Don't explicitly construct ILR matrix using JAX

simplex_transforms/jax/transforms/ilr.py

@@ -2,39 +2,36 @@
 import jax.numpy as jnp
 
 
-def _make_helmert_matrix(N: int):
-    H1 = jnp.full(N, 1 / jnp.sqrt(N))
-    H22 = jnp.tril(jnp.ones((N - 1, N - 1)))
+def _get_V_mul_y(y):
+    N = y.shape[-1] + 1
     ns = jnp.arange(1, N)
-    H22 = H22.at[jnp.diag_indices_from(H22)].set(-ns) / jnp.sqrt(ns * (ns + 1)).reshape(
-        -1, 1
+    w = y / jnp.sqrt(ns * (ns + 1))
+    w_rev_sum = jnp.flip(jnp.cumsum(jnp.flip(w, axis=-1), axis=-1), axis=-1)
+    zeros = jnp.zeros(w_rev_sum.shape[:-1] + (1,))
+    z = jnp.concatenate([w_rev_sum, zeros], axis=-1) - jnp.concatenate(
+        [zeros, ns * w], axis=-1
     )
-    H21 = H22[:, :1].at[0].multiply(-1)
-    H = jnp.block([[H1], [H21, H22]])
-    return H
+    return z
 
 
-def _make_semiorthogonal_matrix(N: int):
-    H = _make_helmert_matrix(N)
-    V = H.T[:, 1:]
-    return V
+def _get_V_trans_mul_z(z):
+    N = z.shape[-1]
+    ns = jnp.arange(1, N)
+    y = (jnp.cumsum(z[..., :-1], axis=-1) - ns * z[..., 1:]) / jnp.sqrt(ns * (ns + 1))
+    return y
 
 
 class ILR:
     def unconstrain(self, x):
-        N = x.shape[-1]
-        V = _make_semiorthogonal_matrix(N)
-        return jnp.dot(jnp.log(x), V)
+        return _get_V_trans_mul_z(jnp.log(x))
 
     def constrain(self, y):
-        N = y.shape[-1] + 1
-        V = _make_semiorthogonal_matrix(N)
-        return jax.nn.softmax(jnp.dot(y, V.T), axis=-1)
+        z = _get_V_mul_y(y)
+        return jax.nn.softmax(z, axis=-1)
 
     def constrain_with_logdetjac(self, y):
         N = y.shape[-1] + 1
-        V = _make_semiorthogonal_matrix(N)
-        z = jnp.dot(y, V.T)
+        z = _get_V_mul_y(y)
         logx = jax.nn.log_softmax(z, axis=-1)
         x = jnp.exp(logx)
         logJ = jnp.sum(logx, axis=-1) + jnp.log(N) / 2

tests/jax/test_transforms.py

@@ -45,6 +45,24 @@ def _allclose(x, y, **kwargs):
         return jnp.allclose(x, y, **kwargs)
 
 
+def _make_helmert_matrix(N: int):
+    H1 = jnp.full(N, 1 / jnp.sqrt(N))
+    H22 = jnp.tril(jnp.ones((N - 1, N - 1)))
+    ns = jnp.arange(1, N)
+    H22 = H22.at[jnp.diag_indices_from(H22)].set(-ns) / jnp.sqrt(ns * (ns + 1)).reshape(
+        -1, 1
+    )
+    H21 = H22[:, :1].at[0].multiply(-1)
+    H = jnp.block([[H1], [H21, H22]])
+    return H
+
+
+def _make_ilr_semiorthogonal_matrix(N: int):
+    H = _make_helmert_matrix(N)
+    V = H.T[:, 1:]
+    return V
+
+
 def logdetjac(f):
     jac = jax.jacobian(f)
 
@@ -124,10 +142,14 @@ def test_normalized_transforms_consistent(N, seed=42):
 
 
 @pytest.mark.parametrize("N", [3, 5, 10])
-def test_ilr_semiorthogonal_matrix_properties(N):
+def test_ilr_semiorthogonal_matrix_properties(N, seed=87):
     from simplex_transforms.jax.transforms import ilr
 
-    V = ilr._make_semiorthogonal_matrix(N)
+    V = _make_ilr_semiorthogonal_matrix(N)
     assert V.shape == (N, N - 1)
     assert jnp.allclose(V.T @ V, jnp.eye(N - 1))
     assert jnp.allclose(V.T @ jnp.ones(N), 0)
+    y = jax.random.normal(key=jax.random.key(seed), shape=(N - 1,))
+    z = V @ y
+    assert jnp.allclose(ilr._get_V_mul_y(y), z)
+    assert jnp.allclose(ilr._get_V_trans_mul_z(z), y)