Merge pull request #323 from turkunov/convert_range

New Problem: Convert Range

Author: moe18

Problems/convert_range/learn.md

@@ -0,0 +1,9 @@
+Shifting one range to another could come in handy in the data preprocessing task, e.g. shift a GPA of $[0, 10]$ range to $[0, 4]$
+
+Lets denote our first range (or interval) as $[a, b]$ and another as $[c, d]$. Let's recall that an **image interval** is some function $F$ applied to an interval $I$, i.e. $F(I)$. With that in mind, let's first apply the map $t\mapsto t - a$ and get an image interval for the first range: $[0, b-a]$. With that operation we've shifted the left point to $0$. 
+
+Then we apply a scaling mapping to bring the same interval to unit length: $t\mapsto\frac{1}{b-a}\cdot t$. Now we obtain an image interval $[0, 1]$ from the original first range.
+
+Now we need a mapping from the unit interval to our sencond desired range $[c, d]$. Firstly, this involves $t\mapsto(d-c)\cdot t$, which results in the image $[0, d-c]$. Then we do $t\mapsto c+t$, which brings us to $[c, d]$.
+
+Combining these operations we get the following mapping function, which shifts a set $x$ from its range of $[a, b]$ to $[c, d]$: $f(x) = c+(\frac{d-c}{b-a})(x-a)$

Problems/convert_range/solution.py

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+import numpy as np
+
+
+def convert_range(values: np.ndarray, c: float, d: float) -> np.ndarray:
+    """
+    Shifts an arbitrary range [values.min(), values.max()] to a desired [c, d]
+
+    Parameters
+    ----------
+    values : np.ndarray
+        An array of random values we want to shift
+    c: float
+        Supremum of the desired range
+    d: float
+        Infimum of the desired range
+
+    Returns
+    -------
+    values_shifted : np.ndarray
+        Original values shifted to [c, d] range
+    """
+
+    a, b = values.min(), values.max()
+    return c + (d-c) / (b-a) * (values-a)
+
+
+def test_convert_range():
+    # Test 1
+    seq = np.array([388, 242, 124, 384, 313, 277, 339, 302, 268, 392])
+    c, d = 0, 1
+    e_shifted = np.array([
+        0.98507463, 0.44029851, 0., 0.97014925, 0.70522388, 0.57089552,
+        0.80223881, 0.6641791, 0.53731343, 1.])
+    assert np.allclose(e_shifted,convert_range(seq, c, d)), 'Test case 1 failed'
+
+    # Test 2
+    seq = np.array([[2028, 4522], [1412, 2502], [3414, 3694], [1747, 1233], [1862, 4868]])
+    c, d = 4, 8
+    e_shifted = np.array(
+        [[4.874828060522696, 7.619257221458047], [4.19697386519945, 5.396423658872077], 
+         [6.4, 6.7081155433287485], [4.565612104539202, 4.0], [4.692159559834938, 8.0]])
+    assert np.allclose(e_shifted,convert_range(seq, c, d)), 'Test case 2 failed'
+
+    print('All tests passed')
+
+
+if __name__ == '__main__':
+    test_convert_range()
+