Before I start, please accept my apologies that I'm a starter developer.
What I want is a grid with data. Only I have a list of an array with 7 points (x, y, value). I want to do this in a grid of 5x5. Only I miss a lot of values. I want to generate the missing values with help of an interpolation function. An algorithm to search through multi-dimension(or interpolation) (x, y) to generate a value for the other grids.
Grid example:
18 - 0 - 0 - 35 - 0
0 - 20 - 0 - 0 - 29
25 - 0 - 0 - 30 - 0
0 - 25 - 0 - 32 - 35
0 - 0 - 28 - 0 - 0
I used the method(from the numerical methods, algorithms and tools in c# book) and it's working, but i don't understand how to pass my values to the function and generate the random 5x5 missing values, because the functions and methods aren't explained in the book.
what is a zdata[,] double 2D array?, is this the values from the points? What are the xdate and the ydata?
Example, i have a array of 7 points (x,y,value)=> 0,0,18 etc. How can i pass correctly to this method to generate the missing values ?
Here is the whole function:
class InterpolationTest
{
static void Main(string[] args)
{
double[] xdata = new double[] { 0, 2 }; //x-coordinate 0 and 2?
double[] ydata = new double[] { 0, 2 }; //y-coordinate 0 and 2?
double[,] zdata = new double[,] { { 0, 20 }, { 20, 10 } }; //what is a zdata??
double[] x = new double[5];
double[] y = new double[5];
RMatrix z = new RMatrix(5, 5);
for (int i = 0; i < 4; i++)
{
x[i] = (i + 2.0) / 20.0;
y[i] = (i + 2.0) / 20.0;
}
RVector xvec = new RVector(x);
RVector yvec = new RVector(y);
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
z[i, j] = BilinearInterpolation(xdata, ydata, zdata, x[i], y[j]);
}
}
Console.Clear();
Console.WriteLine("Running Bilinear Interpolation Test\n\n");
Console.WriteLine("x = " + xvec.ToString());
Console.WriteLine("y = " + yvec.ToString());
Console.WriteLine("\nResults z = \n" + z.ToString() + "\n\n");
Console.WriteLine("Press ENTER key to continue...");
Console.ReadLine();
}
public static double BilinearInterpolation(double[] x, double[] y, double[,] z, double xval, double yval)
{
double zval = 0.0;
for (int i = 0; i < x.Length - 1; i++)
{
for (int j = 0; j < y.Length - 1; j++)
{
if (xval >= x[i] && xval < x[i + 1] && yval >= y[j] && yval < y[j + 1])
{
zval = z[i, j] * (x[i + 1] - xval) * (y[j + 1] - yval) / (x[i + 1] - x[i]) / (y[j + 1] - y[j]) +
z[i + 1, j] * (xval - x[i]) * (y[j + 1] - yval) / (x[i + 1] - x[i]) / (y[j + 1] - y[j]) +
z[i, j + 1] * (x[i + 1] - xval) * (yval - y[j]) / (x[i + 1] - x[i]) / (y[j + 1] - y[j]) +
z[i + 1, j + 1] * (xval - x[i]) * (yval - y[j]) / (x[i + 1] - x[i]) / (y[j + 1] - y[j]);
}
}
}
return zval;
}
public static double[] BilinearInterpolation(double[] x, double[] y, double[,] z, double[] xvals, double[] yvals)
{
double[] zvals = new double[xvals.Length];
for (int i = 0; i < xvals.Length; i++)
zvals[i] = BilinearInterpolation(x, y, z, xvals[i], yvals[i]);
return zvals;
}
}
public struct RMatrix
{
private int nRows;
private int nCols;
private double[,] matrix;
public RMatrix(int nCols, int nRows)
{
this.nRows = nRows;
this.nCols = nCols;
this.matrix = new double[nRows, nCols];
for (int i = 0; i < nRows; i++)
{
for (int j = 0; j < nCols; j++)
{
matrix[i, j] = 0.0;
}
}
}
public RMatrix(double[,] matrix)
{
this.nRows = matrix.GetLength(0);
this.nCols = matrix.GetLength(1);
this.matrix = matrix;
}
public RMatrix(RMatrix m)
{
nRows = m.GetnRows;
nCols = m.GetnCols;
matrix = m.matrix;
}
public RMatrix IdentityMatrix()
{
RMatrix m = new RMatrix(nRows, nCols);
for (int i = 0; i < nRows; i++)
{
for (int j = 0; j < nCols; j++)
{
if (i == j)
{
m[i, j] = 1;
}
}
}
return m;
}
public int GetnRows
{
get { return nRows; }
}
public int GetnCols
{
get { return nCols; }
}
public override string ToString()
{
string strMatrix = "(";
for (int i = 0; i < nRows; i++)
{
string str = "";
for (int j = 0; j < nCols - 1; j++)
{
str += matrix[i, j].ToString() + ", ";
}
str += matrix[i, nCols - 1].ToString();
if (i != nRows - 1 && i == 0)
strMatrix += str + "\n";
else if (i != nRows - 1 && i != 0)
strMatrix += " " + str + "\n";
else
strMatrix += " " + str + ")";
}
return strMatrix;
}
}
public struct RVector
{
private int ndim;
private double[] vector;
public RVector(int ndim)
{
this.ndim = ndim;
this.vector = new double[ndim];
for (int i = 0; i < ndim; i++)
{
vector[i] = 0.0;
}
}
public RVector(double[] vector)
{
this.ndim = vector.Length;
this.vector = vector;
}
public override string ToString()
{
string str = "(";
for (int i = 0; i < ndim - 1; i++)
{
str += vector[i].ToString() + ", ";
}
str += vector[ndim - 1].ToString() + ")";
return str;
}
}
Thanks
