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patch_integrate_besselk_10oct16_1_500.c
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/* This is a c code that ought to fit a spectrum to a set of five measurements
at 22, 45, 150, 408, 1420 and 23G
The spectrum is a model containing a broken power law synthrotron
This version attempts to improve accuracy by scaling values
This version changes from adaptive integration to qromo for writing out the spectrum
in the 2000-6000 MHz range only in steps of 10 MHz.
This version fits using integration in gamma space rather than x=nu/nu_c
The output file generated is in 2 columns with frequency and temperature.
Output is read and processed for smoothness using fit_complex_spectrum_b.py
Original from Mayuri 03 Dec 2015
Modified by Ravi thereafter
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
//#include </usr/local/miriad/inc/maxdimc.h>
#include </home/mayuris/software/jnk/miriad/inc/linux64/maxdimc.h>
//#include </Users/mayuri/work/C/ANSI-C/nrutil.h>
#include </home/mayuris/work/HEALPy/codes/broken_pl_28dec15/nrutil.h>
//#include </Users/rsubrahm/CODESPACE/INCLUDE/nrutil.h>
//#include </usr/local/miriad/inc/miriad.h>
#include </home/mayuris/software/jnk/miriad/inc/miriad.h>
#include <string.h>
typedef double (*func1arg) (double);
void amoeba(float **p, float y[], int ndim, float ftol,
float (*funk)(float []), int *nfunk);
float amotry(float **p, float y[], float psum[], int ndim,
float (*funk)(float []), int ihi, float fac);
void mmbskr_(double *ARG,double *ORDER,int *N, double *BK, int *IER);
void adpint_(double *rint, double *xl, double *xu, double *reps, double *aeps,
double *dif, double (*func)(double), int *ier, int *npt, int *nmax);
double qromo(double (*func)(double), double a, double b,
double (*choose)(double(*)(double), double, double, int));
double midpnt(double (*func)(double), double a, double b, int n);
double qromo_alternate(double (*func)(double), double a, double b,
double (*choose)(double(*)(double), double, double, int));
double midpnt_alternate(double (*func)(double), double a, double b, int n);
void polint(double xa[], double ya[], int n, double x, double *y, double *dy);
void polint_alternate(double xa[], double ya[], int n, double x, double *y, double *dy);
/* functions for interpolation of recombination data
and conversion between brightness intensity and temperature */
void spline(float x[], float y[], int n, float yp1, float ypn, float y2[]);
void splint(float xa[], float ya[], float y2a[], int n, float x, float *y);
#define kk 1.3806488e-23 // m^2 kg s^-1
#define hh 6.62606957e-34 // m^2 kg s^-2 K^-1
#define cvel 2.99792458e+08 // m s^-1
#define m_e 9.1e-31
#define q_e 1.6e-19
#define sin_alph 1.0
#define Bmag 1e-9 // Tesla == 10 micro-Gauss
#define PI 3.14159265358979
#define FTOL 1.0e-6
#define T_e 8000.0 // Thermal electron temperature
#define TCMB 2.72548
#define NHPIX 3072
#define GSPAN 100.0
#define NN 5000 // length of array containing EoR spectrum
/* Global variables */
float *xx, *yy;
double xnu,xri,xrk,xrip,xrkp;
double nu,alpha1,alpha2,temp1,temp2,output,fnorm,fnorm1,fnorm2;
double AA,BB,C1,C2,D,ft,therm,fbreak;
int flag;
double nu_break;
