def _get_integration_limits(self, omega, args, kwds):
a, b = self.a, self.b
M = 30
ab = [a]
scale = (b - a) / 2
n = 30
x = np.linspace(a, b, n + 1)
dg_x = np.asarray([scale * omega * self.dg(xi, *args, **kwds)
for xi in x])
i10 = findcross(dg_x, M)
i1 = findcross(dg_x, 1)
i0 = findcross(dg_x, 0)
im1 = findcross(dg_x, -1)
im10 = findcross(dg_x, -M)
x10 = ecross(x, dg_x, i10, M) if len(i10) else ()
x1 = ecross(x, dg_x, i1, 1) if len(i1) else ()
x0 = ecross(x, dg_x, i0, 0) if len(i0) else ()
xm1 = ecross(x, dg_x, im1, -1) if len(im1) else ()
xm10 = ecross(x, dg_x, im10, -M) if len(im10) else ()
for i in np.unique(np.hstack((x10, x1, x0, xm1, xm10))):
if x[0] < i < x[n]:
ab.append(i)
ab.append(b)
return ab
def _get_integration_limits(self, omega, args, kwds):
a, b = self.a, self.b
M = 30
ab = [a]
scale = (b - a) / 2
n = 30
x = np.linspace(a, b, n + 1)
dg_x = np.asarray([scale * omega * self.dg(xi, *args, **kwds)
for xi in x])
i10 = findcross(dg_x, M)
i1 = findcross(dg_x, 1)
i0 = findcross(dg_x, 0)
im1 = findcross(dg_x, -1)
im10 = findcross(dg_x, -M)
x10 = ecross(x, dg_x, i10, M) if len(i10) else ()
x1 = ecross(x, dg_x, i1, 1) if len(i1) else ()
x0 = ecross(x, dg_x, i0, 0) if len(i0) else ()
xm1 = ecross(x, dg_x, im1, -1) if len(im1) else ()
xm10 = ecross(x, dg_x, im10, -M) if len(im10) else ()
for i in np.unique(np.hstack((x10, x1, x0, xm1, xm10))):
if x[0] < i < x[n]:
ab.append(i)
ab.append(b)
return ab
def test_findcross_and_ecross():
assert_allclose(findcross([0, 0, 1, -1, 1], 0), [1, 2, 3])
assert_allclose(findcross([0, 1, -1, 1], 0), [0, 1, 2])
t = linspace(0, 7 * pi, 250)
x = sin(t)
ind = findcross(x, 0.75)
assert_allclose(ind, [9, 25, 80, 97, 151, 168, 223, 239])
t0 = ecross(t, x, ind, 0.75)
assert_allclose(t0, [0.84910514, 2.2933879, 7.13205663,
8.57630119, 13.41484739, 14.85909194,
19.69776067, 21.14204343])
def test_findcross_and_ecross():
assert_array_equal(findcross([0, 0, 1, -1, 1], 0), np.array([1, 2, 3]))
assert_array_equal(findcross([0, 1, -1, 1], 0), np.array([0, 1, 2]))
t = linspace(0, 7 * pi, 250)
x = sin(t)
ind = findcross(x, 0.75)
assert_array_equal(ind, np.array([9, 25, 80, 97, 151, 168, 223, 239]))
t0 = ecross(t, x, ind, 0.75)
assert_array_almost_equal(t0, np.array([0.84910514, 2.2933879, 7.13205663,
8.57630119, 13.41484739,
14.85909194,
19.69776067, 21.14204343]))
def get_bounds(self, alpha=0.05):
"""Return confidence interval for profiled parameter
"""
if alpha < self.alpha:
warnings.warn("Might not be able to return CI with alpha less than %g" % self.alpha)
cross_level = self.Lmax - 0.5 * chi2isf(alpha, 1)
ind = findcross(self.data, cross_level)
N = len(ind)
if N == 0:
warnings.warn(
"""Number of crossings is zero, i.e.,
upper and lower bound is not found!"""
)
CI = (self.pmin, self.pmax)
elif N == 1:
x0 = ecross(self.args, self.data, ind, cross_level)
isUpcrossing = self.data[ind] > self.data[ind + 1]
if isUpcrossing:
CI = (x0, self.pmax)
warnings.warn("Upper bound is larger")
else:
CI = (self.pmin, x0)
warnings.warn("Lower bound is smaller")
elif N == 2:
CI = ecross(self.args, self.data, ind, cross_level)
else:
warnings.warn("Number of crossings too large! Something is wrong!")
CI = ecross(self.args, self.data, ind[[0, -1]], cross_level)
return CI
def get_bounds(self, alpha=0.05):
'''Return confidence interval for profiled parameter
'''
if alpha < self.alpha:
warnings.warn(
'Might not be able to return CI with alpha less than %g' %
self.alpha)
cross_level = self.Lmax - 0.5 * chi2isf(alpha, 1)
ind = findcross(self.data, cross_level)
N = len(ind)
if N == 0:
warnings.warn('''Number of crossings is zero, i.e.,
upper and lower bound is not found!''')
CI = (self.pmin, self.pmax)
elif N == 1:
x0 = ecross(self.args, self.data, ind, cross_level)
isUpcrossing = self.data[ind] > self.data[ind + 1]
if isUpcrossing:
CI = (x0, self.pmax)
warnings.warn('Upper bound is larger')
else:
CI = (self.pmin, x0)
warnings.warn('Lower bound is smaller')
elif N == 2:
CI = ecross(self.args, self.data, ind, cross_level)
else:
warnings.warn('Number of crossings too large! Something is wrong!')
CI = ecross(self.args, self.data, ind[[0, -1]], cross_level)
return CI