public void AugmentedReducedRowEchelonFormTest()
{
var A = new Matrix(new double[,] { { 1, 2, 3 }, { 0, 1, 4 }, { 5, 6, 0 } });
var I = A.GetIdentity();
var aug = new AugmentedMatrix(new Matrix[] { A, I });
var augGE = aug.ReducedRowEchelonForm();
var identity = new Matrix(new double[,] { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 } });
var inverse = new Matrix(new double[,] { { -24, 18, 5 }, { 20, -15, -4 }, { -5, 4, 1 } });
Assert.That(augGE[0], Is.EqualTo(identity));
Assert.That(augGE[1], Is.EqualTo(inverse));
var B = new Matrix(new double[,] { { 1, 2, 3, 6 }, { 0, 1, 4, 8 }, { 5, 6, 0, 9 }, { 9, 4, 7, 3 } });
I = new Matrix(4, 4).GetIdentity();
var aug2 = new AugmentedMatrix(new Matrix[] { B, I });
var augRref2 = aug2.ReducedRowEchelonForm();
var identity2 = new Matrix(4, 4).GetIdentity();
var inverse2 =
new Matrix(
new double[,]
{
{ -69.0 / 67.0, 36.0 / 67.0, 11.0 / 67.0, 9.0 / 67.0 },
{ 544.0 / 335.0, -69.0 / 67, -44.0 / 335.0, -36.0 / 335.0 },
{ 206.0 / 335.0, -18.0 / 67.0, -61.0 / 335.0, 11.0 / 335.0 },
{ -171.0 / 335.0, 26.0 / 67.0, 36.0 / 335.0, -1.0 / 335.0 }
});
Assert.That(augRref2[0], Is.EqualTo(identity2));
Assert.That(augRref2[1], Is.EqualTo(inverse2));
}
public static Matrix SwapRows(Matrix matrix, int row1, int row2)
{
var identity = matrix.GetIdentity();
identity[row1, row1] = 0;
identity[row1, row2] = 1;
identity[row2, row2] = 0;
identity[row2, row1] = 1;
return(identity * matrix);
}
