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Remove Jama package from main package, add Jama dependency

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This commit is contained in:
Fabian Becker 2015-12-10 21:48:14 +01:00
parent 0320b46a11
commit 49e1d53bd1
19 changed files with 14 additions and 3709 deletions
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7
build.gradle
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@ -26,7 +26,8 @@ repositories {
mavenCentral() mavenCentral()
} }
dependencies { dependencies {
compile group: 'javax.help', name: 'javahelp', version:'2.0.05' compile group: 'javax.help', name: 'javahelp', version: '2.0.05'
compile group: 'org.yaml', name: 'snakeyaml', version:'1.16' compile group: 'org.yaml', name: 'snakeyaml', version: '1.16'
testCompile group: 'junit', name: 'junit', version:'4.11' compile group: 'gov.nist.math', name: 'jama', version: '1.0.3'
testCompile group: 'junit', name: 'junit', version: '4.11'
} }

2
src/main/java/eva2/optimization/operator/mutation/CMAParamSet.java
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@ -5,7 +5,7 @@ import eva2.optimization.population.InterfacePopulationChangedEventListener;
import eva2.optimization.population.Population; import eva2.optimization.population.Population;
import eva2.optimization.strategies.EvolutionStrategies; import eva2.optimization.strategies.EvolutionStrategies;
import eva2.tools.EVAERROR; import eva2.tools.EVAERROR;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import java.io.Serializable; import java.io.Serializable;

4
src/main/java/eva2/optimization/operator/mutation/MutateESCovarianceMatrixAdaption.java
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@ -4,8 +4,8 @@ import eva2.optimization.individuals.AbstractEAIndividual;
import eva2.optimization.individuals.InterfaceESIndividual; import eva2.optimization.individuals.InterfaceESIndividual;
import eva2.optimization.population.Population; import eva2.optimization.population.Population;
import eva2.problems.InterfaceOptimizationProblem; import eva2.problems.InterfaceOptimizationProblem;
import eva2.tools.math.Jama.EigenvalueDecomposition; import Jama.EigenvalueDecomposition;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import eva2.tools.math.RNG; import eva2.tools.math.RNG;
import eva2.util.annotation.Description; import eva2.util.annotation.Description;

2
src/main/java/eva2/optimization/operator/mutation/MutateESCovarianceMatrixAdaptionPlus.java
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@ -4,7 +4,7 @@ import eva2.optimization.individuals.AbstractEAIndividual;
import eva2.optimization.individuals.InterfaceESIndividual; import eva2.optimization.individuals.InterfaceESIndividual;
import eva2.optimization.population.Population; import eva2.optimization.population.Population;
import eva2.problems.InterfaceOptimizationProblem; import eva2.problems.InterfaceOptimizationProblem;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.util.annotation.Description; import eva2.util.annotation.Description;
@Description("This is the CMA mutation according to Igel,Hansen,Roth 2007") @Description("This is the CMA mutation according to Igel,Hansen,Roth 2007")

2
src/main/java/eva2/optimization/operator/mutation/MutateESRankMuCMA.java
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@ -11,7 +11,7 @@ import eva2.optimization.strategies.EvolutionStrategies;
import eva2.problems.InterfaceOptimizationProblem; import eva2.problems.InterfaceOptimizationProblem;
import eva2.tools.EVAERROR; import eva2.tools.EVAERROR;
import eva2.tools.Pair; import eva2.tools.Pair;
import eva2.tools.math.Jama.EigenvalueDecomposition; import Jama.EigenvalueDecomposition;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import eva2.tools.math.RNG; import eva2.tools.math.RNG;
import eva2.util.annotation.Description; import eva2.util.annotation.Description;

2
src/main/java/eva2/optimization/population/Population.java
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@ -10,7 +10,7 @@ import eva2.optimization.operator.selection.probability.AbstractSelProb;
import eva2.tools.EVAERROR; import eva2.tools.EVAERROR;
import eva2.tools.Pair; import eva2.tools.Pair;
import eva2.tools.Serializer; import eva2.tools.Serializer;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import eva2.tools.math.RNG; import eva2.tools.math.RNG;
import eva2.tools.math.StatisticUtils; import eva2.tools.math.StatisticUtils;

2
src/main/java/eva2/optimization/strategies/ParticleSwarmOptimization.java
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@ -20,7 +20,7 @@ import eva2.problems.InterfaceAdditionalPopulationInformer;
import eva2.problems.InterfaceProblemDouble; import eva2.problems.InterfaceProblemDouble;
import eva2.tools.chart2d.DPoint; import eva2.tools.chart2d.DPoint;
import eva2.tools.chart2d.DPointSet; import eva2.tools.chart2d.DPointSet;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import eva2.tools.math.RNG; import eva2.tools.math.RNG;
import eva2.util.annotation.Description; import eva2.util.annotation.Description;

2
src/main/java/eva2/problems/AbstractProblemDouble.java
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@ -19,7 +19,7 @@ import eva2.optimization.strategies.InterfaceOptimizer;
import eva2.tools.Pair; import eva2.tools.Pair;
import eva2.tools.ToolBox; import eva2.tools.ToolBox;
import eva2.tools.diagram.ColorBarCalculator; import eva2.tools.diagram.ColorBarCalculator;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.Mathematics; import eva2.tools.math.Mathematics;
import eva2.tools.math.RNG; import eva2.tools.math.RNG;
import eva2.util.annotation.Parameter; import eva2.util.annotation.Parameter;

