int main(void)
{
int i,j,k,kk;
float xx,*x,*fvec,**fjac;
fjac=matrix(1,N,1,N);
fvec=vector(1,N);
x=vector(1,N);
for (kk=1;kk<=2;kk++) {
for (k=1;k<=3;k++) {
xx=0.2001*k*(2*kk-3);
printf("Starting vector number %2d\n",k);
for (i=1;i<=4;i++) {
x[i]=xx+0.2*i;
printf("%7s%1d%s %5.2f\n",
"x[",i,"] = ",x[i]);
}
printf("\n");
for (j=1;j<=NTRIAL;j++) {
mnewt(1,x,N,TOLX,TOLF);
usrfun(x,N,fvec,fjac);
printf("%5s %13s %13s\n","i","x[i]","f");
for (i=1;i<=N;i++)
printf("%5d %14.6f %15.6f\n",
i,x[i],fvec[i]);
printf("\npress RETURN to continue...\n");
(void) getchar();
}
}
}
free_vector(x,1,N);
free_vector(fvec,1,N);
free_matrix(fjac,1,N,1,N);
return 0;
}
/* ===========================================================================
get_spline x , y - spline points
xx, yy - output (allocated) spline interpolation
=========================================================================== */
void get_spline(int i_x[],int i_y[],int nwhisker_points, int min_x, int max_x, int **yy)
{
int i, status, x_val;
float *x, *y, *y2;
float y_val;
int start_ind, end_ind;
x = allocate_vector( 1, nwhisker_points );
y = allocate_vector( 1, nwhisker_points );
y2 = allocate_vector( 1, nwhisker_points );
for (i = 0; i<nwhisker_points; i++) {
x[i+1] = i_x[i] + 0.;
y[i+1] = i_y[i] + 0.;
}
*yy = allocate_ivector( min_x, max_x );
spline( x,y, y2, nwhisker_points ); /* calculate the 2nd derivatives of y at spline points */
for (x_val = min_x;x_val <= max_x; x_val++) {
status = splint( x, y, y2, nwhisker_points, (float) x_val, &y_val );
if (status != 1)
mexErrMsgTxt("bad spline");
(*yy)[x_val] = round ( y_val );
}
free_vector( x, 1,nwhisker_points);
free_vector( y, 1,nwhisker_points);
free_vector( y2, 1,nwhisker_points);
}
int main(void)
{
int i,j;
float h,x=1.0,*y,*dydx,*yout;
y=vector(1,N);
dydx=vector(1,N);
yout=vector(1,N);
y[1]=bessj0(x);
y[2]=bessj1(x);
y[3]=bessj(2,x);
y[4]=bessj(3,x);
derivs(x,y,dydx);
printf("\n%16s %5s %12s %12s %12s\n",
"Bessel function:","j0","j1","j3","j4");
for (i=1;i<=5;i++) {
h=0.2*i;
rk4(y,dydx,N,x,h,yout,derivs);
printf("\nfor a step size of: %6.2f\n",h);
printf("%12s","rk4:");
for (j=1;j<=4;j++) printf(" %12.6f",yout[j]);
printf("\n%12s %12.6f %12.6f %12.6f %12.6f\n","actual:",
bessj0(x+h),bessj1(x+h),bessj(2,x+h),bessj(3,x+h));
}
free_vector(yout,1,N);
free_vector(dydx,1,N);
free_vector(y,1,N);
return 0;
}
int main(void)
{
/* Test with Gauss-Hermite */
int i,n;
float amu0,check,*a,*b,*x,*w;
a=vector(1,NP);
b=vector(1,NP);
x=vector(1,NP);
w=vector(1,NP);
for (;;) {
printf("Enter N:\n");
if (scanf("%d",&n) == EOF) break;
for (i=1;i<n;i++) {
a[i]=0.0;
