plot for MKN463, CygnusA, NGC1068
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Thibault Barnouin
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// Compute the error from the uncertainties in the direction of polarizer's axes
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#include <iostream>
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#include <math.h>
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using namespace std;
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const double PI=3.14159265359;
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const double I = 8.42755038425555;
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const double Q = -0.7409864902131016;
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const double U = -1.079689321440609;
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const double k1 = 0.986; //from Kishimoto (1999)
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const double k2 = 0.976; //from Kishimoto (1999)
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const double k3 = 0.973; //from Kishimoto (1999)
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const double Theta1 = 180*PI/180.; //radians
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const double Theta2 = 60*PI/180.; //radians
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const double Theta3 = 120*PI/180.; //radians
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const double sigma_theta_1=3*PI/180.; //radians
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const double sigma_theta_2=3*PI/180.; //radians
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const double sigma_theta_3=3*PI/180.; //radians
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double A()
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{
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return k2*k3*sin(-2*Theta2+2*Theta3) + k3*k1*sin(-2*Theta3+2*Theta1) + k1*k2*sin(-2*Theta1+2*Theta2);
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}
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double Ap(int i) //A'_i
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{
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if(i==1) return 2*k3*k1*cos(-2*Theta3+2*Theta1) - 2*k1*k2*cos(-2*Theta1+2*Theta2);
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if(i==2) return -2*k2*k3*cos(-2*Theta2+2*Theta3) + 2*k1*k2*cos(-2*Theta1+2*Theta2);
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if(i==3) return 2*k2*k3*cos(-2*Theta2+2*Theta3) - 2*k3*k1*cos(-2*Theta3+2*Theta1);
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else return 0;
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}
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double Flux(int i) //f'_i
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{
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if(i==1) return I-(k1*cos(2*Theta1))*Q-(k1*sin(2*Theta1))*U;
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if(i==2) return I-(k2*cos(2*Theta2))*Q-(k2*sin(2*Theta2))*U;
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if(i==3) return I-(k3*cos(2*Theta3))*Q-(k3*sin(2*Theta3))*U;
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else return 0;
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}
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double coef(int i, int j) //a_ij
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{
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if(i==1 && j==1) return (1./A())*(k2*k3*sin(-2*Theta2+2*Theta3));
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if(i==1 && j==2) return (1./A())*(k3*k1*sin(-2*Theta3+2*Theta1));
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if(i==1 && j==3) return (1./A())*(k1*k2*sin(-2*Theta1+2*Theta2));
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if(i==2 && j==1) return (1./A())*(-k2*sin(2*Theta2)+k3*sin(2*Theta3));
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if(i==2 && j==2) return (1./A())*(-k3*sin(2*Theta3)+k1*sin(2*Theta1));
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if(i==2 && j==3) return (1./A())*(-k1*sin(2*Theta1)+k2*sin(2*Theta2));
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if(i==3 && j==1) return (1./A())*(k2*cos(2*Theta2)-k3*cos(2*Theta3));
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if(i==3 && j==2) return (1./A())*(k3*cos(2*Theta3)-k1*cos(2*Theta1));
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if(i==3 && j==3) return (1./A())*(k1*cos(2*Theta1)-k2*cos(2*Theta2));
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else return 0;
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}
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double g() // I_2 == Q
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{
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double a,b,c;
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a=coef(2,1)*Flux(1);
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b=coef(2,2)*Flux(2);
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c=coef(2,3)*Flux(3);
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return a+b+c;
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}
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double g_p() // I'_2 == Q'
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{
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double f=coef(2,1)*Flux(1)+coef(2,2)*Flux(2)+coef(2,3)*Flux(3);
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double fp=2*k2*cos(2*Theta2)*(k1*Q*cos(2*Theta1)+k1*U*sin(2*Theta1)-I)+(k1*sin(2*Theta1)-k3*sin(2*Theta3))*(2*k2*Q*sin(2*Theta2)-2*k2*U*cos(2*Theta2))-2*k2*cos(2*Theta2)*(k3*Q*cos(2*Theta3)+k3*U*sin(2*Theta3)-I);
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return (A()+fp-f*Ap(2))/(pow(A(),2));
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}
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double h() // I_3 == U
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{
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double a,b,c;
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a=coef(3,1)*Flux(1);
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b=coef(3,2)*Flux(2);
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c=coef(3,3)*Flux(3);
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return a+b+c;
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}
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double h_p() // I'_3 == U'
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{
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double f=coef(3,1)*Flux(1)+coef(3,2)*Flux(2)+coef(3,3)*Flux(3);
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double fp=-2*k3*sin(2*Theta3)*(k1*Q*cos(2*Theta1)+k1*U*sin(2*Theta1)-I)+2*k3*sin(2*Theta3)*(k2*Q*cos(2*Theta2)+k2*U*sin(2*Theta2)-I)+2*k3*(k2*cos(2*Theta2)-k1*cos(2*Theta1))*(U*cos(2*Theta3)-Q*sin(2*Theta3));
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return (A()+fp-f*Ap(3))/(pow(A(),2));
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}
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double k() // I_1 == I
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{
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double a,b,c;
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a=coef(1,1)*Flux(1);
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b=coef(1,2)*Flux(2);
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c=coef(1,3)*Flux(3);
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return a+b+c;
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}
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double k_p() // I'_1 == I'
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{
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double f=coef(1,1)*Flux(1)+coef(1,2)*Flux(2)+coef(1,3)*Flux(3);
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double fp=2*k1*k2*k3*sin(2*Theta2-2*Theta3)*(U*cos(2*Theta1)-Q*sin(2*Theta1))-2*k1*k3*cos(2*Theta1-2*Theta3)*(k2*Q*cos(2*Theta2)+k2*U*sin(2*Theta2)-I)+2*k1*k2*cos(2*Theta1-2*Theta2)*(k3*Q*cos(2*Theta3)+k3*U*sin(2*Theta3)-I);
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return (A()+fp-f*Ap(1))/(pow(A(),2));
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}
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double dTheta_i(int i)
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{
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double a,b,c;
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if(i==1) //partial derivative with i=1
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{
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a = g()*g_p();
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b = k();
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c = sqrt(pow(g(),2)+pow(h(),2));
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return a/(b*c);
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}
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if(i==2) //partial derivative with i=2
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{
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a = h()*h_p();
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b = k();
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c = sqrt(pow(g(),2)+pow(h(),2));
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return a/(b*c);
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}
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if(i==3) //partial derivative with i=3
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{
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a = k_p();
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b = sqrt(pow(g(),2)+pow(h(),2));
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c = pow(k(),2);
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return -a*b/c;
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}
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else return 0;
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}
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int main()
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{
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double sigma_stat_P;
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sigma_stat_P = 0;
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sigma_stat_P=pow(dTheta_i(1),2)*pow(sigma_theta_1,2)+pow(dTheta_i(2),2)*pow(sigma_theta_2,2)+pow(dTheta_i(3),2)*pow(sigma_theta_3,2);
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cout << "P: " << sqrt(Q*Q+U*U)/I << " +/- " << sqrt(sigma_stat_P) << endl;
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return 0;
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}
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