Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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1answer
74 views

Anonymous function in MATLAB

I want to write the following anonymous function in MATLAB. I have a piecewise function. I want to turn this into a single expression. How can this be accomplished in MATLAB ? $$f(x,t) = \begin{cases}...
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0answers
73 views

If dot product is commutative, why does MATLAB give different answers?

Why does the dot() function in MATLAB return different expressions based on the order in which I pass vectors?
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1answer
52 views

How I can derive the Neuman boundary condition of this system of hyperbolic equations in 1D?

I would like to research the Neuman boundary that can verify the following problem $\begin{aligned} &\text { (} P \text { )}\left\{\begin{array}{l} \frac{\partial U}{\partial t}(x, t)+A \frac{\...
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0answers
19 views

3d surface image for given datasets

I have some data that looks like as follows x-cor y-cor z-cor 0.02 0.0251 0.02 0.01 0.0257 0.02 0.014 0.02 0.03 0.023 0.003 0.05 0.013 0.002 0.77 .................... .................... ...
2
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1answer
84 views

Rank of a double-precision augmented matrix

Let $A$ be a matrix with real entries, and let $A_+$ be $A$ augmented by a single column. From linear algebra we know \begin{equation} \operatorname{rank}(A_+) = \operatorname{rank}(A) \hspace{10pt} ...
3
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0answers
75 views

Numerical Issues with DDE from SEIRU$\delta$ model

I'm new in this community. I moved this question from Math community. I'm reading the following article Article Here and my target is to replicate the results for a project. SEIRU Model: I obtained ...
1
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2answers
92 views

Coding up a toy model for gradient-descent — what step size to choose?

I'm coding up a simple model for gradient-descent, and using it to minimize some simple, deterministic functions. What step size could I choose that's simple enough for me to get started with? Should ...
1
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1answer
77 views

If analytically, a function is not differentiable at a point, does it make sense to write a finite difference code for the function at that point?

What would happen if I wrote a finite-difference code evaluated at a point where the function isn't differentiable analytically? I'm trying to think analytically vs numerically. Thanks,
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1answer
86 views

Coding up Newton's method for a mapping from R^2 to R — the Jacobian wouldn't be invertible

I'm trying to code up in Matlab a multivariable Newton's method, for a mapping from R^2 to R, but the Jacobian would be a 2x1 matrix, not square, so it wouldn't be invertible. Does this mean that ...
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0answers
32 views

How to describe function convergence and function tolerance for numerical root-finding?

I'm currently doing some practice problems on root-finding and am writing up some notes / comments on my code. In my solver code, if my function value is below the tolerance that I've set, should I ...
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0answers
75 views

How can I practice multivariable root-finding?

Recently, I've been reading up on various root-finding / optimization algorithms such as the Levenberg-Marquardt method, Gauss-Newton, Conjugate Gradient, trust-region and trust-region-dogleg. I've ...
2
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2answers
61 views

In a dynamical system, what might be a good reason why periodicity in an object's velocities is important?

I'm studying periodic motions in a dynamical system and, as a newbie, I narrowly think of an object's periodicity in its spatial x-y coordinates, but what might be a good reason why the existence of ...
2
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1answer
83 views

System of moving, non-colliding particles in 1D

I have a system of ODEs for functions $f_i(t)$. At each time $t$, $f_i(t)$ is the position of particle $i$. The functions $f_i$ have a monotonicity property: at all times $0 < f_1(t) < f_2(t) &...
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1answer
115 views

Interpreting multivariable root-finding results from Matlab's fsolve algorithm

Edit: So I was able to get the same value of r that's given, when coding up the sum of squares of function values directly in the script file, rather than on the Command Window. So, maybe there's a ...
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1answer
137 views

Writing a Matlab function after calling the ode45 solver

After using ode45 to solve a set of ODEs, I want to write a Matlab function to take the initial conditions x_0 as inputs and gives the final state x_1 at time T as ...
1
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1answer
289 views

Problems with manufactured solutions for 1D inviscid burgers' equation

I'm having an issue with the easiest example of a nonlinear 1D PDE, the (inviscid) burgers' equation: $u_t + uu_x = 0,~~(1)$ which can be rewritten as some convection equation $u_t + f(u)_x = 0$ with ...
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0answers
61 views

ode15s command for coupled PDEs

I am trying to solve the coupled PDE system given here-Solve System of PDEs, using the method of lines and the ode15s command. Referring to variables $u1$ and $u2$ as $u$ and $v$ respectively, I have ...
2
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2answers
744 views

Generate random smooth 2D closed curves

I would like to know how can I generate a collection of random 2D closed smooth curves. I thought about generating a random 3D surface with random peaks, and then intersecting the Z=0 plane with it, ...
3
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1answer
519 views

Solving the heat diffusion equation with source term

I am trying to solve the 1-D heat equation numerically with a variable source term. The system is basically a tank containing styrene in which it polymerizes to liberate heat. I have assumed that the ...
1
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1answer
63 views

How to optimize nuclear norm subject to positive semidefinite constraints?

