commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/oned/Vector1DTest.java

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You 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
 *
 *      http://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.
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package org.apache.commons.geometry.euclidean.oned;

import java.util.Comparator;
import java.util.regex.Pattern;

import org.apache.commons.geometry.core.Geometry;
import org.apache.commons.geometry.core.GeometryTestUtils;
import org.apache.commons.geometry.core.exception.IllegalNormException;
import org.apache.commons.geometry.core.precision.DoublePrecisionContext;
import org.apache.commons.geometry.core.precision.EpsilonDoublePrecisionContext;
import org.apache.commons.numbers.core.Precision;
import org.junit.Assert;
import org.junit.Test;

public class Vector1DTest {

    private static final double TEST_TOLERANCE = 1e-15;

    @Test
    public void testConstants() {
        // act/assert
        checkVector(Vector1D.ZERO, 0.0);
        checkVector(Vector1D.Unit.PLUS, 1.0);
        checkVector(Vector1D.Unit.MINUS, -1.0);
        checkVector(Vector1D.NaN, Double.NaN);
        checkVector(Vector1D.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);
        checkVector(Vector1D.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
    }

    @Test
    public void testConstants_normalize() {
        // act/assert
        GeometryTestUtils.assertThrows(() -> Vector1D.ZERO.normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NaN.normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.POSITIVE_INFINITY.normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NEGATIVE_INFINITY.normalize(),
                IllegalNormException.class);

        Assert.assertSame(Vector1D.Unit.PLUS.normalize(), Vector1D.Unit.PLUS);
        Assert.assertSame(Vector1D.Unit.MINUS.normalize(), Vector1D.Unit.MINUS);
    }

    @Test
    public void testCoordinateAscendingOrderComparator() {
        // arrange
        Comparator<Vector1D> cmp = Vector1D.COORDINATE_ASCENDING_ORDER;

        // act/assert
        Assert.assertEquals(0, cmp.compare(Vector1D.of(1), Vector1D.of(1)));
        Assert.assertEquals(1, cmp.compare(Vector1D.of(2), Vector1D.of(1)));
        Assert.assertEquals(-1, cmp.compare(Vector1D.of(0), Vector1D.of(1)));

        Assert.assertEquals(0, cmp.compare(Vector1D.of(0), Vector1D.of(0)));
        Assert.assertEquals(1, cmp.compare(Vector1D.of(1e-15), Vector1D.of(0)));
        Assert.assertEquals(-1, cmp.compare(Vector1D.of(-1e-15), Vector1D.of(0)));

        Assert.assertEquals(-1, cmp.compare(Vector1D.of(1), null));
        Assert.assertEquals(1, cmp.compare(null, Vector1D.of(1)));
        Assert.assertEquals(0, cmp.compare(null, null));
    }

    @Test
    public void testCoordinates() {
        // act/assert
        Assert.assertEquals(-1, Vector1D.of(-1).getX(), 0.0);
        Assert.assertEquals(0, Vector1D.of(0).getX(), 0.0);
        Assert.assertEquals(1, Vector1D.of(1).getX(), 0.0);
    }

    @Test
    public void testDimension() {
        // arrange
        Vector1D v = Vector1D.of(2);

        // act/assert
        Assert.assertEquals(1, v.getDimension());
    }

    @Test
    public void testNaN() {
        // act/assert
        Assert.assertTrue(Vector1D.of(Double.NaN).isNaN());

        Assert.assertFalse(Vector1D.of(1).isNaN());
        Assert.assertFalse(Vector1D.of(Double.NEGATIVE_INFINITY).isNaN());
    }

    @Test
    public void testInfinite() {
        // act/assert
        Assert.assertTrue(Vector1D.of(Double.NEGATIVE_INFINITY).isInfinite());
        Assert.assertTrue(Vector1D.of(Double.POSITIVE_INFINITY).isInfinite());

        Assert.assertFalse(Vector1D.of(1).isInfinite());
        Assert.assertFalse(Vector1D.of(Double.NaN).isInfinite());
    }

