def test_imsave(self):
picdir = os.path.join(datapath, "data")
for png in glob.iglob(picdir + "/*.png"):
with suppress_warnings() as sup:
# PIL causes a Py3k ResourceWarning
sup.filter(message="unclosed file")
img = misc.imread(png)
tmpdir = tempfile.mkdtemp()
try:
fn1 = os.path.join(tmpdir, 'test.png')
fn2 = os.path.join(tmpdir, 'testimg')
with suppress_warnings() as sup:
# PIL causes a Py3k ResourceWarning
sup.filter(message="unclosed file")
misc.imsave(fn1, img)
misc.imsave(fn2, img, 'PNG')
with suppress_warnings() as sup:
# PIL causes a Py3k ResourceWarning
sup.filter(message="unclosed file")
data1 = misc.imread(fn1)
data2 = misc.imread(fn2)
assert_allclose(data1, img)
assert_allclose(data2, img)
assert_equal(data1.shape, img.shape)
assert_equal(data2.shape, img.shape)
finally:
shutil.rmtree(tmpdir)
def test_zero_der_nz_dp():
"""Test secant method with a non-zero dp, but an infinite newton step"""
# pick a symmetrical functions and choose a point on the side that with dx
# makes a secant that is a flat line with zero slope, EG: f = (x - 100)**2,
# which has a root at x = 100 and is symmetrical around the line x = 100
# we have to pick a really big number so that it is consistently true
# now find a point on each side so that the secant has a zero slope
dx = np.finfo(float).eps ** 0.33
# 100 - p0 = p1 - 100 = p0 * (1 + dx) + dx - 100
# -> 200 = p0 * (2 + dx) + dx
p0 = (200.0 - dx) / (2.0 + dx)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "RMS of")
x = zeros.newton(lambda y: (y - 100.0)**2, x0=[p0] * 10)
assert_allclose(x, [100] * 10)
# test scalar cases too
p0 = (2.0 - 1e-4) / (2.0 + 1e-4)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "Tolerance of")
x = zeros.newton(lambda y: (y - 1.0) ** 2, x0=p0)
assert_allclose(x, 1)
p0 = (-2.0 + 1e-4) / (2.0 + 1e-4)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "Tolerance of")
x = zeros.newton(lambda y: (y + 1.0) ** 2, x0=p0)
assert_allclose(x, -1)
def test_callback(self):
def store_residual(r, rvec):
rvec[rvec.nonzero()[0].max()+1] = r
# Define, A,b
A = csr_matrix(array([[-2,1,0,0,0,0],[1,-2,1,0,0,0],[0,1,-2,1,0,0],[0,0,1,-2,1,0],[0,0,0,1,-2,1],[0,0,0,0,1,-2]]))
b = ones((A.shape[0],))
maxiter = 1
rvec = zeros(maxiter+1)
rvec[0] = 1.0
callback = lambda r:store_residual(r, rvec)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x,flag = gmres(A, b, x0=zeros(A.shape[0]), tol=1e-16, maxiter=maxiter, callback=callback)
# Expected output from Scipy 1.0.0
assert_allclose(rvec, array([1.0, 0.81649658092772603]), rtol=1e-10)
# Test preconditioned callback
M = 1e-3 * np.eye(A.shape[0])
rvec = zeros(maxiter+1)
rvec[0] = 1.0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, flag = gmres(A, b, M=M, tol=1e-16, maxiter=maxiter, callback=callback)
# Expected output from Scipy 1.0.0 (callback has preconditioned residual!)
assert_allclose(rvec, array([1.0, 1e-3 * 0.81649658092772603]), rtol=1e-10)
def test_moments(distname, arg, normalization_ok, higher_ok):
try:
distfn = getattr(stats, distname)
except TypeError:
distfn = distname
distname = 'rv_histogram_instance'
with suppress_warnings() as sup:
sup.filter(IntegrationWarning, "The integral is probably divergent, or slowly convergent.")
m, v, s, k = distfn.stats(*arg, moments='mvsk')
if normalization_ok:
check_normalization(distfn, arg, distname)
if higher_ok:
check_mean_expect(distfn, arg, m, distname)
with suppress_warnings() as sup:
sup.filter(IntegrationWarning,
"The integral is probably divergent, or slowly convergent.")
check_skew_expect(distfn, arg, m, v, s, distname)
check_var_expect(distfn, arg, m, v, distname)
check_kurt_expect(distfn, arg, m, v, k, distname)
check_loc_scale(distfn, arg, m, v, distname)
check_moment(distfn, arg, m, v, distname)
def test_errprint():
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
flag = sc.errprint(True)
try:
assert_(isinstance(flag, bool))
with pytest.warns(sc.SpecialFunctionWarning):
sc.loggamma(0)
finally:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
sc.errprint(flag)
def test_bytescale_cscale_lowhigh(self):
a = np.arange(10)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
actual = misc.bytescale(a, cmin=3, cmax=6, low=100, high=200)
expected = [100, 100, 100, 100, 133, 167, 200, 200, 200, 200]
assert_equal(actual, expected)
def test_bytescale(self):
x = np.array([0, 1, 2], np.uint8)
y = np.array([0, 1, 2])
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
assert_equal(misc.bytescale(x), x)
assert_equal(misc.bytescale(y), [0, 128, 255])
def test_imread_indexed_png():
# The file `foo3x5x4indexed.png` was created with this array
# (3x5 is (height)x(width)):
data = np.array([[[127, 0, 255, 255],
[127, 0, 255, 255],
[127, 0, 255, 255],
[127, 0, 255, 255],
[127, 0, 255, 255]],
[[192, 192, 255, 0],
[192, 192, 255, 0],
[0, 0, 255, 0],
[0, 0, 255, 0],
[0, 0, 255, 0]],
[[0, 31, 255, 255],
[0, 31, 255, 255],
[0, 31, 255, 255],
[0, 31, 255, 255],
[0, 31, 255, 255]]], dtype=np.uint8)
filename = os.path.join(datapath, 'data', 'foo3x5x4indexed.png')
with open(filename, 'rb') as f:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
im = misc.imread(f)
assert_array_equal(im, data)
def test_bytescale_low_equals_high(self):
a = np.arange(3)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
actual = misc.bytescale(a, low=10, high=10)
expected = [10, 10, 10]
assert_equal(actual, expected)
def test_bytescale_rounding(self):
a = np.array([-0.5, 0.5, 1.5, 2.5, 3.5])
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
actual = misc.bytescale(a, cmin=0, cmax=10, low=0, high=10)
expected = [0, 1, 2, 3, 4]
assert_equal(actual, expected)
def test_spherical_jn_inf_complex(self):
# https://dlmf.nist.gov/10.52.E3
n = 7
x = np.array([-inf + 0j, inf + 0j, inf*(1+1j)])
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in multiply")
assert_allclose(spherical_jn(n, x), np.array([0, 0, inf*(1+1j)]))
def test_breakdown_underdetermined(self):
