// <copyright file="DenseVector.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) 2009-2013 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 System.Collections.Generic;
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using System.Diagnostics;
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using System.Linq;
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using IStation.Numerics.Distributions;
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using IStation.Numerics.LinearAlgebra.Storage;
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using IStation.Numerics.Providers.LinearAlgebra;
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using IStation.Numerics.Threading;
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namespace IStation.Numerics.LinearAlgebra.Complex
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{
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using Complex = System.Numerics.Complex;
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/// <summary>
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/// A vector using dense storage.
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/// </summary>
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[Serializable]
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[DebuggerDisplay("DenseVector {" + nameof(Count) + "}-Complex")]
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public class DenseVector : Vector
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{
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/// <summary>
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/// Number of elements
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/// </summary>
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readonly int _length;
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/// <summary>
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/// Gets the vector's data.
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/// </summary>
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readonly Complex[] _values;
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/// <summary>
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/// Create a new dense vector straight from an initialized vector storage instance.
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/// The storage is used directly without copying.
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/// Intended for advanced scenarios where you're working directly with
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/// storage for performance or interop reasons.
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/// </summary>
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public DenseVector(DenseVectorStorage<Complex> storage)
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: base(storage)
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{
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_length = storage.Length;
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_values = storage.Data;
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}
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/// <summary>
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/// Create a new dense vector with the given length.
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/// All cells of the vector will be initialized to zero.
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/// </summary>
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/// <exception cref="ArgumentException">If length is less than one.</exception>
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public DenseVector(int length)
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: this(new DenseVectorStorage<Complex>(length))
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{
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}
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/// <summary>
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/// Create a new dense vector directly binding to a raw array.
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/// The array is used directly without copying.
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/// Very efficient, but changes to the array and the vector will affect each other.
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/// </summary>
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public DenseVector(Complex[] storage)
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: this(new DenseVectorStorage<Complex>(storage.Length, storage))
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{
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}
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/// <summary>
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/// Create a new dense vector as a copy of the given other vector.
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/// This new vector will be independent from the other vector.
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/// A new memory block will be allocated for storing the vector.
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/// </summary>
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public static DenseVector OfVector(Vector<Complex> vector)
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{
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return new DenseVector(DenseVectorStorage<Complex>.OfVector(vector.Storage));
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}
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/// <summary>
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/// Create a new dense vector as a copy of the given array.
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/// This new vector will be independent from the array.
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/// A new memory block will be allocated for storing the vector.
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/// </summary>
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public static DenseVector OfArray(Complex[] array)
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{
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return new DenseVector(DenseVectorStorage<Complex>.OfVector(new DenseVectorStorage<Complex>(array.Length, array)));
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}
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/// <summary>
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/// Create a new dense vector as a copy of the given enumerable.
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/// This new vector will be independent from the enumerable.
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/// A new memory block will be allocated for storing the vector.
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/// </summary>
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public static DenseVector OfEnumerable(IEnumerable<Complex> enumerable)
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{
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return new DenseVector(DenseVectorStorage<Complex>.OfEnumerable(enumerable));
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}
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/// <summary>
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/// Create a new dense vector as a copy of the given indexed enumerable.
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/// Keys must be provided at most once, zero is assumed if a key is omitted.
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/// This new vector will be independent from the enumerable.
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/// A new memory block will be allocated for storing the vector.
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/// </summary>
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public static DenseVector OfIndexedEnumerable(int length, IEnumerable<Tuple<int, Complex>> enumerable)
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{
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return new DenseVector(DenseVectorStorage<Complex>.OfIndexedEnumerable(length, enumerable));
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}
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/// <summary>
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/// Create a new dense vector and initialize each value using the provided value.
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/// </summary>
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public static DenseVector Create(int length, Complex value)
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{
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if (value == Complex.Zero) return new DenseVector(length);
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return new DenseVector(DenseVectorStorage<Complex>.OfValue(length, value));
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}
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/// <summary>
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/// Create a new dense vector and initialize each value using the provided init function.
