ai-content-maker/.venv/Lib/site-packages/scipy/optimize/tests/test_lsq_linear.py

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2024-05-03 04:18:51 +03:00
import pytest
import numpy as np
from numpy.linalg import lstsq
from numpy.testing import assert_allclose, assert_equal, assert_
from scipy.sparse import rand, coo_matrix
from scipy.sparse.linalg import aslinearoperator
from scipy.optimize import lsq_linear
from scipy.optimize._minimize import Bounds
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:
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])
assert_allclose(res.x, res.unbounded_sol[0])
def test_dense_bounds(self):
# Solutions for comparison are taken from MATLAB.
lb = np.array([-1, -10])
ub = np.array([1, 0])
unbounded_sol = lstsq(A, b, rcond=-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])
assert_allclose(res.unbounded_sol[0], unbounded_sol)
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)
assert_allclose(res.unbounded_sol[0], unbounded_sol)
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)
assert_allclose(res.unbounded_sol[0], unbounded_sol)
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]))
assert_allclose(res.unbounded_sol[0], unbounded_sol)
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]))
assert_allclose(res.unbounded_sol[0], unbounded_sol)
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]))
assert_allclose(res.unbounded_sol[0], unbounded_sol)
def test_bounds_variants(self):
x = np.array([1, 3])
A = self.rnd.uniform(size=(2, 2))
b = A@x
lb = np.array([1, 1])
ub = np.array([2, 2])
bounds_old = (lb, ub)
bounds_new = Bounds(lb, ub)
res_old = lsq_linear(A, b, bounds_old)
res_new = lsq_linear(A, b, bounds_new)
assert not np.allclose(res_new.x, res_new.unbounded_sol[0])
assert_allclose(res_old.x, res_new.x)
def test_np_matrix(self):
# gh-10711
with np.testing.suppress_warnings() as sup:
sup.filter(PendingDeprecationWarning)
A = np.matrix([[20, -4, 0, 2, 3], [10, -2, 1, 0, -1]])
k = np.array([20, 15])
lsq_linear(A, k)
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])
assert_allclose(res.unbounded_sol[0], lstsq(A, b, rcond=-1)[0])
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)
assert_allclose(res.unbounded_sol[0], lstsq(A, b, rcond=-1)[0])
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])
assert_allclose(res.unbounded_sol[0], lstsq(A, b, rcond=-1)[0])
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)
@pytest.mark.xslow
def test_large_rank_deficient(self):
np.random.seed(0)
n, m = np.sort(np.random.randint(2, 1000, size=2))
m *= 2 # make m >> n
A = 1.0 * np.random.randint(-99, 99, size=[m, n])
b = 1.0 * np.random.randint(-99, 99, size=[m])
bounds = 1.0 * np.sort(np.random.randint(-99, 99, size=(2, n)), axis=0)
bounds[1, :] += 1.0 # ensure up > lb
# Make the A matrix strongly rank deficient by replicating some columns
w = np.random.choice(n, n) # Select random columns with duplicates
A = A[:, w]
x_bvls = lsq_linear(A, b, bounds=bounds, method='bvls').x
x_trf = lsq_linear(A, b, bounds=bounds, method='trf').x
cost_bvls = np.sum((A @ x_bvls - b)**2)
cost_trf = np.sum((A @ x_trf - b)**2)
assert_(abs(cost_bvls - cost_trf) < cost_trf*1e-10)
def test_convergence_small_matrix(self):
A = np.array([[49.0, 41.0, -32.0],
[-19.0, -32.0, -8.0],
[-13.0, 10.0, 69.0]])
b = np.array([-41.0, -90.0, 47.0])
bounds = np.array([[31.0, -44.0, 26.0],
[54.0, -32.0, 28.0]])
x_bvls = lsq_linear(A, b, bounds=bounds, method='bvls').x
x_trf = lsq_linear(A, b, bounds=bounds, method='trf').x
cost_bvls = np.sum((A @ x_bvls - b)**2)
cost_trf = np.sum((A @ x_trf - b)**2)
assert_(abs(cost_bvls - cost_trf) < cost_trf*1e-10)
class SparseMixin:
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,
lsmr_maxiter=1500)
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)
def test_sparse_ill_conditioned(self):
# Sparse matrix with condition number of ~4 million
data = np.array([1., 1., 1., 1. + 1e-6, 1.])
row = np.array([0, 0, 1, 2, 2])
col = np.array([0, 2, 1, 0, 2])
A = coo_matrix((data, (row, col)), shape=(3, 3))
# Get the exact solution
exact_sol = lsq_linear(A.toarray(), b, lsq_solver='exact')
# Default lsmr arguments should not fully converge the solution
default_lsmr_sol = lsq_linear(A, b, lsq_solver='lsmr')
with pytest.raises(AssertionError, match=""):
assert_allclose(exact_sol.x, default_lsmr_sol.x)
# By increasing the maximum lsmr iters, it will converge
conv_lsmr = lsq_linear(A, b, lsq_solver='lsmr', lsmr_maxiter=10)
assert_allclose(exact_sol.x, conv_lsmr.x)
class TestTRF(BaseMixin, SparseMixin):
method = 'trf'
lsq_solvers = ['exact', 'lsmr']
class TestBVLS(BaseMixin):
method = 'bvls'
lsq_solvers = ['exact']
class TestErrorChecking:
def test_option_lsmr_tol(self):
# Should work with a positive float, string equal to 'auto', or None
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol=1e-2)
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol='auto')
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol=None)
# Should raise error with negative float, strings
# other than 'auto', and integers
err_message = "`lsmr_tol` must be None, 'auto', or positive float."
with pytest.raises(ValueError, match=err_message):
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol=-0.1)
with pytest.raises(ValueError, match=err_message):
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol='foo')
with pytest.raises(ValueError, match=err_message):
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_tol=1)
def test_option_lsmr_maxiter(self):
# Should work with positive integers or None
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_maxiter=1)
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_maxiter=None)
# Should raise error with 0 or negative max iter
err_message = "`lsmr_maxiter` must be None or positive integer."
with pytest.raises(ValueError, match=err_message):
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_maxiter=0)
with pytest.raises(ValueError, match=err_message):
_ = lsq_linear(A, b, lsq_solver='lsmr', lsmr_maxiter=-1)