    @Test
    public void testFinite() {
        // act/assert
        Assert.assertTrue(Vector1D.ZERO.isFinite());
        Assert.assertTrue(Vector1D.of(1).isFinite());

        Assert.assertFalse(Vector1D.of(Double.NEGATIVE_INFINITY).isFinite());
        Assert.assertFalse(Vector1D.of(Double.POSITIVE_INFINITY).isFinite());

        Assert.assertFalse(Vector1D.of(Double.NaN).isFinite());
    }

    @Test
    public void testZero() {
        // act
        Vector1D zero = Vector1D.of(1).getZero();

        // assert
        checkVector(zero, 0.0);
        checkVector(Vector1D.Unit.PLUS.add(zero), 1.0);
    }

    @Test
    public void testNorm() {
        // act/assert
        Assert.assertEquals(0.0, Vector1D.ZERO.norm(), TEST_TOLERANCE);
        Assert.assertEquals(3.0, Vector1D.of(3).norm(), TEST_TOLERANCE);
        Assert.assertEquals(3.0, Vector1D.of(-3).norm(), TEST_TOLERANCE);
    }

    @Test
    public void testNorm_unitVectors() {
        // arrange
        Vector1D v = Vector1D.of(2.0).normalize();

        // act/assert
        Assert.assertEquals(1.0, v.norm(), 0.0);
    }

    @Test
    public void testNormSq() {
        // act/assert
        Assert.assertEquals(0.0, Vector1D.of(0).normSq(), TEST_TOLERANCE);
        Assert.assertEquals(9.0, Vector1D.of(3).normSq(), TEST_TOLERANCE);
        Assert.assertEquals(9.0, Vector1D.of(-3).normSq(), TEST_TOLERANCE);
    }

    @Test
    public void testNormSq_unitVectors() {
        // arrange
        Vector1D v = Vector1D.of(2.0).normalize();

        // act/assert
        Assert.assertEquals(1.0, v.normSq(), 0.0);
    }

    @Test
    public void testWithNorm() {
        // act/assert
        checkVector(Vector1D.Unit.PLUS.withNorm(0.0), 0.0);

        checkVector(Vector1D.of(0.5).withNorm(2.0), 2.0);
        checkVector(Vector1D.of(5).withNorm(3.0), 3.0);

        checkVector(Vector1D.of(-0.5).withNorm(2.0), -2.0);
        checkVector(Vector1D.of(-5).withNorm(3.0), -3.0);
    }

    @Test
    public void testWithNorm_illegalNorm() {
        // act/assert
        GeometryTestUtils.assertThrows(() -> Vector1D.ZERO.withNorm(2.0),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NaN.withNorm(2.0),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.POSITIVE_INFINITY.withNorm(2.0),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NEGATIVE_INFINITY.withNorm(2.0),
                IllegalNormException.class);
    }

    @Test
    public void testWithNorm_unitVectors() {
        // arrange
        Vector1D v = Vector1D.of(2.0).normalize();

        // act/assert
        checkVector(Vector1D.Unit.PLUS.withNorm(2.5), 2.5);
        checkVector(Vector1D.Unit.MINUS.withNorm(3.14), -3.14);

        for (double mag = -10.0; mag <= 10.0; ++mag)
        {
            Assert.assertEquals(Math.abs(mag), v.withNorm(mag).norm(), TEST_TOLERANCE);
        }
    }

    @Test
    public void testAdd() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(3);

        // act/assert
        checkVector(v1.add(v1), 2);
        checkVector(v1.add(v2), -2);
        checkVector(v2.add(v1), -2);
        checkVector(v2.add(v3), 0);
    }

    @Test
    public void testAdd_scaled() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(3);

        // act/assert
        checkVector(v1.add(1, v1), 2);
        checkVector(v1.add(0.5, v1), 1.5);
        checkVector(v1.add(-1, v1), 0);

        checkVector(v1.add(0, v2), 1);
        checkVector(v2.add(3, v1), 0);
        checkVector(v2.add(2, v3), 3);
    }

    @Test
    public void testSubtract() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(3);

