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import numpy as np
from numpy.linalg import lstsq
from numpy.testing import assert_allclose, assert_equal, assert_
from pytest import raises as assert_raises
from scipy.sparse import rand
from scipy.sparse.linalg import aslinearoperator
from scipy.optimize import lsq_linear
A = np.array([
[0.171, -0.057],
[-0.049, -0.248],
[-0.166, 0.054],
])
b = np.array([0.074, 1.014, -0.383])
class BaseMixin(object):
def setup_method(self):
self.rnd = np.random.RandomState(0)
def test_dense_no_bounds(self):
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, method=self.method, lsq_solver=lsq_solver)
assert_allclose(res.x, lstsq(A, b, rcond=-1)[0])
def test_dense_bounds(self):
# Solutions for comparison are taken from MATLAB.
lb = np.array([-1, -10])
ub = np.array([1, 0])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, lstsq(A, b, rcond=-1)[0])
lb = np.array([0.0, -np.inf])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, np.inf), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, np.array([0.0, -4.084174437334673]),
atol=1e-6)
lb = np.array([-1, 0])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, np.inf), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, np.array([0.448427311733504, 0]),
atol=1e-15)
ub = np.array([np.inf, -5])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (-np.inf, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, np.array([-0.105560998682388, -5]))
ub = np.array([-1, np.inf])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (-np.inf, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, np.array([-1, -4.181102129483254]))
lb = np.array([0, -4])
ub = np.array([1, 0])
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, np.array([0.005236663400791, -4]))
def test_dense_rank_deficient(self):
A = np.array([[-0.307, -0.184]])
b = np.array([0.773])
lb = [-0.1, -0.1]
ub = [0.1, 0.1]
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.x, [-0.1, -0.1])
A = np.array([
[0.334, 0.668],
[-0.516, -1.032],
[0.192, 0.384],
])
b = np.array([-1.436, 0.135, 0.909])
lb = [0, -1]
ub = [1, -0.5]
for lsq_solver in self.lsq_solvers:
res = lsq_linear(A, b, (lb, ub), method=self.method,
lsq_solver=lsq_solver)
assert_allclose(res.optimality, 0, atol=1e-11)
def test_full_result(self):
lb = np.array([0, -4])
ub = np.array([1, 0])
res = lsq_linear(A, b, (lb, ub), method=self.method)
assert_allclose(res.x, [0.005236663400791, -4])
r = A.dot(res.x) - b
assert_allclose(res.cost, 0.5 * np.dot(r, r))
assert_allclose(res.fun, r)
assert_allclose(res.optimality, 0.0, atol=1e-12)
assert_equal(res.active_mask, [0, -1])
assert_(res.nit < 15)
assert_(res.status == 1 or res.status == 3)
assert_(isinstance(res.message, str))
assert_(res.success)
class SparseMixin(object):
def test_sparse_and_LinearOperator(self):
m = 5000
n = 1000
A = rand(m, n, random_state=0)
b = self.rnd.randn(m)
res = lsq_linear(A, b)
assert_allclose(res.optimality, 0, atol=1e-6)
A = aslinearoperator(A)
res = lsq_linear(A, b)
assert_allclose(res.optimality, 0, atol=1e-6)
def test_sparse_bounds(self):
m = 5000
n = 1000
A = rand(m, n, random_state=0)
b = self.rnd.randn(m)
lb = self.rnd.randn(n)
ub = lb + 1
res = lsq_linear(A, b, (lb, ub))
assert_allclose(res.optimality, 0.0, atol=1e-8)
res = lsq_linear(A, b, (lb, ub), lsmr_tol=1e-13)
assert_allclose(res.optimality, 0.0, atol=1e-8)
res = lsq_linear(A, b, (lb, ub), lsmr_tol='auto')
assert_allclose(res.optimality, 0.0, atol=1e-8)
class TestTRF(BaseMixin, SparseMixin):
method = 'trf'
lsq_solvers = ['exact', 'lsmr']
class TestBVLS(BaseMixin):
method = 'bvls'
lsq_solvers = ['exact']
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