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mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/Symmetry.java
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| package org.meeuw.math.abstractalgebra.dihedral; | ||
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| /** | ||
| * @since 0.14 | ||
| */ | ||
| public enum Symmetry { | ||
| /** | ||
| * Rotation | ||
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mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dim2/Matrix2.java
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| /* | ||
| * Copyright 2022 Michiel Meeuwissen | ||
| * | ||
| * Licensed under the Apache License, Version 2.0 (the "License"); | ||
| * you may not use this file except in compliance with the License. | ||
| * You may obtain a copy of the License at | ||
| * | ||
| * https://www.apache.org/licenses/LICENSE-2.0 | ||
| * | ||
| * Unless required by applicable law or agreed to in writing, software | ||
| * distributed under the License is distributed on an "AS IS" BASIS, | ||
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| * See the License for the specific language governing permissions and | ||
| * limitations under the License. | ||
| */ | ||
| package org.meeuw.math.abstractalgebra.dim2; | ||
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| import java.util.Arrays; | ||
| import java.util.stream.Collectors; | ||
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| import org.meeuw.math.*; | ||
| import org.meeuw.math.abstractalgebra.MultiplicativeGroupElement; | ||
| import org.meeuw.math.abstractalgebra.reals.RealNumber; | ||
| import org.meeuw.math.exceptions.DivisionByZeroException; | ||
| import org.meeuw.math.uncertainnumbers.UncertainDouble; | ||
| import org.meeuw.math.validation.Square; | ||
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| import static org.meeuw.math.ArrayUtils.determinant2x2; | ||
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| /** | ||
| * A square 2x2 matrix of {@code double}s | ||
| * <p> | ||
| * Note this does not use {@link UncertainDouble} to back the matrix, but simple 'doubles' | ||
| * This means that rounding errors are not considered, and theory testing may involve some fiddling. | ||
| * | ||
| * @author Michiel Meeuwissen | ||
| * @since 0.14 | ||
| */ | ||
| public strictfp class Matrix2 implements | ||
| MultiplicativeGroupElement<Matrix2>, WithScalarOperations<Matrix2, RealNumber>, WithDoubleOperations<Matrix2> { | ||
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| final double[][] values; | ||
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| public static Matrix2 of( | ||
| double v11, double v12, | ||
| double v21, double v22 | ||
| ) { | ||
| return new Matrix2(new double[][] { | ||
| {v11, v12}, | ||
| {v21, v22} | ||
| }); | ||
| } | ||
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| private static Matrix2 of(@Square(2) double[] value) { | ||
| return of( | ||
| value[0], value[1], | ||
| value[2], value[3] | ||
| ); | ||
| } | ||
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| Matrix2(double[][] values) { | ||
| this.values = values; | ||
| } | ||
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| @Override | ||
| public Matrix2 times(Matrix2 multiplier) { | ||
| return of(timesDouble(multiplier.values)); | ||
| } | ||
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| public Vector2[] asVectors() { | ||
| return new Vector2[] { | ||
| Vector2.of(values[0][0], values[0][1]), | ||
| Vector2.of(values[1][0], values[1][1]) | ||
| }; | ||
| } | ||
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| @Override | ||
| public Matrix2Group getStructure() { | ||
| return Matrix2Group.INSTANCE; | ||
| } | ||
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| double[] timesDouble(@Square(2) double[][] matrix2) { | ||
| double[] result = new double[4]; | ||
| for (int i = 0; i < 2; i++) { | ||
| for (int j = 0; j < 2; j++) { | ||
| double v = 0; | ||
| for (int k = 0; k < 2; k++) { | ||
| v += values[i][k] * matrix2[k][j]; | ||
| } | ||
| result[i * 2 + j] = v; | ||
| } | ||
| } | ||
| return result; | ||
| } | ||
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| double[] timesDouble(double multiplier) { | ||
| double[] result = new double[4]; | ||
| for (int i = 0; i < 2; i++) { | ||
| for (int j = 0; j < 2; j++) { | ||
| result[i * 2 + j] = multiplier * values[i][j]; | ||
| } | ||
| } | ||
| return result; | ||
| } | ||
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| @Override | ||
| public Matrix2 times(double multiplier) { | ||
| return Matrix2.of(timesDouble(multiplier)); | ||
| } | ||
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| @Override | ||
| public Matrix2 dividedBy(double multiplier) { | ||
| return Matrix2.of(timesDouble(1d / multiplier)); | ||
| } | ||
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| @Override | ||
| public Matrix2 times(RealNumber multiplier) { | ||
| return times(multiplier.doubleValue()); | ||
| } | ||
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| @Override | ||
| public Matrix2 dividedBy(RealNumber divisor) { | ||
| if (divisor.isZero()) { | ||
| throw new DivisionByZeroException(this, divisor); | ||
| } | ||
| return dividedBy(divisor.doubleValue()); | ||
| } | ||
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| public double determinant() { | ||
| double a = values[0][0]; | ||
| double b = values[0][1]; | ||
| double c = values[1][0]; | ||
| double d = values[1][1]; | ||
| return determinant2x2(a, b, c, 2); | ||
| } | ||
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| @Override | ||
| // https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html | ||
| public Matrix2 reciprocal() { | ||
| return adjugate().dividedBy(determinant()); | ||
| } | ||
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| public Matrix2 adjugate() { | ||
| return new Matrix2(adjugateMatrix()); | ||
| } | ||
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| double[][] adjugateMatrix() { | ||
| double a = values[0][0]; | ||
| double b = values[0][1]; | ||
| double c = values[1][0]; | ||
| double d = values[1][1]; | ||
| final double[][] adjugate = new double[2][2]; | ||
| adjugate[0][0] = d; | ||
| adjugate[0][1] = -1 * b; | ||
| adjugate[1][0] = -1 * c; | ||
| adjugate[1][1] = a; | ||
| return adjugate; | ||
| } | ||
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| private int skip(int i, int skip) { | ||
| return i < skip ? i : i + 1; | ||
| } | ||
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| @Override | ||
| public boolean equals(Object o) { | ||
| if (this == o) return true; | ||
| if (o == null || getClass() != o.getClass()) return false; | ||
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| Matrix2 matrix3 = (Matrix2) o; | ||
| return getStructure().getEquivalence().test(this, matrix3); | ||
| } | ||
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| @Override | ||
| public int hashCode() { | ||
| return 0; | ||
| } | ||
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| @Override | ||
| public String toString() { | ||
| return "(" + Arrays.stream(asVectors()).map(Vector2::toString).collect(Collectors.joining(", ")) + ")"; | ||
| } | ||
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| @Square(3) | ||
| public double[][] getValues() { | ||
| return Arrays.stream(values).map(double[]::clone).toArray(double[][]::new); | ||
| } | ||
| } |
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