float x,y;
float f1,f2;
float inttolf = 1.0e-8;
float difft[7];
double gama_min,gama_max,gama_break,scale_gam_nu;
int nrecurs = 10000000;
/* Evaulate bessel function of order 5/3, integrand */
double modbessik2(double u)
{
double ARG, ORDER, BK[1];
int N, IER;
xnu = 5.0/3.0;
ORDER = (double) xnu;
N = 1;
ARG = (double)(1.0/u);
mmbskr_(&ARG,&ORDER,&N,BK,&IER);
xrk = BK[0]/exp(ARG);
return (double)(xrk/(u*u));
}
/* Evaulate bessel function of order 5/3, integrand
float modbessik2float(float u)
{
double ARG, ORDER, BK[1];
int N, IER;
xnu = 5.0/3.0;
ORDER = (double) xnu;
N = 1;
ARG = (double)(1.0/u);
mmbskr_(&ARG,&ORDER,&N,BK,&IER);
xrk = BK[0]/exp(ARG);
return (float)(xrk/(u*u));
}
*/
double fofx1(double gama)
{
double p1,nu_c;
double integ;
double x;
double rint, xl, xu, reps, aeps, dif;
int ier, npt, nmax;
nu_c = (gama*gama*scale_gam_nu)/1.0e9; //GHz
x = ((double)nu/nu_c);
xl = (double)0.0;
xu = (double)(1/x);
reps = (double)inttolf;
aeps = (double)inttolf;
nmax = nrecurs;
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,modbessik2,&ier,&npt,&nmax);
//adapt_gq3(modbessik2,xl,xu,reps,&rint,&aeps,&npt);
// rint = (double)qromo(modbessik2float,(float)xl,(float)xu,midpnt);
p1 = (double)((2*C1) - 3.0);
integ = rint*pow(gama,-1.0*p1)*(x);
return integ;
}
double fofx1float(double gamafloat)
{
double p1,nu_c,gama;
double integ;
double x;
double rint, xl, xu, reps, aeps, dif;
int ier, npt, nmax;
gama = (double)gamafloat;
nu_c = (gama*gama*scale_gam_nu)/1.0e9; //GHz
x = ((double)nu/nu_c);
xl = (double)0.0;
xu = (double)(1/x);
reps = (double)inttolf;
aeps = (double)inttolf;
nmax = nrecurs;
// adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,modbessik2,&ier,&npt,&nmax);
// rint = (double)qromo_alternate(modbessik2float,(float)xl,(float)xu,midpnt_alternate);
rint = qromo_alternate(modbessik2,xl,xu,midpnt_alternate);
p1 = (double)((2*C1) - 3.0);
integ = rint*pow(gama,-1.0*p1)*(x);
return integ;
}
float func(float pp[])
{
int i;
double FFIT,nu_min,nu_max,nu_break,Tx,Te,nu_t,extn,d_alph;
float chisq,DDIF;
double rint, rint1, rint2, xl, xu, xb, reps, aeps, dif;
int ier, npt, nmax;
/* Use global variables C1 for temperature spectral index to pass to fofx1 */
fnorm = pow(10.0,(double)pp[1]);
alpha1 = pow(10.0,(double)pp[2]);
d_alph = pow(10.0,(double)pp[3]);
alpha2 = alpha1+d_alph;
nu_break = pow(10.0,(double)pp[4]);
Tx = pow(10.0,(double)pp[5]);
Te = pow(10.0,(double)pp[6]);
nu_t = pow(10.0,(double)pp[7]);
reps = (double)inttolf;
aeps = (double)inttolf;
nmax = nrecurs;
/* Impose conditions on parameters, If violated chisquare explodes */
if ( alpha1 < 2.0 || alpha1 > 3.0)
{ return 100000.0; }
if ( alpha2 < 2.0 || alpha2 > 3.0)
{ return 100000.0; }
if(Te < 0.0 || Te > 10000.0)
{ return 100000.0; }
/* Compute Chisquare */
chisq=0.0;
for (i=1;i<=6;i++)
{
nu = (double)xx[i];
nu_min = nu*1e9/(double)GSPAN;
nu_max = nu*1e9*(double)GSPAN;
gama_min = sqrt((double)(nu_min)/scale_gam_nu);
gama_max = sqrt((double)(nu_max)/scale_gam_nu);
gama_break = sqrt((double)(nu_break)/scale_gam_nu);
xl = (double)gama_min;
xu = (double)gama_max;
xb = (double)gama_break;
if(xl > xb)
{
C1 = alpha2;
//adapt_gq3(fofx1,xl,xu,reps,&rint,&aeps,&npt);
