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import sys
try:
from StringIO import StringIO
except ImportError:
from io import StringIO
import numpy as np
from numpy.testing import (assert_, assert_array_equal, assert_allclose,
assert_equal)
from pytest import raises as assert_raises
from scipy.sparse import coo_matrix
from scipy.special import erf
from scipy.integrate._bvp import (modify_mesh, estimate_fun_jac,
estimate_bc_jac, compute_jac_indices,
construct_global_jac, solve_bvp)
import pytest
def exp_fun(x, y):
return np.vstack((y[1], y[0]))
def exp_fun_jac(x, y):
df_dy = np.empty((2, 2, x.shape[0]))
df_dy[0, 0] = 0
df_dy[0, 1] = 1
df_dy[1, 0] = 1
df_dy[1, 1] = 0
return df_dy
def exp_bc(ya, yb):
return np.hstack((ya[0] - 1, yb[0]))
def exp_bc_complex(ya, yb):
return np.hstack((ya[0] - 1 - 1j, yb[0]))
def exp_bc_jac(ya, yb):
dbc_dya = np.array([
[1, 0],
[0, 0]
])
dbc_dyb = np.array([
[0, 0],
[1, 0]
])
return dbc_dya, dbc_dyb
def exp_sol(x):
return (np.exp(-x) - np.exp(x - 2)) / (1 - np.exp(-2))
def sl_fun(x, y, p):
return np.vstack((y[1], -p[0]**2 * y[0]))
def sl_fun_jac(x, y, p):
n, m = y.shape
df_dy = np.empty((n, 2, m))
df_dy[0, 0] = 0
df_dy[0, 1] = 1
df_dy[1, 0] = -p[0]**2
df_dy[1, 1] = 0
df_dp = np.empty((n, 1, m))
df_dp[0, 0] = 0
df_dp[1, 0] = -2 * p[0] * y[0]
return df_dy, df_dp
def sl_bc(ya, yb, p):
return np.hstack((ya[0], yb[0], ya[1] - p[0]))
def sl_bc_jac(ya, yb, p):
dbc_dya = np.zeros((3, 2))
dbc_dya[0, 0] = 1
dbc_dya[2, 1] = 1
dbc_dyb = np.zeros((3, 2))
dbc_dyb[1, 0] = 1
dbc_dp = np.zeros((3, 1))
dbc_dp[2, 0] = -1
return dbc_dya, dbc_dyb, dbc_dp
def sl_sol(x, p):
return np.sin(p[0] * x)
def emden_fun(x, y):
return np.vstack((y[1], -y[0]**5))
def emden_fun_jac(x, y):
df_dy = np.empty((2, 2, x.shape[0]))
df_dy[0, 0] = 0
df_dy[0, 1] = 1
df_dy[1, 0] = -5 * y[0]**4
df_dy[1, 1] = 0
return df_dy
def emden_bc(ya, yb):
return np.array([ya[1], yb[0] - (3/4)**0.5])
def emden_bc_jac(ya, yb):
dbc_dya = np.array([
[0, 1],
[0, 0]
])
dbc_dyb = np.array([
[0, 0],
[1, 0]
])
return dbc_dya, dbc_dyb
def emden_sol(x):
return (1 + x**2/3)**-0.5
def undefined_fun(x, y):
return np.zeros_like(y)
def undefined_bc(ya, yb):
return np.array([ya[0], yb[0] - 1])
def big_fun(x, y):
f = np.zeros_like(y)
f[::2] = y[1::2]
return f
def big_bc(ya, yb):
return np.hstack((ya[::2], yb[::2] - 1))
def big_sol(x, n):
y = np.ones((2 * n, x.size))
y[::2] = x
return x
def big_fun_with_parameters(x, y, p):
""" Big version of sl_fun, with two parameters.
The two differential equations represented by sl_fun are broadcast to the
number of rows of y, rotating between the parameters p[0] and p[1].
Here are the differential equations:
dy[0]/dt = y[1]
dy[1]/dt = -p[0]**2 * y[0]
dy[2]/dt = y[3]
dy[3]/dt = -p[1]**2 * y[2]
dy[4]/dt = y[5]
dy[5]/dt = -p[0]**2 * y[4]
dy[6]/dt = y[7]
dy[7]/dt = -p[1]**2 * y[6]
.
.
.
