def test_bernstein_distribution_2d():
grid = dt._Grid([51, 51])
cop_tr = tra.TransfFrank
args = (2, )
ca = ArchimedeanCopula(cop_tr())
distr1 = stats.uniform
distr2 = stats.uniform
cad = CopulaDistribution(ca, [distr1, distr2], cop_args=args)
cdfv = cad.cdf(grid.x_flat, args)
cdf_g = cdfv.reshape(grid.k_grid)
bpd = BernsteinDistribution(cdf_g)
cdf_bp = bpd.cdf(grid.x_flat)
assert_allclose(cdf_bp, cdfv, atol=0.005)
assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.001)
grid_eps = dt._Grid([51, 51], eps=1e-8)
pdfv = cad.pdf(grid_eps.x_flat)
pdf_bp = bpd.pdf(grid_eps.x_flat)
assert_allclose(pdf_bp, pdfv, atol=0.01, rtol=0.04)
assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.05)
# check marginal cdfs
# get marginal cdf
xx = np.column_stack((np.linspace(0, 1, 5), np.ones(5)))
cdf_m1 = bpd.cdf(xx)
assert_allclose(cdf_m1, xx[:, 0], atol=1e-13)
xx = np.column_stack((np.ones(5), np.linspace(0, 1, 5)))
cdf_m2 = bpd.cdf(xx)
assert_allclose(cdf_m2, xx[:, 1], atol=1e-13)
xx_ = np.linspace(0, 1, 5)
xx = xx_[:, None] # currently requires 2-dim
bpd_m1 = bpd.get_marginal(0)
cdf_m1 = bpd_m1.cdf(xx)
assert_allclose(cdf_m1, xx_, atol=1e-13)
pdf_m1 = bpd_m1.pdf(xx)
assert_allclose(pdf_m1, np.ones(len(xx)), atol=1e-13)
bpd_m = bpd.get_marginal(1)
cdf_m = bpd_m.cdf(xx)
assert_allclose(cdf_m, xx_, atol=1e-13)
pdf_m = bpd_m.pdf(xx)
assert_allclose(pdf_m, np.ones(len(xx)), atol=1e-13)
def setup_class(cls):
grid = dt._Grid([91, 101])
cop_tr = tra.TransfFrank
args = (2, )
ca = ArchimedeanCopula(cop_tr())
distr1 = stats.beta(4, 3)
distr2 = stats.beta(4, 4) # (5, 2)
cad = CopulaDistribution(ca, [distr1, distr2], cop_args=args)
cdfv = cad.cdf(grid.x_flat, args)
cdf_g = cdfv.reshape(grid.k_grid)
cls.grid = grid
cls.cdfv = cdfv
cls.distr = cad
cls.bpd = BernsteinDistribution(cdf_g)
def test_bernstein_distribution_1d():
grid = dt._Grid([501])
loc = grid.x_flat == 0
grid.x_flat[loc] = grid.x_flat[~loc].min() / 2
grid.x_flat[grid.x_flat == 1] = 1 - grid.x_flat.min()
distr = stats.beta(3, 5)
cdf_g = distr.cdf(np.squeeze(grid.x_flat))
bpd = BernsteinDistribution(cdf_g)
cdf_bp = bpd.cdf(grid.x_flat)
assert_allclose(cdf_bp, cdf_g, atol=0.005)
assert_array_less(np.median(np.abs(cdf_bp - cdf_g)), 0.001)
pdfv = distr.pdf(np.squeeze(grid.x_flat))
pdf_bp = bpd.pdf(grid.x_flat)
assert_allclose(pdf_bp, pdfv, atol=0.02)
assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.01)
# compare with UV class
xf = np.squeeze(grid.x_flat) # UV returns column if x is column
bpd1 = BernsteinDistributionUV(cdf_g)
cdf_bp1 = bpd1.cdf(xf)
assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
pdf_bp1 = bpd1.pdf(xf)
assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
cdf_bp1 = bpd1.cdf(xf, method="beta")
assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
pdf_bp1 = bpd1.pdf(xf, method="beta")
assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
cdf_bp1 = bpd1.cdf(xf, method="bpoly")
