Added vector calc functions

ch4/vector.py

@@ -0,0 +1,78 @@
+"""
+Lists as Vectors is actually not that performant. Numpy gives all of these features straight out of the box.
+"""
+import math
+from typing import List
+from functools import reduce
+
+
+def vector_add(v: List[float], w: List[float]) -> List[float]:
+    """Adds corresponding elements of two Vectors."""
+    return [v_i + w_i
+            for v_i, w_i in zip(v, w)]
+
+
+def vector_subtract(v: List[float], w: List[float]) -> List[float]:
+    """Subtracts corresponding elements of two Vectors."""
+    return [v_i - w_i
+            for v_i, w_i in zip(v, w)]
+
+
+def vector_sum(vectors: List[List[float]]) -> List[float]:
+    """Sums all corresponding elements."""
+    # result = vectors[0]
+    # for vector in vectors[1:0]:
+    #     result = vector_add(result, vector)
+    # return result
+    return reduce(vector_add, vectors)
+
+
+def scalar_multiple(c: float, v: List[float]) -> List[float]:
+    """Scales a vector by a multiplier."""
+    return [c * vi for vi in v]
+
+
+def vector_mean(vectors) -> List[float]:
+    """Compute the vector whose ith element is the mean of the ith element
+    of the input vectors.
+
+    Allows us to calculate the component-wise means of a list of (same-sized)
+    vectors.
+    """
+    n = len(vectors)
+    return scalar_multiple(1 / n, vector_sum(vectors))
+
+
+def dot_product(v: List[float], w: List[float]) -> float:
+    """The dot product of two vectors is the sum of their component wise
+    products.
+
+    The dot product measures how far vector v extends in the w direction.
+    """
+    return sum(v_i * w_i for v_i, w_i in zip(v, w))
+
+
+def sum_of_squares(v: List[float]) -> float:
+    return dot_product(v, v)
+
+
+def magnitude(v: List[float]) -> float:
+    """Calculates the magnitude (length) of a vector.
+
+    The pythagorean theorem a**2 + b**2 = c**2 actually is an example
+    of calculating the magnitude of a vector of length 2.
+    """
+    return math.sqrt(sum_of_squares(v))
+
+
+# def squared_distance(v: List[float], w: List[float]) -> float:
+#     """Calculates t
+#
+#     """
+#     return sum_of_squares(vector_subtract(v, w))
+
+
+def vector_distance(v: List[float], w: List[float]) -> float:
+    """Calculates the distance between vectors."""
+    # return math.sqrt(squared_distance(v, w))
+    return magnitude(vector_subtract(v, w))