The numba-integration-tests failed and I am trying to figure out, if it is a legit failure or if we introduced a new bug in Numba
=================================== FAILURES ===================================
_________________ test_derivatives[binary_crossentropy-0.3-0] __________________
loss = <pygbm.loss.BinaryCrossEntropy object at 0x7f4f2853da50>
x0 = array([[0.3]], dtype=float32), y_true = array([0.], dtype=float32)
@pytest.mark.parametrize('loss, x0, y_true', [
('least_squares', -2., 42),
('least_squares', 117., 1.05),
('least_squares', 0., 0.),
('binary_crossentropy', 0.3, 0),
('binary_crossentropy', -12, 1),
('binary_crossentropy', 30, 1),
])
def test_derivatives(loss, x0, y_true):
# Check that gradients are zero when the loss is minimized on 1D array
# using the Newton-Raphson and the first and second order derivatives
# computed by the Loss instance.
loss = _LOSSES[loss]()
y_true = np.array([y_true], dtype=np.float32)
x0 = np.array([x0], dtype=np.float32).reshape(1, 1)
get_gradients, get_hessians = get_derivatives_helper(loss)
def func(x):
return loss(y_true, x)
def fprime(x):
return get_gradients(y_true, x)
def fprime2(x):
return get_hessians(y_true, x)
> optimum = newton(func, x0=x0, fprime=fprime, fprime2=fprime2)
tests/test_loss.py:78:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
func = <function test_derivatives.<locals>.func at 0x7f4f0c4e6440>
x0 = array([[0.3]], dtype=float32)
fprime = <function test_derivatives.<locals>.fprime at 0x7f4f0c4e67a0>
args = (), tol = 1.48e-08, maxiter = 50
fprime2 = <function test_derivatives.<locals>.fprime2 at 0x7f4f0c4e65f0>
x1 = None, rtol = 0.0, full_output = False, disp = True
def newton(func, x0, fprime=None, args=(), tol=1.48e-8, maxiter=50,
fprime2=None, x1=None, rtol=0.0,
full_output=False, disp=True):
"""
Find a zero of a real or complex function using the Newton-Raphson
(or secant or Halley's) method.
Find a zero of the function `func` given a nearby starting point `x0`.
The Newton-Raphson method is used if the derivative `fprime` of `func`
is provided, otherwise the secant method is used. If the second order
derivative `fprime2` of `func` is also provided, then Halley's method is
used.
If `x0` is a sequence with more than one item, then `newton` returns an
array, and `func` must be vectorized and return a sequence or array of the
same shape as its first argument. If `fprime` or `fprime2` is given then
its return must also have the same shape.
Parameters
----------
func : callable
The function whose zero is wanted. It must be a function of a
single variable of the form ``f(x,a,b,c...)``, where ``a,b,c...``
are extra arguments that can be passed in the `args` parameter.
x0 : float, sequence, or ndarray
An initial estimate of the zero that should be somewhere near the
actual zero. If not scalar, then `func` must be vectorized and return
a sequence or array of the same shape as its first argument.
fprime : callable, optional
The derivative of the function when available and convenient. If it
is None (default), then the secant method is used.
args : tuple, optional
Extra arguments to be used in the function call.
tol : float, optional
The allowable error of the zero value. If `func` is complex-valued,
a larger `tol` is recommended as both the real and imaginary parts
of `x` contribute to ``|x - x0|``.
maxiter : int, optional
Maximum number of iterations.
fprime2 : callable, optional
The second order derivative of the function when available and
convenient. If it is None (default), then the normal Newton-Raphson
or the secant method is used. If it is not None, then Halley's method
is used.
x1 : float, optional
Another estimate of the zero that should be somewhere near the
actual zero. Used if `fprime` is not provided.
rtol : float, optional
Tolerance (relative) for termination.
full_output : bool, optional
If `full_output` is False (default), the root is returned.
If True and `x0` is scalar, the return value is ``(x, r)``, where ``x``
is the root and ``r`` is a `RootResults` object.
If True and `x0` is non-scalar, the return value is ``(x, converged,
zero_der)`` (see Returns section for details).
disp : bool, optional
If True, raise a RuntimeError if the algorithm didn't converge, with
the error message containing the number of iterations and current
function value. Otherwise the convergence status is recorded in a
`RootResults` return object.
Ignored if `x0` is not scalar.
*Note: this has little to do with displaying, however
the `disp` keyword cannot be renamed for backwards compatibility.*
Returns
-------
root : float, sequence, or ndarray
Estimated location where function is zero.
r : `RootResults`, optional
Present if ``full_output=True`` and `x0` is scalar.
