forked from tsai/mathnet-numerics
Marcus Cuda
16 years ago
19 changed files with 2606 additions and 2 deletions
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// <copyright file="DirectSolvers.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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// Copyright (c) 2009-2010 Math.NET
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
|
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
|
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
|
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
|
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace Examples.LinearAlgebra |
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{ |
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using System; |
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using System.Globalization; |
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using MathNet.Numerics.LinearAlgebra.Double; |
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using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
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/// <summary>
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/// Direct solvers (using matrix decompositions)
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/// </summary>
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/// <seealso cref="http://en.wikipedia.org/wiki/Numerical_analysis#Direct_and_iterative_methods"/>
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public class DirectSolvers : IExample |
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{ |
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/// <summary>
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/// Gets the name of this example
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/// </summary>
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public string Name |
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{ |
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get |
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{ |
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return "Direct solvers"; |
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} |
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} |
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/// <summary>
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/// Gets the description of this example
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/// </summary>
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public string Description |
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{ |
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get |
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{ |
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return "Solve linear equations using matrix decompositions"; |
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} |
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} |
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/// <summary>
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/// Run example
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/// </summary>
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public void Run() |
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{ |
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// Format matrix output to console
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var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
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formatProvider.TextInfo.ListSeparator = " "; |
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// Solve next system of linear equations (Ax=b):
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// 5*x + 2*y - 4*z = -7
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// 3*x - 7*y + 6*z = 38
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// 4*x + 1*y + 5*z = 43
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// Create matrix "A" with coefficients
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var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } }); |
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Console.WriteLine(@"Matrix 'A' with coefficients"); |
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Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// Create vector "b" with the constant terms.
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var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 }); |
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Console.WriteLine(@"Vector 'b' with the constant terms"); |
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Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 1. Solve linear equations using LU decomposition
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var resultX = matrixA.LU().Solve(vectorB); |
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Console.WriteLine(@"1. Solution using LU decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 2. Solve linear equations using QR decomposition
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resultX = matrixA.QR().Solve(vectorB); |
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Console.WriteLine(@"2. Solution using QR decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 3. Solve linear equations using SVD decomposition
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matrixA.Svd(true).Solve(vectorB, resultX); |
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Console.WriteLine(@"3. Solution using SVD decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 4. Solve linear equations using Gram-Shmidt decomposition
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matrixA.GramSchmidt().Solve(vectorB, resultX); |
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Console.WriteLine(@"4. Solution using Gram-Shmidt decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 5. Verify result. Multiply coefficient matrix "A" by result vector "x"
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var reconstructVecorB = matrixA * resultX; |
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Console.WriteLine(@"5. Multiply coefficient matrix 'A' by result vector 'x'"); |
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Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// To use Cholesky or Eigenvalue decomposition coefficient matrix must be
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// symmetric (for Evd and Cholesky) and positive definite (for Cholesky)
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// Multipy matrix "A" by its transpose - the result will be symmetric and positive definite matrix
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var newMatrixA = matrixA.TransposeAndMultiply(matrixA); |
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Console.WriteLine(@"Symmetric positive definite matrix"); |
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Console.WriteLine(newMatrixA.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 6. Solve linear equations using Cholesky decomposition
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newMatrixA.Cholesky().Solve(vectorB, resultX); |
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Console.WriteLine(@"6. Solution using Cholesky decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 7. Solve linear equations using eigen value decomposition
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newMatrixA.Evd().Solve(vectorB, resultX); |
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Console.WriteLine(@"7. Solution using eigen value decomposition"); |
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Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 8. Verify result. Multiply new coefficient matrix "A" by result vector "x"
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reconstructVecorB = newMatrixA * resultX; |
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Console.WriteLine(@"8. Multiply new coefficient matrix 'A' by result vector 'x'"); |
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Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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} |
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} |
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} |
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@ -0,0 +1,105 @@ |
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// <copyright file="Cholesky.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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// Copyright (c) 2009-2010 Math.NET
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// Permission is hereby granted, free of charge, to any person
|
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|
// obtaining a copy of this software and associated documentation
|
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|
// files (the "Software"), to deal in the Software without
|
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|
// restriction, including without limitation the rights to use,
|
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|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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|
// copies of the Software, and to permit persons to whom the
|
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|
// Software is furnished to do so, subject to the following
|
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|
// conditions:
|
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|
// The above copyright notice and this permission notice shall be
|
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// included in all copies or substantial portions of the Software.
|
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|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
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|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
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|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
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|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
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// OTHER DEALINGS IN THE SOFTWARE.
|
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// </copyright>
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namespace Examples.LinearAlgebra.Factorization |
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{ |
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using System; |
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using System.Globalization; |
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using MathNet.Numerics.LinearAlgebra.Double; |
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using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
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/// <summary>
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/// Cholesky factorization example. For a symmetric, positive definite matrix A, the Cholesky factorization
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/// is an lower triangular matrix L so that A = L*L'
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/// </summary>
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/// <seealso cref="http://reference.wolfram.com/mathematica/ref/CholeskyDecomposition.html"/>
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public class Cholesky : IExample |
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{ |
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/// <summary>
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/// Gets the name of this example
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/// </summary>
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public string Name |
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{ |
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get |
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{ |
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return "Cholesky factorization"; |
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} |
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} |
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/// <summary>
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/// Gets the description of this example
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/// </summary>
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public string Description |
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{ |
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get |
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{ |
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return "Perform the Cholesky factorization to the appropriate class"; |
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} |
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} |
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/// <summary>
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/// Run example
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/// </summary>
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/// <seealso cref="http://en.wikipedia.org/wiki/Cholesky_decomposition">Cholesky decomposition</seealso>
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public void Run() |
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{ |
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// Format matrix output to console
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var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
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formatProvider.TextInfo.ListSeparator = " "; |
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// Create square, symmetric, positive definite matrix
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var matrix = new DenseMatrix(new[,] { { 2.0, 1.0 }, { 1.0, 2.0 } }); |
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Console.WriteLine(@"Initial square, symmetric, positive definite matrix"); |
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Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// Perform Cholesky decomposition
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var cholesky = matrix.Cholesky(); |
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Console.WriteLine(@"Perform Cholesky decomposition"); |
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// 1. Lower triangular form of the Cholesky matrix
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Console.WriteLine(@"1. Lower triangular form of the Cholesky matrix"); |
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Console.WriteLine(cholesky.Factor.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 2. Reconstruct initial matrix: A = L * LT
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var reconstruct = cholesky.Factor * cholesky.Factor.Transpose(); |
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Console.WriteLine(@"2. Reconstruct initial matrix: A = L*LT"); |
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Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 3. Get determinant of the matrix
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Console.WriteLine(@"3. Determinant of the matrix"); |
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Console.WriteLine(cholesky.Determinant); |
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Console.WriteLine(); |
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// 4. Get log determinant of the matrix
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Console.WriteLine(@"4. Log determinant of the matrix"); |
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Console.WriteLine(cholesky.DeterminantLn); |
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Console.WriteLine(); |
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} |
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} |
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} |
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// <copyright file="Evd.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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// Copyright (c) 2009-2010 Math.NET
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// Permission is hereby granted, free of charge, to any person
|
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|
// obtaining a copy of this software and associated documentation
|
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|
// files (the "Software"), to deal in the Software without
|
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|
// restriction, including without limitation the rights to use,
|
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|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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|
// copies of the Software, and to permit persons to whom the
|
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// Software is furnished to do so, subject to the following
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// conditions:
|
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// The above copyright notice and this permission notice shall be
|
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// included in all copies or substantial portions of the Software.
|
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|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
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|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
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|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
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|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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namespace Examples.LinearAlgebra.Factorization |
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{ |
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using System; |
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using System.Globalization; |
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using MathNet.Numerics.LinearAlgebra.Double; |
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using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
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/// <summary>
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/// EVD factorization example. If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
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/// diagonal and the eigenvector matrix V is orthogonal. I.e. A = V*D*V' and V*VT=I.
