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.
194
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Invert a Pair of Density Plots
I am currently solving the following system of equations:
$$
\begin{bmatrix}
A(x,y) & B(x,y)\\
C(x,y) & D(x,y)
\end{bmatrix} \begin{bmatrix}
\alpha\\
\beta
\end{bmatrix} = \begin{...
- 21
0
votes
1
answer
51
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How do I invert this function?
I have the following function that I want to invert to use in further calculations, i.e. I need to be able to plug in the expression $r = r(p)$ in further calculations where $r$ goes over the range ...
- 131
1
vote
1
answer
66
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Mathematica isn't returning identity matrix when multiplying matrix by its inverse [closed]
I'm trying to solve a coupled system of ODE's. I'm trying to decouple my equations by diagonalizing a matrix. Here's my code:
...
- 53
5
votes
1
answer
282
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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 ...
- 1,856
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votes
0
answers
66
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How can I find an inverse function of solution from NDSolve?
I have the following code.
...
2
votes
2
answers
126
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Simplify inverse of function
This would be a noob question, but I need help simplifying the inverse of an expression
...
- 25
1
vote
0
answers
76
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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 ...
- 1,817
2
votes
1
answer
62
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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:.
...
5
votes
2
answers
137
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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\...
- 1,001
1
vote
1
answer
127
views
1
vote
1
answer
163
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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.
...
- 11
3
votes
5
answers
244
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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 ...
- 609
8
votes
2
answers
420
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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 ...
- 183
7
votes
1
answer
207
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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 ...
- 1,848
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 ...
- 181
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votes
2
answers
1k
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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 ...
2
votes
1
answer
314
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& ... &...
- 251
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votes
0
answers
153
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 ...
- 1
0
votes
0
answers
167
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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.
...
- 2,688
1
vote
2
answers
86
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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.
- 457
0
votes
1
answer
94
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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 ...
- 181
1
vote
2
answers
180
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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?!!
...
- 457
1
vote
1
answer
97
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 $\...
- 13
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 ...
- 21
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 ...
- 75
-1
votes
1
answer
76
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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 ...
- 153
0
votes
0
answers
62
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Inverse VS Reduce
I got a solution I want to get inverse but it is not working in Mathematica or Rubi:
...
- 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
...
- 73
0
votes
0
answers
119
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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
$...
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
<...
- 329
0
votes
0
answers
157
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.
...
- 417
5
votes
3
answers
114
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 ...
- 137
0
votes
0
answers
193
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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 ...
- 241
2
votes
1
answer
87
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
...
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?
...
- 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
...
- 648
0
votes
1
answer
85
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.
...
- 648
1
vote
1
answer
169
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
...
- 181
0
votes
0
answers
67
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 $d$,...
- 101
0
votes
2
answers
86
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]] &...
- 143
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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[...
- 143
5
votes
0
answers
84
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\...
- 7,293
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1
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96
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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
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 ...
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votes
1
answer
131
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?
- 23
12
votes
2
answers
759
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 ...
- 1,255
2
votes
0
answers
258
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 ...
- 173
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.
...
- 497
3
votes
1
answer
105
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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:
...
- 1,536
1
vote
2
answers
167
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 ...
- 203