Neural Networks deep learning Python Basics with numpy (optional) Homework__python

Python Basics with NumPy (optional assignment)

Welcome to your the assignment. This is a brief introduction to Python exercise gives. Even if you ' ve used Python before, this'll help familiarize your with functions we ' ll need.

Instructions:
-You'll be using Python 3.
-Avoid using for-loops and while-loops, unless you are explicitly.
-Don't modify the (# graded function [function name]) comment in some cells. Your work would is graded if you are change this. Each cell containing this comment should only contain one function.
-After coding your function, run the cell right below it to check if your the result is correct.

After this assignment you will:
-Be able to use IPython notebooks
-Be able to use NumPy functions and NumPy matrix/vector operations
-Understand the concept of "broadcasting"
-Is able to vectorize code

Let ' s get started! About IPython Notebooks

IPython notebooks are interactive coding environments embedded in a webpage. You are using IPython notebooks in this class. You have need to write code between the ### START code here ### and ### end code here ### comments. After writing your code, you can run the cell by either pressing ' SHIFT ' + ' ENTER ' or by clicking on ' Run cell ' (denoted by A play symbol) in the upper bar of the notebook.

We'll often specify "(≈x lines of code)" In the comments to tell you about so much code for you need to write. It is just a rough estimate and so don ' t feel bad if your the code is longer or shorter.

Exercise: Set test to ' Hello World ' in the ' cell below to print ' Hello World ' and run the two cells below.

### START code here ### (≈1 line of code)
test = None
test= ' Hello world ' 
### end code here ###

Print ("Test:" + test)

Test:hello World

Expected output:
Test:hello World


What you need to remember:
-Run your cells using Shift+enter (or "Run cell")
-Write code in the designated areas using Python 3 only
-Does not modify the code outside of the designated areas 1-building basic functions with NumPy





NumPy is the main package for scientific computing in Python. It is maintained by a large community (www.numpy.org). In this exercise you'll learn several key numpy functions such as Np.exp, Np.log, and Np.reshape. You'll need to the know how-to-use this functions for future assignments. 1.1-sigmoid function, Np.exp ()

Before using Np.exp (), you'll use MATH.EXP () to implement the Sigmoid function. You'll then why Np.exp () is preferable to Math.exp ().

Exercise: Build a function that returns the sigmoid's a real number X. Use MATH.EXP (x) for the exponential funct Ion.


Reminder:

Sigmoid (x) =11+e−x sigmoid (x) = \frac{1}{1+e^{-x} is sometimes also known as the The logistic function. It is a non-linear function used does not be in Machine Learning (Logistic regression), but also in Deep Learning.

To refer to a function belonging to a specific package your could call it using package_name.function (). Run the code below to the example with Math.exp ().

# graded function:basic_sigmoid

import Math

def basic_sigmoid (x): ""
    "
    Compute sigmoid of X.

    Arguments:
    x--A scalar return

    :
    S--sigmoid (x) ""

    ### START code here ### (≈1 line of CODE)
    s = None
    s=1/(1+math.exp (x))
    ### end CODE Here ### return

    s

Basic_sigmoid (3)

0.9525741268224334

expected Output:

* * BASIC_SIGMOID (3) * *

0.9525741268224334

Actually, we rarely use the ' math ' library in deep learning because the inputs of the functions are real numbers. In deep learning we mostly use matrices and vectors. This is why numpy are more useful.

### One reason why we use "numpy" instead of "math" in Deep Learning ###
x = [1, 2, 3]
basic_sigmoid (x) # The Give an error while you run it, because X is a vector.

---------------------------------------------------------------------------

typeerror                                 traceback (most Recent call last)

<ipython-input-26-2e11097d6860> in <module> ()
      1 ### One reason why we use "NumPy" in  stead of "math" in Deep Learning ###
      2 x = [1, 2, 3]
----> 3 basic_sigmoid (x) # and you'll have to be here give an error When you run it, the because X is a vector.


<ipython-input-24-f2ee07699056> in Basic_sigmoid (x)     ### START CODE here ### (≈1 line of code)
     17s = None
--->     s=1/(1+math.exp (x))
     ### end     CODE here ### 


Typeerror:bad Operand type for unary-: ' list '

In fact, if x= (x1,x2,..., xn) x = (x_1, x_2, ..., x_n) is a row vector then Np.exp (x) np.exp (x) would apply the exponential function to every element of x. The output would thus be:np.exp (x) = (ex1,ex2,..., exn) np.exp (x) = (E^{x_1}, E^{x_2}, ..., e^{x_n})

Import NumPy as NP

# Example of np.exp
x = Np.array ([1, 2, 3])
print (Np.exp (x)) # result is (exp (1), exp (2), E XP (3))

[  2.71828183   7.3890561   20.08553692]

Furthermore, if X is a vector, then a Python operation such as s=x+3 s = x + 3 or s=1x s = \frac{1}{x} 'll output S as a Vector of the same size as x.

# Example of vector operation
x = Np.array ([1, 2, 3])
print (x + 3)

[4 5 6]

Any time for your need more info on a numpy function, we are encourage you to look at the official documentation.

Can also create a new cell in the notebook and write np.exp? [For example] to get quick access to the documentation.

Exercise: Implement the sigmoid function using NumPy.


Instructions : 
X could now is either a real number, a vector, or a matrix. The data structures we numpy to represent the shapes (vectors, matrices ...) are called the NumPy. You don ' t need to know the more for now.

For x∈rn, sigmoid (x) =sig