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/// If A is not symmetric, then the eigenvalue matrix D is block diagonal
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/// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
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/// lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The
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/// columns of V represent the eigenvectors in the sense thatA * V = V * D.
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/// The matrix V may be badly conditioned, or even singular, so the validity of the equation
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/// A = V*D*Inverse(V) depends upon V.Condition()
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/// </summary>
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/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Norm.html"/>
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public class Evd : IExample |
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{ |
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/// <summary>
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/// Gets the name of this example
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/// </summary>
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public string Name |
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{ |
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get |
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{ |
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return "Evd factorization"; |
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} |
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} |
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/// <summary>
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/// Gets the description of this example
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/// </summary>
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public string Description |
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{ |
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get |
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{ |
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return "Perform the Evd factorization: eigenvalues and eigenvectors calculation"; |
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} |
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} |
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/// <summary>
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/// Run example
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/// </summary>
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/// <seealso cref="http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace">EVD decomposition</seealso>
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public void Run() |
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{ |
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// Format matrix output to console
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var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
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formatProvider.TextInfo.ListSeparator = " "; |
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// Create square symmetric matrix
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var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 2.0, 1.0, 4.0 }, { 3.0, 4.0, 1.0 } }); |
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Console.WriteLine(@"Initial square symmetric matrix"); |
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Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// Perform eigenvalue decomposition of symmetric matrix
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var evd = matrix.Evd(); |
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Console.WriteLine(@"Perform eigenvalue decomposition of symmetric matrix"); |
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// 1. Eigen vectors
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Console.WriteLine(@"1. Eigen vectors"); |
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Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 2. Eigen values as a complex vector
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Console.WriteLine(@"2. Eigen values as a complex vector"); |
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Console.WriteLine(evd.EigenValues().ToString("N", formatProvider)); |
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Console.WriteLine(); |
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// 3. Eigen values as the block diagonal matrix
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Console.WriteLine(@"3. Eigen values as the block diagonal matrix"); |
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Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 4. Multiply V by its transpose VT
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var identity = evd.EigenVectors().TransposeAndMultiply(evd.EigenVectors()); |
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Console.WriteLine(@"4. Multiply V by its transpose VT: V*VT = I"); |
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Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 5. Reconstruct initial matrix: A = V*D*V'
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var reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Transpose(); |
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Console.WriteLine(@"5. Reconstruct initial matrix: A = V*D*V'"); |
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Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 6. Determinant of the matrix
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Console.WriteLine(@"6. Determinant of the matrix"); |
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Console.WriteLine(evd.Determinant); |
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Console.WriteLine(); |
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// 7. Rank of the matrix
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Console.WriteLine(@"7. Rank of the matrix"); |
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Console.WriteLine(evd.Rank); |
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Console.WriteLine(); |
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// Fill matrix by random values
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var rnd = new Random(1); |
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for (var i = 0; i < matrix.RowCount; i++) |
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{ |
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for (var j = 0; j < matrix.ColumnCount; j++) |
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{ |
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matrix[i, j] = rnd.NextDouble(); |
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} |
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} |
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Console.WriteLine(@"Fill matrix by random values"); |
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Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// Perform eigenvalue decomposition of non-symmetric matrix
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evd = matrix.Evd(); |
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Console.WriteLine(@"Perform eigenvalue decomposition of non-symmetric matrix"); |
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// 8. Eigen vectors
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Console.WriteLine(@"8. Eigen vectors"); |
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Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider)); |
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Console.WriteLine(); |
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// 9. Eigen values as a complex vector
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Console.WriteLine(@"9. Eigen values as a complex vector"); |
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Console.WriteLine(evd.EigenValues().ToString("N", formatProvider)); |
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Console.WriteLine(); |
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// 10. Eigen values as the block diagonal matrix
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Console.WriteLine(@"10. Eigen values as the block diagonal matrix"); |
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Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 11. Multiply A * V
|
||||
|
var av = matrix * evd.EigenVectors(); |
||||
|
Console.WriteLine(@"11. Multiply A * V"); |
||||
|
Console.WriteLine(av.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 12. Multiply V * D
|
||||
|
var vd = evd.EigenVectors() * evd.D(); |
||||
|
Console.WriteLine(@"12. Multiply V * D"); |
||||
|
Console.WriteLine(vd.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 13. Reconstruct non-symmetriv matrix A = V * D * Vinverse
|
||||
|
reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Inverse(); |
||||
|
Console.WriteLine(@"13. Reconstruct non-symmetriv matrix A = V * D * Vinverse"); |
||||
|
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 14. Determinant of the matrix
|
||||
|
Console.WriteLine(@"14. Determinant of the matrix"); |
||||
|
Console.WriteLine(evd.Determinant); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 15. Rank of the matrix
|
||||
|
Console.WriteLine(@"15. Rank of the matrix"); |
||||
|
Console.WriteLine(evd.Rank); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,135 @@ |
|||||
|
// <copyright file="LU.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra.Factorization |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// LU factorization example. For a matrix A, the LU factorization is a pair of lower triangular matrix L and
|
||||
|
/// upper triangular matrix U so that A = L*U.
|
||||
|
/// In the Math.Net implementation we also store a set of pivot elements for increased
|
||||
|
/// numerical stability. The pivot elements encode a permutation matrix P such that P*A = L*U
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/LUDecomposition.html"/>
|
||||
|
public class LU : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "LU factorization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Perform the LU factorization to the appropriate class"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/LU_decomposition">LU decomposition</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create square matrix
|
||||
|
var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 } }); |
||||
|
Console.WriteLine(@"Initial square matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Perform LU decomposition
|
||||
|
var lu = matrix.LU(); |
||||
|
Console.WriteLine(@"Perform LU decomposition"); |
||||
|
|
||||
|
// 1. Lower triangular factor
|
||||
|
Console.WriteLine(@"1. Lower triangular factor"); |
||||
|
Console.WriteLine(lu.L.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Upper triangular factor
|
||||
|
Console.WriteLine(@"2. Upper triangular factor"); |
||||
|
Console.WriteLine(lu.U.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Permutations applied to LU factorization
|
||||
|
Console.WriteLine(@"3. Permutations applied to LU factorization"); |
||||
|
for (var i = 0; i < lu.P.Dimension; i++) |
||||
|
{ |
||||
|
if (lu.P[i] > i) |
||||
|
{ |
||||
|
Console.WriteLine(@"Row {0} permuted with row {1}", lu.P[i], i); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Reconstruct initial matrix: PA = L * U
|
||||
|
var reconstruct = lu.L * lu.U; |
||||
|
|
||||
|
// The rows of the reconstructed matrix should be permuted to get the initial matrix
|
||||
|
reconstruct.PermuteRows(lu.P.Inverse()); |
||||
|
Console.WriteLine(@"4. Reconstruct initial matrix: PA = L*U"); |
||||
|
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Get the determinant of the matrix
|
||||
|
Console.WriteLine(@"5. Determinant of the matrix"); |
||||
|
Console.WriteLine(lu.Determinant); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Get the inverse of the matrix
|
||||
|
var matrixInverse = lu.Inverse(); |
||||
|
Console.WriteLine(@"6. Inverse of the matrix"); |
||||
|
Console.WriteLine(matrixInverse.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 7. Matrix multiplied by its inverse
|
||||
|
var identity = matrix * matrixInverse; |
||||
|
Console.WriteLine(@"7. Matrix multiplied by its inverse "); |
||||
|
Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,132 @@ |
|||||
|
// <copyright file="QR.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra.Factorization |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// QR factorization example. Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (m x m)
|
||||
|
/// (its columns are orthogonal unit vectors meaning QTQ = I) and R (m x n) is an upper triangular matrix
|
||||
|
/// (also called right triangular matrix).
|
||||
|
/// In this example two methods for actually computing the QR decomposition presented: by means of the Gram–Schmidt process and Householder transformations.
