For questions on writing functions (pure or using Set/SetDelayed) for any purpose, including the features that may be incorporated in those functions, such as options, patterns and conditions.
0
votes
0answers
9 views
How to assign values to a function at discrete points? [duplicate]
Suppose we are interested in a function f[x] that is defined only at discrete points:
x = {1.1, 2.1, 3.1, 4.1, 5.1}
We want to ...
5
votes
3answers
96 views
Applying a function with the HoldAll attribute inside NestList
I'm trying to write an update function, which can be applied to a list and then to NestList it.
As the function has to manipulate the given variable I figured I ...
1
vote
2answers
132 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
24
votes
2answers
393 views
Variable naming changes everything
I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the example of the code ...
3
votes
2answers
76 views
How to define a polynomial/function from an array of coefficients?
I have the coefficients of my desired polynomial in an array CoefArr (I'm new to mathematica, so I think of everything as arrays, it is actually a list I believe) starting with the constant at index ...
2
votes
2answers
66 views
Putting a matrix inside function
I want to fit a function to some data and inside the function there's a list
here's my data
...
-1
votes
2answers
88 views
How can I define a function which is the sum of other functions?
I have a function which is summation of another function over different i,j iterators.
U[r] = Sum[V[r, i, j], {i, 1, 5}, {j, 6, 10}]
and ...
4
votes
3answers
131 views
How can I combine two Pick expressions into one?
I want to speed up my code, i.e., replace Select by Pick. I think using two Pick ...
1
vote
1answer
77 views
Mathematica plots a discontinuity in piecewise function that does not exist [duplicate]
I have the following function defined:
...
2
votes
3answers
96 views
Map several functions in one routine
I have several functions, let's assume they are:
func1[x_]=x;
func2[x_]=3*x-5;
func3[x_]=0.1*x^2;
and a lot more like these.
For each and every one of these I ...
5
votes
4answers
222 views
Any rule of thumb for converting a simple mathematical expression into a pure function?
By simple mathematical expression I mean one with a few functions and few variables copied into MMA in a mechanical way from a math book.
For example this one, giving the distance between two points ...
7
votes
4answers
259 views
How can I shorten this code to rotate a line segment around its center?
I have a list of line segments stored in the form:
{ {{x11,y11},{x12,y12}} , {{x21,y21},{x22,y22}} , ... , {{xn1,yn1},{xn2,yn2}} }
Now I want to rotate all of ...
0
votes
2answers
147 views
Why function cannot be defined inside For loop? [closed]
I have a following code (which is simplified version of what I am doing):
For[i = 1, i <= 5, i++,
f[x_] := Sin[x]^2
Print[{i, f[i]}]
]
And the question ...
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:
...
3
votes
1answer
56 views
User-defined NormFunction in FindFit -
I would like to use a different Norm instead of a p-Norm in FindFit (Mathematica 9). For example, instead of using
Sqrt[Sum[(x_model - x_data)^2]]
I'd like to use
Sum[x_model/x_data].
I can ...
2
votes
2answers
66 views
Rising Recursion Relationships
Lets say I want to compute the following function in mathematica:
$G[n,k]=G[n+1,k-1] + G[n+2,k-2]$ where I know that $G[n,0]=n$ and $G[n,1]=n^2$.
So, for example, $G[3,2]=G[4,1]+G[5,0]=4^2+5$ or, ...
0
votes
1answer
65 views
Function giving negative value when it should be positive [closed]
I am trying to evaluate
$$\displaystyle J=A\sum_{k=0}^{n-2}(-1)^k{n-2 \choose k}B^{n-2-k}\left(\frac{C_1}{k+n}-\frac{C_2}{k+n+1}+\frac{C_3}{k+n+2}-\frac{2}{k+n+3}\right)$$
in Mathematica as a function ...
0
votes
2answers
129 views
Fast Autocorrelation Computation
I want to compute the Autocorrelation Function (ACF) of a data table with $10^6$ entries. I know that there is a built-in function in Mathematica for that, but because I do not know how exactly it is ...
9
votes
3answers
127 views
Pass by reference for an option argument
Pass by reference can be faked by using HoldAll or something similar in the definition of a "Function". But can pass by reference be faked for symbols passed as ...
3
votes
1answer
157 views
Stereographic Projection
Say I want to represent points of the complex plane in the sphere $\Bbb S^2$ using stereographic projection. That is, the Riemann sphere:
Specifically, it would be nice to be able to:
Given the ...
11
votes
1answer
127 views
How can I make threading more flexible?
Threading automatically with Listable functions requires the argument expressions to have the same length (or for one of them to be atomic). For nested lists the ...
1
vote
1answer
55 views
NMaxmize with a list of variables
I want to use NMaximize to find the maximum value of a function with multiple variables. The problem is I would like to set this up so the number of variables is only decided when the function sees ...
4
votes
2answers
73 views
Creating functions from output of other calculations
Apologies in advance if the title is vague, I'm not really sure what to call this.
I have a function (call it 'foo') that generates a largeish polynomial, and it is natural to make the variables be
...
0
votes
0answers
44 views
Finding coefficients that make certain functional expression vanishing
My problem is to find a procedure that gives coefficients which make certain functional expression vanishing.
