Questions tagged [functional]
Questions related to functional methods, e.g. functional differentiation and integration.
38
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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. ...
- 123
1
vote
1
answer
99
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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 ...
- 561
6
votes
1
answer
281
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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 ...
- 63
9
votes
5
answers
547
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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]
...
- 19.5k
2
votes
1
answer
188
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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:
...
- 223
1
vote
1
answer
88
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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 <...
- 137
2
votes
1
answer
184
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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 $s$.
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- 137
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2
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139
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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:
...
- 63
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0
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79
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Recursively rewrite function
Let's imagine I already have a function like
myfac[0] :=1
myfac[n_ /; n>=0] := n myfac[n-1]
this home grown factorial.
Now I want to equip it with tracing (and ...
- 1
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1
answer
63
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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 ...
- 3
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1
answer
154
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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 ...
0
votes
0
answers
38
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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(...
7
votes
3
answers
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[1] == 10, x'[1] == 0}, x[t], {t, 1, 10}]
Two important character of the ...
- 103
1
vote
2
answers
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 ...
- 13
4
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2
answers
190
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How can I solve a functional equation with domain restrictions?
I have three properties for a function:
...
- 207
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4
answers
790
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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, ...
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1
vote
1
answer
96
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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 ...
0
votes
1
answer
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 ...
- 1,699
0
votes
1
answer
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?
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6
votes
1
answer
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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.
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9
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1
answer
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 ...
- 1,281
1
vote
2
answers
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 ...
- 191
1
vote
1
answer
107
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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 ...
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2
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2
answers
209
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3
votes
1
answer
132
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Using functionals in Mathematica [duplicate]
I recently installed Mathematica and I wanted to define a functional in it. This is what I did:
...
- 135
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vote
1
answer
1k
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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:
...
- 11
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votes
1
answer
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 ...
- 2,224
2
votes
0
answers
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 ...
- 121
0
votes
1
answer
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 ...
- 9,113
5
votes
1
answer
108
views
Computing list elements that refer to earlier elements and two other lists without iteration
I am attempting to compute the elements of a list, $\{a_i\}$ given lists $\{b_i\}$ and $\{c_i\}$ using the following formula:
$a_i = \frac{1}{c_1}(b_i - \sum_{j = 2}^{i}c_{j}a_{i-j+1})$ for $1\leq i \...
- 51
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0
answers
551
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Boundary value problem: complicated functionals
I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. The equation below presents the final form ...
1
vote
0
answers
288
views
Optimizing a functional using variational calculus
Here I am, trying to get the trajectory $(x(t),y(t))$ that will minimize the following Lagrangian (i.e. the integrand of the functional) between $(-1,-1)$ and $(-1,y_{eff})$ where $x_{eff}$ is defined ...
- 211
1
vote
1
answer
215
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Apply function to output of previous function
I am trying to write a function that takes 3 tuples. Each tuple contains two lists which are first divided. This results in 3 lists. Then I want to take the Mean of all the columns. I can do this ...
- 2,224
0
votes
1
answer
124
views
Solve equation with two different sets of replacement rules
I want to solve eqn for c0 in the following code. I want to do it with both replacement rules. I realize I could just use solve ...
- 2,224
2
votes
1
answer
1k
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MapThread multiple functions onto multiple lists
I'm trying to learn the functional style which seems to prevail in Mathematica. I'm having trouble accomplishing the following:
Let's say I have multiple lists of arbitrary data (using two lists ...
- 400
2
votes
0
answers
87
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Different delays in notebook and command-line?
I was surprised by the following sequence of expressions:
Remove[foo$, bar$];
foo$ = Function[Set[bar$, 42]];
At this point, I expected ...
- 8,651
6
votes
1
answer
762
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Functional programming Style & Performance
Hello i have been spending time to convert my R tools into Mathematica Packages mainly because i like the functional programming style in Mathematica. In doing so it seems that i run into one ...
- 161
26
votes
6
answers
4k
views
Looking for a way to insert multiple elements into multiple positions simultaneously in a list
I would like to take the following data:
insertValues = {r, x};
insertPositions = {{1}, {5}};
originalList = {a, b, c, d, e, f, g};
and generate output that ...
- 2,114