// <copyright file="Vector.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) 2009-2015 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.Storage;
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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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/// <c>Complex</c> version of the <see cref="Vector{T}"/> class.
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/// </summary>
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[Serializable]
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public abstract class Vector : Vector<Complex>
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{
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/// <summary>
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/// Initializes a new instance of the Vector class.
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/// </summary>
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protected Vector(VectorStorage<Complex> storage)
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: base(storage)
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{
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}
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/// <summary>
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/// Set all values whose absolute value is smaller than the threshold to zero.
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/// </summary>
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public override void CoerceZero(double threshold)
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{
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MapInplace(x => x.Magnitude < threshold ? Complex.Zero : x, Zeros.AllowSkip);
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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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Map(Complex.Conjugate, result, Zeros.AllowSkip);
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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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Map(Complex.Negate, result, Zeros.AllowSkip);
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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">
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/// The scalar to add.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the addition.
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/// </param>
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protected override void DoAdd(Complex scalar, Vector<Complex> result)
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{
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Map(x => x + scalar, result, Zeros.Include);
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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">
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/// The vector to add to this one.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the addition.
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/// </param>
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protected override void DoAdd(Vector<Complex> other, Vector<Complex> result)
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{
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Map2(Complex.Add, other, result, Zeros.AllowSkip);
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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">
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/// The scalar to subtract.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the subtraction.
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/// </param>
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protected override void DoSubtract(Complex scalar, Vector<Complex> result)
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{
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Map(x => x - scalar, result, Zeros.Include);
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}
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/// <summary>
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/// Subtracts 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">
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/// The vector to subtract from this one.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the subtraction.
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/// </param>
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protected override void DoSubtract(Vector<Complex> other, Vector<Complex> result)
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{
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Map2(Complex.Subtract, other, result, Zeros.AllowSkip);
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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">
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/// The scalar to multiply.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the multiplication.
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/// </param>
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protected override void DoMultiply(Complex scalar, Vector<Complex> result)
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{
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Map(x => x*scalar, result, Zeros.AllowSkip);
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}
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/// <summary>
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/// Divides each element of the vector by a scalar and stores the result in the result vector.
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/// </summary>
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/// <param name="divisor">
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/// The scalar to divide with.
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/// </param>
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/// <param name="result">
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/// The vector to store the result of the division.
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/// </param>
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protected override void DoDivide(Complex divisor, Vector<Complex> result)
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{
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Map(x => x/divisor, result, divisor.IsZero() ? Zeros.Include : Zeros.AllowSkip);
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}
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/// <summary>
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/// Divides a scalar by each element of the vector and stores the result in the result vector.
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/// </summary>
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/// <param name="dividend">The scalar to divide.</param>
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/// <param name="result">The vector to store the result of the division.</param>
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protected override void DoDivideByThis(Complex dividend, Vector<Complex> result)
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{
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Map(x => dividend/x, result, Zeros.Include);
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}
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/// <summary>
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/// Pointwise multiplies 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 multiply with this one.</param>
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/// <param name="result">The vector to store the result of the pointwise multiplication.</param>
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protected override void DoPointwiseMultiply(Vector<Complex> other, Vector<Complex> result)
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{
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Map2(Complex.Multiply, other, result, Zeros.AllowSkip);
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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="divisor">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 DoPointwiseDivide(Vector<Complex> divisor, Vector<Complex> result)
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{
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Map2(Complex.Divide, divisor, result, Zeros.Include);
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}
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/// <summary>
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/// Pointwise raise this vector to an exponent and store the result into the result vector.
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/// </summary>
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/// <param name="exponent">The exponent to raise this vector values to.</param>
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/// <param name="result">The vector to store the result of the pointwise power.</param>
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protected override void DoPointwisePower(Complex exponent, Vector<Complex> result)
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{
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Map(x => x.Power(exponent), result, Zeros.Include);
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}
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/// <summary>
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/// Pointwise raise this vector to an exponent vector and store the result into the result vector.