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/QRDecomposition.html"/>
|
||||
|
public class QR : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "QR factorization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Perform the QR factorization by means of the Gram–Schmidt process and Householder transformations"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create 3 x 2 matrix
|
||||
|
var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 }, { 5.0, 6.0 } }); |
||||
|
Console.WriteLine(@"Initial 3x2 matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Perform QR decomposition (Householder transformations)
|
||||
|
var qr = matrix.QR(); |
||||
|
Console.WriteLine(@"QR decomposition (Householder transformations)"); |
||||
|
|
||||
|
// 1. Orthogonal Q matrix
|
||||
|
Console.WriteLine(@"1. Orthogonal Q matrix"); |
||||
|
Console.WriteLine(qr.Q.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Multiply Q matrix by its transpose gives identity matrix
|
||||
|
Console.WriteLine(@"2. Multiply Q matrix by its transpose gives identity matrix"); |
||||
|
Console.WriteLine(qr.Q.TransposeAndMultiply(qr.Q).ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Upper triangular factor R
|
||||
|
Console.WriteLine(@"3. Upper triangular factor R"); |
||||
|
Console.WriteLine(qr.R.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Reconstruct initial matrix: A = Q * R
|
||||
|
var reconstruct = qr.Q * qr.R; |
||||
|
Console.WriteLine(@"4. Reconstruct initial matrix: A = Q*R"); |
||||
|
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Perform QR decomposition (Gram–Schmidt process)
|
||||
|
qr = matrix.GramSchmidt(); |
||||
|
Console.WriteLine(@"QR decomposition (Gram–Schmidt process)"); |
||||
|
|
||||
|
// 5. Orthogonal Q matrix
|
||||
|
Console.WriteLine(@"5. Orthogonal Q matrix"); |
||||
|
Console.WriteLine(qr.Q.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Multiply Q matrix by its transpose gives identity matrix
|
||||
|
Console.WriteLine(@"6. Multiply Q matrix by its transpose gives identity matrix"); |
||||
|
Console.WriteLine((qr.Q.Transpose() * qr.Q).ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 7. Upper triangular factor R
|
||||
|
Console.WriteLine(@"7. Upper triangular factor R"); |
||||
|
Console.WriteLine(qr.R.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 8. Reconstruct initial matrix: A = Q * R
|
||||
|
reconstruct = qr.Q * qr.R; |
||||
|
Console.WriteLine(@"8. Reconstruct initial matrix: A = Q*R"); |
||||
|
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,186 @@ |
|||||
|
// <copyright file="Svd.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra.Factorization |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// SVD factorization example. Suppose M is an m-by-n matrix whose entries are real numbers.
|
||||
|
/// Then there exists a factorization of the form M = UΣVT where:
|
||||
|
/// - U is an m-by-m unitary matrix;
|
||||
|
/// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
|
||||
|
/// - VT denotes transpose of V, an n-by-n unitary matrix;
|
||||
|
/// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
|
||||
|
/// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
|
||||
|
/// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/SingularValueDecomposition.html"/>
|
||||
|
public class Svd : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Svd factorization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Perform the Svd factorization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Singular_value_decomposition">SVD decomposition</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create square matrix
|
||||
|
var matrix = new DenseMatrix(new[,] { { 4.0, 1.0 }, { 3.0, 2.0 } }); |
||||
|
Console.WriteLine(@"Initial square matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Perform full SVD decomposition
|
||||
|
var svd = matrix.Svd(true); |
||||
|
Console.WriteLine(@"Perform full SVD decomposition"); |
||||
|
|
||||
|
// 1. Left singular vectors
|
||||
|
Console.WriteLine(@"1. Left singular vectors"); |
||||
|
Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Singular values as vector
|
||||
|
Console.WriteLine(@"2. Singular values as vector"); |
||||
|
Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Singular values as diagonal matrix
|
||||
|
Console.WriteLine(@"3. Singular values as diagonal matrix"); |
||||
|
Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Right singular vectors
|
||||
|
Console.WriteLine(@"4. Right singular vectors"); |
||||
|
Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Multiply U matrix by its transpose
|
||||
|
var identinty = svd.U() * svd.U().Transpose(); |
||||
|
Console.WriteLine(@"5. Multiply U matrix by its transpose"); |
||||
|
Console.WriteLine(identinty.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Multiply V matrix by its transpose
|
||||
|
identinty = svd.VT().TransposeAndMultiply(svd.VT()); |
||||
|
Console.WriteLine(@"6. Multiply V matrix by its transpose"); |
||||
|
Console.WriteLine(identinty.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 7. Reconstruct initial matrix: A = U*Σ*VT
|
||||
|
var reconstruct = svd.U() * svd.W() * svd.VT(); |
||||
|
Console.WriteLine(@"7. Reconstruct initial matrix: A = U*S*VT"); |
||||
|
Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 8. Condition Number of the matrix
|
||||
|
Console.WriteLine(@"8. Condition Number of the matrix"); |
||||
|
Console.WriteLine(svd.ConditionNumber); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 9. Determinant of the matrix
|
||||
|
Console.WriteLine(@"9. Determinant of the matrix"); |
||||
|
Console.WriteLine(svd.Determinant); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10. 2-norm of the matrix
|
||||
|
Console.WriteLine(@"10. 2-norm of the matrix"); |
||||
|
Console.WriteLine(svd.Norm2); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 11. Rank of the matrix
|
||||
|
Console.WriteLine(@"11. Rank of the matrix"); |
||||
|
Console.WriteLine(svd.Rank); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Perform partial SVD decomposition, without computing the singular U and VT vectors
|
||||
|
svd = matrix.Svd(false); |
||||
|
Console.WriteLine(@"Perform partial SVD decomposition, without computing the singular U and VT vectors"); |
||||
|
|
||||
|
// 12. Singular values as vector
|
||||
|
Console.WriteLine(@"12. Singular values as vector"); |
||||
|
Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 13. Singular values as diagonal matrix
|
||||
|
Console.WriteLine(@"13. Singular values as diagonal matrix"); |
||||
|
Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 14. Access to left singular vectors when partial SVD decomposition was performed
|
||||
|
try |
||||
|
{ |
||||
|
Console.WriteLine(@"14. Access to left singular vectors when partial SVD decomposition was performed"); |
||||
|
Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider)); |
||||
|
} |
||||
|
catch (Exception ex) |
||||
|
{ |
||||
|
Console.WriteLine(ex.Message); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
|
||||
|
// 15. Access to right singular vectors when partial SVD decomposition was performed
|
||||
|
try |
||||
|
{ |
||||
|
Console.WriteLine(@"15. Access to right singular vectors when partial SVD decomposition was performed"); |
||||
|
Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider)); |
||||
|
} |
||||
|
catch (Exception ex) |
||||
|
{ |
||||
|
Console.WriteLine(ex.Message); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,246 @@ |
|||||
|
// <copyright file="MatrixArithmeticOperations.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Basic matrix arithmetic operations as "+", "-", "*", "/"
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/VectorsAndMatrices.html"/>
|
||||
|
public class MatrixArithmeticOperations : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix Arithmetics"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Basic operations between matrix/matrix and matrix/vecor"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Scalar_multiplication">Multiply matrix by scalar</seealso>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html">Multiply matrix by vector</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product">Multiply matrix by matrix</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product">Pointwise multiplie matrix with another matrix</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_%28mathematics%29#Basic_operations">Addition and subtraction</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Initialize IFormatProvider to print matrix/vector data
