Questions about Mathematica's functional programming style, including the use of pure functions (Function[], #, &) and functions such as Map, Apply, Nest, and Through.
0
votes
0answers
362 views
Jacobi eigenvalue and eigenvectors algorithm
Suppose we have a symmetric matrix with dimensions n x n. I need to find the eigenvalues and eigenvectors of this matrix using the Jacobi method. I wrote this code:
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8
votes
3answers
181 views
Map over list of functions
I would like to convert a list of $n$ complex equations to a list of $2n$ real ones. At the moment I am doing it like this:
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0
votes
0answers
52 views
Optimized subset algorithm implementation
I was reading a paper from Mathematica Journal.It mentions a code for calculating subsets.
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0
votes
2answers
59 views
Scripting a visual comparison between the derivative and some finite scheme
I want to make an application where I can specify a function $f:\mathbb R\to \mathbb R$ and a dynamic value $n$ and get the function $\frac{f(x+\frac{1}{n})-f(x)}{\frac{1}{n}}$. I moreover want to ...
0
votes
0answers
52 views
Using NDSolve over a list of functions
I apologize for how messy this explanation will be.
I would like to take a differential equation and iterate that solution over a range of coefficient values. The second part of this is that the ...
3
votes
3answers
71 views
Applying a function of several arguments to the rows of a matrix
I have a user-defined function which takes three vectors as input. Suppose that is like this:
f[a_, b_, u_] := Total[a*Total[u]^b]
Usually I have vectors for ...
2
votes
1answer
98 views
Evaluating a function on permutations of its arguments
Say I have a function "temp" of $n+1$ variables, $y,z1,z2,z3,...,zn$. I want to test if my function has certain symmetries like swapping $y$ with square of any $z$, swapping any two of the zs, ...
1
vote
0answers
42 views
Using anonymous functions instead of module or block. Bad idea? [duplicate]
Here is an example function which returns True if a point p is on an (open) line segment (A, B) assuming that Orientation[A, p, B] returns 0 if the three points are collinear:
...
4
votes
1answer
120 views
Why is this code in functional style is slower than procedural style?
I know that in Mathematica a functional programming style is often more efficient than procedural style programming using For loops. But the code shown below seems ...
12
votes
2answers
294 views
Going full functional (Haskell style)
I'm trying to define some notation so that Mathematica code would be more functional, similar to Haskell (just for fun): currying, lambdas, infix operator to function conversion, etc.. And I have some ...
0
votes
0answers
64 views
How can I get tabular output for the results of my simulation? [closed]
I have code that simulates a simple Markov Chain and looks like this:
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0
votes
1answer
169 views
Arbitrary depth patterns/rules
Temporary message: I am now really confused. I am not sure how using Power and Unevaluated together works in the examples below.
While answering this question, I stumbled upon the following.
We ...
6
votes
3answers
210 views
1
vote
2answers
111 views
Computing distance matrix for a list
Using functional programming in Mathematica, how can I compute a distance matrix for every element in a list of matrices... The distance would be computed between the item in the list and a "target ...
1
vote
1answer
82 views
given n lists, get list of applications of function to n-tuples
Is there a built in function or an easy rule to do the following transformation?
H[{A[0], A[1], ...},{B[0], B[1], ...},...]
into
...
8
votes
4answers
205 views
Transform a list of functions to a composition
How do I apply a list of functions in a nested way?
Example:
functionList = {f1,f2,f3}
RequiredCommand[functionList,Pi]
such that the required command returns
...
0
votes
1answer
104 views
Iterative Function Mapping [duplicate]
Possible Duplicate:
How to nest my own “times” function to get powers
What I want to do is something like :
Sin[...Sin[Sin[Sin[Sin[x]]]]]
Basically, ...
15
votes
3answers
556 views
Programming a numerical method in the functional style
I am new to Mathematica and I would like to learn a bit more about functional programming.
At the moment I have assignments like programming different numerical methods (for integration: ...
4
votes
2answers
125 views
Update a function avoiding infinite recursion
I am quite new to Mathematica and not completely familiar with functional programming. I am currently working with a function (call it foo) and wish to change its behaviour, for example, by adding 1 ...
0
votes
1answer
225 views
How can I define a Step-Wise function in Mathematica (Not using Heaviside Step Function)? [closed]
I need to define a function, which has very different behaviour in different regions. There are about 13 different regions. A sample of my function is the foloowing table:
I want to define it as a ...
2
votes
3answers
111 views
Defining a function to determine when convergence is guaranteed
I'm investigating how many iterations are needed for a particular orbit to reach a fixed point of a function. Since I have many functions to test, I want to define a function
in Mathematica that will ...
2
votes
1answer
110 views
Issue with ListConvolve
I am a new Mathematica user, learning the intricacies of functional programming. I have issues withe applying a function over a moving list. My function seems to work and give correct results but it ...
4
votes
4answers
229 views
How to transform Do loop to more efficient codes?
I'm new to Mathematica. Here is my original program: How to rewrite the Do part?
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5
votes
2answers
182 views
Variant of the cutting-stock problem in Mathematica
I'm pretty new to Mathematica and am trying to learn to solve problems in a functional way. The problem I was solving was to list the ways in which I could sum elements from a list (with repetitions), ...
