# file: lecture_13/p03.py
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# revision history:                                                            
#
# 20230928 (JP): initial version
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# Solution to the third exam problem.
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# To run this script, do this:
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#  python p03.py
#
#------------------------------------------------------------------------------

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

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

# (a) a simple constant matrix
#
T = np.array([[2, 3], [4, 5]])
x = np.array([[5],[10]])
print("x = [5,10]:\n", T @ x)

scale = float(3)
x_sc = scale * x
print("x = [15,30]:\n", T @ x_sc)
print("error = :\n", scale * (T @ x) - T @ (x_sc))

# (b) nonlinear
#
a = float(6.0)
b = float(7.0)
c = float(8.0)
d = float(9.0)
x = np.array([1,2])
y = np.array([a * x[0] * x[0] + b * x[1],
              c * x[0]        + d * x[1] * x[1]])

print("x = \n", x)
print("y = \n", y)

scale = float(3)
x_sc = scale * x
y_sc = np.array([a * x_sc[0] * x_sc[0] + b * x_sc[1],
              c * x_sc[0]           + d * x_sc[1] * x_sc[1]])
print("x_sc = \n", x_sc)
print("y_sc = \n", y_sc)
print("y_est = \n", y_sc / scale)

# (c) nonlinear (a constant)
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print("y1 = 1 * x2")
print("y2 = b * y2 * x1 - or - x1 = 1/b")
print("degenerate case = x1 is constant: y1 scales with x2")

#
# end of file