error while running lasso.py

Question

The following is the error code generated while running lasso.py. Can anybody help in fixing the same.

Here is the code:

from cvxpy import *
import numpy as np
import cvxopt
from multiprocessing import Pool

# Problem data.
n = 10
m = 5
A = cvxopt.normal(n,m)
b = cvxopt.normal(n)
gamma = Parameter(nonneg=True)

# Construct the problem.
x = Variable(m)
objective = Minimize(sum_squares(A*x - b) + gamma*norm(x, 1))
p = Problem(objective)

# Assign a value to gamma and find the optimal x.
def get_x(gamma_value):
    gamma.value = gamma_value
    result = p.solve()
    return x.value

gammas = np.logspace(-1, 2, num=100)
# Serial computation.
x_values = [get_x(value) for value in gammas]

# Parallel computation.
pool = Pool(processes = 4)
par_x = pool.map(get_x, gammas)

for v1,v2 in zip(x_values, par_x):
    if np.linalg.norm(v1 - v2) > 1e-5:
        print("error")

Error: while running

Traceback (most recent call last):
  File "lasso.py", line 31, in <module>
    objective = Minimize(sum_squares(A*x - b) + gamma*norm(x, 1))
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/expressions/expression.py", line 45, in cast_op
    return binary_op(self, other)
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/expressions/expression.py", line 435, in __sub__
    return self + -other
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/expressions/expression.py", line 45, in cast_op
    return binary_op(self, other)
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/expressions/expression.py", line 423, in __add__
    return cvxtypes.add_expr()([self, other])
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/atoms/affine/add_expr.py", line 33, in __init__
    super(AddExpression, self).__init__(*arg_groups)
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/atoms/atom.py", line 41, in __init__
    self._shape = self.shape_from_args()
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/atoms/affine/add_expr.py", line 41, in shape_from_args
    return u.shape.sum_shapes([arg.shape for arg in self.args])
  File "/usr/local/lib/python3.5/dist-packages/cvxpy-1.0.11-py3.5-linux-x86_64.egg/cvxpy/utilities/shape.py", line 49, in sum_shapes
    len(shapes)*" %s" % tuple(shapes))
ValueError: Cannot broadcast dimensions  (10,) (10, 1)

As suggested by multiple links, I tried with all possible python and library versions. But I am unable to fix this. Kindly throw some light.

Answer 1

(A*x) Expression has dimensionality of (10, ) and b has shape of ( 10, 1) - this is why you see this error.

My fix solves the error, but you should double check the results

objective = Minimize(sum_squares(A*x - np.array(b).reshape(10,)) + gamma*norm(x, 1))

Hope this helps!

Answer 2

The fix for your problem would be to change line

x = Variable(m)

into

x = Variable(shape=(m,1))