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<p>where \(\mathbf{v}_{\mathit{known}}\) are the \(n\) knowns, and \(\mathbf{g}\) are the \(m\) functions to calculate the \(m\) unknown variables \(\mathbf{v}_{\mathit{unknwon}}\) from the knowns.</p>
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<p>where \(\mathbf{v}_{\mathit{known}}\) are the \(n\) knowns, and \(\mathbf{g}\) are the \(m\) functions to calculate the \(m\) unknown variables \(\mathbf{v}_{\mathit{unknown}}\) from the knowns.</p>
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<div class="paragraph">
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<p>Both functions can also be used to construct the partial derivative matrices.
<p>(b) <em>Initializes all seed-values to zero; so in the <a href="#example-directional-derivatives">above example</a>: \({\Delta x = \Delta u_1 = \Delta u_3 = \Delta u_4 = 0}\)</em></p>
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<div class="paragraph">
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<p>(c) <em>Computes the directional derivative with the seed-values provided in the function arguments; so in the <a href="#example-directional-derivatives">above example</a>: \({v_{\mathit{sensitivity}} = \Delta y_1 (\Delta x = 0, \Delta u_1 = 1, \Delta u_3 = 0, \Delta u_4 = 0)}\)] and \({v_{\mathit{sensitivity}} = \Delta y_1 (\Delta x = 0, \Delta u_1 = 0, \Delta u_3 = 1, \Delta u_4 = 0)}\)]</em></p>
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<p>(c) <em>Computes the directional derivative with the seed-values provided in the function arguments; so in the <a href="#example-directional-derivatives">above example</a>: \({v_{\mathit{sensitivity}} = \Delta y_1 (\Delta x = 0, \Delta u_1 = 1, \Delta u_3 = 0, \Delta u_4 = 0)}\) and \({v_{\mathit{sensitivity}} = \Delta y_1 (\Delta x = 0, \Delta u_1 = 0, \Delta u_3 = 1, \Delta u_4 = 0)}\)]</em></p>
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<div class="paragraph">
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<p><em>[Note, function <a href="#fmi3GetDirectionalDerivative"><code>fmi3GetDirectionalDerivative</code></a> can be utilized for the following purposes:</em></p>
<p><em>If the FMU shall be linearized, the same <a href="#derivative"><code>derivatives</code></a> as in the previous item are needed.</em></p>
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</li>
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<li>
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<p><em>If the FMU is used as the model for an extended Kalman filter, \({\frac{\partial \mathbf{f}}{\partial \mathbf{x}}}\) and \({\frac{\partial \mathbf{g}}{\partial \mathbf{x}}}\) are needed.</em></p>
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<p><em>If the FMU is used as the model for an extended Kalman filter, \({\frac{\partial \mathbf{f}}{\partial \mathbf{x}}}\) and \({\frac{\partial \mathbf{g}}{\partial \mathbf{x}}}\) are needed.</em>]</p>
<p>When shipping the implementation as a static library an optional ABI (Application Binary Interface) directory <code><arch>-<sys>{-<abi>}</code> may be added to separate binaries for different toolchains on the same platform and a description must be provided in <code>documentation/staticLinking.{txt|html}</code> that contains all necessary information to link against the provided library <em>[e.g. supported compilers]</em>.
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The ABI directory must only contain lowercase characters <code>a…​z</code>, digits <code>0…​9</code>, and underscores <code><em></code> and start with a lowercase character <code>a…​z</code> _[e.g. <code>x86_64-windows-msvc140mt</code> for a static library for 64-bit Windows generated with Visual Studio 2015 with <code>/MT</code> flag]</em>.</p>
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The ABI directory must only contain lowercase characters <code>a…​z</code>, digits <code>0…​9</code>, and underscores <code>_</code> and start with a lowercase character <code>a…​z</code> <em>[e.g. <code>x86_64-windows-msvc140mt</code> for a static library for 64-bit Windows generated with Visual Studio 2015 with <code>/MT</code> flag]</em>.</p>
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