From 487bf8840846b5d4d694b38985268c308aadb36e Mon Sep 17 00:00:00 2001
From: David Luevano <55825613+luevano@users.noreply.github.com>
Date: Wed, 18 Dec 2019 07:21:35 -0700
Subject: Refactor files

---
 lj_matrix/cholesky_solve.py | 64 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 lj_matrix/cholesky_solve.py

(limited to 'lj_matrix/cholesky_solve.py')

diff --git a/lj_matrix/cholesky_solve.py b/lj_matrix/cholesky_solve.py
new file mode 100644
index 000000000..bc6a572a3
--- /dev/null
+++ b/lj_matrix/cholesky_solve.py
@@ -0,0 +1,64 @@
+"""MIT License
+
+Copyright (c) 2019 David Luevano Alvarado
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+"""
+import numpy as np
+from numpy.linalg import cholesky
+
+
+def cholesky_solve(K, y):
+    """
+    Applies Cholesky decomposition to obtain the 'alpha coeficients'.
+    K: kernel.
+    y: known parameters.
+    """
+    # The initial mathematical problem is to solve Ka=y.
+
+    # First, add a small lambda value.
+    K[np.diag_indices_from(K)] += 1e-8
+
+    # Get the Cholesky decomposition of the kernel.
+    L = cholesky(K)
+    size = len(L)
+
+    # Solve Lx=y for x.
+    x = np.zeros(size)
+    x[0] = y[0] / L[0, 0]
+    for i in range(1, size):
+        temp_sum = 0.0
+        for j in range(i):
+            temp_sum += L[i, j] * x[j]
+        x[i] = (y[i] - temp_sum) / L[i, i]
+
+    # Now, solve LTa=x for a.
+    L2 = L.T
+    a = np.zeros(size)
+    a_ms = size - 1
+    a[a_ms] = x[a_ms] / L2[a_ms, a_ms]
+    # Because of the form of L2 (upper triangular matriz), an inversion of
+    # range() needs to be done.
+    for i in range(0, a_ms)[::-1]:
+        temp_sum = 0.0
+        for j in range(i, size)[::-1]:
+            temp_sum += L2[i, j] * a[j]
+        a[i] = (x[i] - temp_sum) / L2[i, i]
+
+    return a
-- 
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