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 $var element = document.getElementById("moose-equation-a035eec3-38fa-4443-9c3f-14ab386d4116");katex.render("n>0", element, {displayMode:false,throwOnError:false});$ using the Horner's method of evaluation, $var element = document.getElementById("moose-equation-b62ec71e-3d10-48a4-b171-d81065b9fa74");katex.render(" p(x) = c_0 + c_1 x + c_2 x^2 + ... + a_n x^n", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-a1ef592b-8d97-4458-9c42-a77bfd693183");katex.render(" p(x) = c_0 + x * (a_1 + x(a_2 + ... + x (a_{n-1} + x a_n)))", element, {displayMode:true,throwOnError:false});$

Clamp

MathUtils::clamp returns a clamped value $var element = document.getElementById("moose-equation-91ee87ff-d9e2-4653-a5eb-e97df4db6d97");katex.render("y", element, {displayMode:false,throwOnError:false});$ between an upper and lower bound, $var element = document.getElementById("moose-equation-305108be-45d0-4e49-9bb2-6761939c39af");katex.render("L_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-ded9ab08-17f9-4d66-a3c3-17b4f9f1b85e");katex.render("L_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, $var element = document.getElementById("moose-equation-e49e4f02-fe5e-4624-bac4-c7c0f66c936c");katex.render(" y = \\begin{cases} L_{lower} & x < L_{lower} \\\\ L_{higher} & x > L_{higher} \\\\ x & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$

SmootherStep

MathUtils::smootherStep returns a smoothed step transition between a starting and ending bounds, $var element = document.getElementById("moose-equation-8fcead81-6e99-47a5-964a-f76efaa68149");katex.render("B_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-e04a2b4b-2854-4d4e-b3c3-bcd2859f6eeb");katex.render("B_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, for a given value $var element = document.getElementById("moose-equation-dd3a949e-0ba9-4ce9-b7fe-843e5ba0d255");katex.render("u", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-29c57617-a569-45f6-999e-a04652e46ef9");katex.render(" x = \\frac{u - B_{lower}}{B_{higher} - B_{lower}}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-064c8107-aafe-4f6e-b665-4ac755c53cd8");katex.render(" y = \\begin{cases} 0 & u <= B_{lower} \\\\ 1 & u >= B_{higher} \\\\ 6x^5 - 15 x^4 + 10x^3 & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$ 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 $var element = document.getElementById("moose-equation-c793f5cd-9726-4dc9-bd26-a263c11d6ed3");katex.render("u", element, {displayMode:false,throwOnError:false});$ is returned using the optional derivative bool. Note that if $var element = document.getElementById("moose-equation-273c1cbc-696b-4d19-9e99-413f5109a4eb");katex.render("u = B_{lower} = B_{higher}", element, {displayMode:false,throwOnError:false});$ , then zero will be returned.

Polynomial evaluations
Clamp
SmootherStep