static void Main()
{
int NPoints = 10;
vector xs = new vector(NPoints);
vector ys = new vector(NPoints);
int i = 0;
double xa = -4.5;
double xb = 4.5;
double delta_x = (xb - xa) / (NPoints - 1);
for (double x = xa; x <= xb; x += delta_x)
{
xs[i] = x;
ys[i] = 1.0 / (1.0 + x * x);
Error.Write("{0} {1}\n", x, ys[i]);
i++;
}
qspline qspliner = new qspline(xs, ys);
cspline cspliner = new cspline(xs, ys);
for (double z = xa; z < xb; z += 0.05)
{
double linterp = linInterp.linterp(xs, ys, z);
double qinterp = qspliner.spline(z);
double cinterp = cspliner.spline(z);
Write("{0} {1} {2} {3}\n", z, linterp, qinterp, cinterp);
}
}
static int Main(String[] args)
{
double[] xs, ys;
// Make linear spline
if (args[0] == "lin")
{
// f(x) = x
if (args[1] == "1")
{
xs = new double[] { 1, 2, 3, 4, 5 };
ys = new double[] { 1, 2, 3, 4, 5 };
}
// f(x) = x**2
else if (args[1] == "2")
{
xs = new double[] { 1, 2, 3, 4, 5 };
ys = new double[] { 1, 4, 9, 16, 25 };
}
// f(x) = sin(x)
else
{
xs = new double[] { 0, PI / 4, PI / 2, 3 * PI / 4, PI, PI *5 / 4, PI *3 / 2,
PI *7 / 4, 2 * PI };
ys = new double[] { 0, 1 / Sqrt(2), 1, 1 / Sqrt(2), 0, -1 / Sqrt(2), -1,
-1 / Sqrt(2), 0 };
}
double eps = 1.0 / 16;
for (double z = xs[0]; z <= xs[xs.Length - 1]; z += eps)
{
WriteLine($"{z} {linterp(xs,ys,z)} {linterpInteg(xs,ys,z)}");
}
}
else if (args[0] == "quad")
{
qspline s;
if (args[1] == "1")
{
xs = new double[] { 1, 2, 3, 4, 5 };
ys = new double[] { 1, 2, 3, 4, 5 };
}
else if (args[1] == "2")
{
xs = new double[] { 1, 2, 3, 4, 5 };
ys = new double[] { 2, 3, 2, 4, 2 };
}
else
{
xs = new double[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
ys = new double[] { 1, 4, 9, 16, 25, 16, 9, 4, 1 };
}
s = new qspline(xs, ys);
double eps = 1.0 / 16;
for (double z = xs[0]; z <= xs[xs.Length - 1]; z += eps)
{
// data printed as z spline(z) deriv(z) int(z)
WriteLine($"{z} {s.spline(z)} {s.derivative(z)} {s.integral(z)}");
}
}
return(0);
}
static int Main()
{
int N = 2000, n = 20;
double z = 0;
double integration = 0;
double[] xs = new double[N];
double[] ys = new double[N];
System.IO.StreamWriter xyfile = new System.IO.StreamWriter("out-xy.txt", append: false);
for (int i = 0; i <= N - 1; i++)
{
xs[i] = 2.5 * PI * i / (N - 1);
ys[i] = Sin(xs[i]);
if (i == 0)
{
integration = 0;
}
else
{
integration += -Cos(xs[i]) + Cos(xs[i - 1]);
}
xyfile.WriteLine("{0} {1} {2} {3}", xs[i], ys[i], integration, Cos(xs[i]));
}
xyfile.Close();
var Q = new qspline(new vector(xs), new vector(ys));
System.IO.StreamWriter qinterpfile = new System.IO.StreamWriter("out-qinterp.txt", append: false);
for (int i = 0; i <= n; i++)
{
z = 2 * PI * i / (n - 1);
qinterpfile.WriteLine("{0} {1} ", z, Q.spline(z));
}
qinterpfile.Close();
System.IO.StreamWriter qintegratefile = new System.IO.StreamWriter("out-qintegrate.txt", append: false);
for (int i = 0; i <= n; i++)
{
z = 2 * PI * i / (n - 1);
qintegratefile.WriteLine("{0} {1} ", z, Q.integral(z));
}
qintegratefile.Close();
System.IO.StreamWriter qderivative = new System.IO.StreamWriter("out-qderivative.txt", append: false);
for (int i = 0; i <= n; i++)
{
z = 2 * PI * i / (n - 1);
qderivative.WriteLine("{0} {1} ", z, Q.derivative(z));
}
qderivative.Close();
return(0);
}
static int Main()
{
//test of qspline using Sin(x)
int n = 9; //number of sample points
//generate sample points:
vector x = new vector(n);
vector y = new vector(n);
var points = new System.IO.StreamWriter("points.txt");
for (int i = 0; i < n; i++)
{
x[i] = 2 * i * (PI / (n - 1));
y[i] = Sin(x[i]);
points.WriteLine($"{x[i]} {y[i]}");
} //end for
points.Close();
//using qspline
qspline qsin = new qspline(x, y);
//generating data to plot
var data = new System.IO.StreamWriter("data.txt");
int N = 100;
for (int i = 0; i < N; i++)
{
double xn = 2 * i * (PI / (N - 1));
data.WriteLine($"{xn} {Sin(xn)} {qsin.spline(xn)} {Cos(xn)} {qsin.derivative(xn)} {1-Cos(xn)} {qsin.integral(xn)}");
} //end for
data.Close();
//end of test using sine
WriteLine($"Part B:");
WriteLine($"Quadratic spline of Sin(x) can be seen in quadratic_splineB.svg.");
WriteLine($"The derivative of the aforementioned spline of can be seen in quadratic_derivativeB.svg, and the integral in quadratic_integralB.svg");
return(0);
}
static void Main()
{
vector[] data = generatedata.read_data("out_dataB.txt");
vector xs = data[0];
vector ys = data[1];
qspline qsplined = new qspline(xs, ys);
double minx = xs[0];
double maxx = xs[xs.size - 1];
double z;
for (z = minx; z < maxx; z += 0.1)
{
double qinterp = qsplined.spline(z);