187
src/main/java/eva2/tools/math/Jama/CholeskyDecomposition.java
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@ -1,187 +0,0 @@
package eva2.tools.math.Jama;
/**
* Cholesky Decomposition.
* <p>
* For a symmetric, positive definite matrix A, the Cholesky decomposition
* is an lower triangular matrix L so that A = L*L'.
* <p>
* If the matrix is not symmetric or positive definite, the constructor
* returns a partial decomposition and sets an internal flag that may
* be queried by the isSPD() method.
*/
public class CholeskyDecomposition implements java.io.Serializable {
/**
* Array for internal storage of decomposition.
*
* @serial internal array storage.
*/
private double[][] L;
/**
* Row and column dimension (square matrix).
*
* @serial matrix dimension.
*/
private int n;
/**
* Symmetric and positive definite flag.
*
* @serial is symmetric and positive definite flag.
*/
private boolean isspd;
/**
* Cholesky algorithm for symmetric and positive definite matrix.
*
* @param arg A square, symmetric matrix.
* @return Structure to access L and isspd flag.
*/
public CholeskyDecomposition(Matrix matrix) {
// Initialize.
double[][] A = matrix.getArray();
n = matrix.getRowDimension();
L = new double[n][n];
isspd = (matrix.getColumnDimension() == n);
// Main loop.
for (int j = 0; j < n; j++) {
double[] Lrowj = L[j];
double d = 0.0;
for (int k = 0; k < j; k++) {
double[] Lrowk = L[k];
double s = 0.0;
for (int i = 0; i < k; i++) {
s += Lrowk[i] * Lrowj[i];
}
Lrowj[k] = s = (A[j][k] - s) / L[k][k];
d += s * s;
isspd &= (A[k][j] == A[j][k]);
}
d = A[j][j] - d;
isspd &= (d > 0.0);
L[j][j] = Math.sqrt(Math.max(d, 0.0));
for (int k = j + 1; k < n; k++) {
L[j][k] = 0.0;
}
}
}
// \** Right Triangular Cholesky Decomposition.
// <P>
// For a symmetric, positive definite matrix A, the Right Cholesky
// decomposition is an upper triangular matrix R so that A = R'*R.
// This constructor computes R with the Fortran inspired column oriented
// algorithm used in LINPACK and MATLAB. In Java, we suspect a row oriented,
// lower triangular decomposition is faster. We have temporarily included
// this constructor here until timing experiments confirm this suspicion.
// *\
private transient double[][] R;
public CholeskyDecomposition(Matrix Arg, int rightflag) {
// Initialize.
double[][] A = Arg.getArray();
n = Arg.getColumnDimension();
R = new double[n][n];
isspd = (Arg.getColumnDimension() == n);
// Main loop.
for (int j = 0; j < n; j++) {
double d = 0.0;
for (int k = 0; k < j; k++) {
double s = A[k][j];
for (int i = 0; i < k; i++) {
s -= R[i][k] * R[i][j];
}
R[k][j] = s /= R[k][k];
d += s * s;
isspd &= (A[k][j] == A[j][k]);
}
d = A[j][j] - d;
isspd &= (d > 0.0);
R[j][j] = Math.sqrt(Math.max(d, 0.0));
for (int k = j + 1; k < n; k++) {
R[k][j] = 0.0;
}
}
}
public Matrix getR() {
return new Matrix(R, n, n);
}
/**
* Is the matrix symmetric and positive definite?
*
* @return true if A is symmetric and positive definite.
*/
public boolean isSPD() {
return isspd;
}
/**
* Return triangular factor.
*
* @return L
*/
public Matrix getL() {
return new Matrix(L, n, n);
}
/**
* Solve A*X = B
*
* @param B A Matrix with as many rows as A and any number of columns.
* @return X so that L*L'*X = B
* @throws IllegalArgumentException Matrix row dimensions must agree.
* @throws RuntimeException Matrix is not symmetric positive definite.
*/
public Matrix solve(Matrix B) {
if (B.getRowDimension() != n) {
throw new IllegalArgumentException("Matrix row dimensions must agree.");
}
if (!isspd) {
throw new RuntimeException("Matrix is not symmetric positive definite.");
}
// Copy right hand side.
double[][] X = B.getArrayCopy();
int nx = B.getColumnDimension();
// Solve L*Y = B;
for (int k = 0; k < n; k++) {
for (int i = k + 1; i < n; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j] * L[i][k];
}
}
for (int j = 0; j < nx; j++) {
X[k][j] /= L[k][k];
}
}
// Solve L'*X = Y;
for (int k = n - 1; k >= 0; k--) {
for (int j = 0; j < nx; j++) {
X[k][j] /= L[k][k];
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j] * L[k][i];
}
}
}
return new Matrix(X, n, nx);
}
}

