You are given a matrix A, vector b and scalar α. Calculate x such that it minimizes the residual for Ax≅b and x2 such that it minimizes the regularization condition. Also calculate the residual and norm for both.
code below
import numpy as np
import scipy.sparse
INPUT:
A
:numpy
array of shape(m, n)
b
:numpy
array of shape(m,)
alpha
: Python float
OUTPUT:
x
:numpy
array of shape(n,)
that minimizes the residual.x2
:numpy
array of shape(n,)
that minimizes the L2-regularization condition.norm_x
: Norm ofx
.norm_x2
: Norm ofx2
.residual_x
: Norm of the residual ofx
.residual_x2
: Norm of the residual ofx2
.
n = np.random.randint(100, 200)
A = scipy.sparse.diags([-1,2,-1],[-1,0,1],shape=(n, n//4)).A
b = np.ones(n)
alpha = 1.5