public void Test_Multiply_Matrix_RectangularMatrix()
{
double[,] lhs =
{
{ +88.409999999999997, -88.043999999999997 },
{ +91.227000000000004, -53.043999999999997 },
{ +15.042000000000000, -29.367999999999999 },
};
double[,] rhs =
{
{ +64.239000000000004, -91.394999999999996, +29.823000000000000, +29.548999999999999 },
{ -96.918999999999997, -66.201999999999998, +46.344000000000001, -09.815000000000000 },
};
double[,] expected =
{
{ 14212.50642600000, -02251.54306200000, -01443.65970600000, +03476.57895000000 },
{ 11001.30268900000, -04826.07277700000, +00262.39168500000, +03216.29348300000 },
{ 03812.60023000000, +00569.45674600000, -00912.43302600000, +00732.72297800000 },
};
double[,] actual = ArrayMatrixUtils.Multiply(lhs, rhs);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_SVD_Rectangular_Matrix()
{
double[,] A =
{
{ 79.2200, 03.5700 },
{ 95.9500, 84.9100 },
{ 65.5700, 93.4000 },
};
double[,] expected_U =
{
{ -0.343225213778742, +0.878072041895140, +0.333445560577190 },
{ -0.710225885367531, -0.010313122653119, -0.703898310308420 },
{ -0.614634561654683, -0.478417316516910, +0.627169217098794 },
};
double[,] expected_S =
{
{ 180.3990135626532, 000.0000000000000 },
{ 000.0000000000000, 056.4255678360587 },
{ 000.0000000000000, 000.0000000000000 },
};
double[,] expected_Vt =
{
{ -0.751878076634585, -0.659302174936711 },
{ +0.659302174936711, -0.751878076634585 },
};
double[,] actual_U, actual_S, actual_Vt;
ArrayMatrixUtils.SVD(A, out actual_U, out actual_S, out actual_Vt);
Assert.That(actual_U, Is.EqualTo(expected_U).Within(precision));
Assert.That(actual_S, Is.EqualTo(expected_S).Within(precision));
Assert.That(actual_Vt, Is.EqualTo(expected_Vt).Within(precision));
}
private Matrix4x4 ComputeTransform(double[,] A, double[] b)
{
double[,] Aplus = ArrayMatrixUtils.MoorePenroseInverse(A);
double[] xOpt = ArrayMatrixUtils.Multiply(Aplus, b);
return(TransformationMatrixFromXOpt(xOpt));
}
public void Test_ToDiagonalMatrix_NonSquareOutput_InvalidNumCols_Helper()
{
double[] diagonal = new double[] { 1, 2, 3 };
int numRows = 3;
int numCols = 2;
ArrayMatrixUtils.ToDiagonalMatrix(diagonal, numRows, numCols);
}
public void Test_MatrixToVector_InvalidSize_Helper()
{
double[,] matrix =
{
{ 1, 2, 3 },
{ 1, 2, 3 }
};
ArrayMatrixUtils.ToVector(matrix);
}
public void Test_InfinityNorm_Vector()
{
double[] vector = { -1, -7 };
double expected = 7;
double actual = ArrayMatrixUtils.InfinityNorm(vector);
Assert.That(actual, Is.EqualTo(expected));
}
public void Test_MatrixToVector_RowMatrix()
{
double[,] matrix =
{
{ 1, 2, 3 }
};
double[] expected = { 1, 2, 3 };
double[] actual = ArrayMatrixUtils.ToVector(matrix);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_RowVectorToMatrix()
{
double[] vector = { 1, 2, 3 };
double[,] expected =
{
{ 1, 2, 3 }
};
double[,] actual = ArrayMatrixUtils.RowVectorToMatrix(vector);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_Multiply_Matrix_IncompatibleSize_Helper()
{
double[,] lhs =
{
{ -26.303000000000001, +56.045000000000002 },
{ +25.123999999999999, -83.775000000000006 },
};
double[,] rhs =
