static int Main()
{
//the data:
//time
vector t = new vector(9);
t[0] = 1; t[1] = 2; t[2] = 3; t[3] = 4; t[4] = 6; t[5] = 9; t[6] = 10; t[7] = 13; t[8] = 15;
//activity
vector y = new vector(9);
y[0] = 117; y[1] = 100; y[2] = 88; y[3] = 72; y[4] = 53; y[5] = 29.5; y[6] = 25.2; y[7] = 15.2; y[8] = 11.1;
//vectors:
vector dy = new vector(y.size);
vector lny = new vector(y.size);
vector dlny = new vector(y.size);
var data = new System.IO.StreamWriter("data.txt");
for (int n = 0; n < y.size; n++)
{
dy[n] = y[n] / 20; //error on y
lny[n] = Log(y[n]);
dlny[n] = dy[n] / y[n]; //error Ln(y)
data.WriteLine($"{t[n]} {y[n]} {dy[n]}");
} //end for
data.Close();
//The function:
Func <double, double>[] f = new Func <double, double>[] { (x) => 1, (x) => - x };
//making the fit:
olsf fit = new olsf(t, lny, dlny, f);
//the calculated parameters:
vector a = fit.c;
//making a new function using the parameters:
Func <double, double> F = (x) => Exp(a[0]) * Exp(-a[1] * x);
//generating points to fit:
var fi = new System.IO.StreamWriter("fit.txt");
for (double n2 = 0; n2 < 20; n2 += 0.05)
{
fi.WriteLine($"{n2} {F(n2)}");
} //end for
fi.Close();
double hl = Log(2) / a[1]; //calculated half life
double hlt = 3.6319;
double devi = Abs(hlt / hl - 1) * 100;
WriteLine("Part A:");
WriteLine("In plotA.svg is a plot of the experimental data and my best calculated fit.");
WriteLine($"The moderen value for the half life of 224Ra is 3.6319 days, the value calulated from the fit is given as {Log(2)/a[1]} days. This is a deviation of {devi} %.");
return(0);
}
static int Main()
{
//time
vector t = new vector(9);
t[0] = 1; t[1] = 2; t[2] = 3; t[3] = 4; t[4] = 6; t[5] = 9; t[6] = 10; t[7] = 13; t[8] = 15;
//activity
vector y = new vector(9);
y[0] = 117; y[1] = 100; y[2] = 88; y[3] = 72; y[4] = 53; y[5] = 29.5; y[6] = 25.2; y[7] = 15.2; y[8] = 11.1;
//vectors:
vector dy = new vector(y.size);
vector lny = new vector(y.size);
vector dlny = new vector(y.size);
var data = new System.IO.StreamWriter("data.txt");
for (int n = 0; n < y.size; n++)
{
dy[n] = y[n] / 20;
lny[n] = Log(y[n]);
dlny[n] = dy[n] / y[n];
data.WriteLine($"{t[n]} {y[n]} {dy[n]}");
} //end for
data.Close();
Func <double, double>[] f = new Func <double, double>[] { (x) => 1, (x) => - x };
olsf fit = new olsf(t, lny, dlny, f);
vector a = fit.c;
Func <double, double> F = (x) => Exp(a[0]) * Exp(-a[1] * x);
vector dc = fit.dc;
Func <double, double> dFp = (x) => Exp(a[0] + dc[0]) * Exp(-(a[1] + dc[1]) * x);
Func <double, double> dFm = (x) => Exp(a[0] - dc[0]) * Exp(-(a[1] - dc[1]) * x);
var fi = new System.IO.StreamWriter("fit.txt");
for (double n2 = 0; n2 < 20; n2 += 0.05)
{
fi.WriteLine($"{n2} {F(n2)} {dFp(n2)} {dFm(n2)}");
} //end for
fi.Close();
WriteLine("Part C:");
WriteLine("The relevant figure is plotC.svg");
return(0);
}
static int Main(string[] args)
{
// input to vector...
var input = new System.IO.StreamReader("time_cyc.txt");
int input_lenght = 0;
while (input.ReadLine() != null)
{
input_lenght++;
}
input.Close();
input = new System.IO.StreamReader("time_cyc.txt");
vector N = new vector(input_lenght);
vector t = new vector(input_lenght);
string line;
for (int n = 0; n < input_lenght; n++)
{
line = input.ReadLine();
string[] words = line.Split(' ');
N[n] = double.Parse(words[0]);
t[n] = double.Parse(words[1]);
}
//end input to vector...
//using oslf to check O(n³)...
