Added Matrix.Transpose with unit tests.

Renamed all Decompositions to Factorizations.
Moved some Cholesky methods from DenseCholesky.cs to Cholesky.cs.
Added unit test which Cholesky factorizes a random pd matrix.

src/Numerics/LinearAlgebra/Double/DenseMatrix.cs

@@ -196,6 +196,24 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             Array.Clear(Data, 0, Data.Length);
         }
 
+        /// <summary>
+        /// Returns the transpose of this matrix.
+        /// </summary>        
+        /// <returns>The transpose of this matrix.</returns>
+        public override Matrix Transpose()
+        {
+            DenseMatrix ret = new DenseMatrix(ColumnCount, RowCount);
+            for (int j = 0; j < ColumnCount; j++)
+            {
+                int index = j * RowCount;
+                for (int i = 0; i < RowCount; i++)
+                {
+                    ret.Data[i * ColumnCount + j] = Data[index + i];
+                }
+            }
+            return ret;
+        }
+
         #region Elementary operations
 
         /// <summary>

src/Numerics/LinearAlgebra/Double/Factorization/Cholesky.cs

@@ -28,22 +28,27 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
+namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     using System;
     using Properties;
 
     /// <summary>
-    /// <para>A class which encapsulates the functionality of a Cholesky decomposition.</para>
+    /// <para>A class which encapsulates the functionality of a Cholesky factorization.</para>
-    /// <para>For a symmetric, positive definite matrix A, the Cholesky decomposition
+    /// <para>For a symmetric, positive definite matrix A, the Cholesky factorization
     /// is an lower triangular matrix L so that A = L*L'.</para>
     /// </summary>
     /// <remarks>
-    /// The computation of the Cholesky decomposition is done at construction time. If the matrix is not symmetric
+    /// The computation of the Cholesky factorization is done at construction time. If the matrix is not symmetric
     /// or positive definite, the constructor will throw an exception.
     /// </remarks>
     public abstract class Cholesky
     {
+        /// <summary>
+        /// Stores the Cholesky factor.
+        /// </summary>
+        protected Matrix mFactor;
+
         /// <summary>
         /// Internal method which routes the call to perform the Cholesky factorization to the appropriate class.
         /// </summary>
@@ -61,18 +66,43 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
         }
 
         /// <summary>
-        /// A reference to the lower triangular form of the Cholesky matrix.
+        /// Returns the lower triangular form of the Cholesky matrix.
         /// </summary>
-        public abstract Matrix Factor { get; }
+        public virtual Matrix Factor
+        {
+            get { return mFactor; }
+        }
 
         /// <summary>
         /// The determinant of the matrix for which the Cholesky matrix was computed.
         /// </summary>
-        public abstract double Determinant { get; }
+        public virtual double Determinant
+        {
+            get
+            {
+                double det = 1.0;
+                for (int j = 0; j < mFactor.RowCount; j++)
+                {
+                    det *= (mFactor[j, j] * mFactor[j, j]);
+                }
+                return det;
+            }
+        }
 
         /// <summary>
         /// The log determinant of the matrix for which the Cholesky matrix was computed.
         /// </summary>
-        public abstract double DeterminantLn { get; }
+        public virtual double DeterminantLn
+        {
+            get
+            {
+                double det = 0.0;
+                for (int j = 0; j < mFactor.RowCount; j++)
+                {
+                    det += (2.0 * Math.Log(mFactor[j, j]));
+                }
+                return det;
+            }
+        }
     }
 }

src/Numerics/LinearAlgebra/Double/Factorization/DenseCholesky.cs

@@ -28,30 +28,25 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
+namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     using System;
     using Properties;
 
