448 lines
14 KiB
Python
448 lines
14 KiB
Python
import os
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import sys
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import time
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from itertools import zip_longest
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import numpy as np
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from numpy.testing import assert_
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import pytest
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from scipy.special._testutils import assert_func_equal
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try:
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import mpmath
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except ImportError:
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pass
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# ------------------------------------------------------------------------------
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# Machinery for systematic tests with mpmath
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# ------------------------------------------------------------------------------
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class Arg:
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"""Generate a set of numbers on the real axis, concentrating on
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'interesting' regions and covering all orders of magnitude.
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"""
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def __init__(self, a=-np.inf, b=np.inf, inclusive_a=True, inclusive_b=True):
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if a > b:
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raise ValueError("a should be less than or equal to b")
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if a == -np.inf:
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a = -0.5*np.finfo(float).max
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if b == np.inf:
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b = 0.5*np.finfo(float).max
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self.a, self.b = a, b
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self.inclusive_a, self.inclusive_b = inclusive_a, inclusive_b
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def _positive_values(self, a, b, n):
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if a < 0:
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raise ValueError("a should be positive")
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# Try to put half of the points into a linspace between a and
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# 10 the other half in a logspace.
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if n % 2 == 0:
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nlogpts = n//2
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nlinpts = nlogpts
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else:
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nlogpts = n//2
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nlinpts = nlogpts + 1
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if a >= 10:
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# Outside of linspace range; just return a logspace.
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pts = np.logspace(np.log10(a), np.log10(b), n)
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elif a > 0 and b < 10:
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# Outside of logspace range; just return a linspace
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pts = np.linspace(a, b, n)
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elif a > 0:
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# Linspace between a and 10 and a logspace between 10 and
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# b.
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linpts = np.linspace(a, 10, nlinpts, endpoint=False)
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logpts = np.logspace(1, np.log10(b), nlogpts)
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pts = np.hstack((linpts, logpts))
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elif a == 0 and b <= 10:
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# Linspace between 0 and b and a logspace between 0 and
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# the smallest positive point of the linspace
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linpts = np.linspace(0, b, nlinpts)
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if linpts.size > 1:
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right = np.log10(linpts[1])
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else:
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right = -30
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logpts = np.logspace(-30, right, nlogpts, endpoint=False)
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pts = np.hstack((logpts, linpts))
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else:
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# Linspace between 0 and 10, logspace between 0 and the
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# smallest positive point of the linspace, and a logspace
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# between 10 and b.
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if nlogpts % 2 == 0:
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nlogpts1 = nlogpts//2
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nlogpts2 = nlogpts1
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else:
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nlogpts1 = nlogpts//2
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nlogpts2 = nlogpts1 + 1
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linpts = np.linspace(0, 10, nlinpts, endpoint=False)
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if linpts.size > 1:
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right = np.log10(linpts[1])
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else:
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right = -30
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logpts1 = np.logspace(-30, right, nlogpts1, endpoint=False)
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logpts2 = np.logspace(1, np.log10(b), nlogpts2)
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pts = np.hstack((logpts1, linpts, logpts2))
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return np.sort(pts)
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def values(self, n):
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"""Return an array containing n numbers."""
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a, b = self.a, self.b
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if a == b:
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return np.zeros(n)
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if not self.inclusive_a:
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n += 1
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if not self.inclusive_b:
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n += 1
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if n % 2 == 0:
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n1 = n//2
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n2 = n1
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else:
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n1 = n//2
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n2 = n1 + 1
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if a >= 0:
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pospts = self._positive_values(a, b, n)
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negpts = []
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elif b <= 0:
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pospts = []
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negpts = -self._positive_values(-b, -a, n)
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else:
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pospts = self._positive_values(0, b, n1)
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negpts = -self._positive_values(0, -a, n2 + 1)
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# Don't want to get zero twice
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negpts = negpts[1:]
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pts = np.hstack((negpts[::-1], pospts))
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if not self.inclusive_a:
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pts = pts[1:]
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if not self.inclusive_b:
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pts = pts[:-1]
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return pts
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class FixedArg:
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def __init__(self, values):
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self._values = np.asarray(values)
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def values(self, n):
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return self._values
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class ComplexArg:
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def __init__(self, a=complex(-np.inf, -np.inf), b=complex(np.inf, np.inf)):
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self.real = Arg(a.real, b.real)
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self.imag = Arg(a.imag, b.imag)
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def values(self, n):
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m = int(np.floor(np.sqrt(n)))
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x = self.real.values(m)
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y = self.imag.values(m + 1)
