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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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FourierTransform and InverseFourierTransform are not inverses when using non-default FourierParameters

FourierTransform and InverseFourierTransform are inverses of each other when using the default ...
tparker's user avatar
  • 1,856
0 votes
0 answers
65 views

How can I find an inverse function of solution from NDSolve?

I have the following code. ...
Jules Alvarez's user avatar
2 votes
2 answers
120 views

Simplify inverse of function

This would be a noob question, but I need help simplifying the inverse of an expression ...
Zain Ahmad's user avatar
1 vote
0 answers
75 views

How to accelerate Inverse[] for positive definite matrices symbolically?

I am trying to construct a positive definite matrix based on the multiquadric radial basis function (RBF) for a set of thirteen points symbolically in order to later approximate the Laplacian operator ...
Faz's user avatar
  • 1,817
2 votes
1 answer
60 views

InverseFourier, Time response from the pressure over frequency

the problem I'm trying to solve is much more involved, that is I'm trying to get the Time Response for an Impulse Input for a loudspeaker starting from the pressure it generates over the frequency:. ...
Teodoro Marinucci's user avatar
5 votes
2 answers
132 views

Looking for the asymptotics of an asymptotics

I am trying to polish my second answer to this question in Mathematics Stack Exchange. The problem is to find the asymptotics of $t$, solution of the implicit equation $$\color{blue}{\left(1-2 x^2\...
Claude Leibovici's user avatar
1 vote
1 answer
125 views

Trouble finding inverse of a function

I have the following Mathematica code: ...
codebpr's user avatar
  • 2,253
1 vote
1 answer
157 views

Newton method and Armijo-Goldstein

I need help with my project. I have three nonlinear systems and I need to write a code for Newton methods and Armijo-Goldstein and see the differences. ...
lidiadesign's user avatar
3 votes
5 answers
243 views

Numerical solution of the inverse contour plot

I have a function $f(u,v)$ on some domain of $(u,v)$ and would like to find (numerically) the set of couples* $(u_0,v_0)$ s.t. $f(u_0,v_0)=0$, for instance (just and example to illustrate, in practice ...
Daniel Castro's user avatar
8 votes
2 answers
406 views

Asymptotic inverse function?

A paper I am reading defines a variable $\theta$ in terms of another variable $\phi$ as an expansion in $u$, where $u$ is understood to be small: $$\theta=\phi-u^2\sin\phi+\mathcal{O}(u^4).$$ They ...
user984949's user avatar
7 votes
1 answer
201 views

How to get more terms with the Series[] expansion of InverseErf[x] around x=1?

The inverse error function, which is given by InverseErf[x], is quite important in statistics as it gives the confidence levels around a 1D Gaussian, for example ...
Hans Olo's user avatar
  • 1,843
8 votes
4 answers
1k views

How can I find the inverse of an interpolating function?

I am numerically solving the coupled differential equations (for $t[\tau]$ and $r[\tau]$) below. Mathematica outputs two interpolating functions as solutions. I would like to invert one of these ...
Aiden's user avatar
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4 votes
2 answers
1k views

Inverse function of y = x + (0.022 - x) ^ 1.414?

I'm a software engineer with math classes through differential equations about 15 years in my past, and I've gotten stuck trying to invert an equation. The equation: $y = x + (0.022 - x)^{1.414}$. In ...
James O'Leary's user avatar
2 votes
1 answer
293 views

Invert a generic n x n matrix

I want to invert a generic n x n matrix. Is it possible to do this with Mathematica? Consider, as a minimal example, the $n\times n$ matrix: \begin{bmatrix}1n&0&...&0\\0&2n& ... &...
black's user avatar
  • 251
0 votes
0 answers
144 views

Variation with respect to inverse metric in a Lagrangian density

I am trying to vary the following Lagrangian density with respect to the inverse metric appearing in the equation, but I am having trouble with how to write the right code in Mathematica. I have ...
liza's user avatar
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0 votes
0 answers
153 views

Inverting function variables

The original equation is a function of x. However, I want to invert the function and get an expression of x in terms of y. ...
user444's user avatar
  • 2,446
1 vote
2 answers
82 views

Inverse Function for an example

I have this funtion i would like to calculate the inverse Inverse[Sqrt[1 - Cosh[2 t] + a Sinh[2 t]]] a is positive number.
Felipe Dura's user avatar
0 votes
1 answer
94 views

InverseFunction fails at some parameter

Currently, I am faced with the difficulty of evaluating the inverse of the function below for certain negative decimal values of the parameter q. Specifically for ...
user583893's user avatar
1 vote
2 answers
179 views

Plot the solution and Inverse as well

I used this code to solve an equation and now I would like to plot the solution with its inverse. I can't get some figures?!! ...
Felipe Dura's user avatar
1 vote
1 answer
96 views

