C# Solvers.Iterator类代码示例

        public void DetermineStatus()
        {
            var criteria = new List<IIterationStopCriterium<float>>
            {
                new FailureStopCriterium(),
                new DivergenceStopCriterium(),
                new IterationCountStopCriterium<float>(1)
            };

            var iterator = new Iterator<float>(criteria);

            // First step, nothing should happen.
            iterator.DetermineStatus(
                0,
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4));
            Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");

            // Second step, should run out of iterations.
            iterator.DetermineStatus(
                1,
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4));
            Assert.AreEqual(IterationStatus.StoppedWithoutConvergence, iterator.Status, "Incorrect status");
        }

        /// <summary>
        /// Creates a default iterator with all the <see cref="IIterationStopCriterium"/> objects.
        /// </summary>
        /// <returns>A new <see cref="IIterator"/> object.</returns>
        public static IIterator CreateDefault()
        {
            var iterator = new Iterator();
            iterator.Add(new FailureStopCriterium());
            iterator.Add(new DivergenceStopCriterium());
            iterator.Add(new IterationCountStopCriterium());
            iterator.Add(new ResidualStopCriterium());

            return iterator;
        }

        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 4 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 IIterationStopCriterium<float>[]
                    {
                        new IterationCountStopCriterium<float>(MaximumIterations),
                        new ResidualStopCriterium((float) Math.Pow(1.0/10.0, iteration))
                    });
                var solver = new TFQMR(monitor);
                var matrixX = solver.Solve(matrixA, matrixB);

                if (!monitor.HasConverged)
                {
                    // 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 - 4));
                    }
                }

                return;
            }
        }

        public void SolveUnitMatrixAndBackMultiply()
        {
            // Create the identity matrix
            var matrix = SparseMatrix.Identity(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 TFQMR();

            // 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);
            }
        }

        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 TFQMR();

            // 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);
            }
        }

        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 TFQMR();
                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;
            }
        }

        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);

            // Due to datatype "float" it can happen that solution will not converge for specific random starting vectors
            // That's why we will do 3 tries
            for (var iteration = 0; iteration <= 3; iteration++)
            {
                // Create an iteration monitor which will keep track of iterative convergence
                var monitor = new Iterator<float>(
                    new IterationCountStopCriterium<float>(MaximumIterations),
                    new ResidualStopCriterium<float>(ConvergenceBoundary),
                    new DivergenceStopCriterium<float>(),
                    new FailureStopCriterium<float>());

                var solver = new MlkBiCgStab();

                // Solve equation Ax = y
                Vector<float> x;
                try
                {
                    x = matrix.SolveIterative(y, solver, monitor);
                }
                catch (Exception)
                {
                    continue;
                }

                if (monitor.Status != IterationStatus.Converged)
                {
                    continue;
                }

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

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

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

                return;
            }
        }

        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<float>.Build.Dense(matrix.RowCount, 1);

            // Create an iteration monitor which will keep track of iterative convergence
            var monitor = new Iterator<float>(
                new IterationCountStopCriterion<float>(MaximumIterations),
                new ResidualStopCriterion<float>(ConvergenceBoundary),
                new DivergenceStopCriterion<float>(),
                new FailureStopCriterion<float>());

            var solver = new MlkBiCgStab();

            // 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, Math.Abs(y[i] - z[i]), "#05-" + i);
            }
        }

        public void SolveUnitMatrixAndBackMultiply()
        {
            // Create the identity matrix
            var matrix = SparseMatrix.CreateIdentity(100);

            // Create the y vector
            var y = Vector<float>.Build.Dense(matrix.RowCount, 1);

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

            var solver = new TFQMR();

            // 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
            Assert.LessOrEqual(Distance.Chebyshev(y, z), 2*ConvergenceBoundary);
        }

        public void DetermineStatusWithNegativeIterationNumberThrowsArgumentOutOfRangeException()
        {
            var criteria = new List<IIterationStopCriterium<float>>
            {
                new FailureStopCriterium(),
                new DivergenceStopCriterium(),
                new IterationCountStopCriterium<float>(),
                new ResidualStopCriterium()
            };
            var iterator = new Iterator<float>(criteria);

            Assert.Throws<ArgumentOutOfRangeException>(() => iterator.DetermineStatus(
                -1,
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 5),
                DenseVector.Create(3, i => 6)));
        }

        public void ResetToPrecalculationState()
        {
            var criteria = new List<IIterationStopCriterium<float>>
            {
                new FailureStopCriterium(),
                new DivergenceStopCriterium(),
                new IterationCountStopCriterium<float>(1)
            };

            var iterator = new Iterator<float>(criteria);

            // First step, nothing should happen.
            iterator.DetermineStatus(
                0,
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4),
                DenseVector.Create(3, i => 4));
            Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");

            iterator.Reset();
            Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");
            Assert.AreEqual(IterationStatus.Continue, criteria[0].Status, "Incorrect status");
            Assert.AreEqual(IterationStatus.Continue, criteria[1].Status, "Incorrect status");
            Assert.AreEqual(IterationStatus.Continue, criteria[2].Status, "Incorrect status");
        }

 public void DetermineStatusWithoutStopCriteriaDoesNotThrow()
 {
     var iterator = new Iterator<float>();
     Assert.DoesNotThrow(() => iterator.DetermineStatus(
         0,
         DenseVector.Create(3, i => 4),
         DenseVector.Create(3, i => 5),
         DenseVector.Create(3, i => 6)));
 }