Questions tagged [function-construction]
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.
2,415
questions
48
votes
6
answers
6k
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Can I make a default for an optional argument the value of another argument?
I'd like to define a function with several optional arguments, some of which default to the value supplied for other arguments. For example, I'd like to be able to write something like
...
- 12.8k
2
votes
1
answer
302
views
Difference between function definitions [duplicate]
Possible Duplicate:
Functions vs. patterns
I thought about describing the context in which I faced this problem, but I figured it is general enough and clear enough to pose it as it is.
What ...
- 7,046
19
votes
2
answers
20k
views
How to define a differential operator?
I have a linear differential operator, for instance, $L\left (\partial _{t} \right )=\partial _{tt} - 3\partial _{t} + 2$. I use it in 2 different ways:
apply the operator to a function: $L\left (\...
- 429
-2
votes
2
answers
2k
views
How to correctly call a Module within another Module?
How to embed and call the correct embedded modules inside another Module?
Say:
...
- 1,963
13
votes
3
answers
5k
views
How do I designate arguments in a nested map?
Say I have two lists,
list1 = {a, b, c}
list2 = {x, y, z}
and I want to map a function f over them to produce
...
- 355
0
votes
1
answer
1k
views
Multivariate Function Approximation With a Large Dataset
I have a nice amount of data from a trading strategy I am working on, where I have two different liquidity parameters as x, y variables.
Before entering a trade I am taking the moving average of <...
- 11
21
votes
2
answers
670
views
Pattern that matches colors
Suppose I'm writing a function that takes a color as a parameter; for example:
drawShape[color_] := Graphics[{Style[Disk[], color]}];
But if the caller inputs an ...
- 2,402
7
votes
2
answers
279
views
How is OptionsPattern[] defined? Can I replicate this?
I am writing several functions which all take similar input parameters (a complicated nested list structure). Is there some way for me to define a pattern that can be used in multiple places and ...
- 1,422
1
vote
1
answer
285
views
Find the derivatives of arbitrary order of a function found using NDSolve
For the following initial value problem
BC[b_]:=x[0]==b;
eq[b_]:=NDSolve[{equation==0, BC[b]}, x, {t,0,1000}];
body[t_,b_]:= x[t]/.eq[b];
one could define the ...
- 507
1
vote
1
answer
99
views
Why function is evaluated backward?
I have a simple function:
f[x0_,y0_]:= Module[{x=x0,y=y0},For[i=0,i<2,i++;Print[x],Print[x+y]];]
So when I call it:
f[2,3]...
- 1,963
4
votes
3
answers
863
views
Generating pairs of additive and multiplicative factors for integers
Given an integer $n$, I want to get two lists:
a) the set of pairs of the divsors $a,b$ into exactly two factors $n=a\cdot b$,
b) the set of pairs $a,b$ of two summands $n=a+b$.
The code I ...
- 1,485
2
votes
0
answers
675
views
Generating a function which outputs possible chemical reactions
I want to make a list of chemical reactions and I write them down in a $\require{mhchem}\LaTeX$ format. They are of the following form
$$NA_n^i+MB_m^j \rightarrow \hat NA_{\hat n}^{\hat i}+\hat MA_{\...
- 1,485
1
vote
0
answers
494
views
Return Functions from parallel execution of module
I wrote a module which numerically solves an ODE using NDSolve. The result from this is e.g. either ...
- 453
1
vote
1
answer
141
views
Defining functions from expressions of variable lengths
I have a list of symbols that I have defined using
d = Table[Symbol["d" <> ToString[i]], {i, 1, n}]
giving
...
- 11
7
votes
2
answers
5k
views
Building matrices by attaching vectors (columns) and matrices
Having the need to attach a column to a matrix or to join matrices to make longer rows is an operation that I use very frequently and I find the Join function ideal ...
- 9,798
4
votes
1
answer
2k
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 ...
- 445
1
vote
0
answers
136
views
Non Commutative Multiply [duplicate]
Possible Duplicate:
Non-commutative symbolic linear algebra
I want to multiply two matrices, for example,
A = {{e, f}, {g, h}}
B = {{a, b}, {c, d}}
Using <...
- 11
1
vote
1
answer
2k
views
Matrix Multiplication Modulo 2
I would like to perform matrix multiplication modulo 2. Hence, instead of the usual:
A.B
I did:
...
- 971
0
votes
1
answer
626
views
0
votes
1
answer
156
views
3
votes
4
answers
277
views
How to create a composite function from a variable number of components?
Background of the problem: A patient takes a drug every $X$ hours with a half-life of $Y$ hours. How much of the drug will be (exactly) in his system after $h$ hours? For $X=24$, and $Y=24$ I made the ...
- 9,637
2
votes
1
answer
158
views
Implementing a For (?) or series or loop (?) for individual results for every x to n
I'm working on improving a modeling formula and have spreadsheets worth of data to use, but my work so far has been quite tedious. I'm essentially pulling 20 rows of data from each separate sheet of a ...
11
votes
3
answers
6k
views
Better solution than returning a list of 3 values?
I have a function (using SetDelayed) that currently returns 3 values in a list. Later on I use the result of this list along with ...
- 1,422
3
votes
1
answer
514
views
Defining a function that handles Dynamic arguments similar to Built-ins
Firstly please note that I'm using simply Dynamic behavior to illustrate my question, I'm not asking how to move a Disk or make ...