For example if I have a polynomial $P(x)$ of one variable $x$ given by $P(x)=a_0+a_1 ...
27
votes
9answers
6k views
Generating a Sierpinski carpet
I am trying to draw a Sierpinski_carpet. I have code that works, but I think there is a more elegant way to do than my way. Maybe I couls use Tuples or ...
5
votes
2answers
234 views
Gram Schmidt Process for Polynomials
I want to implement the Gram Schimdt procedure to the vector space of polynomials of degree up to 5, i.e. I want to find an orthogonal basis from the set of vectors $v=(1,x,x^2,x^3,x^4,x^5)$. The ...
0
votes
1answer
75 views
Given a sequence of expressions, how can I convert them all into functions?
I have a sequence of expressions
1, x, x^2, ..., x^5
I want to define a sequence of functions out of it, what should I do? Namely I want to define a vector of ...
8
votes
4answers
134 views
How to pass a list of arguments into HoldAll
I have a list of arguments (which in reality is lengthy):
arguments = {a, b, c}
arguments2 = {a_, b_, c_}
f[Sequence@@arguments2] := a + b + c
Note: It seems ...
9
votes
2answers
152 views
How can I get the right hand side of a delayed expression?
Imagine there is a given function f, defined with SetDelayed, say
f[x_] := Sin[x]^2 + Cos[x]^2.
Is it possible to get rhs of ...
0
votes
1answer
191 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 ...
4
votes
2answers
93 views
How to only work on sublists with non-zero (or positive) values
i have a large compositional dataset which contains non-zero and zero values. here is a sample:
...
-1
votes
1answer
66 views
Dynamically show a specific number of the fractional part's digits
What is the fastest way to cut off all n z digits of the fractional part of a real number?
(For example 12390.20934230)
I came up with this so far:
...
10
votes
3answers
380 views
What is Mathematica's equivalent to MATLAB's filter function?
The MATLAB code
filter(0.5,[1, -0.5], [1:10])
is equivalent to
Rest@FoldList[(#1 + #2)/2. &, 0, Range[10]]
I don't ...
6
votes
1answer
63 views
Possible to scope an anonymous function within Module?
This is my first question. I'm fairly new to Mathematica and completely new to SE, so I apologize if this question is trivial.
I'm working on a problem that requires a function to be redefined ...
2
votes
3answers
105 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 ...
1
vote
1answer
149 views
Why does the first derivative of a piecewise continuous function turns out with discontinuities?
I have this piecewise continuous function which is also continuously differentiable over time :
...
0
votes
1answer
74 views
Strange function definition result [duplicate]
I'm relatively new to Mathematica, and I'm trying to define a function f(k) that would do the following:
For any positive integer $k$, a finite sequence $a_i$ of fractions $\frac{x_i}{y_i}$ is ...
2
votes
2answers
87 views
Defining a function by pieces using list of interpolated functions in order to use `FindRoot`
I have two lists with the interpolated functions
...
15
votes
4answers
238 views
Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs
Using global variables the following turns an "expression" into a Function:
expr = 2 x;
Function[x, Evaluate[expr]]
Of course ...
5
votes
1answer
127 views
How to find the name of the current function
I would like to know the name of the current function from within that function. For example, consider the following code
...
1
vote
0answers
73 views
How can I obtain the function described by given set of central moments?
I want to investigate how my function P behaves with different probability functions rho as input variables.
This means
...
1
vote
1answer
102 views
Function definition and delayed assignment
I need to define the following function
MyWavelet[n_]["PrimalLowpass", prec_ : MachinePrecision] :=
Table[(-1)^(j - 1) h[[2*n - j]], {j, 0, 2*n - 1}]
which ...
4
votes
4answers
202 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
...
2
votes
4answers
277 views
How to write a differential operator in Mathematica
I have a very basic question. I am trying to code the LHS of the differential equation:
...
3
votes
1answer
78 views
Using NestWhileList to determine smallest prime value in series
I have a function recursively defined as follows:
$a_{n+1}-1=(a_n-1)\times lpf(a_n)$, whe $lpf(x)$ is the least prime factor of $x$.
Now, given an initial value of $a_0$, I would like to find the ...
4
votes
1answer
110 views
Module with “local functions”
I am trying to use a Module having "local functions", i.e., those which I need to define only inside this module.
So I tried this:
...
4
votes
3answers
95 views
Creating a nonperiodic function in mathematica
I want to create a non-periodic square wave with values of 1 and -1(not necessarily alternating).
For e.g. I want to convert an arbitrary array like {1,-1,-1,1,-1,1,-1} into a function.
I tried ...
1
vote
1answer
66 views
Confirming the existence of a function related to a matrix
Is it possible to get an answer to the following question in Mathematica?
Let $M$ be a $n$ by $n$ matrix, is there a function $m:\mathbb{N}\times \mathbb{N}\rightarrow \mathbb{Z}$ such that ...
0
votes
1answer
77 views
How could we define a function recursively?
Let us first consider the constructon of the following simple iteration
...
3
votes
1answer
111 views
Downvalues vs. Scoping for Functions
Regarding my recent question on using a default value for a function argument when a pattern was not met yielded some interesting answers, but the general consensus was "Yes this can be done, but ...