"""
f = np.zeros_like(y)
f[::2] = y[1::2]
f[1::4] = -p[0]**2 * y[::4]
f[3::4] = -p[1]**2 * y[2::4]
return f
def big_fun_with_parameters_jac(x, y, p):
# big version of sl_fun_jac, with two parameters
n, m = y.shape
df_dy = np.zeros((n, n, m))
df_dy[range(0, n, 2), range(1, n, 2)] = 1
df_dy[range(1, n, 4), range(0, n, 4)] = -p[0]**2
df_dy[range(3, n, 4), range(2, n, 4)] = -p[1]**2
df_dp = np.zeros((n, 2, m))
df_dp[range(1, n, 4), 0] = -2 * p[0] * y[range(0, n, 4)]
df_dp[range(3, n, 4), 1] = -2 * p[1] * y[range(2, n, 4)]
return df_dy, df_dp
def big_bc_with_parameters(ya, yb, p):
# big version of sl_bc, with two parameters
return np.hstack((ya[::2], yb[::2], ya[1] - p[0], ya[3] - p[1]))
def big_bc_with_parameters_jac(ya, yb, p):
# big version of sl_bc_jac, with two parameters
n = ya.shape[0]
dbc_dya = np.zeros((n + 2, n))
dbc_dyb = np.zeros((n + 2, n))
dbc_dya[range(n // 2), range(0, n, 2)] = 1
dbc_dyb[range(n // 2, n), range(0, n, 2)] = 1
dbc_dp = np.zeros((n + 2, 2))
dbc_dp[n, 0] = -1
dbc_dya[n, 1] = 1
dbc_dp[n + 1, 1] = -1
dbc_dya[n + 1, 3] = 1
return dbc_dya, dbc_dyb, dbc_dp
def big_sol_with_parameters(x, p):
# big version of sl_sol, with two parameters
return np.vstack((np.sin(p[0] * x), np.sin(p[1] * x)))
def shock_fun(x, y):
eps = 1e-3
return np.vstack((
y[1],
-(x * y[1] + eps * np.pi**2 * np.cos(np.pi * x) +
np.pi * x * np.sin(np.pi * x)) / eps
))
def shock_bc(ya, yb):
return np.array([ya[0] + 2, yb[0]])
def shock_sol(x):
eps = 1e-3
k = np.sqrt(2 * eps)
return np.cos(np.pi * x) + erf(x / k) / erf(1 / k)
def nonlin_bc_fun(x, y):
# laplace eq.
return np.stack([y[1], np.zeros_like(x)])
def nonlin_bc_bc(ya, yb):
phiA, phipA = ya
phiC, phipC = yb
kappa, ioA, ioC, V, f = 1.64, 0.01, 1.0e-4, 0.5, 38.9
# Butler-Volmer Kinetics at Anode
hA = 0.0-phiA-0.0
iA = ioA * (np.exp(f*hA) - np.exp(-f*hA))
res0 = iA + kappa * phipA
# Butler-Volmer Kinetics at Cathode
hC = V - phiC - 1.0
iC = ioC * (np.exp(f*hC) - np.exp(-f*hC))
res1 = iC - kappa*phipC
return np.array([res0, res1])
def nonlin_bc_sol(x):
return -0.13426436116763119 - 1.1308709 * x
def test_modify_mesh():
x = np.array([0, 1, 3, 9], dtype=float)
x_new = modify_mesh(x, np.array([0]), np.array([2]))
assert_array_equal(x_new, np.array([0, 0.5, 1, 3, 5, 7, 9]))
x = np.array([-6, -3, 0, 3, 6], dtype=float)
x_new = modify_mesh(x, np.array([1], dtype=int), np.array([0, 2, 3]))
assert_array_equal(x_new, [-6, -5, -4, -3, -1.5, 0, 1, 2, 3, 4, 5, 6])
def test_compute_fun_jac():
x = np.linspace(0, 1, 5)
y = np.empty((2, x.shape[0]))
y[0] = 0.01
y[1] = 0.02
p = np.array([])
df_dy, df_dp = estimate_fun_jac(lambda x, y, p: exp_fun(x, y), x, y, p)
df_dy_an = exp_fun_jac(x, y)
assert_allclose(df_dy, df_dy_an)
assert_(df_dp is None)
x = np.linspace(0, np.pi, 5)
y = np.empty((2, x.shape[0]))
y[0] = np.sin(x)
y[1] = np.cos(x)
p = np.array([1.0])
df_dy, df_dp = estimate_fun_jac(sl_fun, x, y, p)
df_dy_an, df_dp_an = sl_fun_jac(x, y, p)
assert_allclose(df_dy, df_dy_an)
assert_allclose(df_dp, df_dp_an)
