Linked Questions

172
votes
4answers
15k views

Performance tuning in Mathematica?

What performance tuning tricks do you use to make a Mathematica application faster? MATLAB has an amazing profiler, but from what I can tell, Mathematica has no similar functionality.
0
votes
0answers
18 views

How to memoize with patterns? [duplicate]

Here is an artificial example to explain what I am up to. Define ClearAll[f] f[x_, y_] := f[x, y] = If[x == 0, g[y], g[f[x - 1, y]]] Then ...
3
votes
1answer
88 views

Functions that remember some arguments while not remembering other arguments

I would like to some programming that is very generic. Particularly I am interested in the following: Let's say I want to write a function ...
0
votes
1answer
68 views

Memoization (or otherwise) for a recurrent definition of a (double) sequence of functions

Beside I've found answers to similar questions (e.g. this), I can't adapt them to my case. I am interested in the following sequence of functions $p_{m,n}(t)$, where $m$ and $n$ are integer: $$ \...
3
votes
1answer
248 views

Recursion with substitution mathematica

When writing out some mathematical equation like we see on the picture here I got the problem of writing out all terms. I know what recursion means and have done recursion for example for the ...
0
votes
1answer
148 views

Create recursive sequence of functions with memoization

I am trying to create a sequence of functions and have it properly memoize the results. The recursive operation is simply convolution, so it possible there is a better way to do this (obviously, if I ...
1
vote
2answers
268 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $$K_{i,n}\left(x\right)=\int_{x}^{\infty}K_{i,n-1}\left(y\right)dy$$ where $$K_{i,0}\left(x\right)=...
5
votes
2answers
289 views

Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
132
votes
8answers
8k views

Can one identify the design patterns of Mathematica?

... or are they unnecessary in such a high-level language? I've been thinking about programming style, coding standards and the like quite a bit lately, the result of my current work on a mixed .Net/...
0
votes
0answers
90 views

Dummy variable in nested integral operator

I am trying to make a nested integral operator where the output function of one step must be applied to the dummy variable to be integrated in the next step. Here my code: ...
0
votes
1answer
141 views

Nested integration

I wish to perform the following nested integral: \begin{align} I_n=\int_{-\infty}^\infty dx_n~f(x_n,x_{n+1})\int_{-\infty}^\infty dx_{n-1}~f(x_{n-1},x_n)...\int_{-\infty}^\infty dx_1~f(x_1,x_2)\int_{-\...
0
votes
2answers
236 views

Super recursive function

I have read about how to define a recursive function using RecurrenceTable but for $u(100)$ you need all 99 previous terms. The posts doesn't help me. I want to ...
4
votes
4answers
565 views

Memoization of a function defined by a recurrence relation [duplicate]

I have a function which is defined by the following recurrence relation $$h_{n}(x)=h_{n-1}(x)+\frac{\mathrm{e}^{-x^2}}{2^n n!}H_{n}(x)H_{n-1}(x)$$ with the initial condition $h_{0}(x)=0$ and where the ...
9
votes
4answers
4k views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ y_{n}(x):=y_0+\int_{...
0
votes
0answers
70 views

Reuse symbolic polynomial

Suppose I have a function that returns a polynomial in x, GetPoly[params_,x_]:=GetPoly[params,x]... but it is quite slow, so ...

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