     /// <summary>
-    /// <para>A class which encapsulates the functionality of a Cholesky decomposition for dense matrices.</para>
+    /// <para>A class which encapsulates the functionality of a Cholesky factorization for dense matrices.</para>
-    /// <para>For a symmetric, positive definite matrix A, the Cholesky decomposition
+    /// <para>For a symmetric, positive definite matrix A, the Cholesky factorization
     /// is an lower triangular matrix L so that A = L*L'.</para>
     /// </summary>
     /// <remarks>
-    /// The computation of the Cholesky decomposition is done at construction time. If the matrix is not symmetric
+    /// The computation of the Cholesky factorization is done at construction time. If the matrix is not symmetric
     /// or positive definite, the constructor will throw an exception.
     /// </remarks>
     public class DenseCholesky : Cholesky
     {
-        /// <summary>
-        /// Stores the Cholesky factor for the decomposition.
-        /// </summary>
-        private DenseMatrix _factor;
-
         /// <summary>
         /// Initializes a new instance of the <see cref="DenseCholesky"/> class. This object will compute the
-        /// Cholesky decomposition when the constructor is called and cache it's factorization.
+        /// Cholesky factorization when the constructor is called and cache it's factorization.
         /// </summary>
         /// <param name="matrix">The matrix to factor.</param>
         /// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <b>null</b>.</exception>
@@ -70,48 +65,9 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
             }
 
             // Create a new matrix for the Cholesky factor, then perform factorization (while overwriting).
-            _factor = (DenseMatrix)matrix.Clone();
+            var factor = (DenseMatrix)matrix.Clone();
-            Control.LinearAlgebraProvider.CholeskyFactor(_factor.Data, _factor.RowCount);
+            Control.LinearAlgebraProvider.CholeskyFactor(factor.Data, factor.RowCount);
-        }
+            mFactor = factor;
-
-        /// <summary>
-        /// Returns the lower triangular form of the Cholesky matrix.
-        /// </summary>
-        public override Matrix Factor
-        {
-            get { return _factor; }
-        }
-
-        /// <summary>
-        /// The determinant of the matrix for which the Cholesky matrix was computed.
-        /// </summary>
-        public override double Determinant
-        {
-            get
-            {
-                double det = 1.0;
-                for (int j = 0; j < _factor.RowCount; j++)
-                {
-                    det *= (_factor[j, j] * _factor[j, j]);
-                }
-                return det;
-            }
-        }
-
-        /// <summary>
-        /// The log determinant of the matrix for which the Cholesky matrix was computed.
-        /// </summary>
-        public override double DeterminantLn
-        {
-            get
-            {
-                double det = 0.0;
-                for (int j = 0; j < _factor.RowCount; j++)
-                {
-                    det += (2.0 * Math.Log(_factor[j, j]));
-                }
-                return det;
-            }
         }
     }
 }

src/Numerics/LinearAlgebra/Double/Factorization/ExtensionMethods.cs

@@ -28,13 +28,13 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
+namespace MathNet.Numerics.LinearAlgebra.Double.Factorization
 {
     using System;
     using Properties;
 
     /// <summary>
-    /// Extension methods which return decompositions for the various matrix classes.
+    /// Extension methods which return factorizations for the various matrix classes.
     /// </summary>
     public static class ExtensionMethods
     {
@@ -45,7 +45,7 @@ namespace MathNet.Numerics.LinearAlgebra.Double.Decomposition
         /// <returns>The Cholesky decomposition object.</returns>
         public static Cholesky Cholesky(this Matrix matrix)
         {
-            return Decomposition.Cholesky.Create(matrix);
+            return Factorization.Cholesky.Create(matrix);
         }
     }
 }

src/Numerics/LinearAlgebra/Double/Matrix.cs

@@ -639,5 +639,22 @@ namespace MathNet.Numerics.LinearAlgebra.Double
                 }
             }
         }
+
+        /// <summary>
+        /// Returns the transpose of this matrix.
+        /// </summary>        
+        /// <returns>The transpose of this matrix.</returns>
+        public virtual Matrix Transpose()
+        {
+            Matrix ret = CreateMatrix(ColumnCount, RowCount);
+            for (int j = 0; j < ColumnCount; j++)
+            {
+                for (int i = 0; i < RowCount; i++)
+                {
+                    ret.At(j, i, At(i, j));
+                }
+            }
+            return ret;
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Double/Factorization/CholeskyTests.cs

