// <copyright file="Matrix.Solve.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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//
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// Copyright (c) 2009-2014 Math.NET
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//
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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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//
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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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//
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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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using System;
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using IStation.Numerics.LinearAlgebra.Factorization;
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using IStation.Numerics.LinearAlgebra.Solvers;
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namespace IStation.Numerics.LinearAlgebra
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{
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/// <summary>
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/// Defines the base class for <c>Matrix</c> classes.
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/// </summary>
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public abstract partial class Matrix<T>
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{
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// Factorizations
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/// <summary>
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/// Computes the Cholesky decomposition for a matrix.
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/// </summary>
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/// <returns>The Cholesky decomposition object.</returns>
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public abstract Cholesky<T> Cholesky();
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/// <summary>
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/// Computes the LU decomposition for a matrix.
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/// </summary>
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/// <returns>The LU decomposition object.</returns>
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public abstract LU<T> LU();
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/// <summary>
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/// Computes the QR decomposition for a matrix.
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/// </summary>
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/// <param name="method">The type of QR factorization to perform.</param>
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/// <returns>The QR decomposition object.</returns>
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public abstract QR<T> QR(QRMethod method = QRMethod.Thin);
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/// <summary>
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/// Computes the QR decomposition for a matrix using Modified Gram-Schmidt Orthogonalization.
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/// </summary>
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/// <returns>The QR decomposition object.</returns>
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public abstract GramSchmidt<T> GramSchmidt();
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/// <summary>
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/// Computes the SVD decomposition for a matrix.
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/// </summary>
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/// <param name="computeVectors">Compute the singular U and VT vectors or not.</param>
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/// <returns>The SVD decomposition object.</returns>
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public abstract Svd<T> Svd(bool computeVectors = true);
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/// <summary>
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/// Computes the EVD decomposition for a matrix.
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/// </summary>
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/// <returns>The EVD decomposition object.</returns>
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public abstract Evd<T> Evd(Symmetricity symmetricity = Symmetricity.Unknown);
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// Direct Solvers: Full
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/// <summary>
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/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <b>b</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
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public void Solve(Vector<T> input, Vector<T> result)
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{
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if (ColumnCount == RowCount)
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{
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LU().Solve(input, result);
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return;
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}
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QR().Solve(input, result);
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}
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
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public void Solve(Matrix<T> input, Matrix<T> result)
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{
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if (ColumnCount == RowCount)
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{
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LU().Solve(input, result);
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return;
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}
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QR().Solve(input, result);
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}
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// Direct Solvers: Simple
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
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/// <returns>The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</returns>
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public Matrix<T> Solve(Matrix<T> input)
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{
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var x = Build.SameAs(this, ColumnCount, input.ColumnCount, fullyMutable: true);
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Solve(input, x);
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return x;
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}
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/// <summary>
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/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <b>b</b>.</param>
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/// <returns>The left hand side <see cref="Vector{T}"/>, <b>x</b>.</returns>
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public Vector<T> Solve(Vector<T> input)
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{
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var x = Vector<T>.Build.SameAs(this, ColumnCount);
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Solve(input, x);
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return x;
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}
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// Iterative Solvers: Full
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="result">The result vector <c>x</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="iterator">The iterator to use to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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public IterationStatus TrySolveIterative(Vector<T> input, Vector<T> result, IIterativeSolver<T> solver, Iterator<T> iterator = null, IPreconditioner<T> preconditioner = null)
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{
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if (iterator == null)
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{
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iterator = new Iterator<T>(Build.IterativeSolverStopCriteria());
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}
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if (preconditioner == null)
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{
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preconditioner = new UnitPreconditioner<T>();
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}
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solver.Solve(this, input, result, iterator, preconditioner);
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return iterator.Status;
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="result">The result matrix <c>X</c></param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="iterator">The iterator to use to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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public IterationStatus TrySolveIterative(Matrix<T> input, Matrix<T> result, IIterativeSolver<T> solver, Iterator<T> iterator = null, IPreconditioner<T> preconditioner = null)
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{
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if (RowCount != input.RowCount || input.RowCount != result.RowCount || input.ColumnCount != result.ColumnCount)
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{
