Python-Workshop-3-NumPy.md

@@ -113,7 +113,7 @@ NumPy arrays can be...
         print()
     ```
 
-  - Created from a Python List of `int`s
+  - Created from a Python List of `int`-s
 
     ```python
         python_list = [2, 4, 8, 16, 32, 64]
@@ -122,7 +122,7 @@ NumPy arrays can be...
         print()
     ```
 
-  - Created from a Python List of `floats`s
+  - Created from a Python List of `float`-s
 
     ```python
         python_list = [2., 4., 8., 16., 32., 64.]
@@ -134,6 +134,22 @@ NumPy arrays can be...
 
 ## Broadcasting
 
+The next couple snippets are extracted from
+[braodcasting.py](https://git-community.cs.odu.edu/tkennedy/python-workshop/-/blob/master/NumPy/broadcasting.py).
+
+In Python... each element of a list must be updated one at a time. If a list of
+prices needed to be reduced by 10%, each one would need to be multiplied by 0.9
+within a loop...
+
+```python
+    prices = [1.00, 2.95, 8.40, 3.50, 3.30, 16.91]
+
+    for idx in range(len(prices)):
+        price[idx] *= 0.9
+```
+
+or using a [list comprehension](Python-Workshop#loops-and-listgenerator-comprehensions)...
+
 ```python
     prices = [1.00, 2.95, 8.40, 3.50, 3.30, 16.91]
     prices = [0.9 * price for price in prices]
@@ -141,6 +157,8 @@ NumPy arrays can be...
     print(prices)
 ```
 
+NumPy's broadcasting mechanic allows us to write a simple `prices *= 0.9`.
+
 ```python
     prices = np.array([1.00, 2.95, 8.40, 3.50, 3.30, 16.91])
     prices *= 0.9
@@ -152,36 +170,54 @@ NumPy arrays can be...
     print()
 ```
 
+The obvious benefit is less typing. The more important one is optimization.
+NumPy's core is implemented in C. The official NumPy Documentation provides a
+succinct overview in its [Why is NumPy
+Fast?](https://numpy.org/doc/stable/user/whatisnumpy.html#why-is-numpy-fast)
+section. 
+
+How much faster is NumPy? Let us run a quick using [benchmark_broadcasting.py](https://git-community.cs.odu.edu/tkennedy/python-workshop/-/blob/master/NumPy/benchmark_broadcasting.py).
+
 ```python
+    num_values = 1000000
+    num_runs = 100
+
     def op_wrapper_py():
-        prices = range(1, 1000000, 1)
+        prices = range(1, num_values, 1)
         prices = [0.9 * price for price in prices]
 
-    py_list = timeit.timeit(op_wrapper_py, number=100)
+    py_list = timeit.timeit(op_wrapper_py, number=num_runs)
 
     def op_wrapper_np():
-        prices = np.arange(0, 1000000, 1, dtype=np.float64)
+        prices = np.arange(0, num_values, 1, dtype=np.float64)
         prices[:] *= 0.9
 
-    np_array = timeit.timeit(op_wrapper_np, number=100)
+    np_array = timeit.timeit(op_wrapper_np, number=num_runs)
 
     print(f"Python Time: {py_list:.4f}")
     print(f"NumPy Time : {np_array:.4f}")
 ```
 
+On a Core i7-6700k... For 1 million numbers, run 100 times... The NumPy code is almost
+10 times faster than the pure Python code.
 
-**I/O**
+|        | Time   |
+| :---   | ---:   |
+| Python | 5.1248 |
+| NumPy  | 0.3168 |
 
-**Indexing**
 
-**Index Arrays**
+## Remaining Topics
 
-**Boolean (Mask) Index Arrays**
+There are a few more topics to introduce:
 
+  - **Indexing** - will be covered as part of the Matrix Solver example
+  - **I/O**
+  - **Index Arrays**
+  - **Boolean (Mask) Index Arrays**
 
-# Fun Examples!
 
-The examples in this section are fun!
+# Implementing a Matrix Solver
 
 
 ## Linear Algebra