mathnet-numerics/src/UnitTests/LinearAlgebraTests/Complex/Factorization/CholeskyTests.cs

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namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex.Factorization
{
    using System;
    using System.Numerics;
    using LinearAlgebra.Complex;
    using LinearAlgebra.Generic.Factorization;
    using NUnit.Framework;

    /// <summary>
    /// Cholesky factorization tests for a dense matrix.
    /// </summary>
    public class CholeskyTests
    {
        /// <summary>
        /// Can factorize identity matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(10)]
        [TestCase(100)]
        public void CanFactorizeIdentity(int order)
        {
            var matrixI = DenseMatrix.Identity(order);
            var factorC = matrixI.Cholesky().Factor;

            Assert.AreEqual(matrixI.RowCount, factorC.RowCount);
            Assert.AreEqual(matrixI.ColumnCount, factorC.ColumnCount);

            for (var i = 0; i < factorC.RowCount; i++)
            {
                for (var j = 0; j < factorC.ColumnCount; j++)
                {
                    Assert.AreEqual(i == j ? Complex.One : Complex.Zero, factorC[i, j]);
                }
            }
        }

        /// <summary>
        /// Cholesky factorization fails with diagonal a non-positive definite matrix.
        /// </summary>
        [Test]
        public void CholeskyFailsWithDiagonalNonPositiveDefiniteMatrix()
        {
            var matrixI = DenseMatrix.Identity(8);
            matrixI[3, 3] = -4.0;
            Assert.Throws<ArgumentException>(() => matrixI.Cholesky());
        }

        /// <summary>
        /// Cholesky factorization fails with a non-square matrix.
        /// </summary>
        [Test]
        public void CholeskyFailsWithNonSquareMatrix()
        {
            var matrix = new DenseMatrix(3, 2);
            Assert.Throws<ArgumentException>(() => matrix.Cholesky());
        }

        /// <summary>
        /// Identity determinant is one.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(10)]
        [TestCase(100)]
        public void IdentityDeterminantIsOne(int order)
        {
            var matrixI = DenseMatrix.Identity(order);
            var factorC = matrixI.Cholesky();
            Assert.AreEqual(Complex.One, factorC.Determinant);
            Assert.AreEqual(Complex.Zero, factorC.DeterminantLn);
        }

        /// <summary>
        /// Can factorize a random square matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanFactorizeRandomMatrix(int order)
        {
            var matrixX = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(order);
            var chol = matrixX.Cholesky();
            var factorC = chol.Factor;

            // Make sure the Cholesky factor has the right dimensions.
            Assert.AreEqual(order, factorC.RowCount);
            Assert.AreEqual(order, factorC.ColumnCount);

            // Make sure the Cholesky factor is lower triangular.
            for (var i = 0; i < factorC.RowCount; i++)
            {
                for (var j = i + 1; j < factorC.ColumnCount; j++)
                {
                    Assert.AreEqual(Complex.Zero, factorC[i, j]);
                }
            }

            // Make sure the cholesky factor times it's transpose is the original matrix.
            var matrixXfromC = factorC * factorC.ConjugateTranspose();
            for (var i = 0; i < matrixXfromC.RowCount; i++)
            {
                for (var j = 0; j < matrixXfromC.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixX[i, j], matrixXfromC[i, j], 8);
                }
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random vector (Ax=b).
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVector(int order)
        {
            var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(order);
            var matrixACopy = matrixA.Clone();
            var chol = matrixA.Cholesky();
            var matrixB = MatrixLoader.GenerateRandomDenseVector(order);
            var x = chol.Solve(matrixB);

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

            var matrixBReconstruct = matrixA * x;

            // Check the reconstruction.
            for (var i = 0; i < order; i++)
            {
                AssertHelpers.AlmostEqual(matrixB[i], matrixBReconstruct[i], 8);
            }

            // 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]);
                }
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random matrix (AX=B).
        /// </summary>
        /// <param name="row">Matrix row number.</param>
        /// <param name="col">Matrix column number.</param>
        [TestCase(1, 1)]
        [TestCase(2, 4)]
        [TestCase(5, 8)]
        [TestCase(10, 3)]
        [TestCase(50, 10)]
        [TestCase(100, 100)]
        public void CanSolveForRandomMatrix(int row, int col)
        {
            var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(row);
            var matrixACopy = matrixA.Clone();
            var chol = matrixA.Cholesky();
            var matrixB = MatrixLoader.GenerateRandomDenseMatrix(row, col);
            var matrixX = chol.Solve(matrixB);

            Assert.AreEqual(matrixB.RowCount, matrixX.RowCount);
            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);

            var matrixBReconstruct = matrixA * matrixX;

            // Check the reconstruction.
            for (var i = 0; i < matrixB.RowCount; i++)
            {
                for (var j = 0; j < matrixB.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 7);
                }
            }

            // 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]);
                }
            }
        }

        /// <summary>
        /// Can solve for a random vector into a result vector.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
        {
            var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(order);
            var matrixACopy = matrixA.Clone();
            var chol = matrixA.Cholesky();
            var matrixB = MatrixLoader.GenerateRandomDenseVector(order);
            var matrixBCopy = matrixB.Clone();
            var x = new DenseVector(order);
            chol.Solve(matrixB, x);

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

            var matrixBReconstruct = matrixA * x;

            // Check the reconstruction.
            for (var i = 0; i < order; i++)
            {
                AssertHelpers.AlmostEqual(matrixB[i], matrixBReconstruct[i], 8);
            }

            // 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]);
                }
            }

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

        /// <summary>
        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
        /// </summary>
        /// <param name="row">Matrix row number.</param>
        /// <param name="col">Matrix column number.</param>
        [TestCase(1, 1)]
        [TestCase(2, 4)]
        [TestCase(5, 8)]
        [TestCase(10, 3)]
        [TestCase(50, 10)]
        [TestCase(100, 100)]
        public void CanSolveForRandomMatrixWhenResultMatrixGiven(int row, int col)
        {
            var matrixA = MatrixLoader.GenerateRandomPositiveDefiniteHermitianDenseMatrix(row);
            var matrixACopy = matrixA.Clone();
            var chol = matrixA.Cholesky();
            var matrixB = MatrixLoader.GenerateRandomDenseMatrix(row, col);
            var matrixBCopy = matrixB.Clone();
            var matrixX = new DenseMatrix(row, col);
            chol.Solve(matrixB, matrixX);

            Assert.AreEqual(matrixB.RowCount, matrixX.RowCount);
            Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);

            var matrixBReconstruct = matrixA * matrixX;

            // Check the reconstruction.
            for (var i = 0; i < matrixB.RowCount; i++)
            {
                for (var j = 0; j < matrixB.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixB[i, j], matrixBReconstruct[i, j], 7);
                }
            }

            // 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]);
                }
            }

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