org.ojalgo.matrix.decomposition.BidiagonalDecomposition Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of ojalgo Show documentation
Show all versions of ojalgo Show documentation
oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.
/*
* Copyright 1997-2021 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.Array1D;
import org.ojalgo.function.constant.PrimitiveMath;
import org.ojalgo.matrix.store.DiagonalStore;
import org.ojalgo.matrix.store.GenericStore;
import org.ojalgo.matrix.store.MatrixStore;
import org.ojalgo.matrix.store.PhysicalStore;
import org.ojalgo.matrix.store.Primitive64Store;
import org.ojalgo.matrix.transformation.Householder;
import org.ojalgo.matrix.transformation.HouseholderReference;
import org.ojalgo.scalar.ComplexNumber;
import org.ojalgo.scalar.PrimitiveScalar;
import org.ojalgo.scalar.Quaternion;
import org.ojalgo.scalar.RationalNumber;
import org.ojalgo.structure.Access2D;
abstract class BidiagonalDecomposition> extends InPlaceDecomposition implements Bidiagonal {
static final class Complex extends BidiagonalDecomposition {
Complex() {
this(false);
}
Complex(final boolean fullSize) {
super(GenericStore.COMPLEX, fullSize);
}
@Override
Array1D[] makeReal() {
final DiagonalStore> tmpDiagonalAccessD = this.doGetDiagonal();
final Array1D tmpInitDiagQ1 = Array1D.COMPLEX.makeZero(tmpDiagonalAccessD.getDimension());
tmpInitDiagQ1.fillAll(ComplexNumber.ONE);
final Array1D tmpInitDiagQ2 = Array1D.COMPLEX.makeZero(tmpDiagonalAccessD.getDimension());
tmpInitDiagQ2.fillAll(ComplexNumber.ONE);
final boolean tmpUpper = this.isUpper();
if (tmpUpper) {
final Array1D tmpMainDiagonal = tmpDiagonalAccessD.getMainDiagonal().get();
final Array1D tmpSuperdiagonal = tmpDiagonalAccessD.getSuperdiagonal().get();
final int tmpLimit = (int) tmpSuperdiagonal.count();
for (int i = 0; i < tmpLimit; i++) {
if (!tmpMainDiagonal.get(i).isReal()) {
final ComplexNumber tmpSignum = tmpMainDiagonal.get(i).signum();
tmpMainDiagonal.set(i, tmpMainDiagonal.get(i).divide(tmpSignum));
tmpSuperdiagonal.set(i, tmpSuperdiagonal.get(i).divide(tmpSignum));
tmpInitDiagQ1.set(i, tmpSignum);
}
if (!tmpSuperdiagonal.get(i).isReal()) {
final ComplexNumber tmpSignum = tmpSuperdiagonal.get(i).signum();
tmpSuperdiagonal.set(i, tmpSuperdiagonal.get(i).divide(tmpSignum));
tmpMainDiagonal.set(i + 1, tmpMainDiagonal.get(i + 1).divide(tmpSignum));
tmpInitDiagQ2.set(i + 1, tmpSignum.conjugate());
}
}
if (!tmpMainDiagonal.get(tmpLimit).isReal()) {
final ComplexNumber tmpSignum = tmpMainDiagonal.get(tmpLimit).signum();
tmpMainDiagonal.set(tmpLimit, tmpMainDiagonal.get(tmpLimit).divide(tmpSignum));
tmpInitDiagQ1.set(tmpLimit, tmpSignum);
}
} else {
final Array1D tmpMainDiagonal = tmpDiagonalAccessD.getMainDiagonal().get();
final Array1D tmpSubdiagonal = tmpDiagonalAccessD.getSubdiagonal().get();
final int tmpLimit = (int) tmpSubdiagonal.count();
for (int i = 0; i < tmpLimit; i++) {
if (!tmpMainDiagonal.get(i).isReal()) {
final ComplexNumber tmpSignum = tmpMainDiagonal.get(i).signum();
tmpMainDiagonal.set(i, tmpMainDiagonal.get(i).divide(tmpSignum));
tmpSubdiagonal.set(i, tmpSubdiagonal.get(i).divide(tmpSignum));
tmpInitDiagQ2.set(i, tmpSignum.conjugate());
}
if (!tmpSubdiagonal.get(i).isReal()) {
final ComplexNumber tmpSignum = tmpSubdiagonal.get(i).signum();
tmpSubdiagonal.set(i, tmpSubdiagonal.get(i).divide(tmpSignum));
tmpMainDiagonal.set(i + 1, tmpMainDiagonal.get(i + 1).divide(tmpSignum));
tmpInitDiagQ1.set(i + 1, tmpSignum);
}
}
if (!tmpMainDiagonal.get(tmpLimit).isReal()) {
final ComplexNumber tmpSignum = tmpMainDiagonal.get(tmpLimit).signum();
tmpMainDiagonal.set(tmpLimit, tmpMainDiagonal.get(tmpLimit).divide(tmpSignum));
tmpInitDiagQ2.set(tmpLimit, tmpSignum.conjugate());
