# Questions tagged [functional]

Questions related to functional methods, e.g. functional differentiation and integration.

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### Use Mathematica to derive the probability distributions using the Principle of Maximum Entropy

I am reading the article of Deriving probability distributions using the Principle of Maximum Entropy and I am trying to derive some of the equations in it automatically using Mathematica. 1. ...
1 vote
99 views

### How can I calculate the Euclidean metric in $l^2$ for two functions in Mathematica? [closed]

I have two functions, $f(x)=\sin x$ and $g(x)=\sin\frac{pi}{4}x$, and I want to calculate the average Euclidean metric as an expected value to score for the average distance between the two functions ...
281 views

### How to define a functional by the way it acts on its own output

I want to define a functional E by using the property E[ E[f[x]] ] := E[f[x]] for some arbitrary function f[x]. Meaning, that I ...
547 views

### How do I map a function pairwise?

Given a list of pairs: data = {{a,b},{c,d},{e,f},{g,h},{i,j}} I need the moving map: MapPair[F,data] ...
188 views

### How to reproduce Asymptotic Bounds of Recurrences in Wolframalpha

In Wolframalpha's Examples for Recurrences, there are bunch of Asymptotic Bounds of Recurrences examples, like this It can get perfect result: ...
1 vote
88 views

### Why each iteration takes longer than previous one when using VariationalD in this loop?

I have a function $f$, and I would like to modify it iteratively to approach another one called $a$ (not because I think this is the best way to do anything, but for experimentation). For this, I use <...
184 views

### How to get numerical value of functional derivative at specific point

I have a functional in the form: $$F[s(x)]=\int_0^1(s(x)-a(x))^2\mathrm{d}x$$ where $a(x)$ is a parameter function, and I would like to find the functional derivative of $F$ with respect to $s$. ...
139 views

### How to declare that a function is arbitrary then specify them later? [duplicate]

I need to evaluate an expression, sum in this case, involving an arbitrary function. Below is a simplified version of what I wanted to do: ...
79 views

### Recursively rewrite function

Let's imagine I already have a function like myfac :=1 myfac[n_ /; n>=0] := n myfac[n-1] this home grown factorial. Now I want to equip it with tracing (and ...
63 views

### How to compose an algorithm to create new array (based on array data), if I need a reference to an array being created, no for loop, in mathematica?

I have an array with either 1 or 0. From this, I am trying to create a new array with intervals. I have some base interval, one step, we can say 1 second here. If there is 0, I skip, if there is 1 I ...
154 views

### Implementing an optimization algorithm in WL

I am trying to implement the Jaya optimization algorithm (Jaya). This is a flowchart from the Author 's webpage showing the details of the Algorithm. Note that there is a typo in the equation in the ...
38 views

### Solving constraint optimization problem for different intervals using VariationalD

I have been trying to solve for a constraint optimization problem (which eventually yields to a Laplace distribution). Consider the following equation (1) \begin{equation*} J=\int^{\infty}_{-\infty} p(...
450 views

### How to Solve Functional Differential Equation

I tried to solve this equation numerically. eqnEx = x''[t] + x[2 t] == 0; NDSolve[{eqnEx, x == 10, x' == 0}, x[t], {t, 1, 10}] Two important character of the ...
1 vote
168 views

### Power series expansion in terms of a function

I have a two variable function z[x,y] = f[x,y] + g[x,y], such that I know the functional form of f[x,y] but not of ...
190 views

### How can I solve a functional equation with domain restrictions?

I have three properties for a function: ...
790 views

### How do I define functionals in Mathematica?

When I write W[f_] := Integrate[f[x], {x, 0, π}] I may rightly conclude that W[Sin] = 2, ...
1 vote
96 views

### Is it possible to solve a PDE in NDSolve for a simple functional PDE where the dependent variable is evaluated at a point?

Is it possible to configure NDSolve to approximate solutions of a PDE where the state variable is evaluated at a point? Mathematica detects such a PDE as a delay equation, but clearly all that is ...
91 views

### Could not able to set up a differential equations using EulerEquations command

I have a constructed the Lagrangian of a mechanical system by finding the kinetic and potential energy of the system. Then I tried using EulerEquations to set up a differential equation by taking the ...
513 views

### How do I compute the infinity-norm of a function? [closed]

I have a technical question on Mathematica 11. I have to compute the $\infty$ norm of q function, $f(x,y)$, on a rectangular domain $[a, b] \times [c,d]$. How can I do this with Mathematica?
1k views

### How to compute symbolically the Legendre transform of a function?

Is it possible to compute symbolically the Legendre transform of a function in Mathematica? I find no LegendreTransform function.
532 views

### Non-trivial functional derivatives

Looking for ways to calculate functional derivatives in Mathematica, I found this question. The answer by Jens points to a documented application of DiracDelta ...
1 vote
158 views

### Define a functional and nest it with its arguments

I'm looking for a definition of a functional f which works correctly with varying arguments t while it will be nested. For ...
1 vote
107 views

### How to call a function with an arbitrary list as its arguments inside a functional? [duplicate]

I have the following functional defined (i.e. a function of another function) where variableList contains the variable (arguments if you wish) of the ...
209 views

### Select Only Positive Values and Prepend a Title

I have the following list: ...
132 views

### Using functionals in Mathematica [duplicate]

I recently installed Mathematica and I wanted to define a functional in it. This is what I did: ...
1 vote
1k views

### Using NDSolve initial conditions as parameters for a function and then a replacement rule

I am trying to make a function based on two initial conditions of a set of differential equations: ...
205 views

### Transpose four lists of data into two lists for use in List Plot [closed]

I have four lists of data x1 = {1,3,5,7} y1 = {0,2,4,6} x2 = {10,12,14,16} y2 = {8,10,12,14} In one line is it possible to use transpose to get two lists which ...
129 views

### How to implement time dependence in the DoFun package?

DoFun is a very usefull mathematica package that helps to write Dyson-Schwinger and FRG flow equations when these are to complex to write down by hand. You can download it here and read it's manual ...
83 views

### Folding 3-variate function with 2 iterator

I have a function say $f$ and some initial point $x$ and pairs of iterators $\{\{a_1,b_1\},\{a_2,b_2\},...\}$ I want to foldlist as follows: $\{x,f[x,a_1,b_1],f[f[x,a_1,b_1],a_2,b_2],...\}$ can ...
108 views