        // act/assert
        checkVector(v1.subtract(v1), 0);
        checkVector(v1.subtract(v2), 4);
        checkVector(v2.subtract(v1), -4);
        checkVector(v2.subtract(v3), -6);
    }

    @Test
    public void testSubtract_scaled() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(3);

        // act/assert
        checkVector(v1.subtract(1, v1), 0);
        checkVector(v1.subtract(0.5, v1), 0.5);
        checkVector(v1.subtract(-1, v1), 2);

        checkVector(v1.subtract(0, v2), 1);
        checkVector(v2.subtract(3, v1), -6);
        checkVector(v2.subtract(2, v3), -9);
    }

    @Test
    public void testNormalize() {
        // act/assert
        checkVector(Vector1D.of(1).normalize(), 1);
        checkVector(Vector1D.of(-1).normalize(), -1);
        checkVector(Vector1D.of(5).normalize(), 1);
        checkVector(Vector1D.of(-5).normalize(), -1);
    }

    @Test
    public void testNormalize_illegalNorm() {
        // act/assert
        GeometryTestUtils.assertThrows(() -> Vector1D.of(0.0).normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.of(Double.NaN).normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.of(Double.POSITIVE_INFINITY).normalize(),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.of(Double.NEGATIVE_INFINITY).normalize(),
                IllegalNormException.class);
    }

    @Test
    public void testNormalize_isIdempotent() {
        // arrange
        Vector1D v = Vector1D.of(2).normalize();

        // act/assert
        Assert.assertSame(v, v.normalize());
        checkVector(v.normalize(), 1.0);
    }

    @Test
    public void testNegate() {
        // act/assert
        checkVector(Vector1D.of(0.1).negate(), -0.1);
        checkVector(Vector1D.of(-0.1).negate(), 0.1);
    }

    @Test
    public void testNegate_unitVectors() {
        // arrange
        Vector1D v1 = Vector1D.of(0.1).normalize();
        Vector1D v2 = Vector1D.of(-0.1).normalize();

        // act/assert
        checkVector(v1.negate(), -1);
        checkVector(v2.negate(), 1);
    }

    @Test
    public void testScalarMultiply() {
        // act/assert
        checkVector(Vector1D.of(1).multiply(3), 3);
        checkVector(Vector1D.of(1).multiply(-3), -3);

        checkVector(Vector1D.of(1.5).multiply(7), 10.5);
        checkVector(Vector1D.of(-1.5).multiply(7), -10.5);
    }

    @Test
    public void testDistance() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-4);

        // act/assert
        Assert.assertEquals(0.0, v1.distance(v1), TEST_TOLERANCE);

        Assert.assertEquals(5.0, v1.distance(v2), TEST_TOLERANCE);
        Assert.assertEquals(5.0, v2.distance(v1), TEST_TOLERANCE);
        Assert.assertEquals(v1.subtract(v2).norm(), v1.distance(v2), TEST_TOLERANCE);

        Assert.assertEquals(0.0, Vector1D.of(-1).distance(Vector1D.of(-1)), TEST_TOLERANCE);
    }

    @Test
    public void testDistanceSq() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-4);

        // act/assert
        Assert.assertEquals(0.0, Vector1D.of(-1).distanceSq(Vector1D.of(-1)), TEST_TOLERANCE);
        Assert.assertEquals(25.0, v1.distanceSq(v2), TEST_TOLERANCE);
        Assert.assertEquals(25.0, v2.distanceSq(v1), TEST_TOLERANCE);
    }

    @Test
    public void testDotProduct() {
        // arrange
        Vector1D v1 = Vector1D.of(2);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(3);

        // act/assert
        Assert.assertEquals(-6.0, v1.dot(v2), TEST_TOLERANCE);
        Assert.assertEquals(-6.0, v2.dot(v1), TEST_TOLERANCE);

        Assert.assertEquals(6.0, v1.dot(v3), TEST_TOLERANCE);
        Assert.assertEquals(6.0, v3.dot(v1), TEST_TOLERANCE);
    }

