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oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.
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/*
 * Copyright 1997-2025 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.matrix.store.MatrixStore;
import org.ojalgo.scalar.ComplexNumber;
import org.ojalgo.scalar.Quadruple;
import org.ojalgo.scalar.Quaternion;
import org.ojalgo.scalar.RationalNumber;
import org.ojalgo.structure.Access2D;
import org.ojalgo.type.context.NumberContext;

/**
 * Tridiagonal: [A] = [Q][D][Q]^H Any square symmetric (hermitian) matrix [A] can be factorized by
 * similarity transformations into the form, [A]=[Q][D][Q]^-1 where [Q] is an orthogonal (unitary)
 * matrix and [D] is a real symmetric tridiagonal matrix. Note that [D] can/should be made real even when [A]
 * has complex elements. Since [Q] is orthogonal (unitary) [Q]^-1 = [Q]^H and when it is
 * real [Q]^H = [Q]^T.
 *
 * @author apete
 */
public interface Tridiagonal> extends MatrixDecomposition {

    interface Factory> extends MatrixDecomposition.Factory> {

    }

    Factory C128 = typical -> new DeferredTridiagonal.C128();

    Factory R064 = typical -> new DeferredTridiagonal.R064();

    Factory R128 = typical -> new DeferredTridiagonal.R128();

    Factory H256 = typical -> new DeferredTridiagonal.H256();

    Factory Q128 = typical -> new DeferredTridiagonal.Q128();

    static > boolean equals(final MatrixStore matrix, final Tridiagonal decomposition, final NumberContext context) {

        boolean retVal = true;

        // Check that [A] == [Q][D][Q]^T
        retVal &= Access2D.equals(matrix, decomposition.reconstruct(), context);

        // Check that Q is orthogonal/unitary...

        final MatrixStore mtrxQ = decomposition.getQ();
        MatrixStore identity = mtrxQ.physical().makeEye(mtrxQ.countRows(), mtrxQ.countColumns());

        MatrixStore qqh = mtrxQ.multiply(mtrxQ.conjugate());
        retVal &= qqh.equals(identity, context);

        MatrixStore qhq = mtrxQ.conjugate().multiply(mtrxQ);
        retVal &= qhq.equals(identity, context);

        return retVal;
    }

    MatrixStore getD();

    MatrixStore getQ();

    default MatrixStore reconstruct() {
        MatrixStore mtrxQ = this.getQ();
        MatrixStore mtrxD = this.getD();
        return mtrxQ.multiply(mtrxD).multiply(mtrxQ.conjugate());
    }

}