Internal: Remove private select-style functions because we have eas…

…ier ways of accessing derivatives now (#799)

* Remove self._select from DenseConditional

* Simplify select() for isotropic and blockdiag factorisations, too

* Delete marginal_nth_derivative because it hasn't been used anywhere

probdiffeq/impl/_conditional.py

@@ -147,10 +147,11 @@ def to_derivative(self, i, standard_deviation):
 
 
 class DenseConditional(ConditionalBackend):
-    def __init__(self, ode_shape, num_derivatives, unravel):
+    def __init__(self, ode_shape, num_derivatives, unravel, flat_shape):
         self.ode_shape = ode_shape
         self.num_derivatives = num_derivatives
         self.unravel = unravel
+        self.flat_shape = flat_shape
 
     def apply(self, x, conditional, /):
         matrix, noise = conditional
@@ -178,8 +179,6 @@ def revert(self, rv, conditional, /):
         mean, cholesky = rv.mean, rv.cholesky
 
         # QR-decomposition
-        # (todo: rename revert_conditional_noisefree to
-        #   revert_transformation_cov_sqrt())
         r_obs, (r_cor, gain) = cholesky_util.revert_conditional(
             R_X_F=(matrix @ cholesky).T, R_X=cholesky.T, R_YX=noise.cholesky.T
         )
@@ -208,8 +207,7 @@ def ibm_transitions(self, *, output_scale):
         A = np.kron(a, eye_d)
         Q = np.kron(q_sqrtm, eye_d)
 
-        ndim = d * (self.num_derivatives + 1)
-        q0 = np.zeros((ndim,))
+        q0 = np.zeros(self.flat_shape)
         noise = _normal.Normal(q0, Q)
 
         precon_fun = preconditioner_prepare(num_derivatives=self.num_derivatives)
@@ -230,34 +228,25 @@ def preconditioner_apply(self, cond, p, p_inv, /):
         return Conditional(A, noise)
 
     def to_derivative(self, i, standard_deviation):
-        a0 = functools.partial(self._select, idx_or_slice=i)
+        x = np.zeros(self.flat_shape)
+
+        def select(a):
+            return self.unravel(a)[i]
+
+        linop = functools.jacrev(select)(x)
 
         (d,) = self.ode_shape
         bias = np.zeros((d,))
         eye = np.eye(d)
         noise = _normal.Normal(bias, standard_deviation * eye)
-
-        x = np.zeros(((self.num_derivatives + 1) * d,))
-        linop = _jac_materialize(lambda s, _p: self._autobatch_linop(a0)(s), inputs=x)
         return Conditional(linop, noise)
 
-    def _select(self, x, /, idx_or_slice):
-        return self.unravel(x)[idx_or_slice]
-
-    @staticmethod
-    def _autobatch_linop(fun):
-        def fun_(x):
-            if np.ndim(x) > 1:
-                return functools.vmap(fun_, in_axes=1, out_axes=1)(x)
-            return fun(x)
-
-        return fun_
-
 
 class IsotropicConditional(ConditionalBackend):
-    def __init__(self, *, ode_shape, num_derivatives):
+    def __init__(self, *, ode_shape, num_derivatives, unravel_tree):
         self.ode_shape = ode_shape
         self.num_derivatives = num_derivatives
+        self.unravel_tree = unravel_tree
 
     def apply(self, x, conditional, /):
         A, noise = conditional
@@ -332,22 +321,24 @@ def preconditioner_apply(self, cond, p, p_inv, /):
         return Conditional(A_new, noise)
 
     def to_derivative(self, i, standard_deviation):
-        def A(x):
-            return x[[i], ...]
+        def select(a):
+            return tree_util.ravel_pytree(self.unravel_tree(a)[i])[0]
+
+        m = np.zeros((self.num_derivatives + 1,))
+        linop = functools.jacrev(select)(m)
 
         bias = np.zeros(self.ode_shape)
         eye = np.eye(1)
         noise = _normal.Normal(bias, standard_deviation * eye)
 