Find an inverse function [closed]

this is probably a silly question, but how do I find an inverse function of y$ = a - b \cdot \text{ln}(1-\frac{x}{c})$? I tried doing $\text{exp()}$ on both sides but I don't know how to cope with $\...
niewadzkak's user avatar
1 vote
1 answer
74 views

Selecting the positive solution only

This my first problem on Mathematica and I'm working on version 13.0, and I want to get the inverse z transform for an equation, It works fine but it gives me the solution in the positive and negative ...
Ahmed Redwan's user avatar
2 votes
2 answers
118 views

ParametricPlot inside of ParametricPlot [closed]

I don't know why the following is not working! The code has a function y[x] then I have g[t] then I want to plot ...
M.S MD's user avatar
  • 75
-1 votes
1 answer
73 views

Integrate and InverseFunction

I solve an easy example to check that Mathematica can understand the difference between ArcTan and ArcTanh but as you see here I can't get Arctanh??!! Even I don't know why the inverse function is not ...
Mathecis's user avatar
  • 153
0 votes
0 answers
62 views

Inverse VS Reduce

I got a solution I want to get inverse but it is not working in Mathematica or Rubi: ...
Mathecis's user avatar
  • 153
0 votes
0 answers
80 views

A case for matrix multiplication (a.b).c unequal to a.(b.c) in mathematica 12.0.0.0, why?

The motivation of my calculation is to get the inverse for the following matrix ...
Rui Yu's user avatar
  • 63
0 votes
0 answers
118 views

Bayesian Linear regression (Ill-posed problem)

I want to use the ResourceFunction["BayesianLinearRegression"] from Wolfram function repository. With this function I want to solve the ill-posed problem $...
Michelitus's user avatar
1 vote
0 answers
92 views

Fail to inverse the Piecewise function embedded in a NDSolveValue

I am trying to estimate a function consisting of a Piecewise function that included in a FEM solver. I firstly developed my mesh for the FEM model based on @Tim Laska's work. The code is shown as <...
LingLong's user avatar
  • 329
0 votes
0 answers
154 views

Inverse Functions

I'm new to Mathematica, so I fell sorry for posting relativily naive/dumb questions. I have these two functions that represent X coordinate distortion of an SLA 3D printer. ...
Anton's user avatar
  • 345
5 votes
3 answers
113 views

Does Solve make internally assumptions about the domain of the variables?

I recently tried to invert the innocent looking function $\frac{x}{(1+\sqrt{1-x})^2}$ So I tried the command Solve[x/(1 + Sqrt[1 - x])^2 == y, x], which ...
Rohbar's user avatar
  • 137
0 votes
0 answers
189 views

Command to find the pre-image of a set that is mapped to by the function $f(x)=3^x \mod{17}$

$$f(x)=3^x \mod{17}$$ How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
VLC's user avatar
  • 241
2 votes
1 answer
84 views

Inverse of the matrix with several indices

Suppose I have a square matrix $A_{mn}$ where $m=(i,j)$ and $n=(k,l)$. For example, if $i,j,k,l=1..N$ the matrix is $N^2\times N^2$. For simplicity, let me generate it by ...
Alexander Nikolaenko's user avatar
3 votes
2 answers
362 views

How to get x value where area under curve is some number?

My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it? ...
Soon's user avatar
  • 648
0 votes
1 answer
102 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 ...
Soon's user avatar
  • 648
0 votes
1 answer
84 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. ...
Soon's user avatar
  • 648
1 vote
1 answer
166 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 ...
user583893's user avatar
0 votes
0 answers
64 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 $d$,...
NL1992's user avatar
  • 101
0 votes
2 answers
85 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]] &...
Armin Sharafi's user avatar
0 votes
0 answers
32 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[...
Armin Sharafi's user avatar
5 votes
0 answers
82 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\...
Vladimir Reshetnikov's user avatar
0 votes
1 answer
95 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 ...
user75644's user avatar
0 votes
0 answers
46 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 ...
yarchik's user avatar
  • 18.7k
-1 votes
1 answer
130 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?
BioTechGreek's user avatar
12 votes
2 answers
744 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 ...
Quit007's user avatar
  • 1,255
2 votes
0 answers
247 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 ...
Luqman Saleem's user avatar
2 votes
0 answers
42 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. ...
Z Ming Ma's user avatar
  • 497
3 votes
1 answer
104 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: ...
GarouDan's user avatar
  • 1,536
1 vote
2 answers
160 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 ...
Andrew Yuan's user avatar
0 votes
1 answer
41 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
Harto Saarinen's user avatar
0 votes
1 answer
82 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. ...
Polixeni Vliora's user avatar
2 votes
1 answer
188 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
PiE's user avatar
  • 437