algorithm-archivists
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@@ -478,7 +478,7 @@ paket-files/
 # Python Tools for Visual Studio (PTVS)
 __pycache__/
 *.pyc
-
+*.ipynb_checkpoints*
 # Cake - Uncomment if you are using it
 # tools/**
 # !tools/packages.config
 
@@ -61,4 +61,5 @@ This file lists everyone, who contributed to this repo and wanted to show up her
 - Hugo Salou
 - Dimitri Belopopsky
 - Henrik Abel Christensen
+- K. Shudipto Amin
 - Peanutbutter_Warrior
@@ -20,9 +20,11 @@
         * [Multiplication as a Convolution](contents/convolutions/multiplication/multiplication.md)
         * [Convolutions of Images (2D)](contents/convolutions/2d/2d.md)
         * [Convolutional Theorem](contents/convolutions/convolutional_theorem/convolutional_theorem.md)
+	* [Probability Distributions](contents/probability/distributions/distributions.md)	
 * [Tree Traversal](contents/tree_traversal/tree_traversal.md)
 * [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md)
 * [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md)
+    * [Metropolis](contents/metropolis/metropolis.md)
 * [Matrix Methods](contents/matrix_methods/matrix_methods.md)
     * [Gaussian Elimination](contents/gaussian_elimination/gaussian_elimination.md)
     * [Thomas Algorithm](contents/thomas_algorithm/thomas_algorithm.md)
 
@@ -0,0 +1,90 @@
+import numpy as np
+
+
+def f(x, normalize=False):
+    '''
+    Function proportional to target distribution, a sum of Gaussians.
+    For testing, set normalize to True, to get target distribution exactly.
+    '''
+    # Gaussian heights, width parameters, and mean positions respectively:
+    a = np.array([10., 3., 1.]).reshape(3, 1)
+    b = np.array([ 4., 0.2, 2.]).reshape(3, 1)
+    xs = np.array([-4., -1., 5.]).reshape(3, 1)
+
+    if normalize:
+        norm = (np.sqrt(np.pi) * (a / np.sqrt(b))).sum()
+        a /= norm
+
+    return (a * np.exp(-b * (x - xs)**2)).sum(axis=0)
+
+def g():
+    '''Random step vector.'''
+    return np.random.uniform(-1,1)
+
+def metropolis_step(x, f=f, g=g):
+    '''Perform one full iteration and return new position.'''
+    
+    x_proposed = x + g()
+    a = min(1, (f(x_proposed) / f(x)).item())
+    
+    x_new = np.random.choice([x_proposed, x], p=[a, 1-a])
+        
+    return x_new
+
+def metropolis_iterate(x0, num_steps):
+    '''Iterate metropolis algorithm for num_steps using iniital position x_0'''
+    
+    for n in range(num_steps):
+        if n == 0:
+            x = x0
+        else:
+            x = metropolis_step(x)
+        yield x
+    
+
+def test_metropolis_iterate(num_steps, xmin, xmax, x0):
+    '''
+    Calculate error in normalized density histogram of data  
+    generated by metropolis_iterate() by using 
+    normalized-root-mean-square-deviation metric. 
+    '''
+    
+    bin_width = 0.25
+    bins = np.arange(xmin, xmax + bin_width/2, bin_width)
+    centers = np.arange(xmin + bin_width/2, xmax, bin_width)
+    
+    true_values = f(centers, normalize=True)
+    mean_value = np.mean(true_values - min(true_values))
+
+    x_dat = list(metropolis_iterate(x0, num_steps))
+    heights, _ = np.histogram(x_dat, bins=bins, density=True)
+                    
+    nmsd = np.average((heights - true_values)**2 / mean_value)
+    nrmsd = np.sqrt(nmsd)
+
+    return nrmsd
+
+        
+ 
+if __name__ == "__main__":
+    xmin, xmax = -10, 10
+    x0 = np.random.uniform(xmin, xmax)
+
+    num_steps = 50_000
+
+    x_dat = list(metropolis_iterate(x0, 50_000))
+        
+    # Write data to file
+    output_string = "\n".join(str(x) for x in x_dat)
+    
+    with open("output.dat", "w") as out:
+        out.write(output_string)
+        out.write("\n")
+        
+    
+    # Testing
+    print(f"Testing with x0 = {x0:5.2f}")
+    print(f"{'num_steps':>10s} {'NRMSD':10s}")
+    for num_steps in (500, 5_000, 50_000):
+        nrmsd = test_metropolis_iterate(num_steps, xmin, xmax, x0)
+        print(f"{num_steps:10d} {nrmsd:5.1%}")