Linked Questions

165
votes
3answers
14k 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.
129
votes
8answers
7k 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/...
40
votes
0answers
2k views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
18
votes
3answers
3k views

Why does Mathematica use [[ ]] notation for array indexing?

I am confused by why Mathematica uses [[3]] to get the 3rd element, or [[i,j] to get the i,j-th element of a 2D array. This ...
11
votes
2answers
1k views

Dynamic Programming with delayed evaluation

By using dynamical programming, we can save intermediate steps for recursive relations, as in f[n_]:= f[n] = f[n-1] + f[n-2] However, this only stores ...
9
votes
4answers
3k 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_{...
9
votes
1answer
1k views

Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
9
votes
2answers
264 views

using memoization with conditional statement

I would like some advice about the use of memoization in conjunction with conditional statements. Let me try to explain my problem: I am constructing a function depending on a number of parameters. ...
7
votes
2answers
1k views

Why does Expand not work within a function?

I'm writing this fairly simple function: ...
7
votes
4answers
415 views

Recursive piecewise integral relation with piecewise base case?

How is this recursive formula $$ f_{n+1}(z) = \int_0^1 f_{n}(z-y)\,{\rm d}y $$ implemented in Mathematica? The base case is $$ f_1(z) = \begin{cases} 1 & 0\leq z\leq 1 \\ 0 & \text{...
7
votes
2answers
3k views

Series of piecewise functions

Let $f_{0}(x):[0,1]\to[0,1]$ be defined by $$f_{0}(x):=\begin{cases} 3x, & \text{if } x\in [0,\frac{1}{3}] \\ \\ -3x+2, & \text{if } x\in (\frac{1}{3}, \frac{2}{3}] \\ \\ 3x+2, & \...
6
votes
2answers
375 views

How to implement a numerically efficient Airy Zeta Function

Define the Airy zeta function for $n=2,3,\dots$, by $$ Z(n) := \sum_r \frac{1}{r^n}. $$ where the sum is over the zeros $r$ of the Airy function $\operatorname{Ai}$. In Mathematica the $\operatorname{...
5
votes
3answers
1k views

recursive integration

I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$: $\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') R_{n-1}(...
5
votes
2answers
251 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 ...
4
votes
4answers
501 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 ...

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