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22 votes

What are the counterparts in Wolfram to left and right division of a matrix in other programming language, e.g. Julia and MATLAB?

I just stumbled upon it! At least when storing the factorization in a LinearSolveFunction object, we can use it for the transposed solve by supplying a further (not ...
Henrik Schumacher's user avatar
21 votes

What are the counterparts in Wolfram to left and right division of a matrix in other programming language, e.g. Julia and MATLAB?

The documentation for MATLAB's mrdivide states that The operators / and \ are related to each other by the equation B/A = (A'\B')' In light of this we may ...
C. E.'s user avatar
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14 votes
Accepted

Is there a built-in function to inverse Thread?

Let's make this a little more challenging: ...
Mr.Wizard's user avatar
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13 votes

What are the counterparts in Wolfram to left and right division of a matrix in other programming language, e.g. Julia and MATLAB?

Henrik has already written on the undocumented second argument of a LinearSolveFunction[], so let me just put out a short demo wrapper showing how to use the built-...
J. M.'s missing motivation's user avatar
13 votes

How can I find the inverse of an interpolating function?

...
Bob Hanlon's user avatar
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12 votes

Why doesn't Lambert function (ProductLog) simplify?

The identity does not hold for x < -1: Plot[ProductLog[x*Exp[x]], {x, -5, 5}] ...
Mr.Wizard's user avatar
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11 votes

Can I use Compile to speed up InverseCDF?

This is a little long for a comment, beside which it points out an unexpected difference probably resulting from subsystems evolving independently at different times. In addition to Henrik's comment ...
Michael E2's user avatar
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11 votes
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How to get more terms with the Series[] expansion of InverseErf[x] around x=1?

This is not strictly speaking an answer, but I thought I provide code that can be used to generate the kind of expansion that OP mentions. Perhaps it is useful for other people here. I use $y$ as an ...
user293787's user avatar
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10 votes
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Inverse CDF of non-builtin probability distribution

Clear[RaisedCosineDistribution] As with built-in distributions, you need to include the parameters in the distribution definition, and the constraints on the ...
Bob Hanlon's user avatar
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10 votes
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What is the inverse of the Position function?

I don't know that you can do it in a single command. But it's easy enough to do in two. Say your list is list={2,1,4}; ...
bill s's user avatar
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9 votes
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InverseFunction fails to invert $e^{-x/2}-e^{x/2}$

InverseFunction operates on an abstract function, yielding an abstract, anonymous function. g[x] is not a function, but a ...
John Doty's user avatar
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9 votes

Can I use Compile to speed up InverseCDF?

Let me demonstrate two approaches in this answer. P.J. Acklam (WayBack archive of his page) devised a not-too-long method to approximate the quantile of the Gaussian distribution, with absolute ...
J. M.'s missing motivation's user avatar
9 votes

InverseRadon behaves differently from iradon of MATLAB

As it explained in tutorials functions Radon and InverseRadon are supposed to be used with images only and not with arbitrary ...
Alex Trounev's user avatar
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9 votes

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

Instead of worrying about an analytical solution, it can be done numerically by an interpolating function: ...
Daniel Huber's user avatar
9 votes
Accepted

Asymptotic inverse function?

...
Roman's user avatar
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8 votes

What is the inverse of the Position function?

Normal@SparseArray[Thread[{1, 5} -> 1]] (* {1, 0, 0, 0, 1} *) Normal@SparseArray[Thread[{2, 1, 4} -> 1]] (* {1, 1, 0, 1} *)
Michael E2's user avatar
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8 votes

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

$Version (* "13.1.0 for Mac OS X x86 (64-bit) (June 16, 2022)" *) Clear["Global`*"] Note that 0.022 is <...
Bob Hanlon's user avatar
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7 votes
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Easiest way to have an approximation of binary entropy inverse

I like to use NDSolve to find inverses when symbolic methods won't work. The ODE corresponding to the inverse of a function g ...
Carl Woll's user avatar
  • 131k
7 votes

Evaluate the indefinite integral $\int\sin^{-1}\left(\frac{2x}{1+x^2}\right)\ dx$

...
chyanog's user avatar
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7 votes
Accepted

Can I use Compile to speed up InverseCDF?

Out of curiosity, I tried to write my own version of inverse CDF for the normal distribution. I employ a qualitative approximation of the inverse CDF as initial guess and apply Newton iterations with ...
Henrik Schumacher's user avatar
7 votes

Plotting the inverse function of a complicated function

Inverse functions can be plotted using ParametricPlot or ParametricPlot3D ...
Bob Hanlon's user avatar
  • 160k
7 votes

InverseRadon behaves differently from iradon of MATLAB

As this has come up in the comments, somebody might be interested at least in the discrete version as described here: discrete radon transform: getRadonLinesComped[] is the (compiled) function that ...
Quit007's user avatar
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7 votes
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How to get x value where area under curve is some number?

Your integral has a closed form solution, so take that and give it a name: g[x_] := 1/3 E^(-x/2) Sqrt[2/\[Pi]] Sqrt[x] (3 + x) + Erfc[Sqrt[x]/Sqrt[2]] One way to ...
bill s's user avatar
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7 votes

Asymptotic inverse function?

@Roman's answer is exactly what you asked for, but as a check, here is a second answer using Bessel's series expansion for the solution of the Kepler equation: ...
user293787's user avatar
  • 11.9k
7 votes

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

Mathematica doesn't handle Sign[] correctly. With the substitution Sign[omega]->2 HeavisideTheta[omega]-1 the inverse ...
Ulrich Neumann's user avatar
6 votes

Where is this difference between the solutions of DSolve and NDSolve coming from?

It could also be view as a precision problem: ...
Michael E2's user avatar
  • 237k
6 votes
Accepted

Where is this difference between the solutions of DSolve and NDSolve coming from?

Indeed, the numerical inversion of the DSolve solution, ...
bbgodfrey's user avatar
  • 61.7k
6 votes

Function inversion

define a function of two variables, ...
george2079's user avatar
6 votes

Why doesn't Lambert function (ProductLog) simplify?

PowerExpand[ProductLog[x Exp[x]]] x This assumes $x\ge0$
Feyre's user avatar
  • 8,617
6 votes

InverseFunction fails to invert $e^{-x/2}-e^{x/2}$

Your function g is equal to -2 Sinh[x/2]: ...
Henrik Schumacher's user avatar

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