#!/usr/bin/env python
# coding: utf-8

# # Assignment 1

# *Type your name here*

# 
# This assignment is a warmup to practice your Python skills.
# Your task is to write a Python program that optimizes a cost function that we're going to describe next.
# 
# Consider a system that contains $n$ units labeled $\{0,\ldots,n-1\}$ that are all connected.  Each unit has a state associated with it, where unit $i$ has a state $x_i$, and the overall state is referred to as $\mathbf{x}$, i.e. $\mathbf{x} = \{x_0, x_1, \ldots, x_{n-1}\}$.  Assume that $x_i$ takes on the values -1 or +1.  All the units are interconnected and the weight of the connection between units $i$ and $j$ is given by $w_{ij}$.  We assume that the connectivity matrix is symmetric, i.e. $w_{ij} = w_{ji}$.  The state of the system is associated with a cost function, also referred to as energy, given by:
# 
# $$
# E(\mathbf{x}) = - \frac{1}{2} \sum_{i,j=0}^{n-1} w_{ij} x_i x_j
# $$
# 
# This energy function is the basis of the [Hopfield neural network](https://en.wikipedia.org/wiki/Hopfield_network), which is a model of associative memory, and the [Ising spin-glass model](https://en.wikipedia.org/wiki/Ising_model#Spin_glasses) which has been extensively studied in statistical physics.
# 
# We are interested in finding the global minimum of $E(\mathbf{x})$, i.e. to find $\mathbf{x}^*$ such that $E(\mathbf{x}^*) \leq E(\mathbf{x})$ for all choices of $\mathbf{x}$, and return the value of $E(\mathbf{x}^*)$.
# The problem of finding this global minimum is NP-complete, i.e. there is no known efficient algorithm for computing it.  Therefore, you will need to consider all possible assignments to the variables $x_i$ when searching for the global minimum of $E(\mathbf{x})$.
# 
# For example, with the matrix 
# $$ W = 
# \begin{pmatrix} 
# 0 & 1 \\
# 1 & 0 
# \end{pmatrix}
# $$
# The optimal solution is $\mathbf{x}^* = (1, 1)$, with $E (1,1) = -\frac{1}{2} (1 + 1) = -1$; note that $(-1,-1)$ gives the same result.
# Your task is to complete the following function:

# In[2]:


def ising_optimize(matrix) :
    """
    Return the minimum value of E(x) with the matrix given as the input
    parameter.
    The matrix is provided either as a Python list-of-lists or as a 
    string which is the path to a CSV file.
    """
    return 0


# In[5]:


# the matrix shown above can be provided as input in one of two ways:
w = [[0,1], [1, 0]]
# as a list of lists:
ising_optimize(w)
# or can be read from a comma-delimited file:
f = open("matrix.csv", 'w')
_ = f.write("0,1\n1,0\n")
f.close()
get_ipython().system('cat matrix.csv')
#%more matrix.csv
ising_optimize("matrix.csv")


# In[3]:


# recall that a list of lists can be accessed as W[i][j] for element i,j:
w[1][0]


# Note that to determine the type of input provided to the function you can use the Python `type` built-in function:

# In[4]:


type([]) == list
type('cs440') == str


# Our test cases will look something like:

# In[5]:


if ising_optimize(w) == -1 :
    print("test was successful")
else :
    print("test failed")


# In your code do not use the Python `csv` module or code from the Numpy/pandas libraries.
# 
# Submit your code as a jupyter notebook named `p1.ipynb` via Canvas.

# ## Grading
# 
# Your notebook will be run and graded automatically.  So make sure your code satisfies the specified API, i.e. correct naming and behavior of your methods and classes.
#