MathUtils Namespace

MOOSE includes a number of C++ utility classes and functions that may be useful for developing applications with mathematical expressions.

Polynomial evaluations

MathUtils::poly evaluates a polynomial for any integer order $var element = document.getElementById("moose-equation-04ae00c9-f3bd-4884-8a36-ddaa71801dce");katex.render("n>0", element, {displayMode:false,throwOnError:false});$ using the Horner's method of evaluation, $var element = document.getElementById("moose-equation-2063a6ea-708c-498d-bb17-91b6763daaf1");katex.render(" p(x) = c_0 + c_1 x + c_2 x^2 + ... + a_n x^n", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-ce4c67c8-3448-41fc-8b5a-1c63be5373c1");katex.render(" p(x) = c_0 + x * (a_1 + x(a_2 + ... + x (a_{n-1} + x a_n)))", element, {displayMode:true,throwOnError:false});$

Clamp

MathUtils::clamp returns a clamped value $var element = document.getElementById("moose-equation-637cf8b4-884d-45c9-9161-8e139e563a53");katex.render("y", element, {displayMode:false,throwOnError:false});$ between an upper and lower bound, $var element = document.getElementById("moose-equation-ea2b32f2-4e9f-424c-8320-9ac982d290f1");katex.render("L_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-aeec0625-5add-4da0-b066-34e56e395cca");katex.render("L_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, $var element = document.getElementById("moose-equation-de76b3d5-b0f1-42e3-8fd4-1892ad5ce6d9");katex.render(" y = \\begin{cases} L_{lower} & x < L_{lower} \\\\ L_{higher} & x > L_{higher} \\\\ x & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$

SmootherStep

MathUtils::smootherStep returns a smoothed step transition between a starting and ending bounds, $var element = document.getElementById("moose-equation-0a868414-e08a-4407-b971-932a09ecd26c");katex.render("B_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-85991264-bb72-4ece-b17d-b19352889dd6");katex.render("B_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, for a given value $var element = document.getElementById("moose-equation-df39bc1d-f2c7-4c18-9348-7e8a7ea220fa");katex.render("u", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-4bc1ae3b-e319-41e6-b508-40bfa6e5fe7f");katex.render(" x = \\frac{u - B_{lower}}{B_{higher} - B_{lower}}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-ef0df1b5-f348-4f86-bdb3-af5e6b654628");katex.render(" y = \\begin{cases} 0 & u <= B_{lower} \\\\ 1 & u >= B_{higher} \\\\ 6x^5 - 15 x^4 + 10x^3 & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$ This method ensures a smooth transition from 0 to 1 between the two bounds, while also ensuring the first and second derivatives are zero at the two bounds. Use of this method is especially useful when transitioning between two non-smooth regimes. The derivative with respect to the passed value $var element = document.getElementById("moose-equation-6c4366b7-cd81-4623-8251-4981b5525b57");katex.render("u", element, {displayMode:false,throwOnError:false});$ is returned using the optional derivative bool. Note that if $var element = document.getElementById("moose-equation-3d65eae4-0122-4c2f-84a1-9de7501602e6");katex.render("u = B_{lower} = B_{higher}", element, {displayMode:false,throwOnError:false});$ , then zero will be returned.

Polynomial evaluations
Clamp
SmootherStep