//function to fit:
var ft = new Func <double, double>[] { x => 1, x => x };
//error on time set to 1%:
vector dt = new vector(t.size);
vector lN = new vector(t.size);
vector lt = new vector(t.size);
for (int i = 0; i < t.size; i++)
{
lN[i] = Log(N[i]);
lt[i] = Log(t[i]);
dt[i] = lt[i] / 100;
} //end for
//using olsf:
olsf fit = new olsf(lN, lt, dt, ft);
WriteLine("Part B:");
WriteLine("");
WriteLine("i) Check that the time goes as O(n³).");
WriteLine($"By using my least square fit from Problem 3, i get that the time roughly depends of the matrix size N as t=N^(c), with c={fit.c[1]}.");
WriteLine("");
//check that eigenvalue by eigenvalue give same result as cyc
//new random matrix:
matrix A = randmatrix_sym(4, 4);
//using cyc:
jac_dia ja = new jac_dia(A);
int nr = 0; //number of rotation:
matrix V = new matrix(4, 4);
vector e1 = jac_dia_red(A, V, 4, ref nr);
WriteLine("ii) Implement the value-by-value method");
WriteLine("Check that the eigenvalues becomes the same as using cyclic sweeps.");
WriteLine("Random generated symmetic matrix A:");
for (int i = 0; i < A.size1; i++)
{
for (int k = 0; k < A.size1; k++)
{
Write($"{A[i,k]} ");
} //end for
Write("\n");
} //end for
Write("\n \n");
WriteLine("Calutaled eigenvalues:");
WriteLine("by cyclic: by value-by-value:");
for (int i = 0; i < ja.e.size; i++)
{
WriteLine($"{ja.e[i]} {e1[i]}");
} //end for
WriteLine("");
WriteLine("iii) and iv) Compare speed.");
WriteLine("In plot_time.svg the time used by the cyclic sweeps method to calculate alle the eigenvalues, is compared to the time used by the value-by-value method to calculate the first and all eigenvalue(s).");
WriteLine("It is faster to only calculate the first value by the value-by-value method then using cyclic sweeps. But cyclic sweeps is significant the calculated all eigenvalues by the value-by-value method.");
WriteLine("In plot_rotation.svg the number of rotationes is compared.");
WriteLine("");
//largest eigenvalue
matrix V2 = new matrix(4, 4);
int nr2 = 0;
vector eh = jac_dia_high_e(A, V2, 3, ref nr2);
WriteLine($"v) Largest eigenvalue.");
WriteLine($"By changing the theta angle from Atan2(2*Apq, Aq-Ap) to Atan2(-2*Apq, App-Aqq) the larges eigenvlaue can be calculated.");
WriteLine($"For vector A the value becomes: {eh[0]} the same as found by cyclic sweeps.");
return(0);
} // end Main
static int Main()
{
//the data:
//time
vector t = new vector(9);
t[0] = 1; t[1] = 2; t[2] = 3; t[3] = 4; t[4] = 6; t[5] = 9; t[6] = 10; t[7] = 13; t[8] = 15;
//activity
vector y = new vector(9);
y[0] = 117; y[1] = 100; y[2] = 88; y[3] = 72; y[4] = 53; y[5] = 29.5; y[6] = 25.2; y[7] = 15.2; y[8] = 11.1;
//vectors:
vector dy = new vector(y.size);
vector lny = new vector(y.size);
vector dlny = new vector(y.size);
//var data=new System.IO.StreamWriter("data.txt");
for (int n = 0; n < y.size; n++)
{
dy[n] = y[n] / 20; //error on y
lny[n] = Log(y[n]);
dlny[n] = dy[n] / y[n]; //error Ln(y)
//data.WriteLine($"{t[n]} {y[n]} {dy[n]}");
} //end for
//data.Close();
//The function:
Func <double, double>[] f = new Func <double, double>[] { (x) => 1, (x) => - x };
//making the fit:
olsf fit = new olsf(t, lny, dlny, f);
//the calculated parameters:
vector a = fit.c;
//making a new function using the parameters:
//Func<double, double> F= (x) => Exp(a[0])*Exp(-a[1]*x);
//generating points to fit:
/* var fi=new System.IO.StreamWriter("fit.txt");
* for(double n2=0; n2<20; n2+=0.05){
* fi.WriteLine($"{n2} {F(n2)}");
* }//end for
* fi.Close(); */
double hl = Log(2) / a[1]; //calculated half life
WriteLine("Part B:");
//WriteLine("In plotA.svg is a plot of the experimental data and my best calculated fit.");
//WriteLine($"The moderen value for the half life of 224Ra is 3.6319 days, the value calulated from the fit is given as {Log(2)/a[1]}. This is a deviation of {devi} %.");
matrix sigma = fit.Sigma;
WriteLine("The coveriance matrix to the fit displayed in plotA.svg takes the form:");
WriteLine($"{sigma[0,0]} {sigma[0,1]}");
WriteLine($"{sigma[1,0]} {sigma[1,1]}");
Write("\n");
vector dc = fit.dc;
WriteLine($"The calculated half life (with uncertainty is {hl} +/- {dc[1]/a[1]/a[1]*Log(2)} days. The moderen value for the half life of 224Ra is 3.6319 days, this means the the morderen value is not within estimated uncertainty.");
return(0);
}
