Questions tagged [inverse]

Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.

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3
votes
1answer
200 views

Inverse Fourier transformation discrepancy between Wolfram|Alpha's solution and mine [closed]

I searched for the inverse fourier transformation of $$ \mathcal{F(\omega)} = \frac{2}{(1+i\cdot \omega)^2 +4} \rightarrow i^2=-1 $$ My solution (compliant with the solution from my textbook): $$ \...
10
votes
3answers
681 views

Can I use Compile to speed up InverseCDF?

I'm repeatedly issuing the command P = InverseCDF[NormalDistribution[0, 1], T] where T is either a 36- or 64-vector of real numbers (points in the unit ...
-1
votes
1answer
86 views

Numerical Inversion of an incomplete beta function expressed as gauss hypergeometric function using Mathematica

I am currently working with this hypergeometric function ${_2}F_1$, $\rho(r)=\frac{2b}{1-q}(1-(\frac{b}{r})^{1-q})^{\frac{1}{2}}{_2}F_1(\frac{1}{2},1-\frac{1}{q-1},\frac{3}{2},1-(\frac{b}{r})^{1-q})$ ...
3
votes
3answers
243 views

InverseFunction fails to invert $e^{-x/2}-e^{x/2}$

I need to invert a function. I want to isolate the x basically. By the looks of the graphic I plotted, the function seems to be invertible, however when I call <...
4
votes
1answer
266 views

Help with PseudoInverse

I am trying to (pseudo)solve a linear system $Ax=y$. I have a matrix A, and 2 vectors x and y...
2
votes
1answer
79 views

InverseFunction's domain is not the range of the function that was inverted

I wrote a function to calculate how long of a period has past when a planet traverses an angle theta from perihelion in an orbit of a given eccentricity. ...
0
votes
4answers
193 views

Solving an equation involving elliptic integral

Consider the following function: f[θ_] = Integrate[1/(Cot[θ]^2 - Sin[θ]^2)^(1/2), θ]; Now, I want to determine the value of $\theta$ for which say $f(θ)=1$. I ...
0
votes
1answer
144 views

How can we find all inverses of a multivalued function?

How can we find all inverses of a multivalued function using Mathematica? For example, if we try to find the inverse of $x^2$, Mathematica will say something like this: ...
3
votes
1answer
181 views

Evaluate the indefinite integral $\int\sin^{-1}\left(\frac{2x}{1+x^2}\right)\ dx$

Integrate $\int\sin^{-1}\frac{2x}{1+x^2}.dx$ $$\sin^{-1}\frac{2x}{1+x^2}=\begin{cases}2\tan^{-1}x&\text{ if }|x|\leq{1}\\\pi-2\tan^{-1}x&\text{ if }|x|>{1}&\text{ and }x>0\\-\pi-2\...
1
vote
1answer
249 views

Finding the inverse function of an interpolating function given by NDSolve

Consider the following solution of NDSolve ...
5
votes
3answers
399 views

Easiest way to have an approximation of binary entropy inverse

I call $H_2$ the function $H_2(x) = -x \ln(x)-(1-x) \ln(1-x)$ It is the binary entropy. I call $g(x)=H_2((1+x)/2)$ This last function is bijective on $[0;1]$. I would like to have an inverse, or ...
1
vote
0answers
97 views

Fast method for getting the inverse function of the Hypergeometric function in Mathematica

I didn't manage to obtain the inverse function for this frightening function: ...
1
vote
1answer
158 views

Mapping colours to numbers

Through this post I've learned how to make a function to map a colour gradient to an interval of numbers like ...
1
vote
2answers
252 views

How can I invert this series?

I have a series which is expanded around $x=0$: $$S=2 \sum_{n=0}^4 x^n (c_n\ln x+b_n)$$ where $ c_n=-\frac{1}{2}\left(\frac{(2n-1)!!}{2n!!}\right)^2$ and $b_n=-c_n\left(4 \ln 2+2\sum_{k=1}^n(\frac{1}...
0
votes
1answer
412 views

Inverse of a multivalued function

I try to get the inverse of a simple function like x^2,x≥0. Still, when I use InverseFunction Mathematica gives me back -(y^0.5) ...
2
votes
1answer
181 views

Is there a fast way to get the diagonal of the inverse of a banded Hermitian matrix?

Since inverting a matrix is often a bad idea, I am wondering if there is a better way to get just the diagonal of the inverse without inverting the whole thing. Note I need the whole diagonal, not the ...
2
votes
3answers
394 views

InverseFunction

Considering a well defined function f[x_]:=Tan[Sqrt[x]]/Sqrt[x] (*x>= 0*) I tried to evaluate the inverse function and get an unexpected result ...
3
votes
2answers
145 views

no Plot showed for an Inverse function

The short code is below, but no plot is produced. Are there any errors in my code? Thanks! ...
2
votes
1answer
624 views

Plot function but blank

Sorry, I am a beginner of Mathematica, try to plot a function, my short code is as follow, but the pic is blank. I could not find what is wrong in my code. Thanks a lot! ...
28
votes
3answers
1k views

What are the counterparts in Wolfram to left and right division of a matrix in other programming language, e.g. Julia and MATLAB?

Sometimes, to find the inverse of a matrix is a labor-consuming task, or even "disgusting", especially when the matrix is "ill". It is said, e.g. in Julia, that the left/right division operation is ...
0
votes
0answers
59 views

Reconstruct equation by given solution

How can I reconstruct equation, which solution is given by series $\frac{x^{x-2}}{x!}$? The reverse task is straightforward with Solve function. It seems pretty ...
2
votes
1answer
148 views

Specify a domain of inversion for an inverse function

I'm playing around with some functions related to the Lambert W Function. Namely those of the form: $$W(x;a) = f^{-1}\left(x \left( e^{x} - a\right) \right)$$ And when $a$ gets too large, ...
3
votes
4answers
264 views

What is the inverse of the Position function?

