Questions tagged [piecewise]
Questions about the Piecewise function, which is represented by different expressions for different ranges of values of its independent variable.
414
questions
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Summing `Piecewise` function with many cases efficiently
Schematics of the question: I have two piecewise functions $f_1$ and $f_2$ as
$$f_1 = \begin{cases}
\textrm{value 1}, & \textrm{case 1}, \\
\vdots & \vdots \\
\textrm{value 1024}, & \...
1
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2answers
84 views
Simplifying expressions with `Sign` functions to a single piecewise format
I have the following expression with many Sign functions:
...
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1answer
54 views
Single computation is fast, but 6 computations are extremely slow
I have an expression that involves many Sign functions. I want to expand this in the piecewise format.
My function is:
...
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1answer
49 views
3
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1answer
98 views
What is the scope of the bug where Piecewise breaks DSolve?
Bug introduced after 9.0.1, persisting through 12.3.1.
I have identified a bug in DSolve when differential equation includes a ...
0
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0answers
46 views
NDSolve with Piecewise function consideres some value inside Piecewise as Indeterninate
I'm solving a PDE, with one coefficient being piecewise. The issue appears to be that NDSolve somehow consideres piesewise boundary as ...
0
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1answer
48 views
Piecewise Function Definition
I am new to Mathematica, and I am unsure on how to do this.
I am working with piecewise function
$$
f_N(x) := \begin{cases} 1 & \text{if}\;\;x = j\sqrt{3}, \quad j=1,...,N \\
0 & \text{...
-1
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1answer
108 views
Did Mathematica make a mistake or was it me?
I'm having a little trouble with Mathematica. There are two expressions that should be equal over a given region. Each of which consists of three terms that should be equal individually:
term1 of ...
1
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3answers
181 views
How solve this nonlinear equations system by 12 unknowns?
We consider the following integral equation of mixed type:
$x[t]=\frac{t^4}{6} -\frac{t^3}{3} +t+\Sigma_{\mu=1}^2\int_{0}^t k_\mu[t,s]G_\mu[s,x[s]]ds
,0\leq t\leq 1 $ ; (1)
where
$k_1 [t, s] = s^3$...
1
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1answer
73 views
Maximization of piecewise function
I'm trying to maximize piecewise functions with parameters but haven't been able to do so. Here is a minimum example:
...
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1answer
55 views
How to plot a piece-wise function like this: f[x]=1 when -1<=x<=1, and f[x]=0 when x>1 or x<-1
I want to plot a piece-wise function like this:
f[x]=1 when -1<=x<=1, and f[x]=0 when <...
0
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0answers
33 views
Issue with Piecewise Parametric Plotting
I am trying to make a parametric plot of a piecewise function that is defined locally. For some odd reason, Mathematica will only plot the first two pieces of the piecewise function. If I plug in ...
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0answers
46 views
Different results from polar and cartesian forms of a function?
I am trying to write up and study the given function:
by the following Mathematica input (with N=5 and not infinity)
...
1
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1answer
46 views
NDSolve with embedded piecewise function for state-variable
Given ODE:
$\dot{x}=-2 e^{-x^2} x + U$
where:
$U=-u_{as}$
$u_{as} = \begin{cases} \frac{e}{\psi_+-e}, & \mbox{if } e\mbox{>=0} \\ \frac{e}{e-\psi_-}, & \mbox{if } e\mbox{<0} \end{cases}$
...
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5answers
85 views
Expressing $f(x)=-x \;\;\; -2\leq x \leq 0\\f(x)=x \;\;\; 0< x \leq 2\\f(x+4)=f(x)$ on Mathematica?
Can we express functions such as:
$$f(x)=-x \quad -2\leq x \leq 0\\f(x)=x \quad 0< x \leq 2\\f(x+4)=f(x)$$
On Mathematica? I tried something with piecewise functions but it didn't work. Namely, I ...
1
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1answer
53 views
Different kind of PlotStyle via Piecewise
I have a Piecewise. For vertical line I have to add Exclusions -> None.