b[i+1]=i*0.5;
}
a[n]=0.0;
/* b[1] is arbitrary for call to tqli */
amu0=SQRTPI;
gaucof(n,a,b,amu0,x,w);
printf("%3s %10s %14s\n","#","x(i)","w(i)");
for (i=1;i<=n;i++) printf("%3d %14.6e %14.6e\n",i,x[i],w[i]);
for (check=0.0,i=1;i<=n;i++) check += w[i];
printf("\nCheck value: %15.7e should be: %15.7e\n",check,SQRTPI);
}
free_vector(w,1,NP);
free_vector(x,1,NP);
free_vector(b,1,NP);
free_vector(a,1,NP);
return 0;
}
void arma_linmin(double sdata[], int nobs, int ar_p, int ma_q, double *p,double *xi,int n,double *fret)
//double *p,*xi,*fret;
//long n;
{
long j;
double xx,xmin,fx,fb,fa,bx,ax,tol=1.0e-4;
double arma_brent(),f1dim(),*vector();
void arma_mnbrak(),free_vector();
int z;
double alpha[ar_p];
double beta[ma_q];
ncom=n;
pcom = vector(n);
xicom = vector(n);
//nrfunc = func;
for (j=0;j<n;j++){
pcom[j] = p[j];
xicom[j] = xi[j];
}
ax = 0.;
xx = 1.0;
bx = 2.0;
arma_mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim,sdata,nobs,ar_p,ma_q);
*fret=arma_brent(ax,xx,bx,f1dim,TOL,&xmin,sdata,nobs,ar_p,ma_q);
for(j=0;j<n;j++){
xi[j] *= xmin;
p[j] += xi[j];
}
free_vector(xicom);
free_vector(pcom);
}
void rk4(float y[], float dydx[], int n, float x, float h, float yout[],
void(*derivs)(float, float[], float[]))
{
int i;
float xh, hh, h6, *dym, *dyt, *yt;
dym = vector(1, n);
dyt = vector(1, n);
yt = vector(1, n);
hh = h*0.5;
h6 = h / 6.0;
xh = x + hh;
for (i = 1; i <= n; i++) yt[i] = y[i] + hh*dydx[i];
(*derivs)(xh, yt, dym);
for (i = 1; i <= n; i++){
yt[i] = y[i] + h*dym[i];
dym[i] += dyt[i];
}
(*derivs)(x + h, yt, dyt);
for (i = 1; i <= n; i++)
yout[i] = y[i] + h6*(dydx[i] + dyt[i] + 2.0*dym[i]);
free_vector(yt, 1, n);
free_vector(dyt, 1, n);
free_vector(dym, 1, n);
}
int main(void)
{
int i,j,nflag,nroot=0;
static float p[N+1]={10.0,-18.0,25.0,-24.0,16.0,-6.0,1.0};
float *b,*c;
b=vector(1,NTRY);
c=vector(1,NTRY);
printf("\nP(x)=x^6-6x^5+16x^4-24x^3+25x^2-18x+10\n");
printf("Quadratic factors x^2+bx+c\n\n");
printf("%6s %10s %12s \n\n","factor","b","c");
for (i=1;i<=NTRY;i++) {
c[i]=0.5*i;
b[i] = -0.5*i;
qroot(p,N,&b[i],&c[i],EPS);
if (nroot == 0) {
printf("%4d %15.6f %12.6f\n",nroot,b[i],c[i]);
nroot=1;
} else {
nflag=0;
for (j=1;j<=nroot;j++)
if ((fabs(b[i]-b[j]) < TINY)
&& (fabs(c[i]-c[j]) < TINY))
nflag=1;
if (nflag == 0) {
printf("%4d %15.6f %12.6f\n",nroot,b[i],c[i]);
++nroot;
}
}
}
free_vector(c,1,NTRY);
free_vector(b,1,NTRY);
return 0;
}
int main(void)
{
int i;
static float u[N+1]={-1.0,5.0,-10.0,10.0,-5.0,1.0};
static float v[NV+1]={1.0,3.0,3.0,1.0};
float *q,*r;
q=vector(0,N);
r=vector(0,N);
poldiv(u,N,v,NV,q,r);
printf("\n%10s %10s %10s %10s %10s %10s\n\n",