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else if(xu < xb)
{
C1 = alpha1;
//adapt_gq3(fofx1,xl,xu,reps,&rint,&aeps,&npt);
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else
{
xu = xb;
C1 = alpha1;
//adapt_gq3(fofx1,xl,xu,reps,&rint1,&aeps,&npt);
adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint1 *= pow((double)(gama_break),(double)(2*C1-3));
xl = xb;
xu = (double)gama_max;
C1 = alpha2;
//adapt_gq3(fofx1,xl,xu,reps,&rint2,&aeps,&npt);
adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint2 *= pow((double)(gama_break),(double)(2*C1-3));
rint = rint1 + rint2;
}
extn = exp((double)-1.0*pow((nu_t/nu),(double)2.1));
FFIT = fnorm*((pow(nu,-2.0)*rint) + Tx*pow(nu,-2.1))*extn + Te*((double)1.0-extn);
DDIF = (yy[i] - (float)FFIT)/yy[i];
difft[i]=(DDIF);
if (i <= 6) {chisq += (DDIF*DDIF);}
}
chisq /= 6.0;
return chisq;
}
float func1(float pp[])
{
int i;
double FFIT,d_alph,temp,Tx,Te,extn,nu_t;
float chisq,DDIF;
/* Use global variables C1 for temperature spectral index to pass to fofx1 */
fnorm1 = pow(10.0,(double)pp[1]);
alpha1 = pow(10.0,(double)pp[2]);
d_alph = pow(10.0,(double)pp[3]);
fnorm2 = pow(10.0,(double)pp[4]);
alpha2 = alpha1-d_alph;
Tx = pow(10.0,(double)pp[5]);
Te = pow(10.0,(double)pp[6]);
nu_t = pow(10.0,(double)pp[7]);
/* Impose conditions on parameters, If violated chisquare explodes */
if ( alpha1 < 2.0 || alpha1 > 3.0)
{ return 100000.0; }
if ( alpha2 < 2.0 || alpha2 > 3.0)
{ return 100000.0; }
if(Te < 0.0 || Te > 10000.0)
{ return 100000.0; }
/* Compute Chisquare */
chisq=0.0;
for (i=1;i<=6;i++)
{
extn = exp((double)-1.0*pow((nu_t/xx[i]),2.1));
temp = pow((double)xx[i],-1.0*alpha1) + fnorm2*pow((double)xx[i],-1.0*alpha2);
FFIT = fnorm1*(temp + Tx*pow(xx[i],-2.1))*extn + Te*((double)1.0-extn);
DDIF = (yy[i] - (float)FFIT)/yy[i];
difft[i]=DDIF;
if (i <= 6) {chisq += (DDIF*DDIF);}
}
chisq /= 6.0;
return chisq;
}
main()
{
static const char filename_22[] = "../../data/all_sky_maps_5deg/map_22_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_45[] = "../../data/all_sky_maps_5deg/map_45_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_150[] = "../../data/all_sky_maps_5deg/map_150_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_408[] = "../../data/all_sky_maps_5deg/map_408_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_1420[] = "../../data/all_sky_maps_5deg/map_1420_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_23G[] = "../../data/all_sky_maps_5deg/map_23000_r4_5deg_nested_galactic_Kelvin.txt";
static const char filename_fit_params[]="../../data/eor_sim/total_model_params_10oct16_1_500.txt";
static const char filename_pixel_spec[]="../../data/eor_sim/total_model_spec_10oct16_1_500.txt";
static const char filename_eor[]= "../../data/eor_sim/eor_Tb_values.dat";
double rint, rint1, rint2, xl, xu, xb, reps, aeps, dif,Tx,Te,extn, nu_t;
int ier, npt, nmax;
int npoints1;
float *xarray,*yarray,*y2;
float read1,read2;
float ffmin,ffmax;
float yp1,ypn,yf;
/* Variable declarations */
float *yamoeba,*afit,*aafit,*cof,**pfun,*yfit,*sky_22,
*sky_45,*sky_150,*sky_408,*sky_1420,*sky_23000;
FILE *fptr, *fptr1,*fptr2;
float read_value;
float break_freq;
float correction_150offset = 21.4; // Kelvin, Patra et al. 2015
