def test_bisection_unsupported_output_shape():
def func(x, y):
return x - sin(y), y
with pytest.raises(Exception,
match="The bisection method only supports functions with a single output dimension."):
find_root(function=func, method='bisect', interval=[[-1, 1], [-1, 1]], max_iter=1000)
def test_bisection_no_solution():
def f(x, y):
return x + y
with pytest.raises(Exception,
match="Bisection did not converge, try increasing max_iter."):
find_root(function=f, method='bisect', interval=[[-1, 1], [-1, 1]], max_iter=1)
def test_bisect_noroot_in_interval():
def f(x, y):
return x + y - 100
interval = [[1, 2], [3, 1]]
with pytest.raises(Exception, match="No change in sign, please try different intervals"):
find_root(function=f, method='bisection', interval=interval)
def test_newton_raphson_no_solution_scalar():
def f1var(x):
return x ** 2 + 1
with pytest.raises(Exception, match="Newton-Raphson did not converge, try increasing max_iter or changing "
"start_values."):
find_root(function=f1var, method='newton', start_values=1)
def test_bisect_wrong_interval():
def f(x):
return x
assert np.allclose(f(1), 1)
with pytest.raises(KeyError, match="Incorrect number of variables passed in interval."):
find_root(function=f, method="bisect", interval=[[-1, 2], [-1, 2], [-1, 2]])
def test_bisection_zero_interval():
def f1var(x):
return (x + 2) * (x - 3)
assert np.isclose(f1var(1), -6.)
with pytest.raises(Warning,
match="Please choose a non-zero interval to see informative plot."):
find_root(function=f1var, method='bisect', interval=[0, 0], max_iter=1)
def test_newton_raphson_vector():
def f2var(x, y):
return 2 * x + y, x - 1
this_root = find_root(function=f2var, method='newton', start_values=[1, 2])
assert np.allclose(this_root, np.array([1, -2]))
with pytest.raises(Exception, match="Newton-Raphson did not converge, try increasing max_iter or changing "
"start_values."):
find_root(function=f2var, method='newton', start_values=[1, 2], max_iter=0)
def test_newton_fourier_vector():
def f2var(x, y):
return 2 * x + y, x - 1
this_root = find_root(function=f2var, method='n-f', interval=[[1, 2], [3, 4]])
assert np.allclose(this_root, np.array([1, -2]))
with pytest.raises(Exception,
match="Newton-Fourier did not converge, try another interval or increasing max_iter."):
find_root(function=f2var, method='n-f', interval=[[11, 21], [31, 41]], max_iter=0)
def test_bisect():
def f(x, y):
return x + y
interval = [[-1, 1], [-1, 1]]
this_root = find_root(function=f, method='bisection', interval=interval)
assert np.allclose(this_root, [0.0, 0.0])
def test_newton_fourier_no_solution():
def f1var(x):
return x ** 2 + 1
with pytest.raises(Exception,
match="Newton-Fourier did not converge, try another interval or increasing max_iter."):
find_root(function=f1var, method='newton-fourier', interval=[-1, 1])
def f2var(x, y):
return x**2 + y**2 +1, x**4 + 1
with pytest.raises(Exception,
match="Newton-Fourier did not converge, try another interval or increasing max_iter."):
find_root(function=f2var, method='n-f', interval=[[-1, -1], [0, 0]])
def f3var(x, y, z):
return x + y - z, 2 * x - sin(3 * y)
# testing if two distinct roots are found but they're not equal
with pytest.raises(Exception, match="Newton-Fourier did not converge, but two roots were found"):
find_root(function=f3var, method='n-f', interval=[[0, 0.1], [0.9, 1], [1, 1.1]])
def test_newton_raphson_scalar():
def f1var(x):
return (x + 2) * (x - 3)
this_root = find_root(function=f1var, method='newton', start_values=1)
assert np.isclose(this_root, 3.0)
def test_root_bad_inputs_newton_raphson():
def f2var(x, y):
return 2 * x + y, x - 1
this_root = find_root(function=f2var, method='newton', start_values=[1, 2])
assert np.allclose(this_root, np.array([1, -2]))
this_root = find_root(function=f2var, method='newton', start_values={'x': 1, 'y': 2})
assert np.allclose(this_root, np.array([1, -2]))