# Should find LSQ solution in the Krylov span in one inner
# iteration, despite solver breakdown from nilpotent A.
A = np.array([[0, 1, 1, 1],
[0, 0, 1, 1],
[0, 0, 0, 1],
[0, 0, 0, 0]], dtype=float)
bs = [
np.array([1, 1, 1, 1]),
np.array([1, 1, 1, 0]),
np.array([1, 1, 0, 0]),
np.array([1, 0, 0, 0]),
]
for b in bs:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
xp, info = lgmres(A, b, maxiter=1)
resp = np.linalg.norm(A.dot(xp) - b)
K = np.c_[b, A.dot(b), A.dot(A.dot(b)), A.dot(A.dot(A.dot(b)))]
y, _, _, _ = np.linalg.lstsq(A.dot(K), b, rcond=-1)
x = K.dot(y)
res = np.linalg.norm(A.dot(x) - b)
assert_allclose(resp, res, err_msg=repr(b))
def test_multiple_constraint_objects(self):
fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2 + (x[2] - 0.75)**2
x0 = [2, 0, 1]
coni = [] # only inequality constraints (can use cobyla)
methods = ["slsqp", "cobyla", "trust-constr"]
# mixed old and new
coni.append([{'type': 'ineq', 'fun': lambda x: x[0] - 2 * x[1] + 2},
NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])
coni.append([LinearConstraint([1, -2, 0], -2, np.inf),
NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])
coni.append([NonlinearConstraint(lambda x: x[0] - 2 * x[1] + 2, 0, np.inf),
NonlinearConstraint(lambda x: x[0] - x[1], -1, 1)])
for con in coni:
funs = {}
for method in methods:
with suppress_warnings() as sup:
sup.filter(UserWarning)
result = minimize(fun, x0, method=method, constraints=con)
funs[method] = result.fun
assert_allclose(funs['slsqp'], funs['trust-constr'], rtol=1e-4)
assert_allclose(funs['cobyla'], funs['trust-constr'], rtol=1e-4)
def test_splev(self):
xnew, b, b2 = self.xnew, self.b, self.b2
# check that splev works with 1D array of coefficients
# for array and scalar `x`
assert_allclose(splev(xnew, b),
b(xnew), atol=1e-15, rtol=1e-15)
assert_allclose(splev(xnew, b.tck),
b(xnew), atol=1e-15, rtol=1e-15)
assert_allclose([splev(x, b) for x in xnew],
b(xnew), atol=1e-15, rtol=1e-15)
# With n-D coefficients, there's a quirck:
# splev(x, BSpline) is equivalent to BSpline(x)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning,
"Calling splev.. with BSpline objects with c.ndim > 1 is not recommended.")
assert_allclose(splev(xnew, b2), b2(xnew), atol=1e-15, rtol=1e-15)
# However, splev(x, BSpline.tck) needs some transposes. This is because
# BSpline interpolates along the first axis, while the legacy FITPACK
# wrapper does list(map(...)) which effectively interpolates along the
# last axis. Like so:
sh = tuple(range(1, b2.c.ndim)) + (0,) # sh = (1, 2, 0)
cc = b2.c.transpose(sh)
tck = (b2.t, cc, b2.k)
assert_allclose(splev(xnew, tck),
b2(xnew).transpose(sh), atol=1e-15, rtol=1e-15)
def test_triangularity_perturbation(self):
# Experiment (1) of
# Awad H. Al-Mohy and Nicholas J. Higham (2012)
# Improved Inverse Scaling and Squaring Algorithms
# for the Matrix Logarithm.
A = np.array([
[3.2346e-1, 3e4, 3e4, 3e4],
[0, 3.0089e-1, 3e4, 3e4],
[0, 0, 3.221e-1, 3e4],
[0, 0, 0, 3.0744e-1]],
dtype=float)
A_logm = np.array([
[-1.12867982029050462e+00, 9.61418377142025565e+04,
-4.52485573953179264e+09, 2.92496941103871812e+14],
[0.00000000000000000e+00, -1.20101052953082288e+00,
9.63469687211303099e+04, -4.68104828911105442e+09],
[0.00000000000000000e+00, 0.00000000000000000e+00,
-1.13289322264498393e+00, 9.53249183094775653e+04],
[0.00000000000000000e+00, 0.00000000000000000e+00,
0.00000000000000000e+00, -1.17947533272554850e+00]],
dtype=float)
assert_allclose(expm(A_logm), A, rtol=1e-4)
