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140 lines
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<span>kmath</span> </a> </div>
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<div class="main-content" data-page-type="classlike" id="content" pageids="kmath-core::space.kscience.kmath.expressions/DS///PointingToDeclaration//244675578">
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<div class="breadcrumbs"><a href="../../index.html">kmath-core</a><span class="delimiter">/</span><a href="../index.html">space.kscience.kmath.expressions</a><span class="delimiter">/</span><span class="current">DS</span></div>
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<div class="cover ">
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<h1 class="cover"><span><span>DS</span></span></h1>
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<div class="platform-hinted " data-platform-hinted="data-platform-hinted"><div class="content sourceset-dependent-content" data-active="" data-togglable=":kmath-core:dokkaHtmlPartial/commonMain"><div class="symbol monospace"><div class="block"><div class="block"><span class="token annotation builtin">@</span><a href="../../../kmath-memory/space.kscience.kmath/-unstable-k-math-a-p-i/index.html"><span class="token annotation builtin">UnstableKMathAPI</span></a></div></div><span class="token keyword">interface </span><a href="index.html">DS</a><span class="token operator"><</span><span class="token keyword"></span><a href="index.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="index.html">A</a><span class="token operator"> : </span><a href="../../space.kscience.kmath.operations/-ring/index.html">Ring</a><span class="token operator"><</span><span class="token keyword"></span><a href="index.html">T</a><span class="token operator">></span><span class="token operator">></span><span class="clearfix"><span class="floating-right">(<a href="https://github.com/SciProgCentre/kmath/tree/master/kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/DSAlgebra.kt#L34">source</a>)</span></span></div><p class="paragraph">Class representing both the value and the differentials of a function.</p><p class="paragraph">This class is the workhorse of the differentiation package.</p><p class="paragraph">This class is an implementation of the extension to Rall's numbers described in Dan Kalman's paper <a href="http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf">Doubly Recursive Multivariate Automatic Differentiation</a>, Mathematics Magazine, vol. 75, no. 3, June 2002. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function. Dan Kalman's derivative structures hold all partial derivatives up to any specified order, with respect to any number of free parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.</p><p class="paragraph">Derived from <a href="https://github.com/apache/commons-math/blob/924f6c357465b39beb50e3c916d5eb6662194175/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java">Commons Math's <code class="lang-kotlin">DerivativeStructure</code></a>.</p><h4 class="">Inheritors</h4><div class="table"><div class="table-row" data-filterable-current=":kmath-core:dokkaHtmlPartial/commonMain" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain"><div class="main-subrow keyValue "><div class=""><span class="inline-flex"><div><a href="../-d-s-algebra/-d-s-symbol/index.html">DSSymbol</a></div></span></div><div></div></div></div></div></div></div>
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<div class="tabbedcontent">
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<div class="tabs-section" tabs-section="tabs-section"><button class="section-tab" data-active="" data-togglable="CONSTRUCTOR,TYPE,FUNCTION,PROPERTY">Members</button><button class="section-tab" data-togglable="CONSTRUCTOR,TYPE,FUNCTION,PROPERTY,EXTENSION_PROPERTY,EXTENSION_FUNCTION">Members & Extensions</button></div>
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<div class="tabs-section-body">
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<div data-togglable="EXTENSION_FUNCTION">
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<h2 class="">Functions</h2>
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<div class="table"><a data-name="-1538956488%2FFunctions%2F244675578" anchor-label="derivative" id="-1538956488%2FFunctions%2F244675578" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain"></a>
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<div class="table-row" data-togglable="EXTENSION_FUNCTION" data-filterable-current=":kmath-core:dokkaHtmlPartial/commonMain" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain">
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<div class="main-subrow keyValue ">
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<div class=""><span class="inline-flex">
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<div><a href="../derivative.html"><span><span>derivative</span></span></a></div>
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<div class="copy-popup-wrapper "><span class="copy-popup-icon"></span><span>Link copied to clipboard</span></div>
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<div class="title">
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<div class="platform-hinted " data-platform-hinted="data-platform-hinted"><div class="content sourceset-dependent-content" data-active="" data-togglable=":kmath-core:dokkaHtmlPartial/commonMain"><div class="symbol monospace"><div class="block"><div class="block"><span class="token annotation builtin">@</span><a href="../../../kmath-memory/space.kscience.kmath/-unstable-k-math-a-p-i/index.html"><span class="token annotation builtin">UnstableKMathAPI</span></a></div></div><span class="token keyword"></span><span class="token keyword">fun </span><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../derivative.html">A</a><span class="token operator"> : </span><a href="../../space.kscience.kmath.operations/-ring/index.html">Ring</a><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token operator">></span><span class="token operator">> </span><a href="index.html">DS</a><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../derivative.html">A</a><span class="token operator">></span><span class="token punctuation">.</span><a href="../derivative.html"><span class="token function">derivative</span></a><span class="token punctuation">(</span><span class="parameters "><span class="parameter "><span class="token keyword">vararg </span>symbols<span class="token operator">: </span><a href="../-symbol/index.html">Symbol</a></span></span><span class="token punctuation">)</span><span class="token operator">: </span><a href="../derivative.html">T</a></div><div class="symbol monospace"><div class="block"><div class="block"><span class="token annotation builtin">@</span><a href="../../../kmath-memory/space.kscience.kmath/-unstable-k-math-a-p-i/index.html"><span class="token annotation builtin">UnstableKMathAPI</span></a></div></div><span class="token keyword"></span><span class="token keyword">fun </span><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../derivative.html">A</a><span class="token operator"> : </span><a href="../../space.kscience.kmath.operations/-ring/index.html">Ring</a><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token operator">></span><span class="token operator">> </span><a href="index.html">DS</a><span class="token operator"><</span><span class="token keyword"></span><a href="../derivative.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../derivative.html">A</a><span class="token operator">></span><span class="token punctuation">.</span><a href="../derivative.html"><span class="token function">derivative</span></a><span class="token punctuation">(</span><span class="parameters "><span class="parameter ">symbols<span class="token operator">: </span><a href="https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.collections/-list/index.html">List</a><span class="token operator"><</span><span class="token keyword"></span><a href="../-symbol/index.html">Symbol</a><span class="token operator">></span></span></span><span class="token punctuation">)</span><span class="token operator">: </span><a href="../derivative.html">T</a></div><div class="brief "><p class="paragraph">Provide a partial derivative with given symbols. On symbol could me mentioned multiple times</p></div></div></div>
