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