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create matrix "A"
|
||||
|
var matrixA = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } }); |
||||
|
Console.WriteLine(@"Matrix A"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Create matrix "B"
|
||||
|
var matrixB = new DenseMatrix(new[,] { { 1.0, 3.0, 5.0 }, { 2.0, 4.0, 6.0 }, { 3.0, 5.0, 7.0 } }); |
||||
|
Console.WriteLine(@"Matrix B"); |
||||
|
Console.WriteLine(matrixB.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply matrix by scalar
|
||||
|
// 1. Using operator "*"
|
||||
|
var resultM = 3.0 * matrixA; |
||||
|
Console.WriteLine(@"Multiply matrix by scalar using operator *. (result = 3.0 * A)"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Multiply method and getting result into different matrix instance
|
||||
|
resultM = matrixA.Multiply(3.0); |
||||
|
Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (result = A.Multiply(3.0))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Multiply method and updating matrix itself
|
||||
|
matrixA.Multiply(3.0, matrixA); |
||||
|
Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (A.Multiply(3.0, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply matrix by vector (right-multiply)
|
||||
|
var vector = new DenseVector(new[] { 1.0, 2.0, 3.0 }); |
||||
|
Console.WriteLine(@"Vector"); |
||||
|
Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Using operator "*"
|
||||
|
var resultV = matrixA * vector; |
||||
|
Console.WriteLine(@"Multiply matrix by vector using operator *. (result = A * vec)"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Multiply method and getting result into different vector instance
|
||||
|
resultV = matrixA.Multiply(vector); |
||||
|
Console.WriteLine(@"Multiply matrix by vector using method Multiply. (result = A.Multiply(vec))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Multiply method and updating vector itself
|
||||
|
matrixA.Multiply(vector, vector); |
||||
|
Console.WriteLine(@"Multiply matrix by vector using method Multiply. (A.Multiply(vec, vec))"); |
||||
|
Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply vector by matrix (left-multiply)
|
||||
|
// 1. Using operator "*"
|
||||
|
resultV = vector * matrixA; |
||||
|
Console.WriteLine(@"Multiply vector by matrix using operator *. (result = vec * A)"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using LeftMultiply method and getting result into different vector instance
|
||||
|
resultV = matrixA.LeftMultiply(vector); |
||||
|
Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (result = A.LeftMultiply(vec))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using LeftMultiply method and updating vector itself
|
||||
|
matrixA.LeftMultiply(vector, vector); |
||||
|
Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (A.LeftMultiply(vec, vec))"); |
||||
|
Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply matrix by matrix
|
||||
|
// 1. Using operator "*"
|
||||
|
resultM = matrixA * matrixB; |
||||
|
Console.WriteLine(@"Multiply matrix by matrix using operator *. (result = A * B)"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Multiply method and getting result into different matrix instance
|
||||
|
resultM = matrixA.Multiply(matrixB); |
||||
|
Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (result = A.Multiply(B))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Multiply method and updating matrix itself
|
||||
|
matrixA.Multiply(matrixB, matrixA); |
||||
|
Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (A.Multiply(B, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Pointwise multiplie matrix with another matrix
|
||||
|
// 1. Using PointwiseMultiply method and getting result into different matrix instance
|
||||
|
resultM = matrixA.PointwiseMultiply(matrixB); |
||||
|
Console.WriteLine(@"Pointwise multiplie matrix with another matrix using method PointwiseMultiply. (result = A.PointwiseMultiply(B))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using PointwiseMultiply method and updating matrix itself
|
||||
|
matrixA.PointwiseMultiply(matrixB, matrixA); |
||||
|
Console.WriteLine(@"Pointwise multiplie matrix with another matrix using method PointwiseMultiply. (A.PointwiseMultiply(B, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Pointwise divide matrix with another matrix
|
||||
|
// 1. Using PointwiseDivide method and getting result into different matrix instance
|
||||
|
resultM = matrixA.PointwiseDivide(matrixB); |
||||
|
Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (result = A.PointwiseDivide(B))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using PointwiseDivide method and updating matrix itself
|
||||
|
matrixA.PointwiseDivide(matrixB, matrixA); |
||||
|
Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (A.PointwiseDivide(B, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Addition
|
||||
|
// 1. Using operator "+"
|
||||
|
resultM = matrixA + matrixB; |
||||
|
Console.WriteLine(@"Add matrices using operator +. (result = A + B)"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Add method and getting result into different matrix instance
|
||||
|
resultM = matrixA.Add(matrixB); |
||||
|
Console.WriteLine(@"Add matrices using method Add. (result = A.Add(B))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Add method and updating matrix itself
|
||||
|
matrixA.Add(matrixB, matrixA); |
||||
|
Console.WriteLine(@"Add matrices using method Add. (A.Add(B, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Subtraction
|
||||
|
// 1. Using operator "-"
|
||||
|
resultM = matrixA - matrixB; |
||||
|
Console.WriteLine(@"Subtract matrices using operator -. (result = A - B)"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Subtract method and getting result into different matrix instance
|
||||
|
resultM = matrixA.Subtract(matrixB); |
||||
|
Console.WriteLine(@"Subtract matrices using method Subtract. (result = A.Subtract(B))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Subtract method and updating matrix itself
|
||||
|
matrixA.Subtract(matrixB, matrixA); |
||||
|
Console.WriteLine(@"Subtract matrices using method Subtract. (A.Subtract(B, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Divide by scalar
|
||||
|
// 1. Using Divide method and getting result into different matrix instance
|
||||
|
resultM = matrixA.Divide(3.0); |
||||
|
Console.WriteLine(@"Divide matrix by scalar using method Divide. (result = A.Divide(3.0))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Divide method and updating matrix itself
|
||||
|
matrixA.Divide(3.0, matrixA); |
||||
|
Console.WriteLine(@"Divide matrix by scalar using method Divide. (A.Divide(3.0, A))"); |
||||
|
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,208 @@ |
|||||
|
// <copyright file="MatrixDataAccessor.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Matrix data access, copying and conversion examples
|
||||
|
/// </summary>
|
||||
|
public class MatrixDataAccessor |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix data access, copying and conversion"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of setting/getting values of a matrix, copying and conversion matrix into another matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format vector output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create new empty square matrix
|
||||
|
var matrix = new DenseMatrix(10); |
||||
|
Console.WriteLine(@"Empty matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Fill matrix by data using indexer []
|
||||
|
var k = 0; |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix[i, j] = k++; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"1. Fill matrix by data using indexer []"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Fill matrix by data using At. The element is set without range checking.