"x^0","x^1","x^2","x^3","x^4","x^5");
printf("quotient polynomial coefficients:\n");
for (i=0;i<=5;i++) printf("%10.2f ",q[i]);
printf("\nexpected quotient coefficients:\n");
printf("%10.2f %10.2f %10.2f %10.2f %10.2f %10.2f\n\n",
31.0,-8.0,1.0,0.0,0.0,0.0);
printf("remainder polynomial coefficients:\n");
for (i=0;i<=3;i++) printf("%10.2f ",r[i]);
printf("\nexpected remainder coefficients:\n");
printf("%10.2f %10.2f %10.2f %10.2f\n",-32.0,-80.0,-80.0,0.0);
free_vector(r,0,N);
free_vector(q,0,N);
return 0;
}
int main(void)
{
int i;
float a1=0.5976,a2=1.4023,a3=0.0,*y,*yout,*dfdx,**dfdy,*dydx;
y=vector(1,NVAR);
yout=vector(1,NVAR);
dfdx=vector(1,NVAR);
dfdy=matrix(1,NVAR,1,NVAR);
dydx=vector(1,NVAR);
y[1]=y[2]=1.0;
y[3]=0.0;
derivs(X1,y,dydx);
jacobn(X1,y,dfdx,dfdy,NVAR);
printf("Test Problem:\n");
for (i=5;i<=50;i+=5) {
simpr(y,dydx,dfdx,dfdy,NVAR,X1,HTOT,i,yout,derivs);
printf("\n%s %5.2f %s %5.2f %s %2d %s \n",
"x=",X1," to ",X1+HTOT," in ",i," steps");
printf("%14s %9s\n","integration","bessj");
printf("%12.6f %12.6f\n",yout[1],a1);
printf("%12.6f %12.6f\n",yout[2],a2);
printf("%12.6f %12.6f\n",yout[3],a3);
}
free_vector(dydx,1,NVAR);
free_matrix(dfdy,1,NVAR,1,NVAR);
free_vector(dfdx,1,NVAR);
free_vector(yout,1,NVAR);
free_vector(y,1,NVAR);
return 0;
}
int main(void)
{
unsigned long i,j;
float cmp,*data1,*data2,*ans;
data1=vector(1,N);
data2=vector(1,N);
ans=vector(1,N2);
for (i=1;i<=N;i++) {
if ((i > N/2-N/8) && (i < N/2+N/8))
data1[i]=1.0;
else
data1[i]=0.0;
data2[i]=data1[i];
}
correl(data1,data2,N,ans);
/* Calculate directly */
printf("%3s %14s %18s\n","n","CORREL","direct calc.");
for (i=0;i<=16;i++) {
cmp=0.0;
for (j=1;j<=N;j++)
cmp += data1[((i+j-1) % N)+1]*data2[j];
printf("%3ld %15.6f %15.6f\n",i,ans[i+1],cmp);
}
free_vector(ans,1,N2);
free_vector(data2,1,N);
free_vector(data1,1,N);
return 0;
}
int main(void)
{
float d,**a,**al,*b,*x;
unsigned long i,j,*indx;
long idum=(-1);
a=matrix(1,7,1,4);
x=vector(1,7);
b=vector(1,7);
al=matrix(1,7,1,2);
indx=lvector(1,7);
for (i=1;i<=7;i++) {
x[i]=ran1(&idum);
for (j=1;j<=4;j++) {
a[i][j]=ran1(&idum);
}
}
banmul(a,7,2,1,x,b);
for (i=1;i<=7;i++) printf("%ld %12.6f %12.6f\n",i,b[i],x[i]);
bandec(a,7,2,1,al,indx,&d);
banbks(a,7,2,1,al,indx,b);
for (i=1;i<=7;i++) printf("%ld %12.6f %12.6f\n",i,b[i],x[i]);
free_lvector(indx,1,7);
free_matrix(al,1,7,1,2);
free_vector(b,1,7);
free_vector(x,1,7);
free_matrix(a,1,7,1,4);
return 0;
}
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 rkck(float y[], float dydx[], int n, float x, float h,
float yout[], float yerr[], void (*derivs)(float, float [], float []));