956
src/main/java/eva2/tools/math/Jama/EigenvalueDecomposition.java
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@ -1,956 +0,0 @@
package eva2.tools.math.Jama;
import eva2.tools.math.Jama.util.Maths;
/**
* Eigenvalues and eigenvectors of a real matrix.
* <p>
* If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
* diagonal and the eigenvector matrix V is orthogonal.
* I.e. A = V.times(D.times(V.transpose())) and
* V.times(V.transpose()) equals the identiCty matrix.
* <p>
* If A is not symmetric, then the eigenvalue matrix D is block diagonal
* with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
* lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
* columns of V represent the eigenvectors in the sense that A*V = V*D,
* i.e. A.times(V) equals V.times(D). The matrix V may be badly
* conditioned, or even singular, so the validity of the equation
* A = V*D*inverse(V) depends upon V.cond().
*/
public class EigenvalueDecomposition implements java.io.Serializable {
/**
* Row and column dimension (square matrix).
*
* @serial matrix dimension.
*/
private int n;
/**
* Symmetry flag.
*
* @serial internal symmetry flag.
*/
private boolean issymmetric;
/**
* Arrays for internal storage of eigenvalues.
*
* @serial internal storage of eigenvalues.
*/
private double[] d, e;
/**
* Array for internal storage of eigenvectors.
*
* @serial internal storage of eigenvectors.
*/
private double[][] V;
/**
* Array for internal storage of nonsymmetric Hessenberg form.
*
* @serial internal storage of nonsymmetric Hessenberg form.
*/
private double[][] H;
/**
* Working storage for nonsymmetric algorithm.
*
* @serial working storage for nonsymmetric algorithm.
*/
private double[] ort;
// Symmetric Householder reduction to tridiagonal form.
private void tred2() {
// This is derived from the Algol procedures tred2 by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
System.arraycopy(V[n - 1], 0, d, 0, n);
// Householder reduction to tridiagonal form.
for (int i = n - 1; i > 0; i--) {
// Scale to avoid under/overflow.
double scale = 0.0;
double h = 0.0;
for (int k = 0; k < i; k++) {
scale += Math.abs(d[k]);
}
if (scale == 0.0) {
e[i] = d[i - 1];
for (int j = 0; j < i; j++) {
d[j] = V[i - 1][j];
V[i][j] = 0.0;
V[j][i] = 0.0;
}
} else {
// Generate Householder vector.
for (int k = 0; k < i; k++) {
d[k] /= scale;
h += d[k] * d[k];
}
double f = d[i - 1];
double g = Math.sqrt(h);
if (f > 0) {
g = -g;
}
e[i] = scale * g;
h -= f * g;
d[i - 1] = f - g;
for (int j = 0; j < i; j++) {
e[j] = 0.0;
}
// Apply similarity transformation to remaining columns.
for (int j = 0; j < i; j++) {
f = d[j];
V[j][i] = f;
g = e[j] + V[j][j] * f;
for (int k = j + 1; k <= i - 1; k++) {
g += V[k][j] * d[k];
e[k] += V[k][j] * f;
}
e[j] = g;
}
f = 0.0;
for (int j = 0; j < i; j++) {
e[j] /= h;
f += e[j] * d[j];
}
double hh = f / (h + h);
for (int j = 0; j < i; j++) {
e[j] -= hh * d[j];
}
for (int j = 0; j < i; j++) {
f = d[j];
g = e[j];
for (int k = j; k <= i - 1; k++) {
V[k][j] -= (f * e[k] + g * d[k]);
}
d[j] = V[i - 1][j];
V[i][j] = 0.0;
}
}
d[i] = h;
}
// Accumulate transformations.
for (int i = 0; i < n - 1; i++) {
V[n - 1][i] = V[i][i];
V[i][i] = 1.0;
double h = d[i + 1];
if (h != 0.0) {
for (int k = 0; k <= i; k++) {
d[k] = V[k][i + 1] / h;
}
for (int j = 0; j <= i; j++) {
double g = 0.0;
for (int k = 0; k <= i; k++) {
g += V[k][i + 1] * V[k][j];
}
for (int k = 0; k <= i; k++) {
V[k][j] -= g * d[k];
}
}
}
for (int k = 0; k <= i; k++) {
V[k][i + 1] = 0.0;
}
}
for (int j = 0; j < n; j++) {
d[j] = V[n - 1][j];
V[n - 1][j] = 0.0;
}
V[n - 1][n - 1] = 1.0;
e[0] = 0.0;
}
// Symmetric tridiagonal QL algorithm.
private void tql2() {
// This is derived from the Algol procedures tql2, by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
System.arraycopy(e, 1, e, 0, n - 1);
e[n - 1] = 0.0;
double f = 0.0;
double tst1 = 0.0;
double eps = Math.pow(2.0, -52.0);
for (int l = 0; l < n; l++) {
// Find small subdiagonal element
tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
int m = l;
while (m < n) {
if (Math.abs(e[m]) <= eps * tst1) {
break;
}
m++;
}
// If m == l, d[l] is an eigenvalue,
// otherwise, iterate.
if (m > l) {
int iter = 0;
do {
iter += 1; // (Could check iteration count here.)
// Compute implicit shift
double g = d[l];
double p = (d[l + 1] - g) / (2.0 * e[l]);
double r = Maths.hypot(p, 1.0);
if (p < 0) {
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
double dl1 = d[l + 1];
double h = g - d[l];
for (int i = l + 2; i < n; i++) {
d[i] -= h;
}
f += h;
// Implicit QL transformation.
p = d[m];
double c = 1.0;
double c2 = c;
double c3 = c;
double el1 = e[l + 1];
double s = 0.0;
double s2 = 0.0;
for (int i = m - 1; i >= l; i--) {
c3 = c2;
c2 = c;
s2 = s;
g = c * e[i];
h = c * p;
r = Maths.hypot(p, e[i]);
e[i + 1] = s * r;
s = e[i] / r;
c = p / r;
p = c * d[i] - s * g;
d[i + 1] = h + s * (c * g + s * d[i]);
// Accumulate transformation.
for (int k = 0; k < n; k++) {
h = V[k][i + 1];
V[k][i + 1] = s * V[k][i] + c * h;
V[k][i] = c * V[k][i] - s * h;
}
}
p = -s * s2 * c3 * el1 * e[l] / dl1;
e[l] = s * p;
d[l] = c * p;
// Check for convergence.
} while (Math.abs(e[l]) > eps * tst1);
}
d[l] += f;
e[l] = 0.0;
}
// Sort eigenvalues and corresponding vectors.
for (int i = 0; i < n - 1; i++) {
int k = i;
double p = d[i];
for (int j = i + 1; j < n; j++) {
if (d[j] < p) {
k = j;
p = d[j];
}
}
if (k != i) {
d[k] = d[i];
d[i] = p;
for (int j = 0; j < n; j++) {
p = V[j][i];
V[j][i] = V[j][k];
V[j][k] = p;
}
}
}
}
// Nonsymmetric reduction to Hessenberg form.
private void orthes() {
// This is derived from the Algol procedures orthes and ortran,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutines in EISPACK.
int low = 0;
int high = n - 1;
for (int m = low + 1; m <= high - 1; m++) {
// Scale column.
double scale = 0.0;
for (int i = m; i <= high; i++) {
scale += Math.abs(H[i][m - 1]);
}
if (scale != 0.0) {
// Compute Householder transformation.
double h = 0.0;
for (int i = high; i >= m; i--) {
ort[i] = H[i][m - 1] / scale;
h += ort[i] * ort[i];
}
double g = Math.sqrt(h);
if (ort[m] > 0) {
g = -g;
}
h -= ort[m] * g;
ort[m] -= g;
// Apply Householder similarity transformation
// H = (I-u*u'/h)*H*(I-u*u')/h)
for (int j = m; j < n; j++) {
double f = 0.0;
for (int i = high; i >= m; i--) {
f += ort[i] * H[i][j];
}
f /= h;
for (int i = m; i <= high; i++) {
H[i][j] -= f * ort[i];
}
}
for (int i = 0; i <= high; i++) {
double f = 0.0;
for (int j = high; j >= m; j--) {
f += ort[j] * H[i][j];
}
f /= h;
for (int j = m; j <= high; j++) {
H[i][j] -= f * ort[j];
}
}
ort[m] = scale * ort[m];
H[m][m - 1] = scale * g;
}
}
// Accumulate transformations (Algol's ortran).
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
V[i][j] = (i == j ? 1.0 : 0.0);
}
}
for (int m = high - 1; m >= low + 1; m--) {
if (H[m][m - 1] != 0.0) {
for (int i = m + 1; i <= high; i++) {
ort[i] = H[i][m - 1];
}
for (int j = m; j <= high; j++) {
double g = 0.0;
for (int i = m; i <= high; i++) {
g += ort[i] * V[i][j];
}
// Double division avoids possible underflow
g = (g / ort[m]) / H[m][m - 1];
for (int i = m; i <= high; i++) {
V[i][j] += g * ort[i];
}
}
}
}
}
// Complex scalar division.
private transient double cdivr, cdivi;
private void cdiv(double xr, double xi, double yr, double yi) {
double r, d;
if (Math.abs(yr) > Math.abs(yi)) {
r = yi / yr;
d = yr + r * yi;
cdivr = (xr + r * xi) / d;
cdivi = (xi - r * xr) / d;
} else {
r = yr / yi;
d = yi + r * yr;
cdivr = (r * xr + xi) / d;
cdivi = (r * xi - xr) / d;
}
}
// Nonsymmetric reduction from Hessenberg to real Schur form.
private void hqr2() {
// This is derived from the Algol procedure hqr2,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
// Initialize
int nn = this.n;
int n = nn - 1;
int low = 0;
int high = nn - 1;
double eps = Math.pow(2.0, -52.0);
double exshift = 0.0;
double p = 0, q = 0, r = 0, s = 0, z = 0, t, w, x, y;
// Store roots isolated by balanc and compute matrix norm
double norm = 0.0;
for (int i = 0; i < nn; i++) {
if (i < low | i > high) {
d[i] = H[i][i];
e[i] = 0.0;
}
for (int j = Math.max(i - 1, 0); j < nn; j++) {
norm += Math.abs(H[i][j]);
}
}
// Outer loop over eigenvalue index