x = np.linspace(0, 1, 10)
y = np.empty((2, x.shape[0]))
y[0] = (3/4)**0.5
y[1] = 1e-4
p = np.array([])
df_dy, df_dp = estimate_fun_jac(lambda x, y, p: emden_fun(x, y), x, y, p)
df_dy_an = emden_fun_jac(x, y)
assert_allclose(df_dy, df_dy_an)
assert_(df_dp is None)
def test_compute_bc_jac():
ya = np.array([-1.0, 2])
yb = np.array([0.5, 3])
p = np.array([])
dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(
lambda ya, yb, p: exp_bc(ya, yb), ya, yb, p)
dbc_dya_an, dbc_dyb_an = exp_bc_jac(ya, yb)
assert_allclose(dbc_dya, dbc_dya_an)
assert_allclose(dbc_dyb, dbc_dyb_an)
assert_(dbc_dp is None)
ya = np.array([0.0, 1])
yb = np.array([0.0, -1])
p = np.array([0.5])
dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(sl_bc, ya, yb, p)
dbc_dya_an, dbc_dyb_an, dbc_dp_an = sl_bc_jac(ya, yb, p)
assert_allclose(dbc_dya, dbc_dya_an)
assert_allclose(dbc_dyb, dbc_dyb_an)
assert_allclose(dbc_dp, dbc_dp_an)
ya = np.array([0.5, 100])
yb = np.array([-1000, 10.5])
p = np.array([])
dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(
lambda ya, yb, p: emden_bc(ya, yb), ya, yb, p)
dbc_dya_an, dbc_dyb_an = emden_bc_jac(ya, yb)
assert_allclose(dbc_dya, dbc_dya_an)
assert_allclose(dbc_dyb, dbc_dyb_an)
assert_(dbc_dp is None)
def test_compute_jac_indices():
n = 2
m = 4
k = 2
i, j = compute_jac_indices(n, m, k)
s = coo_matrix((np.ones_like(i), (i, j))).toarray()
s_true = np.array([
[1, 1, 1, 1, 0, 0, 0, 0, 1, 1],
[1, 1, 1, 1, 0, 0, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 1, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 1, 0, 0, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1],
[1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[1, 1, 0, 0, 0, 0, 1, 1, 1, 1],
])
assert_array_equal(s, s_true)
def test_compute_global_jac():
n = 2
m = 5
k = 1
i_jac, j_jac = compute_jac_indices(2, 5, 1)
x = np.linspace(0, 1, 5)
h = np.diff(x)
y = np.vstack((np.sin(np.pi * x), np.pi * np.cos(np.pi * x)))
p = np.array([3.0])
f = sl_fun(x, y, p)
x_middle = x[:-1] + 0.5 * h
y_middle = 0.5 * (y[:, :-1] + y[:, 1:]) - h/8 * (f[:, 1:] - f[:, :-1])
df_dy, df_dp = sl_fun_jac(x, y, p)
df_dy_middle, df_dp_middle = sl_fun_jac(x_middle, y_middle, p)
dbc_dya, dbc_dyb, dbc_dp = sl_bc_jac(y[:, 0], y[:, -1], p)
J = construct_global_jac(n, m, k, i_jac, j_jac, h, df_dy, df_dy_middle,
df_dp, df_dp_middle, dbc_dya, dbc_dyb, dbc_dp)
J = J.toarray()
def J_block(h, p):
return np.array([
[h**2*p**2/12 - 1, -0.5*h, -h**2*p**2/12 + 1, -0.5*h],
[0.5*h*p**2, h**2*p**2/12 - 1, 0.5*h*p**2, 1 - h**2*p**2/12]
])
J_true = np.zeros((m * n + k, m * n + k))
for i in range(m - 1):
J_true[i * n: (i + 1) * n, i * n: (i + 2) * n] = J_block(h[i], p[0])
J_true[:(m - 1) * n:2, -1] = p * h**2/6 * (y[0, :-1] - y[0, 1:])
J_true[1:(m - 1) * n:2, -1] = p * (h * (y[0, :-1] + y[0, 1:]) +
h**2/6 * (y[1, :-1] - y[1, 1:]))
J_true[8, 0] = 1
J_true[9, 8] = 1
J_true[10, 1] = 1
J_true[10, 10] = -1
assert_allclose(J, J_true, rtol=1e-10)
df_dy, df_dp = estimate_fun_jac(sl_fun, x, y, p)