float correction_150scaling = 1.05; // Patra et al. 2015
char inbuf[200];
float T_150,T_408,T_1420,T_23G,gama_1,gama_2,gama_3,nu_min,nu_max;
float chisq;
int i,ii,jj,j,nu_min_MHz,nu_max_MHz,nfunc;
xx = vector(1,6);
yy = vector(1,6);
yamoeba = vector(1,8);
afit = vector(1,7);
aafit = vector(1,7);
cof = vector(1,7);
pfun = matrix(1,8,1,7);
sky_22 = vector(1,NHPIX);
sky_45 = vector(1,NHPIX);
sky_150 = vector(1,NHPIX);
sky_408 = vector(1,NHPIX);
sky_1420 = vector(1,NHPIX);
sky_23000 = vector(1,NHPIX);
// read in the sky maps and coordinates; subtract CMB where necessary;
fptr=fopen(filename_22,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_22[i]=read_value;
++i;
}
fclose(fptr);
//printf(" Read %d values from 22 MHz image \n",i);
fptr=fopen(filename_45,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_45[i]=read_value;
++i;
}
fclose(fptr);
//printf(" Read %d values from 45 MHz image \n",i);
fptr=fopen(filename_150,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_150[i]=(read_value - correction_150offset)*correction_150scaling;
sky_150[i]= sky_150[i]-TCMB;
++i;
}
fclose(fptr);
//printf(" Read %d values from 150 MHz image \n",i);
fptr=fopen(filename_408,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_408[i]=read_value-TCMB;
++i;
}
fclose(fptr);
//printf(" Read %d values from 408 MHz image \n",i);
fptr=fopen(filename_1420,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_1420[i]=read_value-TCMB;
++i;
}
fclose(fptr);
//printf(" Read %d values from 1420 MHz image \n",i);
fptr=fopen(filename_23G,"r");
i=1;
while (fgets (inbuf, sizeof inbuf, fptr) != NULL)
{
sscanf(inbuf,"%g",&read_value);
sky_23000[i]=read_value;
++i;
}
fclose(fptr);
//printf(" Read %d values from 23000 MHz image \n",i);
int fflush(FILE *fptr);
fptr = fopen(filename_fit_params,"a+");
fptr2 = fopen(filename_pixel_spec,"a+");
scale_gam_nu = (double)(3.0*q_e*Bmag*sin_alph)/(4.0*PI*m_e*cvel);
for(ii=60; ii<76; ii++)
{
nu = powf(1.05,(float)ii)/1e3;
fprintf(fptr2,"%f ",nu);
}
for (ii=40; ii<201; ii++)
{
nu = (float)(ii)/1e3;
fprintf(fptr2,"%f ",nu);
}
for(ii=109; ii<210; ii++)
{
nu = powf(1.05,(float)ii)/1e3;
fprintf(fptr2,"%f ",nu);
}
fprintf(fptr2," \n");
/* Frequency in GHz */
xx[1]=0.022;
xx[2]=0.045;
xx[3]=0.150;
xx[4]=0.408;
xx[5]=1.420;
xx[6]=22.690;
reps = (double)inttolf;
aeps = (double)inttolf;
nmax = nrecurs;
// printf("Pixel alpha1 alpha2\n");
for (j=1;j<=500;++j)
{
printf("\n\n****************\n\nPixel number: %d\n",j);
{
yy[1] = sky_22[j];
yy[2] = sky_45[j];
yy[3] = sky_150[j];
yy[4] = sky_408[j];
yy[5] = sky_1420[j];
yy[6] = sky_23000[j];
printf("temperatures : %f %f %f %f %f %f \n",yy[1],yy[2],yy[3],yy[4],yy[5],yy[6]);
/* Spectral index between 45 MHz and 150 MHz */
alpha1 = (double)(log10f(yy[2]) - log10f(yy[3]))/(log10f(xx[3]) - log10f(xx[2]));
if(alpha1 < 2.0) alpha1 = 2.0001;
if(alpha1 > 3.0) alpha1 = 2.9999;
/* Spectral index between 408 MHz and 1420 MHz */
alpha2 = (double)(log10f(yy[4]) - log10f(yy[5]))/(log10f(xx[5]) - log10f(xx[4]));
if(alpha2 < 2.0) alpha2 = 2.0001;
if(alpha2 > 3.0) alpha2 = 2.9999;
// printf("%d %f %f\n",j,alpha1,alpha2);
nu_break = sqrt(0.150*0.408)*1e9;
Te = 8000.0;
nu_t = 0.001;