int iter = 0;
while (n >= low) {
// Look for single small sub-diagonal element
int l = n;
while (l > low) {
s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
if (s == 0.0) {
s = norm;
}
if (Math.abs(H[l][l - 1]) < eps * s) {
break;
}
l--;
}
// Check for convergence
// One root found
if (l == n) {
H[n][n] += exshift;
d[n] = H[n][n];
e[n] = 0.0;
n--;
iter = 0;
// Two roots found
} else if (l == n - 1) {
w = H[n][n - 1] * H[n - 1][n];
p = (H[n - 1][n - 1] - H[n][n]) / 2.0;
q = p * p + w;
z = Math.sqrt(Math.abs(q));
H[n][n] += exshift;
H[n - 1][n - 1] += exshift;
x = H[n][n];
// Real pair
if (q >= 0) {
if (p >= 0) {
z = p + z;
} else {
z = p - z;
}
d[n - 1] = x + z;
d[n] = d[n - 1];
if (z != 0.0) {
d[n] = x - w / z;
}
e[n - 1] = 0.0;
e[n] = 0.0;
x = H[n][n - 1];
s = Math.abs(x) + Math.abs(z);
p = x / s;
q = z / s;
r = Math.sqrt(p * p + q * q);
p /= r;
q /= r;
// Row modification
for (int j = n - 1; j < nn; j++) {
z = H[n - 1][j];
H[n - 1][j] = q * z + p * H[n][j];
H[n][j] = q * H[n][j] - p * z;
}
// Column modification
for (int i = 0; i <= n; i++) {
z = H[i][n - 1];
H[i][n - 1] = q * z + p * H[i][n];
H[i][n] = q * H[i][n] - p * z;
}
// Accumulate transformations
for (int i = low; i <= high; i++) {
z = V[i][n - 1];
V[i][n - 1] = q * z + p * V[i][n];
V[i][n] = q * V[i][n] - p * z;
}
// Complex pair
} else {
d[n - 1] = x + p;
d[n] = x + p;
e[n - 1] = z;
e[n] = -z;
}
n -= 2;
iter = 0;
// No convergence yet
} else {
// Form shift
x = H[n][n];
y = 0.0;
w = 0.0;
if (l < n) {
y = H[n - 1][n - 1];
w = H[n][n - 1] * H[n - 1][n];
}
// Wilkinson's original ad hoc shift
if (iter == 10) {
exshift += x;
for (int i = low; i <= n; i++) {
H[i][i] -= x;
}
s = Math.abs(H[n][n - 1]) + Math.abs(H[n - 1][n - 2]);
x = y = 0.75 * s;
w = -0.4375 * s * s;
}
// MATLAB's new ad hoc shift
if (iter == 30) {
s = (y - x) / 2.0;
s = s * s + w;
if (s > 0) {
s = Math.sqrt(s);
if (y < x) {
s = -s;
}
s = x - w / ((y - x) / 2.0 + s);
for (int i = low; i <= n; i++) {
H[i][i] -= s;
}
exshift += s;
x = y = w = 0.964;
}
}
iter += 1; // (Could check iteration count here.)
// Look for two consecutive small sub-diagonal elements
int m = n - 2;
while (m >= l) {
z = H[m][m];
r = x - z;
s = y - z;
p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
q = H[m + 1][m + 1] - z - r - s;
r = H[m + 2][m + 1];
s = Math.abs(p) + Math.abs(q) + Math.abs(r);
p /= s;
q /= s;
r /= s;
if (m == l) {
break;
}
if (Math.abs(H[m][m - 1]) * (Math.abs(q) + Math.abs(r)) <
eps * (Math.abs(p) * (Math.abs(H[m - 1][m - 1]) + Math.abs(z) +
Math.abs(H[m + 1][m + 1])))) {
break;
}
m--;
}
for (int i = m + 2; i <= n; i++) {
H[i][i - 2] = 0.0;
if (i > m + 2) {
H[i][i - 3] = 0.0;
}
}
// Double QR step involving rows l:n and columns m:n
for (int k = m; k <= n - 1; k++) {
boolean notlast = (k != n - 1);
if (k != m) {
p = H[k][k - 1];
q = H[k + 1][k - 1];
r = (notlast ? H[k + 2][k - 1] : 0.0);
x = Math.abs(p) + Math.abs(q) + Math.abs(r);
if (x != 0.0) {
p /= x;
q /= x;
r /= x;
}
}
if (x == 0.0) {
break;
}
s = Math.sqrt(p * p + q * q + r * r);
if (p < 0) {
s = -s;
}
if (s != 0) {
if (k != m) {
H[k][k - 1] = -s * x;
} else if (l != m) {
H[k][k - 1] = -H[k][k - 1];
}
p += s;
x = p / s;
y = q / s;
z = r / s;
q /= p;
r /= p;
// Row modification
for (int j = k; j < nn; j++) {
p = H[k][j] + q * H[k + 1][j];
if (notlast) {
p += r * H[k + 2][j];
H[k + 2][j] -= p * z;
}
H[k][j] -= p * x;
H[k + 1][j] -= p * y;
}
// Column modification
for (int i = 0; i <= Math.min(n, k + 3); i++) {
p = x * H[i][k] + y * H[i][k + 1];
if (notlast) {
p += z * H[i][k + 2];
H[i][k + 2] -= p * r;
}
H[i][k] -= p;
H[i][k + 1] -= p * q;
}
// Accumulate transformations
for (int i = low; i <= high; i++) {
p = x * V[i][k] + y * V[i][k + 1];
if (notlast) {
p += z * V[i][k + 2];
V[i][k + 2] -= p * r;
}
V[i][k] -= p;
V[i][k + 1] -= p * q;
}
} // (s != 0)
} // k loop
} // check convergence
} // while (n >= low)
// Backsubstitute to find vectors of upper triangular form
if (norm == 0.0) {
return;
}
for (n = nn - 1; n >= 0; n--) {
p = d[n];
q = e[n];
// Real vector
if (q == 0) {
int l = n;
H[n][n] = 1.0;
for (int i = n - 1; i >= 0; i--) {
w = H[i][i] - p;
r = 0.0;
for (int j = l; j <= n; j++) {
r += H[i][j] * H[j][n];
}
if (e[i] < 0.0) {
z = w;
s = r;
} else {
l = i;
if (e[i] == 0.0) {
if (w != 0.0) {
H[i][n] = -r / w;
} else {
H[i][n] = -r / (eps * norm);
}
// Solve real equations
} else {
x = H[i][i + 1];
y = H[i + 1][i];
q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
t = (x * s - z * r) / q;
H[i][n] = t;
if (Math.abs(x) > Math.abs(z)) {
H[i + 1][n] = (-r - w * t) / x;
} else {
H[i + 1][n] = (-s - y * t) / z;
}
}
// Overflow control
t = Math.abs(H[i][n]);
if ((eps * t) * t > 1) {
for (int j = i; j <= n; j++) {
H[j][n] /= t;
}
}
}
}
// Complex vector
} else if (q < 0) {
int l = n - 1;
// Last vector component imaginary so matrix is triangular
if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
H[n - 1][n - 1] = q / H[n][n - 1];
H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
} else {
cdiv(0.0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
H[n - 1][n - 1] = cdivr;
H[n - 1][n] = cdivi;
}
H[n][n - 1] = 0.0;
H[n][n] = 1.0;
for (int i = n - 2; i >= 0; i--) {
double ra, sa, vr, vi;
ra = 0.0;
sa = 0.0;
for (int j = l; j <= n; j++) {
ra += H[i][j] * H[j][n - 1];
sa += H[i][j] * H[j][n];
}
w = H[i][i] - p;
if (e[i] < 0.0) {
z = w;
r = ra;
s = sa;
} else {
l = i;
if (e[i] == 0) {
cdiv(-ra, -sa, w, q);
H[i][n - 1] = cdivr;
H[i][n] = cdivi;
} else {
// Solve complex equations
x = H[i][i + 1];
y = H[i + 1][i];
vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
vi = (d[i] - p) * 2.0 * q;
if (vr == 0.0 & vi == 0.0) {
vr = eps * norm * (Math.abs(w) + Math.abs(q) +
Math.abs(x) + Math.abs(y) + Math.abs(z));
}
cdiv(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi);
H[i][n - 1] = cdivr;
H[i][n] = cdivi;
if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
H[i + 1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
H[i + 1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
} else {
cdiv(-r - y * H[i][n - 1], -s - y * H[i][n], z, q);
H[i + 1][n - 1] = cdivr;
H[i + 1][n] = cdivi;
}
}
// Overflow control
t = Math.max(Math.abs(H[i][n - 1]), Math.abs(H[i][n]));
if ((eps * t) * t > 1) {
for (int j = i; j <= n; j++) {
H[j][n - 1] /= t;
H[j][n] /= t;
}
}
}
}
}
}
// Vectors of isolated roots
for (int i = 0; i < nn; i++) {
if (i < low | i > high) {
System.arraycopy(H[i], i, V[i], i, nn - i);
}
}
// Back transformation to get eigenvectors of original matrix
for (int j = nn - 1; j >= low; j--) {
for (int i = low; i <= high; i++) {
z = 0.0;
for (int k = low; k <= Math.min(j, high); k++) {
z += V[i][k] * H[k][j];
}
V[i][j] = z;
}
}
}
/**
* Check for symmetry, then construct the eigenvalue decomposition
*
* @param arg A Square matrix
* @return Structure to access D and V.
*/
public EigenvalueDecomposition(Matrix matrix) {
double[][] A = matrix.getArray();
n = matrix.getColumnDimension();
V = new double[n][n];
d = new double[n];
e = new double[n];
issymmetric = true;
for (int j = 0; (j < n) & issymmetric; j++) {
for (int i = 0; (i < n) & issymmetric; i++) {
issymmetric = (A[i][j] == A[j][i]);
}
}
if (issymmetric) {
for (int i = 0; i < n; i++) {
System.arraycopy(A[i], 0, V[i], 0, n);
}
// Tridiagonalize.
tred2();
// Diagonalize.
tql2();
} else {
H = new double[n][n];
ort = new double[n];
for (int j = 0; j < n; j++) {
for (int i = 0; i < n; i++) {
H[i][j] = A[i][j];
}
}
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
}
}
/**
* Return the eigenvector matrix
*
* @return V
*/
public Matrix getV() {
return new Matrix(V, n, n);
}
/**
* Return the real parts of the eigenvalues
*
* @return real(diag(D))
*/
public double[] getRealEigenvalues() {
return d;
}
/**
* Return the imaginary parts of the eigenvalues
*
* @return imag(diag(D))
*/
public double[] getImagEigenvalues() {
return e;
}
/**
* Return the block diagonal eigenvalue matrix
*
* @return D
*/
public Matrix getD() {
Matrix X = new Matrix(n, n);
double[][] D = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
D[i][j] = 0.0;
}
D[i][i] = d[i];
if (e[i] > 0) {
D[i][i + 1] = e[i];
} else if (e[i] < 0) {
D[i][i - 1] = e[i];
}
}
return X;
}
}

