feat (advanced) : add NumPy array operations and math functions tutorial

advanced/numpy_tutorial.py

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+import numpy as np
+
+# create one-dimensional array with five elements
+a = np.array([1, 2, 3, 4, 5])
+print("Array a:", a)
+
+# create 2D array (matrix) of shape 3x3
+b = np.array([[1, 2, 3],
+              [4, 5, 6],
+              [7, 8, 9]])
+print("Matrix b:\n", b)
+
+# array attributes
+print("Shape of b:", b.shape)
+print("Number of dimensions of b:", b.ndim)
+print("Data type of b elements:", b.dtype)
+# convert to float type
+b = b.astype(float)
+print("Converted matrix b to float, new dtype:", b.dtype)
+
+# indexing and slicing
+print("b[0, 0]:", b[0, 0])
+print("First row of b:", b[0, :])
+print("Second column of b:", b[:, 1])
+# slicing with step
+print("Elements of a with step 2:", a[::2])
+
+# basic array operations
+sum_array = a + np.array([5, 5, 5, 5, 5])  # adding two arrays
+print("a + [5,5,5,5,5]:", sum_array)
+
+scaled = a * 2  # element-wise multiplication by scalar
+print("a * 2:", scaled)
+
+# matrix multiplication (dot product)
+c = np.dot(b, b)
+print("Dot product b * b:\n", c)
+
+# sum of elements
+print("Sum of elements in a:", a.sum())
+print("Sum of each column in b:", b.sum(axis=0))
+# example of an invalid axis in sum (to show an error)
+try:
+    print("Sum with invalid axis 2:", b.sum(axis=2))
+except Exception as e:
+    print("Error summing along axis 2 (invalid):", e)
+
+# use of universal functions (ufuncs)
+d = np.array([0, np.pi/2, np.pi])
+print("Angles d:", d)
+print("sin(d):", np.sin(d))
+print("log of d (with -inf for zero):", np.log(d))
+
+# broadcasting example
+e = np.arange(1, 4)
+f = np.array([[1], [2], [3]])
+print("e:", e)
+print("f:", f)
+print("Broadcasted sum e+f:\n", e + f)
+
+# reshape example
+g = np.arange(8)
+g = g.reshape((2,4))
+print("Reshaped g to 2x4:\n", g)
+
+# simple statistics
+print("Mean of a:", a.mean())
+print("Standard deviation of g:", g.std())
+
+# find unique elements
+h = np.array([1, 2, 2, 3, 3, 3])
+print("Unique elements in h:", np.unique(h))
+
+# sort elements of an array in descending order
+print("Sorted a in descending:", np.sort(a)[::-1])
+
+# random array example
+np.random.seed(0)
+rand_arr = np.random.rand(3, 3)
+print("Random array:", rand_arr)
+
+# element-wise comparison
+print("Elements of rand_arr > 0.5:\n", rand_arr > 0.5)
+
+# creating arrays using linspace
+lin = np.linspace(0, 1, 5)
+print("Linearly spaced array:", lin)