extn = (double)exp((double)-1.0*pow((nu_t/xx[5]),(double)2.1));
/* If data requires alpha2 steeper than alpha1, then model as synchrotron with break */
if(alpha1 < alpha2)
{
printf("Alpha2 steeper than alpha1! \n");
/* Initial computation of normalization */
nu = (double)1.420;
flag = 0;
nu_min = nu*1e9/GSPAN;
nu_max = nu*1e9*GSPAN;
gama_min = sqrt((double)(nu_min)/scale_gam_nu);
gama_max = sqrt((double)(nu_max)/scale_gam_nu);
gama_break = sqrt((double)(nu_break)/scale_gam_nu);
xb = gama_break;
xl = gama_min;
xu = gama_max;
if(xl > xb)
{
C1 = alpha2;
// adapt_gq3(fofx1,xl,xu,reps,&rint,&aeps,&npt);
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else if(xu < xb)
{
C1 = alpha1;
//adapt_gq3(fofx1,xl,xu,reps,&rint,&aeps,&npt);
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else
{
xu = xb;
C1 = alpha1;
//adapt_gq3(fofx1,xl,xu,reps,&rint1,&aeps,&npt);
adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint1 *= pow((double)(gama_break),(double)(2*C1-3));
xl = xb;
xu = (double)gama_max;
C1 = alpha2;
//adapt_gq3(fofx1,xl,xu,reps,&rint2,&aeps,&npt);
adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint2 *= pow((double)(gama_break),(double)(2*C1-3));
rint = rint1 + rint2;
}
fnorm = (double)(yy[5] - (Te*((double)1.0-(double)extn)))/((powf(nu,-2.0)*(float)rint)*extn);
printf("fnorm is %f\n",fnorm);
printf("rint is %f\n",rint);
printf("extn is %f\n",extn);
nu = (double)22.690;
nu_min = nu*1e9/GSPAN;
nu_max = nu*1e9*GSPAN;
gama_min = sqrt((double)(nu_min)/scale_gam_nu);
gama_max = sqrt((double)(nu_max)/scale_gam_nu);
gama_break = sqrt((double)(nu_break)/scale_gam_nu);
xb = gama_break;
xl = gama_min;
xu = gama_max;
if(xl > xb)
{
C1 = alpha2;
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else if(xu < xb)
{
C1 = alpha1;
adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else
{
xu = xb;
C1 = alpha1;
adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint1 *= pow((double)(gama_break),(double)(2*C1-3));
xl = xb;
xu = (double)gama_max;
C1 = alpha2;
adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint2 *= pow((double)(gama_break),(double)(2*C1-3));
rint = rint1 + rint2;
}
extn = exp((double)-1.0*pow((nu_t/nu),2.1));
temp1 = fnorm*extn;
Tx = (((yy[6] - Te*(1.0-extn))/temp1)-(powf(nu,-2.0)*(float)rint))/pow(xx[5],-2.1);
if (Tx <= 0.0)
{
Tx = (double)1.0e-10;
printf("Tx negative!\n");
}
printf("Te is %f\n",Te);
printf("Initial values of fnorm, alpha1, alpha2 fbreak (MHz), Tx, Te, nu_t: %e %f %f %f %e %f %f\n",fnorm,alpha1,alpha2,nu_break/1e6,Tx,Te,nu_t);
afit[1] = (float)log10(fnorm);
afit[2] = (float)log10(alpha1);
afit[3] = (float)log10(alpha2 - alpha1);
afit[4] = (float)log10(nu_break);
afit[5] = (float)log10(Tx);
afit[6] = (float)log10(Te);
afit[7] = (float)log10(nu_t);
chisq = func(afit);
printf("Chisq and sqrt(chisq) before optimization = %e %e \n",chisq,sqrtf(chisq));
printf(" differences: %f %f %f %f %f %f\n",
difft[1],difft[2],difft[3],difft[4],difft[5],difft[6]);
for(ii=1;ii<=8;ii++)
{
for(jj=1;jj<=7;jj++)
{
aafit[jj]=pfun[ii][jj]=(ii==(jj+1) ? afit[jj]*1.5 : afit[jj]);
}
yamoeba[ii]=func(aafit);
}
printf("Going to optimize\n");
amoeba(pfun,yamoeba,7,FTOL,func,&nfunc);
printf("\n OPTIMIZATION DONE\n\n");
cof[1]=pfun[1][1];
cof[2]=pfun[1][2];