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/// </summary>
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public static DenseVector Create(int length, Func<int, Complex> init)
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{
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return new DenseVector(DenseVectorStorage<Complex>.OfInit(length, init));
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}
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/// <summary>
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/// Create a new dense vector with values sampled from the provided random distribution.
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/// </summary>
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public static DenseVector CreateRandom(int length, IContinuousDistribution distribution)
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{
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var samples = Generate.RandomComplex(length, distribution);
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return new DenseVector(new DenseVectorStorage<Complex>(length, samples));
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}
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/// <summary>
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/// Gets the vector's data.
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/// </summary>
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/// <value>The vector's data.</value>
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public Complex[] Values => _values;
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/// <summary>
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/// Returns a reference to the internal data structure.
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/// </summary>
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/// <param name="vector">The <c>DenseVector</c> whose internal data we are
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/// returning.</param>
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/// <returns>
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/// A reference to the internal date of the given vector.
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/// </returns>
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public static explicit operator Complex[](DenseVector vector)
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{
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if (vector == null)
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{
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throw new ArgumentNullException(nameof(vector));
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}
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return vector.Values;
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}
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/// <summary>
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/// Returns a vector bound directly to a reference of the provided array.
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/// </summary>
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/// <param name="array">The array to bind to the <c>DenseVector</c> object.</param>
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/// <returns>
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/// A <c>DenseVector</c> whose values are bound to the given array.
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/// </returns>
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public static implicit operator DenseVector(Complex[] array)
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{
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if (array == null)
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{
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throw new ArgumentNullException(nameof(array));
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}
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return new DenseVector(array);
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}
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/// <summary>
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/// Adds a scalar to each element of the vector and stores the result in the result vector.
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/// </summary>
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/// <param name="scalar">The scalar to add.</param>
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/// <param name="result">The vector to store the result of the addition.</param>
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protected override void DoAdd(Complex scalar, Vector<Complex> result)
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{
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if (result is DenseVector dense)
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{
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CommonParallel.For(0, _values.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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dense._values[i] = _values[i] + scalar;
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}
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});
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}
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else
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{
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base.DoAdd(scalar, result);
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}
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}
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/// <summary>
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/// Adds another vector to this vector and stores the result into the result vector.
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/// </summary>
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/// <param name="other">The vector to add to this one.</param>
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/// <param name="result">The vector to store the result of the addition.</param>
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protected override void DoAdd(Vector<Complex> other, Vector<Complex> result)
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{
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if (other is DenseVector otherDense && result is DenseVector resultDense)
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{
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LinearAlgebraControl.Provider.AddArrays(_values, otherDense._values, resultDense._values);
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}
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else
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{
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base.DoAdd(other, result);
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}
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}
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/// <summary>
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/// Adds two <strong>Vectors</strong> together and returns the results.
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/// </summary>
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/// <param name="leftSide">One of the vectors to add.</param>
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/// <param name="rightSide">The other vector to add.</param>
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/// <returns>The result of the addition.</returns>
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/// <exception cref="ArgumentException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> are not the same size.</exception>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Vector<Complex> operator +(DenseVector leftSide, DenseVector rightSide)
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{
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if (leftSide == null)
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{
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throw new ArgumentNullException(nameof(leftSide));
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}
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return leftSide.Add(rightSide);
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}
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/// <summary>
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/// Subtracts a scalar from each element of the vector and stores the result in the result vector.
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/// </summary>
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/// <param name="scalar">The scalar to subtract.</param>
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/// <param name="result">The vector to store the result of the subtraction.</param>
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protected override void DoSubtract(Complex scalar, Vector<Complex> result)
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{
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if (result is DenseVector dense)
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{
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CommonParallel.For(0, _values.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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dense._values[i] = _values[i] - scalar;
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}
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});
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}
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else
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{
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base.DoSubtract(scalar, result);
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}
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}
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/// <summary>
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/// Subtracts another vector from this vector and stores the result into the result vector.
