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
-1
votes
1answer
38 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?
2
votes
0answers
56 views

InverseRadon function - possible bug?

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 ...
1
vote
0answers
71 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
32 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
37 views

establish matrix and inversion of a uppertriangularized matrix

Trying to create an uppertriangularized matrix with Poisson Distribution, find its inverse and multiply the inverse by a vector, i.e. ...
3
votes
1answer
96 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
votes
1answer
50 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
20 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
0
votes
1answer
65 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
64 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
1
vote
1answer
88 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
112 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
59 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
votes
0answers
44 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
vote
1answer
80 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
53 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
235 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
193 views

Strange NSolve failure [duplicate]

...
0
votes
0answers
23 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
votes
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
votes
1answer
90 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
126 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
0answers
38 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
votes
1answer
107 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
68 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
120 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
62 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
68 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
103 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
184 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
75 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
56 views

Find inverse of a complicated function

I am looking for an analytic inverse function for ...
1
vote
1answer
156 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
115 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
67 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
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
votes
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
votes
0answers
73 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
538 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
172 views

Finding the symbolic inverse of a function

Is there a way of inverting this function to obtain $r(\rho)$? ...
0
votes
0answers
35 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
38 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
197 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
50 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
78 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
vote
0answers
49 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
177 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
668 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
85 views

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

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