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/// </summary>
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/// <param name="exponent">The exponent vector to raise this vector values to.</param>
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/// <param name="result">The vector to store the result of the pointwise power.</param>
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protected override void DoPointwisePower(Vector<Complex> exponent, Vector<Complex> result)
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{
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Map2(Complex.Pow, exponent, result, Zeros.Include);
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}
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/// <summary>
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/// Pointwise canonical modulus, where the result has the sign of the divisor,
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/// of 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 pointwise denominator vector to use.</param>
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/// <param name="result">The result of the modulus.</param>
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protected sealed override void DoPointwiseModulus(Vector<Complex> divisor, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Pointwise remainder (% operator), where the result has the sign of the dividend,
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/// of 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 pointwise denominator vector to use.</param>
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/// <param name="result">The result of the modulus.</param>
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protected sealed override void DoPointwiseRemainder(Vector<Complex> divisor, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Pointwise applies the exponential function to each value and stores the result into the result vector.
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/// </summary>
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/// <param name="result">The vector to store the result.</param>
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protected override void DoPointwiseExp(Vector<Complex> result)
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{
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Map(Complex.Exp, result, Zeros.Include);
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}
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/// <summary>
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/// Pointwise applies the natural logarithm function to each value and stores the result into the result vector.
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/// </summary>
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/// <param name="result">The vector to store the result.</param>
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protected override void DoPointwiseLog(Vector<Complex> result)
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{
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Map(Complex.Log, result, Zeros.Include);
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}
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protected override void DoPointwiseAbs(Vector<Complex> result)
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{
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Map(x => (Complex)Complex.Abs(x), result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseAcos(Vector<Complex> result)
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{
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Map(Complex.Acos, result, Zeros.Include);
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}
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protected override void DoPointwiseAsin(Vector<Complex> result)
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{
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Map(Complex.Asin, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseAtan(Vector<Complex> result)
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{
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Map(Complex.Atan, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseAtan2(Vector<Complex> other, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseAtan2(Complex scalar, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseCeiling(Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseCos(Vector<Complex> result)
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{
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Map(Complex.Cos, result, Zeros.Include);
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}
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protected override void DoPointwiseCosh(Vector<Complex> result)
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{
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Map(Complex.Cosh, result, Zeros.Include);
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}
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protected override void DoPointwiseFloor(Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseLog10(Vector<Complex> result)
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{
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Map(Complex.Log10, result, Zeros.Include);
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}
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protected override void DoPointwiseRound(Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseSign(Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseSin(Vector<Complex> result)
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{
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Map(Complex.Sin, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseSinh(Vector<Complex> result)
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{
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Map(Complex.Sinh, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseSqrt(Vector<Complex> result)
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{
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Map(Complex.Sqrt, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseTan(Vector<Complex> result)
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{
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Map(Complex.Tan, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseTanh(Vector<Complex> result)
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{
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Map(Complex.Tanh, result, Zeros.AllowSkip);
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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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var dot = Complex.Zero;
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for (var i = 0; i < Count; i++)
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{
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dot += At(i) * other.At(i);
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}
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return dot;
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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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var dot = Complex.Zero;
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for (var i = 0; i < Count; i++)
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{
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dot += At(i).Conjugate() * other.At(i);
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}
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return dot;
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}
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/// <summary>
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/// Computes the canonical modulus, where the result has the sign of the divisor,
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/// for each element of the vector for the given divisor.
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/// </summary>
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/// <param name="divisor">The scalar denominator to use.</param>
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/// <param name="result">A vector to store the results in.</param>
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protected sealed override void DoModulus(Complex divisor, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Computes the canonical modulus, where the result has the sign of the divisor,
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/// for the given dividend for each element of the vector.
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/// </summary>
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/// <param name="dividend">The scalar numerator to use.</param>
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/// <param name="result">A vector to store the results in.</param>
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protected sealed override void DoModulusByThis(Complex dividend, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Computes the canonical modulus, where the result has the sign of the divisor,
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/// for each element of the vector for the given divisor.
