Use ScalarLoop for betainc gradient

Author: ricardoV94

pytensor/scalar/math.py

@@ -14,10 +14,9 @@
 
 from pytensor.configdefaults import config
 from pytensor.gradient import grad_not_implemented
+from pytensor.scalar.basic import BinaryScalarOp, ScalarOp, UnaryScalarOp
+from pytensor.scalar.basic import abs as scalar_abs
 from pytensor.scalar.basic import (
-    BinaryScalarOp,
-    ScalarOp,
-    UnaryScalarOp,
     as_scalar,
     complex_types,
     constant,
@@ -27,9 +26,12 @@
     expm1,
     float64,
     float_types,
+    identity,
     isinf,
     log,
     log1p,
+    reciprocal,
+    scalar_maximum,
     sqrt,
     switch,
     true_div,
@@ -1329,8 +1331,8 @@ def grad(self, inp, grads):
         (gz,) = grads
 
         return [
-            gz * betainc_der(a, b, x, True),
-            gz * betainc_der(a, b, x, False),
+            gz * betainc_grad(a, b, x, True),
+            gz * betainc_grad(a, b, x, False),
             gz
             * exp(
                 log1p(-x) * (b - 1)
@@ -1346,28 +1348,28 @@ def c_code(self, *args, **kwargs):
 betainc = BetaInc(upgrade_to_float_no_complex, name="betainc")
 
 
-class BetaIncDer(ScalarOp):
-    """
-    Gradient of the regularized incomplete beta function wrt to the first
-    argument (alpha) or the second argument (beta), depending on whether the
-    fourth argument to betainc_der is `True` or `False`, respectively.
+def betainc_grad(p, q, x, wrtp: bool):
+    """Gradient of the regularized lower gamma function (P) wrt to the first
+    argument (k, a.k.a. alpha).
 
-    Reference: Boik, R. J., & Robison-Cox, J. F. (1998). Derivatives of the incomplete beta function.
-    Journal of Statistical Software, 3(1), 1-20.
+    Adapted from STAN `grad_reg_lower_inc_gamma.hpp`
+
+    Reference: Gautschi, W. (1979). A computational procedure for incomplete gamma functions.
+    ACM Transactions on Mathematical Software (TOMS), 5(4), 466-481.
     """
 
-    nin = 4
+    def _betainc_der(p, q, x, wrtp, skip_loop):
+        dtype = upcast(p.type.dtype, q.type.dtype, x.type.dtype, "float32")
+
+        def betaln(a, b):
+            return gammaln(a) + (gammaln(b) - gammaln(a + b))
 
-    def impl(self, p, q, x, wrtp):
         def _betainc_a_n(f, p, q, n):
             """
             Numerator (a_n) of the nth approximant of the continued fraction
             representation of the regularized incomplete beta function
             """
 
-            if n == 1:
-                return p * f * (q - 1) / (q * (p + 1))
-
             p2n = p + 2 * n
             F1 = p**2 * f**2 * (n - 1) / (q**2)
             F2 = (
@@ -1377,7 +1379,11 @@ def _betainc_a_n(f, p, q, n):
                 / ((p2n - 3) * (p2n - 2) ** 2 * (p2n - 1))
             )
 
-            return F1 * F2
+            return switch(
+                eq(n, 1),
+                p * f * (q - 1) / (q * (p + 1)),
+                F1 * F2,
+            )
 
         def _betainc_b_n(f, p, q, n):
             """
@@ -1397,9 +1403,6 @@ def _betainc_da_n_dp(f, p, q, n):
             Derivative of a_n wrt p
             """
 
-            if n == 1:
-                return -p * f * (q - 1) / (q * (p + 1) ** 2)
-
             pp = p**2
             ppp = pp * p
             p2n = p + 2 * n
@@ -1414,20 +1417,25 @@ def _betainc_da_n_dp(f, p, q, n):
             D1 = q**2 * (p2n - 3) ** 2
             D2 = (p2n - 2) ** 3 * (p2n - 1) ** 2
 
-            return (N1 / D1) * (N2a + N2b + N2c + N2d + N2e) / D2
+            return switch(
+                eq(n, 1),
+                -p * f * (q - 1) / (q * (p + 1) ** 2),
+                (N1 / D1) * (N2a + N2b + N2c + N2d + N2e) / D2,
+            )
 
         def _betainc_da_n_dq(f, p, q, n):
             """
             Derivative of a_n wrt q
             """
-            if n == 1:
-                return p * f / (q * (p + 1))
-
             p2n = p + 2 * n
             F1 = (p**2 * f**2 / (q**2)) * (n - 1) * (p + n - 1) * (2 * q + p - 2)
             D1 = (p2n - 3) * (p2n - 2) ** 2 * (p2n - 1)
 
-            return F1 / D1
+            return switch(
+                eq(n, 1),
+                p * f / (q * (p + 1)),
+                F1 / D1,
+            )
 
         def _betainc_db_n_dp(f, p, q, n):
             """
@@ -1452,42 +1460,44 @@ def _betainc_db_n_dq(f, p, q, n):
             p2n = p + 2 * n
             return -(p**2 * f) / (q * (p2n - 2) * p2n)
 
-        # Input validation
-        if not (0 <= x <= 1) or p < 0 or q < 0:
-            return np.nan
-
-        if x > (p / (p + q)):
-            return -self.impl(q, p, 1 - x, not wrtp)
-
-        min_iters = 3
-        max_iters = 200
-        err_threshold = 1e-12
-
-        derivative_old = 0
+        min_iters = np.array(3, dtype="int32")
+        max_iters = switch(
+            skip_loop, np.array(0, dtype="int32"), np.array(200, dtype="int32")
+        )
+        err_threshold = np.array(1e-12, dtype=config.floatX)
 