4
votes
4answers
213 views
Differentiating space curves
I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by
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7
votes
2answers
246 views
Feedback on Functional Programming: Propagation of uncertainty
Lately I've been trying to use functional prgramming and tried to implement the gaussian propagation of uncertainty (without correlation) in an elegant way, here is the outcome:
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24
votes
3answers
285 views
FoldWhile and FoldWhileList
Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in ...
2
votes
1answer
109 views
Can my permutations function be defined using iteration?
I have two functions, tuples and perm. They are similar.
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2
votes
0answers
62 views
From notebook,how can I change variable value with in .m file dynamically?
I wrote a function named Testing.
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7
votes
3answers
342 views
Rewriting For loop to FoldList or similar
In CrossValidated, the answer to a question on prediction of number of viewers of Gangnam Style is given in R. I have mapped the answer directly to Mathematica:
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21
votes
6answers
877 views
Can this be written well, without loops?
Inspired by this question I would like to know if the following code can be written without explicit loops (For, While, etc.) in a clean, efficient and non-contrived way. I have been unable to do so.
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10
votes
4answers
491 views
How to write this without For loop
Suppose I have a few lists of numbers and want to exponentiate element-wise, then sum up everything into a polynomial.
For example, if I have
...
0
votes
1answer
195 views
How can I improve my code with efficient mathematica built-in functions?
I have written a module for my assignment like below.
V[n + 1] = rk[x[n], y[n] ,z[n], V[n]];
vs = V[n].V[n+1];
V[n + 1] =
I want to modify it with efficient ...
4
votes
1answer
111 views
Functional Programming: modify EdgeList based on condition
I have a simple functional programming question: I have a simple EdgeList defined in Mathematica, I would like to modify the value of certain element of the list based on a condition.
I see how to ...
14
votes
3answers
431 views
How can I improve my code for drawing a tree?
This code draws a tree, but it's not in the functional style.
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5
votes
3answers
144 views
All values for a function with two arguments without Outer
Given two lists $l_a = \{a_1, a_2, a_3\}$, $l_b = \{b_1, b_2, b_3, b_4\}$ and some function $f$ accepting two arguments, how can I produce a list of all values $f(a, b)$ for $a\in l_a$ and $b \in l_b$ ...
4
votes
2answers
157 views
How can I improve this trial division procedure?
My background is procedural programming, so I find this construction quite natural. Is there a way to get rid of the While?
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4
votes
6answers
177 views
Filter list with different list in it
I have a list like:
{{{4, 14}, 1}, {{4, 15}, 1}, {{4, 16}, 1}, {{4, 17}, 1},
{{4, 18}, 1}, {{4, 14}, 3}, {4,15}, {{4, 16}, 2},{4,18}}
Now I want to ...
12
votes
5answers
569 views
How to improve this code for solving the “Mr.S and Mr.P” puzzle?
Mr.S and Mr. P puzzle — "Formalization of two Puzzles Involving Knowledge", McCarthy, John (1987)
We pick two numbers $a$ and $b$, such that $a\geq b$ and both numbers are within
the range ...
2
votes
1answer
119 views
#[[1]]//FullForm = 1?
I have a set of symbolic algebraic expressions that I'm trying to get some speed into. To illustrate the issue, I'll use a simple form like { k0 X, k1 Y, k1 Z}, ...
1
vote
4answers
138 views
Order of operations for the Table function [duplicate]
Possible Duplicate:
Using pure functions in Table
I have run into a situation that I do not understand when trying to generate a nested list of pure functions. I have the following code.
...
2
votes
1answer
128 views
Converting expressions into functions
I have defined an expression, such as
a = x
I would like to convert this into a function, such as
f[x_]:=x
However, in my ...
4
votes
3answers
285 views
4
votes
2answers
189 views
Define product derivative
How do I define the $n$th product derivative of a function in Mathematica?
The first product derivative $f^\ast$ of a function $f$ is
$$
f^\ast(x)=\exp\left(\frac{f^\prime(x)}{f(x)}\right)
$$
The ...
6
votes
4answers
439 views
Alternatives to While Loops?
I am using Mathematica to run a probabilistic simulation. Essentially, I have a list of members of a population (they only have one, numerical, attribute, so it's just implemented as a list of ...
11
votes
2answers
421 views
Using a list of tuples in a pure function
I want to use a list of tuples within a function to make assignments.
Say I want to make assignments of the form
value[i,j] = val
What I have is a list of ...
11
votes
2answers
201 views
From iterative to functional
How to write this small piece in a functional way (ie. without state variables)?:
...
4
votes
1answer
173 views
Timing differences between multiple executions of identical code
I have a
list of pairs of numbers and I'd like to change the sign of the second element in each pair i.e. $(a,b)\rightarrow (a,-b)$.
I'm sure there are many ...
1
vote
2answers
138 views
How to create a list of variable names to some function of that variable
For example, for a single variable I can write
Print[Unevaluated[a], "=", f[a]]
But if I try the next thing I'd think of doing, assuming I want a list, it ...
3
votes
2answers
121 views
How do I convert an argument list to a list of arguments? [closed]
I think this is a basic question, but I am having difficulty finding the answer in the documentation. Thread is not what I am looking for, I think.
Suppose that I ...
