mathnet-numerics/src/UnitTests/LinearAlgebraTests/Complex/MatrixTests.Arithmetic.cs

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namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Complex
{
    using System;
    using System.Numerics;
    using Distributions;
    using LinearAlgebra.Complex;
    using LinearAlgebra.Generic;
    using MbUnit.Framework;

    public abstract partial class MatrixTests
    {
        [Test]
        [Row(1.0, 1.0)]
        [Row(2.0, 1.0)]
        [Row(2.2, 1.0)]
        [MultipleAsserts]
        public void CanMultiplyWithComplex(double real, double imaginary)
        {
            var value = new Complex(real, imaginary);
            var matrix = TestMatrices["Singular3x3"];
            var clone = matrix.Clone();
            var result = clone.Multiply(value);

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(matrix[i, j] * value, result[i, j]);
                }
            }
        }

        [Test]
        public void CanMultiplyWithVector()
        {
            var matrixA = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            var y = matrixA * x;

            Assert.AreEqual(matrixA.RowCount, y.Count);

            for (var i = 0; i < matrixA.RowCount; i++)
            {
                var ar = matrixA.Row(i);
                var dot = ar * x;
                AssertHelpers.AreEqual(dot, y[i]);
            }
        }

        [Test]
        public void CanMultiplyWithVectorIntoResult()
        {
            var matrixA = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            var y = new DenseVector(3);
            matrixA.Multiply(x, y);

            for (var i = 0; i < matrixA.RowCount; i++)
            {
                var ar = matrixA.Row(i);
                var dot = ar * x;
                AssertHelpers.AreEqual(dot, y[i]);
            }
        }

        [Test]
        public void CanMultiplyWithVectorIntoResultWhenUpdatingInputArgument()
        {
            var matrixA = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            var y = x;
            matrixA.Multiply(x, x);

            Assert.AreSame(y, x);

            y = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                var ar = matrixA.Row(i);
                var dot = ar * y;
                AssertHelpers.AreEqual(dot, x[i]);
            }
        }

        [Test]
        [ExpectedArgumentNullException]
        public void MultiplyWithVectorIntoResultFailsWhenResultIsNull()
        {
            var matrixA = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            Vector<Complex> y = null;
            matrixA.Multiply(x, y);
        }

        [Test]
        [ExpectedArgumentException]
        public void MultiplyWithVectorIntoResultFailsWhenResultIsTooLarge()
        {
            var matrixA = TestMatrices["Singular3x3"];
            var x = new DenseVector(new[] { new Complex(1, 1), new Complex(2, 1), new Complex(3, 1) });
            Vector<Complex> y = new DenseVector(4);
            matrixA.Multiply(x, y);
        }

        [Test]
        [Row(1.0, 1.0)]
        [Row(2.0, 1.0)]
        [Row(2.2, 1.0)]
        [MultipleAsserts]
        public void CanOperatorLeftMultiplyWithComplex(double real, double imaginary)
        {
            var value = new Complex(real, imaginary);
            var matrix = TestMatrices["Singular3x3"];
            var clone = matrix * value;

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(matrix[i, j] * value, clone[i, j]);
                }
            }
        }

        [Test]
        [Row(1.0, 1.0)]
        [Row(2.0, 1.0)]
        [Row(2.2, 1.0)]
        [MultipleAsserts]
        public void CanOperatorRightMultiplyWithComplex(double real, double imaginary)
        {
            var value = new Complex(real, imaginary);
            var matrix = TestMatrices["Singular3x3"];
            var clone = matrix * value;

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(matrix[i, j] * value, clone[i, j]);
                }
            }
        }

        [Test]
        [Row(1.0, 1.0)]
        [Row(2.0, 1.0)]
        [Row(2.2, 1.0)]
        [MultipleAsserts]
        public void CanMultiplyWithComplexIntoResult(double real, double imaginary)
        {
            var value = new Complex(real, imaginary);
            var matrix = TestMatrices["Singular3x3"];
            var result = matrix.Clone();
            matrix.Multiply(value, result);

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    var expected = matrix[i, j] * value;
                    AssertHelpers.AreEqual(expected, result[i, j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void MultiplyWithComplexIntoResultFailsWhenResultIsNull()
        {
            var matrix = TestMatrices["Singular3x3"];
            Matrix<Complex> result = null;
            matrix.Multiply(2.3, result);
        }

