public void TestCalculatingTheInverseOfAMatrix()
{
var a = new Matrix4x4(
-5, 2, 6, -8,
1, -5, 1, 8,
7, 7, -6, -7,
1, -3, 7, 4);
var b = a.Inverse();
var expected = new Matrix4x4(
0.21805, 0.45113, 0.24060, -0.04511,
-0.80827, -1.45677, -0.44361, 0.52068,
-0.07895, -0.22368, -0.05263, 0.19737,
-0.52256, -0.81391, -0.30075, 0.30639);
Assert.Equal(532, a.Determinant());
Assert.Equal(-160, a.Cofactor(2, 3));
Assert.Equal(-160.0 / 532, b[3, 2]);
Assert.Equal(105, a.Cofactor(3, 2));
Assert.Equal(105.0 / 532, b[2, 3]);
var comparer = Matrix4x4.GetEqualityComparer(0.00001);
Assert.Equal(expected, b, comparer);
}
public static T Determinant <T>(this Matrix4x4 <T> a)
where T : IComparable <T> =>
Operations.Add(
Operations.Add(
Operations.Multiply(a[0, 0], a.Cofactor(0, 0)),
Operations.Multiply(a[0, 1], a.Cofactor(0, 1))),
Operations.Add(
Operations.Multiply(a[0, 2], a.Cofactor(0, 2)),
Operations.Multiply(a[0, 3], a.Cofactor(0, 3))));
public void Inverse()
{
var matrix = new Matrix4x4(
-5, 2, 6, -8,
1, -5, 1, 8,
7, 7, -6, -7,
1, -3, 7, 4);
var inverse = Matrix4x4.Inverse(matrix);
Assert.Equal(532, Matrix4x4.Determinate(matrix));
Assert.Equal(-160, Matrix4x4.Cofactor(matrix, 2, 3));
Assert.Equal(-160 / 532f, inverse[3, 2]);
Assert.Equal(105, Matrix4x4.Cofactor(matrix, 3, 2));
Assert.Equal(105 / 532f, inverse[2, 3]);
var expected = new Matrix4x4(
0.21805f, 0.45113f, 0.24060f, -0.04511f,
-0.80827f, -1.45677f, -0.44361f, 0.52068f,
-0.07895f, -0.22368f, -0.05263f, 0.19737f,
-0.52256f, -0.81391f, -0.30075f, 0.30639f);
Assert.Equal(expected, inverse);
matrix = new Matrix4x4(
8, -5, 9, 2,
7, 5, 6, 1,
-6, 0, 9, 6,
-3, 0, -9, -4);
expected = new Matrix4x4(
-0.15385f, -0.15385f, -0.28205f, -0.53846f,
-0.07692f, 0.12308f, 0.02564f, 0.03077f,
0.35897f, 0.35897f, 0.43590f, 0.92308f,
-0.69231f, -0.69231f, -0.76923f, -1.92308f);
Assert.Equal(expected, Matrix4x4.Inverse(matrix));
matrix = new Matrix4x4(
9, 3, 0, 9,
-5, -2, -6, -3,
-4, 9, 6, 4,
-7, 6, 6, 2);
expected = new Matrix4x4(
-0.04074f, -0.07778f, 0.14444f, -0.22222f,
-0.07778f, 0.03333f, 0.36667f, -0.33333f,
-0.02901f, -0.14630f, -0.10926f, 0.12963f,
0.17778f, 0.06667f, -0.26667f, 0.33333f);
Assert.Equal(expected, Matrix4x4.Inverse(matrix));
}
public void Determinate()
{
var matrix = new Matrix4x4(
-2, -8, 3, 5,
-3, 1, 7, 3,
1, 2, -9, 6,
-6, 7, 7, -9);
Assert.Equal(690, Matrix4x4.Cofactor(matrix, 0, 0));
Assert.Equal(447, Matrix4x4.Cofactor(matrix, 0, 1));
Assert.Equal(210, Matrix4x4.Cofactor(matrix, 0, 2));
Assert.Equal(51, Matrix4x4.Cofactor(matrix, 0, 3));
Assert.Equal(-4071, Matrix4x4.Determinate(matrix));
}
/// <summary>
/// Returns the inverse of the given matrix. Note that it is up to the
/// client to make sure the matrix specified by argument `a` is
/// invertible at all. The `IsInvertible` method is provided for this
/// purpose.
/// </summary>
public static Matrix4x4 Inverse(this Matrix4x4 a)
{
var m = new Matrix4x4(0);
var d = a.Determinant();
for (var i = 0; i < 4; i++)
{
for (var j = 0; j < 4; j++)
{
m[j, i] = a.Cofactor(i, j) / d;
}
}
return(m);
}
public static Matrix4x4 <T> Inverse <T>(this Matrix4x4 <T> a)
where T : IComparable <T>
{
var m = new Matrix4x4 <T>(default(T));
var d = a.Determinant();
for (var i = 0; i < 4; i++)
{
for (var j = 0; j < 4; j++)
{
m[j, i] = Operations.Divide(a.Cofactor(i, j), d);
}
}
return(m);
}
public void Cofactor_should_return_the_minor_of_the_matrix_which_is_the_determinant_of_the_submatrix()
{
var matrix = new Matrix4x4(
3, 5, 0, 4,
2, -1, -7, 9,
6, -1, 5, 2,
3, 7, -4, 6);
matrix.Cofactor(0, 0).Should().Be(-457);
matrix.Cofactor(0, 1).Should().Be(65);
matrix.Cofactor(0, 2).Should().Be(395);
matrix.Cofactor(0, 3).Should().Be(416);
matrix.Cofactor(1, 0).Should().Be(-66);
matrix.Cofactor(1, 1).Should().Be(-42);
matrix.Cofactor(1, 2).Should().Be(30);
matrix.Cofactor(1, 3).Should().Be(102);
matrix.Cofactor(2, 0).Should().Be(182);
matrix.Cofactor(2, 1).Should().Be(-34);
matrix.Cofactor(2, 2).Should().Be(-64);
matrix.Cofactor(2, 3).Should().Be(-94);
}
/// <summary> /// Calculates the determinant of given matrix `a` using Laplace /// expansion. /// </summary> public static double Determinant(this Matrix4x4 a) => (a[0, 0] * a.Cofactor(0, 0)) + (a[0, 1] * a.Cofactor(0, 1)) + (a[0, 2] * a.Cofactor(0, 2)) + (a[0, 3] * a.Cofactor(0, 3));