df_dy_middle, df_dp_middle = estimate_fun_jac(sl_fun, x_middle, y_middle, p)
dbc_dya, dbc_dyb, dbc_dp = estimate_bc_jac(sl_bc, y[:, 0], y[:, -1], p)
J = construct_global_jac(n, m, k, i_jac, j_jac, h, df_dy, df_dy_middle,
df_dp, df_dp_middle, dbc_dya, dbc_dyb, dbc_dp)
J = J.toarray()
assert_allclose(J, J_true, rtol=2e-8, atol=2e-8)
def test_parameter_validation():
x = [0, 1, 0.5]
y = np.zeros((2, 3))
assert_raises(ValueError, solve_bvp, exp_fun, exp_bc, x, y)
x = np.linspace(0, 1, 5)
y = np.zeros((2, 4))
assert_raises(ValueError, solve_bvp, exp_fun, exp_bc, x, y)
def fun(x, y, p):
return exp_fun(x, y)
def bc(ya, yb, p):
return exp_bc(ya, yb)
y = np.zeros((2, x.shape[0]))
assert_raises(ValueError, solve_bvp, fun, bc, x, y, p=[1])
def wrong_shape_fun(x, y):
return np.zeros(3)
assert_raises(ValueError, solve_bvp, wrong_shape_fun, bc, x, y)
S = np.array([[0, 0]])
assert_raises(ValueError, solve_bvp, exp_fun, exp_bc, x, y, S=S)
def test_no_params():
x = np.linspace(0, 1, 5)
x_test = np.linspace(0, 1, 100)
y = np.zeros((2, x.shape[0]))
for fun_jac in [None, exp_fun_jac]:
for bc_jac in [None, exp_bc_jac]:
sol = solve_bvp(exp_fun, exp_bc, x, y, fun_jac=fun_jac,
bc_jac=bc_jac)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_equal(sol.x.size, 5)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0], exp_sol(x_test), atol=1e-5)
f_test = exp_fun(x_test, sol_test)
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res**2, axis=0)**0.5
assert_(np.all(norm_res < 1e-3))
assert_(np.all(sol.rms_residuals < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_with_params():
x = np.linspace(0, np.pi, 5)
x_test = np.linspace(0, np.pi, 100)
y = np.ones((2, x.shape[0]))
for fun_jac in [None, sl_fun_jac]:
for bc_jac in [None, sl_bc_jac]:
sol = solve_bvp(sl_fun, sl_bc, x, y, p=[0.5], fun_jac=fun_jac,
bc_jac=bc_jac)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_(sol.x.size < 10)
assert_allclose(sol.p, [1], rtol=1e-4)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0], sl_sol(x_test, [1]),
rtol=1e-4, atol=1e-4)
f_test = sl_fun(x_test, sol_test, [1])
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res ** 2, axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_(np.all(sol.rms_residuals < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_singular_term():
x = np.linspace(0, 1, 10)
x_test = np.linspace(0.05, 1, 100)
y = np.empty((2, 10))
y[0] = (3/4)**0.5
y[1] = 1e-4
S = np.array([[0, 0], [0, -2]])
for fun_jac in [None, emden_fun_jac]:
for bc_jac in [None, emden_bc_jac]:
sol = solve_bvp(emden_fun, emden_bc, x, y, S=S, fun_jac=fun_jac,
bc_jac=bc_jac)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_equal(sol.x.size, 10)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0], emden_sol(x_test), atol=1e-5)
f_test = emden_fun(x_test, sol_test) + S.dot(sol_test) / x_test
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res ** 2, axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_complex():