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/// </summary>
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/// <param name="other">The vector to subtract from this one.</param>
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/// <param name="result">The vector to store the result of the subtraction.</param>
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protected override void DoSubtract(Vector<Complex> other, Vector<Complex> result)
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{
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if (other is DenseVector otherDense && result is DenseVector resultDense)
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{
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LinearAlgebraControl.Provider.SubtractArrays(_values, otherDense._values, resultDense._values);
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}
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else
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{
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base.DoSubtract(other, result);
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}
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}
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/// <summary>
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/// Returns a <strong>Vector</strong> containing the negated values of <paramref name="rightSide"/>.
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/// </summary>
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/// <param name="rightSide">The vector to get the values from.</param>
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/// <returns>A vector containing the negated values as <paramref name="rightSide"/>.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Vector<Complex> operator -(DenseVector rightSide)
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{
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if (rightSide == null)
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{
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throw new ArgumentNullException(nameof(rightSide));
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}
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return rightSide.Negate();
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}
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/// <summary>
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/// Subtracts two <strong>Vectors</strong> and returns the results.
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/// </summary>
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/// <param name="leftSide">The vector to subtract from.</param>
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/// <param name="rightSide">The vector to subtract.</param>
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/// <returns>The result of the subtraction.</returns>
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/// <exception cref="ArgumentException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> are not the same size.</exception>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Vector<Complex> operator -(DenseVector leftSide, DenseVector rightSide)
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{
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if (leftSide == null)
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{
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throw new ArgumentNullException(nameof(leftSide));
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}
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return leftSide.Subtract(rightSide);
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}
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/// <summary>
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/// Negates vector and saves result to <paramref name="result"/>
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/// </summary>
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/// <param name="result">Target vector</param>
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protected override void DoNegate(Vector<Complex> result)
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{
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if (result is DenseVector denseResult)
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{
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LinearAlgebraControl.Provider.ScaleArray(-Complex.One, _values, denseResult.Values);
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}
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else
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{
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base.DoNegate(result);
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}
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}
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/// <summary>
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/// Conjugates vector and save result to <paramref name="result"/>
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/// </summary>
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/// <param name="result">Target vector</param>
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protected override void DoConjugate(Vector<Complex> result)
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{
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if (result is DenseVector resultDense)
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{
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LinearAlgebraControl.Provider.ConjugateArray(_values, resultDense._values);
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}
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else
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{
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base.DoConjugate(result);
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}
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}
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/// <summary>
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/// Multiplies a scalar to each element of the vector and stores the result in the result vector.
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/// </summary>
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/// <param name="scalar">The scalar to multiply.</param>
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/// <param name="result">The vector to store the result of the multiplication.</param>
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/// <remarks></remarks>
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protected override void DoMultiply(Complex scalar, Vector<Complex> result)
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{
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if (result is DenseVector denseResult)
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{
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LinearAlgebraControl.Provider.ScaleArray(scalar, _values, denseResult.Values);
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}
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else
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{
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base.DoMultiply(scalar, result);
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}
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}
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/// <summary>
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/// Computes the dot product between this vector and another vector.
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/// </summary>
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/// <param name="other">The other vector.</param>
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/// <returns>The sum of a[i]*b[i] for all i.</returns>
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protected override Complex DoDotProduct(Vector<Complex> other)
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{
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return other is DenseVector denseVector
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? LinearAlgebraControl.Provider.DotProduct(_values, denseVector.Values)
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: base.DoDotProduct(other);
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}
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/// <summary>
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/// Computes the dot product between the conjugate of this vector and another vector.
