mathnet-numerics/src/UnitTests/LinearAlgebraTests/Double/Factorization/LUTests.cs

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namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
{
    using System.Collections.Generic;
    using MbUnit.Framework;
    using LinearAlgebra.Double;
    using LinearAlgebra.Double.Factorization;

    public class LUTests
    {
        [Test]
        [Row(1)]
        [Row(10)]
        [Row(100)]
        public void CanFactorizeIdentity(int order)
        {
            var I = DenseMatrix.Identity(order);
            var lu = I.LU();

            // Check lower triangular part.
            var L = lu.L;
            Assert.AreEqual(I.RowCount, L.RowCount);
            Assert.AreEqual(I.ColumnCount, L.ColumnCount);
            for (var i = 0; i < L.RowCount; i++)
            {
                for (var j = 0; j < L.ColumnCount; j++)
                {
                    if (i == j)
                    {
                        Assert.AreEqual(1.0, L[i, j]);
                    }
                    else
                    {
                        Assert.AreEqual(0.0, L[i, j]);
                    }
                }
            }

            // Check upper triangular part.
            var U = lu.U;
            Assert.AreEqual(I.RowCount, U.RowCount);
            Assert.AreEqual(I.ColumnCount, U.ColumnCount);
            for (var i = 0; i < U.RowCount; i++)
            {
                for (var j = 0; j < U.ColumnCount; j++)
                {
                    if (i == j)
                    {
                        Assert.AreEqual(1.0, U[i, j]);
                    }
                    else
                    {
                        Assert.AreEqual(0.0, U[i, j]);
                    }
                }
            }
        }

        [Test]
        [Row(3,5)]
        [Row(5,3)]
        [ExpectedArgumentException]
        public void LUFailsWithNonSquareMatrix(int row, int col)
        {
            var I = new DenseMatrix(row, col);
            var lu = I.LU();
        }

        [Test]
        [Row(1)]
        [Row(10)]
        [Row(100)]
        public void IdentityDeterminantIsOne(int order)
        {
            var I = DenseMatrix.Identity(order);
            var lu = I.LU();
            Assert.AreEqual(1.0, lu.Determinant);
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(5)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanFactorizeRandomMatrix(int order)
        {
            var X = MatrixLoader.GenerateRandomMatrix(order, order);
            var lu = X.LU();
            var L = lu.L;
            var U = lu.U;

            // Make sure the factors have the right dimensions.
            Assert.AreEqual(order, L.RowCount);
            Assert.AreEqual(order, L.ColumnCount);
            Assert.AreEqual(order, U.RowCount);
            Assert.AreEqual(order, U.ColumnCount);

            // Make sure the L factor is lower triangular.
            for (int i = 0; i < L.RowCount; i++) 
            {
                Assert.AreEqual(1.0, L[i, i]);
                for (int j = i+1; j < L.ColumnCount; j++)
                {
                    Assert.AreEqual(0.0, L[i, j]);
                }
            }

            // Make sure the U factor is upper triangular.
            for (int i = 0; i < L.RowCount; i++)
            {
                for (int j = 0; j < i; j++)
                {
                    Assert.AreEqual(0.0, U[i, j]);
                }
            }

            // Make sure the cholesky factor times it's transpose is the original matrix.
            var XfromLU = L * U;
            lu.Pivot(XfromLU);
            for (int i = 0; i < XfromLU.RowCount; i++) 
            {
                for (int j = 0; j < XfromLU.ColumnCount; j++)
                {
                    Assert.AreApproximatelyEqual(X[i, j], XfromLU[i, j], 1.0e-11);
                }
            }
        }

        /*[Test]
        [Row(1)]
        [Row(2)]
        [Row(5)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomVector(int order)
        {
            var A = MatrixLoader.GenerateRandomPositiveDefiniteMatrix(order);
            var ACopy = A.Clone();
            var chol = A.Cholesky();
            var b = MatrixLoader.GenerateRandomVector(order);
            var x = chol.Solve(b);

            Assert.AreEqual(b.Count, x.Count);

            var bReconstruct = A * x;

            // Check the reconstruction.
            for (int i = 0; i < order; i++)
            {
                Assert.AreApproximatelyEqual(b[i], bReconstruct[i], 1.0e-11);
            }

