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 $var element = document.getElementById("moose-equation-2bcc8673-a53f-48f5-9ff5-607b1db905a6");katex.render("n>0", element, {displayMode:false,throwOnError:false});$ using the Horner's method of evaluation, $var element = document.getElementById("moose-equation-70027583-d1b5-4d08-8aa9-a5fac5e7f35e");katex.render(" p(x) = c_0 + c_1 x + c_2 x^2 + ... + a_n x^n", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-833a9a87-9ae0-4fb2-8476-6abcd0de7c3c");katex.render(" p(x) = c_0 + x * (a_1 + x(a_2 + ... + x (a_{n-1} + x a_n)))", element, {displayMode:true,throwOnError:false});$

Clamp

MathUtils::clamp returns a clamped value $var element = document.getElementById("moose-equation-0e5c31b4-dbbf-4f39-b91a-831d7ffbfaee");katex.render("y", element, {displayMode:false,throwOnError:false});$ between an upper and lower bound, $var element = document.getElementById("moose-equation-0e9eccac-1467-4ca9-94b8-f8f34da088c0");katex.render("L_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d210df3a-e103-4fd4-b10c-c17ac1ba519f");katex.render("L_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, $var element = document.getElementById("moose-equation-b9a70372-02a8-42c4-9725-8a16853c030b");katex.render(" y = \\begin{cases} L_{lower} & x < L_{lower} \\\\ L_{higher} & x > L_{higher} \\\\ x & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$

SmootherStep

MathUtils::smootherStep returns a smoothed step transition between a starting and ending bounds, $var element = document.getElementById("moose-equation-3d09033f-d1c5-4c81-a7f8-824237cb6745");katex.render("B_{lower}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-736c0d91-df24-4f72-a9e5-c45c736f2a61");katex.render("B_{higher}", element, {displayMode:false,throwOnError:false});$ respectively, for a given value $var element = document.getElementById("moose-equation-205ed9cc-f8b9-4b20-832b-8ce8facd2322");katex.render("u", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-6325d013-6738-407e-b30b-8d24503a201d");katex.render(" x = \\frac{u - B_{lower}}{B_{higher} - B_{lower}}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-8f70def2-d4c2-4c17-a041-2c15197db9e9");katex.render(" y = \\begin{cases} 0 & u <= B_{lower} \\\\ 1 & u >= B_{higher} \\\\ 6x^5 - 15 x^4 + 10x^3 & \\text{Otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false});$ 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 $var element = document.getElementById("moose-equation-3ab18045-cb6c-4cf3-a68d-d1200a7bedc1");katex.render("u", element, {displayMode:false,throwOnError:false});$ is returned using the optional derivative bool. Note that if $var element = document.getElementById("moose-equation-188a4d44-98ed-4f4c-bcf8-ade2ade2d6c2");katex.render("u = B_{lower} = B_{higher}", element, {displayMode:false,throwOnError:false});$ , then zero will be returned.

Polynomial evaluations
Clamp
SmootherStep