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.
189
questions
2
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2
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107
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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
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0
answers
66
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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
58
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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:.
...
4
votes
2
answers
131
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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
$$\color{blue}{\left(1-2 x^2\...
- 731
1
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1
answer
125
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1
vote
1
answer
137
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Newton method and Armijo-Goldstein
I need help with my project. I have three nonlinear systems and I need to write a code for Newton methods and Armijo-Goldstein and see the differences.
...
- 11
3
votes
5
answers
238
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Numerical solution of the inverse contour plot
I have a function $f(u,v)$ on some domain of $(u,v)$ and would like to find (numerically) the set of couples* $(u_0,v_0)$ s.t. $f(u_0,v_0)=0$, for instance (just and example to illustrate, in practice ...
- 729
8
votes
2
answers
390
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Asymptotic inverse function?
A paper I am reading defines a variable $\theta$ in terms of another variable $\phi$ as an expansion in $u$, where $u$ is understood to be small:
$$\theta=\phi-u^2\sin\phi+\mathcal{O}(u^4).$$
They ...
- 183
7
votes
1
answer
196
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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 ...
- 1,525
8
votes
4
answers
1k
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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
4
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
247
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
134
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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
126
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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.
...
- 1,554
1
vote
2
answers
78
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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.
- 447
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
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2
answers
176
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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?!!
...
- 447
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vote
1
answer
96
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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
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vote
1
answer
73
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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
116
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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
69
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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
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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
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0
answers
78
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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
...
- 63
0
votes
0
answers
112
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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
89
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
150
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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.
...
- 345
5
votes
3
answers
113
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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 ...
- 127
0
votes
0
answers
169
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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}$$
How to find the pre-image of the set if this function maps from real numbers to real numbers. What command would I use, to see the pre-image if the function would map from ...
- 241
2
votes
1
answer
80
views
Inverse of the matrix with several indices
Suppose I have a square matrix $A_{mn}$ where $m=(i,j)$ and $n=(k,l)$. For example, if $i,j,k,l=1..N$ the matrix is $N^2\times N^2$. For simplicity, let me generate it by
...
3
votes
2
answers
355
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How to get x value where area under curve is some number?
My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it?
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- 399
0
votes
1
answer
100
views
Getting inverse of x^2 with positive x
My goal it to get inverse of x^2 for positive x.
But the result shows always minus -Sqrt[y].
How to correct
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- 399
0
votes
1
answer
77
views
Condition at Inverse function
My goal is to get inverse of -Log[1 - x]. But the result shows conditional expression.
Could I know Why the condition -[Pi] <= Im[y] < [Pi] shows? There wass no assumption at variable y.
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- 399
1
vote
1
answer
156
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Asymptotic expansion at infinity given a branch cut
Basically, I have obtained the function $\rho (r)$ below as a result of integrating
$$\rho(r)=\int_{b_0}^{r}\frac{dx}{\sqrt{1-(b_{0}/x)^{1-q}}}$$
which results to
...
- 181
0
votes
0
answers
58
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How to return an inverse function based on parameters (for formal differentiation)
I want to return a different function for any given parameter in order to later calculate a value of the inverse of that function given the parameter as an indeterminate.
That is, I want, for each $d$,...
- 101
0
votes
2
answers
82
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Plot Parametric f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)
I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)
f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &...
- 143
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votes
0
answers
32
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Plotting Inverse Function - more complicated [duplicate]
I would like to plot the inverse of $f$ using the same method that was suggested to me in my previous question:
f[x_] := [(2 μ ArcTanh[(# μ)/Sqrt[-α + #^2 ν]] + μ Log[α + #^2 (μ^2 - ν)] - 2 Sqrt[ν]Log[...
- 143
5
votes
0
answers
79
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How to get an asymptotic of the real-valued branch of the inverse function?
Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
- 7,163
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1
answer
91
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InverseSeries slower than it should be
I am running into problems with InverseSeries taking far longer than it should. Given (for example)
$$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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1
answer
127
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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
723
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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
228
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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 ...
- 153
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.
...
- 487
3
votes
1
answer
102
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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
140
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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
0
votes
1
answer
40
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Plotting CDFs of transformed normal random variables
I'm using the following transformed random variables
...
- 153
0
votes
1
answer
81
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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
1
answer
178
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Numerically Inverting Characteristic Function with Inverse Fourier Transform
I'm trying to numerically invert this characteristic function:
...
- 427
1
vote
1
answer
171
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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?
...
- 13
3
votes
1
answer
181
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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?