        [Test]
        [ExpectedArgumentException]
        public void MultiplyWithComplexFailsWhenResultHasMoreRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var result = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            matrix.Multiply(2.3, result);
        }

        [Test]
        [ExpectedArgumentException]
        public void MultiplyWithComplexFailsWhenResultHasMoreColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var result = CreateMatrix(matrix.RowCount, matrix.ColumnCount + 1);
            matrix.Multiply(2.3, result);
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void OperatorLeftMultiplyWithComplexFailsWhenMatrixIsNull()
        {
            Matrix<Complex> matrix = null;
            var result = 2.3 * matrix;
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void OperatorRightMultiplyWithComplexFailsWhenMatrixIsNull()
        {
            Matrix<Complex> matrix = null;
            var result = matrix * 2.3;
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        public void CanAddMatrix(string mtxA, string mtxB)
        {
            var matrixA = TestMatrices[mtxA];
            var matrixB = TestMatrices[mtxB];

            var matrix = matrixA.Clone();
            var result = matrix.Add(matrixB);
            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(matrixA[i, j] + matrixB[i, j], result[i,j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void AddMatrixThrowsExceptionWhenArgumentIsNull()
        {
            var matrix = TestMatrices["Singular4x4"];
            Matrix<Complex> other = null;
            matrix.Add(other);
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void AddMatrixThrowsExceptionArgumentHasTooFewColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Tall3x2"];
            matrix.Add(other);
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void AddMatrixThrowsExceptionArgumentHasTooFewRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Wide2x3"];
            matrix.Add(other);
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        public void AddOperator(string mtxA, string mtxB)
        {
            var matrixA = TestMatrices[mtxA];
            var matrixB = TestMatrices[mtxB];

            var result = matrixA + matrixB;
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                for (var j = 0; j < matrixA.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(result[i, j], matrixA[i, j] + matrixB[i, j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void AddOperatorThrowsExceptionWhenLeftsideIsNull()
        {
            Matrix<Complex> matrix = null;
            var other = TestMatrices["Singular3x3"];
            var result = matrix + other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void AddOperatorThrowsExceptionWhenRightsideIsNull()
        {
            var matrix = TestMatrices["Singular3x3"];
            Matrix<Complex> other = null;
            var result = matrix + other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void AddOperatorThrowsExceptionWhenRightsideHasTooFewColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Tall3x2"];
            var result = matrix + other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void AddOperatorThrowsExceptionWhenRightsideHasTooFewRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Wide2x3"];
            var result = matrix + other;
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        public void CanSubtractMatrix(string mtxA, string mtxB)
        {
            var matrixA = TestMatrices[mtxA];
            var matrixB = TestMatrices[mtxB];

            var matrix = matrixA.Clone();
            var result = matrix.Subtract(matrixB);
            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(matrixA[i, j] - matrixB[i, j], result[i, j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void SubtractMatrixThrowsExceptionWhenRightSideIsNull()
        {
            var matrix = TestMatrices["Singular4x4"];
            Matrix<Complex> other = null;
            matrix.Subtract(other);
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void SubtractMatrixThrowsExceptionWhenRightSideHasTooFewColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Tall3x2"];
            matrix.Subtract(other);
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void SubtractMatrixThrowsExceptionWhenRightSideHasTooFewRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Wide2x3"];
            matrix.Subtract(other);
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        public void SubtractOperator(string mtxA, string mtxB)
        {
            var matrixA = TestMatrices[mtxA];
            var matrixB = TestMatrices[mtxB];

            var result = matrixA - matrixB;
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                for (var j = 0; j < matrixA.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(result[i, j], matrixA[i, j] - matrixB[i, j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void SubtractOperatorThrowsExceptionWhenLeftsideIsNull()
        {
            Matrix<Complex> matrix = null;
            var other = TestMatrices["Singular3x3"];
            var result = matrix - other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void SubtractOperatorThrowsExceptionWhenRightsideIsNull()
        {
            var matrix = TestMatrices["Singular3x3"];
            Matrix<Complex> other = null;
            var result = matrix - other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void SubtractOperatorThrowsExceptionWhenRightsideHasTooFewColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Tall3x2"];
            var result = matrix - other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentOutOfRangeException))]
        public void SubtractOperatorThrowsExceptionWhenRightsideHasTooFewRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Wide2x3"];
            var result = matrix - other;
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        [Row("Wide2x3", "Square3x3")]
        [Row("Wide2x3", "Tall3x2")]
        [Row("Tall3x2", "Wide2x3")]
        [MultipleAsserts]
        public void CanMultiplyMatrixWithMatrix(string nameA, string nameB)
        {
            var matrixA = TestMatrices[nameA];
            var matrixB = TestMatrices[nameB];
            var matrixC = matrixA * matrixB;