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src/main/java/eva2/tools/math/Jama/LUDecomposition.java
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package eva2.tools.math.Jama;
/**
* LU Decomposition.
* <p>
* For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
* unit lower triangular matrix L, an n-by-n upper triangular matrix U,
* and a permutation vector piv of length m so that A(piv,:) = L*U.
* If m < n, then L is m-by-m and U is m-by-n.
* <p>
* The LU decompostion with pivoting always exists, even if the matrix is
* singular, so the constructor will never fail. The primary use of the
* LU decomposition is in the solution of square systems of simultaneous
* linear equations. This will fail if isNonsingular() returns false.
*/
public class LUDecomposition implements java.io.Serializable {
/**
* Array for internal storage of decomposition.
*
* @serial internal array storage.
*/
private double[][] LU;
/**
* Row and column dimensions, and pivot sign.
*
* @serial column dimension.
* @serial row dimension.
* @serial pivot sign.
*/
private int m, n, pivsign;
/**
* Internal storage of pivot vector.
*
* @serial pivot vector.
*/
private int[] piv;
/**
* LU Decomposition
*
* @param A Rectangular matrix
* @return Structure to access L, U and piv.
*/
public LUDecomposition(Matrix A) {
LU = A.getArrayCopy();
m = A.getRowDimension();
n = A.getColumnDimension();
piv = new int[m];
for (int i = 0; i < m; i++) {
piv[i] = i;
}
pivsign = 1;
double[] LUrowi;
double[] LUcolj = new double[m];
// Outer loop.
for (int j = 0; j < n; j++) {
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++) {
LUcolj[i] = LU[i][j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++) {
LUrowi = LU[i];
// Most of the time is spent in the following dot product.
int kmax = Math.min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++) {
s += LUrowi[k] * LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++) {
if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {
p = i;
}
}
if (p != j) {
for (int k = 0; k < n; k++) {
double t = LU[p][k];
LU[p][k] = LU[j][k];
LU[j][k] = t;
}
int k = piv[p];
piv[p] = piv[j];
piv[j] = k;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m & LU[j][j] != 0.0) {
for (int i = j + 1; i < m; i++) {
LU[i][j] /= LU[j][j];
}
}
}
}
/**
* Is the matrix nonsingular?
*
* @return true if U, and hence A, is nonsingular.
*/
public boolean isNonsingular() {
for (int j = 0; j < n; j++) {
if (LU[j][j] == 0) {
return false;
}
}
return true;
}
/**
* Return lower triangular factor
*
* @return L
*/
public Matrix getL() {
Matrix X = new Matrix(m, n);
double[][] L = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i > j) {
L[i][j] = LU[i][j];
} else if (i == j) {
L[i][j] = 1.0;
} else {
L[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return upper triangular factor
*
* @return U
*/
public Matrix getU() {
Matrix X = new Matrix(n, n);
double[][] U = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i <= j) {
U[i][j] = LU[i][j];
} else {
U[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return pivot permutation vector
*
* @return piv
*/
public int[] getPivot() {
int[] p = new int[m];
System.arraycopy(piv, 0, p, 0, m);
return p;
}
/**
* Return pivot permutation vector as a one-dimensional double array
*
* @return (double) piv
*/
public double[] getDoublePivot() {
double[] vals = new double[m];
for (int i = 0; i < m; i++) {
vals[i] = (double) piv[i];
}
return vals;
}
/**
* Determinant
*
* @return det(A)
* @throws IllegalArgumentException Matrix must be square
*/
public double det() {
if (m != n) {
throw new IllegalArgumentException("Matrix must be square.");
}
double d = (double) pivsign;
for (int j = 0; j < n; j++) {
d *= LU[j][j];
}
return d;
}
/**
* Solve A*X = B
*
* @param B A Matrix with as many rows as A and any number of columns.
* @return X so that L*U*X = B(piv,:)
* @throws IllegalArgumentException Matrix row dimensions must agree.
* @throws RuntimeException Matrix is singular.
*/
public Matrix solve(Matrix B) {
if (B.getRowDimension() != m) {
throw new IllegalArgumentException("Matrix row dimensions must agree.");
}
if (!this.isNonsingular()) {
throw new RuntimeException("Matrix is singular.");
}
// Copy right hand side with pivoting
int nx = B.getColumnDimension();
Matrix Xmat = B.getMatrix(piv, 0, nx - 1);
double[][] X = Xmat.getArray();
// Solve L*Y = B(piv,:)
for (int k = 0; k < n; k++) {
for (int i = k + 1; i < n; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j] * LU[i][k];
}
}
}
// Solve U*X = Y;
for (int k = n - 1; k >= 0; k--) {
for (int j = 0; j < nx; j++) {
X[k][j] /= LU[k][k];
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j] * LU[i][k];
}
}
}
return Xmat;
}
}

