# Python versions of nearest correlation matrix algorithms.
[](https://travis-ci.org/mikecroucher/nearest_correlation)
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:
```python
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):.
```python
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`
```python
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.
```python
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`:
```python
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)
```
最近相关矩阵算法的Python版本_Python_下载.zip
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