public void PuttingItTogether()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 3, -9, 7, 3 });
a.SetRow(1, new double[] { 3, -8, 2, -9 });
a.SetRow(2, new double[] { -4, 4, 4, 1 });
a.SetRow(3, new double[] { -6, 5, -1, 1 });
var identity = RTF.Matrix.GetIdentity(4, 4);
Assert.Equal(identity, identity.Inverse());
var idInverted = a * a.Inverse();
CustomAssert.Equal(identity, idInverted, 0);
var transposeInvert = a.Transpose().Inverse();
var invertTranspose = a.Inverse().Transpose();
CustomAssert.Equal(transposeInvert, invertTranspose, 5);
var modifiedIdentity = RTF.Matrix.GetIdentity(4, 4);
modifiedIdentity[2, 2] = 6;
var tuple = new double[] { 1, 2, 3, 4 };
var tupleIdentity = identity * tuple;
var newTuple = modifiedIdentity * tuple;
Assert.Equal(tuple, tupleIdentity);
Assert.NotEqual(tuple, newTuple);
}
public void Inverse()
{
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -5, 2, 6, -8 });
e.SetRow(1, new double[] { 1, -5, 1, 8 });
e.SetRow(2, new double[] { 7, 7, -6, -7 });
e.SetRow(3, new double[] { 1, -3, 7, 4 });
double r1 = -160d / 532;
double r2 = 105d / 532;
var b = e.Inverse();
Assert.Equal(532, e.Determinant());
Assert.Equal(-160, RTF.Matrix.Cofactor(e, 2, 3));
Assert.Equal(r1, b[3, 2]);
Assert.Equal(105, RTF.Matrix.Cofactor(e, 3, 2));
Assert.Equal(r2, b[2, 3]);
}
public void Inverse3()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 9, 3, 0, 9 });
a.SetRow(1, new double[] { -5, -2, -6, -3 });
a.SetRow(2, new double[] { -4, 9, 6, 4 });
a.SetRow(3, new double[] { -7, 6, 6, 2 });
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -0.04074, -0.07778, 0.14444, -0.22222 });
e.SetRow(1, new double[] { -0.07778, 0.03333, 0.36667, -0.33333 });
e.SetRow(2, new double[] { -0.02901, -0.14630, -0.10926, 0.12963 });
e.SetRow(3, new double[] { 0.17778, 0.06667, -0.26667, 0.33333 });
var inverse = a.Inverse();
CustomAssert.Equal(e, inverse, 5);
}
public void Inverse2()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 8, -5, 9, 2 });
a.SetRow(1, new double[] { 7, 5, 6, 1 });
a.SetRow(2, new double[] { -6, 0, 9, 6 });
a.SetRow(3, new double[] { -3, 0, -9, -4 });
var e = new RTF.Matrix(4, 4);
e.SetRow(0, new double[] { -0.15385, -0.15385, -0.28205, -0.53846 });
e.SetRow(1, new double[] { -0.07692, 0.12308, 0.02564, 0.03077 });
e.SetRow(2, new double[] { 0.35897, 0.35897, 0.43590, 0.92308 });
e.SetRow(3, new double[] { -0.69231, -0.69231, -0.76923, -1.92308 });
var inverse = a.Inverse();
CustomAssert.Equal(e, inverse, 5);
}
public void MultiplyingProductByInverse()
{
var a = new RTF.Matrix(4, 4);
a.SetRow(0, new double[] { 3, -9, 7, 3 });
a.SetRow(1, new double[] { 3, -8, 2, -9 });
a.SetRow(2, new double[] { -4, 4, 4, 1 });
a.SetRow(3, new double[] { -6, 5, -1, 1 });
var b = new RTF.Matrix(4, 4);
b.SetRow(0, new double[] { 8, 2, 2, 2 });
b.SetRow(1, new double[] { 3, -1, 7, 0 });
b.SetRow(2, new double[] { 7, 0, 5, 4 });
b.SetRow(3, new double[] { 6, -2, 0, 5 });
var c = a * b;
var e = c * b.Inverse();
CustomAssert.Equal(e, a, 0);
}