def test_characterize_function(self):
with self.assertRaises(ValueError):
util.characterize_function([1,2,-1],
[1,1,1])
fc, slopes = util.characterize_function([1,2,3],
[1,1,1])
self.assertEqual(fc, 1) # affine
self.assertEqual(slopes, [0,0])
fc, slopes = util.characterize_function([1,2,3],
[1,0,1])
self.assertEqual(fc, 2) # convex
self.assertEqual(slopes, [-1,1])
fc, slopes = util.characterize_function([1,2,3],
[1,2,1])
self.assertEqual(fc, 3) # concave
self.assertEqual(slopes, [1,-1])
fc, slopes = util.characterize_function([1,1,2],
[1,2,1])
self.assertEqual(fc, 4) # step
self.assertEqual(slopes, [None,-1])
fc, slopes = util.characterize_function([1,2,3,4],
[1,2,1,2])
self.assertEqual(fc, 5) # none of the above
self.assertEqual(slopes, [1,-1,1])
def validate(self,
equal_slopes_tolerance=1e-6):
"""
Validate this piecewise linear function by verifying
various properties of the breakpoints and values
lists (e.g., that the list of breakpoints is
nondecreasing).
Args:
equal_slopes_tolerance (float): Tolerance used
check if consecutive slopes are nearly
equal. If any are found, validation will
fail. Default is 1e-6.
Returns:
int:
a function characterization code (see \
:func:`util.characterize_function`)
Raises:
PiecewiseValidationError: if validation fails
"""
breakpoints = [_value(x) for x in self._breakpoints]
values = [_value(x) for x in self._values]
if not is_nondecreasing(breakpoints):
raise PiecewiseValidationError(
"The list of breakpoints is not nondecreasing: %s"
% (str(breakpoints)))
ftype, slopes = characterize_function(breakpoints, values)
for i in range(1, len(slopes)):
if (slopes[i-1] is not None) and \
(slopes[i] is not None) and \
(abs(slopes[i-1] - slopes[i]) <= equal_slopes_tolerance):
raise PiecewiseValidationError(
"Piecewise function validation detected slopes "
"of consecutive line segments to be within %s "
"of one another. This may cause numerical issues. "
"To avoid this error, set the 'equal_slopes_tolerance' "
"keyword to a smaller value or disable validation."
% (equal_slopes_tolerance))
return ftype