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oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.
/*
* Copyright 1997-2022 Optimatika
*
* 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.
*/
package org.ojalgo.matrix.decomposition;
import org.ojalgo.array.DenseArray;
import org.ojalgo.matrix.store.MatrixStore;
import org.ojalgo.scalar.ComplexNumber;
import org.ojalgo.scalar.Quaternion;
import org.ojalgo.scalar.RationalNumber;
import org.ojalgo.structure.Access2D;
import org.ojalgo.type.context.NumberContext;
/**
*
* Cholesky: [A] = [L][L]H (or [R]H[R])
*
*
* [A]H = [A] = [L][L]H
*
*
* If [A] is symmetric and positive definite then the general LU decomposition - [P][L][D][U] - becomes
* [I][L][D][L]T (or [I][U]T[D][U]). [I] can be left out and [D] is normally split in
* halves and merged with [L] (and/or [U]). We'll express it as [A] = [L][L]T.
*
*
* A cholesky decomposition is still/also an LU decomposition where [P][L][D][U] => [L][L]T.
*
*
* @author apete
*/
public interface Cholesky> extends LDU, MatrixDecomposition.Hermitian {
interface Factory> extends MatrixDecomposition.Factory> {
}
Factory COMPLEX = typical -> new CholeskyDecomposition.Complex();
Factory PRIMITIVE = typical -> {
if ((32L < typical.countColumns()) && (typical.count() <= DenseArray.MAX_ARRAY_SIZE)) {
return new CholeskyDecomposition.Primitive();
} else {
return new RawCholesky();
}
};
Factory QUATERNION = typical -> new CholeskyDecomposition.Quat();
Factory RATIONAL = typical -> new CholeskyDecomposition.Rational();
static > boolean equals(final MatrixStore matrix, final Cholesky decomposition, final NumberContext context) {
boolean retVal = false;
final MatrixStore tmpL = decomposition.getL();
retVal = Access2D.equals(tmpL.multiply(tmpL.conjugate()), matrix, context);
return retVal;
}
/**
* Must implement either {@link #getL()} or {@link #getR()}.
*/
default MatrixStore getL() {
return this.getR().conjugate();
}
/**
* Must implement either {@link #getL()} or {@link #getR()}.
*/
default MatrixStore getR() {
return this.getL().conjugate();
}
/**
* To use the Cholesky decomposition rather than the LU decomposition the matrix must be symmetric and
* positive definite. It is recommended that the decomposition algorithm checks for this during
* calculation. Possibly the matrix could be assumed to be symmetric (to improve performance) but tests
* should be made to assure the matrix is positive definite.
*
* @return true if the tests did not fail.
*/
boolean isSPD();
default MatrixStore reconstruct() {
final MatrixStore mtrxL = this.getL();
return mtrxL.multiply(mtrxL.conjugate());
}
}