    @Test
    public void testAngle() {
        // arrange
        Vector1D v1 = Vector1D.of(2);
        Vector1D v2 = Vector1D.of(-3);
        Vector1D v3 = Vector1D.of(4);
        Vector1D v4 = Vector1D.of(-5);

        // act/assert
        Assert.assertEquals(0.0, v1.angle(v1), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v1.angle(v2), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v1.angle(v3), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v1.angle(v4), TEST_TOLERANCE);

        Assert.assertEquals(Geometry.PI, v2.angle(v1), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v2.angle(v2), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v2.angle(v3), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v2.angle(v4), TEST_TOLERANCE);

        Assert.assertEquals(0.0, v3.angle(v1), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v3.angle(v2), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v3.angle(v3), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v3.angle(v4), TEST_TOLERANCE);

        Assert.assertEquals(Geometry.PI, v4.angle(v1), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v4.angle(v2), TEST_TOLERANCE);
        Assert.assertEquals(Geometry.PI, v4.angle(v3), TEST_TOLERANCE);
        Assert.assertEquals(0.0, v4.angle(v4), TEST_TOLERANCE);
    }

    @Test
    public void testAngle_illegalNorm() {
        // arrange
        Vector1D v = Vector1D.of(1.0);

        // act/assert
        GeometryTestUtils.assertThrows(() -> Vector1D.ZERO.angle(v),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NaN.angle(v),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.POSITIVE_INFINITY.angle(v),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NEGATIVE_INFINITY.angle(v),
                IllegalNormException.class);

        GeometryTestUtils.assertThrows(() -> v.angle(Vector1D.ZERO),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.angle(Vector1D.NaN),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.angle(Vector1D.POSITIVE_INFINITY),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.angle(Vector1D.NEGATIVE_INFINITY),
                IllegalNormException.class);
    }

    @Test
    public void testVectorTo() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-4);
        Vector1D v3 = Vector1D.of(10);

        // act/assert
        checkVector(v1.vectorTo(v1), 0.0);
        checkVector(v2.vectorTo(v2), 0.0);
        checkVector(v3.vectorTo(v3), 0.0);

        checkVector(v1.vectorTo(v2), -5.0);
        checkVector(v2.vectorTo(v1), 5.0);

        checkVector(v1.vectorTo(v3), 9.0);
        checkVector(v3.vectorTo(v1), -9.0);

        checkVector(v2.vectorTo(v3), 14.0);
        checkVector(v3.vectorTo(v2), -14.0);
    }

    @Test
    public void testDirectionTo() {
        // act/assert
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(5);
        Vector1D v3 = Vector1D.of(-2);

        // act/assert
        checkVector(v1.directionTo(v2), 1);
        checkVector(v2.directionTo(v1), -1);

        checkVector(v1.directionTo(v3), -1);
        checkVector(v3.directionTo(v1), 1);
    }

    @Test
    public void testDirectionTo_illegalNorm() {
        // arrange
        Vector1D v = Vector1D.of(2);

        // act/assert
        GeometryTestUtils.assertThrows(() -> Vector1D.ZERO.directionTo(Vector1D.ZERO),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.directionTo(v),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.directionTo(Vector1D.NaN),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.NEGATIVE_INFINITY.directionTo(v),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> v.directionTo(Vector1D.POSITIVE_INFINITY),
                IllegalNormException.class);
    }

    @Test
    public void testLerp() {
        // arrange
        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-4);
        Vector1D v3 = Vector1D.of(10);

        // act/assert
        checkVector(v1.lerp(v1, 0), 1);
        checkVector(v1.lerp(v1, 1), 1);

        checkVector(v1.lerp(v2, -0.25), 2.25);
        checkVector(v1.lerp(v2, 0), 1);
        checkVector(v1.lerp(v2, 0.25), -0.25);
        checkVector(v1.lerp(v2, 0.5), -1.5);
        checkVector(v1.lerp(v2, 0.75), -2.75);
        checkVector(v1.lerp(v2, 1), -4);
        checkVector(v1.lerp(v2, 1.25), -5.25);

        checkVector(v1.lerp(v3, 0), 1);
        checkVector(v1.lerp(v3, 0.25), 3.25);
        checkVector(v1.lerp(v3, 0.5), 5.5);
        checkVector(v1.lerp(v3, 0.75), 7.75);
        checkVector(v1.lerp(v3, 1), 10);
    }

