# file: lecture_13/p01.py
#                                                                              
# revision history:                                                            
#
# 20230928 (JP): initial version
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# Solution to the first exam problem.
#
# To run this script, do this:
#
#  python p01.py
#
#------------------------------------------------------------------------------

# import required system modules                                               
#
import os
import sys
import math
import numpy as np

#------------------------------------------------------------------------------
#
# Let's try a 2x2 where the solution is exact
#
#------------------------------------------------------------------------------
 
# declare a matrix X
#
X = np.array([[1, 0], [0, 2]])
print(X)
Y = np.array([[1], [3]])
print(Y)

# find a = (X^TX)^-1 X^T Y
#
X_t = np.transpose(X)

a = (np.linalg.inv(X_t @ X) @ X_t) @ Y
print(a)

# check the result
#
y_est = X @ a
print(y_est)

# how would you compute the mean-square error?
#
MSE = np.square(np.subtract(Y, y_est)).mean()
print("MSE = %f" % (MSE))
print("----")

#------------------------------------------------------------------------------
#
# Let's try the exam problem
#
#------------------------------------------------------------------------------

# declare a matrix X
#
X = np.array([[1, 0], [0, 1], [1, 1]])
print(X)
Y = np.array([[1], [1], [1]])
print(Y)

# find a = (X^TX)^-1 X^T Y
#
X_t = np.transpose(X)

a = (np.linalg.inv(X_t @ X) @ X_t) @ Y
print(a)

# check the result
#
y_est = X @ a

# how would you compute the mean-square error?
#
MSE = np.square(np.subtract(Y, y_est)).mean()
print("MSE = %f" % (MSE))
print("----")

#
# end of file