}
}
return new Array1D[] { tmpInitDiagQ1, tmpInitDiagQ2 };
}
}
static final class Primitive extends BidiagonalDecomposition {
Primitive() {
this(false);
}
Primitive(final boolean fullSize) {
super(Primitive64Store.FACTORY, fullSize);
}
@Override
Array1D[] makeReal() {
return null;
}
}
static final class Quat extends BidiagonalDecomposition {
Quat() {
this(false);
}
Quat(final boolean fullSize) {
super(GenericStore.QUATERNION, fullSize);
}
@Override
Array1D[] makeReal() {
// TODO Implement something similar to what's in "Complex"
return null;
}
}
static final class Rational extends BidiagonalDecomposition {
Rational() {
this(false);
}
Rational(final boolean fullSize) {
super(GenericStore.RATIONAL, fullSize);
}
@Override
Array1D[] makeReal() {
return null;
}
}
private transient DiagonalStore> myDiagonal;
private final boolean myFullSize;
private Array1D myInitDiagLQ = null;
private Array1D myInitDiagRQ = null;
private transient DecompositionStore myLQ;
private transient DecompositionStore myRQ;
protected BidiagonalDecomposition(final DecompositionStore.Factory> factory, final boolean fullSize) {
super(factory);
myFullSize = fullSize;
}
public boolean decompose(final Access2D.Collectable> matrix) {
this.reset();
final DecompositionStore storage = this.setInPlace(matrix);
final int tmpRowDim = this.getRowDim();
final int tmpColDim = this.getColDim();
final int tmpLimit = Math.min(tmpRowDim, tmpColDim);
final Householder tmpHouseholderRow = this.makeHouseholder(tmpColDim);
final Householder tmpHouseholderCol = this.makeHouseholder(tmpRowDim);
if (this.isAspectRatioNormal()) {
for (int ij = 0; ij < tmpLimit; ij++) {
if (ij + 1 < tmpRowDim && storage.generateApplyAndCopyHouseholderColumn(ij, ij, tmpHouseholderCol)) {
storage.transformLeft(tmpHouseholderCol, ij + 1);
}
if (ij + 2 < tmpColDim && storage.generateApplyAndCopyHouseholderRow(ij, ij + 1, tmpHouseholderRow)) {
storage.transformRight(tmpHouseholderRow, ij + 1);
}
}
final Array1D[] tmpInitDiags = this.makeReal();
if (tmpInitDiags != null) {
myInitDiagLQ = tmpInitDiags[0];
myInitDiagRQ = tmpInitDiags[1];
}
} else {
for (int ij = 0; ij < tmpLimit; ij++) {
if (ij + 1 < tmpColDim && storage.generateApplyAndCopyHouseholderRow(ij, ij, tmpHouseholderRow)) {
storage.transformRight(tmpHouseholderRow, ij + 1);
}
if (ij + 2 < tmpRowDim && storage.generateApplyAndCopyHouseholderColumn(ij + 1, ij, tmpHouseholderCol)) {
storage.transformLeft(tmpHouseholderCol, ij + 1);
}
}
final Array1D[] tmpInitDiags = this.makeReal();
if (tmpInitDiags != null) {
myInitDiagLQ = tmpInitDiags[0];
myInitDiagRQ = tmpInitDiags[1];
}
}
return this.computed(true);
}
public MatrixStore getD() {
MatrixStore retVal = this.doGetDiagonal();
if (myFullSize) {
if (this.getRowDim() > retVal.getRowDim()) {
retVal = retVal.logical().below(this.getRowDim() - retVal.countRows()).get();
} else if (this.getColDim() > retVal.getColDim()) {
retVal = retVal.logical().right(this.getColDim() - retVal.countColumns()).get();
}
}
return retVal;
}
public MatrixStore getLQ() {
return this.doGetLQ();
}
public MatrixStore getRQ() {
return this.doGetRQ();
}
public boolean isFullSize() {
return myFullSize;
}
public boolean isUpper() {
return this.isAspectRatioNormal();
}
@Override
public void reset() {
super.reset();
myLQ = null;
myRQ = null;
myDiagonal = null;
myInitDiagLQ = null;
myInitDiagRQ = null;
}
private DiagonalStore> makeDiagonal() {
final DecompositionStore storage = this.getInPlace();
final Array1D diagMain = storage.sliceDiagonal(0, 0);
Array1D diagSuper;
Array1D diagSub;
if (this.isAspectRatioNormal()) {
diagSuper = storage.sliceDiagonal(0, 1);
diagSub = null;
} else {
diagSuper = null;
diagSub = storage.sliceDiagonal(1, 0);
}
