Python versions of nearest correlation matrix algorithms
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ReadMe.md

Python versions of nearest correlation matrix algorithms.

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This module will eventually contain several algorithms for solving nearest correlation matrix problems.

The only algorithm currently implemented is Nick Higham's. The code in this module is a port of the MATLAB original at http://nickhigham.wordpress.com/2013/02/13/the-nearest-correlation-matrix/

Run the test suite as follows:

python nearest_correlation_unittests.py

An example computation that finds the nearest correlation matrix to the input matrix:

In [1]: from nearest_correlation import nearcorr

In [2]: import numpy as np

In [3]: A = np.array([[2, -1, 0, 0], 
   ...:               [-1, 2, -1, 0],
   ...:               [0, -1, 2, -1], 
   ...:               [0, 0, -1, 2]])

In [4]: X = nearcorr(A)

In [5]: X
Out[5]: 
array([[ 1.        , -0.8084125 ,  0.1915875 ,  0.10677505],
       [-0.8084125 ,  1.        , -0.65623269,  0.1915875 ],
       [ 0.1915875 , -0.65623269,  1.        , -0.8084125 ],
       [ 0.10677505,  0.1915875 , -0.8084125 ,  1.        ]])

Here's an example using the weights parameter. weights is a vector defining a diagonal weight matrix diag(W):.

In [1]: from nearest_correlation import nearcorr

In [2]: import numpy as np

In [3]: A = np.array([[1, 1, 0],
   ...:               [1, 1, 1],
   ...:               [0, 1, 1]])

In [4]: weights = np.array([1,2,3])

In [5]: X = nearcorr(A, weights = weights)

In [6]: X
Out[6]: 
array([[ 1.        ,  0.66774961,  0.16723692],
       [ 0.66774961,  1.        ,  0.84557496],
       [ 0.16723692,  0.84557496,  1.        ]])

By default, the maximum number of iterations allowed before the algorithm gives up is 100. This can be changed using the max_iterations parameter. When the number of iterations exceeds max_iterations an exception is raised unless except_on_too_many_iterations = False

In [7]: A = np.array([[1, 1, 0],
   ...:               [1, 1, 1],
   ...:               [0, 1, 1]])

In [8]: nearcorr(A,max_iterations=10)
---------------------------------------------------------------------------
ExceededMaxIterationsError                Traceback (most recent call last)
<ipython-input-8-a79bc46a3452> in <module>()
----> 1 nearcorr(A,max_iterations=10)

/Users/walkingrandomly/Dropbox/nearest_correlation/nearest_correlation.py in nearcorr(A, tol, flag, max_iterations, n_pos_eig, weights, verbose, except_on_too_many_iterations)
    106                     message = "No solution found in "\
    107                               + str(max_iterations) + " iterations"
--> 108                 raise ExceededMaxIterationsError(message, X, iteration, ds)
    109             else:
    110                 # exceptOnTooManyIterations is false so just silently

ExceededMaxIterationsError: 'No solution found in 10 iterations'

If except_on_too_many_iterations=False, the best matrix found so far is quiety returned.

In [10]: nearcorr(A,max_iterations=10,except_on_too_many_iterations=False)
Out[10]: 
array([[ 1.        ,  0.76073699,  0.15727601],
       [ 0.76073699,  1.        ,  0.76073699],
       [ 0.15727601,  0.76073699,  1.        ]])

#Continuing failed computations If a computation failed because the the number of iterations exceeded max_iterations, it is possible to continue by passing the exception obejct to nearcorr:

from nearest_correlation import nearcorr, ExceededMaxIterationsError
import numpy as np

A = np.array([[1, 1, 0],
              [1, 1, 1],
              [0, 1, 1]])

# Is one iteration enough?
try:
    X = nearcorr(A, max_iterations=1)
except ExceededMaxIterationsError as e:
    restart = e # capture the Exception object
    print("1 iteration wasn't enough")

# start from where we left off using the default number of `max_iterations`
X = nearcorr(restart)

# This will give the correct result
print(X)