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538 lines
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538 lines
26 KiB
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<h2 class="fixed">Types in MathNet.Numerics.Differentiation</h2>
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<a href="../MathNet.Numerics.Differentiation/FiniteDifferenceCoefficients.htm">FiniteDifferenceCoefficients</a>
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<a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm" class="current">NumericalDerivative</a>
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<a href="../MathNet.Numerics.Differentiation/NumericalHessian.htm">NumericalHessian</a>
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<a href="../MathNet.Numerics.Differentiation/NumericalJacobian.htm">NumericalJacobian</a>
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<a href="../MathNet.Numerics.Differentiation/StepType.htm">StepType</a>
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</div>
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<div class="header">
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<p class="class"><strong>Type</strong> NumericalDerivative</p>
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<p><strong>Namespace</strong> MathNet.Numerics.Differentiation</p>
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</div>
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<div class="sub-header">
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<div id="summary">Class to evaluate the numerical derivative of a function using finite difference approximations.
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Variable point and center methods can be initialized .
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This class can also be used to return function handles (delegates) for a fixed derivative order and variable.
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It is possible to evaluate the derivative and partial derivative of univariate and multivariate functions respectively.
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</div>
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<h3 class="section">Constructors</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#.ctor">NumericalDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#.ctor">NumericalDerivative</a></li>
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</ul>
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<h3 class="section">Methods</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#CreateDerivativeFunctionHandle">CreateDerivativeFunctionHandle</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#CreateMixedPartialDerivativeFunctionHandle">CreateMixedPartialDerivativeFunctionHandle</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#CreateMixedPartialDerivativeFunctionHandle">CreateMixedPartialDerivativeFunctionHandle</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#CreatePartialDerivativeFunctionHandle">CreatePartialDerivativeFunctionHandle</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#CreatePartialDerivativeFunctionHandle">CreatePartialDerivativeFunctionHandle</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Equals">Equals</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluateDerivative">EvaluateDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluateDerivative">EvaluateDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluateMixedPartialDerivative">EvaluateMixedPartialDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluateMixedPartialDerivative">EvaluateMixedPartialDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluatePartialDerivative">EvaluatePartialDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluatePartialDerivative">EvaluatePartialDerivative</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#GetHashCode">GetHashCode</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#GetType">GetType</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#ResetEvaluations">ResetEvaluations</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#ToString">ToString</a></li>
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</ul>
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<h3 class="section">Properties</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#BaseStepSize">BaseStepSize</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Center">Center</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Epsilon">Epsilon</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Evaluations">Evaluations</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#StepSize">StepSize</a></li>
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<li><a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#StepType">StepType</a></li>
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</ul>
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</div>
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<h3 class="section">Public Constructors</h3>
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<div id=".ctor" class="method">
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<h4> <strong>NumericalDerivative</strong>(<span title="System.int">int</span> points, <span title="System.int">int</span> center)</h4>
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<div class="content">Initialized a NumericalDerivative class.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.int">int</span></code> points</h6>
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<p class="comments">Number of points for finite difference derivatives. </p>
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<h6><code><span title="System.int">int</span></code> center</h6>
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<p class="comments">Location of the center with respect to other points. Value ranges from zero to points-1. </p>
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</div>
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</div>
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</div>
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<div id=".ctor" class="method">
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<h4> <strong>NumericalDerivative</strong>()</h4>
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<div class="content">Initializes a NumericalDerivative class with the default 3 point center difference method.