# Incorrect number of vars in start_values
with pytest.raises(KeyError, match="Incorrect number of variables passed in start_values."):
find_root(function=f2var, method='newton', start_values=2)
# Function signature variable missing from dictionary keys
with pytest.raises(KeyError, match="key y in function signature missing from start_values."):
find_root(function=f2var, method='newton', start_values={'x': 2})
# Too many start_values dictionary keys passed
with pytest.raises(KeyError, match="Too many keys passed in start_values dictionary."):
find_root(function=f2var, method='newton', start_values={'x': 2, 'y': 2, 'z': 4})
# Incorrect type for start_values
with pytest.raises(TypeError, match="Must include start_values as dict or list/array."):
find_root(function=f2var, method='newton', start_values=f2var)
# Argument start_values not passed
with pytest.raises(ValueError, match="Must include start_values as dict or list/array for this method."):
find_root(function=f2var, method='newton', interval=[1, 2])
def test_root_bad_inputs_newton_fourier():
def f1var(x):
return (x + 2) * (x - 3)
this_root = find_root(function=f1var, method='newton-fourier', interval=[2, 4])
assert np.isclose(this_root, 3.0)
def f2var(x, y):
return 2 * x + y, x - 1
this_root = find_root(function=f2var, method='newton-fourier', interval=[[1, 2], [3, 4]])
assert np.allclose(this_root, np.array([1, -2]))
# Incorrect number of variables
with pytest.raises(ValueError, match="Incorrect number of elements passed in interval."):
find_root(function=f2var, method='newton-fourier', interval=[1, 2, 3])
# Incorrect number of variables
with pytest.raises(ValueError, match="Incorrect number of elements passed in interval."):
find_root(function=f1var, method='newton-fourier', interval=[1, 2, 3])
# Function signature variable missing from dictionary keys
with pytest.raises(KeyError, match="key y in function signature missing from interval dictionary."):
find_root(function=f2var, method='newton-fourier', interval=[{'x': 2}, {'x': 4}])
# Too many interval_dict keys passed
with pytest.raises(KeyError, match="Too many keys passed in interval dictionary."):
interval_dict = [{'x': 0, 'y': -1, 'z': 6}, {'x': 2, 'y': -3, 'z': 6}]
find_root(function=f2var, method='newton-fourier', interval=interval_dict)
# Number of interval_dict keys don't match for start_interval and end_interval
with pytest.raises(KeyError, match="The interval_start and interval_end dictionaries must have the same number of "
"keys."):
interval_dict = [{'x': 0, 'y': -1}, {'x': 2, 'y': -3, 'z': 6}]
find_root(function=f2var, method='newton-fourier', interval=interval_dict)
# Incorrect type for interval
with pytest.raises(TypeError, match="Must include interval as list of two dicts or list/array."):
find_root(function=f2var, method='newton-fourier', interval={'x': 2})
with pytest.raises(TypeError, match="Must include interval as list of two dicts or list/array."):
find_root(function=f2var, method='newton-fourier', interval=f2var)
# Different types for start_interval and end_interval
with pytest.raises(TypeError, match="Must include interval as list of two dicts or numeric list/array."):
find_root(function=f2var, method='newton-fourier', interval=[1, {'x': 2}])
# Argument interval not passed
with pytest.raises(TypeError, match="Must include interval as list of two dicts or list/array."):
find_root(function=f2var, method='newton-fourier', start_values=[1, 2])
def test_invalid_method():
with pytest.raises(ValueError, match="Invalid method supplied. See documentation for accepted methods."):
find_root(function=lambda x: x ** 2 + 1, method='n', interval=[-1, 1])
def test_newton_fourier_scalar():
def f1var(x):
return (x + 2) * (x - 3)
this_root = find_root(function=f1var, method='newton-fourier', interval=[2, 4])
assert np.isclose(this_root, 3.0)
def test_bisection_interval_not_in_domain():
def asin(x):
return arcsin(x)
with pytest.raises(ValueError):
find_root(function=asin, method='bisect', interval=[2, 3], max_iter=1)