int i;
float errmax,h,xnew,*yerr,*ytemp;
yerr=vector(1,n);
ytemp=vector(1,n);
h=htry;
for (;;) {
rkck(y,dydx,n,*x,h,ytemp,yerr,derivs);
errmax=0.0;
for (i=1;i<=n;i++) errmax=FMAX(errmax,fabs(yerr[i]/yscal[i]));
errmax /= eps;
if (errmax > 1.0) {
h=SAFETY*h*pow(errmax,PSHRNK);
if (h < 0.1*h) h *= 0.1;
xnew=(*x)+h;
if (xnew == *x) nrerror("stepsize underflow in rkqs");
continue;
} else {
if (errmax > ERRCON) *hnext=SAFETY*h*pow(errmax,PGROW);
else *hnext=5.0*h;
*x += (*hdid=h);
for (i=1;i<=n;i++) y[i]=ytemp[i];
break;
}
}
free_vector(ytemp,1,n);
free_vector(yerr,1,n);
}
int main(void)
{
int i,nbad,nok;
float eps=1.0e-4,h1=0.1,hmin=0.0,x1=1.0,x2=10.0,*ystart;
ystart=vector(1,N);
xp=vector(1,200);
yp=matrix(1,10,1,200);
ystart[1]=bessj0(x1);
ystart[2]=bessj1(x1);
ystart[3]=bessj(2,x1);
ystart[4]=bessj(3,x1);
nrhs=0;
kmax=100;
dxsav=(x2-x1)/20.0;
odeint(ystart,N,x1,x2,eps,h1,hmin,&nok,&nbad,derivs,rkqs);
printf("\n%s %13s %3d\n","successful steps:"," ",nok);
printf("%s %20s %3d\n","bad steps:"," ",nbad);
printf("%s %9s %3d\n","function evaluations:"," ",nrhs);
printf("\n%s %3d\n","stored intermediate values: ",kount);
printf("\n%8s %18s %15s\n","x","integral","bessj(3,x)");
for (i=1;i<=kount;i++)
printf("%10.4f %16.6f %14.6f\n",
xp[i],yp[4][i],bessj(3,xp[i]));
free_matrix(yp,1,10,1,200);
free_vector(xp,1,200);
free_vector(ystart,1,N);
return 0;
}
int main(void)
{
int i,j;
float x1x2,*x1,*x2,**y,**y2;
x1=vector(1,N);
x2=vector(1,N);
y=matrix(1,M,1,N);
y2=matrix(1,M,1,N);
for (i=1;i<=M;i++) x1[i]=0.2*i;
for (i=1;i<=N;i++) x2[i]=0.2*i;
for (i=1;i<=M;i++)
for (j=1;j<=N;j++) {
x1x2=x1[i]*x2[j];
y[i][j]=x1x2*x1x2;
}
splie2(x1,x2,y,M,N,y2);
printf("\nsecond derivatives from SPLIE2\n");
printf("natural spline assumed\n");
for (i=1;i<=5;i++) {
for (j=1;j<=5;j++) printf("%12.6f",y2[i][j]);
printf("\n");
}
printf("\nactual second derivatives\n");
for (i=1;i<=5;i++) {
for (j=1;j<=5;j++) printf("%12.6f",2.0*x1[i]*x1[i]);
printf("\n");
}
free_matrix(y2,1,M,1,N);
free_matrix(y,1,M,1,N);
free_vector(x2,1,N);
free_vector(x1,1,N);
return 0;
}
int main(void)
{
long idum=(-1984);
int i,mwt=1;
float a,abdev,b,chi2,q,siga,sigb;
float *x,*y,*sig;
x=vector(1,NDATA);
y=vector(1,NDATA);
sig=vector(1,NDATA);
for (i=1;i<=NPT;i++) {
x[i]=0.1*i;
y[i] = -2.0*x[i]+1.0+SPREAD*gasdev(&idum);
sig[i]=SPREAD;
}
fit(x,y,NPT,sig,mwt,&a,&b,&siga,&sigb,&chi2,&q);
printf("\nAccording to routine FIT the result is:\n");
printf(" a = %8.4f uncertainty: %8.4f\n",a,siga);
printf(" b = %8.4f uncertainty: %8.4f\n",b,sigb);
printf(" chi-squared: %8.4f for %4d points\n",chi2,NPT);