cof[3]=pfun[1][3];
cof[4]=pfun[1][4];
cof[5]=pfun[1][5];
cof[6]=pfun[1][6];
cof[7]=pfun[1][7];
afit[1] = cof[1];
afit[2] = cof[2];
afit[3] = cof[3];
afit[4] = cof[4];
afit[5] = cof[5];
afit[6] = cof[6];
afit[7] = cof[7];
fnorm = powf(10.0,cof[1]);
printf("Fit variables fnorm, alpha1, alpha2, nu_break (MHz), Tx, Te, nu_t: %e %f %f %f %f %f %f\n",
fnorm,powf(10.0,cof[2]),powf(10.0,cof[3])+powf(10.0,cof[2]),powf(10.0,cof[4])/1e6,powf(10.0,cof[5]),powf(10.0,cof[6]),powf(10.0,cof[7]));
chisq = func(afit);
printf("Chisq and sqrt(chisq) after optimization = %e %e \n",chisq,sqrtf(chisq));
printf(" differences: %f %f %f %f %f %f \n",difft[1],difft[2],difft[3],difft[4],difft[5],difft[6]);
fprintf(fptr,"%d %d %f %f %f %f %f %f %f %f\n",j,flag,cof[1],cof[2],cof[3],cof[4],cof[5],cof[6],cof[7],chisq);
/* for(ii=60; ii<76; ii++) */
/* { */
/* nu = pow((double)1.05,(double)ii)/(double)1e3; */
/* nu_min = nu*1e9/GSPAN; */
/* nu_max = nu*1e9*GSPAN; */
/* gama_min = sqrt((nu_min)/scale_gam_nu); */
/* gama_max = sqrt((nu_max)/scale_gam_nu); */
/* xl = (double)gama_min; */
/* xu = (double)gama_max; */
/* fnorm = pow((double)10.0,(double)afit[1]); */
/* alpha1 = pow(10.0,(double)afit[2]); */
/* alpha2 = pow(10.0,(double)afit[3])+pow(10.0,(double)afit[2]); */
/* nu_break = pow(10.0,(double)afit[4]); */
/* gama_break = sqrt((nu_break)/scale_gam_nu); */
/* xb = (double)gama_break; */
/* Tx = pow((double)10.0,(double)afit[5]); */
/* Te = pow((double)10.0,(double)afit[6]); */
/* nu_t = pow((double)10.0,(double)afit[7]); */
/* if(xl > xb) */
/* { */
/* C1 = alpha2; */
/* adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint *= pow((double)(gama_break),(double)(2*C1-3)); */
/* } */
/* else if(xu < xb) */
/* { */
/* C1 = alpha1; */
/* adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint *= pow((double)(gama_break),(double)(2*C1-3)); */
/* } */
/* else */
/* { */
/* xu = xb; */
/* C1 = alpha1; */
/* adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint1 *= pow((double)(gama_break),(double)(2*C1-3)); */
/* xl = xb; */
/* xu = (double)gama_max; */
/* C1 = alpha2; */
/* adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint2 *= pow((double)(gama_break),(double)(2*C1-3)); */
/* rint = rint1 + rint2; */
/* } */
/* extn = exp((double)-1.0*pow((nu_t/nu),2.1)); */
/* output = fnorm*(powf(nu,-2.0)*(float)rint + Tx*pow(nu,-2.1))*extn + Te*(1.0-extn); */
/* fprintf(fptr2,"%20.15lf ",output); */
/* } */
for(ii=2000; ii<6001; ii=ii+10)
{
//printf(" Computing output spectrum at freq %d MHz \n",ii);
nu = (double)(ii)/(double)1e3;
nu_min = nu*(double)1e9/(double)GSPAN;
nu_max = nu*(double)1e9*(double)GSPAN;
gama_min = sqrt((nu_min)/scale_gam_nu);
gama_max = sqrt((nu_max)/scale_gam_nu);
xl = (double)gama_min;
xu = (double)gama_max;
fnorm = pow((double)10.0,(double)afit[1]);
alpha1 = pow(10.0,(double)afit[2]);
alpha2 = pow(10.0,(double)afit[3])+pow(10.0,(double)afit[2]);
nu_break = pow(10.0,(double)afit[4]);
gama_break = sqrt((nu_break)/scale_gam_nu);
xb = (double)gama_break;
Tx = pow((double)10.0,(double)afit[5]);
Te = pow((double)10.0,(double)afit[6]);
nu_t = pow((double)10.0,(double)afit[7]);
if(xl > xb)
{
C1 = alpha2;
// adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint = (double)qromo(fofx1float,(float)xl,(float)xu,midpnt);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else if(xu < xb)
{
C1 = alpha1;
// adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint = (double)qromo(fofx1float,(float)xl,(float)xu,midpnt);
rint *= pow((double)(gama_break),(double)(2*C1-3));
}
else
{
xu = xb;
C1 = alpha1;
// adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint1 = (double)qromo(fofx1float,(float)xl,(float)xu,midpnt);
rint1 *= pow((double)(gama_break),(double)(2*C1-3));
xl = xb;
xu = (double)gama_max;
C1 = alpha2;
// adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax);
rint2 = (double)qromo(fofx1float,(float)xl,(float)xu,midpnt);
rint2 *= pow((double)(gama_break),(double)(2*C1-3));
rint = rint1 + rint2;
}
extn = exp((double)-1.0*pow((nu_t/nu),2.1));
output = fnorm*(powf(nu,-2.0)*(float)rint + Tx*pow(nu,-2.1))*extn + Te*(1.0-extn);/* + (double)yf */
fprintf(fptr2,"%20.15lf ",output);
}
/* for(ii=109; ii<210; ii++) */
/* { */
/* nu = pow((double)1.05,(double)ii)/(double)1e3; */
/* nu_min = nu*1e9/GSPAN; */
/* nu_max = nu*1e9*GSPAN; */
/* gama_min = sqrt((nu_min)/scale_gam_nu); */
/* gama_max = sqrt((nu_max)/scale_gam_nu); */
/* xl = (double)gama_min; */
/* xu = (double)gama_max; */
/* fnorm = pow((double)10.0,(double)afit[1]); */
/* alpha1 = pow(10.0,(double)afit[2]); */
/* alpha2 = pow(10.0,(double)afit[3])+pow(10.0,(double)afit[2]); */
/* nu_break = pow(10.0,(double)afit[4]); */
/* gama_break = sqrt((nu_break)/scale_gam_nu); */
/* xb = (double)gama_break; */
/* Tx = pow((double)10.0,(double)afit[5]); */
/* Te = pow((double)10.0,(double)afit[6]); */
/* nu_t = pow((double)10.0,(double)afit[7]); */
/* if(xl > xb) */
/* { */
/* C1 = alpha2; */
/* adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint *= pow((double)(gama_break),(double)(2*C1-3)); */
/* } */
/* else if(xu < xb) */
/* { */
/* C1 = alpha1; */
/* adpint_(&rint,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint *= pow((double)(gama_break),(double)(2*C1-3)); */
/* } */
/* else */
/* { */
/* xu = xb; */
/* C1 = alpha1; */
/* adpint_(&rint1,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint1 *= pow((double)(gama_break),(double)(2*C1-3)); */
/* xl = xb; */
/* xu = (double)gama_max; */
/* C1 = alpha2; */
/* adpint_(&rint2,&xl,&xu,&reps,&aeps,&dif,fofx1,&ier,&npt,&nmax); */
/* rint2 *= pow((double)(gama_break),(double)(2*C1-3)); */
/* rint = rint1 + rint2; */
/* } */
/* extn = exp((double)-1.0*pow((nu_t/nu),2.1)); */
/* output = fnorm*(powf(nu,-2.0)*(float)rint + Tx*pow(nu,-2.1))*extn + Te*(1.0-extn); */
/* fprintf(fptr2,"%20.15lf ",output); */
/* } */
fprintf(fptr2,"\n");
/********************************************/
}
/* If data requires alpha2 flatter than alpha1, then model as sum of power laws, i.e. steep and flat spectrum sources */
else
{
printf("alpha2 flatter than alpha1!\n");
flag = 1;
/* Initial computation of normalization of the form: T(nu) = fnorm1*(nu^-alpha1) + fnorm2*(nu^-alpha2) */
fnorm1 = yy[3]/(pow(xx[3],-1.0*alpha1));
fnorm2 = (yy[4]/(pow(xx[4],-1.0*alpha2)))/fnorm1;
extn = exp((double)-1.0*pow((nu_t/xx[6]),2.1));
