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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30
votes
3answers
5k views

How to symbolically do matrix “Block Inversion”?

Consider a block (partitioned) matrix matrix = ArrayFlatten[{{a, b}, {c, d}}] where, a, b,...
28
votes
3answers
1k views

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

Sometimes, to find the inverse of a matrix is a labor-consuming task, or even "disgusting", especially when the matrix is "ill". It is said, e.g. in Julia, that the left/right division operation is ...
12
votes
1answer
215 views

Is there a built-in function to inverse Thread?

Namely, while Thread @ f[{a, b}, {x, y}] gives {f[a, x], f[b, y]} the InverseThread (if it existed) should reverse the ...
12
votes
2answers
1k views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
11
votes
2answers
8k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
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 ...
8
votes
0answers
1k views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
7
votes
3answers
827 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
7
votes
2answers
6k views

How to invert an integral equation

There have been numerous times when I've needed to invert an integral equation, i.e. I have something like $$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$ for arbitrary functions $g_1$ and $g_2$, and ...
7
votes
2answers
699 views

How to reverse irreversible function in Mathematica?

How to reverse formula $y(x)=x (\frac{1}{sin \frac{\pi x}{2}})^\alpha$ i.e. express it as $x = x(y)$ in Mathematica? I did this way ...
7
votes
1answer
187 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
6
votes
1answer
2k views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
6
votes
3answers
646 views

How to tell Mathematica to get the real-only inverse function?

The problem I have is that Mathematica seems to play better with complex numbers so that the result of N[InverseFunction[Function[x,x^3]][-1]] is ...
6
votes
1answer
1k views

InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
6
votes
1answer
117 views

InverseFunction oddity

InverseFunction[ConditionalExpression[#, 0 <= # <= 1] &] InverseFunction[ConditionalExpression[#, -1 <= # <= 1] &] The first line produces ...
5
votes
2answers
17k views

How do I get the inverse of a homogeneous transformation matrix?

I want to get the inverse of this homogeneous transformation matrix: iab = { {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 3}, {0, 0, 0, 1} } using the ...
5
votes
3answers
388 views

Easiest way to have an approximation of binary entropy inverse

I call $H_2$ the function $H_2(x) = -x \ln(x)-(1-x) \ln(1-x)$ It is the binary entropy. I call $g(x)=H_2((1+x)/2)$ This last function is bijective on $[0;1]$. I would like to have an inverse, or ...
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: ...
5
votes
2answers
581 views

How can I get the inverse of my function?

The original function is $$f=\frac{1}{e^{\frac{\phi }{k t}}-1}-\frac{m+1}{e^{\frac{(m+1) \phi }{k t}}-1}$$ I want to express $e^{\frac{\phi }{k t}}$ about $m$ and $f$, so I tried: ...
5
votes
1answer
438 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; \...
5
votes
0answers
460 views

Inverse of piecewise function with pieces invertible on specific domain

I have piecewise continuous function defined below: f=Piecewise[{ {15 + 1/6*(# - 3), # <= 27}, {# - 12 + 4 * Exp[-5/24*(#-27)], 27 < #} }]; This ...
5
votes
0answers
640 views

How to invert a matrix with 100 trillion elements?

I have a $10^{7}\times 10^{7}$ matrix with the following properties: it is sparse it is gamma-5 it is almost Hermitian. If $M$ is the matrix we are trying to invert, we know $M=A M^{\dagger} A$ ...
4
votes
2answers
5k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
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 ...
4
votes
2answers
228 views

Inverse of LogIntegral

I wanted the inverse logarithmic intgral, so I typed InverseFunction[LogIntegral] and received the expected symbolic answer. But when I try to integrate it or ...
4
votes
3answers
2k views

Changing variables algebraically

Suppose one has two functions, $y(x)$ and $z(x)$, and one seeks to obtain $y(z)$ by substituting $x(z)$ into $y(x)$. Can this be done in a single step? Or must $z(x)$ first be inverted independently? ...
4
votes
1answer
121 views

Function inversion [closed]

I have an expression of this kind ...
4
votes
1answer
237 views

Help with PseudoInverse

I am trying to (pseudo)solve a linear system $Ax=y$. I have a matrix A, and 2 vectors x and y...
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 \...
3
votes
3answers
235 views

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

I need to invert a function. I want to isolate the x basically. By the looks of the graphic I plotted, the function seems to be invertible, however when I call <...
3
votes
5answers
3k views

Plotting the solutions to a transcendental equation

I am trying, to no avail, to use Mathematica to produce a plot in (x, y)-space of the solutions to the equation Cos[Sqrt[y]] + Sin[Sqrt[y]]/Sqrt[y] == Cos[x] ...
3
votes
4answers
244 views

What is the inverse of the Position function?

What is the inverse of the Position? I have an array which contains the positions of elements and I want a function which returns an List which contains 1 where ...
3
votes
3answers
1k views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
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 ...
3
votes
2answers
208 views

Inverse CDF of non-builtin probability distribution

I'm trying to get the inverse CDF of the Raised Cosine probability distribution function. It has parameters $\mu$ and $s$, support $x \in [\mu - s, \mu + s]$, PDF ...
3
votes
2answers
193 views

Strange NSolve failure [duplicate]

...
3
votes
2answers
302 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
3
votes
1answer
1k views

How to get the determinant and inverse of a large sparse symmetric matrix?

For example, the following is a $12\times 12$ symmetric matrix. Det and Inverse take too much time and don't even work on my ...
3
votes
2answers
447 views

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

I am trying to solve this DE: DSolve[{r'[t] == r[t]^2/3 (1 - r[t]), r[0] == 2}, r[t], t] // Simplify For which I get the solution ...
3
votes
1answer
857 views

Find an inverse matrix, regarding a parameter as real

I have the matrix ...
3
votes
1answer
176 views

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

Integrate $\int\sin^{-1}\frac{2x}{1+x^2}.dx$ $$\sin^{-1}\frac{2x}{1+x^2}=\begin{cases}2\tan^{-1}x&\text{ if }|x|\leq{1}\\\pi-2\tan^{-1}x&\text{ if }|x|>{1}&\text{ and }x>0\\-\pi-2\...
3
votes
1answer
2k views

Invert Colors Stylesheet White on Black

There have been a couple studies done that showed that white text on a black background increase recall of data. Although this is certainly debatable how might I invert the colors of Notebook font ...
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: ...
3
votes
1answer
234 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
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?
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 ...
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): $$ \...
3
votes
2answers
142 views

no Plot showed for an Inverse function

The short code is below, but no plot is produced. Are there any errors in my code? Thanks! ...
3
votes
1answer
88 views

Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
3
votes
1answer
550 views

Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f = Piecewise[{{Exp[-β * (-Log[#])^α], 0 < # <= 1}}, #]& with ...