/*
* Encog(tm) Core v3.4 - Java Version
* http://www.heatonresearch.com/encog/
* https://github.com/encog/encog-java-core
* Copyright 2008-2016 Heaton Research, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* For more information on Heaton Research copyrights, licenses
* and trademarks visit:
* http://www.heatonresearch.com/copyright
*/
package org.encog.neural.rbf.training;
import org.encog.mathutil.rbf.RadialBasisFunction;
/**
* Perform a SVD decomp on a matrix.
*
* Contributed to Encog By M.Fletcher and M.Dean University of Cambridge, Dept.
* of Physics, UK
*/
public class SVD {
public static double svdfit(double[][] x, double[][] y, double[][] a, RadialBasisFunction[] funcs)
{
int i, j, k;
double wmax, tmp, thresh, sum, TOL = 1e-13;
//Allocated memory for svd matrices
double[][] u = new double[x.length][funcs.length];
double[][] v = new double[funcs.length][funcs.length];
double[] w = new double[funcs.length];
//Fill input matrix with values based on fitting functions and input coordinates
for (i = 0; i < x.length; i++)
{
for (j = 0; j < funcs.length; j++)
u[i][j] = funcs[j].calculate(x[i]);
}
//Perform decomposition
svdcmp(u, w, v);
//Check for w values that are close to zero and replace them with zeros such that they are ignored in backsub
wmax = 0;
for (j = 0; j < funcs.length; j++)
if (w[j] > wmax) wmax = w[j];
thresh = TOL * wmax;
for (j = 0; j < funcs.length; j++)
if (w[j] < thresh) w[j] = 0;
//Perform back substitution to get result
svdbksb(u, w, v, y, a);
//Calculate chi squared for the fit
double chisq = 0;
for (k = 0; k < y[0].length; k++)
{
for (i = 0; i < y.length; i++)
{
sum = 0.0;
for (j = 0; j < funcs.length; j++) sum += a[j][k] * funcs[j].calculate(x[i]);
tmp = (y[i][k] - sum);
chisq += tmp * tmp;
}
}
return Math.sqrt(chisq / (y.length * y[0].length));
}
public static void svdbksb(double[][] u, double[] w, double[][] v, double[][] b, double[][] x)
{
int jj, j, i, m, n, k;
double s;
m = u.length;
n = u[0].length;
double[] temp = new double[n];
for (k = 0; k < b[0].length; k++)
{
for (j = 0; j < n; j++)
{
s = 0;
if (w[j] != 0)
{
for (i = 0; i < m; i++)
s += u[i][j] * b[i][k];
s /= w[j];
}
temp[j] = s;
}
for (j = 0; j < n; j++)
{
s = 0;
for (jj = 0; jj < n; jj++)
s += v[j][jj] * temp[jj];
x[j][k] = s;
}
}
}
///
/// Given a matrix a[1..m][1..n], this routine computes its singular value
/// decomposition, A = U.W.VT. The matrix U replaces a on output. The diagonal
/// matrix of singular values W is output as a vector w[1..n]. The matrix V (not
/// the transpose VT) is output as v[1..n][1..n].
///
///
///
///
public static void svdcmp(double[][] a, double[] w, double[][] v)
{
boolean flag;
int i, its, j, jj, k, l = 0, nm = 0;
double anorm, c, f, g, h, s, scale, x, y, z;
int m = a.length;
int n = a[0].length;
double[] rv1 = new double[n];
g = scale = anorm = 0.0;
for (i = 0; i < n; i++)
{
l = i + 2;
rv1[i] = scale * g;
g = s = scale = 0.0;
if (i < m)
{
for (k = i; k < m; k++) scale += Math.abs(a[k][i]);
if (scale != 0.0)
{
for (k = i; k < m; k++)
{
a[k][i] /= scale;
s += a[k][i] * a[k][i];
}
f = a[i][i];
g = -SIGN(Math.sqrt(s), f);
h = f * g - s;
a[i][i] = f - g;
for (j = l - 1; j < n; j++)
{
for (s = 0.0, k = i; k < m; k++) s += a[k][i] * a[k][j];
f = s / h;
for (k = i; k < m; k++) a[k][j] += f * a[k][i];
}
for (k = i; k < m; k++) a[k][i] *= scale;