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src/main/java/eva2/tools/math/Jama/Matrix.java
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src/main/java/eva2/tools/math/Jama/QRDecomposition.java
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package eva2.tools.math.Jama;
import eva2.tools.math.Jama.util.Maths;
/**
* QR Decomposition.
* <p>
* For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
* orthogonal matrix Q and an n-by-n upper triangular matrix R so that
* A = Q*R.
* <p>
* The QR decompostion always exists, even if the matrix does not have
* full rank, so the constructor will never fail. The primary use of the
* QR decomposition is in the least squares solution of nonsquare systems
* of simultaneous linear equations. This will fail if isFullRank()
* returns false.
*/
public class QRDecomposition implements java.io.Serializable {
/**
* Array for internal storage of decomposition.
*
* @serial internal array storage.
*/
private double[][] QR;
/**
* Row and column dimensions.
*
* @serial column dimension.
* @serial row dimension.
*/
private int m, n;
/**
* Array for internal storage of diagonal of R.
*
* @serial diagonal of R.
*/
private double[] Rdiag;
/**
* QR Decomposition, computed by Householder reflections.
*
* @param A Rectangular matrix
* @return Structure to access R and the Householder vectors and compute Q.
*/
public QRDecomposition(Matrix A) {
// Initialize.
QR = A.getArrayCopy();
m = A.getRowDimension();
n = A.getColumnDimension();
Rdiag = new double[n];
// Main loop.
for (int k = 0; k < n; k++) {
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
for (int i = k; i < m; i++) {
nrm = Maths.hypot(nrm, QR[i][k]);
}
if (nrm != 0.0) {
// Form k-th Householder vector.
if (QR[k][k] < 0) {
nrm = -nrm;
}
for (int i = k; i < m; i++) {
QR[i][k] /= nrm;
}
QR[k][k] += 1.0;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k] * QR[i][j];
}
s = -s / QR[k][k];
for (int i = k; i < m; i++) {
QR[i][j] += s * QR[i][k];
}
}
}
Rdiag[k] = -nrm;
}
}
/**
* Is the matrix full rank?
*
* @return true if R, and hence A, has full rank.
*/
public boolean isFullRank() {
for (int j = 0; j < n; j++) {
if (Rdiag[j] == 0) {
return false;
}
}
return true;
}
/**
* Return the Householder vectors
*
* @return Lower trapezoidal matrix whose columns define the reflections
*/
public Matrix getH() {
Matrix X = new Matrix(m, n);
double[][] H = X.getArray();
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i >= j) {
H[i][j] = QR[i][j];
} else {
H[i][j] = 0.0;
}
}
}
return X;
}
/**
* Return the upper triangular factor
*
* @return R
*/
public Matrix getR() {
Matrix X = new Matrix(n, n);
double[][] R = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i < j) {
R[i][j] = QR[i][j];
} else if (i == j) {
R[i][j] = Rdiag[i];
} else {
R[i][j] = 0.0;
}
}
}
return X;
}
/**
* Generate and return the (economy-sized) orthogonal factor
*
* @return Q
*/
public Matrix getQ() {
Matrix X = new Matrix(m, n);
double[][] Q = X.getArray();
for (int k = n - 1; k >= 0; k--) {
for (int i = 0; i < m; i++) {
Q[i][k] = 0.0;
}
Q[k][k] = 1.0;
for (int j = k; j < n; j++) {
if (QR[k][k] != 0) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k] * Q[i][j];
}
s = -s / QR[k][k];
for (int i = k; i < m; i++) {
Q[i][j] += s * QR[i][k];
}
}
}
}
return X;
}
/**
* Least squares solution of A*X = B
*
* @param B A Matrix with as many rows as A and any number of columns.
* @return X that minimizes the two norm of Q*R*X-B.
* @throws IllegalArgumentException Matrix row dimensions must agree.
* @throws RuntimeException Matrix is rank deficient.
*/
public Matrix solve(Matrix B) {
if (B.getRowDimension() != m) {
throw new IllegalArgumentException("Matrix row dimensions must agree.");
}
if (!this.isFullRank()) {
throw new RuntimeException("Matrix is rank deficient.");
}
// Copy right hand side
int nx = B.getColumnDimension();
double[][] X = B.getArrayCopy();
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++) {
for (int j = 0; j < nx; j++) {
double s = 0.0;
for (int i = k; i < m; i++) {
s += QR[i][k] * X[i][j];
}
s = -s / QR[k][k];
for (int i = k; i < m; i++) {
X[i][j] += s * QR[i][k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--) {
for (int j = 0; j < nx; j++) {
X[k][j] /= Rdiag[k];
}
for (int i = 0; i < k; i++) {
for (int j = 0; j < nx; j++) {
X[i][j] -= X[k][j] * QR[i][k];
}
}
}
return (new Matrix(X, n, nx).getMatrix(0, n - 1, 0, nx - 1));
}
}

