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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59 views

Inversion of a hypergeometric function

I have been trying to invert the hypergeometric function $$\rho(r)=\frac{2b}{1-q}\sqrt{1-\left(\frac br\right)^{1-q}}\,_2F_1\left(\frac{1}{2},1-\frac{1}{q-1};\frac{3}{2};1-\left(\frac br\right)^{1-q}\...
3
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2answers
121 views

Plotting the inverse function of a complicated function

So I have a function F[x_] = Assuming[{Element[x, Reals], -1 < x < 1}, Integrate[1/Sqrt[(x^2 - 1)^2 + alpha*x], x]] I'm now interested in the ...
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1answer
55 views

How to carry a matrix in algebric form under “set delayed”

I have a small query and a related problem regarding the working methodology of Mathematica under set delayed/Do functions. Here is a simplified version of my problem. ...
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0answers
41 views

Find inverse of a complicated function

I am looking for an analytic inverse function for ...
1
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1answer
57 views

Inverse matrix not computing [closed]

Hi just wondering why my Inverse of matrix will not compute? I don't believe its wrapped from //MatrixForm because I copied it by hand into a new document and it still would not work. Any ides? ...
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0answers
45 views

Fourier Transform and Inverse Fourier Transform of Lists

I am trying to compute the Fourier transform of a list, say an array of the form {{t1, y[t1]},.....{tn, y[tn]}}; apply some filters in the spectral components, and then back transform in time domain. ...
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1answer
46 views

Evaluation Control for Equation Input to NDSolve

I am trying to numerically integrate a system of equations using NDSolve and am having issues with symbolic matrix inversion taking a long time. The actual system is much more complicated, but I have ...
1
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1answer
43 views

InverseFunction never stops running

I have a problem finding the inverse of a function, perhaps I'm missing something.. I'd appreciate it if someone can help me out. First, I calculate an Integral of the form ...
0
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1answer
36 views

Inverse stochastic problem solution

I am trying to determine a probability density $p(\mu)$ such that, when $\mu$ is inputted into a forward simulation equation: $d \sim \mathcal{N}(\mu,0.1)$, I obtain a distribution on $d\sim \mathcal{...
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0answers
38 views

Inverse of Poly Log function? Asymptotic behavior of Poly Log function?

I am unable to answer important questions such as what is the inverse of PolyLog[3/2,z]? I mean can you express the solution to w = PolyLog[3/2,z] (solve for z in terms of w) in terms of functions ...
4
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2answers
413 views

Using LinearSolve instead of Inverse does not give a good enough precision

If I want to calculate $B^{-1}A$, then instead of using Inverse, I should in theory just be able to use LinearSolve[B,A]. Now ...
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1answer
106 views

Finding the symbolic inverse of a function

Is there a way of inverting this function to obtain $r(\rho)$? ...
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0answers
32 views

Inverting a matrix when its elements are given by difficult expressions?

I have a matrix which is composed by these elements: $$\mathcal{K}_{11} = \frac{3\alpha^{4/3}(4\mathcal{V} - \xi +6\alpha \sum_{k = 2}^n\lambda_k \tau_k^{3/2})}{4(2\mathcal{V}+\xi)^2(\mathcal{V}+\...
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0answers
35 views

Inverting a series

How do I invert the following, \[Rho]=r + b0 Sum[Pochhammer[1/2, k]/(k! ((1 - q) k - 1)), {k, 0, \[Infinity]}] + b0^(1 - q)/(2 q) r^q + O[r^(2 q - 1)] to get $r(...
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0answers
36 views

Inverting a lengthy matrix

I have a rather lengthy 10X10 matrix that I want to invert it. The matrix reads: ...
0
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1answer
83 views

Finding the inverse of a function

I am to solve for $r(\rho)$ given the function, \[Rho]Asymp[r_,b_,q_] := 1/(1 - q) Gamma[1/(1 - q)]/Gamma[(q - 2)/(q - 1)] r Sqrt[1 - (b/r)^(1 - q)] This can be ...
2
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1answer
46 views

Peculiar result of InverseHankelTransform

In using the HankelTransform and its inverse I find that the inverse does not lead to the initial input. I begin with r (the independent variable) in the denominator but end up with r0 (a constant) in ...
1
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1answer
54 views

Laplace transform giving incorrect result

In Mathematica: LaplaceTransform[Exp[-Exp[-t]], t, s] Out:= Gamma[s]-Gamma[s,1] But performing InverseLaplaceTransform on the ...
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0answers
24 views

Inverting the asymptotic expansion of Gauss Hypergeometric Function

I am interested in obtaining the asymptotic expansion of $r(\rho)$ (which is the inverse of the object rho[r_,b_,q_] below). Basically I want to series expand rho[r_,b_,q_] for large $r$ (i.e. as $r\...
3
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1answer
55 views

Solving $\det{(A+\epsilon B)}=0$ for large, symmetric and dense $A$ and $B$

In an algorithm I am writing, I need to solve the equation $$ \det{(A+\epsilon B)} = 0, $$ for the smallest value of $\epsilon$, given large ($n$x$n$ ideally up to 150x150), dense and symmetric A ...
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0answers
33 views

Inverse of Normal Distribution CDF incorrect for large value?

I have a function F which is the CDF of the standard normal distribution. The inverse of F should be infinity at 1. However, I ...
3
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1answer
67 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
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3answers
604 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 ...
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1answer
73 views

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

I am currently working with this hypergeometric function ${_2}F_1$, $\rho(r)=\frac{2b}{1-q}(1-(\frac{b}{r})^{1-q})^{\frac{1}{2}}{_2}F_1(\frac{1}{2},1-\frac{1}{q-1},\frac{3}{2},1-(\frac{b}{r})^{1-q})$ ...
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3answers
195 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
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1answer
154 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
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1answer
77 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
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4answers
118 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
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1answer
104 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: ...
2
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1answer
162 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\...
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1answer
135 views

Finding the inverse function of an interpolating function given by NDSolve

Consider the following solution of NDSolve ...
5
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3answers
326 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
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0answers
76 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
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1answer
71 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
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2answers
118 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
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1answer
176 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
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1answer
130 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
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3answers
285 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
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2answers
118 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
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2answers
412 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! ...
26
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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
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0answers
47 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
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1answer
103 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
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4answers
190 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 ...
0
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0answers
259 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
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1answer
215 views

Using user-defined inverse functions with Solve

I am trying to solve with: ClearAll[myCeiling]; myCeiling /: InverseFunction[myCeiling[x_]] := myFloor[x]; using ...
2
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0answers
547 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
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1answer
150 views

Numerical Integration With Many Singularities

Is possible a solution to this Numerical Integration? The constant values are as follows: ...
-1
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1answer
197 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
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2answers
134 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 ...