return this.makeDiagonal(diagMain).superdiagonal(diagSuper).subdiagonal(diagSub).get();
}
private DecompositionStore makeLQ() {
final HouseholderReference tmpReference = HouseholderReference.makeColumn(this.getInPlace());
final int tmpRowDim = this.getRowDim();
final int tmpMinDim = this.getMinDim();
DecompositionStore retVal = null;
if (myInitDiagLQ != null) {
retVal = this.makeZero(tmpRowDim, myFullSize ? tmpRowDim : tmpMinDim);
for (int ij = 0; ij < tmpMinDim; ij++) {
retVal.set(ij, ij, myInitDiagLQ.get(ij));
}
} else {
retVal = this.makeEye(tmpRowDim, myFullSize ? tmpRowDim : tmpMinDim);
}
final boolean tmpUpper = this.isUpper();
for (int ij = tmpUpper && tmpRowDim != tmpMinDim ? tmpMinDim - 1 : tmpMinDim - 2; ij >= 0; ij--) {
tmpReference.point(tmpUpper ? ij : ij + 1, ij);
if (!tmpReference.isZero()) {
retVal.transformLeft(tmpReference, ij);
}
}
return retVal;
}
private DecompositionStore makeRQ() {
final HouseholderReference tmpReference = HouseholderReference.makeRow(this.getInPlace());
final int tmpColDim = this.getColDim();
final int tmpMinDim = this.getMinDim();
DecompositionStore retVal = null;
if (myInitDiagRQ != null) {
retVal = this.makeZero(tmpColDim, myFullSize ? tmpColDim : tmpMinDim);
for (int ij = 0; ij < tmpMinDim; ij++) {
retVal.set(ij, ij, myInitDiagRQ.get(ij));
}
} else {
retVal = this.makeEye(tmpColDim, myFullSize ? tmpColDim : tmpMinDim);
}
final boolean tmpUpper = this.isUpper();
for (int ij = tmpUpper ? tmpMinDim - 2 : tmpMinDim - 1; ij >= 0; ij--) {
tmpReference.point(ij, tmpUpper ? ij + 1 : ij);
if (!tmpReference.isZero()) {
retVal.transformLeft(tmpReference, ij);
}
}
return retVal;
}
/**
* Will solve the equation system [aMtrxV][aMtrxD][X]=[aMtrxSimilar]T and overwrite the
* solution [X] to [aV].
*/
private void solve(final PhysicalStore aMtrxV, final MatrixStore aMtrxD, final DiagonalStore aMtrxSimilar) {
final int tmpDim = (int) aMtrxV.countRows();
final int tmpLim = tmpDim - 1;
double tmpSingular;
for (int j = 0; j < tmpDim; j++) {
tmpSingular = aMtrxD.doubleValue(j, j);
final double value = tmpSingular;
if (PrimitiveScalar.isSmall(PrimitiveMath.ONE, value)) {
for (int i = 0; i < tmpDim; i++) {
aMtrxV.set(i, j, PrimitiveMath.ZERO);
}
} else {
for (int i = 0; i < tmpLim; i++) {
aMtrxV.set(i, j,
(aMtrxSimilar.doubleValue(i, i) * aMtrxV.doubleValue(i, j) + aMtrxSimilar.doubleValue(i, i + 1) * aMtrxV.doubleValue(i + 1, j))
/ tmpSingular);
}
aMtrxV.set(tmpLim, j, aMtrxSimilar.doubleValue(tmpLim, tmpLim) * aMtrxV.doubleValue(tmpLim, j) / tmpSingular);
}
}
}
private DecompositionStore solve2(final PhysicalStore aMtrxV, final MatrixStore aMtrxD, final DiagonalStore aMtrxSimilar) {
final int tmpDim = (int) aMtrxV.countRows();
final int tmpLim = tmpDim - 1;
final DecompositionStore retVal = this.makeZero(tmpDim, tmpDim);
double tmpSingular;
for (int j = 0; j < tmpDim; j++) {
tmpSingular = aMtrxD.doubleValue(j, j);
final double value = tmpSingular;
if (PrimitiveScalar.isSmall(PrimitiveMath.ONE, value)) {
for (int i = 0; i < tmpDim; i++) {
retVal.set(i, j, aMtrxV.doubleValue(i, j));
}
} else {
for (int i = 0; i < tmpLim; i++) {
retVal.set(i, j,
(aMtrxSimilar.doubleValue(i, i) * aMtrxV.doubleValue(i, j) + aMtrxSimilar.doubleValue(i, i + 1) * aMtrxV.doubleValue(i + 1, j))
/ tmpSingular);
}
retVal.set(tmpLim, j, aMtrxSimilar.doubleValue(tmpLim, tmpLim) * aMtrxV.doubleValue(tmpLim, j) / tmpSingular);
}
}
return retVal;
}
DiagonalStore> doGetDiagonal() {
if (myDiagonal == null) {
myDiagonal = this.makeDiagonal();
}
return myDiagonal;
}
DecompositionStore doGetLQ() {
if (myLQ == null) {
myLQ = this.makeLQ();
}
return myLQ;
}
DecompositionStore doGetRQ() {
if (myRQ == null) {
myRQ = this.makeRQ();
}
return myRQ;
}
abstract Array1D[] makeReal();
}