-        m = np.zeros((self.num_derivatives + 1,))
-        linop = _jac_materialize(lambda s, _p: A(s), inputs=m)
         return Conditional(linop, noise)
 
 
 class BlockDiagConditional(ConditionalBackend):
-    def __init__(self, *, ode_shape, num_derivatives):
+    def __init__(self, *, ode_shape, num_derivatives, unravel_tree):
         self.ode_shape = ode_shape
         self.num_derivatives = num_derivatives
+        self.unravel_tree = unravel_tree
 
     def apply(self, x, conditional, /):
         if np.ndim(x) == 1:
@@ -434,15 +425,11 @@ def preconditioner_apply(self, cond, p, p_inv, /):
         return Conditional(A_new, noise)
 
     def to_derivative(self, i, standard_deviation):
-        def A(x):
-            return x[[i], ...]
-
-        @functools.vmap
-        def lo(y):
-            return _jac_materialize(lambda s, _p: A(s), inputs=y)
+        def select(a):
+            return tree_util.ravel_pytree(self.unravel_tree(a)[i])[0]
 
         x = np.zeros((*self.ode_shape, self.num_derivatives + 1))
-        linop = lo(x)
+        linop = functools.vmap(functools.jacrev(select))(x)
 
         bias = np.zeros((*self.ode_shape, 1))
         eye = np.ones((*self.ode_shape, 1, 1)) * np.eye(1)[None, ...]
@@ -494,7 +481,3 @@ def _batch_gram(k, /):
 
 def _binom(n, k):
     return np.factorial(n) / (np.factorial(n - k) * np.factorial(k))
-
-
-def _jac_materialize(func, /, *, inputs, params=None):
-    return functools.jacrev(lambda v: func(v, params))(inputs)

probdiffeq/impl/_stats.py

@@ -42,10 +42,6 @@ def rescale_cholesky(self, rv, factor, /):
     def qoi(self, rv):
         raise NotImplementedError
 
-    @abc.abstractmethod
-    def marginal_nth_derivative(self, rv):
-        raise NotImplementedError
-
     @abc.abstractmethod
     def qoi_from_sample(self, sample, /):
         raise NotImplementedError
@@ -105,37 +101,11 @@ def to_multivariate_normal(self, rv):
     def qoi(self, rv):
         return self.qoi_from_sample(rv.mean)
 
-    def marginal_nth_derivative(self, rv, i):
-        if rv.mean.ndim > 1:
-            return functools.vmap(self.marginal_nth_derivative, in_axes=(0, None))(
-                rv, i
-            )
-
-        m = self._select(rv.mean, i)
-        c = functools.vmap(self._select, in_axes=(1, None), out_axes=1)(rv.cholesky, i)
-        c = cholesky_util.triu_via_qr(c.T)
-        return _normal.Normal(m, c.T)
-
     def qoi_from_sample(self, sample, /):
         if np.ndim(sample) > 1:
             return functools.vmap(self.qoi_from_sample)(sample)
         return self.unravel(sample)
 
-    def _select(self, x, /, idx_or_slice):
-        x_reshaped = np.reshape(x, (-1, *self.ode_shape), order="F")
-        if isinstance(idx_or_slice, int) and idx_or_slice > x_reshaped.shape[0]:
-            raise ValueError
-        return x_reshaped[idx_or_slice]
-
-    @staticmethod
-    def _autobatch_linop(fun):
-        def fun_(x):
-            if np.ndim(x) > 1:
-                return functools.vmap(fun_, in_axes=1, out_axes=1)(x)
-            return fun(x)
-
-        return fun_
-
     def update_mean(self, mean, x, /, num):
         nominator = cholesky_util.sqrt_sum_square_scalar(np.sqrt(num) * mean, x)
         denominator = np.sqrt(num + 1)
@@ -198,19 +168,6 @@ def to_multivariate_normal(self, rv):
         mean = rv.mean.reshape((-1,), order="F")
         return (mean, cov)
 