            Assert.AreEqual(matrixC.RowCount, matrixA.RowCount);
            Assert.AreEqual(matrixC.ColumnCount, matrixB.ColumnCount);

            for (var i = 0; i < matrixC.RowCount; i++)
            {
                for (var j = 0; j < matrixC.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixA.Row(i) * matrixB.Column(j), matrixC[i, j], 15);
                }
            }
        }

        [Test]
        [Row("Singular3x3")]
        [Row("Singular4x4")]
        [Row("Wide2x3")]
        [Row("Tall3x2")]
        [MultipleAsserts]
        public void CanTransposeAndMultiplyMatrixWithMatrix(string nameA)
        {
            var matrixA = TestMatrices[nameA];
            var matrixB = TestMatrices[nameA];
            var matrixC = matrixA.TransposeAndMultiply(matrixB);

            Assert.AreEqual(matrixC.RowCount, matrixA.RowCount);
            Assert.AreEqual(matrixC.ColumnCount, matrixB.RowCount);

            for (var i = 0; i < matrixC.RowCount; i++)
            {
                for (var j = 0; j < matrixC.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixA.Row(i) * matrixB.Row(j), matrixC[i, j], 15);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void TransposeAndMultiplyMatrixMatrixFailsWhenSizesAreIncompatible()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Tall3x2"];
            var result = matrix.TransposeAndMultiply(other);
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void TransposeAndMultiplyMatrixMatrixFailsWhenRightArgumentIsNull()
        {
            var matrix = TestMatrices["Wide2x3"];
            Matrix<Complex> other = null;
            var result = matrix.TransposeAndMultiply(other);
        }

        [Test]
        [Row("Singular3x3")]
        [Row("Singular4x4")]
        [Row("Wide2x3")]
        [Row("Wide2x3")]
        [Row("Tall3x2")]
        [MultipleAsserts]
        public void CanTransposeAndMultiplyMatrixWithMatrixIntoResult(string nameA)
        {
            var matrixA = TestMatrices[nameA];
            var matrixB = TestMatrices[nameA];
            var matrixC = CreateMatrix(matrixA.RowCount, matrixB.RowCount);
            matrixA.TransposeAndMultiply(matrixB, matrixC);

            Assert.AreEqual(matrixC.RowCount, matrixA.RowCount);
            Assert.AreEqual(matrixC.ColumnCount, matrixB.RowCount);

            for (var i = 0; i < matrixC.RowCount; i++)
            {
                for (var j = 0; j < matrixC.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixA.Row(i) * matrixB.Row(j), matrixC[i, j], 15);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void MultiplyMatrixMatrixFailsWhenSizesAreIncompatible()
        {
            var matrix = TestMatrices["Singular3x3"];
            var other = TestMatrices["Wide2x3"];
            var result = matrix * other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void MultiplyMatrixMatrixFailsWhenLeftArgumentIsNull()
        {
            Matrix<Complex> matrix = null;
            var other = TestMatrices["Wide2x3"];
            var result = matrix * other;
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void MultiplyMatrixMatrixFailsWhenRightArgumentIsNull()
        {
            var matrix = TestMatrices["Wide2x3"];
            Matrix<Complex> other = null;
            var result = matrix * other;
        }

        [Test]
        [Row("Singular3x3", "Square3x3")]
        [Row("Singular4x4", "Square4x4")]
        [Row("Wide2x3", "Square3x3")]
        [Row("Wide2x3", "Tall3x2")]
        [Row("Tall3x2", "Wide2x3")]
        [MultipleAsserts]
        public virtual void CanMultiplyMatrixWithMatrixIntoResult(string nameA, string nameB)
        {
            var matrixA = TestMatrices[nameA];
            var matrixB = TestMatrices[nameB];
            var matrixC = CreateMatrix(matrixA.RowCount, matrixB.ColumnCount);
            matrixA.Multiply(matrixB, matrixC);

