From 4f2c813a3f23a6f65f5cdf875123438f48b9a359 Mon Sep 17 00:00:00 2001
From: Andreas Dutzler <a.dutzler@gmail.com>
Date: Sun, 2 Jun 2024 00:50:24 +0200
Subject: [PATCH] Add the (Gauss) error function `math.special.erf(z)`

---
 src/tensortrax/__about__.py                    |  2 +-
 src/tensortrax/math/special/__init__.py        |  2 ++
 src/tensortrax/math/special/_special_tensor.py | 18 ++++++++++++++++++
 tests/test_math.py                             |  1 +
 4 files changed, 22 insertions(+), 1 deletion(-)

diff --git a/src/tensortrax/__about__.py b/src/tensortrax/__about__.py
index 10a4943..826ea2b 100644
--- a/src/tensortrax/__about__.py
+++ b/src/tensortrax/__about__.py
@@ -2,4 +2,4 @@
 tensorTRAX: Math on (Hyper-Dual) Tensors with Trailing Axes.
 """
 
-__version__ = "0.24.0"
+__version__ = "0.25.0"
diff --git a/src/tensortrax/math/special/__init__.py b/src/tensortrax/math/special/__init__.py
index f11fc68..a9bac1b 100644
--- a/src/tensortrax/math/special/__init__.py
+++ b/src/tensortrax/math/special/__init__.py
@@ -5,6 +5,7 @@
 from ._special_tensor import (
     ddot,
     dev,
+    erf,
     from_triu_1d,
     from_triu_2d,
     sym,
@@ -17,6 +18,7 @@
 __all__ = [
     "ddot",
     "dev",
+    "erf",
     "from_triu_1d",
     "from_triu_2d",
     "sym",
diff --git a/src/tensortrax/math/special/_special_tensor.py b/src/tensortrax/math/special/_special_tensor.py
index b8bbc25..56d1f98 100644
--- a/src/tensortrax/math/special/_special_tensor.py
+++ b/src/tensortrax/math/special/_special_tensor.py
@@ -4,6 +4,7 @@
 
 import numpy as np
 
+from ..._helpers import Δ, Δδ, f, δ
 from ..._tensor import Tensor
 from .. import _math_array as array
 from .._math_tensor import einsum, sqrt, stack, trace, transpose
@@ -20,6 +21,23 @@ def dev(A):
     return A - trace(A) / dim * array.eye(A)
 
 
+def erf(z):
+    "The (Gauss) error function."
+    from scipy.special import erf
+
+    if isinstance(z, Tensor):
+        derf = 2 / np.sqrt(np.pi) * np.exp(-f(z) ** 2)
+        return Tensor(
+            x=erf(f(z)),
+            δx=derf * δ(z),
+            Δx=derf * Δ(z),
+            Δδx=-2 * f(z) * derf * δ(z) * Δ(z) + derf * Δδ(z),
+            ntrax=z.ntrax,
+        )
+    else:
+        return erf(z)
+
+
 def sym(A):
     "Symmetric part of a Tensor."
     return (A + transpose(A)) / 2
diff --git a/tests/test_math.py b/tests/test_math.py
index a154c4d..4b9f2e9 100644
--- a/tests/test_math.py
+++ b/tests/test_math.py
@@ -69,6 +69,7 @@ def test_math():
         tm.ravel,
         tm.abs,
         tm.sign,
+        tm.special.erf,
     ]:
         assert np.allclose(fun(F), fun(T).x)