From d2ace996da361c23658efc1e9fdcdc90a0c1a52f Mon Sep 17 00:00:00 2001
From: androiddrew <bednar.andrew@gmail.com>
Date: Sun, 3 Mar 2019 20:54:33 -0500
Subject: [PATCH] Added vector calc functions

---
 ch4/__init__.py |  0
 ch4/vector.py   | 78 +++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 78 insertions(+)
 create mode 100644 ch4/__init__.py
 create mode 100644 ch4/vector.py

diff --git a/ch4/__init__.py b/ch4/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/ch4/vector.py b/ch4/vector.py
new file mode 100644
index 0000000..7746514
--- /dev/null
+++ b/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))