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Thread: approximate derivative of matrix
 07062011, 11:35 PM #1Member
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approximate derivative of matrix
The assignment question is: "Approximate the derivative of a matrix with respect to X"
Using this formula to create a new matrix from the original int[][] m:
m′[i][j] = (m[i−1][j +1]−m[i−1][j −1])+2∗(m[i][j +1]−m[i][j −1])+(m[i+1][j +1]−m[i+1][j −1]
Also, boundary cases (ex: m[0][0]) must be treated differently. For example, if the formula says to take m[1][0], you should use the value for m[0][0] instead.
This is the code i have written so far:
public static int[][] approximateDerivativeX(int[][] m) {
int h = m.length;
int w = m[0].length;
int[][] derivativeXArray = new int[h][w];
for (int i=0; i < h; i++) {
for (int j=0; j < w; j++) {
if (i==0 && j==0) {
derivativeXArray[i][j] = 2*(m[i][j+1]m[i][j]);
}
else if (i==0 && j!=0 && j < w1) {
derivativeXArray[i][j] = (m[i][j+1]m[i][j1]) + 2*(m[i][j+1]m[i][j1]) + (m[i+1][j+1]m[i+1][j1]);
}
else if (i==0 && j==w1) {
derivativeXArray[i][j] = (m[i][j]m[i][j1]) + 2*(m[i][j]m[i][j1]) + (m[i+1][j]m[i+1][j1]);
}
else if (i!=0 && i < h1 && j==0) {
derivativeXArray[i][j] = (m[i1][j+1]m[i1][j]) + 2*(m[i][j+1]m[i][j]) + (m[i+1][j+1]m[i+1][j]);
}
else if (i!=0 && i < h1 && j!=0 && j < w1) {
derivativeXArray[i][j] = (m[i1][j+1]m[i1][j1]) + 2*(m[i][j+1]m[i][j1]) + (m[i+1][j+1]m[i+1][j1]);
}
else if (i!=0 && i < h1 && j==w1) {
derivativeXArray[i][j] = (m[i1][j]m[i1][j1]) + 2*(m[i][j]m[i][j1]) + (m[i+1][j]m[i+1][j1]);
}
else if (i==h1 && j==0) {
derivativeXArray[i][j] = (m[i1][j+1]m[i1][j]) + 2*(m[i][j+1]m[i][j]) + (m[i][j+1]m[i][j]);
}
else if (i==h1 && j!=0 && j < w1) {
derivativeXArray[i][j] = (m[i1][j+1]m[i1][j1]) + 2*(m[i][j+1]m[i][j1]) + (m[i][j+1]m[i][j1]);
}
else if (i==h1 && j==w1) {
derivativeXArray[i][j] = (m[i1][j]m[i1][j1]) + 2*(m[i][j]m[i][j1]) + (m[i][j]m[i][j1]);
}
}
}
return derivativeXArray;
}
If the original matrix is this:
7 2 2 5 5
8 8 1 1 4
8 4 1 8 0
0 9 8 6 2
3 1 5 3 1
Then the derivative with respect to x should be:
10 17 1 9 3
9 26 7 8 2
1 13 2 5 17
12 11 0 17 18
5 12 1 14 8
But the output I am getting is:
10 22 2 12 3
9 26 7 8 2
1 13 2 5 17
12 11 0 17 18
3 14 3 18 10
Any insight in what I am doing wrong?
 07072011, 01:52 AM #2Member
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i am not a person. i am a slice of pizza. i keep getting pepperoni on my keyboard. please help me.
 07072011, 02:11 AM #3
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Knowing the start point and end point, try doing this mechanically with pen and paper, it may help you understand it better.
 07072011, 05:35 AM #4
Hello,
I checked your calculation, and got the same result (your third matrix).
I checked your code and found no mistakes, except that the two terms that you threw away in the first line (i and j both zero) don't seem to cancel out.
The bad news is that when I left them in, only the 10 (upper left, as expected) changed to 15, so my result also is not your desired output.
Some questions:
 I have no idea what this "approximateDerivative" is, or is good for. Can you just explain a bit of what you use it for or what it does? (Yes I tried google)
 What is your source of knowing what the output should be? Is there a link to this source? (Maybe including the calculationinstruction)Last edited by Jodokus; 07072011 at 10:54 PM.
No bug ever had to calculate its fitnessfunction.
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