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
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1answer
91 views

Inverse of DiracDelta at 0 is 99/5?

Here in this other question of mine I asked the question, but maybe here is more pertinent. When using Mathematica we can find the following result: ...
0
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1answer
37 views

Finding the inverse of possibly non-invertible interpolation function

Consider the following sample code pts = Table[{i, i^2}, {i, -10, 10}]; foo = Interpolation[pts]; Plot[InverseFunction[foo][y], {y, 0, 10}] From the plot, we see ...
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0answers
19 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
0
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1answer
62 views

How can I calculate this integral?

I would like to calculate the integral in equation pol[x] if the quantity is positive or negative. ...
2
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1answer
57 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
1
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1answer
84 views

InverseLaplaceTransform not working

I am trying to find the Inverse Laplace transform of a function I previously obtained from a Laplace transform, but the result obtained does not agree with the initial function. Why is this happening? ...
1
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1answer
68 views

Inverse Laplace Transform how to find the exact solution

So I want to obtain a inverse Laplace transform from mathematica but I get this: How can I get the solution?
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0answers
42 views

Inverse::luc Badly conditioned matrix may contain significant numerical errors. Why?

I want to find the inverse of the following matrix, which is given in terms of the following constants: ...
0
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0answers
40 views

Solving a System and taking inverse Laplace/Fourier Transforms

I have a set of linear equations for 4 quantities which have been both Fourier transformed and Laplace transformed. The system needs to be solved for the quantities and then each of the quantities ...
1
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1answer
72 views

Plot Arc Length Parametrization

I want to plot the parametrization of the curve with respect to arc length. It is all known that we have to find the inverse of the arc length of the original function i.e. $F(t)$, and ...
2
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1answer
49 views

Inverse of matrix up to some order

Let $A(t,s)$ be a matrix of any size (potentially large), whose entries are polynomials functions wrt $(t,s)$ of order $N$. I would like to compute the inverse $X$ of $A$ up to the order $N$ that is $...
3
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1answer
192 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
3
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2answers
180 views

Strange NSolve failure [duplicate]

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0answers
20 views

InverseFunction cannot evaluate negative arguments

I have difficulty figuring out where my code fails. I want to obtain $\textbf{ry}$ which is the inverse function of rho (see below). When I input positive values for its argument, there's no problem. ...
0
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1answer
41 views

Issue With Example of Series Inversion

I am having a problem with the Mathematica InverseSeries command. Looking at the information page here, we have the following example; ...
0
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1answer
81 views

Domain specifications for InverseFunction

I have difficulty implementing on how to specify the domain that I want for ry which is the inverse function of rho. The necessary condition is that, $\textbf{ry}$ must remain $\textbf{positive}$ for ...
1
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3answers
114 views

Inverting series with symbolic coefficients?

I am trying to invert the series symbolically. Is this possible in Mathematica? Example 1 - Let $p = u + au^2 + bu^3$, where $a,b$ are symbolic variables. I am trying to invert the series around $u=...
0
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0answers
34 views

Why does the numerical inverse laplace function FT for small times give erroeous results and what is the alternative

I am trying to do the numerical laplace inverse of a very complicated transfer function, subject to a trapezoidal pulse input. For the sake of understanding, I will use a simple transfer function to ...
0
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1answer
100 views

Asymptotic solution of a second-order ODE containing InverseFunction

Essentially, I have a second-order differential equation given by ode below. In order to solve it, I need to obtain an asymptotic solution where $g(x)$ must vanish at infinity which will be used after ...
5
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1answer
64 views

Weirdness with Interpolation of data and InverseFunction

Bug introduced in 8 or earlier and persisting through 12.0 Something strange is happening with this list of data: ...
4
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1answer
96 views

Inverse of vector-valued function

Having a differentiable function $f : \mathbb{R}^2 \longrightarrow \mathbb{R}^2$ such that $\det D(f)$ (Jacobi determinant) does not vanish. How can we get the inverse function $f^{-1} : \mathbb{R}^2 \...
-1
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1answer
60 views

Invert a series with coefficients depending on x

Let's say I have the equation: $\qquad (8x^{15}+4x^{14}+\ldots)G^9 + (3x^{3}+\ldots)G^{8} + \ldots + (5x+4)G + x = x$. $G$ is an infinite series of $x$. I want to find the first 10 coefficients of $...
0
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1answer
64 views

Get Inverse Function in a certain domain

I'm trying to make Mathematica giving me the inverse function of $f$ (below) when restricted to the interval $[v,1]$. Using ConditionalExpression or ...
1
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1answer
89 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
votes
2answers
164 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 ...
0
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1answer
66 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. ...
0
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0answers
52 views

Find inverse of a complicated function

I am looking for an analytic inverse function for ...
1
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1answer
123 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? ...
0
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0answers
91 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. ...
0
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1answer
55 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
49 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
43 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{...
0
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0answers
66 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
499 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 ...
1
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1answer
149 views

Finding the symbolic inverse of a function

Is there a way of inverting this function to obtain $r(\rho)$? ...
0
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0answers
34 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}+\...
1
vote
0answers
37 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(...
0
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0answers
39 views

Inverting a lengthy matrix

I have a rather lengthy 10X10 matrix that I want to invert it. The matrix reads: ...
3
votes
2answers
191 views

Finding the inverse of a function

I am to solve for $r(\rho)$ given the function, ρAsymp[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
votes
1answer
49 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
vote
1answer
73 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 ...
1
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0answers
44 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
votes
1answer
151 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
650 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
82 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
227 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
218 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
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
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4answers
169 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
124 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: ...