def test_2d(self):
print("\n|Test_Trapz:test_2d()|")
from kalepy import utils
extr = [sorted(np.random.uniform(-10, 10, 2)) for ii in range(2)]
edges = [np.linspace(*ex, 100) for ex in extr]
grid = np.meshgrid(*edges, indexing='ij')
shp = np.shape(grid[0])
vals = np.random.uniform(0.0, 1.0, size=shp)
test = utils.trapz_nd(vals, edges)
def sum_corner(ii, jj):
area = np.diff(edges[0]) * np.diff(edges[1])
temp = area * vals[ii, jj]
return np.sum(temp)
tot = 0.0
for ii in range(2):
for jj in range(2):
cuts = []
for kk in [ii, jj]:
if kk == 0:
cuts.append(slice(None, -1, None))
else:
cuts.append(slice(1, None, None))
tot += sum_corner(*cuts) * 0.25
print("test = {}, tot = {}".format(test, tot))
utils.allclose(test, tot)
return
def test_1d(self):
print("\n|Test_Trapz:test_1d()|")
from kalepy import utils
extr = sorted(np.random.uniform(-10, 10, 2))
xx = np.linspace(*extr, 1000)
yy = np.random.uniform(0.0, 1.0, xx.size)
np_trapz = np.trapz(yy, xx)
test = utils.trapz_nd(yy, xx)
utils.allclose(test, np_trapz)
return
def _test_dim(dim, num=1e7):
from kalepy import utils
num_per_dim = int(np.power(num, 1 / dim))
norm = np.random.normal(10.0, 1.0)
extr = [sorted(np.random.uniform(-10, 10, 2)) for ii in range(dim)]
edges = [np.linspace(*ex, num_per_dim) for ex in extr]
shp = [len(ed) for ed in edges]
vals = norm * np.ones(shp)
tot = utils.trapz_nd(vals, edges)
truth = np.product(np.diff(extr, axis=-1)) * norm
print("\t{:.4e} vs {:.4e}".format(tot, truth))
utils.allclose(tot, truth)
return
def _test_ndim(self, ndim):
from kalepy import utils
print("`ndim` = {}".format(ndim))
BIN_SIZE_RANGE = [10, 30]
extr = [[0.0, np.random.uniform(0.0, 2.0)] for ii in range(ndim)]
norm = np.random.uniform(0.0, 10.0)
# extr = [[0.0, 1.0] for ii in range(ndim)]
# norm = 1.0
edges = [
np.linspace(*ex, np.random.randint(*BIN_SIZE_RANGE)) for ex in extr
]
grid = np.meshgrid(*edges, indexing='ij')
lengths = np.max(extr, axis=-1)
xx = np.min(np.moveaxis(grid, 0, -1) / lengths, axis=-1)
pdf = norm * xx
area = np.product(lengths)
pmf = utils.trapz_dens_to_mass(pdf, edges)
# Known area of a pyramid in ndim
vol = area * norm / (ndim + 1)
tot = np.sum(pmf)
print("Volume = {:.4e}, Total Mass = {:.4e}; ratio = {:.4e}".format(
vol, tot, tot / vol))
utils.allclose(vol,
tot,
rtol=1e-2,
msg="total volume does {fail:}match analytic value")
test = utils.trapz_nd(pdf, edges)
print("Volume = {:.4e}, Total Mass = {:.4e}; ratio = {:.4e}".format(
test, tot, tot / test))
utils.allclose(vol,
tot,
rtol=1e-2,
msg="total volume does {fail:}match `trapz_nd` value")
return