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src/main/java/eva2/tools/math/Jama/SingularValueDecomposition.java
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@ -1,556 +0,0 @@
package eva2.tools.math.Jama;
import eva2.tools.math.Jama.util.Maths;
/**
* Singular Value Decomposition.
* <p>
* For an m-by-n matrix A with m >= n, the singular value decomposition is
* an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
* an n-by-n orthogonal matrix V so that A = U*S*V'.
* <p>
* The singular values, sigma[k] = S[k][k], are ordered so that
* sigma[0] >= sigma[1] >= ... >= sigma[n-1].
* <p>
* The singular value decompostion always exists, so the constructor will
* never fail. The matrix condition number and the effective numerical
* rank can be computed from this decomposition.
*/
public class SingularValueDecomposition implements java.io.Serializable {
/**
* Arrays for internal storage of U and V.
*
* @serial internal storage of U.
* @serial internal storage of V.
*/
private double[][] U, V;
/**
* Array for internal storage of singular values.
*
* @serial internal storage of singular values.
*/
private double[] s;
/**
* Row and column dimensions.
*
* @serial row dimension.
* @serial column dimension.
*/
private int m, n;
/**
* Construct the singular value decomposition
*
* @param arg A Rectangular matrix
* @return Structure to access U, S and V.
*/
public SingularValueDecomposition(Matrix matrix) {
// Derived from LINPACK code.
// Initialize.
double[][] A = matrix.getArrayCopy();
m = matrix.getRowDimension();
n = matrix.getColumnDimension();
int nu = Math.min(m, n);
s = new double[Math.min(m + 1, n)];
U = new double[m][nu];
V = new double[n][n];
double[] e = new double[n];
double[] work = new double[m];
boolean wantu = true;
boolean wantv = true;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
int nct = Math.min(m - 1, n);
int nrt = Math.max(0, Math.min(n - 2, m));
for (int k = 0; k < Math.max(nct, nrt); k++) {
if (k < nct) {
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
s[k] = 0;
for (int i = k; i < m; i++) {
s[k] = Maths.hypot(s[k], A[i][k]);
}
if (s[k] != 0.0) {
if (A[k][k] < 0.0) {
s[k] = -s[k];
}
for (int i = k; i < m; i++) {
A[i][k] /= s[k];
}
A[k][k] += 1.0;
}
s[k] = -s[k];
}
for (int j = k + 1; j < n; j++) {
if ((k < nct) & (s[k] != 0.0)) {
// Apply the transformation.
double t = 0;
for (int i = k; i < m; i++) {
t += A[i][k] * A[i][j];
}
t = -t / A[k][k];
for (int i = k; i < m; i++) {
A[i][j] += t * A[i][k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = A[k][j];
}
if (wantu & (k < nct)) {
// Place the transformation in U for subsequent back
// multiplication.
for (int i = k; i < m; i++) {
U[i][k] = A[i][k];
}
}
if (k < nrt) {
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (int i = k + 1; i < n; i++) {
e[k] = Maths.hypot(e[k], e[i]);
}
if (e[k] != 0.0) {
if (e[k + 1] < 0.0) {
e[k] = -e[k];
}
for (int i = k + 1; i < n; i++) {
e[i] /= e[k];
}
e[k + 1] += 1.0;
}
e[k] = -e[k];
if ((k + 1 < m) & (e[k] != 0.0)) {
// Apply the transformation.
for (int i = k + 1; i < m; i++) {
work[i] = 0.0;
}
for (int j = k + 1; j < n; j++) {
for (int i = k + 1; i < m; i++) {
work[i] += e[j] * A[i][j];
}
}
for (int j = k + 1; j < n; j++) {
double t = -e[j] / e[k + 1];
for (int i = k + 1; i < m; i++) {
A[i][j] += t * work[i];
}
}
}
if (wantv) {
// Place the transformation in V for subsequent
// back multiplication.
for (int i = k + 1; i < n; i++) {
V[i][k] = e[i];
}
}
}
}
// Set up the final bidiagonal matrix or order p.
int p = Math.min(n, m + 1);
if (nct < n) {
s[nct] = A[nct][nct];
}
if (m < p) {
s[p - 1] = 0.0;
}
if (nrt + 1 < p) {
e[nrt] = A[nrt][p - 1];
}
e[p - 1] = 0.0;
// If required, generate U.
if (wantu) {
for (int j = nct; j < nu; j++) {
for (int i = 0; i < m; i++) {
U[i][j] = 0.0;
}
U[j][j] = 1.0;
}
for (int k = nct - 1; k >= 0; k--) {
if (s[k] != 0.0) {
for (int j = k + 1; j < nu; j++) {
double t = 0;
for (int i = k; i < m; i++) {
t += U[i][k] * U[i][j];
}
t = -t / U[k][k];
for (int i = k; i < m; i++) {
U[i][j] += t * U[i][k];
}
}
for (int i = k; i < m; i++) {
U[i][k] = -U[i][k];
}
U[k][k] = 1.0 + U[k][k];
for (int i = 0; i < k - 1; i++) {
U[i][k] = 0.0;
}
} else {
for (int i = 0; i < m; i++) {
U[i][k] = 0.0;
}
U[k][k] = 1.0;
}
}
}
// If required, generate V.
if (wantv) {
for (int k = n - 1; k >= 0; k--) {
if ((k < nrt) & (e[k] != 0.0)) {
for (int j = k + 1; j < nu; j++) {
double t = 0;
for (int i = k + 1; i < n; i++) {
t += V[i][k] * V[i][j];
}
t = -t / V[k + 1][k];
for (int i = k + 1; i < n; i++) {
V[i][j] += t * V[i][k];
}
}
}
for (int i = 0; i < n; i++) {
V[i][k] = 0.0;
}
V[k][k] = 1.0;
}
}
// Main iteration loop for the singular values.
int pp = p - 1;
int iter = 0;
double eps = Math.pow(2.0, -52.0);
while (p > 0) {
int k, kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p - 2; k >= -1; k--) {
if (k == -1) {
break;
}
if (Math.abs(e[k]) <= eps * (Math.abs(s[k]) + Math.abs(s[k + 1]))) {
e[k] = 0.0;
break;
}
}
if (k == p - 2) {
kase = 4;
} else {
int ks;
for (ks = p - 1; ks >= k; ks--) {
if (ks == k) {
break;
}
double t = (ks != p ? Math.abs(e[ks]) : 0.) +
(ks != k + 1 ? Math.abs(e[ks - 1]) : 0.);
if (Math.abs(s[ks]) <= eps * t) {
s[ks] = 0.0;
break;
}
}
if (ks == k) {
kase = 3;
} else if (ks == p - 1) {
kase = 1;
} else {
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
switch (kase) {
// Deflate negligible s(p).
case 1: {
double f = e[p - 2];
e[p - 2] = 0.0;
for (int j = p - 2; j >= k; j--) {
double t = Maths.hypot(s[j], f);
double cs = s[j] / t;
double sn = f / t;
s[j] = t;
if (j != k) {
f = -sn * e[j - 1];
e[j - 1] = cs * e[j - 1];
}
if (wantv) {
for (int i = 0; i < n; i++) {
t = cs * V[i][j] + sn * V[i][p - 1];
V[i][p - 1] = -sn * V[i][j] + cs * V[i][p - 1];
V[i][j] = t;
}
}
}
}
break;
// Split at negligible s(k).
case 2: {
double f = e[k - 1];
e[k - 1] = 0.0;
for (int j = k; j < p; j++) {
double t = Maths.hypot(s[j], f);
double cs = s[j] / t;
double sn = f / t;
s[j] = t;
f = -sn * e[j];
e[j] = cs * e[j];
if (wantu) {
for (int i = 0; i < m; i++) {
t = cs * U[i][j] + sn * U[i][k - 1];
U[i][k - 1] = -sn * U[i][j] + cs * U[i][k - 1];
U[i][j] = t;
}
}
}
}
break;
// Perform one qr step.
case 3: {
// Calculate the shift.
double scale = Math.max(Math.max(Math.max(Math.max(
Math.abs(s[p - 1]), Math.abs(s[p - 2])), Math.abs(e[p - 2])),
Math.abs(s[k])), Math.abs(e[k]));
double sp = s[p - 1] / scale;
double spm1 = s[p - 2] / scale;
double epm1 = e[p - 2] / scale;
double sk = s[k] / scale;
double ek = e[k] / scale;
double b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2.0;
double c = (sp * epm1) * (sp * epm1);
double shift = 0.0;
if ((b != 0.0) | (c != 0.0)) {
shift = Math.sqrt(b * b + c);
if (b < 0.0) {
shift = -shift;
}
shift = c / (b + shift);
}
double f = (sk + sp) * (sk - sp) + shift;
double g = sk * ek;
// Chase zeros.
for (int j = k; j < p - 1; j++) {
double t = Maths.hypot(f, g);
double cs = f / t;
double sn = g / t;
if (j != k) {
e[j - 1] = t;
}
f = cs * s[j] + sn * e[j];
e[j] = cs * e[j] - sn * s[j];
g = sn * s[j + 1];
s[j + 1] = cs * s[j + 1];
if (wantv) {
for (int i = 0; i < n; i++) {
t = cs * V[i][j] + sn * V[i][j + 1];
V[i][j + 1] = -sn * V[i][j] + cs * V[i][j + 1];
V[i][j] = t;
}
}
t = Maths.hypot(f, g);
cs = f / t;
sn = g / t;
s[j] = t;
f = cs * e[j] + sn * s[j + 1];
s[j + 1] = -sn * e[j] + cs * s[j + 1];
g = sn * e[j + 1];
e[j + 1] = cs * e[j + 1];
if (wantu && (j < m - 1)) {
for (int i = 0; i < m; i++) {
t = cs * U[i][j] + sn * U[i][j + 1];
U[i][j + 1] = -sn * U[i][j] + cs * U[i][j + 1];
U[i][j] = t;
}
}
}
e[p - 2] = f;
iter += 1;
}
break;
// Convergence.
case 4: {
// Make the singular values positive.
if (s[k] <= 0.0) {
s[k] = (s[k] < 0.0 ? -s[k] : 0.0);
if (wantv) {
for (int i = 0; i <= pp; i++) {
V[i][k] = -V[i][k];
}
}
}
// Order the singular values.
while (k < pp) {
if (s[k] >= s[k + 1]) {
break;
}
double t = s[k];
s[k] = s[k + 1];
s[k + 1] = t;
if (wantv && (k < n - 1)) {
for (int i = 0; i < n; i++) {
t = V[i][k + 1];
V[i][k + 1] = V[i][k];
V[i][k] = t;
}
}
if (wantu && (k < m - 1)) {
for (int i = 0; i < m; i++) {
t = U[i][k + 1];
U[i][k + 1] = U[i][k];
U[i][k] = t;
}
}
k++;
}
iter = 0;
p--;
}
break;
}
}
}
/**
* Return the left singular vectors
*
* @return U
*/
public Matrix getU() {
return new Matrix(U, m, Math.min(m + 1, n));
}
/**
* Return the right singular vectors
*
* @return V
*/
public Matrix getV() {
return new Matrix(V, n, n);
}
/**
* Return the one-dimensional array of singular values
*
* @return diagonal of S.
*/
public double[] getSingularValues() {
return s;
}
/**
* Return the diagonal matrix of singular values
*
* @return S
*/
public Matrix getS() {
Matrix X = new Matrix(n, n);
double[][] S = X.getArray();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
S[i][j] = 0.0;
}
S[i][i] = this.s[i];
}
return X;
}
/**
* Two norm
*
* @return max(S)
*/
public double norm2() {
return s[0];
}
/**
* Two norm condition number
*
* @return max(S)/min(S)
*/
public double cond() {
return s[0] / s[Math.min(m, n) - 1];
}
/**
* Effective numerical matrix rank
*
* @return Number of nonnegligible singular values.
*/
public int rank() {
double eps = Math.pow(2.0, -52.0);
double tol = Math.max(m, n) * s[0] * eps;
int r = 0;
for (int i = 0; i < s.length; i++) {
if (s[i] > tol) {
r++;
}
}
return r;
}
}