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/// </summary>
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/// <param name="other">The other vector.</param>
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/// <returns>The sum of conj(a[i])*b[i] for all i.</returns>
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protected override Complex DoConjugateDotProduct(Vector<Complex> other)
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{
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if (other is DenseVector denseVector)
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{
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var dot = Complex.Zero;
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for (var i = 0; i < _values.Length; i++)
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{
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dot += _values[i].Conjugate() * denseVector._values[i];
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}
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return dot;
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}
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// TODO: provide native zdotc routine
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return base.DoConjugateDotProduct(other);
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}
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/// <summary>
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/// Multiplies a vector with a complex.
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/// </summary>
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/// <param name="leftSide">The vector to scale.</param>
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/// <param name="rightSide">The Complex value.</param>
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/// <returns>The result of the multiplication.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> is <see langword="null" />.</exception>
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public static DenseVector operator *(DenseVector leftSide, Complex rightSide)
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{
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if (leftSide == null)
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{
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throw new ArgumentNullException(nameof(leftSide));
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}
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return (DenseVector)leftSide.Multiply(rightSide);
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}
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/// <summary>
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/// Multiplies a vector with a complex.
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/// </summary>
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/// <param name="leftSide">The Complex value.</param>
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/// <param name="rightSide">The vector to scale.</param>
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/// <returns>The result of the multiplication.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static DenseVector operator *(Complex leftSide, DenseVector rightSide)
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{
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if (rightSide == null)
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{
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throw new ArgumentNullException(nameof(rightSide));
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}
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return (DenseVector)rightSide.Multiply(leftSide);
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}
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/// <summary>
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/// Computes the dot product between two <strong>Vectors</strong>.
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/// </summary>
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/// <param name="leftSide">The left row vector.</param>
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/// <param name="rightSide">The right column vector.</param>
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/// <returns>The dot product between the two vectors.</returns>
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/// <exception cref="ArgumentException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> are not the same size.</exception>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Complex operator *(DenseVector leftSide, DenseVector rightSide)
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{
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if (leftSide == null)
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{
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throw new ArgumentNullException(nameof(leftSide));
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}
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return leftSide.DotProduct(rightSide);
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}
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/// <summary>
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/// Divides a vector with a complex.
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/// </summary>
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/// <param name="leftSide">The vector to divide.</param>
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/// <param name="rightSide">The Complex value.</param>
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/// <returns>The result of the division.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> is <see langword="null" />.</exception>
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public static DenseVector operator /(DenseVector leftSide, Complex rightSide)
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{
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if (leftSide == null)
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{
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throw new ArgumentNullException(nameof(leftSide));
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}
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return (DenseVector)leftSide.Divide(rightSide);
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}
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/// <summary>
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/// Returns the index of the absolute minimum element.
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/// </summary>
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/// <returns>The index of absolute minimum element.</returns>
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public override int AbsoluteMinimumIndex()
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{
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var index = 0;
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var min = _values[index].Magnitude;
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for (var i = 1; i < _length; i++)
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{
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var test = _values[i].Magnitude;
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if (test < min)
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{
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index = i;
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min = test;
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}
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}
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return index;
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}
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/// <summary>
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/// Returns the index of the absolute maximum element.
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/// </summary>
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/// <returns>The index of absolute maximum element.</returns>
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public override int AbsoluteMaximumIndex()
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{
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var index = 0;
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var max = _values[index].Magnitude;
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for (var i = 1; i < _length; i++)
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{
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var test = _values[i].Magnitude;
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if (test > max)
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{
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index = i;
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max = test;
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}
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}
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return index;
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}
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/// <summary>
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/// Computes the sum of the vector's elements.
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/// </summary>
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/// <returns>The sum of the vector's elements.</returns>
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public override Complex Sum()
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{
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var sum = Complex.Zero;
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for (var i = 0; i < _length; i++)
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{
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sum += _values[i];
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}
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return sum;
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}
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/// <summary>
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/// Calculates the L1 norm of the vector, also known as Manhattan norm.
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/// </summary>
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/// <returns>The sum of the absolute values.</returns>
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public override double L1Norm()
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{
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double sum = 0d;
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for (var i = 0; i < _length; i++)
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{
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sum += _values[i].Magnitude;
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}
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return sum;
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}
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/// <summary>
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/// Calculates the L2 norm of the vector, also known as Euclidean norm.