# Perturb the upper triangular matrix by tiny amounts,
# so that it becomes technically not upper triangular.
random.seed(1234)
tiny = 1e-17
A_logm_perturbed = A_logm.copy()
A_logm_perturbed[1, 0] = tiny
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "Ill-conditioned.*")
A_expm_logm_perturbed = expm(A_logm_perturbed)
rtol = 1e-4
atol = 100 * tiny
assert_(not np.allclose(A_expm_logm_perturbed, A, rtol=rtol, atol=atol))
def test_cornercase(self):
np.random.seed(1234)
# Rounding error may prevent convergence with tol=0 --- ensure
# that the return values in this case are correct, and no
# exceptions are raised
for n in [3, 5, 10, 100]:
A = 2*eye(n)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
b = np.ones(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
b = np.random.rand(n)
x, info = gcrotmk(A, b, maxiter=10)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
x, info = gcrotmk(A, b, tol=0, maxiter=10)
if info == 0:
assert_allclose(A.dot(x) - b, 0, atol=1e-14)
def test_integral(self):
x = [1,1,1,2,2,2,4,4,4]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
with suppress_warnings() as sup:
# This seems to fail (ier=1, see ticket 1642).
sup.filter(UserWarning, "\nThe required storage space")
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
tx = [1,2,4]
ty = [1,2,3]
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_singular(self):
A = csc_matrix((5,5), dtype='d')
b = array([1, 2, 3, 4, 5],dtype='d')
with suppress_warnings() as sup:
sup.filter(MatrixRankWarning, "Matrix is exactly singular")
x = spsolve(A, b)
assert_(not np.isfinite(x).any())
def test_reentrancy():
non_reentrant = [cg, cgs, bicg, bicgstab, gmres, qmr]
reentrant = [lgmres, minres, gcrotmk]
for solver in reentrant + non_reentrant:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
_check_reentrancy(solver, solver in reentrant)
def test_zero_rhs(solver):
np.random.seed(1234)
A = np.random.rand(10, 10)
A = A.dot(A.T) + 10 * np.eye(10)
b = np.zeros(10)
tols = np.r_[np.logspace(np.log10(1e-10), np.log10(1e2), 7)]
for tol in tols:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = solver(A, b, tol=tol)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-15)
x, info = solver(A, b, tol=tol, x0=ones(10))
assert_equal(info, 0)
assert_allclose(x, 0, atol=tol)
if solver is not minres:
x, info = solver(A, b, tol=tol, atol=0, x0=ones(10))
if info == 0:
assert_allclose(x, 0)
x, info = solver(A, b, tol=tol, atol=tol)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-300)
x, info = solver(A, b, tol=tol, atol=0)
assert_equal(info, 0)
assert_allclose(x, 0, atol=1e-300)
def test_atol_legacy(self):
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
# Check the strange legacy behavior: the tolerance is interpreted
# as atol, but only for the initial residual
A = eye(2)
b = 1e-6 * ones(2)
x, info = gmres(A, b, tol=1e-5)
assert_array_equal(x, np.zeros(2))
A = eye(2)
b = ones(2)
x, info = gmres(A, b, tol=1e-5)
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-5*np.linalg.norm(b))
assert_allclose(x, b, atol=0, rtol=1e-8)
rndm = np.random.RandomState(12345)
A = rndm.rand(30, 30)
b = 1e-6 * ones(30)
x, info = gmres(A, b, tol=1e-7, restart=20)
assert_(np.linalg.norm(A.dot(x) - b) > 1e-7)
A = eye(2)
b = 1e-10 * ones(2)
x, info = gmres(A, b, tol=1e-8, atol=0)
assert_(np.linalg.norm(A.dot(x) - b) <= 1e-8*np.linalg.norm(b))
def test_bug_6690(self):
# https://github.com/scipy/scipy/issues/6690
A_eq = np.array([[0., 0., 0., 0.93, 0., 0.65, 0., 0., 0.83, 0.]])
b_eq = np.array([0.9626])
A_ub = np.array([[0., 0., 0., 1.18, 0., 0., 0., -0.2, 0.,
-0.22],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0.43, 0., 0., 0., 0., 0., 0.],
[0., -1.22, -0.25, 0., 0., 0., -2.06, 0., 0.,
1.37],
[0., 0., 0., 0., 0., 0., 0., -0.25, 0., 0.]])
b_ub = np.array([0.615, 0., 0.172, -0.869, -0.022])
bounds = np.array(
[[-0.84, -0.97, 0.34, 0.4, -0.33, -0.74, 0.47, 0.09, -1.45, -0.73],
[0.37, 0.02, 2.86, 0.86, 1.18, 0.5, 1.76, 0.17, 0.32, -0.15]]).T
c = np.array([-1.64, 0.7, 1.8, -1.06, -1.16,
0.26, 2.13, 1.53, 0.66, 0.28])
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...")
sup.filter(OptimizeWarning, "Solving system with option...")
sol = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq,
bounds=bounds, method=self.method,
options=self.options)
_assert_success(sol, desired_fun=-1.191)
def test_network_flow_limited_capacity(self):
# A network flow problem with supply and demand at nodes
# and with costs and capacities along directed edges.
# http://blog.sommer-forst.de/2013/04/10/
cost = [2, 2, 1, 3, 1]
bounds = [
[0, 4],
[0, 2],
[0, 2],
[0, 3],
[0, 5]]
n, p = -1, 1
A_eq = [
[n, n, 0, 0, 0],
[p, 0, n, n, 0],
[0, p, p, 0, n],
[0, 0, 0, p, p]]
b_eq = [-4, 0, 0, 4]
if self.method == "simplex":
# Including the callback here ensures the solution can be
# calculated correctly, even when phase 1 terminated
# with some of the artificial variables as pivots
# (i.e. basis[:m] contains elements corresponding to
# the artificial variables)
res = linprog(c=cost, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
method=self.method, options=self.options,
callback=lambda x, **kwargs: None)
else:
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...")