{
{ 85.876999999999995, -02.642000000000000 },
};
ArrayMatrixUtils.Multiply(lhs, rhs);
}
public void Test_InfinityNorm_Matrix()
{
double[,] matrix =
{
{ +1, -7 },
{ -2, -3 }
};
double expected = 8;
double actual = ArrayMatrixUtils.InfinityNorm(matrix);
Assert.That(actual, Is.EqualTo(expected));
}
public void Test_ToDiagonalMatrix()
{
double[] diagonal = new double[] { 1, 2, 3 };
double[,] expected = new double[, ] {
{ 1, 0, 0 },
{ 0, 2, 0 },
{ 0, 0, 3 },
};
double[,] actual = ArrayMatrixUtils.ToDiagonalMatrix(diagonal);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_Multiply_Vector_IncompatibleSize_Helper()
{
double[,] lhs =
{
{ -1.064000000000000, +0.215000000000000 },
{ -3.873000000000000, +6.353000000000000 },
{ +0.170000000000000, +5.897000000000000 },
};
double[] rhs =
{
+2.886000000000000, -2.428000000000000, -13.827296000000000
};
ArrayMatrixUtils.Multiply(lhs, rhs);
}
public void Test_GetDiagonal_SquareMatrix()
{
double[,] matrix =
{
{ +1, -7, +0 },
{ -2, -3, -8 },
{ -2, -3, +9 }
};
double[] expected = { +1, -3, +9 };
double[] actual = ArrayMatrixUtils.GetDiagonal(matrix);
Assert.That(actual, Is.EqualTo(expected));
}
public void Test_ToDiagonalMatrix_NonSquareOutput()
{
double[] diagonal = new double[] { 1, 2, 3 };
int numRows = 4;
int numCols = 3;
double[,] expected = new double[, ] {
{ 1, 0, 0 },
{ 0, 2, 0 },
{ 0, 0, 3 },
{ 0, 0, 0 },
};
double[,] actual = ArrayMatrixUtils.ToDiagonalMatrix(diagonal, numRows, numCols);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_MoorePenroseInverse_SquareMatrix()
{
double[,] array =
{
{ -6.040000000000000, +4.880000000000000 },
{ -9.390000000000001, +0.000000000000001 },
};
double[,] expected =
{
{ +0.000000000000000, -0.106496272630458 },
{ +0.204918032786885, -0.131810960386878 },
};
double[,] actual = ArrayMatrixUtils.MoorePenroseInverse(array);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_MoorePenroseInverse_RectangularMatrix()
{
double[,] array =
{
{ +5.5800, +7.8200 },
{ +4.3000, -3.3200 },
{ +8.0700, +3.9700 },
};
double[,] expected =
{
{ +0.0017, +0.0921, +0.0737 },
{ +0.0878, -0.1020, -0.0063 },
};
double[,] actual = ArrayMatrixUtils.MoorePenroseInverse(array);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_PseudoInverseOfDiagonalMatrix_RectangularMatrix2_WithTolerance()
{
double[,] matrix =
{
{ 0.1, 0.0 },
{ 0.0, 5.0 },
};
double tolerance = 0.2;
double[,] expected =
{
{ 0.0, 0.0 },
{ 0.0, 0.2 },
};
double[,] actual = ArrayMatrixUtils.PseudoInverseOfDiagonalMatrix(matrix, tolerance);
Assert.That(actual, Is.EqualTo(expected));
}
public void Test_Transpose_Rectangular_Matrix()
{
double[,] matrix =
{
{ +56.049999999999997, -19.218000000000000 },
{ -22.052000000000000, -80.709000000000003 },
{ -51.661999999999999, -73.605000000000004 },
};
double[,] expected =
{
{ +56.049999999999997, -22.052000000000000, -51.661999999999999 },
{ -19.218000000000000, -80.709000000000003, -73.605000000000004 },
};
double[,] actual = ArrayMatrixUtils.Transpose(matrix);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_Transpose_Square_Matrix()
{
double[,] matrix =