|
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix.At(i, j, k--); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"2. Fill matrix by data using At"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Clone matrix
|
||||
|
var clone = matrix.Clone(); |
||||
|
Console.WriteLine(@"3. Clone matrix"); |
||||
|
Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Clear matrix
|
||||
|
clone.Clear(); |
||||
|
Console.WriteLine(@"4. Clear matrix"); |
||||
|
Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Copy matrix into another matrix
|
||||
|
matrix.CopyTo(clone); |
||||
|
Console.WriteLine(@"5. Copy matrix into another matrix"); |
||||
|
Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Get submatrix into another matrix
|
||||
|
var submatrix = matrix.SubMatrix(2, 2, 3, 3); |
||||
|
Console.WriteLine(@"6. Copy submatrix into another matrix"); |
||||
|
Console.WriteLine(submatrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 7. Get part of the row as vector. In this example: get 4 elements from row 5 starting from column 3
|
||||
|
var row = matrix.Row(5, 3, 4); |
||||
|
Console.WriteLine(@"7. Get part of the row as vector"); |
||||
|
Console.WriteLine(row.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 8. Get part of the column as vector. In this example: get 3 elements from column 2 starting from row 6
|
||||
|
var column = matrix.Column(2, 6, 3); |
||||
|
Console.WriteLine(@"8. Get part of the column as vector"); |
||||
|
Console.WriteLine(column.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 9. Get columns using column enumerator. If you need all columns you may use ColumnEnumerator without parameters
|
||||
|
Console.WriteLine(@"9. Get columns using column enumerator"); |
||||
|
foreach (var keyValuePair in matrix.ColumnEnumerator(2, 4)) |
||||
|
{ |
||||
|
Console.WriteLine(@"Column {0}: {1}", keyValuePair.Key, keyValuePair.Value.ToString("#0.00\t", formatProvider)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10. Get rows using row enumerator. If you need all rows you may use RowEnumerator without parameters
|
||||
|
Console.WriteLine(@"10. Get rows using row enumerator"); |
||||
|
foreach (var keyValuePair in matrix.RowEnumerator(4, 3)) |
||||
|
{ |
||||
|
Console.WriteLine(@"Row {0}: {1}", keyValuePair.Key, keyValuePair.Value.ToString("#0.00\t", formatProvider)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 11. Convert matrix into multidimensional array
|
||||
|
var data = matrix.ToArray(); |
||||
|
Console.WriteLine(@"11. Convert matrix into multidimensional array"); |
||||
|
for (var i = 0; i < data.GetLongLength(0); i++) |
||||
|
{ |
||||
|
for (var j = 0; j < data.GetLongLength(1); j++) |
||||
|
{ |
||||
|
Console.Write(data[i, j].ToString("#0.00\t")); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 12. Convert matrix into row-wise array
|
||||
|
var rowwise = matrix.ToRowWiseArray(); |
||||
|
Console.WriteLine(@"12. Convert matrix into row-wise array"); |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
Console.Write(rowwise[(i * matrix.ColumnCount) + j].ToString("#0.00\t")); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 13. Convert matrix into column-wise array
|
||||
|
var columnise = matrix.ToColumnWiseArray(); |
||||
|
Console.WriteLine(@"13. Convert matrix into column-wise array"); |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
Console.Write(columnise[(j * matrix.RowCount) + i].ToString("#0.00\t")); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 14. Get matrix diagonal as vector
|
||||
|
var diagonal = matrix.Diagonal(); |
||||
|
Console.WriteLine(@"14. Get matrix diagonal as vector"); |
||||
|
Console.WriteLine(diagonal.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,112 @@ |
|||||
|
// <copyright file="MatrixInitialization.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Matrix initialization examples
|
||||
|
/// </summary>
|
||||
|
public class MatrixInitialization : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix initialization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of creating matrix instances"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// 1. Initialize a new instance of the matrix from a 2D array. This constructor will allocate a completely new memory block for storing the dense matrix.
|
||||
|
var matrix1 = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 } }); |
||||
|
|
||||
|
// 2. Initialize a new instance of the empty square matrix with a given order.
|
||||
|
var matrix2 = new DenseMatrix(3); |
||||
|
|
||||
|
// 3. Initialize a new instance of the empty matrix with a given size.
|
||||
|
var matrix3 = new DenseMatrix(2, 3); |
||||
|
|
||||
|
// 4. Initialize a new instance of the matrix with all entries set to a particular value.
|
||||
|
var matrix4 = new DenseMatrix(2, 3, 3.0); |
||||
|
|
||||
|
// 4. Initialize a new instance of the matrix from a one dimensional array. This array should store the matrix in column-major order.
|
||||
|
var matrix5 = new DenseMatrix(2, 3, new[] { 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 }); |
||||
|
|
||||
|
// 5. Initialize a square matrix with all zero's except for ones on the diagonal. Identity matrix (http://en.wikipedia.org/wiki/Identity_matrix).
|
||||
|
var matrixI = DenseMatrix.Identity(5); |
||||
|
|
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
Console.WriteLine(@"Matrix 1"); |
||||
|
Console.WriteLine(matrix1.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Matrix 2"); |
||||
|
Console.WriteLine(matrix2.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Matrix 3"); |
||||
|
Console.WriteLine(matrix3.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Matrix 4"); |
||||
|
Console.WriteLine(matrix4.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Matrix 5"); |
||||
|
Console.WriteLine(matrix5.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Identity matrix"); |
||||
|
Console.WriteLine(matrixI.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,129 @@ |
|||||
|
// <copyright file="MatrixNorms.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Matrix norms
|
||||
|
/// </summary>
|
||||
|
public class MatrixNorms : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix norms"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of matrix norms: L1 norm, L2 norm, Frobenius norm and infinity norm"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Matrix_norm">Matrix norm</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create square matrix
|
||||
|
var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 6.0, 5.0, 4.0 }, { 8.0, 9.0, 7.0 } }); |
||||
|
Console.WriteLine(@"Initial square matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. 1-norm of the matrix
|
||||
|
Console.WriteLine(@"1. 1-norm of the matrix"); |
||||
|
Console.WriteLine(matrix.L1Norm()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. 2-norm of the matrix
|
||||
|
Console.WriteLine(@"2. 2-norm of the matrix"); |
||||
|
Console.WriteLine(matrix.L2Norm()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Frobenius norm of the matrix
|
||||
|
Console.WriteLine(@"3. Frobenius norm of the matrix"); |
||||
|
Console.WriteLine(matrix.FrobeniusNorm()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Infinity norm of the matrix
|
||||
|
Console.WriteLine(@"4. Infinity norm of the matrix"); |
||||
|
Console.WriteLine(matrix.InfinityNorm()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Normalize matrix columns
|
||||
|
Console.WriteLine(@"5. Normalize matrix columns: before normalize"); |
||||
|
foreach (var keyValuePair in matrix.ColumnEnumerator()) |
||||
|
{ |
||||
|
Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
var normalized = matrix.NormalizeColumns(2); |
||||
|
Console.WriteLine(@"5. Normalize matrix columns: after normalize"); |
||||
|
foreach (var keyValuePair in normalized.ColumnEnumerator()) |
||||
|
{ |
||||
|
Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Normalize matrix columns
|
||||
|
Console.WriteLine(@"6. Normalize matrix rows: before normalize"); |
||||
|
foreach (var keyValuePair in matrix.RowEnumerator()) |
||||
|
{ |
||||
|
Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
normalized = matrix.NormalizeRows(2); |
||||
|
Console.WriteLine(@"6. Normalize matrix rows: after normalize"); |
||||
|
foreach (var keyValuePair in normalized.RowEnumerator()) |
||||
|
{ |
||||
|
Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Key, keyValuePair.Value.Norm(2)); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,173 @@ |
|||||
|
// <copyright file="MatrixRowColumnOperations.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Matrix operations with rows and columns
|
||||
|
/// </summary>
|
||||
|
public class MatrixRowColumnOperations : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix row and column operations"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of permuting, modifying, inserting columns and rows in a matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create square matrix
|
||||
|
var matrix = new DenseMatrix(5); |
||||
|
var k = 0; |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix[i, j] = k++; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"Initial matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Create vector
|
||||
|
var vector = new DenseVector(new[] { 50.0, 51.0, 52.0, 53.0, 54.0 }); |
||||
|
Console.WriteLine(@"Sample vector"); |
||||
|
Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Insert new column
|
||||
|
var result = matrix.InsertColumn(3, vector); |
||||
|
Console.WriteLine(@"1. Insert new column"); |
||||
|
Console.WriteLine(result.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Insert new row
|
||||
|
result = matrix.InsertRow(3, vector); |
||||
|
Console.WriteLine(@"2. Insert new row"); |
||||
|
Console.WriteLine(result.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Set column values
|
||||
|
matrix.SetColumn(2, (Vector)vector); |
||||
|
Console.WriteLine(@"3. Set column values"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Set row values.