# The test is essentially the same as test_no_params, but boundary
# conditions are turned into complex.
x = np.linspace(0, 1, 5)
x_test = np.linspace(0, 1, 100)
y = np.zeros((2, x.shape[0]), dtype=complex)
for fun_jac in [None, exp_fun_jac]:
for bc_jac in [None, exp_bc_jac]:
sol = solve_bvp(exp_fun, exp_bc_complex, x, y, fun_jac=fun_jac,
bc_jac=bc_jac)
assert_equal(sol.status, 0)
assert_(sol.success)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0].real, exp_sol(x_test), atol=1e-5)
assert_allclose(sol_test[0].imag, exp_sol(x_test), atol=1e-5)
f_test = exp_fun(x_test, sol_test)
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(np.real(rel_res * np.conj(rel_res)),
axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_(np.all(sol.rms_residuals < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_failures():
x = np.linspace(0, 1, 2)
y = np.zeros((2, x.size))
res = solve_bvp(exp_fun, exp_bc, x, y, tol=1e-5, max_nodes=5)
assert_equal(res.status, 1)
assert_(not res.success)
x = np.linspace(0, 1, 5)
y = np.zeros((2, x.size))
res = solve_bvp(undefined_fun, undefined_bc, x, y)
assert_equal(res.status, 2)
assert_(not res.success)
def test_big_problem():
n = 30
x = np.linspace(0, 1, 5)
y = np.zeros((2 * n, x.size))
sol = solve_bvp(big_fun, big_bc, x, y)
assert_equal(sol.status, 0)
assert_(sol.success)
sol_test = sol.sol(x)
assert_allclose(sol_test[0], big_sol(x, n))
f_test = big_fun(x, sol_test)
r = sol.sol(x, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(np.real(rel_res * np.conj(rel_res)), axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_(np.all(sol.rms_residuals < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_big_problem_with_parameters():
n = 30
x = np.linspace(0, np.pi, 5)
x_test = np.linspace(0, np.pi, 100)
y = np.ones((2 * n, x.size))
for fun_jac in [None, big_fun_with_parameters_jac]:
for bc_jac in [None, big_bc_with_parameters_jac]:
sol = solve_bvp(big_fun_with_parameters, big_bc_with_parameters, x,
y, p=[0.5, 0.5], fun_jac=fun_jac, bc_jac=bc_jac)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_allclose(sol.p, [1, 1], rtol=1e-4)
sol_test = sol.sol(x_test)
for isol in range(0, n, 4):
assert_allclose(sol_test[isol],
big_sol_with_parameters(x_test, [1, 1])[0],
rtol=1e-4, atol=1e-4)
assert_allclose(sol_test[isol + 2],
big_sol_with_parameters(x_test, [1, 1])[1],
rtol=1e-4, atol=1e-4)
f_test = big_fun_with_parameters(x_test, sol_test, [1, 1])
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res ** 2, axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_(np.all(sol.rms_residuals < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_shock_layer():
x = np.linspace(-1, 1, 5)
x_test = np.linspace(-1, 1, 100)
y = np.zeros((2, x.size))
sol = solve_bvp(shock_fun, shock_bc, x, y)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_(sol.x.size < 110)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0], shock_sol(x_test), rtol=1e-5, atol=1e-5)
f_test = shock_fun(x_test, sol_test)
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res ** 2, axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
def test_nonlin_bc():
x = np.linspace(0, 0.1, 5)
x_test = x
y = np.zeros([2, x.size])
sol = solve_bvp(nonlin_bc_fun, nonlin_bc_bc, x, y)
assert_equal(sol.status, 0)
assert_(sol.success)
assert_(sol.x.size < 8)
sol_test = sol.sol(x_test)
assert_allclose(sol_test[0], nonlin_bc_sol(x_test), rtol=1e-5, atol=1e-5)
f_test = nonlin_bc_fun(x_test, sol_test)
r = sol.sol(x_test, 1) - f_test
rel_res = r / (1 + np.abs(f_test))
norm_res = np.sum(rel_res ** 2, axis=0) ** 0.5
assert_(np.all(norm_res < 1e-3))
assert_allclose(sol.sol(sol.x), sol.y, rtol=1e-10, atol=1e-10)
assert_allclose(sol.sol(sol.x, 1), sol.yp, rtol=1e-10, atol=1e-10)
@pytest.mark.thread_unsafe
def test_verbose():
# Smoke test that checks the printing does something and does not crash
x = np.linspace(0, 1, 5)
y = np.zeros((2, x.shape[0]))
for verbose in [0, 1, 2]:
old_stdout = sys.stdout
sys.stdout = StringIO()
try:
sol = solve_bvp(exp_fun, exp_bc, x, y, verbose=verbose)
text = sys.stdout.getvalue()
finally:
sys.stdout = old_stdout
assert_(sol.success)
if verbose == 0:
assert_(not text, text)
if verbose >= 1:
assert_("Solved in" in text, text)
if verbose >= 2:
assert_("Max residual" in text, text)
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