mathnet-numerics/src/UnitTests/LinearAlgebraTests/Complex32/Solvers/Iterative/GpBiCgTest.cs

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using System;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Complex32;
using MathNet.Numerics.LinearAlgebra.Complex32.Solvers;
using MathNet.Numerics.LinearAlgebra.Solvers;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex32.Solvers.Iterative
{
    using Numerics;

    /// <summary>
    /// Tests for Generalized Product Bi-Conjugate Gradient iterative matrix solver.
    /// </summary>
    [TestFixture]
    public class GpBiCgTest
    {
        /// <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 GpBiCg();
            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 GpBiCg();
            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 = Vector<Complex32>.Build.Dense(matrix.RowCount, 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<Complex32>(
                new IterationCountStopCriterium<Complex32>(MaximumIterations),
                new ResidualStopCriterium<Complex32>(ConvergenceBoundary),
                new DivergenceStopCriterium<Complex32>(),
                new FailureStopCriterium<Complex32>());

            var solver = new GpBiCg();

            // 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.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#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 = Vector<Complex32>.Build.Dense(matrix.RowCount, 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<Complex32>(
                new IterationCountStopCriterium<Complex32>(MaximumIterations),
                new ResidualStopCriterium<Complex32>(ConvergenceBoundary),
                new DivergenceStopCriterium<Complex32>(),
                new FailureStopCriterium<Complex32>());

            var solver = new GpBiCg();

            // 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.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#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 = Vector<Complex32>.Build.Dense(matrix.RowCount, 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<Complex32>(
                new IterationCountStopCriterium<Complex32>(MaximumIterations),
                new ResidualStopCriterium<Complex32>(ConvergenceBoundary),
                new DivergenceStopCriterium<Complex32>(),
                new FailureStopCriterium<Complex32>());

            var solver = new GpBiCg();

            // 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.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#05-" + i);
            }
        }

        /// <summary>
        /// Can solve for a random vector.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(4)]
        public void CanSolveForRandomVector(int order)
        {
            for (var iteration = 5; iteration > 3; iteration--)
            {
                var matrixA = Matrix<Complex32>.Build.Random(order, order, 1);
                var vectorb = Vector<Complex32>.Build.Random(order, 1);

                var monitor = new Iterator<Complex32>(
                    new IterationCountStopCriterium<Complex32>(1000),
                    new ResidualStopCriterium<Complex32>(Math.Pow(1.0 / 10.0, iteration)));

                var solver = new GpBiCg();

                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].Real, matrixBReconstruct[i].Real, (float) Math.Pow(1.0/10.0, iteration - 3));
                    Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, (float) Math.Pow(1.0/10.0, iteration - 3));
                }

                return;
            }

            Assert.Fail("Solution was not found in 3 tries");
        }
    }
}