|
||||
|
matrix.SetRow(3, (double[])vector); |
||||
|
Console.WriteLine(@"4. Set row values"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Set diagonal values. SetRow/SetColumn/SetDiagonal accepts Vector and double[] as input parameter
|
||||
|
matrix.SetDiagonal(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 }); |
||||
|
Console.WriteLine(@"5. Set diagonal values"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Set submatrix values
|
||||
|
matrix.SetSubMatrix(1, 3, 1, 3, DenseMatrix.Identity(3)); |
||||
|
Console.WriteLine(@"6. Set submatrix values"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Permutations.
|
||||
|
// Initialize a new instance of the Permutation class. An array represents where each integer is permuted too:
|
||||
|
// indices[i] represents that integer "i" is permuted to location indices[i]
|
||||
|
var permutations = new Permutation(new[] { 0, 1, 3, 2, 4 }); |
||||
|
|
||||
|
// 7. Permute rows 3 and 4
|
||||
|
matrix.PermuteRows(permutations); |
||||
|
Console.WriteLine(@"7. Permute rows 3 and 4"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 8. Permute columns 1 and 2, 3 and 5
|
||||
|
permutations = new Permutation(new[] { 1, 0, 4, 3, 2 }); |
||||
|
matrix.PermuteColumns(permutations); |
||||
|
Console.WriteLine(@"8. Permute columns 1 and 2, 3 and 5"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 9. Concatenate the matrix with the given matrix
|
||||
|
var append = matrix.Append(matrix); |
||||
|
|
||||
|
// Concatenate into result matrix
|
||||
|
matrix.Append(matrix, append); |
||||
|
Console.WriteLine(@"9. Append matrix to matrix"); |
||||
|
Console.WriteLine(append.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10. Stack the matrix on top of the given matrix matrix
|
||||
|
var stack = matrix.Stack(matrix); |
||||
|
|
||||
|
// Stack into result matrix
|
||||
|
matrix.Stack(matrix, stack); |
||||
|
Console.WriteLine(@"10. Stack the matrix on top of the given matrix matrix"); |
||||
|
Console.WriteLine(stack.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 11. Diagonally stack the matrix on top of the given matrix matrix
|
||||
|
var diagoinalStack = matrix.DiagonalStack(matrix); |
||||
|
|
||||
|
// Diagonally stack into result matrix
|
||||
|
matrix.DiagonalStack(matrix, diagoinalStack); |
||||
|
Console.WriteLine(@"11. Diagonally stack the matrix on top of the given matrix matrix"); |
||||
|
Console.WriteLine(diagoinalStack.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,112 @@ |
|||||
|
// <copyright file="MatrixSpecialNumbers.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Special numbers associated with any square matrix
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Det.html">The determinant of the square matrix</seealso>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Tr.html">The trace of the matrix</seealso>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/MatrixRank.html">The rank of the matrix</seealso>
|
||||
|
public class MatrixSpecialNumbers : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Special numbers associated with any square matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix properties as: Determinant, Condition Number, Rank and Trace"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Determinant">Determinant</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29">Rank (linear algebra)</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Trace_%28linear_algebra%29">Trace (linear algebra)</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Condition_number">Condition number</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create random square matrix
|
||||
|
var matrix = new DenseMatrix(5); |
||||
|
var rnd = new Random(1); |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix[i, j] = rnd.NextDouble(); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"Initial matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Determinant
|
||||
|
Console.WriteLine(@"1. Determinant"); |
||||
|
Console.WriteLine(matrix.Determinant()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Rank
|
||||
|
Console.WriteLine(@"2. Rank"); |
||||
|
Console.WriteLine(matrix.Rank()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Condition number
|
||||
|
Console.WriteLine(@"2. Condition number"); |
||||
|
Console.WriteLine(matrix.ConditionNumber()); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Trace
|
||||
|
Console.WriteLine(@"4. Trace"); |
||||
|
Console.WriteLine(matrix.Trace()); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,120 @@ |
|||||
|
// <copyright file="MatrixTransposeAndInverse.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
using MathNet.Numerics.LinearAlgebra.Generic.Factorization; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Matrix transpose and inverse
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Transpose.html">Transpose</seealso>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/ref/Inverse.html">Inverse</seealso>
|
||||
|
public class MatrixTransposeAndInverse : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Matrix transpose and inverse"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Transpose matrix, inverse matrix, transpose-and-multiply matrix examples"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Transpose">Transpose</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create random square matrix
|
||||
|
var matrix = new DenseMatrix(5); |
||||
|
var rnd = new Random(1); |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix[i, j] = rnd.NextDouble(); |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"Initial matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Get matrix inverse
|
||||
|
var inverse = matrix.Inverse(); |
||||
|
Console.WriteLine(@"1. Matrix inverse"); |
||||
|
Console.WriteLine(inverse.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Matrix multiplied by its inverse gives identity matrix
|
||||
|
var identity = matrix * inverse; |
||||
|
Console.WriteLine(@"2. Matrix multiplied by its inverse"); |
||||
|
Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Get matrix transpose
|
||||
|
var transpose = matrix.Transpose(); |
||||
|
Console.WriteLine(@"3. Matrix transpose"); |
||||
|
Console.WriteLine(transpose.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Get orthogonal matrix, i.e. do QR decomposition and get matrix Q
|
||||
|
var orthogonal = matrix.QR().Q; |
||||
|
Console.WriteLine(@"4. Orthogonal matrix"); |
||||
|
Console.WriteLine(orthogonal.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Transpose and multiply orthogonal matrix by iteslf gives identity matrix
|
||||
|
identity = orthogonal.TransposeAndMultiply(orthogonal); |
||||
|
Console.WriteLine(@"Transpose and multiply orthogonal matrix by iteslf"); |
||||
|
Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,123 @@ |
|||||
|
// <copyright file="MatrixTriangular.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Triangular matrices
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/guide/PartsOfMatrices.html"/>
|
||||
|
public class MatrixTriangular : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Retrieving special forms of the matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Retrieving different forms of triangular matrices from existing matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Triangular_matrix">Triangular matrix</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format matrix output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create square matrix
|
||||
|
var matrix = new DenseMatrix(10); |
||||
|
var k = 0; |
||||
|
for (var i = 0; i < matrix.RowCount; i++) |
||||
|
{ |
||||
|
for (var j = 0; j < matrix.ColumnCount; j++) |
||||
|
{ |
||||
|
matrix[i, j] = k++; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"Initial square matrix"); |
||||
|
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Retrieve a new matrix containing the lower triangle of the matrix
|
||||
|
var lower = matrix.LowerTriangle(); |
||||
|
|
||||
|
// Puts the lower triangle of the matrix into the result matrix.