            // Make sure A didn't change.
            for (int i = 0; i < A.RowCount; i++)
            {
                for (int j = 0; j < A.ColumnCount; j++)
                {
                    Assert.AreEqual(ACopy[i, j], A[i, j]);
                }
            }
        }

        [Test]
        [Row(1,1)]
        [Row(2,4)]
        [Row(5,8)]
        [Row(10,3)]
        [Row(50,10)]
        [Row(100,100)]
        [MultipleAsserts]
        public void CanSolveForRandomMatrix(int row, int col)
        {
            var A = MatrixLoader.GenerateRandomPositiveDefiniteMatrix(row);
            var ACopy = A.Clone();
            var chol = A.Cholesky();
            var B = MatrixLoader.GenerateRandomMatrix(row, col);
            var X = chol.Solve(B);

            Assert.AreEqual(B.RowCount, X.RowCount);
            Assert.AreEqual(B.ColumnCount, X.ColumnCount);

            var BReconstruct = A * X;

            // Check the reconstruction.
            for (int i = 0; i < B.RowCount; i++)
            {
                for (int j = 0; j < B.ColumnCount; j++)
                {
                    Assert.AreApproximatelyEqual(B[i, j], BReconstruct[i, j], 1.0e-11);
                }
            }

            // Make sure A didn't change.
            for (int i = 0; i < A.RowCount; i++)
            {
                for (int j = 0; j < A.ColumnCount; j++)
                {
                    Assert.AreEqual(ACopy[i, j], A[i, j]);
                }
            }
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(5)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
        {
            var A = MatrixLoader.GenerateRandomPositiveDefiniteMatrix(order);
            var ACopy = A.Clone();
            var chol = A.Cholesky();
            var b = MatrixLoader.GenerateRandomVector(order);
            var bCopy = b.Clone();
            var x = new DenseVector(order);
            chol.Solve(b, x);

            Assert.AreEqual(b.Count, x.Count);

            var bReconstruct = A * x;

            // Check the reconstruction.
            for (int i = 0; i < order; i++)
            {
                Assert.AreApproximatelyEqual(b[i], bReconstruct[i], 1.0e-11);
            }

            // Make sure A didn't change.
            for (int i = 0; i < A.RowCount; i++)
            {
                for (int j = 0; j < A.ColumnCount; j++)
                {
                    Assert.AreEqual(ACopy[i, j], A[i, j]);
                }
            }

            // Make sure b didn't change.
            for (int i = 0; i < order; i++)
            {
                Assert.AreEqual(bCopy[i], b[i]);
            }
        }

        [Test]
        [Row(1, 1)]
        [Row(2, 4)]
        [Row(5, 8)]
        [Row(10, 3)]
        [Row(50, 10)]
        [Row(100, 100)]
        [MultipleAsserts]
        public void CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int col)
        {
            var A = MatrixLoader.GenerateRandomPositiveDefiniteMatrix(row);
            var ACopy = A.Clone();
            var chol = A.Cholesky();
            var B = MatrixLoader.GenerateRandomMatrix(row, col);
            var BCopy = B.Clone();
            var X = new DenseMatrix(row, col);
            chol.Solve(B, X);

            Assert.AreEqual(B.RowCount, X.RowCount);
            Assert.AreEqual(B.ColumnCount, X.ColumnCount);

            var BReconstruct = A * X;

            // Check the reconstruction.
            for (int i = 0; i < B.RowCount; i++)
            {
                for (int j = 0; j < B.ColumnCount; j++)
                {
                    Assert.AreApproximatelyEqual(B[i, j], BReconstruct[i, j], 1.0e-11);
                }
            }

            // Make sure A didn't change.
            for (int i = 0; i < A.RowCount; i++)
            {
                for (int j = 0; j < A.ColumnCount; j++)
                {
                    Assert.AreEqual(ACopy[i, j], A[i, j]);
                }
            }

            // Make sure B didn't change.
            for (int i = 0; i < B.RowCount; i++)
            {
                for (int j = 0; j < B.ColumnCount; j++)
                {
                    Assert.AreEqual(BCopy[i, j], B[i, j]);
                }
            }
        }*/
    }
}