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419 lines
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419 lines
18 KiB
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<div class="header">
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<p class="class"><strong>Type</strong> FindRoots</p>
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<p><strong>Namespace</strong> MathNet.Numerics</p>
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</div>
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<div class="sub-header">
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<h3 class="section">Static Functions</h3>
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<ul>
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<li><a href="../MathNet.Numerics/FindRoots.htm#ChebychevPolynomialFirstKind">ChebychevPolynomialFirstKind</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#ChebychevPolynomialSecondKind">ChebychevPolynomialSecondKind</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#Cubic">Cubic</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#OfFunction">OfFunction</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#OfFunctionDerivative">OfFunctionDerivative</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#Polynomial">Polynomial</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#Polynomial">Polynomial</a></li>
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<li><a href="../MathNet.Numerics/FindRoots.htm#Quadratic">Quadratic</a></li>
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</ul>
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</div>
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<h3 class="section">Public Static Functions</h3>
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<div id="ChebychevPolynomialFirstKind" class="method">
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<h4><span title="System.Double[]">Double[]</span> <strong>ChebychevPolynomialFirstKind</strong>(<span title="System.int">int</span> degree, <span title="System.double">double</span> intervalBegin, <span title="System.double">double</span> intervalEnd)</h4>
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<div class="content">Find all roots of the Chebychev polynomial of the first kind.
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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> degree</h6>
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<p class="comments">The polynomial order and therefore the number of roots. </p>
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<h6><code><span title="System.double">double</span></code> intervalBegin</h6>
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<p class="comments">The real domain interval begin where to start sampling. </p>
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<h6><code><span title="System.double">double</span></code> intervalEnd</h6>
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<p class="comments">The real domain interval end where to stop sampling. </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>Samples in [a,b] at (b+a)/2+(b-1)/2*cos(pi*(2i-1)/(2n)) </p>
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</div>
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</div>
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</div>
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<div id="ChebychevPolynomialSecondKind" class="method">
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<h4><span title="System.Double[]">Double[]</span> <strong>ChebychevPolynomialSecondKind</strong>(<span title="System.int">int</span> degree, <span title="System.double">double</span> intervalBegin, <span title="System.double">double</span> intervalEnd)</h4>
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<div class="content">Find all roots of the Chebychev polynomial of the second kind.
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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> degree</h6>
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<p class="comments">The polynomial order and therefore the number of roots. </p>
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<h6><code><span title="System.double">double</span></code> intervalBegin</h6>
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<p class="comments">The real domain interval begin where to start sampling. </p>
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<h6><code><span title="System.double">double</span></code> intervalEnd</h6>
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<p class="comments">The real domain interval end where to stop sampling. </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>Samples in [a,b] at (b+a)/2+(b-1)/2*cos(pi*i/(n-1)) </p>
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</div>
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</div>
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</div>
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<div id="Cubic" class="method">
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<h4><span title="System.ValueTuple<Complex, Complex, Complex>">ValueTuple<Complex, Complex, Complex></span> <strong>Cubic</strong>(<span title="System.double">double</span> d, <span title="System.double">double</span> c, <span title="System.double">double</span> b, <span title="System.double">double</span> a)</h4>
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<div class="content">Find all three complex roots of the cubic equation d + c*x + b*x^2 + a*x^3 = 0.
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Note the special coefficient order ascending by exponent (consistent with polynomials).
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</div>
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</div>
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<div id="OfFunction" class="method">
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<h4><span title="System.double">double</span> <strong>OfFunction</strong>(<span title="System.Func<double, double>">Func<double, double></span> f, <span title="System.double">double</span> lowerBound, <span title="System.double">double</span> upperBound, <span title="System.double">double</span> accuracy, <span title="System.int">int</span> maxIterations)</h4>
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<div class="content">Find a solution of the equation f(x)=0.
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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">The function to find roots from. </p>
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<h6><code><span title="System.double">double</span></code> lowerBound</h6>
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<p class="comments">The low value of the range where the root is supposed to be. </p>
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<h6><code><span title="System.double">double</span></code> upperBound</h6>
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<p class="comments">The high value of the range where the root is supposed to be. </p>
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<h6><code><span title="System.double">double</span></code> accuracy</h6>
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<p class="comments">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Example: 1e-14. </p>
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<h6><code><span title="System.int">int</span></code> maxIterations</h6>
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<p class="comments">Maximum number of iterations. Example: 100. </p>
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</div>
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</div>
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</div>
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<div id="OfFunctionDerivative" class="method">
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<h4><span title="System.double">double</span> <strong>OfFunctionDerivative</strong>(<span title="System.Func<double, double>">Func<double, double></span> f, <span title="System.Func<double, double>">Func<double, double></span> df, <span title="System.double">double</span> lowerBound, <span title="System.double">double</span> upperBound, <span title="System.double">double</span> accuracy, <span title="System.int">int</span> maxIterations)</h4>
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<div class="content">Find a solution of the equation f(x)=0.
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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">The function to find roots from. </p>
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<h6><code><span title="System.Func<double, double>">Func<double, double></span></code> df</h6>
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<p class="comments">The first derivative of the function to find roots from. </p>
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<h6><code><span title="System.double">double</span></code> lowerBound</h6>
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<p class="comments">The low value of the range where the root is supposed to be. </p>
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<h6><code><span title="System.double">double</span></code> upperBound</h6>
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<p class="comments">The high value of the range where the root is supposed to be. </p>
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<h6><code><span title="System.double">double</span></code> accuracy</h6>
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<p class="comments">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached. Example: 1e-14. </p>
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<h6><code><span title="System.int">int</span></code> maxIterations</h6>
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<p class="comments">Maximum number of iterations. Example: 100. </p>
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</div>
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</div>
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</div>
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<div id="Polynomial" class="method">
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<h4><span title="System.Numerics.Complex[]">Complex[]</span> <strong>Polynomial</strong>(<span title="System.Double[]">Double[]</span> coefficients)</h4>
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<div class="content">Find all roots of a polynomial by calculating the characteristic polynomial of the companion matrix
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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> coefficients</h6>
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<p class="comments">The coefficients of the polynomial in ascending order, e.g. new double[] {5, 0, 2} = "5 + 0 x^1 + 2 x^2" </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.Numerics.Complex[]">Complex[]</span></code></h6>
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<p>The roots of the polynomial </p>
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</div>
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</div>
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</div>
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<div id="Polynomial" class="method">
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<h4><span title="System.Numerics.Complex[]">Complex[]</span> <strong>Polynomial</strong>(<a href="../MathNet.Numerics/Polynomial.htm">Polynomial</a> polynomial)</h4>
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<div class="content">Find all roots of a polynomial by calculating the characteristic polynomial of the companion matrix
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><a href="../MathNet.Numerics/Polynomial.htm">Polynomial</a></code> polynomial</h6>
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<p class="comments">The polynomial. </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.Numerics.Complex[]">Complex[]</span></code></h6>
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<p>The roots of the polynomial </p>
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<div id="Quadratic" class="method">
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<h4><span title="System.ValueTuple<Complex, Complex>">ValueTuple<Complex, Complex></span> <strong>Quadratic</strong>(<span title="System.double">double</span> c, <span title="System.double">double</span> b, <span title="System.double">double</span> a)</h4>
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<div class="content">Find both complex roots of the quadratic equation c + b*x + a*x^2 = 0.
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Note the special coefficient order ascending by exponent (consistent with polynomials).
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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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