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/// </summary>
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/// <returns>The square root of the sum of the squared values.</returns>
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public override double L2Norm()
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{
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// TODO: native provider
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return _values.Aggregate(Complex.Zero, SpecialFunctions.Hypotenuse).Magnitude;
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}
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/// <summary>
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/// Calculates the infinity norm of the vector.
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/// </summary>
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/// <returns>The maximum absolute value.</returns>
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public override double InfinityNorm()
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{
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return CommonParallel.Aggregate(_values, (i, v) => v.Magnitude, Math.Max, 0d);
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}
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/// <summary>
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/// Computes the p-Norm.
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/// </summary>
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/// <param name="p">The p value.</param>
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/// <returns>Scalar <c>ret = ( ∑|this[i]|^p )^(1/p)</c></returns>
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public override double Norm(double p)
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{
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if (p < 0d) throw new ArgumentOutOfRangeException(nameof(p));
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if (p == 1d) return L1Norm();
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if (p == 2d) return L2Norm();
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if (double.IsPositiveInfinity(p)) return InfinityNorm();
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|
double sum = 0d;
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for (var i = 0; i < _length; i++)
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{
|
sum += Math.Pow(_values[i].Magnitude, p);
|
}
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return Math.Pow(sum, 1.0 / p);
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}
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|
/// <summary>
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/// Pointwise divide this vector with another vector and stores the result into the result vector.
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/// </summary>
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/// <param name="other">The vector to pointwise divide this one by.</param>
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/// <param name="result">The vector to store the result of the pointwise division.</param>
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protected override void DoPointwiseMultiply(Vector<Complex> other, Vector<Complex> result)
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{
|
if (other is DenseVector denseOther && result is DenseVector denseResult)
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{
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LinearAlgebraControl.Provider.PointWiseMultiplyArrays(_values, denseOther._values, denseResult._values);
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}
|
else
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{
|
base.DoPointwiseMultiply(other, result);
|
}
|
}
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|
/// <summary>
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/// Pointwise divide this vector with another vector and stores the result into the result vector.
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/// </summary>
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/// <param name="divisor">The vector to pointwise divide this one by.</param>
|
/// <param name="result">The vector to store the result of the pointwise division.</param>
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/// <remarks></remarks>
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protected override void DoPointwiseDivide(Vector<Complex> divisor, Vector<Complex> result)
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{
|
if (divisor is DenseVector denseDivisor && result is DenseVector denseResult)
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{
|
LinearAlgebraControl.Provider.PointWiseDivideArrays(_values, denseDivisor._values, denseResult._values);
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}
|
else
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{
|
base.DoPointwiseDivide(divisor, result);
|
}
|
}
|
|
/// <summary>
|
/// Pointwise raise this vector to an exponent vector and store the result into the result vector.
|
/// </summary>
|
/// <param name="exponent">The exponent vector to raise this vector values to.</param>
|
/// <param name="result">The vector to store the result of the pointwise power.</param>
|
protected override void DoPointwisePower(Vector<Complex> exponent, Vector<Complex> result)
|
{
|
if (exponent is DenseVector denseExponent && result is DenseVector denseResult)
|
{
|
LinearAlgebraControl.Provider.PointWisePowerArrays(_values, denseExponent._values, denseResult._values);
|
}
|
else
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{
|
base.DoPointwisePower(exponent, result);
|
}
|
}
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|
#region Parse Functions
|
|
/// <summary>
|
/// Creates a Complex dense vector based on a string. The string can be in the following formats (without the
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/// quotes): 'n', 'n;n;..', '(n;n;..)', '[n;n;...]', where n is a double.
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/// </summary>
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/// <returns>
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/// A Complex dense vector containing the values specified by the given string.
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/// </returns>
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/// <param name="value">
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/// the string to parse.
