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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.array.operation;
import org.ojalgo.function.constant.PrimitiveMath;
import org.ojalgo.matrix.transformation.Householder;
import org.ojalgo.scalar.PrimitiveScalar;
import org.ojalgo.scalar.Scalar;
public abstract class GenerateApplyAndCopyHouseholderColumn implements ArrayOperation {
public static int THRESHOLD = 128;
public static boolean invoke(final double[] data, final int structure, final int row, final int col, final Householder.Primitive64 destination) {
int tmpColBase = col * structure;
double[] tmpVector = destination.vector;
destination.first = row;
double tmpNormInf = PrimitiveMath.ZERO; // Copy column and calculate its infinity-norm.
for (int i = row; i < structure; i++) {
tmpNormInf = Math.max(tmpNormInf, PrimitiveMath.ABS.invoke(tmpVector[i] = data[i + tmpColBase]));
}
boolean retVal = tmpNormInf != PrimitiveMath.ZERO;
double tmpVal;
double tmpNorm2 = PrimitiveMath.ZERO;
if (retVal) {
for (int i = row + 1; i < structure; i++) {
tmpVal = tmpVector[i] /= tmpNormInf;
tmpNorm2 += tmpVal * tmpVal;
}
retVal = !PrimitiveScalar.isSmall(PrimitiveMath.ONE, tmpNorm2);
}
if (retVal) {
double tmpScale = tmpVector[row] / tmpNormInf;
tmpNorm2 += tmpScale * tmpScale;
tmpNorm2 = PrimitiveMath.SQRT.invoke(tmpNorm2); // 2-norm of the vector to transform (scaled by inf-norm)
if (tmpScale <= PrimitiveMath.ZERO) {
data[row + tmpColBase] = tmpNorm2 * tmpNormInf;
tmpScale -= tmpNorm2;
} else {
data[row + tmpColBase] = -tmpNorm2 * tmpNormInf;
tmpScale += tmpNorm2;
}
tmpVector[row] = PrimitiveMath.ONE;
for (int i = row + 1; i < structure; i++) {
data[i + tmpColBase] = tmpVector[i] /= tmpScale;
}
destination.beta = PrimitiveMath.ABS.invoke(tmpScale) / tmpNorm2;
}
return retVal;
}
public static boolean invoke(final float[] data, final int structure, final int row, final int col, final Householder.Primitive32 destination) {
int tmpColBase = col * structure;
float[] tmpVector = destination.vector;
destination.first = row;
double tmpNormInf = PrimitiveMath.ZERO; // Copy column and calculate its infinity-norm.
for (int i = row; i < structure; i++) {
tmpNormInf = PrimitiveMath.MAX.invoke(tmpNormInf, PrimitiveMath.ABS.invoke(tmpVector[i] = data[i + tmpColBase]));
}
boolean retVal = tmpNormInf != PrimitiveMath.ZERO;
double tmpVal;
double tmpNorm2 = PrimitiveMath.ZERO;
if (retVal) {
for (int i = row + 1; i < structure; i++) {
tmpVal = tmpVector[i] /= tmpNormInf;
tmpNorm2 += tmpVal * tmpVal;
}
retVal = !PrimitiveScalar.isSmall(PrimitiveMath.ONE, tmpNorm2);
}
if (retVal) {
double tmpScale = tmpVector[row] / tmpNormInf;
tmpNorm2 += tmpScale * tmpScale;
tmpNorm2 = PrimitiveMath.SQRT.invoke(tmpNorm2); // 2-norm of the vector to transform (scaled by inf-norm)
if (tmpScale <= PrimitiveMath.ZERO) {
data[row + tmpColBase] = (float) (tmpNorm2 * tmpNormInf);
tmpScale -= tmpNorm2;
} else {
data[row + tmpColBase] = (float) (-tmpNorm2 * tmpNormInf);
tmpScale += tmpNorm2;
}
tmpVector[row] = (float) PrimitiveMath.ONE;
for (int i = row + 1; i < structure; i++) {
data[i + tmpColBase] = tmpVector[i] /= tmpScale;
}
destination.beta = (float) (PrimitiveMath.ABS.invoke(tmpScale) / tmpNorm2);
}
return retVal;
}
public static > boolean invoke(final N[] data, final int structure, final int row, final int col,
final Householder.Generic destination, final Scalar.Factory scalar) {
int tmpColBase = col * structure;
N[] tmpVector = destination.vector;
destination.first = row;
double tmpNormInf = PrimitiveMath.ZERO;
for (int i = row; i < structure; i++) {
tmpNormInf = PrimitiveMath.MAX.invoke(tmpNormInf, (tmpVector[i] = data[i + tmpColBase]).norm());
}
boolean retVal = tmpNormInf != PrimitiveMath.ZERO;
Scalar tmpVal;
double tmpNorm2 = PrimitiveMath.ZERO;
if (retVal) {
for (int i = row + 1; i < structure; i++) {
tmpVal = tmpVector[i].divide(tmpNormInf);
tmpNorm2 += tmpVal.norm() * tmpVal.norm();
tmpVector[i] = tmpVal.get();
}
retVal = !PrimitiveScalar.isSmall(PrimitiveMath.ONE, tmpNorm2);
}
if (retVal) {
Scalar tmpScale = tmpVector[row].divide(tmpNormInf);
tmpNorm2 += tmpScale.norm() * tmpScale.norm();
tmpNorm2 = PrimitiveMath.SQRT.invoke(tmpNorm2);
// data[row + tmpColBase] = ComplexNumber.makePolar(tmpNorm2 * tmpNormInf, tmpScale.phase());
data[row + col * structure] = tmpScale.signum().multiply(tmpNorm2 * tmpNormInf).get();
// tmpScale = tmpScale.subtract(ComplexNumber.makePolar(tmpNorm2, tmpScale.phase()));
tmpScale = tmpScale.subtract(tmpScale.signum().multiply(tmpNorm2)).get();
tmpVector[row] = scalar.one().get();
for (int i = row + 1; i < structure; i++) {
data[i + tmpColBase] = tmpVector[i] = tmpVector[i].divide(tmpScale).get();
}
destination.beta = scalar.cast(tmpScale.norm() / tmpNorm2);
}
return retVal;
}
}