Java Code Examples for org.apache.commons.math3.linear.RealMatrix#operate()
The following examples show how to use
org.apache.commons.math3.linear.RealMatrix#operate() .
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Example 1
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 2
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 3
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares1() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1.0e-6);
}
Example 4
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 5
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 6
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares1() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1.0e-6);
}
Example 7
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 8
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 9
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 10
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 11
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares3() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
{ 1, 1.2 }, { 1.2, 2 }
}));
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 12
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 13
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares1() {
final RealMatrix factors
= new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum =
optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 3e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 4e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1.0e-6);
}
Example 14
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 6 votes |
|
@Test
public void testLeastSquares2() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new double[] { 10, 0.1 });
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
optimizer.setSimplex(new NelderMeadSimplex(2));
PointValuePair optimum =
optimizer.optimize(200, ls, GoalType.MINIMIZE, new double[] { 10, 10 });
Assert.assertEquals( 2, optimum.getPointRef()[0], 5e-5);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 15
| Source File: MatrixUtils.java From incubator-hivemall with Apache License 2.0 | 5 votes |
|
/**
* Find the first singular vector/value of a matrix A based on the Power method.
*
* @see http://www.cs.yale.edu/homes/el327/datamining2013aFiles/07_singular_value_decomposition.pdf
* @param A target matrix
* @param x0 initial vector
* @param nIter number of iterations for the Power method
* @param u 1st left singular vector
* @param v 1st right singular vector
* @return 1st singular value
*/
public static double power1(@Nonnull final RealMatrix A, @Nonnull final double[] x0,
final int nIter, @Nonnull final double[] u, @Nonnull final double[] v) {
Preconditions.checkArgument(A.getColumnDimension() == x0.length,
"Column size of A and length of x should be same");
Preconditions.checkArgument(A.getRowDimension() == u.length,
"Row size of A and length of u should be same");
Preconditions.checkArgument(x0.length == v.length, "Length of x and u should be same");
Preconditions.checkArgument(nIter >= 1, "Invalid number of iterations: " + nIter);
RealMatrix AtA = A.transpose().multiply(A);
RealVector x = new ArrayRealVector(x0);
for (int i = 0; i < nIter; i++) {
x = AtA.operate(x);
}
double xNorm = x.getNorm();
for (int i = 0, n = v.length; i < n; i++) {
v[i] = x.getEntry(i) / xNorm;
}
RealVector Av = new ArrayRealVector(A.operate(v));
double s = Av.getNorm();
for (int i = 0, n = u.length; i < n; i++) {
u[i] = Av.getEntry(i) / s;
}
return s;
}
Example 16
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testLeastSquares3() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
{ 1, 1.2 }, { 1.2, 2 }
}));
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 17
| Source File: RidgeRegression.java From Surus with Apache License 2.0 | 5 votes |
|
public void updateCoefficients(double l2penalty) {
if (this.X_svd == null) {
this.X_svd = new SingularValueDecomposition(X);
}
RealMatrix V = this.X_svd.getV();
double[] s = this.X_svd.getSingularValues();
RealMatrix U = this.X_svd.getU();
for (int i = 0; i < s.length; i++) {
s[i] = s[i] / (s[i]*s[i] + l2penalty);
}
RealMatrix S = MatrixUtils.createRealDiagonalMatrix(s);
RealMatrix Z = V.multiply(S).multiply(U.transpose());
this.coefficients = Z.operate(this.Y);
this.fitted = this.X.operate(this.coefficients);
double errorVariance = 0;
for (int i = 0; i < residuals.length; i++) {
this.residuals[i] = this.Y[i] - this.fitted[i];
errorVariance += this.residuals[i] * this.residuals[i];
}
errorVariance = errorVariance / (X.getRowDimension() - X.getColumnDimension());
RealMatrix errorVarianceMatrix = MatrixUtils.createRealIdentityMatrix(this.Y.length).scalarMultiply(errorVariance);
RealMatrix coefficientsCovarianceMatrix = Z.multiply(errorVarianceMatrix).multiply(Z.transpose());
this.standarderrors = getDiagonal(coefficientsCovarianceMatrix);
}
Example 18
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testLeastSquares3() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
{ 1, 1.2 }, { 1.2, 2 }
}));
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 19
| Source File: SimplexOptimizerNelderMeadTest.java From astor with GNU General Public License v2.0 | 5 votes |
|
@Test
public void testLeastSquares3() {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1, 0 },
{ 0, 1 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2, -3 }, new Array2DRowRealMatrix(new double [][] {
{ 1, 1.2 }, { 1.2, 2 }
}));
SimplexOptimizer optimizer = new SimplexOptimizer(-1, 1e-6);
PointValuePair optimum
= optimizer.optimize(new MaxEval(200),
new ObjectiveFunction(ls),
GoalType.MINIMIZE,
new InitialGuess(new double[] { 10, 10 }),
new NelderMeadSimplex(2));
Assert.assertEquals( 2, optimum.getPointRef()[0], 2e-3);
Assert.assertEquals(-3, optimum.getPointRef()[1], 8e-4);
Assert.assertTrue(optimizer.getEvaluations() > 60);
Assert.assertTrue(optimizer.getEvaluations() < 80);
Assert.assertTrue(optimum.getValue() < 1e-6);
}
Example 20
| Source File: MatrixUtils.java From incubator-hivemall with Apache License 2.0 | 4 votes |
|
/**
* Lanczos tridiagonalization for a symmetric matrix C to make s * s tridiagonal matrix T.
*
* @see http://www.cas.mcmaster.ca/~qiao/publications/spie05.pdf
* @param C target symmetric matrix
* @param a initial vector
* @param T result is stored here
*/
public static void lanczosTridiagonalization(@Nonnull final RealMatrix C,
@Nonnull final double[] a, @Nonnull final RealMatrix T) {
Preconditions.checkArgument(Arrays.deepEquals(C.getData(), C.transpose().getData()),
"Target matrix C must be a symmetric matrix");
Preconditions.checkArgument(C.getColumnDimension() == a.length,
"Column size of A and length of a should be same");
Preconditions.checkArgument(T.getRowDimension() == T.getColumnDimension(),
"T must be a square matrix");
int s = T.getRowDimension();
// initialize T with zeros
T.setSubMatrix(new double[s][s], 0, 0);
RealVector a0 = new ArrayRealVector(a.length);
RealVector r = new ArrayRealVector(a);
double beta0 = 1.d;
for (int i = 0; i < s; i++) {
RealVector a1 = r.mapDivide(beta0);
RealVector Ca1 = C.operate(a1);
double alpha1 = a1.dotProduct(Ca1);
r = Ca1.add(a1.mapMultiply(-1.d * alpha1)).add(a0.mapMultiply(-1.d * beta0));
double beta1 = r.getNorm();
T.setEntry(i, i, alpha1);
if (i - 1 >= 0) {
T.setEntry(i, i - 1, beta0);
}
if (i + 1 < s) {
T.setEntry(i, i + 1, beta1);
}
a0 = a1.copy();
beta0 = beta1;
}
}
