Numpy_submission

numpy_questions.py

@@ -1,4 +1,5 @@
-"""Assignment - using numpy and making a PR.
+"""
+Assignment - using numpy and making a PR.
 
 The goals of this assignment are:
     * Use numpy in practice with two easy exercises.
@@ -19,49 +20,51 @@
 
 
 def max_index(X):
-    """Return the index of the maximum in a numpy array.
-
-    Parameters
-    ----------
-    X : ndarray of shape (n_samples, n_features)
-        The input array.
-
-    Returns
-    -------
-    (i, j) : tuple(int)
-        The row and columnd index of the maximum.
-
-    Raises
-    ------
-    ValueError
-        If the input is not a numpy array or
-        if the shape is not 2D.
     """
-    i = 0
-    j = 0
+    Return the indices (i, j) of the maximum value in a 2D matrix.
+
+    Parameters:
+    X (np.ndarray): A 2D numpy array.
 
-    # TODO
+    Returns:
+    tuple: Indices (i, j) of the maximum value in the array.
+
+    Raises:
+    ValueError: If X is not a numpy array or not a 2D array.
+    """
+    if not isinstance(X, np.ndarray):
+        raise ValueError("X must be a numpy array.")
+    if X.ndim != 2:
+        raise ValueError("X must be a 2D array.")
 
+    # Find the flattened index of the maximum value
+    flat_index = np.argmax(X)
+    # Convert to 2D indices
+    i, j = divmod(flat_index, X.shape[1])
     return i, j
 
 
 def wallis_product(n_terms):
-    """Implement the Wallis product to compute an approximation of pi.
+    """
+    Approximate the value of pi using the Wallis product.
 
-    See:
-    https://en.wikipedia.org/wiki/Wallis_product
+    Parameters:
+    n_terms (int): The number of terms in the Wallis product.
 
-    Parameters
-    ----------
-    n_terms : int
-        Number of steps in the Wallis product. Note that `n_terms=0` will
-        consider the product to be `1`.
+    Returns:
+    float: Approximation of pi.
 
-    Returns
-    -------
-    pi : float
-        The approximation of order `n_terms` of pi using the Wallis product.
+    Raises:
+    ValueError: If n_terms is negative.
     """
-    # XXX : The n_terms is an int that corresponds to the number of
-    # terms in the product. For example 10000.
-    return 0.
+    if not isinstance(n_terms, int) or n_terms < 0:
+        raise ValueError("n_terms must be a non-negative integer.")
+
+    product = 1.0
+    if n_terms == 0:
+        return 2.0
+
+    for i in range(1, n_terms + 1):
+        product *= (4 * i**2) / (4 * i**2 - 1)
+
+    return 2 * product