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return (x[:,None] + 1j*y[None,:]).ravel()
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class IntArg:
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def __init__(self, a=-1000, b=1000):
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self.a = a
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self.b = b
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def values(self, n):
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v1 = Arg(self.a, self.b).values(max(1 + n//2, n-5)).astype(int)
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v2 = np.arange(-5, 5)
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v = np.unique(np.r_[v1, v2])
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v = v[(v >= self.a) & (v < self.b)]
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return v
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def get_args(argspec, n):
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if isinstance(argspec, np.ndarray):
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args = argspec.copy()
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else:
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nargs = len(argspec)
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ms = np.asarray([1.5 if isinstance(spec, ComplexArg) else 1.0 for spec in argspec])
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ms = (n**(ms/sum(ms))).astype(int) + 1
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args = [spec.values(m) for spec, m in zip(argspec, ms)]
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args = np.array(np.broadcast_arrays(*np.ix_(*args))).reshape(nargs, -1).T
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return args
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class MpmathData:
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def __init__(self, scipy_func, mpmath_func, arg_spec, name=None,
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dps=None, prec=None, n=None, rtol=1e-7, atol=1e-300,
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ignore_inf_sign=False, distinguish_nan_and_inf=True,
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nan_ok=True, param_filter=None):
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# mpmath tests are really slow (see gh-6989). Use a small number of
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# points by default, increase back to 5000 (old default) if XSLOW is
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# set
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if n is None:
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try:
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is_xslow = int(os.environ.get('SCIPY_XSLOW', '0'))
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except ValueError:
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is_xslow = False
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n = 5000 if is_xslow else 500
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self.scipy_func = scipy_func
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self.mpmath_func = mpmath_func
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self.arg_spec = arg_spec
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self.dps = dps
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self.prec = prec
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self.n = n
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self.rtol = rtol
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self.atol = atol
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self.ignore_inf_sign = ignore_inf_sign
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self.nan_ok = nan_ok
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if isinstance(self.arg_spec, np.ndarray):
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self.is_complex = np.issubdtype(self.arg_spec.dtype, np.complexfloating)
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else:
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self.is_complex = any([isinstance(arg, ComplexArg) for arg in self.arg_spec])
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self.ignore_inf_sign = ignore_inf_sign
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self.distinguish_nan_and_inf = distinguish_nan_and_inf
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if not name or name == '<lambda>':
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name = getattr(scipy_func, '__name__', None)
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if not name or name == '<lambda>':
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name = getattr(mpmath_func, '__name__', None)
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self.name = name
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self.param_filter = param_filter
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def check(self):
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np.random.seed(1234)
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# Generate values for the arguments
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argarr = get_args(self.arg_spec, self.n)
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# Check
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old_dps, old_prec = mpmath.mp.dps, mpmath.mp.prec
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try:
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if self.dps is not None:
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dps_list = [self.dps]
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else:
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dps_list = [20]
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if self.prec is not None:
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mpmath.mp.prec = self.prec
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# Proper casting of mpmath input and output types. Using
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# native mpmath types as inputs gives improved precision
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# in some cases.
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if np.issubdtype(argarr.dtype, np.complexfloating):
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pytype = mpc2complex
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def mptype(x):
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return mpmath.mpc(complex(x))
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else:
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def mptype(x):
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return mpmath.mpf(float(x))
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def pytype(x):
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if abs(x.imag) > 1e-16*(1 + abs(x.real)):
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return np.nan
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else:
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return mpf2float(x.real)
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# Try out different dps until one (or none) works
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for j, dps in enumerate(dps_list):
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mpmath.mp.dps = dps
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try:
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assert_func_equal(self.scipy_func,
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lambda *a: pytype(self.mpmath_func(*map(mptype, a))),
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argarr,
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vectorized=False,
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rtol=self.rtol, atol=self.atol,
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ignore_inf_sign=self.ignore_inf_sign,
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distinguish_nan_and_inf=self.distinguish_nan_and_inf,
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nan_ok=self.nan_ok,
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param_filter=self.param_filter)
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break
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except AssertionError:
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if j >= len(dps_list)-1:
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# reraise the Exception
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tp, value, tb = sys.exc_info()
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if value.__traceback__ is not tb:
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raise value.with_traceback(tb)
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raise value
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finally:
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mpmath.mp.dps, mpmath.mp.prec = old_dps, old_prec
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def __repr__(self):
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if self.is_complex:
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return "<MpmathData: %s (complex)>" % (self.name,)
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else:
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return "<MpmathData: %s>" % (self.name,)
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def assert_mpmath_equal(*a, **kw):
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d = MpmathData(*a, **kw)
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d.check()
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def nonfunctional_tooslow(func):
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return pytest.mark.skip(reason=" Test not yet functional (too slow), needs more work.")(func)
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# ------------------------------------------------------------------------------
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# Tools for dealing with mpmath quirks
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# ------------------------------------------------------------------------------