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<div data-togglable="PROPERTY">
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<h2 class="">Properties</h2>
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<div class="table"><a data-name="-1813774289%2FProperties%2F244675578" anchor-label="data" id="-1813774289%2FProperties%2F244675578" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain"></a>
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<div><a href="data.html"><span><span>data</span></span></a></div>
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<span class="anchor-wrapper"><span class="anchor-icon" pointing-to="-1813774289%2FProperties%2F244675578"></span>
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<div class="platform-hinted " data-platform-hinted="data-platform-hinted"><div class="content sourceset-dependent-content" data-active="" data-togglable=":kmath-core:dokkaHtmlPartial/commonMain"><div class="symbol monospace"><span class="token keyword">abstract </span><span class="token keyword"></span><span class="token keyword">val </span><a href="data.html">data</a><span class="token operator">: </span><a href="../../space.kscience.kmath.structures/-buffer/index.html">Buffer</a><span class="token operator"><</span><span class="token keyword"></span><a href="index.html">T</a><span class="token operator">></span></div></div></div>
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<a data-name="1471405024%2FProperties%2F244675578" anchor-label="derivativeAlgebra" id="1471405024%2FProperties%2F244675578" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain"></a>
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<div class="table-row" data-filterable-current=":kmath-core:dokkaHtmlPartial/commonMain" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain">
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<div class="main-subrow keyValue ">
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<div class=""><span class="inline-flex">
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<div><a href="derivative-algebra.html"><span>derivative</span><wbr><span><span>Algebra</span></span></a></div>
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<span class="anchor-wrapper"><span class="anchor-icon" pointing-to="1471405024%2FProperties%2F244675578"></span>
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<div class="copy-popup-wrapper "><span class="copy-popup-icon"></span><span>Link copied to clipboard</span></div>
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</span></span></div>
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<div>
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<div class="title">
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<div class="platform-hinted " data-platform-hinted="data-platform-hinted"><div class="content sourceset-dependent-content" data-active="" data-togglable=":kmath-core:dokkaHtmlPartial/commonMain"><div class="symbol monospace"><span class="token keyword">abstract </span><span class="token keyword"></span><span class="token keyword">val </span><a href="derivative-algebra.html">derivativeAlgebra</a><span class="token operator">: </span><a href="../-d-s-algebra/index.html">DSAlgebra</a><span class="token operator"><</span><span class="token keyword"></span><a href="index.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="index.html">A</a><span class="token operator">></span></div></div></div>
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</div>
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</div>
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<a data-name="-1554686425%2FProperties%2F244675578" anchor-label="value" id="-1554686425%2FProperties%2F244675578" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain"></a>
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<div class="table-row" data-togglable="EXTENSION_PROPERTY" data-filterable-current=":kmath-core:dokkaHtmlPartial/commonMain" data-filterable-set=":kmath-core:dokkaHtmlPartial/commonMain">
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<div class="main-subrow keyValue ">
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<div class=""><span class="inline-flex">
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<div><a href="../value.html"><span><span>value</span></span></a></div>
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<span class="anchor-wrapper"><span class="anchor-icon" pointing-to="-1554686425%2FProperties%2F244675578"></span>
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<div class="copy-popup-wrapper "><span class="copy-popup-icon"></span><span>Link copied to clipboard</span></div>
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</span></span></div>
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<div>
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<div class="title">
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<div class="platform-hinted " data-platform-hinted="data-platform-hinted"><div class="content sourceset-dependent-content" data-active="" data-togglable=":kmath-core:dokkaHtmlPartial/commonMain"><div class="symbol monospace"><div class="block"><div class="block"><span class="token annotation builtin">@</span><a href="../../../kmath-memory/space.kscience.kmath/-unstable-k-math-a-p-i/index.html"><span class="token annotation builtin">UnstableKMathAPI</span></a></div></div><span class="token keyword"></span><span class="token keyword">val </span><span class="token operator"><</span><span class="token keyword"></span><a href="../value.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../value.html">A</a><span class="token operator"> : </span><a href="../../space.kscience.kmath.operations/-ring/index.html">Ring</a><span class="token operator"><</span><span class="token keyword"></span><a href="../value.html">T</a><span class="token operator">></span><span class="token operator">> </span><a href="index.html">DS</a><span class="token operator"><</span><span class="token keyword"></span><a href="../value.html">T</a><span class="token punctuation">, </span><span class="token keyword"></span><a href="../value.html">A</a><span class="token operator">></span><span class="token punctuation">.</span><a href="../value.html">value</a><span class="token operator">: </span><a href="../value.html">T</a></div><div class="brief "><p class="paragraph">The value part of the derivative structure.</p></div></div></div>
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