For finite dimensional symmetric positive semidefinite matrices $A$ and $B$, I would like to solve \begin{align}&\min |X - A|_1 \\ &\text{subject to}\\ &X \preceq B \\ &0 \preceq X\...
1
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1answer
61 views

How to effectively find a starting point solving a non-linear equation?

I have the following equation (the Kurz-Giovanola-Trivedi model [1]) $$ v^2 \frac{\pi^2 \Gamma}{P^2 D^2} + v \frac{mC_0(1-k)\xi}{D[1-(1-k)Iv(P)]} + G = 0, $$ where $Iv(P)=P \cdot \exp(P) \cdot E(P)$, $...
3
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1answer
163 views

Scaling/Performance of Matlab's svds function (Lanczos bidiagonalization)

I have a simple Matlab script which aims to compute $k$ singular values of a matrix $A$. $A$ is a random dense square matrix of size $5000\times5000$, with 100 of its singular values constrained to ...
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2answers
81 views

How do I speed up this function evaluation in matlab?

Half the run time of my code right now is evaluating a big function over many, many points, it takes maybe about 20 seconds per evaluation The function consists of a bunch of simple operations that ...
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2answers
67 views

Uniaxial stretching solution not uniform in FEM code

I am trapped here for a long time. I wrote a toy Matlab FEM code. I want to run the follow simulation. Mesh Suppose we have a cube, and we divide it into subcube along $x,y,z$ axis, then each subcube ...
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1answer
208 views

Matlab - Fast Computation of Truncated SVD / PCA

I'm working with a Matlab codebase wherein I'm attempting to solve A*c = b by approximating the (square) matrix A with its ...
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0answers
60 views

Non-linear differential equation

I have this equation $$y\left(\dot y^2+1\right)=m + \Lambda y^3,$$ where $\Lambda=1.1\cdot 10^{-52} $ (Cosmological constant). I want to get the graph of the solution of this equation (2-parametric ...
2
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1answer
317 views

Solution of the linear system using Sherman-Morrison formula for 1000000x1000000 (7450.6GB) matrix using MATLAB

Let $n = 10^6.$ Let $A \in \mathbb{R}^{n\times n} $ be the lower triangular matrix having 1's on and below the main diagonal. We want to solve the following linear system: $$ (A + uv^T)x = b$$ by the ...
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1answer
264 views

Bode diagram without bode() function

Is there any way to make a bode plot without using the MATLAB/GNU Octave function bode()? As an example, here is a function I am working on: $$H(s) = \frac{1}{2s^...
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1answer
125 views

Plotting the difference between an exponential and its Taylor expansion as a function of number of terms?

I'm terribly green, please forgive me. I need to plot the difference between a chosen calculated Taylor expansion $e^x=1+x+\frac {x^2}{2!}+\frac {x^3}{3!}+\frac {x^4}{4!}+\frac {x^5}{5!}$... and the ...
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0answers
153 views

Two-dimensional modelling of a flate-plate reactor

I am trying to simulate the unsteady pollutant concentration along the reactor by solving the 2nd order PDE below with the stated BC and IC. which method is appropriate to solve convection-diffusion-...
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2answers
94 views

Rewriting matrix multiplication

I have a matrix multiplication in Matlab that goes as follows $$\hat{W} = N W N^{T},$$ where $^T$ means a transposition. $N$ is an incidence matrix with the dimensions m x n and W = diag(G), where G ...
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0answers
34 views

Simulating the response of nonlinear system with stiff differential equations

I want to simulate the response of a nonlinear system given in the following form: $$ \dot{x_1} = f_1(\bar{x_1})+g_1(\bar{x_1})x_2, \ x_1(0) = 0.2 $$ $$ \dot{x_2} = f_2(\bar{x_2})+g_2(\bar{x_2})x_3, \...
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1answer
71 views

