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// Math.NET Numerics, part of the Math.NET Project
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using System;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Factorization;
using MathNet.Numerics.LinearAlgebra.Single.Factorization;
using NUnit.Framework;

namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Single.Factorization
{
    /// <summary>
    /// QR factorization tests for a user matrix.
    /// </summary>
    public class UserQRTests
    {
        /// <summary>
        /// Constructor with wide matrix throws <c>ArgumentException</c>.
        /// </summary>
        [Test]
        public void ConstructorWideMatrixThrowsInvalidMatrixOperationException()
        {
            Assert.Throws<ArgumentException>(() => UserQR.Create(new UserDefinedMatrix(3, 4)));
        }

        /// <summary>
        /// Can factorize identity matrix.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(10)]
        [TestCase(100)]
        public void CanFactorizeIdentity(int order)
        {
            var matrixI = UserDefinedMatrix.Identity(order);
            var factorQR = matrixI.QR();
            var r = factorQR.R;

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

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

        /// <summary>
        /// Can factorize identity matrix using thin QR.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(10)]
        [TestCase(100)]
        public void CanFactorizeIdentityUsingThinQR(int order)
        {
            var matrixI = UserDefinedMatrix.Identity(order);
            var factorQR = matrixI.QR(QRMethod.Thin);
            var r = factorQR.R;

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

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

        /// <summary>
        /// Identity determinant is one.
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(10)]
        [TestCase(100)]
        public void IdentityDeterminantIsOne(int order)
        {
            var matrixI = UserDefinedMatrix.Identity(order);
            var factorQR = matrixI.QR();
            Assert.AreEqual(1.0, factorQR.Determinant);
        }

        /// <summary>
        /// Can factorize a random matrix.
        /// </summary>
        /// <param name="row">Matrix row number.</param>
        /// <param name="column">Matrix column number.</param>
        [TestCase(1, 1)]
        [TestCase(2, 2)]
        [TestCase(5, 5)]
        [TestCase(10, 6)]
        [TestCase(50, 48)]
        [TestCase(100, 98)]
        public void CanFactorizeRandomMatrix(int row, int column)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
            var factorQR = matrixA.QR(QRMethod.Full);
            var q = factorQR.Q;
            var r = factorQR.R;

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

            // Make sure the Q has the right dimensions.
            Assert.AreEqual(row, q.RowCount);
            Assert.AreEqual(row, q.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(0.0, 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++)
                {
                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1e-4);
                }
            }
        }

        /// <summary>
        /// Can factorize a random matrix using thin QR.
        /// </summary>
        /// <param name="row">Matrix row number.</param>
        /// <param name="column">Matrix column number.</param>
        [TestCase(1, 1)]
        [TestCase(2, 2)]
        [TestCase(5, 5)]
        [TestCase(10, 6)]
        [TestCase(50, 48)]
        [TestCase(100, 98)]
        public void CanFactorizeRandomMatrixUsingThinQR(int row, int column)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(row, column, 1).ToArray());
            var factorQR = matrixA.QR(QRMethod.Thin);
            var q = factorQR.Q;
            var r = factorQR.R;

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

            // Make sure the Q has the right dimensions.
            Assert.AreEqual(row, q.RowCount);
            Assert.AreEqual(column, q.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(0.0, 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++)
                {
                    Assert.AreEqual(matrixA[i, j], matrixQfromR[i, j], 1.0e-4);
                }
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random vector (Ax=b).
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVector(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR();

            var vectorb = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
            var resultx = factorQR.Solve(vectorb);

            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], 1e-4);
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomMatrix(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR();

            var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixX = factorQR.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.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
                }
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVectorWhenResultVectorGiven(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR();
            var vectorb = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
            var vectorbCopy = vectorb.Clone();
            var resultx = new UserDefinedVector(order);
            factorQR.Solve(vectorb, resultx);

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

            var matrixBReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < vectorb.Count; i++)
            {
                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1e-4);
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomMatrixWhenResultMatrixGiven(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR();

            var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixBCopy = matrixB.Clone();

            var matrixX = new UserDefinedMatrix(order, order);
            factorQR.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.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
                }
            }

            // 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]);
                }
            }
        }

        /// <summary>
        /// Can solve a system of linear equations for a random vector (Ax=b).
        /// </summary>
        /// <param name="order">Matrix order.</param>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVectorUsingThinQR(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR(QRMethod.Thin);

            var vectorb = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
            var resultx = factorQR.Solve(vectorb);

            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], 1e-4);
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomMatrixUsingThinQR(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR(QRMethod.Thin);

            var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixX = factorQR.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.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
                }
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomVectorWhenResultVectorGivenUsingThinQR(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR(QRMethod.Thin);
            var vectorb = new UserDefinedVector(Vector<float>.Build.Random(order, 1).ToArray());
            var vectorbCopy = vectorb.Clone();
            var resultx = new UserDefinedVector(order);
            factorQR.Solve(vectorb, resultx);

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

            var matrixBReconstruct = matrixA * resultx;

            // Check the reconstruction.
            for (var i = 0; i < vectorb.Count; i++)
            {
                Assert.AreEqual(vectorb[i], matrixBReconstruct[i], 1e-4);
            }

            // 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>
        [TestCase(1)]
        [TestCase(2)]
        [TestCase(5)]
        [TestCase(10)]
        [TestCase(50)]
        [TestCase(100)]
        public void CanSolveForRandomMatrixWhenResultMatrixGivenUsingThinAR(int order)
        {
            var matrixA = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixACopy = matrixA.Clone();
            var factorQR = matrixA.QR(QRMethod.Thin);

            var matrixB = new UserDefinedMatrix(Matrix<float>.Build.Random(order, order, 1).ToArray());
            var matrixBCopy = matrixB.Clone();

            var matrixX = new UserDefinedMatrix(order, order);
            factorQR.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.AreEqual(matrixB[i, j], matrixBReconstruct[i, j], 1e-4);
                }
            }

            // 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]);
                }
            }
        }
    }
}