// <copyright file="Matrix.Arithmetic.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.Runtime.CompilerServices;
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namespace IStation.Numerics.LinearAlgebra
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{
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/// <summary>
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/// Defines the base class for <c>Matrix</c> classes.
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/// </summary>
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public abstract partial class Matrix<T>
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{
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/// <summary>
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/// Returns a <strong>Matrix</strong> containing the same values of <paramref name="rightSide"/>.
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/// </summary>
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/// <param name="rightSide">The matrix to get the values from.</param>
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/// <returns>A matrix containing a the same 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 Matrix<T> operator +(Matrix<T> rightSide)
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{
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return rightSide.Clone();
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}
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/// <summary>
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/// Negates each element of the matrix.
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/// </summary>
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/// <param name="rightSide">The matrix to negate.</param>
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/// <returns>A matrix containing the negated values.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator -(Matrix<T> 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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/// Adds two matrices together and returns the results.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
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/// is denser.</remarks>
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/// <param name="leftSide">The left matrix to add.</param>
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/// <param name="rightSide">The right matrix to add.</param>
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/// <returns>The result of the addition.</returns>
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/// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</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 Matrix<T> operator +(Matrix<T> leftSide, Matrix<T> rightSide)
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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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/// Adds a scalar to each element of the matrix.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of the provided matrix.</remarks>
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/// <param name="leftSide">The left matrix to add.</param>
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/// <param name="rightSide">The scalar value to add.</param>
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/// <returns>The result of the addition.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator +(Matrix<T> leftSide, T rightSide)
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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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/// Adds a scalar to each element of the matrix.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of the provided matrix.</remarks>
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/// <param name="leftSide">The scalar value to add.</param>
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/// <param name="rightSide">The right matrix to add.</param>
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/// <returns>The result of the addition.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="rightSide"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator +(T leftSide, Matrix<T> rightSide)
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{
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return rightSide.Add(leftSide);
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}
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/// <summary>
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/// Subtracts two matrices together and returns the results.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
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/// is denser.</remarks>
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/// <param name="leftSide">The left matrix to subtract.</param>
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/// <param name="rightSide">The right matrix to subtract.</param>
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/// <returns>The result of the subtraction.</returns>
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/// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</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 Matrix<T> operator -(Matrix<T> leftSide, Matrix<T> rightSide)
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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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/// Subtracts a scalar from each element of a matrix.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of the provided matrix.</remarks>
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/// <param name="leftSide">The left matrix to subtract.</param>
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/// <param name="rightSide">The scalar value to subtract.</param>
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/// <returns>The result of the subtraction.</returns>
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/// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</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 Matrix<T> operator -(Matrix<T> leftSide, T rightSide)
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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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/// Subtracts each element of a matrix from a scalar.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of the provided matrix.</remarks>
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/// <param name="leftSide">The scalar value to subtract.</param>
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/// <param name="rightSide">The right matrix to subtract.</param>
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/// <returns>The result of the subtraction.</returns>
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/// <exception cref="ArgumentOutOfRangeException">If <paramref name="leftSide"/> and <paramref name="rightSide"/> don't have the same dimensions.</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 Matrix<T> operator -(T leftSide, Matrix<T> rightSide)
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{
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return rightSide.SubtractFrom(leftSide);
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}
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/// <summary>
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/// Multiplies a <strong>Matrix</strong> by a constant and returns the result.
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/// </summary>
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/// <param name="leftSide">The matrix to multiply.</param>
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/// <param name="rightSide">The constant to multiply the matrix by.</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 Matrix<T> operator *(Matrix<T> leftSide, T rightSide)
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{
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return leftSide.Multiply(rightSide);
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}
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/// <summary>
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/// Multiplies a <strong>Matrix</strong> by a constant and returns the result.
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/// </summary>
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/// <param name="leftSide">The matrix to multiply.</param>
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/// <param name="rightSide">The constant to multiply the matrix by.</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 Matrix<T> operator *(T leftSide, Matrix<T> rightSide)
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{
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return rightSide.Multiply(leftSide);
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}
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/// <summary>
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/// Multiplies two matrices.
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/// </summary>
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/// <remarks>This operator will allocate new memory for the result. It will
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/// choose the representation of either <paramref name="leftSide"/> or <paramref name="rightSide"/> depending on which
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/// is denser.</remarks>
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/// <param name="leftSide">The left matrix to multiply.</param>
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/// <param name="rightSide">The right matrix to multiply.</param>
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/// <returns>The result of multiplication.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="leftSide"/> or <paramref name="rightSide"/> is <see langword="null" />.</exception>
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/// <exception cref="ArgumentException">If the dimensions of <paramref name="leftSide"/> or <paramref name="rightSide"/> don't conform.</exception>
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public static Matrix<T> operator *(Matrix<T> leftSide, Matrix<T> rightSide)
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{
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return leftSide.Multiply(rightSide);
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}
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/// <summary>
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/// Multiplies a <strong>Matrix</strong> and a Vector.
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/// </summary>
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/// <param name="leftSide">The matrix to multiply.</param>
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/// <param name="rightSide">The vector to multiply.</param>
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/// <returns>The result of multiplication.</returns>
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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<T> operator *(Matrix<T> leftSide, Vector<T> rightSide)
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{
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return leftSide.Multiply(rightSide);
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}
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/// <summary>
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/// Multiplies a Vector and a <strong>Matrix</strong>.
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/// </summary>
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/// <param name="leftSide">The vector to multiply.</param>
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/// <param name="rightSide">The matrix to multiply.</param>
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/// <returns>The result of multiplication.</returns>
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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<T> operator *(Vector<T> leftSide, Matrix<T> rightSide)
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{
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return rightSide.LeftMultiply(leftSide);
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}
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/// <summary>
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/// Divides a scalar with a matrix.