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/// </param>
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/// <param name="formatProvider">
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/// An <see cref="IFormatProvider"/> that supplies culture-specific formatting information.
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/// </param>
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public static DenseVector Parse(string value, IFormatProvider formatProvider = null)
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{
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if (value == null)
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{
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throw new ArgumentNullException(nameof(value));
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}
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value = value.Trim();
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if (value.Length == 0)
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{
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throw new FormatException();
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}
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// strip out parens
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if (value.StartsWith("(", StringComparison.Ordinal))
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{
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if (!value.EndsWith(")", StringComparison.Ordinal))
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{
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throw new FormatException();
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}
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value = value.Substring(1, value.Length - 2).Trim();
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}
|
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if (value.StartsWith("[", StringComparison.Ordinal))
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{
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if (!value.EndsWith("]", StringComparison.Ordinal))
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{
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throw new FormatException();
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}
|
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value = value.Substring(1, value.Length - 2).Trim();
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}
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// parsing
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var strongTokens = value.Split(new[] { formatProvider.GetTextInfo().ListSeparator }, StringSplitOptions.RemoveEmptyEntries);
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var data = new List<Complex>();
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foreach (string strongToken in strongTokens)
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{
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var weakTokens = strongToken.Split(new[] { " ", "\t" }, StringSplitOptions.RemoveEmptyEntries);
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string current = string.Empty;
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for (int i = 0; i < weakTokens.Length; i++)
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{
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current += weakTokens[i];
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if (current.EndsWith("+") || current.EndsWith("-") || current.StartsWith("(") && !current.EndsWith(")"))
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{
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continue;
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}
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var ahead = i < weakTokens.Length - 1 ? weakTokens[i + 1] : string.Empty;
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if (ahead.StartsWith("+") || ahead.StartsWith("-"))
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{
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continue;
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}
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data.Add(current.ToComplex(formatProvider));
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current = string.Empty;
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}
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if (current != string.Empty)
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{
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throw new FormatException();
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}
|
}
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if (data.Count == 0)
|
{
|
throw new FormatException();
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}
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return new DenseVector(data.ToArray());
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}
|
|
/// <summary>
|
/// Converts the string representation of a complex dense vector to double-precision dense vector equivalent.
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/// A return value indicates whether the conversion succeeded or failed.
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/// </summary>
|
/// <param name="value">
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/// A string containing a complex vector to convert.
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/// </param>
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/// <param name="result">
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/// The parsed value.
|
/// </param>
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/// <returns>
|
/// If the conversion succeeds, the result will contain a complex number equivalent to value.
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/// Otherwise the result will be <c>null</c>.
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/// </returns>
|
public static bool TryParse(string value, out DenseVector result)
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{
|
return TryParse(value, null, out result);
|
}
|
|
/// <summary>
|
/// Converts the string representation of a complex dense vector to double-precision dense vector equivalent.
|
/// A return value indicates whether the conversion succeeded or failed.
|
/// </summary>
|
/// <param name="value">
|
/// A string containing a complex vector to convert.
|
/// </param>
|
/// <param name="formatProvider">
|
/// An <see cref="IFormatProvider"/> that supplies culture-specific formatting information about value.
|
/// </param>
|
/// <param name="result">
|
/// The parsed value.
|
/// </param>
|
/// <returns>
|
/// If the conversion succeeds, the result will contain a complex number equivalent to value.
|
/// Otherwise the result will be <c>null</c>.
|
/// </returns>
|
public static bool TryParse(string value, IFormatProvider formatProvider, out DenseVector result)
|
{
|
bool ret;
|
try
|
{
|
result = Parse(value, formatProvider);
|
ret = true;
|
}
|
catch (ArgumentNullException)
|
{
|
result = null;
|
ret = false;
|
}
|
catch (FormatException)
|
{
|
result = null;
|
ret = false;
|
}
|
|
return ret;
|
}
|
|
#endregion
|
}
|
}
|