double integral = qsplined.integral(z);
double derivative = qsplined.derivative(z);
WriteLine($"{z} {qinterp} {integral} {derivative}");
}
}
static void Main(string[] args)
{
vector[] testData = dataMaker.readFileToVector(args[0]);
vector xs = testData[0];
vector ys = testData[1];
qspline qspliner = new qspline(xs, ys);
double xa = xs[0];
double xb = xs[xs.size - 1];
double delta_z = 0.01;
for (double z = xa; z < xb; z += delta_z)
{
double interp = qspliner.spline(z);
double derivative = qspliner.derivative(z);
double integral = qspliner.integral(z);
Write("{0:f16} {1:f16} {2:f16} {3:f16}\n", z, interp, derivative, integral);
}
}
public static int Main()
{
int n = 6;
double x1 = 0, xend = 2 * PI;
vector xs = new vector(n);
vector ys = new vector(n);
System.IO.StreamWriter outputfile = new System.IO.StreamWriter("out-xydata.txt", append: false);
for (int i = 0; i < n; i++)
{
xs[i] = x1 + (xend - x1) / (n - 1) * i;
ys[i] = Sin(xs[i]);
outputfile.WriteLine("{0} {1}", xs[i], ys[i]);
}
outputfile.Close();
int N = 2000;
double z = 0;
double z1 = x1;
double zend = xend;
System.IO.StreamWriter outputfileSpline = new System.IO.StreamWriter("out-qSpline.txt", append: false);
System.IO.StreamWriter outputfileIntegral = new System.IO.StreamWriter("out-qIntegral.txt", append: false);
System.IO.StreamWriter outputfileDerivative = new System.IO.StreamWriter("out-qDerivative.txt", append: false);
qspline spline = new qspline(xs, ys);
for (int i = 0; i < N; i++)
{
z = z1 + (zend - z1) / (N - 1) * i;
outputfileSpline.WriteLine("{0} {1} {2}", z, spline.spline(z), Sin(z));
outputfileIntegral.WriteLine("{0} {1} {2}", z, spline.integral(z), 1 - Cos(z));
outputfileDerivative.WriteLine("{0} {1} {2}", z, spline.derivative(z), Cos(z));
}
outputfileSpline.Close();
outputfileIntegral.Close();
outputfileDerivative.Close();
return(0);
}
public static int Main()
{
// The interpolation routines will be tested on the function f(x) = sin(x)
double xmin = 0; // Minimum x value
double xmax = 3 * PI; // Maximum x value
misc.generate_data(f1, xmin, xmax, 0.5, "./datafiles/data.txt"); // Generate tabulated function values
misc.generate_data(f2, xmin, xmax, 0.5, "./datafiles/data2.txt"); // Generate tabulated integration values
misc.generate_data(f3, xmin, xmax, 0.5, "./datafiles/data3.txt"); // Generate tabulated integration values
// Load tabulated data values into double arrays
List <double[]> data = misc.load_data("./datafiles/data.txt");
double[] x = data[0];
double[] y = data[1];
int n = x.Length;
// Preparation of output files for plotting
var lspline_out = new System.IO.StreamWriter("./datafiles/lspline_out.txt", append: false);
var qspline_out = new System.IO.StreamWriter("./datafiles/qspline_out.txt", append: false);
var cspline_out = new System.IO.StreamWriter("./datafiles/cspline_out.txt", append: false);
var outfile = new System.IO.StreamWriter("./out.txt", append: false);
double dz = 0.01;
// Output files for linear interpolation
var res1 = new lspline(x, y);
for (double z = x[0]; z <= x[x.Length - 1]; z += dz)
{
lspline_out.WriteLine($"{z} {res1.spline(z)} {res1.integral(z)}");
}
lspline_out.Close();
// Output files for quadratic interpolation
var res2 = new qspline(x, y);
for (double z = x[0]; z <= x[x.Length - 1]; z += dz)
{
qspline_out.WriteLine($"{z} {res2.spline(z)} {res2.integral(z)} {res2.derivative(z)}");
}
qspline_out.Close();
// Output files for cubic interpolation
var res3 = new cspline(x, y);
for (double z = x[0]; z <= x[x.Length - 1]; z += dz)
{
cspline_out.WriteLine($"{z} {res3.spline(z)} {res3.integral(z)} {res3.derivative(z)}");
}
cspline_out.Close();
// Output files for comparsion of interpolation routines in terms of the integration values
outfile.WriteLine($"In the following, the interpolation routines are compared with their integration values.");
outfile.WriteLine($"For comparison, f(x) = sin(x) is interpolated and integrated from 0 to 2*pi (analytical value: 0).\n");
outfile.WriteLine($"Linear interpolation:");
outfile.WriteLine($"Integration result: {res1.integral(2*PI)}");
outfile.WriteLine($"Error: {0-res1.integral(2*PI)}\n");
outfile.WriteLine($"Quadratic interpolation:");
outfile.WriteLine($"Integration result: {res2.integral(2*PI)}");
outfile.WriteLine($"Error: {0-res2.integral(2*PI)}\n");
outfile.WriteLine($"Cubic interpolation:");
outfile.WriteLine($"Integration result: {res3.integral(2*PI)}");
outfile.WriteLine($"Error: {0-res3.integral(2*PI)}\n");
outfile.Close();
return(0);
}