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

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

    /// <summary>
    /// GramSchmidt factorization tests for a user matrix.
    /// </summary>
    public class UserGramSchmidtTests
    {
        /// <summary>
        /// Constructor with <c>null</c> throws <c>ArgumentNullException</c>.
        /// </summary>
        public void ConstructorNullThrowsArgumentNullException()
        {
            Assert.Throws<ArgumentNullException>(() => new UserGramSchmidt(null));
        }

        /// <summary>
        /// Constructor with wide matrix throws <c>ArgumentException</c>.
        /// </summary>
        [Test]
        public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
        {
            Assert.Throws<ArgumentException>(() => new UserGramSchmidt(new UserDefinedMatrix(3, 4)));
        }

        /// <summary>
        /// Can factorize identity matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [Test]
        public void CanFactorizeIdentity([Values(1, 10, 100)] int order)
        {
            var matrixI = UserDefinedMatrix.Identity(order);
            var factorGramSchmidt = matrixI.GramSchmidt();
            var q = factorGramSchmidt.Q;
            var r = factorGramSchmidt.R;

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

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

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

        /// <summary>
        /// Identity determinant is one.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [Test]
        public void IdentityDeterminantIsOne([Values(1, 10, 100)] int order)
        {
            var matrixI = UserDefinedMatrix.Identity(order);
            var factorGramSchmidt = matrixI.GramSchmidt();
            Assert.AreEqual(Complex.One, factorGramSchmidt.Determinant);
        }

        /// <summary>
        /// Can factorize a random matrix.
        /// </summary>
        /// <param name="row">Matrix row number.</param>
        /// <param name="column">Matrix column number.</param>
        [Test, Sequential]
        public void CanFactorizeRandomMatrix([Values(1, 2, 5, 10, 50, 100)] int row, [Values(1, 2, 5, 6, 48, 98)] int column)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
            var factorGramSchmidt = matrixA.GramSchmidt();
            var q = factorGramSchmidt.Q;
            var r = factorGramSchmidt.R;

            // Make sure the Q has the right dimensions.
            Assert.AreEqual(row, q.RowCount);
            Assert.AreEqual(column, q.ColumnCount);

            // Make sure the R has the right dimensions.
            Assert.AreEqual(column, r.RowCount);
            Assert.AreEqual(column, r.ColumnCount);

            // Make sure the R factor is upper triangular.
            for (var i = 0; i < r.RowCount; i++)
            {
                for (var j = 0; j < r.ColumnCount; j++)
                {
                    if (i > j)
                    {
                        Assert.AreEqual(Complex.Zero, r[i, j]);
                    }
                }
            }

            // Make sure the Q*R is the original matrix.
            var matrixQfromR = q * r;
            for (var i = 0; i < matrixQfromR.RowCount; i++)
            {
                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixA[i, j], matrixQfromR[i, j], 9);
                }
            }

            // Make sure the Q is unitary --> (Q*)x(Q) = I
            var matrixQсtQ = q.ConjugateTranspose() * q;
            for (var i = 0; i < matrixQсtQ.RowCount; i++)
            {
                for (var j = 0; j < matrixQсtQ.ColumnCount; j++)
                {
                    if (i == j)
                    {
                        AssertHelpers.AlmostEqual(matrixQсtQ[i, j], Complex.One, 9);
                    }
                    else
                    {
                        AssertHelpers.AlmostEqual(matrixQсtQ[i, j], Complex.Zero, 9);
                    }
                }
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random vector (Ax=b).
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [Test]
        public void CanSolveForRandomVector([Values(1, 2, 5, 10, 50, 100)] int order)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixACopy = matrixA.Clone();
            var factorGramSchmidt = matrixA.GramSchmidt();

            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
            var resultx = factorGramSchmidt.Solve(vectorb);

            Assert.AreEqual(matrixA.ColumnCount, resultx.Count);

            var matrixBReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < order; i++)
            {
                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
            }

            // 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="order">Matrix order.</param>
        [Test]
        public void CanSolveForRandomMatrix([Values(1, 2, 5, 10, 50, 100)] int order)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixACopy = matrixA.Clone();
            var factorGramSchmidt = matrixA.GramSchmidt();

            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixX = factorGramSchmidt.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 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], 9);
                }
            }

            // 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>
        [Test]
        public void CanSolveForRandomVectorWhenResultVectorGiven([Values(1, 2, 5, 10, 50, 100)] int order)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixACopy = matrixA.Clone();
            var factorGramSchmidt = matrixA.GramSchmidt();
            var vectorb = MatrixLoader.GenerateRandomUserDefinedVector(order);
            var vectorbCopy = vectorb.Clone();
            var resultx = new UserDefinedVector(order);
            factorGramSchmidt.Solve(vectorb, resultx);

            Assert.AreEqual(vectorb.Count, resultx.Count);

            var matrixBReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < vectorb.Count; i++)
            {
                AssertHelpers.AlmostEqual(vectorb[i], matrixBReconstruct[i], 9);
            }

            // 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 < vectorb.Count; i++)
            {
                Assert.AreEqual(vectorbCopy[i], vectorb[i]);
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random matrix (AX=B) into a result matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [Test]
        public void CanSolveForRandomMatrixWhenResultMatrixGiven([Values(1, 2, 5, 10, 50, 100)] int order)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixACopy = matrixA.Clone();
            var factorGramSchmidt = matrixA.GramSchmidt();

            var matrixB = MatrixLoader.GenerateRandomUserDefinedMatrix(order, order);
            var matrixBCopy = matrixB.Clone();

            var matrixX = new UserDefinedMatrix(order, order);
            factorGramSchmidt.Solve(matrixB, matrixX);

            // 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 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], 9);
                }
            }

            // 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]);
                }
            }
        }
    }
}