sup.filter(OptimizeWarning, "A_eq does not appear...")
res = linprog(c=cost, A_eq=A_eq, b_eq=b_eq, bounds=bounds,
method=self.method, options=self.options)
_assert_success(res, desired_fun=14)
def test_integration():
rtol = 1e-3
atol = 1e-6
y0 = [1/3, 2/9]
for vectorized, method, t_span, jac in product(
[False, True],
['RK23', 'RK45', 'Radau', 'BDF', 'LSODA'],
[[5, 9], [5, 1]],
[None, jac_rational, jac_rational_sparse]):
if vectorized:
fun = fun_rational_vectorized
else:
fun = fun_rational
with suppress_warnings() as sup:
sup.filter(UserWarning,
"The following arguments have no effect for a chosen solver: `jac`")
res = solve_ivp(fun, t_span, y0, rtol=rtol,
atol=atol, method=method, dense_output=True,
jac=jac, vectorized=vectorized)
assert_equal(res.t[0], t_span[0])
assert_(res.t_events is None)
assert_(res.success)
assert_equal(res.status, 0)
assert_(res.nfev < 40)
if method in ['RK23', 'RK45', 'LSODA']:
assert_equal(res.njev, 0)
assert_equal(res.nlu, 0)
else:
assert_(0 < res.njev < 3)
assert_(0 < res.nlu < 10)
y_true = sol_rational(res.t)
e = compute_error(res.y, y_true, rtol, atol)
assert_(np.all(e < 5))
tc = np.linspace(*t_span)
yc_true = sol_rational(tc)
yc = res.sol(tc)
e = compute_error(yc, yc_true, rtol, atol)
assert_(np.all(e < 5))
tc = (t_span[0] + t_span[-1]) / 2
yc_true = sol_rational(tc)
yc = res.sol(tc)
e = compute_error(yc, yc_true, rtol, atol)
assert_(np.all(e < 5))
# LSODA for some reasons doesn't pass the polynomial through the
# previous points exactly after the order change. It might be some
# bug in LSOSA implementation or maybe we missing something.
if method != 'LSODA':
assert_allclose(res.sol(res.t), res.y, rtol=1e-15, atol=1e-15)
def test_convergence():
for solver in params.solvers:
for case in params.cases:
if solver in case.skip:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_convergence(solver, case)
def test_precond_dummy():
case = params.Poisson1D
for solver in params.solvers:
if solver in case.skip:
continue
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
check_precond_dummy(solver, case)
def test_nearest(self):
N = 5
x = arange(N)
y = arange(N)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`nearest` is deprecated")
assert_allclose(y, nearest(x, y, x+.1))
assert_allclose(y, nearest(x, y, x-.1))
def test_cheb_even_low_attenuation(self):
cheb_even_low_at_true = array([1.000000, 0.451924, 0.51027,
0.541338, 0.541338, 0.51027,
0.451924, 1.000000])
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_even = windows.chebwin(8, at=-10)
assert_array_almost_equal(cheb_even, cheb_even_low_at_true, decimal=4)
def test_magic_square_bug_7044(self):
# test linprog with a problem with a rank-deficient A_eq matrix
A, b, c, N = magic_square(3)
with suppress_warnings() as sup:
sup.filter(OptimizeWarning, "A_eq does not appear...")
res = linprog(c, A_eq=A, b_eq=b, bounds=(0, 1),
method=self.method, options=self.options)
_assert_success(res, desired_fun=1.730550597)
def test_cheb_odd_low_attenuation(self):
cheb_odd_low_at_true = array([1.000000, 0.519052, 0.586405,
0.610151, 0.586405, 0.519052,
1.000000])
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
cheb_odd = windows.chebwin(7, at=10)
assert_array_almost_equal(cheb_odd, cheb_odd_low_at_true, decimal=4)
def test_magic_square_sparse_no_presolve(self):
# test linprog with a problem with a rank-deficient A_eq matrix
A, b, c, N = magic_square(3)
with suppress_warnings() as sup:
sup.filter(MatrixRankWarning, "Matrix is exactly singular")
sup.filter(OptimizeWarning, "Solving system with option...")
