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

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namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
{
    using LinearAlgebra.Generic.Factorization;
    using MbUnit.Framework;
    using LinearAlgebra.Double.Factorization;

    public class UserGramSchmidtTests
    {
        [Test]
        [ExpectedArgumentNullException]
        public void ConstructorNull()
        {
            new UserGramSchmidt(null);
        }

        [Test]
        [ExpectedArgumentException]
        public void WideMatrixThrowsInvalidMatrixOperationException()
        {
            new UserGramSchmidt(new UserDefinedMatrix(3, 4));
        }
        
        [Test]
        [Row(1)]
        [Row(10)]
        [Row(100)]
        public void CanFactorizeIdentity(int order)
        {
            var I = UserDefinedMatrix.Identity(order);
            var factorGramSchmidt = I.GramSchmidt();

            Assert.AreEqual(I.RowCount, factorGramSchmidt.Q.RowCount);
            Assert.AreEqual(I.ColumnCount, factorGramSchmidt.Q.ColumnCount);

            for (var i = 0; i < factorGramSchmidt.R.RowCount; i++)
            {
                for (var j = 0; j < factorGramSchmidt.R.ColumnCount; j++)
                {
                    if (i == j)
                    {
                        Assert.AreEqual(1.0, factorGramSchmidt.R[i, j]);
                    }
                    else
                    {
                        Assert.AreEqual(0.0, factorGramSchmidt.R[i, j]);
                    }
                }
            }

            for (var i = 0; i < factorGramSchmidt.Q.RowCount; i++)
            {
                for (var j = 0; j < factorGramSchmidt.Q.ColumnCount; j++)
                {
                    if (i == j)
                    {
                        Assert.AreEqual(1.0, factorGramSchmidt.Q[i, j]);
                    }
                    else
                    {
                        Assert.AreEqual(0.0, factorGramSchmidt.Q[i, j]);
                    }
                }
            }
        }

      
        [Test]
        [Row(1)]
        [Row(10)]
        [Row(100)]
        public void IdentityDeterminantIsOne(int order)
        {
            var I = UserDefinedMatrix.Identity(order);
            var factorGramSchmidt = I.GramSchmidt();
            Assert.AreEqual(1.0, factorGramSchmidt.Determinant);
        }

        [Test]
        [Row(1,1)]
        [Row(2,2)]
        [Row(5,5)]
        [Row(10,6)]
        [Row(50,48)]
        [Row(100,98)]
        [MultipleAsserts]
        public void CanFactorizeRandomMatrix(int row, int column)
        {
            var matrixA = MatrixLoader.GenerateRandomUserDefinedMatrix(row, column);
            var factorGramSchmidt = matrixA.GramSchmidt();

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

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

            // Make sure the R factor is upper triangular.
            for (var i = 0; i < factorGramSchmidt.R.RowCount; i++) 
            {
                for (var j = 0; j < factorGramSchmidt.R.ColumnCount; j++)
                {
                    if (i > j)
                    {
                        Assert.AreEqual(0.0, factorGramSchmidt.R[i, j]);
                    }
                }
            }

            // Make sure the Q*R is the original matrix.
            var matrixQfromR = factorGramSchmidt.Q * factorGramSchmidt.R;
            for (var i = 0; i < matrixQfromR.RowCount; i++) 
            {
                for (var j = 0; j < matrixQfromR.ColumnCount; j++)
                {
                    Assert.AreApproximatelyEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-11);
                }
            }
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(5)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomVector(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 bReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < order; i++)
            {
                Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], 1.0e-11);
            }

            // 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]);
                }
            }
        }

        [Test]
        [Row(1)]
        [Row(4)]
        [Row(8)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomMatrix(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++)
                {
                    Assert.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
                }
            }

            // 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]);
                }
            }
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(5)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomVectorWhenResultVectorGiven(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 bReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < vectorb.Count; i++)
            {
                Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], 1.0e-11);
            }

            // 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]);
            }
        }

        [Test]
        [Row(1)]
        [Row(4)]
        [Row(8)]
        [Row(10)]
        [Row(50)]
        [Row(100)]
        [MultipleAsserts]
        public void CanSolveForRandomMatrixWhenResultMatrixGiven(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++)
                {
                    Assert.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], 1.0e-11);
                }
            }

            // 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]);
                }
            }
        }
    }
}