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funcs.c
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funcs.c
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/* ----------------------------------------------------
This has various functions - needed in cosmology
Df(aa) - calculates normalized D(a) (growing mode) at scale factor
aa=1/(1+z) D(1) = 1
ff(aa) - calculates f(a) (dlnD/dlna) at scale factor aa=1/(1+z)
ONLY works for FRW universe with ordinary matter (vomegam), cosmological
constant(vomegalam) and curvature(1.0-vomegam-vomegalam).
Also calculates a random number (routine copied from NRC) ran1(long *)
/*---------------------------------------------------------------------------*/
#include<stdio.h>
#include<math.h>
#define FUNC(x) ((*func)(x))
#define EPS1 1.0e-4 /* Fractional accuracy */
#define JMAX 20
extern float vhh,vomegam,vomegalam;
/* Hubble parameter,Omega-Matter,Cosmological Const */
/*---------------------------------------------------------------------------*/
/* Does integration using trapezoidal rule */
/*---------------------------------------------------------------------------*/
float trapzd(float (*func)(float), float a, float b, int n)
{
float x,tnm,sum,del;
static float s;
int it,j;
if (n == 1) {
return (s=0.5*(b-a)*(FUNC(a)+FUNC(b)));
} else {
for (it=1,j=1;j<n-1;j++) it <<= 1;
tnm=it;
del=(b-a)/tnm;
x=a+0.5*del;
for (sum=0.0,j=1;j<=it;j++,x+=del) sum += FUNC(x);
s=0.5*(s+(b-a)*sum/tnm);
return s;
}
}
float qtrap(float (*func)(float), float a, float b)
{
float trapzd(float (*func)(float), float a, float b, int n);
int j;
float s,olds;
float dummy;
olds = -1.0e30;
for (j=1;j<=JMAX;j++) {
s=trapzd(func,a,b,j);
if (fabs(s-olds) < EPS1*fabs(olds)) return s;
olds=s;
}
printf("\nToo many steps in routine qtrap...exiting routine...\n");
return 0.0; /* Never gets here normally */
}
/*---------------------------------------------------------------------------*/
/*Trapezoidal Rule done */
/*---------------------------------------------------------------------------*/
float Hf(float aa)
{
return(sqrt(vomegam*pow(aa,-3.) + (1.0-vomegam-vomegalam)*pow(aa,-2.)+ vomegalam));
}
float qf(float aa)
{
return(0.5*(vomegam*pow(aa,-3.0) - 2.0*vomegalam)/(Hf(aa)*Hf(aa)));
}
float Integrandf(float aa)
{
return(pow(aa*Hf(aa),-3.0));
}
float Integralf(float aa)
{
/* The Integrand blows up at 0.0 so we take a small step 0.0001 */
return( qtrap(Integrandf,0.00001,aa) );
}
/*---------------------------------------------------------------------------*/
/*Returns the growing mode of denisty perturbation normalized to unity at present */
/*---------------------------------------------------------------------------*/
float Df(float aa)
{
return( Hf(aa)*Integralf(aa)/( Hf(1.0)*Integralf(1.0) ) );
}
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/*Returns the logarithmic derivative of the growing mode of denisty perturbatio */
/*---------------------------------------------------------------------------*/
float ff(float aa)
{
return( (1.0/( aa*aa*pow(Hf(aa),3.0)*Integralf(aa) ) ) - (1.0 + qf(aa) ) );
}
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* function ran1 copied from Numerical Recipes*/
/*---------------------------------------------------------------------------*/
#define IA 16807
#define IM 2147483647
#define AM (1.0/IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)
float ran1(long *idum)
{
int j;
long k;
static long iy=0;
static long iv[NTAB];
float temp;
if (*idum <= 0 || !iy) {
if (-(*idum) < 1) *idum=1;
else *idum = -(*idum);
for (j=NTAB+7;j>=0;j--) {
k=(*idum)/IQ;
*idum=IA*(*idum-k*IQ)-IR*k;
if (*idum < 0) *idum += IM;
if (j < NTAB) iv[j] = *idum;
}
iy=iv[0];
}
k=(*idum)/IQ;
*idum=IA*(*idum-k*IQ)-IR*k;
if (*idum < 0) *idum += IM;
j=iy/NDIV;
iy=iv[j];
iv[j] = *idum;
if ((temp=AM*iy) > RNMX) return RNMX;
else return temp;
}
#undef IA
#undef IM
#undef AM
#undef IQ
#undef IR
#undef NTAB
#undef NDIV
#undef EPS
#undef RNMX
#undef EPS1
#undef FUNC
#undef JMAX
/*---------------------------------------------------------------------------*/
/* ran1 done*/
/*---------------------------------------------------------------------------*/
/*---------------------------------------------------------------------------*/
/* function gasdev copied from Numerical Recipes*/
/*---------------------------------------------------------------------------*/
float gasdev(long *idum)
{
float ran1(long *idum);
static int iset=0;
static float gset;
float fac,rsq,v1,v2;
if (iset == 0) {
do {
v1=2.0*ran1(idum)-1.0;
v2=2.0*ran1(idum)-1.0;
rsq=v1*v1+v2*v2;
} while (rsq >= 1.0 || rsq == 0.0);
fac=sqrt(-2.0*log(rsq)/rsq);
gset=v1*fac;
iset=1;
return v2*fac;
} else {
iset=0;
return gset;
}
}
/*---------------------------------------------------------------------------*/
/* gasdev done*/
/*---------------------------------------------------------------------------*/