o = {key: self.options[key] for key in self.options}
o["presolve"] = False
res = linprog(c, A_eq=A, b_eq=b, bounds=(0, 1),
options=o, method=self.method)
_assert_success(res, desired_fun=1.730550597)
def test_L3(self):
# Lampinen ([5]) test problem 3
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = (x[1]**2 + x[2]**2 + x[1] * x[2] - 14 * x[1] - 16 * x[2] +
(x[3] - 10)**2 + 4 * (x[4] - 5)**2 + (x[5] - 3)**2 + 2 *
(x[6] - 1)**2 + 5 * x[7]**2 + 7 * (x[8] - 11)**2 + 2 *
(x[9] - 10)**2 + (x[10] - 7)**2 + 45)
return fun # maximize
A = np.zeros((4, 11))
A[1, [1, 2, 7, 8]] = -4, -5, 3, -9
A[2, [1, 2, 7, 8]] = -10, 8, 17, -2
A[3, [1, 2, 9, 10]] = 8, -2, -5, 2
A = A[1:, 1:]
b = np.array([-105, 0, -12])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
3 * x[1] - 6 * x[2] - 12 * (x[9] - 8)**2 + 7 * x[10],
-3 * (x[1] - 2)**2 - 4 * (x[2] - 3)**2 - 2 * x[3]**2 +
7 * x[4] + 120, -x[1]**2 - 2 * (x[2] - 2)**2 +
2 * x[1] * x[2] - 14 * x[5] + 6 * x[6],
-5 * x[1]**2 - 8 * x[2] - (x[3] - 6)**2 + 2 * x[4] + 40, -0.5 *
(x[1] - 8)**2 - 2 * (x[2] - 4)**2 - 3 * x[5]**2 + x[6] + 30
]
L = LinearConstraint(A, b, np.inf)
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(-10, 10)] * 10
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f,
bounds,
seed=1234,
constraints=constraints,
popsize=3)
x_opt = (2.171996, 2.363683, 8.773926, 5.095984, 0.9906548, 1.430574,
1.321644, 9.828726, 8.280092, 8.375927)
f_opt = 24.3062091
assert_allclose(f(x_opt), f_opt, atol=1e-5)
assert_allclose(res.x, x_opt, atol=1e-6)
assert_allclose(res.fun, f_opt, atol=1e-5)
assert res.success
assert_(np.all(A @ res.x >= b))
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_leftright_precond(self):
"""Check that QMR works with left and right preconditioners"""
from scipy.sparse.linalg.dsolve import splu
from scipy.sparse.linalg.interface import LinearOperator
n = 100
dat = ones(n)
A = spdiags([-2*dat, 4*dat, -dat], [-1,0,1],n,n)
b = arange(n,dtype='d')
L = spdiags([-dat/2, dat], [-1,0], n, n)
U = spdiags([4*dat, -dat], [0,1], n, n)
with suppress_warnings() as sup:
sup.filter(SparseEfficiencyWarning, "splu requires CSC matrix format")
L_solver = splu(L)
U_solver = splu(U)
def L_solve(b):
return L_solver.solve(b)
def U_solve(b):
return U_solver.solve(b)
def LT_solve(b):
return L_solver.solve(b,'T')
def UT_solve(b):
return U_solver.solve(b,'T')
M1 = LinearOperator((n,n), matvec=L_solve, rmatvec=LT_solve)
M2 = LinearOperator((n,n), matvec=U_solve, rmatvec=UT_solve)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x,info = qmr(A, b, tol=1e-8, maxiter=15, M1=M1, M2=M2)
assert_equal(info,0)
assert_normclose(A*x, b, tol=1e-8)
def test_linear2(self):
N = 3000
x = arange(N, dtype=float)
y = ones((100, N)) * arange(N)
new_x = arange(N) + 0.5
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`linear` is deprecated")
new_y = linear(x, y, new_x)
assert_allclose(new_y[:5, :5],
[[0.5, 1.5, 2.5, 3.5, 4.5], [0.5, 1.5, 2.5, 3.5, 4.5],
[0.5, 1.5, 2.5, 3.5, 4.5], [0.5, 1.5, 2.5, 3.5, 4.5],
[0.5, 1.5, 2.5, 3.5, 4.5]])
def test_remove_redundancy_infeasibility(self):
m, n = 10, 10
c = np.random.rand(n)
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = 2 * A0[-2, :]
b0[-1] *= -1
with suppress_warnings() as sup:
sup.filter(OptimizeWarning, "A_eq does not appear...")
res = linprog(c, A_eq=A0, b_eq=b0,
method=self.method, options=self.options)
_assert_infeasible(res)
def test_docformat():
with suppress_warnings() as sup:
sup.filter(category=DeprecationWarning)
udd = doccer.unindent_dict(doc_dict)
formatted = doccer.docformat(docstring, udd)
assert_equal(formatted, filled_docstring)
single_doc = 'Single line doc %(strtest1)s'
formatted = doccer.docformat(single_doc, doc_dict)
# Note - initial indent of format string does not
# affect subsequent indent of inserted parameter
assert_equal(formatted, """Single line doc Another test
with some indent""")
def test_truncate(self):
np.random.seed(1234)
A = np.random.rand(30, 30) + np.eye(30)
b = np.random.rand(30)
for truncate in ['oldest', 'smallest']:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x, info = gcrotmk(A, b, m=10, k=10, truncate=truncate, tol=1e-4,
maxiter=200)
assert_equal(info, 0)
assert_allclose(A.dot(x) - b, 0, atol=1e-3)
def test_magic_square_bug_7044(self):
# test linprog with a problem with a rank-deficient A_eq matrix
A, b, c, N = magic_square(3)
with suppress_warnings() as sup:
sup.filter(OptimizeWarning, "A_eq does not appear...")
res = linprog(c,
A_eq=A,
b_eq=b,
bounds=(0, 1),
method=self.method,
options=self.options)
_assert_success(res, desired_fun=1.730550597)
def test_padecases_dtype_sparse_complex(self):
# float32 and complex64 lead to errors in spsolve/UMFpack
dtype = np.complex128
for scale in [1e-2, 1e-1, 5e-1, 1, 10]:
a = scale * speye(3, 3, dtype=dtype, format='csc')
e = exp(scale) * eye(3, dtype=dtype)
with suppress_warnings() as sup:
sup.filter(
SparseEfficiencyWarning,
"Changing the sparsity structure of a csc_matrix is expensive."