-    def marginal_nth_derivative(self, rv, i):
-        if np.ndim(rv.mean) > 2:
-            return functools.vmap(self.marginal_nth_derivative, in_axes=(0, None))(
-                rv, i
-            )
-
-        if i > np.shape(rv.mean)[0]:
-            raise ValueError
-
-        mean = rv.mean[i, :]
-        cholesky = cholesky_util.triu_via_qr(rv.cholesky[[i], :].T).T
-        return _normal.Normal(mean, cholesky)
-
     def qoi(self, rv):
         return self.qoi_from_sample(rv.mean)
 
@@ -287,22 +244,6 @@ def qoi_from_sample(self, sample, /):
             return functools.vmap(self.qoi_from_sample)(sample)
         return self.unravel(sample)
 
-    def marginal_nth_derivative(self, rv, i):
-        if np.ndim(rv.mean) > 2:
-            return functools.vmap(self.marginal_nth_derivative, in_axes=(0, None))(
-                rv, i
-            )
-
-        if i > np.shape(rv.mean)[0]:
-            raise ValueError
-
-        mean = rv.mean[:, i]
-        cholesky = functools.vmap(cholesky_util.triu_via_qr)(
-            (rv.cholesky[:, i, :])[..., None]
-        )
-        cholesky = np.transpose(cholesky, axes=(0, 2, 1))
-        return _normal.Normal(mean, cholesky)
-
     def update_mean(self, mean, x, /, num):
         if np.ndim(mean) > 0:
             assert np.shape(mean) == np.shape(x)

probdiffeq/impl/impl.py

@@ -40,7 +40,7 @@ def choose(which: str, /, *, tcoeffs_like) -> FactImpl:
 
 def _select_dense(*, tcoeffs_like) -> FactImpl:
     ode_shape = tcoeffs_like[0].shape
-    _, unravel = tree_util.ravel_pytree(tcoeffs_like)
+    flat, unravel = tree_util.ravel_pytree(tcoeffs_like)
 
     num_derivatives = len(tcoeffs_like) - 1
 
@@ -49,7 +49,10 @@ def _select_dense(*, tcoeffs_like) -> FactImpl:
     linearise = _linearise.DenseLinearisation(ode_shape=ode_shape, unravel=unravel)
     stats = _stats.DenseStats(ode_shape=ode_shape, unravel=unravel)
     conditional = _conditional.DenseConditional(
-        ode_shape=ode_shape, num_derivatives=num_derivatives, unravel=unravel
+        ode_shape=ode_shape,
+        num_derivatives=num_derivatives,
+        unravel=unravel,
+        flat_shape=flat.shape,
     )
     transform = _conditional.DenseTransform()
     return FactImpl(
@@ -76,7 +79,7 @@ def _select_isotropic(*, tcoeffs_like) -> FactImpl:
     stats = _stats.IsotropicStats(ode_shape=ode_shape, unravel=unravel)
     linearise = _linearise.IsotropicLinearisation()
     conditional = _conditional.IsotropicConditional(
-        ode_shape=ode_shape, num_derivatives=num_derivatives
+        ode_shape=ode_shape, num_derivatives=num_derivatives, unravel_tree=unravel_tree
     )
     transform = _conditional.IsotropicTransform()
     return FactImpl(
@@ -103,7 +106,7 @@ def _select_blockdiag(*, tcoeffs_like) -> FactImpl:
     stats = _stats.BlockDiagStats(ode_shape=ode_shape, unravel=unravel)
     linearise = _linearise.BlockDiagLinearisation()
     conditional = _conditional.BlockDiagConditional(
-        ode_shape=ode_shape, num_derivatives=num_derivatives
+        ode_shape=ode_shape, num_derivatives=num_derivatives, unravel_tree=unravel_tree
     )
     transform = _conditional.BlockDiagTransform(ode_shape=ode_shape)
     return FactImpl(