Tx = ((double)1.0/pow(xx[6],-2.1))*(((yy[6]-Te*((double)1.0-extn))/(fnorm1*extn))-((pow(xx[6],-1.0*alpha1))+(fnorm2*pow(xx[6],-1.0*alpha2))));
if (Tx <=0.0)
{
printf("Tx negative!\n");
Tx = (double)1.0e-10;
}
afit[1] = (float)log10(fnorm1);
afit[2] = (float)log10(alpha1);
afit[3] = (float)log10(alpha1 - alpha2);
afit[4] = (float)log10(fnorm2);
afit[5] = (float)log10(Tx);
afit[6] = (float)log10(Te);
afit[7] = (float)log10(nu_t);
printf("Initial values of fnorm1, alpha1, alpha1-alpha2 fnorm2: %e %f %f %f %f %f %f\n",fnorm1,alpha1,alpha2,fnorm2,Tx,Te,nu_t);
chisq = func1(afit);
printf("Chisq and sqrt(chisq) before optimization = %e %e \n",chisq,sqrtf(chisq));
printf(" differences: %f %f %f %f %f %f\n",
difft[1],difft[2],difft[3],difft[4],difft[5],difft[6]);
for(ii=1;ii<=8;ii++)
{
for(jj=1;jj<=7;jj++)
{
aafit[jj]=pfun[ii][jj]=(ii==(jj+1) ? afit[jj]*1.5 : afit[jj]);
}
yamoeba[ii]=func1(aafit);
}
amoeba(pfun,yamoeba,7,FTOL,func1,&nfunc);
printf("\n OPTIMIZATION DONE\n\n");
cof[1]=pfun[1][1];
cof[2]=pfun[1][2];
cof[3]=pfun[1][3];
cof[4]=pfun[1][4];
cof[5]=pfun[1][5];
cof[6]=pfun[1][6];
cof[7]=pfun[1][7];
afit[1] = cof[1];
afit[2] = cof[2];
afit[3] = cof[3];
afit[4] = cof[4];
afit[5] = cof[5];
afit[6] = cof[6];
afit[7] = cof[7];
fnorm1 = pow(10.0,(double)cof[1]);
fnorm2 = pow(10.0,(double)cof[4]);
alpha1 = pow(10.0,(double)cof[2]);
alpha2 = alpha1 - pow(10.0,(double)cof[3]);
printf("Fit variables fnorm1, alpha1, alpha2, fnorm2: %e %f %f %f\n",
fnorm1,powf(10.0,cof[2]),powf(10.0,cof[2])-powf(10.0,cof[3]),fnorm2);
Tx = pow((double)10.0,(double)afit[5]);
Te = pow((double)10.0,(double)afit[6]);
nu_t = pow((double)10.0,(double)afit[7]);
chisq = func1(afit);
printf("Chisq and sqrt(chisq) after optimization = %e %e \n",chisq,sqrtf(chisq));
printf(" differences: %f %f %f %f %f %f \n",difft[0],difft[1],difft[2],difft[3],difft[4],difft[5]);
fprintf(fptr,"%d %d %f %f %f %f %f %f %f %f\n",j,flag,fnorm1,cof[2],cof[3],fnorm2,cof[5],cof[6],cof[7],chisq);
/* for(ii=60; ii<76; ii++) */
/* { */
/* nu = powf(1.05,(float)ii)/1e3; */
/* extn = exp((double)-1.0*pow((nu_t/nu),(double)2.1)); */
/* output = fnorm1*(pow(nu,-1.0*alpha1) + fnorm2*(pow(nu,-1.0*alpha2)) + Tx*pow(nu,-2.1))*extn + Te*((double)1.0 - extn); */
/* fprintf(fptr2,"%20.15lf ",output); */
/* } */
for(ii=2000; ii<6001; ii=ii+10)
{
nu = (float)(ii)/1e3;
extn = exp((double)-1.0*pow((nu_t/nu),(double)2.1));
output = fnorm1*(pow(nu,-1.0*alpha1) + fnorm2*(pow(nu,-1.0*alpha2)) + Tx*pow(nu,-2.1))*extn + Te*((double)1.0 - extn);
fprintf(fptr2,"%20.15lf ",output);
}
/* for(ii=109; ii<210; ii++) */
/* { */
/* nu = powf(1.05,(float)ii)/1e3; */
/* extn = exp((double)-1.0*pow((nu_t/nu),(double)2.1)); */
/* output = fnorm1*(pow(nu,-1.0*alpha1) + fnorm2*(pow(nu,-1.0*alpha2)) + Tx*pow(nu,-2.1))*extn + Te*((double)1.0 - extn); */
/* fprintf(fptr2,"%20.15lf ",output); */
/* } */
fprintf(fptr2," \n");
}
}
}
fclose(fptr);
fclose(fptr2);
free_vector(sky_22,1,NHPIX);
free_vector(sky_45,1,NHPIX);
free_vector(sky_150,1,NHPIX);
free_vector(sky_408,1,NHPIX);
free_vector(sky_1420,1,NHPIX);
free_vector(sky_23000,1,NHPIX);
free_vector(xx,1,6);
free_vector(yy,1,6);
free_vector(yamoeba,1,7);
free_vector(afit,1,7);
free_vector(aafit,1,7);
free_matrix(pfun,1,8,1,7);
free_vector(cof,1,7);
}