printf(" goodness-of-fit: %8.4f\n",q);
printf("\nAccording to routine MEDFIT the result is:\n");
medfit(x,y,NPT,&a,&b,&abdev);
printf(" a = %8.4f\n",a);
printf(" b = %8.4f\n",b);
printf(" absolute deviation (per data point): %8.4f\n",abdev);
printf(" (note: gaussian SPREAD is %8.4f)\n",SPREAD);
free_vector(sig,1,NDATA);
free_vector(y,1,NDATA);
free_vector(x,1,NDATA);
return 0;
}
int main(void)
{
long idum=(-11);
int i;
float b,rf,*x,*y;
x=vector(1,NDATA);
y=vector(1,NDATA);
ndatat=NDATA;
xt=x;
yt=y;
for (i=1;i<=NDATA;i++) {
x[i]=0.1*i;
y[i] = -2.0*x[i]+1.0+SPREAD*gasdev(&idum);
}
printf("%9s %9s %12s %10s\n","b","a","ROFUNC","ABDEVT");
for (i = -5;i<=5;i++) {
b = -2.0+0.02*i;
rf=rofunc(b);
printf("%10.2f %9.2f %11.2f %10.2f\n",
b,aa,rf,abdevt);
}
free_vector(y,1,NDATA);
free_vector(x,1,NDATA);
return 0;
}
void polcof(float xa[], float ya[], int n, float cof[])
{
void polint(float xa[], float ya[], int n, float x, float *y, float *dy);
int k,j,i;
float xmin,dy,*x,*y;
x=vector(0,n);
y=vector(0,n);
for (j=0;j<=n;j++) {
x[j]=xa[j];
y[j]=ya[j];
}
for (j=0;j<=n;j++) {
polint(x-1,y-1,n+1-j,0.0,&cof[j],&dy);
xmin=1.0e38;
k = -1;
for (i=0;i<=n-j;i++) {
if (fabs(x[i]) < xmin) {
xmin=fabs(x[i]);
k=i;
}
if (x[i]) y[i]=(y[i]-cof[j])/x[i];
}
for (i=k+1;i<=n-j;i++) {
y[i-1]=y[i];
x[i-1]=x[i];
}
}
free_vector(y,0,n);
free_vector(x,0,n);
}
int main(void)
{
long idum=(-51773);
int i,j;
float fctr1,fctr2,prob,t,*data1,*data2;
data1=vector(1,NPTS);
data2=vector(1,MPTS);
/* Generate two gaussian distributions of different variance */
fctr1=sqrt(VAR1);
for (i=1;i<=NPTS;i++) data1[i]=fctr1*gasdev(&idum);
fctr2=sqrt(VAR2);
for (i=1;i<=MPTS;i++)
data2[i]=NSHFT/2.0*EPS+fctr2*gasdev(&idum);
printf("\nDistribution #1 : variance = %6.2f\n",VAR1);
printf("Distribution #2 : variance = %6.2f\n\n",VAR2);
printf("%7s %8s %16s\n","shift","t","probability");
for (i=1;i<=NSHFT+1;i++) {
tutest(data1,NPTS,data2,MPTS,&t,&prob);
printf("%6.2f %10.2f %11.2f\n",(i-1)*EPS,t,prob);
for (j=1;j<=NPTS;j++) data1[j] += EPS;
}
free_vector(data2,1,MPTS);
free_vector(data1,1,NPTS);
return 0;
}
/* Free()s the given graph_node but NOT its command. */
static void free_graph_node(struct graph_node *node)
{
free_vector(node->input_files);
free_vector(node->output_files);
free_vector(node->node_deps);
free(node);
}
void cyclic(float a[], float b[], float c[], float alpha, float beta,
float r[], float x[], unsigned long n)
{
void tridag(float a[], float b[], float c[], float r[], float u[], unsigned long i;
unsigned long i;
float fact, gamma, *bb, *u, *z;
if (n <= 2) nrerror("n too small in cyclic");
