mathnet-numerics/src/UnitTests/LinearAlgebraTests/Single/Solvers/Iterative/BiCgStabTest.cs

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using System;
using MathNet.Numerics.LinearAlgebra.Single;
using MathNet.Numerics.LinearAlgebra.Single.Solvers;
using MathNet.Numerics.LinearAlgebra.Solvers;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Solvers.Iterative
{
    /// <summary>
    /// Tests of Bi-Conjugate Gradient stabilized iterative matrix solver.
    /// </summary>
    [TestFixture]
    public class BiCgStabTest
    {
        /// <summary>
        /// Convergence boundary.
        /// </summary>
        const float ConvergenceBoundary = 1e-5f;

        /// <summary>
        /// Maximum iterations.
        /// </summary>
        const int MaximumIterations = 1000;

        /// <summary>
        /// Solve wide matrix throws <c>ArgumentException</c>.
        /// </summary>
        [Test]
        public void SolveWideMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(2, 3);
            var input = new DenseVector(2);

            var solver = new BiCgStab();
            Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
        }

        /// <summary>
        /// Solve long matrix throws <c>ArgumentException</c>.
        /// </summary>
        [Test]
        public void SolveLongMatrixThrowsArgumentException()
        {
            var matrix = new SparseMatrix(3, 2);
            var input = new DenseVector(3);

            var solver = new BiCgStab();
            Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
        }

        /// <summary>
        /// Solve unit matrix and back multiply.
        /// </summary>
        [Test]
        public void SolveUnitMatrixAndBackMultiply()
        {
            // Create the identity matrix
            var matrix = SparseMatrix.CreateIdentity(100);

            // Create the y vector
            var y = DenseVector.Create(matrix.RowCount, i => 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<float>(
                new IterationCountStopCriterium<float>(MaximumIterations),
                new ResidualStopCriterium(ConvergenceBoundary),
                new DivergenceStopCriterium(),
                new FailureStopCriterium());

            var solver = new BiCgStab();

            // Solve equation Ax = y
            var x = matrix.SolveIterative(y, solver, monitor);

            // Now compare the results
            Assert.IsNotNull(x, "#02");
            Assert.AreEqual(y.Count, x.Count, "#03");

            // Back multiply the vector
            var z = matrix.Multiply(x);

            // Check that the solution converged
            Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");

            // Now compare the vectors
            for (var i = 0; i < y.Count; i++)
            {
                Assert.IsTrue((y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
            }
        }

        /// <summary>
        /// Solve scaled unit matrix and back multiply.
        /// </summary>
        [Test]
        public void SolveScaledUnitMatrixAndBackMultiply()
        {
            // Create the identity matrix
            var matrix = SparseMatrix.CreateIdentity(100);

            // Scale it with a funny number
            matrix.Multiply((float) Math.PI, matrix);

            // Create the y vector
            var y = DenseVector.Create(matrix.RowCount, i => 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<float>(
                new IterationCountStopCriterium<float>(MaximumIterations),
                new ResidualStopCriterium(ConvergenceBoundary),
                new DivergenceStopCriterium(),
                new FailureStopCriterium());

            var solver = new BiCgStab();

            // Solve equation Ax = y
            var x = matrix.SolveIterative(y, solver, monitor);

            // Now compare the results
            Assert.IsNotNull(x, "#02");
            Assert.AreEqual(y.Count, x.Count, "#03");

            // Back multiply the vector
            var z = matrix.Multiply(x);

            // Check that the solution converged
            Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");

            // Now compare the vectors
            for (var i = 0; i < y.Count; i++)
            {
                Assert.IsTrue((y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
            }
        }

        /// <summary>
        /// Solve poisson matrix and back multiply.
        /// </summary>
        [Test]
        public void SolvePoissonMatrixAndBackMultiply()
        {
            // Create the matrix
            var matrix = new SparseMatrix(25);