            Assert.AreEqual(matrixC.RowCount, matrixA.RowCount);
            Assert.AreEqual(matrixC.ColumnCount, matrixB.ColumnCount);

            for (var i = 0; i < matrixC.RowCount; i++)
            {
                for (var j = 0; j < matrixC.ColumnCount; j++)
                {
                    AssertHelpers.AlmostEqual(matrixA.Row(i) * matrixB.Column(j), matrixC[i, j], 15);
                }
            }
        }

        [Test]
        [Row("Singular3x3")]
        [Row("Square3x3")]
        [Row("Square4x4")]
        [Row("Tall3x2")]
        [Row("Wide2x3")]
        [MultipleAsserts]
        public void CanNegate(string name)
        {
            var matrix = TestMatrices[name];
            var copy = matrix.Clone();

            var result = copy.Negate();

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(-matrix[i, j], result[i, j]);
                }
            }
        }

        [Test]
        [Row("Singular3x3")]
        [Row("Square3x3")]
        [Row("Square4x4")]
        [Row("Tall3x2")]
        [Row("Wide2x3")]
        [MultipleAsserts, Ignore]
        public void CanNegateIntoResult(string name)
        {
            var matrix = TestMatrices[name];
            var copy = matrix.Clone();
            var result = CreateMatrix(copy.RowCount, copy.ColumnCount);
            //matrix.Negate(copy, result);

            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(-matrix[i, j], copy[i, j]);
                }
            }
        }

        [Test]
        [ExpectedArgumentNullException]
        public void NegateIntoResultFailsWhenResultIsNull()
        {
            var matrix = TestMatrices["Singular3x3"];
            Matrix<Complex> copy = null;
            matrix.Negate(copy);
        }

        [Test]
        [ExpectedArgumentException]
        public void NegateIntoResultFailsWhenResultHasMoreRows()
        {
            var matrix = TestMatrices["Singular3x3"];
            var target = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            matrix.Negate(target);
        }

        [Test]
        [ExpectedArgumentException]
        public void NegateIntoResultFailsWhenResultHasMoreColumns()
        {
            var matrix = TestMatrices["Singular3x3"];
            var target = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            matrix.Negate(target);
        }


        [Test]
        public void KroneckerProduct()
        {
            var matrixA = TestMatrices["Wide2x3"];
            var matrixB = TestMatrices["Square3x3"];
            var result = CreateMatrix(matrixA.RowCount * matrixB.RowCount, matrixA.ColumnCount * matrixB.ColumnCount);
            matrixA.KroneckerProduct(matrixB, result);
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                for (var j = 0; j < matrixA.ColumnCount; j++)
                {
                    for (var ii = 0; ii < matrixB.RowCount; ii++)
                    {
                        for (var jj = 0; jj < matrixB.ColumnCount; jj++)
                        {
                            AssertHelpers.AreEqual(result[i * matrixB.RowCount + ii, j * matrixB.ColumnCount + jj], matrixA[i, j] * matrixB[ii, jj]);
                        }
                    }
                }
            }
        }

        [Test]
        public void KroneckerProductResult()
        {
            var matrixA = TestMatrices["Wide2x3"];
            var matrixB = TestMatrices["Square3x3"];
            var result = matrixA.KroneckerProduct(matrixB);
            for (var i = 0; i < matrixA.RowCount; i++)
            {
                for (var j = 0; j < matrixA.ColumnCount; j++)
                {
                    for (var ii = 0; ii < matrixB.RowCount; ii++)
                    {
                        for (var jj = 0; jj < matrixB.ColumnCount; jj++)
                        {
                            AssertHelpers.AreEqual(result[i * matrixB.RowCount + ii, j * matrixB.ColumnCount + jj], matrixA[i, j] * matrixB[ii, jj]);
                        }
                    }
                }
            }
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(-4, ExpectedException = typeof(ArgumentOutOfRangeException))]
        public void NormalizeColumns(int pValue)
        {
            var matrix = TestMatrices["Square4x4"];

            var result = matrix.NormalizeColumns(pValue);
            for (var j = 0; j < result.ColumnCount; j++)
            {
                var col = result.Column(j);
                AssertHelpers.AlmostEqual(Complex.One, col.Norm(pValue), 12);
            }
        }

        [Test]
        [Row(1)]
        [Row(2)]
        [Row(-3, ExpectedException = typeof(ArgumentOutOfRangeException))]
        public void NormalizeRows(int pValue)
        {
            var matrix = TestMatrices["Square4x4"].NormalizeRows(pValue);
            for (var i = 0; i < matrix.RowCount; i++)
            {
                var row = matrix.Row(i);
                AssertHelpers.AlmostEqual(Complex.One, row.Norm(pValue), 12);
            }
        }