assert_allclose(cdf_bp1, cdf_bp, atol=1e-13)
pdf_bp1 = bpd1.pdf(xf, method="bpoly")
assert_allclose(pdf_bp1, pdf_bp, atol=1e-13)
# check rvs
# currently smoke test
rvs = bpd.rvs(100)
assert len(rvs) == 100
def test_basic(self):
bpd = self.bpd
grid = self.grid
cdfv = self.cdfv
distr = self.distr
if grid.x_flat.shape[0] < 51**2:
cdf_bp = bpd.cdf(grid.x_flat)
assert_allclose(cdf_bp, cdfv, atol=0.05)
assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.01)
grid_eps = dt._Grid([51, 51], eps=1e-2)
cdfv = distr.cdf(grid_eps.x_flat)
cdf_bp = bpd.cdf(grid_eps.x_flat)
assert_allclose(cdf_bp, cdfv, atol=0.01, rtol=0.01)
assert_array_less(np.median(np.abs(cdf_bp - cdfv)), 0.05)
pdfv = distr.pdf(grid_eps.x_flat)
pdf_bp = bpd.pdf(grid_eps.x_flat)
assert_allclose(pdf_bp, pdfv, atol=0.06, rtol=0.1)
assert_array_less(np.median(np.abs(pdf_bp - pdfv)), 0.05)
def test_grid_class():
res = {
'k_grid': [3, 5],
'x_marginal':
[np.array([0., 0.5, 1.]),
np.array([0., 0.25, 0.5, 0.75, 1.])],
'idx_flat.T':
np.array([[0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 2., 2., 2., 2., 2.],
[0., 1., 2., 3., 4., 0., 1., 2., 3., 4., 0., 1., 2., 3.,
4.]])
}
gg = dt._Grid([3, 5])
assert_equal(gg.k_grid, res["k_grid"])
assert gg.x_marginal, res["x_marginal"]
assert_allclose(gg.idx_flat, res["idx_flat.T"].T, atol=1e-12)
assert_allclose(gg.x_flat, res["idx_flat.T"].T / [2, 4], atol=1e-12)
gg = dt._Grid([3, 5], eps=0.001)
assert_allclose(gg.x_flat.min(), 0.001, atol=1e-12)
assert_allclose(gg.x_flat.max(), 0.999, atol=1e-12)
xmf = np.concatenate(gg.x_marginal)
assert_allclose(xmf.min(), 0.001, atol=1e-12)
assert_allclose(xmf.max(), 0.999, atol=1e-12)
# 1-dim
gg = dt._Grid([5], eps=0.001)
res = {
'k_grid': [5],
'x_marginal': [np.array([0.001, 0.25, 0.5, 0.75, 0.999])],
'idx_flat.T': np.array([[0., 1., 2., 3., 4.]])
}
assert_equal(gg.k_grid, res["k_grid"])
assert gg.x_marginal, res["x_marginal"]
assert_allclose(gg.idx_flat, res["idx_flat.T"].T, atol=1e-12)
# x_flat is 2-dim even if grid is 1-dim, TODO: maybe change
assert_allclose(gg.x_flat, res["x_marginal"][0][:, None], atol=1e-12)
# 3-dim
gg = dt._Grid([3, 3, 2], eps=0.)
res = {
'k_grid': [3, 3, 2],
'x_marginal':
[np.array([0., 0.5, 1.]),
np.array([0., 0.5, 1.]),
np.array([0., 1.])],
'idx_flat.T':
np.array([[
0., 0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 2., 2., 2., 2., 2.,
2.
],
[
0., 0., 1., 1., 2., 2., 0., 0., 1., 1., 2., 2., 0., 0.,
1., 1., 2., 2.
],
[
0., 1., 0., 1., 0., 1., 0., 1., 0., 1., 0., 1., 0., 1.,
0., 1., 0., 1.
]])
}
assert_equal(gg.k_grid, res["k_grid"])
assert gg.x_marginal, res["x_marginal"]
assert_allclose(gg.idx_flat, res["idx_flat.T"].T, atol=1e-12)
assert_allclose(gg.x_flat, res["idx_flat.T"].T / [2, 2, 1], atol=1e-12)
def __init__(self, cdf_grid):
self.cdf_grid = cdf_grid = np.asarray(cdf_grid)
self.k_dim = cdf_grid.ndim
self.k_grid = cdf_grid.shape
self.k_grid_product = np.product([i-1 for i in self.k_grid])
self._grid = _Grid(self.k_grid)