Article Outline
Python matplotlib example 'constrained least squares'
Modules used in program:
import numpy as np
import matplotlib.pyplot as plt
import pandas
import seaborn as sns
import matplotlib
import numpy as np
python constrained least squares
Python matplotlib example: constrained least squares
import numpy as np
from matplotlib import pyplot as plt
import matplotlib
import seaborn as sns
import pandas
font = {'family' : 'Helvetica',
'size' : 18}
matplotlib.rc('font', **font)
np.random.seed(222)
DPPD = 200
X = np.random.normal(0,2, (DPPD, 2))
# target w
w_target = np.random.normal(0,1, (2,1))
# constraints (overdetermined for multiple solutions)
d = np.random.normal(0,1, (1,1))
C = np.random.normal(0,1, (1,2))
# objective
y = X@w_target + np.random.normal(0, 0.2, (DPPD,1))
Y_tilde = [y, d]
X_tilde = [X, C]
# objective weights
lambd = np.asarray([1.0, 10000.0])
A_tilde = np.bmat([[np.sqrt(l)*x] for l,x in zip(lambd, X_tilde)])
y_tilde = np.bmat([[np.sqrt(l)*y] for l,y in zip(lambd, Y_tilde)])
# least squares
w_estimate = np.linalg.inv(A_tilde.T@A_tilde)@A_tilde.T@y_tilde
y_estimate = X@w_estimate
# This import registers the 3D projection, but is otherwise unused.
from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
import matplotlib.pyplot as plt
import numpy as np
x1 = y_estimate.flatten()
x2 = X[:, 0].flatten()
y_estimate = y_estimate.flatten()
y_true = y.flatten()
fig = plt.figure(figsize=(20,10))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x1,x2,y_estimate, label="Estimate")
ax.scatter(x1,x2,y_true, label="Ground Truth")
ax.view_init(elev=10., azim=20)
ax.set_xlabel('X0')
ax.set_ylabel('X1')
ax.set_zlabel('Y')
plt.legend()
plt.tight_layout()
plt.savefig("3d.png")
plt.show()
Python links
- Learn Python: https://pythonbasics.org/
- Python Tutorial: https://pythonprogramminglanguage.com