        [Test]
        public void PointwiseMultiplyResult()
        {
            foreach (var  data in TestMatrices.Values)
            {
                var other = data.Clone();
                var result = data.Clone();
                data.PointwiseMultiply(other, result);
                for (var i = 0; i < data.RowCount; i++)
                {
                    for (var j = 0; j < data.ColumnCount; j++)
                    {
                        AssertHelpers.AreEqual(data[i, j] * other[i, j], result[i, j]);
                    }
                }

                result = data.PointwiseMultiply(other);
                for (var i = 0; i < data.RowCount; i++)
                {
                    for (var j = 0; j < data.ColumnCount; j++)
                    {
                        AssertHelpers.AreEqual(data[i, j] * other[i, j], result[i, j]);
                    }
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void PointwiseMultiplyWithNullOtherShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            Matrix<Complex> other = null;
            var result = matrix.Clone();
            matrix.PointwiseMultiply(other, result);
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void PointwiseMultiplyWithResultNullShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = matrix.Clone();
            matrix.PointwiseMultiply(other, null);
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void PointwiseMultiplyWithInvalidOtherMatrixDimensionsShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            var result = matrix.Clone();
            matrix.PointwiseMultiply(other, result);
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void PointwiseMultiplyWithInvalidResultMatrixDimensionsShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = matrix.Clone();
            var result = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            matrix.PointwiseMultiply(other, result);
        }

        [Test]
        public virtual void PointwiseDivideResult()
        {
            var data = TestMatrices["Singular3x3"];
            var other = data.Clone();
            var result = data.Clone();
            data.PointwiseDivide(other, result);
            for (var i = 0; i < data.RowCount; i++)
            {
                for (var j = 0; j < data.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(data[i, j] / other[i, j], result[i, j]);
                }
            }

            result = data.PointwiseDivide(other);
            for (var i = 0; i < data.RowCount; i++)
            {
                for (var j = 0; j < data.ColumnCount; j++)
                {
                    AssertHelpers.AreEqual(data[i, j] / other[i, j], result[i, j]);
                }
            }
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void PointwiseDivideWithNullOtherShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            Matrix<Complex> other = null;
            var result = matrix.Clone();
            matrix.PointwiseDivide(other, result);
        }

        [Test]
        [ExpectedException(typeof(ArgumentNullException))]
        public void PointwiseDivideWithResultNullShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = matrix.Clone();
            matrix.PointwiseDivide(other, null);
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void PointwiseDivideWithInvalidOtherMatrixDimensionsShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            var result = matrix.Clone();
            matrix.PointwiseDivide(other, result);
        }

        [Test]
        [ExpectedException(typeof(ArgumentException))]
        public void PointwiseDivideWithInvalidResultMatrixDimensionsShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var other = matrix.Clone();
            var result = CreateMatrix(matrix.RowCount + 1, matrix.ColumnCount);
            matrix.PointwiseDivide(other, result);
        }

        [Test]
        [Row(0, ExpectedException = typeof(ArgumentException))]
        [Row(-2, ExpectedException = typeof(ArgumentException))]
        public void RandomWithNonPositiveNumberOfRowsShouldThrowException(int numberOfRows)
        {
            var matrix = CreateMatrix(2, 3);
            matrix = matrix.Random(numberOfRows, 4, new ContinuousUniform());
        }

        [Test]
        [Row(0, ExpectedException = typeof(ArgumentException))]
        [Row(-2, ExpectedException = typeof(ArgumentException))]
        public void RandomWithNonPositiveNumberOfRowsShouldThrowException2(int numberOfRows)
        {
            var matrix = CreateMatrix(2, 3);
            matrix = matrix.Random(numberOfRows, 4, new DiscreteUniform(0, 2));
        }

        [Test]
        public void Trace()
        {
            var matrix = TestMatrices["Square3x3"];
            var trace = matrix.Trace();
            AssertHelpers.AreEqual(new Complex(6.6, 3), trace);
        }

        [Test]
        [ExpectedArgumentException]
        public void TraceOfNonSquareMatrixShouldThrowException()
        {
            var matrix = TestMatrices["Wide2x3"];
            var trace = matrix.Trace();
        }
    }
}