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/// </summary>
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/// <param name="dividend">The scalar to divide.</param>
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/// <param name="divisor">The matrix.</param>
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/// <returns>The result of the division.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="divisor"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator /(T dividend, Matrix<T> divisor)
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{
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return divisor.DivideByThis(dividend);
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}
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/// <summary>
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/// Divides a matrix with a scalar.
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/// </summary>
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/// <param name="dividend">The matrix to divide.</param>
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/// <param name="divisor">The scalar value.</param>
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/// <returns>The result of the division.</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="dividend"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator /(Matrix<T> dividend, T divisor)
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{
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return dividend.Divide(divisor);
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}
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/// <summary>
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/// Computes the pointwise remainder (% operator), where the result has the sign of the dividend,
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/// of each element of the matrix of the given divisor.
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/// </summary>
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/// <param name="dividend">The matrix whose elements we want to compute the modulus of.</param>
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/// <param name="divisor">The divisor to use.</param>
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/// <returns>The result of the calculation</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="dividend"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator %(Matrix<T> dividend, T divisor)
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{
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return dividend.Remainder(divisor);
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}
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/// <summary>
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/// Computes the pointwise remainder (% operator), where the result has the sign of the dividend,
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/// of the given dividend of each element of the matrix.
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/// </summary>
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/// <param name="dividend">The dividend we want to compute the modulus of.</param>
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/// <param name="divisor">The matrix whose elements we want to use as divisor.</param>
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/// <returns>The result of the calculation</returns>
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/// <exception cref="ArgumentNullException">If <paramref name="divisor"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator %(T dividend, Matrix<T> divisor)
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{
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return divisor.RemainderByThis(dividend);
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}
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/// <summary>
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/// Computes the pointwise remainder (% operator), where the result has the sign of the dividend,
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/// of each element of two matrices.
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/// </summary>
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/// <param name="dividend">The matrix whose elements we want to compute the remainder of.</param>
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/// <param name="divisor">The divisor to use.</param>
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/// <exception cref="ArgumentException">If <paramref name="dividend"/> and <paramref name="divisor"/> are not the same size.</exception>
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/// <exception cref="ArgumentNullException">If <paramref name="dividend"/> is <see langword="null" />.</exception>
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public static Matrix<T> operator %(Matrix<T> dividend, Matrix<T> divisor)
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{
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return dividend.PointwiseRemainder(divisor);
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}
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[SpecialName]
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public static Matrix<T> op_DotMultiply(Matrix<T> x, Matrix<T> y)
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{
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return x.PointwiseMultiply(y);
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}
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[SpecialName]
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public static Matrix<T> op_DotDivide(Matrix<T> dividend, Matrix<T> divisor)
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{
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return dividend.PointwiseDivide(divisor);
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}
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[SpecialName]
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public static Matrix<T> op_DotPercent(Matrix<T> dividend, Matrix<T> divisor)
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{
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return dividend.PointwiseRemainder(divisor);
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}
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[SpecialName]
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public static Matrix<T> op_DotHat(Matrix<T> matrix, Matrix<T> exponent)
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{
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return matrix.PointwisePower(exponent);
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}
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[SpecialName]
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public static Matrix<T> op_DotHat(Matrix<T> matrix, T exponent)
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{
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return matrix.PointwisePower(exponent);
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}
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/// <summary>
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/// Computes the sqrt of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Sqrt(Matrix<T> x)
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{
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return x.PointwiseSqrt();
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}
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/// <summary>
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/// Computes the exponential of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Exp(Matrix<T> x)
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{
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return x.PointwiseExp();
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}
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/// <summary>
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/// Computes the log of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Log(Matrix<T> x)
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{
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return x.PointwiseLog();
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}
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/// <summary>
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/// Computes the log10 of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Log10(Matrix<T> x)
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{
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return x.PointwiseLog10();
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}
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/// <summary>
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/// Computes the sin of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Sin(Matrix<T> x)
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{
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return x.PointwiseSin();
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}
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/// <summary>
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/// Computes the cos of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Cos(Matrix<T> x)
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{
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return x.PointwiseCos();
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}
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/// <summary>
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/// Computes the tan of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Tan(Matrix<T> x)
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{
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return x.PointwiseTan();
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}
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/// <summary>
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/// Computes the asin of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Asin(Matrix<T> x)
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{
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return x.PointwiseAsin();
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}
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/// <summary>
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/// Computes the acos of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Acos(Matrix<T> x)
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{
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return x.PointwiseAcos();
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}
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/// <summary>
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/// Computes the atan of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Atan(Matrix<T> x)
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{
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return x.PointwiseAtan();
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}
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/// <summary>
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/// Computes the sinh of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Sinh(Matrix<T> x)
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{
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return x.PointwiseSinh();
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}
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/// <summary>
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/// Computes the cosh of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Cosh(Matrix<T> x)
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{
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return x.PointwiseCosh();
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}
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/// <summary>
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/// Computes the tanh of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Tanh(Matrix<T> x)
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{
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return x.PointwiseTanh();
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}
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/// <summary>
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/// Computes the absolute value of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Abs(Matrix<T> x)
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{
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return x.PointwiseAbs();
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}
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/// <summary>
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/// Computes the floor of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Floor(Matrix<T> x)
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{
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return x.PointwiseFloor();
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}
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/// <summary>
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/// Computes the ceiling of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Ceiling(Matrix<T> x)
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{
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return x.PointwiseCeiling();
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}
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/// <summary>
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/// Computes the rounded value of a matrix pointwise
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/// </summary>
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/// <param name="x">The input matrix</param>
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/// <returns></returns>
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public static Matrix<T> Round(Matrix<T> x)
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{
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return x.PointwiseRound();
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}
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}
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}
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