    @Test
    public void testTransform() {
        // arrange
        AffineTransformMatrix1D transform = AffineTransformMatrix1D.identity()
                .scale(2)
                .translate(1);

        Vector1D v1 = Vector1D.of(1);
        Vector1D v2 = Vector1D.of(-4);

        // act/assert
        checkVector(v1.transform(transform), 3);
        checkVector(v2.transform(transform), -7);
    }

    @Test
    public void testPrecisionEquals() {
        // arrange
        DoublePrecisionContext smallEps = new EpsilonDoublePrecisionContext(1e-6);
        DoublePrecisionContext largeEps = new EpsilonDoublePrecisionContext(1e-1);

        Vector1D vec = Vector1D.of(1);

        // act/assert
        Assert.assertTrue(vec.eq(vec, smallEps));
        Assert.assertTrue(vec.eq(vec, largeEps));

        Assert.assertTrue(vec.eq(Vector1D.of(1.0000007), smallEps));
        Assert.assertTrue(vec.eq(Vector1D.of(1.0000007), largeEps));

        Assert.assertFalse(vec.eq(Vector1D.of(1.004), smallEps));
        Assert.assertTrue(vec.eq(Vector1D.of(1.004), largeEps));

        Assert.assertFalse(vec.eq(Vector1D.of(2), smallEps));
        Assert.assertFalse(vec.eq(Vector1D.of(-2), largeEps));
    }

    @Test
    public void testIsZero() {
        // arrange
        DoublePrecisionContext smallEps = new EpsilonDoublePrecisionContext(1e-6);
        DoublePrecisionContext largeEps = new EpsilonDoublePrecisionContext(1e-1);

        // act/assert
        Assert.assertTrue(Vector1D.of(0.0).isZero(smallEps));
        Assert.assertTrue(Vector1D.of(-0.0).isZero(largeEps));

        Assert.assertTrue(Vector1D.of(1e-7).isZero(smallEps));
        Assert.assertTrue(Vector1D.of(-1e-7).isZero(largeEps));

        Assert.assertFalse(Vector1D.of(1e-2).isZero(smallEps));
        Assert.assertTrue(Vector1D.of(-1e-2).isZero(largeEps));

        Assert.assertFalse(Vector1D.of(0.2).isZero(smallEps));
        Assert.assertFalse(Vector1D.of(-0.2).isZero(largeEps));
    }

    @Test
    public void testHashCode() {
        // arrange
        Vector1D u = Vector1D.of(1);
        Vector1D v = Vector1D.of(1 + 10 * Precision.EPSILON);
        Vector1D w = Vector1D.of(1);

        // act/assert
        Assert.assertTrue(u.hashCode() != v.hashCode());
        Assert.assertEquals(u.hashCode(), w.hashCode());

        Assert.assertEquals(Vector1D.of(Double.NaN).hashCode(), Vector1D.NaN.hashCode());
        Assert.assertEquals(Vector1D.of(Double.NaN).hashCode(), Vector1D.of(Double.NaN).hashCode());
    }

    @Test
    public void testEquals() {
        // arrange
        Vector1D u1 = Vector1D.of(1);
        Vector1D u2 = Vector1D.of(1);

        // act/assert
        Assert.assertFalse(u1.equals(null));
        Assert.assertFalse(u1.equals(new Object()));

        Assert.assertTrue(u1.equals(u1));
        Assert.assertTrue(u1.equals(u2));

        Assert.assertFalse(u1.equals(Vector1D.of(-1)));
        Assert.assertFalse(u1.equals(Vector1D.of(1 + 10 * Precision.EPSILON)));