|
||||
|
matrix.LowerTriangle(lower); |
||||
|
Console.WriteLine(@"1. Lower triangle of the matrix"); |
||||
|
Console.WriteLine(lower.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Retrieve a new matrix containing the upper triangle of the matrix
|
||||
|
var upper = matrix.UpperTriangle(); |
||||
|
|
||||
|
// Puts the upper triangle of the matrix into the result matrix.
|
||||
|
matrix.UpperTriangle(lower); |
||||
|
Console.WriteLine(@"2. Upper triangle of the matrix"); |
||||
|
Console.WriteLine(upper.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Retrieve a new matrix containing the strictly lower triangle of the matrix
|
||||
|
var strictlylower = matrix.StrictlyLowerTriangle(); |
||||
|
|
||||
|
// Puts the strictly lower triangle of the matrix into the result matrix.
|
||||
|
matrix.StrictlyLowerTriangle(strictlylower); |
||||
|
Console.WriteLine(@"3. Strictly lower triangle of the matrix"); |
||||
|
Console.WriteLine(strictlylower.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Retrieve a new matrix containing the strictly upper triangle of the matrix
|
||||
|
var strictlyupper = matrix.StrictlyUpperTriangle(); |
||||
|
|
||||
|
// Puts the strictly upper triangle of the matrix into the result matrix.
|
||||
|
matrix.StrictlyUpperTriangle(strictlyupper); |
||||
|
Console.WriteLine(@"4. Strictly upper triangle of the matrix"); |
||||
|
Console.WriteLine(strictlyupper.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,209 @@ |
|||||
|
// <copyright file="VectorArithmeticOperations.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Basic vector arithmetic operations as "+", "-", "*", "/"
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/VectorsAndMatrices.html"/>
|
||||
|
public class VectorArithmeticOperations : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Vector Arithmetics"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Basic operations between vector/vector and vector/matrix"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example.
|
||||
|
/// </summary>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Scalar_multiplication">Multiply vector by scalar</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Dot_product">Multiply vector by vector (compute the dot product between two vectors)</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction">Vector addition and subtraction</seealso>
|
||||
|
/// <seealso cref="http://en.wikipedia.org/wiki/Outer_product">Outer Product of two vectors</seealso>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Initialize IFormatProvider to print matrix/vector data
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create vector "X"
|
||||
|
var vectorX = new DenseVector(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 }); |
||||
|
Console.WriteLine(@"Vector X"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Create vector "Y"
|
||||
|
var vectorY = new DenseVector(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 }); |
||||
|
Console.WriteLine(@"Vector Y"); |
||||
|
Console.WriteLine(vectorY.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply vector by scalar
|
||||
|
// 1. Using Multiply method and getting result into different vector instance
|
||||
|
var resultV = vectorX.Multiply(3.0); |
||||
|
Console.WriteLine(@"Multiply vector by scalar using method Multiply. (result = X.Multiply(3.0))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using operator "*"
|
||||
|
resultV = 3.0 * vectorX; |
||||
|
Console.WriteLine(@"Multiply vector by scalar using operator *. (result = 3.0 * X)"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Multiply method and updating vector itself
|
||||
|
vectorX.Multiply(3.0, vectorX); |
||||
|
Console.WriteLine(@"Multiply vector by scalar using method Multiply. (X.Multiply(3.0, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Multiply vector by vector (compute the dot product between two vectors)
|
||||
|
// 1. Using operator "*"
|
||||
|
var dotProduct = vectorX * vectorY; |
||||
|
Console.WriteLine(@"Dot product between two vectors using operator *. (result = X * Y)"); |
||||
|
Console.WriteLine(dotProduct); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using DotProduct method and getting result into different vector instance
|
||||
|
dotProduct = vectorX.DotProduct(vectorY); |
||||
|
Console.WriteLine(@"Dot product between two vectors using method DotProduct. (result = X.DotProduct(Y))"); |
||||
|
Console.WriteLine(dotProduct.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Pointwise multiplie vector with another vector
|
||||
|
// 1. Using PointwiseMultiply method and getting result into different vector instance
|
||||
|
resultV = vectorX.PointwiseMultiply(vectorY); |
||||
|
Console.WriteLine(@"Pointwise multiplie vector with another vector using method PointwiseMultiply. (result = X.PointwiseMultiply(Y))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using PointwiseMultiply method and updating vector itself
|
||||
|
vectorX.PointwiseMultiply(vectorY, vectorX); |
||||
|
Console.WriteLine(@"Pointwise multiplie vector with another vector using method PointwiseMultiply. (X.PointwiseMultiply(Y, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Pointwise divide vector with another vector
|
||||
|
// 1. Using PointwiseDivide method and getting result into different vector instance
|
||||
|
resultV = vectorX.PointwiseDivide(vectorY); |
||||
|
Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (result = X.PointwiseDivide(Y))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using PointwiseDivide method and updating vector itself
|
||||
|
vectorX.PointwiseDivide(vectorY, vectorX); |
||||
|
Console.WriteLine(@"Pointwise divide vector with another vector using method PointwiseDivide. (X.PointwiseDivide(Y, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Addition
|
||||
|
// 1. Using operator "+"
|
||||
|
resultV = vectorX + vectorY; |
||||
|
Console.WriteLine(@"Add vectors using operator +. (result = X + Y)"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Add method and getting result into different vector instance
|
||||
|
resultV = vectorX.Add(vectorY); |
||||
|
Console.WriteLine(@"Add vectors using method Add. (result = X.Add(Y))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Add method and updating vector itself
|
||||
|
vectorX.Add(vectorY, vectorX); |
||||
|
Console.WriteLine(@"Add vectors using method Add. (X.Add(Y, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Subtraction
|
||||
|
// 1. Using operator "-"
|
||||
|
resultV = vectorX - vectorY; |
||||
|
Console.WriteLine(@"Subtract vectors using operator -. (result = X - Y)"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Subtract method and getting result into different vector instance
|
||||
|
resultV = vectorX.Subtract(vectorY); |
||||
|
Console.WriteLine(@"Subtract vectors using method Subtract. (result = X.Subtract(Y))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Using Subtract method and updating vector itself
|
||||
|
vectorX.Subtract(vectorY, vectorX); |
||||
|
Console.WriteLine(@"Subtract vectors using method Subtract. (X.Subtract(Y, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Divide by scalar
|
||||
|
// 1. Using Divide method and getting result into different vector instance
|
||||
|
resultV = vectorX.Divide(3.0); |
||||
|
Console.WriteLine(@"Divide vector by scalar using method Divide. (result = A.Divide(3.0))"); |
||||
|
Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using Divide method and updating vector itself
|
||||
|
vectorX.Divide(3.0, vectorX); |
||||
|
Console.WriteLine(@"Divide vector by scalar using method Divide. (X.Divide(3.0, X))"); |
||||
|
Console.WriteLine(vectorX.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// Outer Product of two vectors
|
||||
|
// 1. Using instanse method OuterProduct
|
||||
|
var resultM = vectorX.OuterProduct(vectorY); |
