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oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.
/*
* Copyright 1997-2024 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 static org.ojalgo.function.constant.PrimitiveMath.MACHINE_SMALLEST;
import static org.ojalgo.function.constant.PrimitiveMath.ZERO;
import org.ojalgo.RecoverableCondition;
import org.ojalgo.array.BasicArray;
import org.ojalgo.function.BinaryFunction;
import org.ojalgo.function.aggregator.Aggregator;
import org.ojalgo.function.aggregator.AggregatorFunction;
import org.ojalgo.function.constant.PrimitiveMath;
import org.ojalgo.matrix.store.GenericStore;
import org.ojalgo.matrix.store.MatrixStore;
import org.ojalgo.matrix.store.PhysicalStore;
import org.ojalgo.matrix.store.R064Store;
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.structure.Access2D.Collectable;
import org.ojalgo.structure.Structure2D;
import org.ojalgo.type.NumberDefinition;
import org.ojalgo.type.context.NumberContext;
abstract class LDLDecomposition> extends InPlaceDecomposition implements LDL {
static final class C128 extends LDLDecomposition {
C128() {
super(GenericStore.C128);
}
}
static final class H256 extends LDLDecomposition {
H256() {
super(GenericStore.H256);
}
}
static final class Q128 extends LDLDecomposition {
Q128() {
super(GenericStore.Q128);
}
}
static final class R064 extends LDLDecomposition {
R064() {
super(R064Store.FACTORY);
}
}
static final class R128 extends LDLDecomposition {
R128() {
super(GenericStore.R128);
}
}
private final Pivot myPivot = new Pivot();
private double myThreshold = Double.NaN;
protected LDLDecomposition(final PhysicalStore.Factory> factory) {
super(factory);
}
public final void btran(final PhysicalStore arg) {
int[] order = myPivot.getOrder();
if (myPivot.isModified()) {
arg.rows(order).copy().supplyTo(arg);
}
DecompositionStore body = this.getInPlace();
arg.substituteForwards(body, true, false, false);
BinaryFunction divide = this.function().divide();
for (int i = 0; i < order.length; i++) {
arg.modifyRow(i, divide.by(body.get(i, i)));
}
arg.substituteBackwards(body, true, true, false);
if (myPivot.isModified()) {
arg.rows(myPivot.reverseOrder()).copy().supplyTo(arg);
}
}
public N calculateDeterminant(final Access2D matrix) {
this.decompose(this.wrap(matrix));
return this.getDeterminant();
}
public int countSignificant(final double threshold) {
DecompositionStore internal = this.getInPlace();
int significant = 0;
for (int ij = 0, limit = this.getMinDim(); ij < limit; ij++) {
if (Math.abs(internal.doubleValue(ij, ij)) > threshold) {
significant++;
}
}
return significant;
}
public boolean decompose(final Access2D.Collectable> matrix) {
return this.doDecompose(matrix, true);
}
public boolean decomposeWithoutPivoting(final Collectable> matrix) {
return this.doDecompose(matrix, false);
}
public MatrixStore getD() {
return this.getInPlace().diagonal();
}
public N getDeterminant() {
AggregatorFunction aggregator = this.aggregator().product();
this.getInPlace().visitDiagonal(aggregator);
if (myPivot.signum() == -1) {
return aggregator.toScalar().negate().get();
}
return aggregator.get();
}
@Override
public MatrixStore getInverse(final PhysicalStore preallocated) {
int[] order = myPivot.getOrder();
boolean modified = myPivot.isModified();
if (modified) {
preallocated.fillAll(this.scalar().zero().get());
for (int i = 0; i < order.length; i++) {
preallocated.set(i, order[i], PrimitiveMath.ONE);
}
}
DecompositionStore body = this.getInPlace();
preallocated.substituteForwards(body, true, false, !modified);
BinaryFunction divide = this.function().divide();
for (int i = 0; i < order.length; i++) {
preallocated.modifyRow(i, 0, divide.by(body.doubleValue(i, i)));
}
preallocated.substituteBackwards(body, true, true, false);
return preallocated.rows(myPivot.reverseOrder());
}
public MatrixStore getL() {
DecompositionStore tmpInPlace = this.getInPlace();
MatrixStore tmpBuilder = tmpInPlace;
return tmpBuilder.triangular(false, true);
}
public int[] getPivotOrder() {
return myPivot.getOrder();
}
public double getRankThreshold() {