        Assert.assertTrue(Vector1D.of(Double.NaN).equals(Vector1D.of(Double.NaN)));
        Assert.assertTrue(Vector1D.of(Double.POSITIVE_INFINITY).equals(Vector1D.of(Double.POSITIVE_INFINITY)));
        Assert.assertTrue(Vector1D.of(Double.NEGATIVE_INFINITY).equals(Vector1D.of(Double.NEGATIVE_INFINITY)));
    }

    @Test
    public void testToString() {
        // arrange
        Vector1D v = Vector1D.of(3);
        Pattern pattern = Pattern.compile("\\(3.{0,2}\\)");

        // act
        String str = v.toString();

        // assert
        Assert.assertTrue("Expected string " + str + " to match regex " + pattern,
                    pattern.matcher(str).matches());
    }

    @Test
    public void testParse() {
        // act/assert
        checkVector(Vector1D.parse("(1)"), 1);
        checkVector(Vector1D.parse("(-1)"), -1);

        checkVector(Vector1D.parse("(0.01)"), 1e-2);
        checkVector(Vector1D.parse("(-1e-3)"), -1e-3);

        checkVector(Vector1D.parse("(NaN)"), Double.NaN);

        checkVector(Vector1D.parse(Vector1D.ZERO.toString()), 0);
        checkVector(Vector1D.parse(Vector1D.Unit.PLUS.toString()), 1);
    }

    @Test(expected = IllegalArgumentException.class)
    public void testParse_failure() {
        // act/assert
        Vector1D.parse("abc");
    }

    @Test
    public void testOf() {
        // act/assert
        checkVector(Vector1D.of(0), 0.0);
        checkVector(Vector1D.of(-1), -1.0);
        checkVector(Vector1D.of(1), 1.0);
        checkVector(Vector1D.of(Math.PI), Math.PI);
        checkVector(Vector1D.of(Double.NaN), Double.NaN);
        checkVector(Vector1D.of(Double.NEGATIVE_INFINITY), Double.NEGATIVE_INFINITY);
        checkVector(Vector1D.of(Double.POSITIVE_INFINITY), Double.POSITIVE_INFINITY);
    }

    @Test
    public void testNormalize_static() {
        // act/assert
        checkVector(Vector1D.Unit.from(2.0), 1);
        checkVector(Vector1D.Unit.from(-4.0), -1);
    }

    @Test
    public void testNormalize_static_illegalNorm() {
        GeometryTestUtils.assertThrows(() -> Vector1D.Unit.from(0.0),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.Unit.from(Double.NaN),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.Unit.from(Double.NEGATIVE_INFINITY),
                IllegalNormException.class);
        GeometryTestUtils.assertThrows(() -> Vector1D.Unit.from(Double.POSITIVE_INFINITY),
                IllegalNormException.class);
    }

    @Test
    public void testLinearCombination() {
        // act/assert
        checkVector(Vector1D.linearCombination(2, Vector1D.of(3)), 6);
        checkVector(Vector1D.linearCombination(-2, Vector1D.of(3)), -6);
    }

    @Test
    public void testLinearCombination2() {
        // act/assert
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                5, Vector1D.of(7)), 41);
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                -5, Vector1D.of(7)),-29);
    }

    @Test
    public void testLinearCombination3() {
        // act/assert
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                5, Vector1D.of(7),
                11, Vector1D.of(13)), 184);
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                5, Vector1D.of(7),
                -11, Vector1D.of(13)), -102);
    }

    @Test
    public void testLinearCombination4() {
        // act/assert
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                5, Vector1D.of(7),
                11, Vector1D.of(13),
                17, Vector1D.of(19)), 507);
        checkVector(Vector1D.linearCombination(
                2, Vector1D.of(3),
                5, Vector1D.of(7),
                11, Vector1D.of(13),
                -17, Vector1D.of(19)), -139);
    }

    @Test
    public void testUnitFactoryOptimization() {
        // An already normalized vector will avoid unnecessary creation.
        final Vector1D v = Vector1D.of(3).normalize();
        Assert.assertSame(v, v.normalize());
    }

    private void checkVector(Vector1D v, double x) {
        Assert.assertEquals(x, v.getX(), TEST_TOLERANCE);
    }
}