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</div>
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</div>
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<h3 class="section">Public Methods</h3>
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<div id="CreateDerivativeFunctionHandle" class="method">
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<h4><span title="System.Func<double, double>">Func<double, double></span> <strong>CreateDerivativeFunctionHandle</strong>(<span title="System.Func<double, double>">Func<double, double></span> f, <span title="System.int">int</span> order)</h4>
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<div class="content">Creates a function handle for the derivative of a scalar univariate function.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<double, double>">Func<double, double></span></code> f</h6>
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<p class="comments">Input function handle. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Derivative order. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Func<double, double>">Func<double, double></span></code></h6>
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<p>Function handle that evaluates the derivative of input function at a fixed order. </p>
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</div>
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</div>
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</div>
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<div id="CreateMixedPartialDerivativeFunctionHandle" class="method">
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<h4><span title="System.Func<Double[], Double[]>">Func<Double[], Double[]></span> <strong>CreateMixedPartialDerivativeFunctionHandle</strong>(<span title="System.Func`2[]">Func`2[]</span> f, <span title="System.Int32[]">Int32[]</span> parameterIndex, <span title="System.int">int</span> order)</h4>
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<div class="content">
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</div>
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</div>
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<div id="CreateMixedPartialDerivativeFunctionHandle" class="method">
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<h4><span title="System.Func<Double[], double>">Func<Double[], double></span> <strong>CreateMixedPartialDerivativeFunctionHandle</strong>(<span title="System.Func<Double[], double>">Func<Double[], double></span> f, <span title="System.Int32[]">Int32[]</span> parameterIndex, <span title="System.int">int</span> order)</h4>
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<div class="content">Creates a function handle for the mixed partial derivative of a multivariate function.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code> f</h6>
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<p class="comments">Input function handle. </p>
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<h6><code><span title="System.Int32[]">Int32[]</span></code> parameterIndex</h6>
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<p class="comments">Vector of indices for the independent variables at descending derivative orders. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Highest derivative order. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code></h6>
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<p>Function handle that evaluates the fixed mixed partial derivative of input function at fixed order. </p>
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</div>
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</div>
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</div>
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<div id="CreatePartialDerivativeFunctionHandle" class="method">
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<h4><span title="System.Func<Double[], double>">Func<Double[], double></span> <strong>CreatePartialDerivativeFunctionHandle</strong>(<span title="System.Func<Double[], double>">Func<Double[], double></span> f, <span title="System.int">int</span> parameterIndex, <span title="System.int">int</span> order)</h4>
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<div class="content">Creates a function handle for the partial derivative of a multivariate function.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code> f</h6>
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<p class="comments">Input function handle. </p>
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<h6><code><span title="System.int">int</span></code> parameterIndex</h6>
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<p class="comments">Index of the independent variable for partial derivative. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Derivative order. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code></h6>
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<p>Function handle that evaluates partial derivative of input function at a fixed order. </p>
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</div>
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</div>
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</div>
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<div id="CreatePartialDerivativeFunctionHandle" class="method">
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<h4><span title="System.Func<Double[], Double[]>">Func<Double[], Double[]></span> <strong>CreatePartialDerivativeFunctionHandle</strong>(<span title="System.Func`2[]">Func`2[]</span> f, <span title="System.int">int</span> parameterIndex, <span title="System.int">int</span> order)</h4>
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<div class="content">
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</div>
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</div>
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<div id="Equals" class="method">
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<h4><span title="System.bool">bool</span> <strong>Equals</strong>(<span title="System.object">object</span> obj)</h4>
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<div class="content">
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</div>
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</div>
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<div id="EvaluateDerivative" class="method">
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<h4><span title="System.double">double</span> <strong>EvaluateDerivative</strong>(<span title="System.Double[]">Double[]</span> points, <span title="System.int">int</span> order, <span title="System.double">double</span> stepSize)</h4>
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<div class="content">Evaluates the derivative of equidistant points using the finite difference method.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Double[]">Double[]</span></code> points</h6>
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<p class="comments">Vector of points StepSize apart. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Derivative order. </p>
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<h6><code><span title="System.double">double</span></code> stepSize</h6>
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<p class="comments">Finite difference step size. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Derivative of points of the specified order. </p>
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</div>
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</div>
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</div>
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<div id="EvaluateDerivative" class="method">
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<h4><span title="System.double">double</span> <strong>EvaluateDerivative</strong>(<span title="System.Func<double, double>">Func<double, double></span> f, <span title="System.double">double</span> x, <span title="System.int">int</span> order, <span title="System.Nullable<double>">Nullable<double></span> currentValue)</h4>
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<div class="content">Evaluates the derivative of a scalar univariate function. <blockquote class="remarks">
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Supplying the optional argument currentValue will reduce the number of function evaluations
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required to calculate the finite difference derivative.