...
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2answers
87 views
Piecewise function within a vectorplot
I'm trying to do a vector plot with some code that includes piecewise functions and I keep getting the following error:
Part::partw: Part 1 of {} does not exist.
Here is the code:
...
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1answer
86 views
Piecewise Numerical results used in NDsolve
I have a solution of LinearSolve. And there are four conditions in single period. Then I used Which to expand this solution.
<...
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0answers
63 views
Generate piecewise function using for loop
I want to specify a piecewise function by writing f[x_]:=Piecewise[piecewiseComponents], and use a loop to specify the components. I have tried
...
3
votes
1answer
62 views
Creating a dynamic piecewise plot
I'm trying to create a dynamic piecewise function. I can get 3 points, but after that, everything gets a bit complicated:
...
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0answers
29 views
Simplifying piecewise function containing symmetric equation terms
I have this large piecewise function that I'd like to simplify (click on image):
I see that two first piecewise equations contain terms that are either completely equal or symmetrical. I would like ...
1
vote
1answer
64 views
Solving ODE for emptying water tank, exclude branch with complex infinity
I'm trying to simulate a water tank. The dynamic of the system should be described by:
DSolve[{y'[x] == Piecewise[{{-Sqrt[y[x]], 0 < y[x]}}, 0.],
y[0] == 10}, y[x], x]
An infinite object ...
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1answer
63 views
Solving a complicated time-dependent function
I want to solve the following time-dependent system of equations:
...
2
votes
0answers
51 views
Piecewise PDE Over 3 Regions with Continuity Boundary Conditions
I am using Wolfram Language for the first time for my research and could really use some help! I am trying to find the analytical solution of a PDE which has piecewise constants and a piecewise input.
...
4
votes
1answer
132 views
Problem with NDSolve and piecewise functions: Failure computing Filippov continuation
I am trying to solve a first order differential equation using NDSolve. The differential equation is
...
1
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1answer
46 views
Plotting iterates of a piecewise defined map
This is a follow up question to the one I asked here. I’ve succeeded in figuring out how to plot the first image of my piecewise defined transformation $T: [-1,1]^2 \to [-1,1]^2$, but now I want to ...
1
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1answer
50 views
Plotting image of piecewise-defined transformation
I have a transformation $T : [-1,1]^2 \to [-1,1]^2$ that is piecewise defined in the following way:
\begin{align*}
T(x,y) &= \big(a(x-1)+1,\:\left(b-cx\right)(y-1)+1\big) \quad \textrm{if } y > ...
3
votes
2answers
176 views
Approximate the piecewise constant with a smooth function
Let us first define a two regions as follow :
inner=1;outer=2;
reg1 = Disk[{0, 0}, inner];
reg2 = Annulus[{0, 0}, {inner, outer}];
glass=1.5;air=1;
Now let's say I ...
2
votes
1answer
290 views
How to illustrate the optimal solution with kinked constraint?
I have a simple optimization problem with a linear, continuous constraint or a kinked constraint. The optimal solution is either a tangent point with f*<T or at the kink with f*=T. The standard ...
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0answers
59 views
Manipulate and Plot of Tangent Point in Optimization Problem with Kinked Constraint: Solve and PieceWise Problems
I'm trying to illustrate an optimization problem with a piecewise constraint creating a kink at the maximum value of T if n>0.
...
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0answers
24 views
Assumptions with piecewise problem?
I am trying to apply the assumpion of 0<s<1 throughout the calculation however the piecewise condition does not accept it automatically. Is there any way to avoid the manual choice of x>0.
...
2
votes
2answers
103 views
Benefits/pitfalls of defining function that is discontinuous at a point "explicitly" vs using piecewise?
For example, suppose I wanted to define a function, f that is $f(x)=x^2$ except at $x=1$, where $f(x)=5$
Two ways I can define this are
...
3
votes
1answer
87 views
How to convert a Piecewise function in a HeavisideTheta function?
