👾 Add some machine learning experiments

machine_learning_examples/numpy_examples/gradient.py

@@ -0,0 +1,31 @@
+# compute the gradient numerically:
+# a generic function takes a function f, a vector x o evaluate 
+# the gradient on, and returns the gradient of f at x:
+
+def eval_numerical_gradient(f, x):
+  """ 
+  a naive implementation of numerical gradient of f at x 
+  - f should be a function that takes a single argument
+  - x is the point (numpy array) to evaluate the gradient at
+  """ 
+
+  fx = f(x) # evaluate function value at original point
+  grad = np.zeros(x.shape)
+  h = 0.00001
+
+  # iterate over all indexes in x
+  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
+  while not it.finished:
+
+    # evaluate function at x+h
+    ix = it.multi_index
+    old_value = x[ix]
+    x[ix] = old_value + h # increment by h
+    fxh = f(x) # evalute f(x + h)
+    x[ix] = old_value # restore to previous value (very important!)
+
+    # compute the partial derivative
+    grad[ix] = (fxh - fx) / h # the slope
+    it.iternext() # step to next dimension
+
+  return grad