)
assert_array_almost_equal_nulp(expm(a).toarray(), e, nulp=100)
def test_ellip_potential():
def change_coefficient(lambda1, mu, nu, h2, k2):
x = sqrt(lambda1**2 * mu**2 * nu**2 / (h2 * k2))
y = sqrt(
(lambda1**2 - h2) * (mu**2 - h2) * (h2 - nu**2) / (h2 * (k2 - h2)))
z = sqrt(
(lambda1**2 - k2) * (k2 - mu**2) * (k2 - nu**2) / (k2 * (k2 - h2)))
return x, y, z
def solid_int_ellip(lambda1, mu, nu, n, p, h2, k2):
return (ellip_harm(h2, k2, n, p, lambda1) *
ellip_harm(h2, k2, n, p, mu) * ellip_harm(h2, k2, n, p, nu))
def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
return (ellip_harm_2(h2, k2, n, p, lambda1) *
ellip_harm(h2, k2, n, p, mu) * ellip_harm(h2, k2, n, p, nu))
def summation(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
tol = 1e-8
sum1 = 0
for n in range(20):
xsum = 0
for p in range(1, 2 * n + 2):
xsum += (4 * pi *
(solid_int_ellip(lambda2, mu2, nu2, n, p, h2, k2) *
solid_int_ellip2(lambda1, mu1, nu1, n, p, h2, k2)) /
(ellip_normal(h2, k2, n, p) * (2 * n + 1)))
if abs(xsum) < 0.1 * tol * abs(sum1):
break
sum1 += xsum
return sum1, xsum
def potential(lambda1, mu1, nu1, lambda2, mu2, nu2, h2, k2):
x1, y1, z1 = change_coefficient(lambda1, mu1, nu1, h2, k2)
x2, y2, z2 = change_coefficient(lambda2, mu2, nu2, h2, k2)
res = sqrt((x2 - x1)**2 + (y2 - y1)**2 + (z2 - z1)**2)
return 1 / res
pts = [
(120, sqrt(19), 2, 41, sqrt(17), 2, 15, 25),
(120, sqrt(16), 3.2, 21, sqrt(11), 2.9, 11, 20),
]
with suppress_warnings() as sup:
sup.filter(IntegrationWarning, "The occurrence of roundoff error")
sup.filter(IntegrationWarning, "The maximum number of subdivisions")
for p in pts:
err_msg = repr(p)
exact = potential(*p)
result, last_term = summation(*p)
assert_allclose(exact, result, atol=0, rtol=1e-8, err_msg=err_msg)
assert_(abs(result - exact) < 10 * abs(last_term), err_msg)
def test_intermediate_overlow():
# Make sure we avoid overflow in situations where cosh/sinh would
# overflow but the product with sin/cos would not
sinpi_pts = [complex(1 + 1e-14, 227),
complex(1e-35, 250),
complex(1e-301, 445)]
# Data generated with mpmath
sinpi_std = [complex(-8.113438309924894e+295, -np.inf),
complex(1.9507801934611995e+306, np.inf),
complex(2.205958493464539e+306, np.inf)]
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in multiply")
for p, std in zip(sinpi_pts, sinpi_std):
assert_allclose(sinpi(p), std)
# Test for cosine, less interesting because cos(0) = 1.
p = complex(0.5 + 1e-14, 227)
std = complex(-8.113438309924894e+295, -np.inf)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "invalid value encountered in multiply")
assert_allclose(cospi(p), std)
def test_alternate_initial_point(self):
# Test with a rather large problem (400 variables,
# 40 constraints) generated by https://gist.github.com/denis-bz/8647461
# use "improved" initial point
A, b, c = lpgen_2d(20, 20)
with suppress_warnings() as sup:
sup.filter(RuntimeWarning, "scipy.linalg.solve\nIll...")
sup.filter(OptimizeWarning, "Solving system with option...")
res = linprog(c, A_ub=A, b_ub=b, method=self.method,
options={"ip": True, "disp": True})
# ip code is independent of sparse/dense
_assert_success(res, desired_fun=-64.049494229)
def test_delaunay(self):
# Smoke test
fig = plt.figure()
obj = Delaunay(self.points)
s_before = obj.simplices.copy()
with suppress_warnings() as sup:
# filter can be removed when matplotlib 1.x is dropped
sup.filter(message="The ishold function was deprecated in version")
r = delaunay_plot_2d(obj, ax=fig.gca())
assert_array_equal(obj.simplices, s_before) # shouldn't modify
assert_(r is fig)
delaunay_plot_2d(obj, ax=fig.gca())
def test_windowfunc_basics():
for window_name, params in window_funcs:
window = getattr(windows, window_name)
with suppress_warnings() as sup:
sup.filter(UserWarning, "This window is not suitable")
if window_name in ('slepian', 'hanning'):
sup.filter(DeprecationWarning)
# Check symmetry for odd and even lengths
w1 = window(8, *params, sym=True)
w2 = window(7, *params, sym=False)
assert_array_almost_equal(w1[:-1], w2)
w1 = window(9, *params, sym=True)
w2 = window(8, *params, sym=False)
assert_array_almost_equal(w1[:-1], w2)
# Check that functions run and output lengths are correct
assert_equal(len(window(6, *params, sym=True)), 6)
assert_equal(len(window(6, *params, sym=False)), 6)
assert_equal(len(window(7, *params, sym=True)), 7)
assert_equal(len(window(7, *params, sym=False)), 7)
# Check invalid lengths
assert_raises(ValueError, window, 5.5, *params)
assert_raises(ValueError, window, -7, *params)
# Check degenerate cases
assert_array_equal(window(0, *params, sym=True), [])
assert_array_equal(window(0, *params, sym=False), [])
assert_array_equal(window(1, *params, sym=True), [1])
assert_array_equal(window(1, *params, sym=False), [1])
# Check dtype
assert_(window(0, *params, sym=True).dtype == 'float')
assert_(window(0, *params, sym=False).dtype == 'float')
assert_(window(1, *params, sym=True).dtype == 'float')
assert_(window(1, *params, sym=False).dtype == 'float')
assert_(window(6, *params, sym=True).dtype == 'float')
assert_(window(6, *params, sym=False).dtype == 'float')
# Check normalization
assert_array_less(window(10, *params, sym=True), 1.01)
assert_array_less(window(10, *params, sym=False), 1.01)
assert_array_less(window(9, *params, sym=True), 1.01)
assert_array_less(window(9, *params, sym=False), 1.01)
# Check that DFT-even spectrum is purely real for odd and even
assert_allclose(fftpack.fft(window(10, *params, sym=False)).imag,
0,
atol=1e-14)
assert_allclose(fftpack.fft(window(11, *params, sym=False)).imag,
0,
atol=1e-14)
def test_imread():
lp = os.path.join(os.path.dirname(__file__), 'dots.png')
with suppress_warnings() as sup:
# PIL causes a Py3k ResourceWarning
sup.filter(message="unclosed file")
sup.filter(DeprecationWarning)
img = ndi.imread(lp, mode="RGB")
assert_array_equal(img.shape, (300, 420, 3))
with suppress_warnings() as sup:
# PIL causes a Py3k ResourceWarning
sup.filter(message="unclosed file")
sup.filter(DeprecationWarning)
img = ndi.imread(lp, flatten=True)
assert_array_equal(img.shape, (300, 420))
with open(lp, 'rb') as fobj:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
img = ndi.imread(fobj, mode="RGB")
assert_array_equal(img.shape, (300, 420, 3))
def test_regression_2359(self):
# Check regression --- for certain point sets, gradient
# estimation could end up in an infinite loop
points = np.load(data_file('estimate_gradients_hang.npy'))
values = np.random.rand(points.shape[0])
tri = qhull.Delaunay(points)
# This should not hang
with suppress_warnings() as sup:
sup.filter(interpnd.GradientEstimationWarning,
"Gradient estimation did not converge")
interpnd.estimate_gradients_2d_global(tri, values, maxiter=1)
def do_solve(**kw):
count[0] = 0
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, ".*called without specifying.*")
x0, flag = lgmres(A,
b,
x0=zeros(A.shape[0]),
inner_m=6,
tol=1e-14,
**kw)
count_0 = count[0]
assert_(allclose(A * x0, b, rtol=1e-12, atol=1e-12), norm(A * x0 - b))
return x0, count_0
def test_imread_4bit():
