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Diffstat (limited to 'ml_exp/math.py')
-rw-r--r-- | ml_exp/math.py | 92 |
1 files changed, 92 insertions, 0 deletions
diff --git a/ml_exp/math.py b/ml_exp/math.py new file mode 100644 index 000000000..781985118 --- /dev/null +++ b/ml_exp/math.py @@ -0,0 +1,92 @@ +"""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 +import math + + +def frob_norm(array): + """ + Calculates the frobenius norm of a given array or matrix. + array: array of data. + """ + + arr_sh_len = len(array.shape) + arr_range = range(len(array)) + fn = 0.0 + + # If it is a 'vector'. + if arr_sh_len == 1: + for i in arr_range: + fn += array[i]*array[i] + + return math.sqrt(fn) + + # If it is a matrix. + elif arr_sh_len == 2: + for i in arr_range: + for j in arr_range: + fn += array[i, j]*array[i, j] + + return math.sqrt(fn) + else: + print('Error. Array size greater than 2 ({}).'.format(arr_sh_len)) + + +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 = np.linalg.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 |