Generate correlated data in Python (3.3)

Question

In R there is a function (cm.rnorm.cor, from package CreditMetrics), that takes the amount of samples, the amount of variables, and a correlation matrix in order to create correlated data.

Is there an equivalent in Python?

Answer 1

numpy.random.multivariate_normal is the function that you want.

Example:

import numpy as np
import matplotlib.pyplot as plt


num_samples = 400

# The desired mean values of the sample.
mu = np.array([5.0, 0.0, 10.0])

# The desired covariance matrix.
r = np.array([
        [  3.40, -2.75, -2.00],
        [ -2.75,  5.50,  1.50],
        [ -2.00,  1.50,  1.25]
    ])

# Generate the random samples.
y = np.random.multivariate_normal(mu, r, size=num_samples)


# Plot various projections of the samples.
plt.subplot(2,2,1)
plt.plot(y[:,0], y[:,1], 'b.')
plt.plot(mu[0], mu[1], 'ro')
plt.ylabel('y[1]')
plt.axis('equal')
plt.grid(True)

plt.subplot(2,2,3)
plt.plot(y[:,0], y[:,2], 'b.')
plt.plot(mu[0], mu[2], 'ro')
plt.xlabel('y[0]')
plt.ylabel('y[2]')
plt.axis('equal')
plt.grid(True)

plt.subplot(2,2,4)
plt.plot(y[:,1], y[:,2], 'b.')
plt.plot(mu[1], mu[2], 'ro')
plt.xlabel('y[1]')
plt.axis('equal')
plt.grid(True)

plt.show()

Result:

See also CorrelatedRandomSamples in the SciPy Cookbook.