# pattern4bit.png is a 12(h) x 31(w) grayscale image with bit depth 4.
# The value in row j and column i is maximum(j, i) % 16.
# When scaled up to 8 bits, the values become [0, 17, 34, ..., 255].
filename = os.path.join(datapath, 'data', 'pattern4bit.png')
with open(filename, 'rb') as f:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning)
im = misc.imread(f)
assert_equal(im.dtype, np.uint8)
j, i = np.meshgrid(np.arange(12), np.arange(31), indexing='ij')
expected = 17 * (np.maximum(j, i) % 16).astype(np.uint8)
assert_equal(im, expected)
def test_linear_constant(self):
x = [1, 1, 1, 2, 2, 2, 3, 3, 3]
y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
z = [3, 3, 3, 3, 3, 3, 3, 3, 3]
s = 0.1
tx = [1 + s, 3 - s]
ty = [1 + s, 3 - s]
with suppress_warnings() as sup:
r = sup.record(UserWarning, "\nThe coefficients of the spline")
lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
assert_equal(len(r), 1)
assert_almost_equal(lut(2, 2), 3.)
def test_sparse_solve_options(self):
A, b, c, N = magic_square(3)
with suppress_warnings() as sup:
sup.filter(OptimizeWarning, "A_eq does not appear...")
sup.filter(OptimizeWarning, "Invalid permc_spec option")
o = {key: self.options[key] for key in self.options}
permc_specs = ('NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A',
'COLAMD', 'ekki-ekki-ekki')
for permc_spec in permc_specs:
o["permc_spec"] = permc_spec
res = linprog(c, A_eq=A, b_eq=b, bounds=(0, 1),
method=self.method, options=o)
_assert_success(res, desired_fun=1.730550597)
def check_rvs_broadcast(distfunc, distname, allargs, shape, shape_only, otype):
np.random.seed(123)
with suppress_warnings() as sup:
# frechet_l and frechet_r are deprecated, so all their
# methods generate DeprecationWarnings.
sup.filter(category=DeprecationWarning, message=".*frechet_")
sample = distfunc.rvs(*allargs)
assert_equal(sample.shape, shape, "%s: rvs failed to broadcast" % distname)
if not shape_only:
rvs = np.vectorize(lambda *allargs: distfunc.rvs(*allargs), otypes=otype)
np.random.seed(123)
expected = rvs(*allargs)
assert_allclose(sample, expected, rtol=1e-15)
def test_read_4():
for mmap in [False, True]:
with suppress_warnings() as sup:
sup.filter(wavfile.WavFileWarning,
"Chunk .non-data. not understood, skipping it")
rate, data = wavfile.read(datafile('test-48000Hz-2ch-64bit-float-le-wavex.wav'),
mmap=mmap)
assert_equal(rate, 48000)
assert_(np.issubdtype(data.dtype, np.float64))
assert_equal(data.shape, (480, 2))
del data
def test_itemset_no_segfault_on_readonly():
# Regression test for ticket #1202.
# Open the test file in read-only mode.
filename = pjoin(TEST_DATA_PATH, 'example_1.nc')
with suppress_warnings() as sup:
sup.filter(RuntimeWarning,
"Cannot close a netcdf_file opened with mmap=True, when netcdf_variables or arrays referring to its data still exist")
with netcdf_file(filename, 'r', mmap=True) as f:
time_var = f.variables['time']