What is the inverse of the Position? I have an array which contains the positions of elements and I want a function which returns an List which contains 1 where ...
1
vote
0answers
430 views

Inverse of a sparse 21x21 symbolic matrix

I am trying to compute the inverse of the following symmetric sparse(density 0.37) 21x21 matrix involving symbolic expressions in the entries(the variables ...
3
votes
1answer
262 views

Using user-defined inverse functions with Solve

I am trying to solve with: ClearAll[myCeiling]; myCeiling /: InverseFunction[myCeiling[x_]] := myFloor[x]; using ...
3
votes
0answers
1k views

What does the @ symbol do in Mathematica? [duplicate]

I have the folllowing array $$h = \left(\begin{array}{cccc}1 & 0 & 0 & 0\\ 0 & f^2 & 0 & f^2 \cos\theta\\ ...
0
votes
1answer
174 views

Numerical Integration With Many Singularities

Is possible a solution to this Numerical Integration? The constant values are as follows: ...
-1
votes
1answer
288 views

Inverse Kinematics of a 3R Spatial Manipulator

I want to solve the make a module for the inverse kinematics of a 3R Spatial Manipulator. I am new to Mathematica and cant seem to figure out how to write it. The forward kinematics equations are : <...
3
votes
2answers
223 views

Inverse CDF of non-builtin probability distribution

I'm trying to get the inverse CDF of the Raised Cosine probability distribution function. It has parameters $\mu$ and $s$, support $x \in [\mu - s, \mu + s]$, PDF ...
0
votes
1answer
480 views

How to define a power series with unknown coefficients

I'm trying to invert the following power series \begin{equation} \omega(x) = \frac{6}{5}\frac{1}{x^5} - \sum_{k = 1}^\infty \frac{6}{4k - 5}A_ks^kx^{4k - 5} \end{equation} so that I get $x = x(\omega)...
1
vote
2answers
413 views

Inverse of a 3x3 Matrix [closed]

So I know the definition of the Inverse of a Matrix A is that there exists matrix B such that AB=BA=I3, where I3 is the identity matrix. If A is invertible, then the matrix B is called the inverse of ...
1
vote
1answer
263 views

Taylor expansion of two variable function without cross terms

I have the matrix symmetric matrix ...
5
votes
3answers
508 views

Where is this difference between the solutions of DSolve and NDSolve coming from?

I am trying to solve this DE: DSolve[{r'[t] == r[t]^2/3 (1 - r[t]), r[0] == 2}, r[t], t] // Simplify For which I get the solution ...
0
votes
1answer
96 views

Inverting a series with both positive and negative powers

I have an asymptotic series expansion that I would like to invert of the form $ t_2 z + t_3 z^2 + t_4 z^3 + \frac{A_1}{z} + \frac{A_2}{z^2} + ... + \frac{A_9}{z^9} + \mathcal{O}(z^{-10}) = w$ i.e. I ...
0
votes
1answer
170 views

How to invert boolean byte coding function?

I've got simple byte coding function: y = x and E0 or x and 1F xor 05 Now I want to express x = ...? Is it possible using Mathematica (for more complex ones), please? TIA Correct answer (right?): ...
12
votes
1answer
219 views

Is there a built-in function to inverse Thread?

Namely, while Thread @ f[{a, b}, {x, y}] gives {f[a, x], f[b, y]} the InverseThread (if it existed) should reverse the ...
2
votes
1answer
194 views

Treat symbols as elements of a non-commutative field

I want to invert a matrix, {{a,b},{c,d}}, where a,b,c,d are elements of a non-commutative field (for example invertible matrices)...
2
votes
2answers
220 views

Inverse Function in Mathematica

How to find bConst in the following code ...
1
vote
1answer
76 views

Solving for $\beta$ in $\tan\gamma = C \tan\beta$, $0 \leq C \leq 1$, where $\beta$ must be in same quadrant as $\gamma$

I am pretty weak with Mathematica, so please, nothing overly complicated. The ArcTan[x, y] function allows for a full range of $2 \pi$ in the output. However, for ...
3
votes
1answer
89 views

Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
7
votes
3answers
930 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
1
vote
0answers
195 views

How to invert an Elliptic function where the elliptic nome is a function of an independent variable?

I have a Jacobian elliptic function as a function of two independent variables $x$ and $y$. The elliptic parameter $m=m(y)$, $0 \leq m \leq 1$, is also a function of the variable $y$, and thus the ...
1
vote
4answers
486 views

Implicitly inverting a function from numerical solution [closed]

I have the following piecewise continuous function: ...
4
votes
1answer
122 views

Function inversion [closed]

I have an expression of this kind ...
1
vote
1answer
156 views

A question on JordanDecomposition in Mathematica

How can I have Mathematica show me also the inverse matrix of the similarity matrix of JordanDecomposition of a matrix? Obviously I need to use here the ...
2
votes
0answers
311 views

How do I invert a function with two arguments? [closed]

I begin with a function defined by c[u_, mH_] I won't go into details because it comes from countless lines of partial differential equations, boundary ...
0
votes
1answer
154 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
5
votes
2answers
19k views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } using the ...
6
votes
3answers
671 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
2
votes
1answer
127 views

How to find selected elements of inverse of a banded matrix without inverting it?

Is it possible to find some selected elements of the inverse of a large sparse matrix without inverting it? For example consider this Hermitian matrix (as a general case). ...