def test_basis2():
# test orthonormality in Aitchison inner product
b = basis(4)
for i in range(len(b)):
ii = inner(b[i], b[i])
assert ii == pytest.approx(1.0)
for j in range(i + 1, len(b)):
ij = inner(b[i], b[j])
assert ij == pytest.approx(0.0)
def test_basis2():
# test orthonormality in Aitchison inner product
b = basis(4)
for i in range(len(b)):
ii = inner(b[i], b[i])
assert_almost_equal(ii, 1.0)
for j in range(i + 1, len(b)):
ij = inner(b[i], b[j])
assert_almost_equal(ij, 0.0)
def test_basis2():
# test orthonormality in Aitchison inner product
b = basis(4)
for i in range(len(b)):
ii = inner(b[i], b[i])
assert_almost_equal(ii, 1.0)
for j in range(i+1, len(b)):
ij = inner(b[i], b[j])
assert_almost_equal(ij, 0.0)
def test_inner():
# 1D
x = np.array([1 / 3.0, 2 / 3.0])
y = np.array([1 / 4.0, 3 / 4.0])
z = np.array([2 / 5.0, 3 / 5.0])
xy_ = 0.79248125036057804
xy = inner(x, y)
yx = inner(y, x)
assert xy_ == pytest.approx(xy)
assert xy_ == pytest.approx(yx)
yz_ = 0.46357181398555231
yz = inner(y, z)
zy = inner(z, y)
assert yz_ == pytest.approx(yz)
assert yz_ == pytest.approx(zy)
xz_ = 0.29248125036057804
xz = inner(x, z)
zx = inner(z, x)
assert xz_ == pytest.approx(xz)
assert xz_ == pytest.approx(zx)
# 2D with multiple rows
xx = np.array([x, y, z])
yy = np.array([y, z, x])
xxyy = inner(xx, yy)
xxyy_ = np.array([xy_, yz_, xz_])
assert np.allclose(xxyy_, xxyy)
# 2D with multiple rows in x and single row in y
yy_ = 1.2560530643461303
xx = np.array([x, y, z])
yy = np.array([y])
xxyy = inner(xx, yy)
xxyy_ = np.array([xy_, yy_, yz_])
assert np.allclose(xxyy_, xxyy)
yyxx = inner(yy, xx)
assert np.allclose(xxyy_, yyxx)
# 2D with single rows
x2d = np.atleast_2d(x)
y2d = np.atleast_2d(y)
xy2d = inner(x2d, y2d)
xy2d_ = np.array([xy_])
assert np.allclose(xy2d_, xy2d)
def test_inner():
# 1D
x = np.array([1/3.0, 2/3.0])
y = np.array([1/4.0, 3/4.0])
z = np.array([2/5.0, 3/5.0])
xy_ = 0.79248125036057804
xy = inner(x, y)
yx = inner(y, x)
assert_almost_equal(xy_, xy)
assert_almost_equal(xy_, yx)
yz_ = 0.46357181398555231
yz = inner(y, z)
zy = inner(z, y)
assert_almost_equal(yz_, yz)
assert_almost_equal(yz_, zy)
xz_ = 0.29248125036057804
xz = inner(x, z)
zx = inner(z, x)
assert_almost_equal(xz_, xz)
assert_almost_equal(xz_, zx)
# 2D with multiple rows
xx = np.array([x, y, z])
yy = np.array([y, z, x])
xxyy = inner(xx, yy)
xxyy_ = np.array([xy_, yz_, xz_])
assert_true(allclose(xxyy_, xxyy))
# 2D with multiple rows in x and single row in y
yy_ = 1.2560530643461303
xx = np.array([x, y, z])
yy = np.array([y])
xxyy = inner(xx, yy)
xxyy_ = np.array([xy_, yy_, yz_])
assert_true(allclose(xxyy_, xxyy))
yyxx = inner(yy, xx)
assert_true(allclose(xxyy_, yyxx))
# 2D with single rows
x2d = np.atleast_2d(x)
y2d = np.atleast_2d(y)
xy2d = inner(x2d, y2d)
xy2d_ = np.array([xy_])
assert_true(allclose(xy2d_, xy2d))
def test_equiv_inner2():
x = np.array([1, 2, 3, 4])
y = np.array([3, 5, 1, 1])
clrx = clr(x)
clry = clr(y)
D = len(x)
M = -1 * np.ones((D, D))
M.flat[::D + 1] = D - 1
z1 = inner(x, y)
z2 = 1 / D * np.dot(np.dot(clrx, M), clry[:, np.newaxis])
assert z1 == pytest.approx(z2[0])
def test_equiv_inner2():
x = np.array([1, 2, 3, 4])
y = np.array([3, 5, 1, 1])
clrx = clr(x)
clry = clr(y)
D = len(x)
M = -1 * np.ones((D, D))
M.flat[::D+1] = D - 1
z1 = inner(x, y)
z2 = 1/D * np.dot(np.dot(clrx, M), clry[:, np.newaxis])
assert_almost_equal(z1, z2)
def test_equiv_inner1():
x = np.array([1, 2, 3, 4])
y = np.array([3, 5, 1, 1])
aitchison_inner = inner(x, y)
euclidean_inner = np.inner(ilr(x), ilr(y))
assert aitchison_inner == pytest.approx(euclidean_inner)
def test_equiv_inner1():
x = np.array([1, 2, 3, 4])
y = np.array([3, 5, 1, 1])
aitchison_inner = inner(x, y)
euclidean_inner = np.inner(ilr(x), ilr(y))
assert_almost_equal(aitchison_inner, euclidean_inner)
def test_equiv_inner1():
x = np.array([1, 2, 3, 4])
y = np.array([3, 5, 1, 1])
aitchison_inner = inner(x, y)
euclidean_inner = np.inner(ilr(x), ilr(y))
assert_almost_equal(aitchison_inner, euclidean_inner)