# time_var.assignValue(42) should raise a RuntimeError--not seg. fault!
assert_raises(RuntimeError, time_var.assignValue, 42)
def test_isintlike(self):
assert_equal(sputils.isintlike(-4), True)
assert_equal(sputils.isintlike(np.array(3)), True)
assert_equal(sputils.isintlike(np.array([3])), False)
with suppress_warnings() as sup:
sup.filter(DeprecationWarning,
"Inexact indices into sparse matrices are deprecated")
assert_equal(sputils.isintlike(3.0), True)
assert_equal(sputils.isintlike(2.5), False)
assert_equal(sputils.isintlike(1 + 3j), False)
assert_equal(sputils.isintlike((1,)), False)
assert_equal(sputils.isintlike((1, 2)), False)
def test_romb_gh_3731(self):
# Check that romb makes maximal use of data points
x = np.arange(2*2*2*2+1)
y = np.cos(0.2*x)
val = romb(y)
val2, err = quad(lambda x: np.cos(0.2*x), x.min(), x.max())
assert_allclose(val, val2, rtol=1e-8, atol=0)
# should be equal to romb with 2**k+1 samples
with suppress_warnings() as sup:
sup.filter(AccuracyWarning, "divmax .4. exceeded")
val3 = romberg(lambda x: np.cos(0.2*x), x.min(), x.max(), divmax=4)
assert_allclose(val, val3, rtol=1e-12, atol=0)
def test_list_of_problems(self):
for prob in self.list_of_problems:
with suppress_warnings() as sup:
sup.filter(UserWarning)
result = minimize(prob.fun,
prob.x0,
method=self.method,
bounds=prob.bounds,
constraints=prob.constr)
assert_array_almost_equal(result.x, prob.x_opt, decimal=3)
def test_L8(self):
def f(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
fun = 3 * x[1] + 0.000001 * x[1]**3 + 2 * x[2] + 0.000002 / 3 * x[
2]**3
return fun
A = np.zeros((3, 5))
A[1, [4, 3]] = 1, -1
A[2, [3, 4]] = 1, -1
A = A[1:, 1:]
b = np.array([-.55, -.55])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
1000 * np.sin(-x[3] - 0.25) + 1000 * np.sin(-x[4] - 0.25) +
894.8 - x[1], 1000 * np.sin(x[3] - 0.25) +
1000 * np.sin(x[3] - x[4] - 0.25) + 894.8 - x[2],
1000 * np.sin(x[4] - 0.25) +
1000 * np.sin(x[4] - x[3] - 0.25) + 1294.8
]
L = LinearConstraint(A, b, np.inf)
N = NonlinearConstraint(c1, np.full(3, -0.001), np.full(3, 0.001))
bounds = [(0, 1200)] * 2 + [(-.55, .55)] * 2
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f,
bounds,
strategy='rand1bin',
seed=1234,
constraints=constraints,
maxiter=5000)
x_opt = (679.9453, 1026.067, 0.1188764, -0.3962336)
f_opt = 5126.4981
assert_allclose(f(x_opt), f_opt, atol=1e-3)
assert_allclose(res.x[:2], x_opt[:2], atol=2e-3)
assert_allclose(res.x[2:], x_opt[2:], atol=2e-3)
assert_allclose(res.fun, f_opt, atol=2e-2)
assert res.success
assert_(np.all(A @ res.x >= b))
assert_(np.all(np.array(c1(res.x)) >= -0.001))
assert_(np.all(np.array(c1(res.x)) <= 0.001))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
def test_warn_mixed_constraints(self):
# warns about inefficiency of mixed equality/inequality constraints
fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2 + (x[2] - 0.75)**2
cons = NonlinearConstraint(lambda x: [x[0]**2 - x[1], x[1] - x[2]],
[1.1, .8], [1.1, 1.4])
bnds = ((0, None), (0, None), (0, None))
with suppress_warnings() as sup:
sup.filter(UserWarning, "delta_grad == 0.0")
_assert_warns(OptimizeWarning,
minimize,
fun, (2, 0, 1),
method=self.method,
bounds=bnds,
constraints=cons)
def check_fit_args(distfn, arg, rvs):
with np.errstate(all='ignore'), suppress_warnings() as sup:
sup.filter(category=DeprecationWarning, message=".*frechet_")
sup.filter(category=RuntimeWarning,
message="The shape parameter of the erlang")
sup.filter(category=RuntimeWarning,
message="floating point number truncated")
vals = distfn.fit(rvs)
vals2 = distfn.fit(rvs, optimizer='powell')
# Only check the length of the return
# FIXME: should check the actual results to see if we are 'close'
# to what was created --- but what is 'close' enough
npt.assert_(len(vals) == 2 + len(arg))
npt.assert_(len(vals2) == 2 + len(arg))
def test_L4(self):
# Lampinen ([5]) test problem 4
def f(x):
return np.sum(x[:3])
A = np.zeros((4, 9))
A[1, [4, 6]] = 0.0025, 0.0025
A[2, [5, 7, 4]] = 0.0025, 0.0025, -0.0025
A[3, [8, 5]] = 0.01, -0.01
A = A[1:, 1:]
b = np.array([1, 1, 1])
def c1(x):
x = np.hstack(([0], x)) # 1-indexed to match reference
return [
x[1] * x[6] - 833.33252 * x[4] - 100 * x[1] + 83333.333,
x[2] * x[7] - 1250 * x[5] - x[2] * x[4] + 1250 * x[4],
x[3] * x[8] - 1250000 - x[3] * x[5] + 2500 * x[5]
]
L = LinearConstraint(A, -np.inf, 1)
N = NonlinearConstraint(c1, 0, np.inf)
bounds = [(100, 10000)] + [(1000, 10000)] * 2 + [(10, 1000)] * 5
constraints = (L, N)
with suppress_warnings() as sup:
sup.filter(UserWarning)
res = differential_evolution(f,
bounds,
strategy='rand1bin',
seed=1234,
constraints=constraints,
popsize=3)
f_opt = 7049.248
x_opt = [
579.306692, 1359.97063, 5109.9707, 182.0177, 295.601172, 217.9823,
286.416528, 395.601172
]
assert_allclose(f(x_opt), f_opt, atol=0.001)
assert_allclose(res.fun, f_opt, atol=0.001)
assert_allclose(res.x, x_opt, atol=0.002)
assert res.success
assert_(np.all(A @ res.x <= b))
assert_(np.all(np.array(c1(res.x)) >= 0))
assert_(np.all(res.x >= np.array(bounds)[:, 0]))
assert_(np.all(res.x <= np.array(bounds)[:, 1]))
