org.xmlobjects.gml.util.jama.CholeskyDecomposition Maven / Gradle / Ivy
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/*
* gml-objects - A Java mapping for the OGC Geography Markup Language (GML)
* https://github.com/xmlobjects/gml-objects
*
* Copyright 2019-2024 Claus Nagel
*
* 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.
*/
package org.xmlobjects.gml.util.jama;
/**
* Cholesky Decomposition.
*
* For a symmetric, positive definite matrix A, the Cholesky decomposition
* is an lower triangular matrix L so that A = L*L'.
*
* 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 {
/* ------------------------
Class variables
* ------------------------ */
/**
* 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;
/* ------------------------
Constructor
* ------------------------ */
/**
* Cholesky algorithm for symmetric and positive definite matrix.
* Structure to access L and isspd flag.
*
* @param Arg Square, symmetric matrix.
*/
public CholeskyDecomposition(Matrix Arg) {
// Initialize.
double[][] A = Arg.getArray();
n = Arg.getRowDimension();
L = new double[n][n];
isspd = (Arg.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 = d + s * s;
isspd = isspd & (A[k][j] == A[j][k]);
}
d = A[j][j] - d;
isspd = 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;
}
}
}
/* ------------------------
Temporary, experimental code.
* ------------------------ *\
\** Right Triangular Cholesky Decomposition.
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.
*\
\** Array for internal storage of right triangular decomposition. **\
private transient double[][] R;
\** Cholesky algorithm for symmetric and positive definite matrix.
@param A Square, symmetric matrix.
@param rightflag Actual value ignored.
@return Structure to access R and isspd flag.
*\
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 = s - R[i][k]*R[i][j];
}
R[k][j] = s = s/R[k][k];
d = d + s*s;
isspd = isspd & (A[k][j] == A[j][k]);
}
d = A[j][j] - d;
isspd = 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;
}
}
}
\** Return upper triangular factor.
@return R
*\
public Matrix getR () {
return new Matrix(R,n,n);
}
\* ------------------------
End of temporary code.
* ------------------------ */
/* ------------------------
Public Methods
* ------------------------ */
/**
* 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 j = 0; j < nx; j++) {
for (int i = 0; i < k; i++) {
X[k][j] -= X[i][j] * L[k][i];
}
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++) {
for (int i = k + 1; i < n; i++) {
X[k][j] -= X[i][j] * L[i][k];
}
X[k][j] /= L[k][k];
}
}
return new Matrix(X, n, nx);
}
private static final long serialVersionUID = 1;
}