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def mpf2float(x):
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"""
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Convert an mpf to the nearest floating point number. Just using
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float directly doesn't work because of results like this:
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with mp.workdps(50):
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float(mpf("0.99999999999999999")) = 0.9999999999999999
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"""
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return float(mpmath.nstr(x, 17, min_fixed=0, max_fixed=0))
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def mpc2complex(x):
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return complex(mpf2float(x.real), mpf2float(x.imag))
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def trace_args(func):
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def tofloat(x):
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if isinstance(x, mpmath.mpc):
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return complex(x)
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else:
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return float(x)
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def wrap(*a, **kw):
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sys.stderr.write("%r: " % (tuple(map(tofloat, a)),))
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sys.stderr.flush()
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try:
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r = func(*a, **kw)
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sys.stderr.write("-> %r" % r)
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finally:
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sys.stderr.write("\n")
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sys.stderr.flush()
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return r
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return wrap
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try:
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import posix
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import signal
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POSIX = ('setitimer' in dir(signal))
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except ImportError:
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POSIX = False
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class TimeoutError(Exception):
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pass
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def time_limited(timeout=0.5, return_val=np.nan, use_sigalrm=True):
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"""
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Decorator for setting a timeout for pure-Python functions.
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If the function does not return within `timeout` seconds, the
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value `return_val` is returned instead.
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On POSIX this uses SIGALRM by default. On non-POSIX, settrace is
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used. Do not use this with threads: the SIGALRM implementation
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does probably not work well. The settrace implementation only
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traces the current thread.
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The settrace implementation slows down execution speed. Slowdown
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by a factor around 10 is probably typical.
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"""
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if POSIX and use_sigalrm:
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def sigalrm_handler(signum, frame):
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raise TimeoutError()
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def deco(func):
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def wrap(*a, **kw):
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old_handler = signal.signal(signal.SIGALRM, sigalrm_handler)
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signal.setitimer(signal.ITIMER_REAL, timeout)
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try:
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return func(*a, **kw)
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except TimeoutError:
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return return_val
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finally:
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signal.setitimer(signal.ITIMER_REAL, 0)
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signal.signal(signal.SIGALRM, old_handler)
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return wrap
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else:
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def deco(func):
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def wrap(*a, **kw):
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start_time = time.time()
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def trace(frame, event, arg):
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if time.time() - start_time > timeout:
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raise TimeoutError()
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return trace
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sys.settrace(trace)
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try:
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return func(*a, **kw)
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except TimeoutError:
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sys.settrace(None)
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return return_val
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finally:
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sys.settrace(None)
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return wrap
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return deco
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def exception_to_nan(func):
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"""Decorate function to return nan if it raises an exception"""
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def wrap(*a, **kw):
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try:
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return func(*a, **kw)
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except Exception:
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return np.nan
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return wrap
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def inf_to_nan(func):
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"""Decorate function to return nan if it returns inf"""
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def wrap(*a, **kw):
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v = func(*a, **kw)
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if not np.isfinite(v):
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return np.nan
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return v
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return wrap
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def mp_assert_allclose(res, std, atol=0, rtol=1e-17):
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"""
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Compare lists of mpmath.mpf's or mpmath.mpc's directly so that it
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can be done to higher precision than double.
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"""
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failures = []
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for k, (resval, stdval) in enumerate(zip_longest(res, std)):
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if resval is None or stdval is None:
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raise ValueError('Lengths of inputs res and std are not equal.')
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if mpmath.fabs(resval - stdval) > atol + rtol*mpmath.fabs(stdval):
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failures.append((k, resval, stdval))
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nfail = len(failures)
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if nfail > 0:
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ndigits = int(abs(np.log10(rtol)))
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msg = [""]
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msg.append("Bad results ({} out of {}) for the following points:"
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.format(nfail, k + 1))
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for k, resval, stdval in failures:
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resrep = mpmath.nstr(resval, ndigits, min_fixed=0, max_fixed=0)
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stdrep = mpmath.nstr(stdval, ndigits, min_fixed=0, max_fixed=0)
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if stdval == 0:
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rdiff = "inf"
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else:
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rdiff = mpmath.fabs((resval - stdval)/stdval)
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rdiff = mpmath.nstr(rdiff, 3)
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msg.append("{}: {} != {} (rdiff {})".format(k, resrep, stdrep,
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rdiff))
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assert_(False, "\n".join(msg))
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