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throw DimensionsDontMatch<ArgumentException>(this, input, result);
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}
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if (iterator == null)
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{
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iterator = new Iterator<T>(Build.IterativeSolverStopCriteria());
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}
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if (preconditioner == null)
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{
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preconditioner = new UnitPreconditioner<T>();
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}
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for (var column = 0; column < input.ColumnCount; column++)
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{
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var solution = Vector<T>.Build.Dense(RowCount);
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solver.Solve(this, input.Column(column), solution, iterator, preconditioner);
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foreach (var element in solution.EnumerateIndexed(Zeros.AllowSkip))
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{
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result.At(element.Item1, column, element.Item2);
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}
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}
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return iterator.Status;
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}
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="result">The result vector <c>x</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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public IterationStatus TrySolveIterative(Vector<T> input, Vector<T> result, IIterativeSolver<T> solver, IPreconditioner<T> preconditioner, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var iterator = new Iterator<T>(stopCriteria.Length == 0 ? Build.IterativeSolverStopCriteria() : stopCriteria);
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return TrySolveIterative(input, result, solver, iterator, preconditioner);
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="result">The result matrix <c>X</c></param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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public IterationStatus TrySolveIterative(Matrix<T> input, Matrix<T> result, IIterativeSolver<T> solver, IPreconditioner<T> preconditioner, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var iterator = new Iterator<T>(stopCriteria.Length == 0 ? Build.IterativeSolverStopCriteria() : stopCriteria);
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return TrySolveIterative(input, result, solver, iterator, preconditioner);
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}
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="result">The result vector <c>x</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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public IterationStatus TrySolveIterative(Vector<T> input, Vector<T> result, IIterativeSolver<T> solver, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var iterator = new Iterator<T>(stopCriteria.Length == 0 ? Build.IterativeSolverStopCriteria() : stopCriteria);
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return TrySolveIterative(input, result, solver, iterator);
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="result">The result matrix <c>X</c></param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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public IterationStatus TrySolveIterative(Matrix<T> input, Matrix<T> result, IIterativeSolver<T> solver, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var iterator = new Iterator<T>(stopCriteria.Length == 0 ? Build.IterativeSolverStopCriteria() : stopCriteria);
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return TrySolveIterative(input, result, solver, iterator);
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}
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// Iterative Solvers: Simple
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="iterator">The iterator to use to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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/// <returns>The result vector <c>x</c>.</returns>
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public Vector<T> SolveIterative(Vector<T> input, IIterativeSolver<T> solver, Iterator<T> iterator = null, IPreconditioner<T> preconditioner = null)
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{
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var result = Vector<T>.Build.Dense(RowCount);
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TrySolveIterative(input, result, solver, iterator, preconditioner);
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return result;
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="iterator">The iterator to use to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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/// <returns>The result matrix <c>X</c>.</returns>
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public Matrix<T> SolveIterative(Matrix<T> input, IIterativeSolver<T> solver, Iterator<T> iterator = null, IPreconditioner<T> preconditioner = null)
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{
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var result = Build.Dense(input.RowCount, input.ColumnCount);
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TrySolveIterative(input, result, solver, iterator, preconditioner);
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return result;
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}
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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/// <returns>The result vector <c>x</c>.</returns>
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public Vector<T> SolveIterative(Vector<T> input, IIterativeSolver<T> solver, IPreconditioner<T> preconditioner, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var result = Vector<T>.Build.Dense(RowCount);
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TrySolveIterative(input, result, solver, preconditioner, stopCriteria);
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return result;
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <param name="preconditioner">The preconditioner to use for approximations.</param>
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/// <returns>The result matrix <c>X</c>.</returns>
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public Matrix<T> SolveIterative(Matrix<T> input, IIterativeSolver<T> solver, IPreconditioner<T> preconditioner, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var result = Build.Dense(input.RowCount, input.ColumnCount);
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TrySolveIterative(input, result, solver, preconditioner, stopCriteria);
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return result;
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}
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/// <summary>
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/// Solves the matrix equation Ax = b, where A is the coefficient matrix (this matrix), b is the solution vector and x is the unknown vector.
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/// </summary>
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/// <param name="input">The solution vector <c>b</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <returns>The result vector <c>x</c>.</returns>
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public Vector<T> SolveIterative(Vector<T> input, IIterativeSolver<T> solver, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var result = Vector<T>.Build.Dense(RowCount);
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TrySolveIterative(input, result, solver, stopCriteria);
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return result;
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}
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/// <summary>
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/// Solves the matrix equation AX = B, where A is the coefficient matrix (this matrix), B is the solution matrix and X is the unknown matrix.
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/// </summary>
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/// <param name="input">The solution matrix <c>B</c>.</param>
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/// <param name="solver">The iterative solver to use.</param>
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/// <param name="stopCriteria">Criteria to control when to stop iterating.</param>
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/// <returns>The result matrix <c>X</c>.</returns>
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public Matrix<T> SolveIterative(Matrix<T> input, IIterativeSolver<T> solver, params IIterationStopCriterion<T>[] stopCriteria)
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{
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var result = Build.Dense(input.RowCount, input.ColumnCount);
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TrySolveIterative(input, result, solver, stopCriteria);
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return result;
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}
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}
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}
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