N largest = this.getInPlace().aggregateDiagonal(Aggregator.LARGEST);
double epsilon = this.getDimensionalEpsilon();
return epsilon * Math.max(MACHINE_SMALLEST, NumberDefinition.doubleValue(largest));
}
public int[] getReversePivotOrder() {
return myPivot.reverseOrder();
}
public MatrixStore getSolution(final Collectable> rhs) {
return this.getSolution(rhs, this.preallocate(this.getInPlace(), rhs));
}
@Override
public MatrixStore getSolution(final Collectable> rhs, final PhysicalStore preallocated) {
int[] order = myPivot.getOrder();
preallocated.fillMatching(this.collect(rhs).rows(order));
DecompositionStore body = this.getInPlace();
preallocated.substituteForwards(body, true, false, false);
BinaryFunction divide = this.function().divide();
for (int i = 0; i < order.length; i++) {
preallocated.modifyRow(i, divide.by(body.get(i, i)));
}
preallocated.substituteBackwards(body, true, true, false);
return preallocated.rows(myPivot.reverseOrder());
}
public MatrixStore invert(final Access2D original) throws RecoverableCondition {
this.decompose(this.wrap(original));
if (this.isSolvable()) {
return this.getInverse();
}
throw RecoverableCondition.newMatrixNotInvertible();
}
public MatrixStore invert(final Access2D original, final PhysicalStore preallocated) throws RecoverableCondition {
this.decompose(this.wrap(original));
if (this.isSolvable()) {
return this.getInverse(preallocated);
}
throw RecoverableCondition.newMatrixNotInvertible();
}
public boolean isPivoted() {
return myPivot.isModified();
}
@Override
public boolean isSolvable() {
return super.isSolvable();
}
public PhysicalStore preallocate(final Structure2D template) {
long tmpCountRows = template.countRows();
return this.allocate(tmpCountRows, tmpCountRows);
}
public PhysicalStore preallocate(final Structure2D templateBody, final Structure2D templateRHS) {
return this.allocate(templateRHS.countRows(), templateRHS.countColumns());
}
public MatrixStore solve(final Access2D body, final Access2D rhs) throws RecoverableCondition {
this.decompose(this.wrap(body));
if (this.isSolvable()) {
return this.getSolution(this.wrap(rhs));
}
throw RecoverableCondition.newEquationSystemNotSolvable();
}
public MatrixStore solve(final Access2D body, final Access2D rhs, final PhysicalStore preallocated) throws RecoverableCondition {
this.decompose(this.wrap(body));
if (this.isSolvable()) {
return this.getSolution(this.wrap(rhs), preallocated);
}
throw RecoverableCondition.newEquationSystemNotSolvable();
}
private boolean doDecompose(final Access2D.Collectable> matrix, final boolean pivoting) {
this.reset();
DecompositionStore store = this.setInPlace(matrix);
int dim = this.getMinDim();
myPivot.reset(dim);
BasicArray multipliers = this.makeArray(dim);
// Main loop - along the diagonal
for (int ij = 0; ij < dim; ij++) {
if (pivoting) {
// Find next pivot row
int pivotRow = store.indexOfLargestOnDiagonal(ij, ij);
// Pivot?
if (pivotRow != ij) {
store.exchangeHermitian(pivotRow, ij);
myPivot.change(pivotRow, ij);
}
}
double storeDiagVal = store.doubleValue(ij, ij);
if (Double.isFinite(myThreshold) && myThreshold > ZERO) {
// double maxColVal = ZERO;
// for (int i = ij + 1; i < dim; i++) {
// maxColVal = Math.max(maxColVal, Math.abs(store.doubleValue(i, ij)));
// }
// maxColVal *= myThreshold;
// maxColVal *= maxColVal;
double candidate = Math.max(Math.abs(storeDiagVal), myThreshold);
if (candidate > storeDiagVal) {
storeDiagVal = candidate;
store.set(ij, ij, storeDiagVal);
}
}
// Do the calculations...
if (NumberContext.compare(storeDiagVal, PrimitiveMath.ZERO) != 0) {
// Calculate multipliers and copy to local column
// Current column, below the diagonal
store.divideAndCopyColumn(ij, ij, multipliers);
// Apply transformations to everything below and to the right of the pivot element
store.applyLDL(ij, multipliers);
} else {
store.set(ij, ij, ZERO);
}
}
return this.computed(true);
}
@Override
protected boolean checkSolvability() {
return this.isSquare() && this.isFullRank();
}
void setThreshold(final N threshold) {
myThreshold = NumberDefinition.doubleValue(threshold);
}
}