From 304bf5bb9e2cf1850798ba1575524a9edb5697a0 Mon Sep 17 00:00:00 2001
From: fernandezfran <fernandezfrancisco2195@gmail.com>
Date: Thu, 15 Jun 2023 23:42:48 -0300
Subject: [PATCH] numerical method for uncertainties estimations

---
 galpynostatic/model.py | 17 ++++++-----------
 tests/conftest.py      | 28 ++++++++++++++--------------
 tests/test_model.py    |  8 ++++----
 3 files changed, 24 insertions(+), 29 deletions(-)

diff --git a/galpynostatic/model.py b/galpynostatic/model.py
index 503a8b2..1455afd 100644
--- a/galpynostatic/model.py
+++ b/galpynostatic/model.py
@@ -201,7 +201,7 @@ def fit(self, X, y, sample_weight=None):
         self.mse_ = mse[idx]
 
         self.dcoeff_err_, self.k0_err_ = _estimate_uncertainties(
-            self, X, y, ("dcoeff_", "k0_"), 1e-6
+            self, X, y, ("dcoeff_", "k0_"), np.cbrt(np.finfo(float).eps)
         )
 
         return self
@@ -301,9 +301,7 @@ def plot(self):
 
 def _estimate_uncertainties(greg, X, y, attrs, delta):
     """Uncertainties of `attrs` estimations."""
-    residuals = y - greg.predict(X)
-
-    sigmas = np.zeros(len(attrs))
+    jacobian = np.zeros((len(attrs), len(y)))
     for i, attr in enumerate(attrs):
         param = greg.__dict__[attr]
 
@@ -313,13 +311,10 @@ def _estimate_uncertainties(greg, X, y, attrs, delta):
         greg.__dict__[attr] = (1 - delta) * param
         lower = greg.predict(X)
 
-        diff = upper - lower
-        mask = diff != 0
+        jacobian[i] = (upper - lower) / (2 * delta * param)
 
-        derivative = diff[mask] / (2 * delta * param)
+    hessian = np.dot(jacobian, jacobian.T)
 
-        ws = residuals[mask] / 2
-        norm = np.sum(ws**2) / (len(ws) - 1)
-        sigmas[i] = norm * np.sum((ws / derivative) ** 2)
+    covariance = np.var((y - greg.predict(X)) ** 2) * np.linalg.inv(hessian)
 
-    return np.sqrt(sigmas) / len(residuals)
+    return np.sqrt(np.diag(covariance))
diff --git a/tests/conftest.py b/tests/conftest.py
index 5eab73d..6a3406a 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -70,8 +70,8 @@ def nishikawa():
             ),
             "dcoeff": 1.0e-9,
             "k0": 1.0e-6,
-            "dcoeff_err": 6.034833e-12,
-            "k0_err": 2.977453e-08,
+            "dcoeff_err": 1.08424e-10,
+            "k0_err": 4.790873e-07,
             "mse": 0.00469549,
             "soc": np.array([0.937788, 0.878488, 0.81915, 0.701, 0.427025]),
             "r2": 0.8443919,
@@ -109,8 +109,8 @@ def mancini():
             "dc": None,
             "dcoeff": 1.0e-10,
             "k0": 1.0e-6,
-            "dcoeff_err": 8.774595e-14,
-            "k0_err": 3.971127e-08,
+            "dcoeff_err": 3.755249e-13,
+            "k0_err": 1.031205e-07,
             "mse": 0.00069059,
             "soc": np.array(
                 [
@@ -148,8 +148,8 @@ def he():
             ),
             "dcoeff": 1.0e-11,
             "k0": 1.0e-8,
-            "dcoeff_err": 1.004282e-13,
-            "k0_err": 1.051095e-10,
+            "dcoeff_err": 1.80632e-12,
+            "k0_err": 1.5790638e-09,
             "mse": 0.006482,
             "soc": np.array(
                 [0.978918, 0.906247, 0.815342, 0.633649, 0.179112]
@@ -186,8 +186,8 @@ def wang():
             ),
             "dcoeff": 1.0e-8,
             "k0": 1.0e-6,
-            "dcoeff_err": 2.594406e-11,
-            "k0_err": 3.213356e-09,
+            "dcoeff_err": 2.667671e-09,
+            "k0_err": 3.22267e-07,
             "mse": 0.000863,
             "soc": np.array(
                 [0.985938, 0.974779, 0.952477, 0.885544, 0.774095, 0.550382]
@@ -231,8 +231,8 @@ def lei():
             ),
             "dcoeff": 1.0e-13,
             "k0": 1.0e-8,
-            "dcoeff_err": 4.695216e-16,
-            "k0_err": 5.017805e-10,
+            "dcoeff_err": 2.834146e-15,
+            "k0_err": 3.682211e-09,
             "mse": 0.006019,
             "soc": np.array(
                 [0.918072, 0.799457, 0.604216, 0.325994, 0.112047, 0.046371]
@@ -276,8 +276,8 @@ def bak():
             ),
             "dcoeff": 1.0e-13,
             "k0": 1.0e-8,
-            "dcoeff_err": 1.033602e-14,
-            "k0_err": 1.614446e-09,
+            "dcoeff_err": 4.23587e-12,
+            "k0_err": 6.579867e-07,
             "mse": 0.016352,
             "soc": np.array(
                 [0.993918, 0.981223, 0.965346, 0.933609, 0.838375, 0.679639]
@@ -303,8 +303,8 @@ def dokko():
             "dc": None,
             "dcoeff": 1.0e-9,
             "k0": 1.0e-6,
-            "dcoeff_err": 2.999896e-11,
-            "k0_err": 5.388039e-08,
+            "dcoeff_err": 1.472138e-10,
+            "k0_err": 5.238026e-07,
             "mse": 0.02627097,
             "soc": np.array(
                 [
diff --git a/tests/test_model.py b/tests/test_model.py
index 352b791..028f08f 100644
--- a/tests/test_model.py
+++ b/tests/test_model.py
@@ -53,14 +53,14 @@ def test_fit(self, experiment, request, spherical):
         greg = greg.fit(experiment["C_rates"], experiment["soc"])
 
         np.testing.assert_almost_equal(
-            greg.dcoeff_, experiment["ref"]["dcoeff"], 14
+            greg.dcoeff_, experiment["ref"]["dcoeff"], 13
         )
         np.testing.assert_almost_equal(
-            greg.dcoeff_err_, experiment["ref"]["dcoeff_err"], 14
+            greg.dcoeff_err_, experiment["ref"]["dcoeff_err"], 13
         )
-        np.testing.assert_almost_equal(greg.k0_, experiment["ref"]["k0"], 12)
+        np.testing.assert_almost_equal(greg.k0_, experiment["ref"]["k0"], 11)
         np.testing.assert_almost_equal(
-            greg.k0_err_, experiment["ref"]["k0_err"], 12
+            greg.k0_err_, experiment["ref"]["k0_err"], 11
         )
         np.testing.assert_almost_equal(greg.mse_, experiment["ref"]["mse"], 6)