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/// </summary>
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/// <param name="divisor">The scalar denominator to use.</param>
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/// <param name="result">A vector to store the results in.</param>
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protected sealed override void DoRemainder(Complex divisor, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Computes the canonical modulus, where the result has the sign of the divisor,
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/// for the given dividend for each element of the vector.
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/// </summary>
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/// <param name="dividend">The scalar numerator to use.</param>
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/// <param name="result">A vector to store the results in.</param>
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protected sealed override void DoRemainderByThis(Complex dividend, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseMinimum(Complex scalar, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseMaximum(Complex scalar, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseAbsoluteMinimum(Complex scalar, Vector<Complex> result)
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{
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double absolute = scalar.Magnitude;
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Map(x => Math.Min(absolute, x.Magnitude), result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseAbsoluteMaximum(Complex scalar, Vector<Complex> result)
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{
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double absolute = scalar.Magnitude;
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Map(x => Math.Max(absolute, x.Magnitude), result, Zeros.Include);
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}
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protected override void DoPointwiseMinimum(Vector<Complex> other, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseMaximum(Vector<Complex> other, Vector<Complex> result)
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{
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throw new NotSupportedException();
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}
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protected override void DoPointwiseAbsoluteMinimum(Vector<Complex> other, Vector<Complex> result)
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{
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Map2((x, y) => Math.Min(x.Magnitude, y.Magnitude), other, result, Zeros.AllowSkip);
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}
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protected override void DoPointwiseAbsoluteMaximum(Vector<Complex> other, Vector<Complex> result)
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{
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Map2((x, y) => Math.Max(x.Magnitude, y.Magnitude), other, result, Zeros.AllowSkip);
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}
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/// <summary>
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/// Returns the value of the absolute minimum element.
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/// </summary>
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/// <returns>The value of the absolute minimum element.</returns>
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public sealed override Complex AbsoluteMinimum()
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{
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return At(AbsoluteMinimumIndex()).Magnitude;
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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 = At(index).Magnitude;
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for (var i = 1; i < Count; i++)
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{
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var test = At(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 value of the absolute maximum element.
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/// </summary>
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/// <returns>The value of the absolute maximum element.</returns>
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public override Complex AbsoluteMaximum()
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{
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return At(AbsoluteMaximumIndex()).Magnitude;
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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 = At(index).Magnitude;
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for (var i = 1; i < Count; i++)
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{
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var test = At(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 < Count; i++)
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{
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sum += At(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 < Count; i++)
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{
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sum += At(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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return DoConjugateDotProduct(this).SquareRoot().Real;
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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(0, Count, i => At(i).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">
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/// The p value.
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/// </param>
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/// <returns>
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/// <c>Scalar ret = ( ∑|At(i)|^p )^(1/p)</c>
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/// </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 index = 0; index < Count; index++)
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{
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sum += Math.Pow(At(index).Magnitude, p);
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}
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return Math.Pow(sum, 1.0/p);
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}
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/// <summary>
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/// Returns the index of the maximum element.
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/// </summary>
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/// <returns>The index of maximum element.</returns>
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public override int MaximumIndex()
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Returns the index of the minimum element.
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/// </summary>
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/// <returns>The index of minimum element.</returns>
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public override int MinimumIndex()
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Normalizes this vector to a unit vector with respect to the p-norm.
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/// </summary>
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/// <param name="p">
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/// The p value.
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/// </param>
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/// <returns>
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/// This vector normalized to a unit vector with respect to the p-norm.
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/// </returns>
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public override Vector<Complex> Normalize(double p)
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{
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if (p < 0d)
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{
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throw new ArgumentOutOfRangeException(nameof(p));
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}
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double norm = Norm(p);
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var clone = Clone();
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if (norm == 0d)
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{
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return clone;
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}
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clone.Multiply(1d / norm, clone);
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return clone;
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}
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}
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}
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