bb = vector(1, n);
u = vector(1, n);
z = vector(1, n);
gamma = -b[1];
bb[1] = b[1] - gamma;
bb[n] = b[n] - alpha*beta / gamma;
for (i = 2; i < n; i++) bb[i] = b[i];
tridag(a, bb, c, r, x, n);
u[1] = gamma;
u[n] = alpha;
for (i = 2; i <= n; i++) u[i] = 0.0;
tridag(a, bb, c, u, z, n);
fact = (x[1] + beta*x[n] / gamma);
for (i = 1; i <= n; i++) x[i] -= fact*z[i];
free_vector(z, 1, n);
free_vector(u, 1, n);
free_vector(bb, 1, n);
}
int main(void)
{
unsigned long i;
int isign;
float *data1,*data2,*fft1,*fft2;
data1=vector(1,N);
data2=vector(1,N);
fft1=vector(1,N2);
fft2=vector(1,N2);
for (i=1;i<=N;i++) {
data1[i]=floor(0.5+cos(i*2.0*PI/PER));
data2[i]=floor(0.5+sin(i*2.0*PI/PER));
}
twofft(data1,data2,fft1,fft2,N);
printf("Fourier transform of first function:\n");
prntft(fft1,N);
printf("Fourier transform of second function:\n");
prntft(fft2,N);
/* Invert transform */
isign = -1;
four1(fft1,N,isign);
printf("inverted transform = first function:\n");
prntft(fft1,N);
four1(fft2,N,isign);
printf("inverted transform = second function:\n");
prntft(fft2,N);
free_vector(fft2,1,N2);
free_vector(fft1,1,N2);
free_vector(data2,1,N);
free_vector(data1,1,N);
return 0;
}
void j_linmin( double p[],double xi[],int n,double *fret,double (*func)(double x[], void *localdata),void *localdata)
{
int j;
double xx,xmin,fx,fb,fa,bx,ax;
J_LINMIN_STRUCT jls;
jls.ncom=n;
jls.pcom=vector(1,n);
jls.xicom=vector(1,n);
jls.nrfunc=func;
jls.localdata=localdata;
for (j=1;j<=n;j++) {
jls.pcom[j]=p[j];
jls.xicom[j]=xi[j];
}
ax=0.0;
xx=1.0;
bx=2.0;
j_mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,j_f1dim,(void *) &jls);
*fret=j_brent(ax,xx,bx,j_f1dim,TOL,&xmin,(void *) &jls);
for (j=1;j<=n;j++) {
xi[j] *= xmin;
p[j] += xi[j];
}
free_vector(jls.xicom,1,n);
free_vector(jls.pcom,1,n);
}
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 rkck(float y[], float dydx[], int n, float x, float h,
float yout[], float yerr[], void (*derivs)(float, float [], float []));
int i;
float errmax,h,htemp,xnew,*yerr,*ytemp;
yerr=vector(1,n);
ytemp=vector(1,n);
h=htry;
for (;;) {
rkck(y,dydx,n,*x,h,ytemp,yerr,derivs);
errmax=0.0;
for (i=1;i<=n;i++) errmax=FMAX(errmax,fabs(yerr[i]/yscal[i]));
errmax /= eps;
if (errmax <= 1.0) break;
htemp=SAFETY*h*pow(float(errmax),float(PSHRNK));
h=(h >= 0.0 ? FMAX(htemp,0.1*h) : FMIN(htemp,0.1*h));
xnew=(*x)+h;
if (xnew == *x) nrerror("stepsize underflow in rkqs");
}
if (errmax > ERRCON) *hnext=SAFETY*h*pow(float(errmax),float(PGROW));
else *hnext=5.0*h;
*x += (*hdid=h);
for (i=1;i<=n;i++) y[i]=ytemp[i];
free_vector(ytemp,1,n);
free_vector(yerr,1,n);
}
