* always return that original instance.
   */
  public abstract LinearTransformation inverse();

  private static final class RegularLinearTransformation extends LinearTransformation {

    final double slope;
    final double yIntercept;

    @LazyInit @Nullable LinearTransformation inverse;

    RegularLinearTransformation(double slope, double yIntercept) {
      this.slope = slope;

    double xDelta = 3.4;
    double y = 5.6;
    LinearTransformation transformation = LinearTransformation.mapping(x1, y).and(x1 + xDelta, y);
    assertHorizontalLinearTransformation(transformation, y);
  }

  public void testMappingAnd_vertical() {
    double x = 1.2;
    double y1 = 3.4;
    double yDelta = 5.6;
    LinearTransformation transformation = LinearTransformation.mapping(x, y1).and(x, y1 + yDelta);

    double xDelta = 3.4;
    double y = 5.6;
    LinearTransformation transformation = LinearTransformation.mapping(x1, y).and(x1 + xDelta, y);
    assertHorizontalLinearTransformation(transformation, y);
  }

  public void testMappingAnd_vertical() {
    double x = 1.2;
    double y1 = 3.4;
    double yDelta = 5.6;
    LinearTransformation transformation = LinearTransformation.mapping(x, y1).and(x, y1 + yDelta);