I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
1
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1answer
53 views
Both Dsolve and NDsolve for a differential equation failed
I tried both Dsolve and NDsolve for the following differential equation, it failed:
It contains piecewise function
...
1
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2answers
73 views
How to plot HeavisideTheta with y=0.5 at x=0, and similar piecewise functions
How does one plot piecewise functions, with the ability to plot individual points along with open points to clearly show how values are defined at discontinuities?
Example:
Image Credit
with the ...
2
votes
0answers
57 views
How to get Integrate to determine units
In a similar fashion to the question asked here, I am having trouble trying to get Integrate to correctly determine the units of the integrand:
Here I have plugged in specific values into the general ...
0
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0answers
45 views
Piecewise function inside ProbabilityDistribution causing errors
I'm using a complicated Piecewise function to create a probability distribution and draw random points from it.
...
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2answers
78 views
How to take limits in Fourier series?
I have a Fourier series which produces an impulse train of period j+1. In principle, it is given by
...
1
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1answer
110 views
Continuity and derivability of a multivariable function at a specific point
I have this function:
f = Sqrt(Abs(x^2 - x*y))
So, how can I prove that it is derivable and/or continue in a point, like (0,0)?
1
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1answer
30 views
Plotting an iterated piecewise function with endogenous nodes
I am trying to plot a piecewise function that I can define recursively, where the nodes are endogenous as well. Basically, $f(l)=a^{t}$ when $l \in \left( \frac{\mu}{\alpha^{t-1}(1-\alpha)+\mu(1-\...
0
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1answer
58 views
Error in drawing a Piecewise function!
I want to plot the piecewise function (FP), which is define as:
$$FP=\cases{1,&$\text{Eta}<J$\\
\frac{1-\left| \text{Gam}\right| }{2}, &$\text{Eta}=J$\\
\frac{\left| \text{Gam}*J\...
2
votes
1answer
148 views
Limit of multivariate piecewise function
Let's say we have a multivariate piecewise function
f[x1_,x2_]:=Piecewise[{{Sin[x1]/x1,x1>x2},{Sin[x2]/x2,x1<=x2}}]
Now we want to determine the limit in f(0,...
1
vote
1answer
64 views
How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables
I have a function f which looks similar to this :
f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}]
and ...
0
votes
1answer
74 views
How do I introduce an assumption when defining a piecewise function?
Define m as an integer. I want to specify a Piecewise function f[x,n] that takes value ...
1
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0answers
39 views
Find edges of a piecewise curve
I have a continuous function f[x], and I want to calculate the coordinates of the discontinuities in Round[f[x]]. My code needs ...
1
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1answer
56 views
Should be a Piecewise function, a ConditionalExpression or Indeterminate, but it is a number
I apologize in advance for the lack of focus of my question. Consider the function:
f[x_, y_] := x/(x + y);
f[0,0] evaluates to ...
2
votes
0answers
111 views
How do I create a piecewise function using Do[] or While[]?
The following non-linear circuit is an uncontrolled three-phase full-wave 6-pulse rectifier. The inputs are $v_{an}(t) = V_m \sin (\omega t)$, $v_{bn}(t) = V_m \sin (\omega t-120°)$ and $v_{cn}(t) = ...
2
votes
2answers
231 views
Finding the maximum of a piecewise function
I have the following piecewise function of the variable $e_f$:
$$g(a,b,c,w,F,e_h,e_f)=\begin{cases}
\frac{(c-a e_f) (e_f (4e_f w-a)+c)}{8 b e_f^2} & \left(e_f=e_h\land e_f>\frac{c}{a}\...
5
votes
1answer
71 views
Piecewise function not evaluating properly
I have a simple Piecewise function that defines a square pulse:
...
1
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1answer
62 views
ParametricNDSolve "delayed time" error message
Issue reported to Wolfram, Inc as a possible bug in Version 12.1; CASE:4554034.
When trying to solve a system of delay-differential equations with ParametricNDSolve...
