public void CanSolveForVectorWithTallRandomMatrix()
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(20, 10);
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.GramSchmidt();
var vectorB = MatrixLoader.GenerateRandomDenseVector(20);
var vectorX = factorQR.Solve(vectorB);
// The solution x dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, vectorX.Count);
var test = (matrixA.Transpose() * matrixA).Inverse() * matrixA.Transpose() * vectorB;
for (var i = 0; i < vectorX.Count; i++)
{
AssertHelpers.AlmostEqualAbsolute(test[i], vectorX[i], 12);
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
}
public void CanSolveForMatrixWithTallRandomMatrix()
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(20, 10);
var matrixACopy = matrixA.Clone();
var factorQR = matrixA.GramSchmidt();
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(20, 5);
var matrixX = factorQR.Solve(matrixB);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var test = (matrixA.Transpose() * matrixA).Inverse() * matrixA.Transpose() * matrixB;
for (var i = 0; i < matrixX.RowCount; i++)
{
for (var j = 0; j < matrixX.ColumnCount; j++)
{
AssertHelpers.AlmostEqualAbsolute(test[i, j], matrixX[i, j], 12);
}
}
// Make sure A didn't change.
for (var i = 0; i < matrixA.RowCount; i++)
{
for (var j = 0; j < matrixA.ColumnCount; j++)
{
Assert.AreEqual(matrixACopy[i, j], matrixA[i, j]);
}
}
}