            // Assemble the matrix. We assume we're solving the Poisson equation
            // on a rectangular 5 x 5 grid
            const int GridSize = 5;

            // The pattern is:
            // 0 .... 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 ... 0
            for (var i = 0; i < matrix.RowCount; i++)
            {
                // Insert the first set of -1's
                if (i > (GridSize - 1))
                {
                    matrix[i, i - GridSize] = -1;
                }

                // Insert the second set of -1's
                if (i > 0)
                {
                    matrix[i, i - 1] = -1;
                }

                // Insert the centerline values
                matrix[i, i] = 4;

                // Insert the first trailing set of -1's
                if (i < matrix.RowCount - 1)
                {
                    matrix[i, i + 1] = -1;
                }

                // Insert the second trailing set of -1's
                if (i < matrix.RowCount - GridSize)
                {
                    matrix[i, i + GridSize] = -1;
                }
            }

            // Create the y vector
            var y = DenseVector.Create(matrix.RowCount, i => 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<float>(
                new IterationCountStopCriterium<float>(MaximumIterations),
                new ResidualStopCriterium(ConvergenceBoundary),
                new DivergenceStopCriterium(),
                new FailureStopCriterium());

            var solver = new BiCgStab();

            // Solve equation Ax = y
            var x = matrix.SolveIterative(y, solver, monitor);

            // Now compare the results
            Assert.IsNotNull(x, "#02");
            Assert.AreEqual(y.Count, x.Count, "#03");

            // Back multiply the vector
            var z = matrix.Multiply(x);

            // Check that the solution converged
            Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");

            // Now compare the vectors
            for (var i = 0; i < y.Count; i++)
            {
                Assert.IsTrue(Math.Abs(y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
            }
        }

        /// <summary>
        /// Can solve for a random vector.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(5)]
        public void CanSolveForRandomVector(int order)
        {
            // Due to datatype "float" it can happen that solution will not converge for specific random matrix
            // That's why we will do 3 tries and downgrade stop criterium each time
            for (var iteration = 6; iteration > 3; iteration--)
            {
                var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
                var vectorb = MatrixLoader.GenerateRandomDenseVector(order);

                var monitor = new Iterator<float>(
                    new IterationCountStopCriterium<float>(MaximumIterations),
                    new ResidualStopCriterium((float) Math.Pow(1.0/10.0, iteration)));

                var solver = new BiCgStab();
                var resultx = matrixA.SolveIterative(vectorb, solver, monitor);

                if (monitor.Status != IterationStatus.Converged)
                {
                    // Solution was not found, try again downgrading convergence boundary
                    continue;
                }

                Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
                var matrixBReconstruct = matrixA*resultx;

                // Check the reconstruction.
                for (var i = 0; i < order; i++)
                {
                    Assert.AreEqual(vectorb[i], matrixBReconstruct[i], (float) Math.Pow(1.0/10.0, iteration - 3));
                }

                return;
            }
        }

        /// <summary>
        /// Can solve for random matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(5)]
        public void CanSolveForRandomMatrix(int order)
        {
            // Due to datatype "float" it can happen that solution will not converge for specific random matrix
            // That's why we will do 3 tries and downgrade stop criterium each time
            for (var iteration = 6; iteration > 3; iteration--)
            {
                var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
                var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);

                var monitor = new Iterator<float>(
                    new IterationCountStopCriterium<float>(MaximumIterations),
                    new ResidualStopCriterium((float) Math.Pow(1.0/10.0, iteration)));

                var solver = new BiCgStab();
                var matrixX = matrixA.SolveIterative(matrixB, solver, monitor);

                if (monitor.Status != IterationStatus.Converged)
                {
                    // Solution was not found, try again downgrading convergence boundary
                    continue;
                }

                // 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++)
                    {
                        Assert.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], (float) Math.Pow(1.0/10.0, iteration - 3));
                    }
                }

                return;
            }
        }
    }
}