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src/main/java/eva2/tools/math/Jama/package-info.java
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@ -1 +0,0 @@
package eva2.tools.math.Jama;

27
src/main/java/eva2/tools/math/Jama/util/Maths.java
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@ -1,27 +0,0 @@
package eva2.tools.math.Jama.util;
public class Maths {
/**
* sqrt(a^2 + b^2) without under/overflow.
*
* @param a
* @param b
* @return
*/
public static double hypot(double a, double b) {
double r;
double aa = Math.abs(a);
double bb = Math.abs(b);
if (aa > bb) {
r = b / a;
r = aa * Math.sqrt(1 + r * r);
} else if (b != 0) {
r = a / b;
r = bb * Math.sqrt(1 + r * r);
} else {
r = 0.0;
}
return r;
}
}

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src/main/java/eva2/tools/math/Jama/util/package-info.java
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@ -1 +0,0 @@
package eva2.tools.math.Jama.util;

2
src/main/java/eva2/tools/math/Mathematics.java
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@ -2,7 +2,7 @@ package eva2.tools.math;
import eva2.optimization.tools.DoubleArrayComparator; import eva2.optimization.tools.DoubleArrayComparator;
import eva2.tools.EVAERROR; import eva2.tools.EVAERROR;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import eva2.tools.math.interpolation.BasicDataSet; import eva2.tools.math.interpolation.BasicDataSet;
import eva2.tools.math.interpolation.InterpolationException; import eva2.tools.math.interpolation.InterpolationException;
import eva2.tools.math.interpolation.SplineInterpolation; import eva2.tools.math.interpolation.SplineInterpolation;

2
src/main/java/eva2/tools/math/StatisticUtils.java
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@ -1,6 +1,6 @@
package eva2.tools.math; package eva2.tools.math;
import eva2.tools.math.Jama.Matrix; import Jama.Matrix;
import java.util.ArrayList; import java.util.ArrayList;
import java.util.Collections; import java.util.Collections;