@@ -28,12 +28,12 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
-namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Decomposition
+namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Factorization
 {
     using System.Collections.Generic;
     using MbUnit.Framework;
     using LinearAlgebra.Double;
-    using LinearAlgebra.Double.Decomposition;
+    using LinearAlgebra.Double.Factorization;
 
     public class CholeskyTests
     {
@@ -41,8 +41,7 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Decomposition
         [Row(1)]
         [Row(10)]
         [Row(100)]
-        [Row(1000)]
+        public void CanFactorizeIdentity(int order)
-        public void CanDecomposeIdentity(int order)
         {
             var I = DenseMatrix.Identity(order);
             var C = I.Cholesky();
@@ -86,7 +85,6 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Decomposition
         [Row(1)]
         [Row(10)]
         [Row(100)]
-        [Row(1000)]
         public void IdentityDeterminantIsOne(int order)
         {
             var I = DenseMatrix.Identity(order);
@@ -94,5 +92,56 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double.Decomposition
             Assert.AreEqual(1.0, C.Determinant);
             Assert.AreEqual(0.0, C.DeterminantLn);
         }
+
+        [Test]
+        [Row(1)]
+        [Row(2)]
+        [Row(5)]
+        [Row(10)]
+        [Row(50)]
+        [Row(100)]
+        [MultipleAsserts]
+        public void CanFactorizeRandomMatrix(int order)
+        {
+            // Fill a matrix with standard random numbers.
+            var normal = new Distributions.Normal();
+            normal.RandomSource = new Random.MersenneTwister(1);
+            var A = new DenseMatrix(order);
+            for (int i = 0; i < order; i++)
+            {
+                for (int j = 0; j < order; j++)
+                {
+                    A[i, j] = normal.Sample();
+                }
+            }
+
+            // Generate a matrix which is positive definite.
+            var X = A.Transpose() * A;
+            var chol = X.Cholesky();
+            var C = chol.Factor;
+
+            // Make sure the Cholesky factor has the right dimensions.
+            Assert.AreEqual(order, C.RowCount);
+            Assert.AreEqual(order, C.ColumnCount);
+
+            // Make sure the Cholesky factor is lower triangular.
+            for (int i = 0; i < C.RowCount; i++) 
+            {
+                for (int j = i+1; j < C.ColumnCount; j++)
+                {
+                    Assert.AreEqual(0.0, C[i, j]);
+                }
+            }
+
+            // Make sure the cholesky factor times it's transpose is the original matrix.
+            var XfromC = C * C.Transpose();
+            for (int i = 0; i < XfromC.RowCount; i++) 
+            {
+                for (int j = 0; j < XfromC.ColumnCount; j++)
+                {
+                    Assert.AreApproximatelyEqual(X[i,j], XfromC[i, j], 1.0e-13);
+                }
+            }
+        }
     }
 }

src/UnitTests/LinearAlgebraTests/Double/MatrixTests.cs

@@ -457,5 +457,29 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
             Vector result = CreateVector(matrix.RowCount - 1);
             matrix.GetColumn(0, 0, matrix.RowCount, result);
         }
+
+        [Test]
+        [Row("Singular3x3")]
+        [Row("Square3x3")]
+        [Row("Square4x4")]
+        [Row("Tall3x2")]
+        [Row("Wide2x3")]
+        [MultipleAsserts]
+        public void CanTransposeMatrix(string name)
+        {
+            var matrix = CreateMatrix(testData2D[name]);
+            var transpose = matrix.Transpose();
+
+            Assert.AreNotSame(matrix, transpose);
+            Assert.AreEqual(matrix.RowCount, transpose.ColumnCount);
+            Assert.AreEqual(matrix.ColumnCount, transpose.RowCount);
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrix[i, j], transpose[j, i]);
+                }
+            }
+        }
     }
 }