Floating Point error when computing Binomial Distribution Probability

I have been given a binomial distribution: $$B(m+n;n,p)=\frac{(m+n)!}{m!n!}p^mq^n.$$ Here $m = 10^3$, $n=10^2$, $p=10^{-2}$, $q=1-p.$ I'm using MATLAB to compute log $B(m+n;n,p)$ and store the value ...
2
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2answers
99 views

Solution of symmeric/non-symmetric linear system

I would like to understand what happens in the following: I have a really simple Poisson problem, in 1D, with $u_0 = u_N = 0$. I assembled the stiffness matrix and the right-hand side, and I applied ...
0
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1answer
53 views

MATLAB ode45 doesn't start at initial conditions

I wrote a code in MATLAB to solve a system of differential equations, but my solution doesn't seem to take into consideration the initial conditions I specified. I am not sure how to interpret this ...
0
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1answer
62 views

Efficient way to store array where elements are added and removed frequently

At any point in time I have a list of N points, points will be added and removed making the number of total points change over time. If I just use an array to store this information, I'm concerned ...
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0answers
44 views

Finding isocontour lines, populating points on said lines (in MATLAB)

I'm trying to extract data from a potential field. I have an example code of a potential field, using meshgrid in MATLAB. I've pasted the code below. What I'd like to do next is 'convert' this field ...
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0answers
38 views

How does Block-diagonal Schur factorization in Matlab works?

Can anyone explain how does the bdschur command of Matlab works? And how should the CONDMAX and ...
1
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1answer
88 views

Efficient Arbitrary Order Finite Differences in 1D

I am implementing on Matlab a high-order finite differences scheme to approximate the first derivative of $f(x_i)$ given $x = [x(1), x(2),..., x(i),..., x(n)]$ and $f = [f(x(1)),..,f(x(n))]$ with $x$ ...
1
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1answer
52 views

Using Axis Equal for Matlab simulation plots of the SIR model gives very flat solution curves

My professor taught us to always use the Matlab command axis equal for our simulation data plots - for all of our homework assignments. However, in studying the ...
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0answers
59 views

Modelling of Stefan Maxwell equation

I am trying to solve Maxwell Stefan's equation over a membrane to get the transient mole fraction distribution over the membrane thickness 'z'. But somehow I am not able to code it using ODE45, more ...
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2answers
143 views

Reorder eigenvalues in Schur factorization in descending order

In this command: [US,TS] = ordschur(U,T,select) what should replace the select to rearrange the eigenvalues in descending ...
1
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1answer
82 views

When is a dynamical system discrete vs. continuous?

I have a basic question to ask: Let's say I am reading a paper which gives a good model that consists of a set of ordinary differential equations, with first and second derivatives. Continuity is a ...
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0answers
65 views

How to determine the finite difference coefficient matrix in 2D with periodic BC?

I'm solving a PDE in matlab using ode15s, and since the spatial dimension is 2, and number of variables grow large very quickly, I need to supply the structure of ...
2
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1answer
102 views

Crank-Nicholson scheme for transport equation

This is my attempt to find the approximate solution of the folowing transport equation $$\left\{\begin{array}{ll} \partial_{t} u+\partial_{x} u= (x^2-x)t+x^3/3-x^2/2, & t \in(0,0.4), x \in(0,1) \\ ...
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0answers
45 views

Inverse Newton Method for optimization: is this the correct algorithm?

I am trying to implement the algorithm in this article. I have already asked a question before about it here, and I am trying to figure out what I am doing wrong. This time, it's this section of the ...
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0answers
146 views

Automatically generate constraints for trajectory optimization

This is a follow up to my previous post here I'm interested in performing trajectory optimization from the problem mentioned in abov link. I want to supply the following as dynamical constraints to ...
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2answers
126 views

Solving a parameter estimation problem using trajectory optimization

This is a follow-up to my previous question here I've the following system of equations for studying information flow in the below graph, $$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise ...
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1answer
101 views

If not MATLAB, what software/programming language should I use to simulate/animate wave functions in various potentials + more? (example given)

I want to integrate programming into my learning in math and science in a very specific way. I want to create visualizations and simulations of concepts I am learning. When I learn a numerical method ...
3
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1answer
332 views

Question on how MATLAB's pdepe solver works

I'm solving the following 1D transport equation in MATLAB's pdepe solver. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ At the inlet (left ...

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