121회, 2교시 5번 문제¶

최소 자승 풀이

In [1]:
!python -m pip install sympy
!python -m pip install control

Requirement already satisfied: sympy in /usr/local/lib/python3.9/dist-packages (1.12)
Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.9/dist-packages (from sympy) (1.3.0)
WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv
WARNING: You are using pip version 21.2.4; however, version 24.0 is available.
You should consider upgrading via the '/usr/local/bin/python -m pip install --upgrade pip' command.
Requirement already satisfied: control in /usr/local/lib/python3.9/dist-packages (0.9.4)
Requirement already satisfied: numpy in /usr/local/lib/python3.9/dist-packages (from control) (1.24.4)
Requirement already satisfied: scipy>=1.3 in /usr/local/lib/python3.9/dist-packages (from control) (1.8.1)
Requirement already satisfied: matplotlib in /usr/local/lib/python3.9/dist-packages (from control) (3.5.2)
Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (4.33.3)
Requirement already satisfied: pyparsing>=2.2.1 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (3.0.9)
Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (9.1.1)
Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (1.4.2)
Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (2.8.2)
Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (21.3)
Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.9/dist-packages (from matplotlib->control) (0.11.0)
Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.9/dist-packages (from python-dateutil>=2.7->matplotlib->control) (1.16.0)
WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv
WARNING: You are using pip version 21.2.4; however, version 24.0 is available.
You should consider upgrading via the '/usr/local/bin/python -m pip install --upgrade pip' command.
In [2]:
import sympy
import control as ct
import numpy as np
import matplotlib.pyplot as plt
a, b = sympy.symbols('a b')
A = np.asarray([
    [3, 1],
    [2, 1],
    [1 ,1],
    [2, 1],
    [3, 1]
])
B = np.asarray([
    [4],
    [3],
    [3],
    [4],
    [5]
])
In [7]:
np.linalg.pinv(A)@B
Out[7]:
array([[0.78571429],
       [2.07142857]])
In [10]:
np.linalg.inv(A.transpose()@A)@A.transpose()@B
Out[10]:
array([[0.78571429],
       [2.07142857]])