}
}
w[i] = scale * g;
g = s = scale = 0.0;
if (i + 1 <= m && i + 1 != n)
{
for (k = l - 1; k < n; k++) scale += Math.abs(a[i][k]);
if (scale != 0.0)
{
for (k = l - 1; k < n; k++)
{
a[i][k] /= scale;
s += a[i][k] * a[i][k];
}
f = a[i][l - 1];
g = -SIGN(Math.sqrt(s), f);
h = f * g - s;
a[i][l - 1] = f - g;
for (k = l - 1; k < n; k++) rv1[k] = a[i][k] / h;
for (j = l - 1; j < m; j++)
{
for (s = 0.0, k = l - 1; k < n; k++) s += a[j][k] * a[i][k];
for (k = l - 1; k < n; k++) a[j][k] += s * rv1[k];
}
for (k = l - 1; k < n; k++) a[i][k] *= scale;
}
}
anorm = MAX(anorm, (Math.abs(w[i]) + Math.abs(rv1[i])));
}
for (i = n - 1; i >= 0; i--)
{
if (i < n - 1)
{
if (g != 0.0)
{
for (j = l; j < n; j++)
v[j][i] = (a[i][j] / a[i][l]) / g;
for (j = l; j < n; j++)
{
for (s = 0.0, k = l; k < n; k++) s += a[i][k] * v[k][j];
for (k = l; k < n; k++) v[k][j] += s * v[k][i];
}
}
for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
}
v[i][i] = 1.0;
g = rv1[i];
l = i;
}
for (i = MIN(m, n) - 1; i >= 0; i--)
{
l = i + 1;
g = w[i];
for (j = l; j < n; j++) a[i][j] = 0.0;
if (g != 0.0)
{
g = 1.0 / g;
for (j = l; j < n; j++)
{
for (s = 0.0, k = l; k < m; k++) s += a[k][i] * a[k][j];
f = (s / a[i][i]) * g;
for (k = i; k < m; k++) a[k][j] += f * a[k][i];
}
for (j = i; j < m; j++) a[j][i] *= g;
}
else for (j = i; j < m; j++) a[j][i] = 0.0;
++a[i][i];
}
for (k = n - 1; k >= 0; k--)
{
for (its = 0; its < 30; its++)
{
flag = true;
for (l = k; l >= 0; l--)
{
nm = l - 1;
if (Math.abs(rv1[l]) + anorm == anorm)
{
flag = false;
break;
}
if (Math.abs(w[nm]) + anorm == anorm) break;
}
if (flag)
{
c = 0.0;
s = 1.0;
for (i = l; i < k + 1; i++)
{
f = s * rv1[i];
rv1[i] = c * rv1[i];
if (Math.abs(f) + anorm == anorm) break;
g = w[i];
h = pythag(f, g);
w[i] = h;
h = 1.0 / h;
c = g * h;
s = -f * h;
for (j = 0; j < m; j++)
{
y = a[j][nm];
z = a[j][i];
a[j][nm] = y * c + z * s;
a[j][i] = z * c - y * s;
}
}
}
z = w[k];
if (l == k)
{
if (z < 0.0)
{
w[k] = -z;
for (j = 0; j < n; j++) v[j][k] = -v[j][k];
}
break;
}
if (its == 29)
{
// Debug.Print("no convergence in 30 svdcmp iterations");
}
x = w[l];
nm = k - 1;
y = w[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = pythag(f, 1.0);
f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x;
c = s = 1.0;
for (j = l; j <= nm; j++)
{
i = j + 1;
g = rv1[i];
y = w[i];
h = s * g;
g = c * g;
z = pythag(f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y *= c;
for (jj = 0; jj < n; jj++)
{
x = v[jj][j];
z = v[jj][i];
v[jj][j] = x * c + z * s;
v[jj][i] = z * c - x * s;
}
z = pythag(f, h);
w[j] = z;
if (z != 0)
{
z = 1.0 / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
for (jj = 0; jj < m; jj++)
{
y = a[jj][j];
z = a[jj][i];
a[jj][j] = y * c + z * s;
a[jj][i] = z * c - y * s;
}
}
rv1[l] = 0.0;
rv1[k] = f;
w[k] = x;
}
}
}
public static int MIN(int m, int n)
{
return m < n ? m : n;
}
public static double MAX(double a, double b)
{
return (a > b) ? a : b;
}
public static double SIGN(double a, double b)
{
return ((b) >= 0.0 ? Math.abs(a) : -Math.abs(a));
}
public static double pythag(double a, double b)
{
double absa, absb;
absa = Math.abs(a);
absb = Math.abs(b);
if (absa > absb) return absa * Math.sqrt(1.0 + (absb / absa) * (absb / absa));
else return (absb == 0.0 ? 0.0 : absb * Math.sqrt(1.0 + (absa / absb) * (absa / absb)));
}
}
Ads help maintain this website.