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.

Filter by
Sorted by
Tagged with
0
votes
1answer
60 views

Getting inverse of x^2 with positive x

My goal it to get inverse of x^2 for positive x. But the result shows always minus -Sqrt[y]. How to correct ...
0
votes
1answer
35 views

Condition at Inverse function

My goal is to get inverse of -Log[1 - x]. But the result shows conditional expression. Could I know Why the condition -[Pi] <= Im[y] < [Pi] shows? There wass no assumption at variable y. ...
1
vote
1answer
75 views

Asymptotic expansion at infinity given a branch cut

Basically, I have obtained the function $\rho (r)$ below as a result of integrating $$\rho(r)=\int_{b_0}^{r}\frac{dx}{\sqrt{1-(b_{0}/x)^{1-q}}}$$ which results to ...
0
votes
0answers
29 views

How to return an inverse function based on parameters (for formal differentiation)

I want to return a different function for any given parameter in order to later calculate a value of the inverse of that function given the parameter as an indeterminate. That is, I want, for each $d$,...
0
votes
2answers
55 views

Plot Parametric f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)

I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x) f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &...
0
votes
0answers
28 views

Plotting Inverse Function - more complicated [duplicate]

I would like to plot the inverse of $f$ using the same method that was suggested to me in my previous question: f[x_] := [(2 μ ArcTanh[(# μ)/Sqrt[-α + #^2 ν]] + μ Log[α + #^2 (μ^2 - ν)] - 2 Sqrt[ν]Log[...
4
votes
0answers
67 views

How to get an asymptotic of the real-valued branch of the inverse function?

Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
0
votes
1answer
71 views

InverseSeries slower than it should be

I am running into problems with InverseSeries taking far longer than it should. Given (for example) $$F = q + a_2 q^2 + a_3 q^3 + \ldots + a_{99} q^{99} + O(q^{100}),$$ Computing the inverse series is ...
0
votes
0answers
38 views

Series of inverse functions, unclear numerical constant

I was answering another question here and came up with this simple illustrative example that should have an analytic solution. Indeed it has, but I do not understand it. In particular, where 85 is ...
-1
votes
1answer
62 views

What is the inverse Jacobian of a 4D model? [closed]

For a Jacobian Matrix where the elements are represented as J11 J12 J13 J14 J21 J22 J23 J24 J31 J32 J33 J34 J41 J42 J43 J44 what is the inverse jacobian of this Matrix?
12
votes
2answers
405 views

InverseRadon behaves differently from iradon of MATLAB

I have to calculate a 2-dimensional radially symmetric distribution from a single projection. I know that InverseRadon should actually do the job, but I get the ...
2
votes
0answers
124 views

Integration that involves inverse of a big symbolic matrix

I have a $300\times300$ symbolic matrix and I want to calculate its inverse matrix. It has been two days and Mathematica is still executing Inverse[T]. $T$ is the name of that matrix. Why am I ...
0
votes
0answers
54 views

How to find the Inverse of numeric Function that was created from NDSolve

I'm a newbie to Mathematica and i do have a simple question. I have a function H that was created numerically as solution form NDSolve (like H(R)), and i'm trying to create the Inverse function R(H) ...
2
votes
0answers
40 views

establish matrix and inversion of a uppertriangularized matrix [closed]

Trying to create an uppertriangularized matrix with Poisson Distribution, find its inverse and multiply the inverse by a vector, i.e. ...
3
votes
1answer
99 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: ...
1
vote
2answers
76 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 ...
0
votes
0answers
23 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
0
votes
1answer
72 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
votes
1answer
78 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
1
vote
1answer
115 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? ...
3
votes
1answer
116 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?
0
votes
0answers
106 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: ...
1
vote
1answer
96 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
votes
1answer
58 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
votes
1answer
301 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
votes
2answers
224 views

Strange NSolve failure [duplicate]

...
0
votes
1answer
44 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
votes
1answer
107 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
vote
3answers
134 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
votes
1answer
124 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
votes
1answer
70 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
votes
1answer
200 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
votes
1answer
73 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
votes
1answer
80 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
vote
1answer
135 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
207 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
votes
1answer
85 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
votes
0answers
60 views

Find inverse of a complicated function

I am looking for an analytic inverse function for ...
1
vote
1answer
265 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
votes
0answers
180 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
votes
1answer
82 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
vote
1answer
50 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
votes
1answer
48 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
votes
0answers
101 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
votes
2answers
601 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
vote
1answer
203 views

Finding the symbolic inverse of a function

Is there a way of inverting this function to obtain $r(\rho)$? ...
1
vote
0answers
42 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
votes
0answers
40 views

Inverting a lengthy matrix

I have a rather lengthy 10X10 matrix that I want to invert it. The matrix reads: ...
3
votes
2answers
213 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
51 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 ...