int main(void)
{
long idum=(-17);
int i,ibin,j;
float chsq,df,prob,x,*bins1,*bins2;
bins1=vector(1,NBINS);
bins2=vector(1,NBINS);
for (j=1;j<=NBINS;j++) {
bins1[j]=0.0;
bins2[j]=0.0;
}
for (i=1;i<=NPTS;i++) {
x=expdev(&idum);
ibin=(int) (x*NBINS/3.0+1);
if (ibin <= NBINS) ++bins1[ibin];
x=expdev(&idum);
ibin=(int) (x*NBINS/3.0+1);
if (ibin <= NBINS) ++bins2[ibin];
}
chstwo(bins1,bins2,NBINS,0,&df,&chsq,&prob);
printf("\n%15s %15s\n","dataset 1","dataset 2");
for (i=1;i<=NBINS;i++)
printf("%13.2f %15.2f\n",bins1[i],bins2[i]);
printf("\n%18s %12.4f\n","chi-squared:",chsq);
printf("%18s %12.4f\n","probability:",prob);
free_vector(bins2,1,NBINS);
free_vector(bins1,1,NBINS);
return 0;
}
/* following 3 routines do romberg integration on closed intervals */
void polint(float xa[], float ya[], int n, float x, float *y, float *dy)
{
int i,m,ns=1;
float den,dif,dift,ho,hp,w;
float *c,*d;
dif=fabs(x-xa[1]);
c=vector(1,n);
d=vector(1,n);
for (i=1;i<=n;i++) {
if ( (dift=fabs(x-xa[i])) < dif) {
ns=i;
dif=dift;
}
c[i]=ya[i];
d[i]=ya[i];
}
*y=ya[ns--];
for (m=1;m<n;m++) {
for (i=1;i<=n-m;i++) {
ho=xa[i]-x;
hp=xa[i+m]-x;
w=c[i+1]-d[i];
if ( (den=ho-hp) == 0.0) error("Error in routine polint");
den=w/den;
d[i]=hp*den;
c[i]=ho*den;
}
*y += (*dy=(2*ns < (n-m) ? c[ns+1] : d[ns--]));
}
free_vector(d,1,n);
free_vector(c,1,n);
}
int main(void)
{
int i,j;
float eps,hdid,hnext,htry,x=1.0,*y,*dydx,*dysav,*ysav,*yscal;
y=vector(1,N);
dydx=vector(1,N);
dysav=vector(1,N);
ysav=vector(1,N);
yscal=vector(1,N);
ysav[1]=bessj0(x);
ysav[2]=bessj1(x);
ysav[3]=bessj(2,x);
ysav[4]=bessj(3,x);
derivs(x,ysav,dysav);
for (i=1;i<=N;i++) yscal[i]=1.0;
htry=0.6;
printf("%10s %11s %12s %13s\n","eps","htry","hdid","hnext");
for (i=1;i<=15;i++) {
eps=exp((double) -i);
x=1.0;
for (j=1;j<=N;j++) {
y[j]=ysav[j];
dydx[j]=dysav[j];
}
rkqs(y,dydx,N,&x,htry,eps,yscal,&hdid,&hnext,derivs);
printf("%13f %8.2f %14.6f %12.6f \n",eps,htry,hdid,hnext);
}
free_vector(yscal,1,N);
free_vector(ysav,1,N);
free_vector(dysav,1,N);
free_vector(dydx,1,N);
free_vector(y,1,N);
return 0;
}
void dlinmin(float p[], float xi[], int n, float *fret, float (*func)(float []),
void (*dfunc)(float [], float []))
{
float dbrent(float ax, float bx, float cx,
float (*f)(float), float (*df)(float), float tol, float *xmin);
float f1dim(float x);
float df1dim(float x);
void mnbrak(float *ax, float *bx, float *cx, float *fa, float *fb,
float *fc, float (*func)(float));
int j;
float xx,xmin,fx,fb,fa,bx,ax;
ncom=n;
pcom=vector(1,n);
xicom=vector(1,n);
nrfunc=func;
nrdfun=dfunc;
for (j=1;j<=n;j++) {
pcom[j]=p[j];
xicom[j]=xi[j];
}
ax=0.0;