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
converged : ndarray of bool, optional
Present if ``full_output=True`` and `x0` is non-scalar.
For vector functions, indicates which elements converged successfully.
zero_der : ndarray of bool, optional
Present if ``full_output=True`` and `x0` is non-scalar.
For vector functions, indicates which elements had a zero derivative.
See Also
--------
brentq, brenth, ridder, bisect
fsolve : find zeros in n dimensions.
Notes
-----
The convergence rate of the Newton-Raphson method is quadratic,
the Halley method is cubic, and the secant method is
sub-quadratic. This means that if the function is well behaved
the actual error in the estimated zero after the n-th iteration
is approximately the square (cube for Halley) of the error
after the (n-1)-th step. However, the stopping criterion used
here is the step size and there is no guarantee that a zero
has been found. Consequently the result should be verified.
Safer algorithms are brentq, brenth, ridder, and bisect,
but they all require that the root first be bracketed in an
interval where the function changes sign. The brentq algorithm
is recommended for general use in one dimensional problems
when such an interval has been found.
When `newton` is used with arrays, it is best suited for the following
types of problems:
* The initial guesses, `x0`, are all relatively the same distance from
the roots.
* Some or all of the extra arguments, `args`, are also arrays so that a
class of similar problems can be solved together.
* The size of the initial guesses, `x0`, is larger than O(100) elements.
Otherwise, a naive loop may perform as well or better than a vector.
Examples
--------
>>> from scipy import optimize
>>> import matplotlib.pyplot as plt
>>> def f(x):
... return (x**3 - 1) # only one real root at x = 1
``fprime`` is not provided, use the secant method:
>>> root = optimize.newton(f, 1.5)
>>> root
1.0000000000000016
>>> root = optimize.newton(f, 1.5, fprime2=lambda x: 6 * x)
>>> root
1.0000000000000016
Only ``fprime`` is provided, use the Newton-Raphson method:
>>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2)
>>> root
1.0
Both ``fprime2`` and ``fprime`` are provided, use Halley's method:
>>> root = optimize.newton(f, 1.5, fprime=lambda x: 3 * x**2,
... fprime2=lambda x: 6 * x)
>>> root
1.0
When we want to find zeros for a set of related starting values and/or
function parameters, we can provide both of those as an array of inputs:
>>> f = lambda x, a: x**3 - a
>>> fder = lambda x, a: 3 * x**2
>>> np.random.seed(4321)
>>> x = np.random.randn(100)
>>> a = np.arange(-50, 50)
>>> vec_res = optimize.newton(f, x, fprime=fder, args=(a, ))
The above is the equivalent of solving for each value in ``(x, a)``
separately in a for-loop, just faster:
>>> loop_res = [optimize.newton(f, x0, fprime=fder, args=(a0,))
... for x0, a0 in zip(x, a)]
>>> np.allclose(vec_res, loop_res)
True
Plot the results found for all values of ``a``:
>>> analytical_result = np.sign(a) * np.abs(a)**(1/3)
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(a, analytical_result, 'o')
>>> ax.plot(a, vec_res, '.')
>>> ax.set_xlabel('$a$')
>>> ax.set_ylabel('$x$ where $f(x, a)=0$')
>>> plt.show()
"""
if tol <= 0:
raise ValueError("tol too small (%g <= 0)" % tol)
if maxiter < 1:
raise ValueError("maxiter must be greater than 0")
if np.size(x0) > 1:
return _array_newton(func, x0, fprime, args, tol, maxiter, fprime2,
full_output)
# Convert to float (don't use float(x0); this works also for complex x0)
p0 = 1.0 * x0
funcalls = 0
if fprime is not None:
# Newton-Raphson method
for itr in range(maxiter):
# first evaluate fval
fval = func(p0, *args)
funcalls += 1
# If fval is 0, a root has been found, then terminate
if fval == 0:
return _results_select(
full_output, (p0, funcalls, itr, _ECONVERGED))
fder = fprime(p0, *args)
funcalls += 1
if fder == 0:
msg = "Derivative was zero."
if disp:
msg += (
" Failed to converge after %d iterations, value is %s."
% (itr + 1, p0))
> raise RuntimeError(msg)
E RuntimeError: Derivative was zero. Failed to converge after 46 iterations, value is [[-89.88232]].
../miniconda3/envs/pygbm/lib/python3.7/site-packages/scipy/optimize/zeros.py:294: RuntimeError
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