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</blockquote>
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<double, double>">Func<double, double></span></code> f</h6>
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<p class="comments">Function handle. </p>
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<h6><code><span title="System.double">double</span></code> x</h6>
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<p class="comments">Point at which to compute the derivative. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Derivative order. </p>
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<h6><code><span title="System.Nullable<double>">Nullable<double></span></code> currentValue</h6>
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<p class="comments">Current function value at center. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Function derivative at x of the specified order. </p>
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</div>
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</div>
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</div>
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<div id="EvaluateMixedPartialDerivative" class="method">
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<h4><span title="System.double">double</span> <strong>EvaluateMixedPartialDerivative</strong>(<span title="System.Func<Double[], double>">Func<Double[], double></span> f, <span title="System.Double[]">Double[]</span> x, <span title="System.Int32[]">Int32[]</span> parameterIndex, <span title="System.int">int</span> order, <span title="System.Nullable<double>">Nullable<double></span> currentValue)</h4>
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<div class="content">Evaluates the mixed partial derivative of variable order for multivariate functions. <blockquote class="remarks">
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This function recursively uses <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluatePartialDerivative">EvaluatePartialDerivative</a> to evaluate mixed partial derivative.
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Therefore, it is more efficient to call <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#EvaluatePartialDerivative">EvaluatePartialDerivative</a> for higher order derivatives of
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a single independent variable.
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</blockquote>
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code> f</h6>
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<p class="comments">Multivariate function handle. </p>
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<h6><code><span title="System.Double[]">Double[]</span></code> x</h6>
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<p class="comments">Points at which to evaluate the derivative. </p>
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<h6><code><span title="System.Int32[]">Int32[]</span></code> parameterIndex</h6>
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<p class="comments">Vector of indices for the independent variables at descending derivative orders. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Highest order of differentiation. </p>
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<h6><code><span title="System.Nullable<double>">Nullable<double></span></code> currentValue</h6>
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<p class="comments">Current function value at center. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Function mixed partial derivative at x of the specified order. </p>
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</div>
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</div>
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</div>
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<div id="EvaluateMixedPartialDerivative" class="method">
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<h4><span title="System.Double[]">Double[]</span> <strong>EvaluateMixedPartialDerivative</strong>(<span title="System.Func`2[]">Func`2[]</span> f, <span title="System.Double[]">Double[]</span> x, <span title="System.Int32[]">Int32[]</span> parameterIndex, <span title="System.int">int</span> order, <span title="System.Nullable`1[]">Nullable`1[]</span> currentValue)</h4>
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<div class="content">
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</div>
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</div>
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<div id="EvaluatePartialDerivative" class="method">
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<h4><span title="System.Double[]">Double[]</span> <strong>EvaluatePartialDerivative</strong>(<span title="System.Func`2[]">Func`2[]</span> f, <span title="System.Double[]">Double[]</span> x, <span title="System.int">int</span> parameterIndex, <span title="System.int">int</span> order, <span title="System.Nullable`1[]">Nullable`1[]</span> currentValue)</h4>
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<div class="content">
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</div>
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</div>
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<div id="EvaluatePartialDerivative" class="method">
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<h4><span title="System.double">double</span> <strong>EvaluatePartialDerivative</strong>(<span title="System.Func<Double[], double>">Func<Double[], double></span> f, <span title="System.Double[]">Double[]</span> x, <span title="System.int">int</span> parameterIndex, <span title="System.int">int</span> order, <span title="System.Nullable<double>">Nullable<double></span> currentValue)</h4>
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<div class="content">Evaluates the partial derivative of a multivariate function.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.Func<Double[], double>">Func<Double[], double></span></code> f</h6>
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<p class="comments">Multivariate function handle. </p>
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<h6><code><span title="System.Double[]">Double[]</span></code> x</h6>
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<p class="comments">Vector at which to evaluate the derivative. </p>
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<h6><code><span title="System.int">int</span></code> parameterIndex</h6>
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<p class="comments">Index of independent variable for partial derivative. </p>
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<h6><code><span title="System.int">int</span></code> order</h6>
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<p class="comments">Derivative order. </p>
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<h6><code><span title="System.Nullable<double>">Nullable<double></span></code> currentValue</h6>
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<p class="comments">Current function value at center. </p>
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</div>
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<div class="return">
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<h5>Return</h5>
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<h6><code><span title="System.double">double</span></code></h6>
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<p>Function partial derivative at x of the specified order. </p>
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</div>
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</div>
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</div>
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<div id="GetHashCode" class="method">
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<h4><span title="System.int">int</span> <strong>GetHashCode</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<div id="GetType" class="method">
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<h4><span title="System.Type">Type</span> <strong>GetType</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<div id="ResetEvaluations" class="method">
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<h4><span title="System.void">void</span> <strong>ResetEvaluations</strong>()</h4>
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<div class="content">Resets the evaluation counter.
