sp

gistfile1.py

import numpy as np

import numpy.linalg as linalg
import matplotlib.pyplot as plt
import math

def p4():
    A = np.array([[1, 3, 2],
                  [-1, 2, -5],
                  [2, -4, 3]])

    Sigma = np.array([[5, 2, 1],
                      [2, 8, -3],
                      [1, -3, 9]])

    print np.dot(np.dot(A.T, Sigma), A)
    #print A.T * Sigma * A



def p5():
    ux = np.array([2, 1, 1, 0])
    sigmax = np.array([[6, 3, 2, 1],
                       [3, 4, 3, 2],
                       [2, 3, 4, 3],
                       [1, 2, 3, 3]])

    ux1 = ux[0:2]
    ux2 = ux[2:4]
    sigma11 = sigmax[0:2, 0:2]
    sigma12 = sigmax[0:2, 2:4]
    sigma21 = sigmax[2:4, 0:2]
    sigma22 = sigmax[2:4, 2:4]

    print np.dot(sigma12, linalg.inv(sigma22))
    print sigma11 - np.dot(np.dot(sigma12, linalg.inv(sigma22)), sigma21)


def p9(s2):
    A = np.random.normal(0, 1, (100,))
    X_vec = [0]*100
    s = math.sqrt(s2)
    for i in xrange(0, 100):
        X_vec[i] = np.random.normal(A[i], s, (1,))[0]

    X = np.array(X_vec)
    coeff = 1.0 / (s2+1)
    A_est_vec = [0] * 100
    for i in xrange(0, 100):
        A_est_vec[i] = coeff * X_vec[i]
    A_est = np.array(A_est_vec)

    xc = np.linspace(0, 100, num=100, endpoint=False)
    plt.plot(xc, A, 'r', xc, X, 'g', xc, A_est, 'b')

def demo():
    plt.figure(1)
    plt.subplot(211)
    p9(0.01)
    plt.subplot(212)
    p9(2)
    plt.show()