add generate_2d_dirac_delta function and test

odak/learn/tools/matrix.py

@@ -184,6 +184,40 @@ def generate_2d_gaussian(kernel_length = [21, 21], nsigma = [3, 3], mu = [0, 0],
         kernel_2d = kernel_2d / kernel_2d.max()
     return kernel_2d
 
+def generate_2d_dirac_delta(kernel_length = [21, 21], a = [3, 3], mu = [0, 0], theta=0, normalize = False):
+    """
+    Generate 2D Dirac delta function by using Gaussian distribution. Inspired from https://en.wikipedia.org/wiki/Dirac_delta_function
+
+    Parameters
+    ----------
+    kernel_length : list
+                    Length of the Dirac delta function along X and Y axes.
+    a             : list
+                    The scale factor in Gaussian distribution to approximate the Dirac delta function. 
+                    As a approaches zero, the Gaussian distribution becomes infinitely narrow and tall at the center (x=0), approaching the Dirac delta function.
+    mu            : list
+                    Mu of the Gaussian kernel along X and Y axes.
+    theta         : float
+                    The rotation angle of the 2D Dirac delta function.
+    normalize     : bool
+                    If set True, normalize the output.
+
+    Returns
+    ----------
+    kernel_2d     : torch.tensor
+                    Generated 2D Dirac delta function.
+    """
+    x = torch.linspace(-kernel_length[0]/2., kernel_length[0]/2., kernel_length[0])
+    y = torch.linspace(-kernel_length[1]/2., kernel_length[1]/2., kernel_length[1])
+    X, Y = torch.meshgrid(x, y, indexing='ij')
+    X = X - mu[0]
+    Y = Y - mu[1]
+    X_rot = X * np.cos(theta) - Y * np.sin(theta)
+    Y_rot = X * np.sin(theta) + Y * np.cos(theta)
+    kernel_2d = (1 / (abs(a[0] * a[1]) * np.pi)) * np.exp(-((X_rot/a[0])**2 + (Y_rot/a[1])**2))
+    if normalize:
+        kernel_2d = kernel_2d / kernel_2d.max()
+    return kernel_2d
 
 def blur_gaussian(field, kernel_length = [21, 21], nsigma = [3, 3], padding = 'same'):
     """

test/test_generate_2d_dirac_delta.py

@@ -0,0 +1,10 @@
+import sys
+from odak.learn.tools.matrix import generate_2d_dirac_delta
+
+
+def test():
+    dirac_delta = generate_2d_dirac_delta(normalize=True, a=[0.1, 0.1])
+    assert dirac_delta[10][10] == 1., "The Dirac delta fucntion does not approximate peak correctly"
+
+if __name__ == '__main__':
+    sys.exit(test())