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</div>
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</div>
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<div id="ToString" class="method">
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<h4><span title="System.string">string</span> <strong>ToString</strong>()</h4>
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<div class="content">
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</div>
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</div>
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<h3 class="section">Public Properties</h3>
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<div id="BaseStepSize" class="method">
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<h4><span title="System.double">double</span> <strong>BaseStepSize</strong> get; set;</h4>
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<div class="content">Sets and gets the base finite difference step size. This assigned value to this parameter is only used if <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#StepType">StepType</a> is set to RelativeX.
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However, if the StepType is Relative, it will contain the base step size computed from <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Epsilon">Epsilon</a> based on the finite difference order.
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</div>
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</div>
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<div id="Center" class="method">
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<h4><span title="System.int">int</span> <strong>Center</strong> get; set;</h4>
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<div class="content">Sets and gets the location of the center point for the finite difference derivative.
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</div>
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</div>
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<div id="Epsilon" class="method">
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<h4><span title="System.double">double</span> <strong>Epsilon</strong> get; set;</h4>
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<div class="content">Sets and gets the base finite difference step size. This parameter is only used if <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#StepType">StepType</a> is set to Relative.
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By default this is set to machine epsilon, from which <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#BaseStepSize">BaseStepSize</a> is computed.
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</div>
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</div>
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<div id="Evaluations" class="method">
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<h4><span title="System.int">int</span> <strong>Evaluations</strong> get; set;</h4>
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<div class="content">Number of times a function is evaluated for numerical derivatives.
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</div>
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</div>
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<div id="StepSize" class="method">
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<h4><span title="System.double">double</span> <strong>StepSize</strong> get; set;</h4>
|
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<div class="content">Sets and gets the finite difference step size. This value is for each function evaluation if relative step size types are used.
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If the base step size used in scaling is desired, see <a href="../MathNet.Numerics.Differentiation/NumericalDerivative.htm#Epsilon">Epsilon</a>. <blockquote class="remarks">
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Setting then getting the StepSize may return a different value. This is not unusual since a user-defined step size is converted to a
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base-2 representable number to improve finite difference accuracy.
|
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</blockquote>
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</div>
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</div>
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<div id="StepType" class="method">
|
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<h4><a href="../MathNet.Numerics.Differentiation/StepType.htm">StepType</a> <strong>StepType</strong> get; set;</h4>
|
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<div class="content">Type of step size for computing finite differences. If set to absolute, dx = h.
|
|
If set to relative, dx = (1+abs(x))*h^(2/(order+1)). This provides accurate results when
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h is approximately equal to the square-root of machine accuracy, epsilon.
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</div>
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</div>
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<div id="footer">
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<p>Based on v5.0.0.0 of MathNet.Numerics (Math.NET Numerics)</p>
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<p>Generated by <a href="http://docu.jagregory.com">docu</a></p>
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