{
{ -90.069000000000003, -01.827000000000000, +80.010999999999996 },
{ +80.543000000000006, -02.149000000000000, -26.151000000000000 },
{ +88.956999999999994, -32.456000000000003, -77.759000000000000 },
};
double[,] expected =
{
{ -90.069000000000003, +80.543000000000006, +88.956999999999994 },
{ -01.827000000000000, -02.149000000000000, -32.456000000000003 },
{ +80.010999999999996, -26.151000000000000, -77.759000000000000 },
};
double[,] actual = ArrayMatrixUtils.Transpose(matrix);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_PseudoInverseOfDiagonalMatrix_SquareMatrix_WithTolerance()
{
double[,] matrix =
{
{ 1.0, 0.0, 0.0 },
{ 0.0, 0.5, 0.0 },
{ 0.0, 0.0, 0.1 },
};
double tolerance = 0.2;
double[,] expected =
{
{ 1.0, 0.0, 0.0 },
{ 0.0, 2.0, 0.0 },
{ 0.0, 0.0, 0.0 },
};
double[,] actual = ArrayMatrixUtils.PseudoInverseOfDiagonalMatrix(matrix, tolerance);
Assert.That(actual, Is.EqualTo(expected));
}
public void Test_Multiply_Matrix_Vector()
{
double[,] lhs =
{
{ -1.064000000000000, +0.215000000000000 },
{ -3.873000000000000, +6.353000000000000 },
{ +0.170000000000000, +5.897000000000000 },
};
double[] rhs =
{
+2.886000000000000, -2.428000000000000
};
double[] expected =
{
-03.592724000000000, -26.602561999999999, -13.827296000000000,
};
double[] actual = ArrayMatrixUtils.Multiply(lhs, rhs);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_Multiply_Matrix_SquareMatrix()
{
double[,] lhs =
{
{ -26.303000000000001, +56.045000000000002 },
{ +25.123999999999999, -83.775000000000006 },
};
double[,] rhs =
{
{ 85.876999999999995, -02.642000000000000 },
{ 55.143000000000001, -12.827999999999999 },
};
double[,] expected =
{
{ +0831.666704000000, -0649.452734000000 },
{ -2462.031077000001, +1008.288092000000 },
};
double[,] actual = ArrayMatrixUtils.Multiply(lhs, rhs);
Assert.That(actual, Is.EqualTo(expected).Within(precision));
}
public void Test_SVD_Square_Matrix()
{
double[,] A =
{
{ -29.809999999999999, -84.807000000000002, -63.218000000000004 },
{ +02.650000000000000, -52.017000000000003, -52.009000000000000 },
{ -19.638000000000002, -75.335999999999999, -16.547000000000001 },
};
double[,] expected_U =
{
{ -0.729908087739305, -0.123505763730895, -0.672294957424195 },
{ -0.465764528149259, -0.630004873055934, +0.621415532670109 },
{ -0.500297499264836, +0.766707366764547, +0.402321048390866 },
};
double[,] expected_S =
{
{ 149.7913869700865, 000.0000000000000, 000.0000000000000 },
{ 000.0000000000000, 034.0373717936407, 000.0000000000000 },
{ 000.0000000000000, 000.0000000000000, 015.2993660966482 },
};
double[,] expected_Vt =
{
{ +0.202609288827379, +0.826612287707770, +0.525034857786977 },
{ -0.383237737754462, -0.426459172115321, +0.819305444190112 },
{ +0.901153878336938, -0.367212064520276, +0.230384433564968 },
};
double[,] actual_U, actual_S, actual_Vt;
ArrayMatrixUtils.SVD(A, out actual_U, out actual_S, out actual_Vt);
Assert.That(actual_U, Is.EqualTo(expected_U).Within(precision));
Assert.That(actual_S, Is.EqualTo(expected_S).Within(precision));
Assert.That(actual_Vt, Is.EqualTo(expected_Vt).Within(precision));
}