-        Am2, Am1 = 1, 1
-        Bm2, Bm1 = 0, 1
-        dAm2, dAm1 = 0, 0
-        dBm2, dBm1 = 0, 0
+        Am2, Am1 = np.array(1, dtype=dtype), np.array(1, dtype=dtype)
+        Bm2, Bm1 = np.array(0, dtype=dtype), np.array(1, dtype=dtype)
+        dAm2, dAm1 = np.array(0, dtype=dtype), np.array(0, dtype=dtype)
+        dBm2, dBm1 = np.array(0, dtype=dtype), np.array(0, dtype=dtype)
 
         f = (q * x) / (p * (1 - x))
-        K = np.exp(
-            p * np.log(x)
-            + (q - 1) * np.log1p(-x)
-            - np.log(p)
-            - scipy.special.betaln(p, q)
-        )
+        K = exp(p * log(x) + (q - 1) * log1p(-x) - log(p) - betaln(p, q))
         if wrtp:
-            dK = (
-                np.log(x)
-                - 1 / p
-                + scipy.special.digamma(p + q)
-                - scipy.special.digamma(p)
-            )
+            dK = log(x) - reciprocal(p) + psi(p + q) - psi(p)
         else:
-            dK = np.log1p(-x) + scipy.special.digamma(p + q) - scipy.special.digamma(q)
-
-        for n in range(1, max_iters + 1):
+            dK = log1p(-x) + psi(p + q) - psi(q)
+
+        derivative = np.array(0, dtype=dtype)
+        n = np.array(1, dtype="int16")  # Enough for 200 max iters
+
+        def inner_loop(
+            derivative,
+            Am2,
+            Am1,
+            Bm2,
+            Bm1,
+            dAm2,
+            dAm1,
+            dBm2,
+            dBm1,
+            n,
+            f,
+            p,
+            q,
+            K,
+            dK,
+        ):
             a_n_ = _betainc_a_n(f, p, q, n)
             b_n_ = _betainc_b_n(f, p, q, n)
             if wrtp:
@@ -1502,36 +1512,53 @@ def _betainc_db_n_dq(f, p, q, n):
             dA = da_n * Am2 + a_n_ * dAm2 + db_n * Am1 + b_n_ * dAm1
             dB = da_n * Bm2 + a_n_ * dBm2 + db_n * Bm1 + b_n_ * dBm1
 
-            Am2, Am1 = Am1, A
-            Bm2, Bm1 = Bm1, B
-            dAm2, dAm1 = dAm1, dA
-            dBm2, dBm1 = dBm1, dB
-
-            if n < min_iters - 1:
-                continue
+            Am2, Am1 = identity(Am1), identity(A)
+            Bm2, Bm1 = identity(Bm1), identity(B)
+            dAm2, dAm1 = identity(dAm1), identity(dA)
+            dBm2, dBm1 = identity(dBm1), identity(dB)
 
             F1 = A / B
             F2 = (dA - F1 * dB) / B
-            derivative = K * (F1 * dK + F2)
+            derivative_new = K * (F1 * dK + F2)
 
-            errapx = abs(derivative_old - derivative)
-            d_errapx = errapx / max(err_threshold, abs(derivative))
-            derivative_old = derivative
-
-            if d_errapx <= err_threshold:
-                return derivative
+            errapx = scalar_abs(derivative - derivative_new)
+            d_errapx = errapx / scalar_maximum(
+                err_threshold, scalar_abs(derivative_new)
+            )
 
-        warnings.warn(
-            f"betainc_der did not converge after {n} iterations",
-            RuntimeWarning,
-        )
-        return np.nan
+            min_iters_cond = n > (min_iters - 1)
+            derivative = switch(
+                min_iters_cond,
+                derivative_new,
+                derivative,
+            )
+            n += 1
 
-    def c_code(self, *args, **kwargs):
-        raise NotImplementedError()
+            return (
+                (derivative, Am2, Am1, Bm2, Bm1, dAm2, dAm1, dBm2, dBm1, n),
+                (d_errapx <= err_threshold) & min_iters_cond,
+            )
 
+        init = [derivative, Am2, Am1, Bm2, Bm1, dAm2, dAm1, dBm2, dBm1, n]
+        constant = [f, p, q, K, dK]
+        grad = _make_scalar_loop(
+            max_iters, init, constant, inner_loop, name="betainc_grad"
+        )
+        return grad
 
-betainc_der = BetaIncDer(upgrade_to_float_no_complex, name="betainc_der")
+    # Input validation
+    nan_branch = (x < 0) | (x > 1) | (p < 0) | (q < 0)
+    flip_branch = x > (p / (p + q))
+    grad = switch(
+        nan_branch,
+        np.nan,
+        switch(
+            flip_branch,
+            -_betainc_der(q, p, 1 - x, not wrtp, skip_loop=nan_branch | (~flip_branch)),
+            _betainc_der(p, q, x, wrtp, skip_loop=nan_branch | flip_branch),
+        ),
+    )
+    return grad
 
 
 class Hyp2F1(ScalarOp):

tests/scalar/test_math.py

@@ -8,7 +8,7 @@
 from pytensor.link.c.basic import CLinker
 from pytensor.scalar.math import (
     betainc,
-    betainc_der,
+    betainc_grad,
     gammainc,
     gammaincc,
     gammal,
@@ -82,7 +82,7 @@ def test_betainc():
 
 def test_betainc_derivative_nan():
     a, b, x = at.scalars("a", "b", "x")
-    res = betainc_der(a, b, x, True)
+    res = betainc_grad(a, b, x, True)
     test_func = function([a, b, x], res, mode=Mode("py"))
     assert not np.isnan(test_func(1, 1, 1))
     assert np.isnan(test_func(1, 1, -1))