||||
|
Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (X.OuterProduct(Y))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Using static method of the Vector class
|
||||
|
resultM = Vector.OuterProduct(vectorX, vectorY); |
||||
|
Console.WriteLine(@"Outer Product of two vectors using method OuterProduct. (Vector.OuterProduct(X,Y))"); |
||||
|
Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,158 @@ |
|||||
|
// <copyright file="VectorDataAccessor.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Vector data access, copying and conversion examples
|
||||
|
/// </summary>
|
||||
|
public class VectorDataAccessor |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Vector data access, copying and conversion"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of setting/getting values of a vector, copying and conversion vector into another vector"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// Format vector output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
// Create new empty vector
|
||||
|
var vectorA = new DenseVector(10); |
||||
|
Console.WriteLine(@"Empty vector A"); |
||||
|
Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 1. Fill vector by data using indexer []
|
||||
|
for (var i = 0; i < vectorA.Count; i++) |
||||
|
{ |
||||
|
vectorA[i] = i; |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(@"1. Fill vector by data using indexer []"); |
||||
|
Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 2. Fill vector by data using SetValues method
|
||||
|
vectorA.SetValues(new[] { 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0 }); |
||||
|
Console.WriteLine(@"2. Fill vector by data using SetValues method"); |
||||
|
Console.WriteLine(vectorA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 3. Convert Vector to double[]
|
||||
|
var data = vectorA.ToArray(); |
||||
|
Console.WriteLine(@"3. Convert vector to double array"); |
||||
|
for (var i = 0; i < data.Length; i++) |
||||
|
{ |
||||
|
Console.Write(data[i].ToString("#0.00\t", formatProvider) + @" "); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 4. Convert Vector to column matrix. A matrix based on this vector in column form (one single column)
|
||||
|
var columnMatrix = vectorA.ToColumnMatrix(); |
||||
|
Console.WriteLine(@"4. Convert vector to column matrix"); |
||||
|
Console.WriteLine(columnMatrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 5. Convert Vector to row matrix. A matrix based on this vector in row form (one single row)
|
||||
|
var rowMatrix = vectorA.ToRowMatrix(); |
||||
|
Console.WriteLine(@"5. Convert vector to row matrix"); |
||||
|
Console.WriteLine(rowMatrix.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 6. Clone vector
|
||||
|
var cloneA = vectorA.Clone(); |
||||
|
Console.WriteLine(@"6. Clone vector"); |
||||
|
Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 7. Clear vector
|
||||
|
cloneA.Clear(); |
||||
|
Console.WriteLine(@"7. Clear vector"); |
||||
|
Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 8. Copy part of vector into another vector. If you need to copy all data then use CopoTy(vector) method.
|
||||
|
vectorA.CopyTo(cloneA, 3, 3, 4); |
||||
|
Console.WriteLine(@"8. Copy part of vector into another vector"); |
||||
|
Console.WriteLine(cloneA.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 9. Get part of vector as another vector
|
||||
|
var subvector = vectorA.SubVector(0, 5); |
||||
|
Console.WriteLine(@"9. Get subvector"); |
||||
|
Console.WriteLine(subvector.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 10. Enumerator usage
|
||||
|
Console.WriteLine(@"10. Enumerator usage"); |
||||
|
foreach (var value in vectorA) |
||||
|
{ |
||||
|
Console.Write(value.ToString("#0.00\t", formatProvider) + @" "); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
// 11. Indexed enumerator usage
|
||||
|
Console.WriteLine(@"11. Enumerator usage"); |
||||
|
foreach (var value in vectorA.GetIndexedEnumerator()) |
||||
|
{ |
||||
|
Console.WriteLine(@"Index = {0}; Value = {1}", value.Key, value.Value.ToString("#0.00\t", formatProvider)); |
||||
|
} |
||||
|
|
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
@ -0,0 +1,98 @@ |
|||||
|
// <copyright file="VectorInitialization.cs" company="Math.NET">
|
||||
|
// Math.NET Numerics, part of the Math.NET Project
|
||||
|
// http://numerics.mathdotnet.com
|
||||
|
// http://github.com/mathnet/mathnet-numerics
|
||||
|
// http://mathnetnumerics.codeplex.com
|
||||
|
// Copyright (c) 2009-2010 Math.NET
|
||||
|
// Permission is hereby granted, free of charge, to any person
|
||||
|
// obtaining a copy of this software and associated documentation
|
||||
|
// files (the "Software"), to deal in the Software without
|
||||
|
// restriction, including without limitation the rights to use,
|
||||
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
|
// copies of the Software, and to permit persons to whom the
|
||||
|
// Software is furnished to do so, subject to the following
|
||||
|
// conditions:
|
||||
|
// The above copyright notice and this permission notice shall be
|
||||
|
// included in all copies or substantial portions of the Software.
|
||||
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
||||
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
||||
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
||||
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
||||
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
||||
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
||||
|
// OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
// </copyright>
|
||||
|
|
||||
|
namespace Examples.LinearAlgebra |
||||
|
{ |
||||
|
using System; |
||||
|
using System.Globalization; |
||||
|
using MathNet.Numerics.LinearAlgebra.Double; |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Vector initialization examples
|
||||
|
/// </summary>
|
||||
|
public class VectorInitialization : IExample |
||||
|
{ |
||||
|
/// <summary>
|
||||
|
/// Gets the name of this example
|
||||
|
/// </summary>
|
||||
|
public string Name |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Vector initialization"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Gets the description of this example
|
||||
|
/// </summary>
|
||||
|
public string Description |
||||
|
{ |
||||
|
get |
||||
|
{ |
||||
|
return "Examples of creating vector instances"; |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// <summary>
|
||||
|
/// Run example
|
||||
|
/// </summary>
|
||||
|
public void Run() |
||||
|
{ |
||||
|
// 1. Initialize a new instance of the empty vector with a given size
|
||||
|
var vector1 = new DenseVector(5); |
||||
|
|
||||
|
// 2. Initialize a new instance of the vector with a given size and each element set to the given value
|
||||
|
var vector2 = new DenseVector(5, 3.0); |
||||
|
|
||||
|
// 3. Initialize a new instance of the vector from an array.
|
||||
|
var vector3 = new DenseVector(new[] { 1.0, 2.0, 3.0, 4.0, 5.0 }); |
||||
|
|
||||
|
// 4. Initialize a new instance of the vector by copying the values from another.
|
||||
|
var vector4 = new DenseVector(vector3); |
||||
|
|
||||
|
// Format vector output to console
|
||||
|
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); |
||||
|
formatProvider.TextInfo.ListSeparator = " "; |
||||
|
|
||||
|
Console.WriteLine(@"Vector 1"); |
||||
|
Console.WriteLine(vector1.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Vector 2"); |
||||
|
Console.WriteLine(vector2.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Vector 3"); |
||||
|
Console.WriteLine(vector3.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
|
||||
|
Console.WriteLine(@"Vector 4"); |
||||
|
Console.WriteLine(vector4.ToString("#0.00\t", formatProvider)); |
||||
|
Console.WriteLine(); |
||||
|
} |
||||
|
} |
||||
|
} |
||||
Loading…
Reference in new issue