- 14.8k
3
votes
2
answers
144
views
Why does this function fail when a non-function version of the same code works?
This works:
...
- 5,422
1
vote
2
answers
201
views
How to mix Unevaluated property of function arguments with expression assignments?
This is a follow-up to my (solved) question How to distribute a generic function of two arguments (without evaluating the arguments)
Say, I have a binary function
...
- 431
4
votes
3
answers
366
views
How to distribute a generic function of two arguments (without evaluating the arguments)
I guess there is an easy way to do this, but I can't seem to figure it out. What I would like to do is to distribute a generic (i.e. without specifying what this function really does) binary function. ...
- 431
7
votes
4
answers
1k
views
Composition of mappings not working as expected
I have two functions $f,g:\mathbb{R}^2 \to \mathbb{R}^2$ and I define a third one $h:\mathbb{R}^2 \to \mathbb{R}^2$ as the composition $$h(x,y) = g(f(x,y))$$
I'm trying to get this function into <...
- 173
9
votes
2
answers
896
views
Define product derivative
How do I define the $n$th product derivative of a function in Mathematica?
The first product derivative $f^\ast$ of a function $f$ is
$$
f^\ast(x)=\exp\left(\frac{f^\prime(x)}{f(x)}\right)
$$
The $n$...
- 235
4
votes
3
answers
1k
views
How to pull scalars out of a function that should act on lists?
Suppose I have
A = a vecA
B = b vecB
where a and b are supposed to be arbitrary scalars ...
- 431
2
votes
1
answer
198
views
Specifying form in MemberQ
This seems like a very simple question, the answer to which should be obvious to me. So I won't be offended if this question is closed. But I'm having trouble figuring out the answer.
I would ...
- 10.4k
4
votes
2
answers
315
views
Function to select a row whose kth element is closest to a given number
I'm trying to write a function that picks out the row of a Matrix whose kth element is closest to some given number that will be given to me.
So for example,
<...
- 6,818
17
votes
1
answer
535
views
Modules that initialize themselves on first call
I use a lot of functions that extract a specific data item from a file with many data items. I want these functions to load data (slow) and return the item (fast) on first call, but just return the ...
- 5,422
16
votes
2
answers
4k
views
NestList on a function of several arguments
I'd like to know if it is possible to use NestList on a regular function of several arguments, such as:
...
- 263
8
votes
2
answers
9k
views
How to find (numerical) value of a derivative at point?
I have the following function:
f[0, 0] = 0
f[x_, y_] := Exp[-(x^2 + y^2)^(-1)]
How do I find its partial derivatives at any given point, including $(0,0)$? This ...
- 949
2
votes
2
answers
225
views
Constraining a random function
This question is a follow-up from here. I have a function that generates a list of correlations between some random variables:
...
- 891
9
votes
1
answer
1k
views
Functional programming and Do loops
I'm writing a Monte Carlo simulation. I'm using a Do loop to create the different simulations, iterating over different ...
- 891
18
votes
1
answer
826
views
Is it possible to Clear all variables (but not functions)?
I have written a Mathematica script in which I define functions and variables. Here is a vastly simplified example:
...
- 10.4k
11
votes
2
answers
317
views
can a ColorFunction have side effects?
Can anyone explain this (to me) odd behavior. If I run this code once (fresh kernel) it works as intended.
...
- 38.8k
3
votes
2
answers
623
views
Using Functions as Arguments to Function
I am trying to make a function like Norm but defined like so: MyNorm[{x_,y_,z_}]=Sqrt[x^2+y^2+z^2]. Mathematica assumes that x, ...
- 215
10
votes
4
answers
874
views
Generating a position lookup function for an arbitrary list of integers
In my code, I generate a list of integers called numlist. Here is an example numlist:
...
- 10.4k
1
vote
2
answers
617
views
Piecewise function with a function as argument
I want to define a piecewise function, which has two arguments, one of which is a function of the other's piecewise argument. I am giving an example
...
- 993
1
vote
2
answers
224
views
How can define a set of nested parameters
I would like to know how I to define a function with a nested set of parameters (or whatever you would like to call it). For example, how would I get the following function ...
- 807
2
votes
3
answers
8k
views
Variables Inside Functions Not Evaluating
x = 5*y
function1[y_] := x
function1[5]
Am I wrong in thinking that function1[5] should equal 25? Instead this comes out.
...
- 123
1
vote
1
answer
315
views
3
votes
4
answers
245
views
Pack Solve results into a vector
I am currently using a really easy function to get the eigenvectors of a corresponding eigenspace:
...
11
votes
3
answers
641
views
Where in the documentation can I find a list of function argument types?
Recently, I learned that it is possible to assign "types" to function arguments in the definition of a function. Suppose I have a function stringFun that does some ...
- 10.4k
12
votes
2
answers
488
views
Manipulating OptionsPatterns[]
How do you combine OptionsPatterns?
For example, I would like to have a function that can take both options that I specify, and options for all graphs:
...
- 1,571
23
votes
3
answers
981
views
Nested definition: How can I define a function with a passed-in expression?
Here's a simplified version of what I'm trying to do:
...
- 19.1k
29
votes
6
answers
3k
views
Convert an expression to a Function
I need a function which can take an expression and return a pure function based on the symbols in the expression. The symbols might have values so must be protected from evaluation. It is probably ...
- 84.6k