unsigned long ija[], float sb[], unsigned long ijb[]);
wolffd@0: void sprstx(float sa[], unsigned long ija[], float x[], float b[],
wolffd@0: 	unsigned long n);
wolffd@0: void stifbs(float y[], float dydx[], int nv, float *xx,
wolffd@0: 	float htry, float eps, float yscal[], float *hdid, float *hnext,
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void stiff(float y[], float dydx[], int n, float *x,
wolffd@0: 	float htry, float eps, float yscal[], float *hdid, float *hnext,
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void stoerm(float y[], float d2y[], int nv, float xs,
wolffd@0: 	float htot, int nstep, float yout[],
wolffd@0: 	void (*derivs)(float, float [], float []));
wolffd@0: void svbksb(float **u, float w[], float **v, int m, int n, float b[],
wolffd@0: 	float x[]);
wolffd@0: void svdcmp(float **a, int m, int n, float w[], float **v);
wolffd@0: void svdfit(float x[], float y[], float sig[], int ndata, float a[],
wolffd@0: 	int ma, float **u, float **v, float w[], float *chisq,
wolffd@0: 	void (*funcs)(float, float [], int));
wolffd@0: void svdvar(float **v, int ma, float w[], float **cvm);
wolffd@0: void toeplz(float r[], float x[], float y[], int n);
wolffd@0: void tptest(float data1[], float data2[], unsigned long n, float *t, float *prob);
wolffd@0: void tqli(float d[], float e[], int n, float **z);
wolffd@0: float trapzd(float (*func)(float), float a, float b, int n);
wolffd@0: void tred2(float **a, int n, float d[], float e[]);
wolffd@0: void tridag(float a[], float b[], float c[], float r[], float u[],
wolffd@0: 	unsigned long n);
wolffd@0: float trncst(float x[], float y[], int iorder[], int ncity, int n[]);
wolffd@0: void trnspt(int iorder[], int ncity, int n[]);
wolffd@0: void ttest(float data1[], unsigned long n1, float data2[], unsigned long n2,
wolffd@0: 	float *t, float *prob);
wolffd@0: void tutest(float data1[], unsigned long n1, float data2[], unsigned long n2,
wolffd@0: 	float *t, float *prob);
wolffd@0: void twofft(float data1[], float data2[], float fft1[], float fft2[],
wolffd@0: 	unsigned long n);
wolffd@0: void vander(double x[], double w[], double q[], int n);
wolffd@0: void vegas(float regn[], int ndim, float (*fxn)(float [], float), int init,
wolffd@0: 	unsigned long ncall, int itmx, int nprn, float *tgral, float *sd,
wolffd@0: 	float *chi2a);
wolffd@0: void voltra(int n, int m, float t0, float h, float *t, float **f,
wolffd@0: 	float (*g)(int, float), float (*ak)(int, int, float, float));
wolffd@0: void wt1(float a[], unsigned long n, int isign,
wolffd@0: 	void (*wtstep)(float [], unsigned long, int));
wolffd@0: void wtn(float a[], unsigned long nn[], int ndim, int isign,
wolffd@0: 	void (*wtstep)(float [], unsigned long, int));
wolffd@0: void wwghts(float wghts[], int n, float h,
wolffd@0: 	void (*kermom)(double [], double ,int));
wolffd@0: int zbrac(float (*func)(float), float *x1, float *x2);
wolffd@0: void zbrak(float (*fx)(float), float x1, float x2, int n, float xb1[],
wolffd@0: 	float xb2[], int *nb);
wolffd@0: float zbrent(float (*func)(float), float x1, float x2, float tol);
wolffd@0: void zrhqr(float a[], int m, float rtr[], float rti[]);
wolffd@0: float zriddr(float (*func)(float), float x1, float x2, float xacc);
wolffd@0: void zroots(fcomplex a[], int m, fcomplex roots[], int polish);
wolffd@0: 
wolffd@0: #endif /* _NR_H_ */