xx=1.0;
mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);
*fret=dbrent(ax,xx,bx,f1dim,df1dim,TOL,&xmin);
for (j=1;j<=n;j++) {
xi[j] *= xmin;
p[j] += xi[j];
}
free_vector(xicom,1,n);
free_vector(pcom,1,n);
}
void rk4(double y[], double dydx[], int n, double x, double h, double yout[],
void (*derivs)(double, double [], double []))
{
int i;
double xh, hh, h6, *dym, *dyt, *yt;
dym = vector(1,n); /* define vector! */
dyt = vector(1,n);
yt = vector(1,n);
hh = h*0.5;
h6 = h/6.0;
xh = x+hh;
for (i=1;i<=n;i++) yt[i]=y[i]+hh*dydx[i]; /* 1st step */
(*derivs)(xh,yt,dyt); /* 2nd step */
for (i=1;i<=n;i++) yt[i]=y[i]+hh*dyt[i];
(*derivs)(xh,yt,dym); /* 3rd step */
for (i=1;i<=n;i++)
{
yt[i]=y[i]+h*dym[i];
dym[i] += dyt[i];
}
(*derivs)(x+h,yt,dyt); /* 4th step */
for (i=1;i<=n;i++)
yout[i]=y[i]+h6*(dydx[i]+dyt[i]+2.0*dym[i]);
free_vector(yt,1,n);
free_vector(dyt,1,n);
free_vector(dym,1,n);
}
int main(void)
{
int i;
float b1,b2,b3,b4,xf=X1+HTOT,*y,*yout,*dydx;
y=vector(1,NVAR);
yout=vector(1,NVAR);
dydx=vector(1,NVAR);
y[1]=bessj0(X1);
y[2]=bessj1(X1);
y[3]=bessj(2,X1);
y[4]=bessj(3,X1);
derivs(X1,y,dydx);
b1=bessj0(xf);
b2=bessj1(xf);
b3=bessj(2,xf);
b4=bessj(3,xf);
printf("First four Bessel functions:\n");
for (i=5;i<=50;i+=5) {
mmid(y,dydx,NVAR,X1,HTOT,i,yout,derivs);
printf("\n%s %5.2f %s %5.2f %s %2d %s \n",
"x=",X1," to ",X1+HTOT," in ",i," steps");
printf("%14s %9s\n","integration","bessj");
printf("%12.6f %12.6f\n",yout[1],b1);
printf("%12.6f %12.6f\n",yout[2],b2);
printf("%12.6f %12.6f\n",yout[3],b3);
printf("%12.6f %12.6f\n",yout[4],b4);
printf("\nPress RETURN to continue...\n");
(void) getchar();
}
free_vector(dydx,1,NVAR);
free_vector(yout,1,NVAR);
free_vector(y,1,NVAR);
return 0;
}
int main(void)
{
int i,n;
float ak,alf=(-0.5),bet=(-0.5),checkw,checkx,xx,*x,*w;
x=vector(1,NP);
w=vector(1,NP);
for (;;) {
printf("Enter N\n");
if (scanf("%d",&n) == EOF) break;
gaujac(x,w,n,alf,bet);
printf("%3s %10s %14s\n","#","x(i)","w(i)");
for (i=1;i<=n;i++) printf("%3d %14.6e %14.6e\n",i,x[i],w[i]);
checkx=checkw=0.0;
for (i=1;i<=n;i++) {
checkx += x[i];
checkw += w[i];
}
printf("\nCheck value: %15.7e should be: %15.7e\n",
checkx,n*(bet-alf)/(alf+bet+2*n));
printf("\nCheck value: %15.7e should be: %15.7e\n",
checkw,exp(gammln(1.0+alf)+gammln(1.0+bet)-
gammln(2.0+alf+bet))*pow(2.0,alf+bet+1.0));
/* demonstrate the use of GAUJAC for an integral */
ak=0.5;
for (xx=0.0,i=1;i<=n;i++) xx += w[i]*func(ak,x[i]);
printf("\nIntegral from gaujac: %12.6f\n",xx);
printf("Actual value: %12.6f\n",2.0*ellf(PIBY2,ak));
}
free_vector(w,1,NP);
free_vector(x,1,NP);
return 0;
}