162 lines
5.4 KiB
Python
162 lines
5.4 KiB
Python
import numpy as np
|
|
from numpy.linalg import lstsq
|
|
from numpy.testing import assert_allclose, assert_equal, assert_
|
|
|
|
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)
|
|
|
|
# This is a test for issue #9982.
|
|
def test_almost_singular(self):
|
|
A = np.array(
|
|
[[0.8854232310355122, 0.0365312146937765, 0.0365312146836789],
|
|
[0.3742460132129041, 0.0130523214078376, 0.0130523214077873],
|
|
[0.9680633871281361, 0.0319366128718639, 0.0319366128718388]])
|
|
|
|
b = np.array(
|
|
[0.0055029366538097, 0.0026677442422208, 0.0066612514782381])
|
|
|
|
result = lsq_linear(A, b, method=self.method)
|
|
assert_(result.cost < 1.1e-8)
|
|
|
|
|
|
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-6)
|
|
|
|
res = lsq_linear(A, b, (lb, ub), lsmr_tol=1e-13)
|
|
assert_allclose(res.optimality, 0.0, atol=1e-6)
|
|
|
|
res = lsq_linear(A, b, (lb, ub), lsmr_tol='auto')
|
|
assert_allclose(res.optimality, 0.0, atol=1e-6)
|
|
|
|
|
|
class TestTRF(BaseMixin, SparseMixin):
|
|
method = 'trf'
|
|
lsq_solvers = ['exact', 'lsmr']
|
|
|
|
|
|
class TestBVLS(BaseMixin):
|
|
method = 'bvls'
|
|
lsq_solvers = ['exact']
|
|
|