Questions tagged [matlab]

Questions about the numerical programming language MATLAB.

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3
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0answers
40 views

Find $x$ that satisfy $(I-A^*A)+x(\frac{A+A^*}{2})\prec0$ using LMI or SDP on Matlab

Given $A\in\mathbb{C}^{n\times n}$, I want to use LMI or SDP to find feasibility of $x>0$ in the following inequality: $$(I-A^*A)+x(\frac{A+A^*}{2})\prec0,$$ where $D\prec0$ means that $D$ is ...
3
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2answers
1k 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, ...
1
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0answers
68 views

Improve code of logarithmic quantizer

I am implementing a logarithmic quantizer which is defined as follows: $$ q(u) = \begin{cases} u_i , \frac{u_i}{1+\delta} < u < \frac{u_i}{1-\delta} \\ 0 , 0 \leq u \leq \frac{u_o}{1+\delta} \\ -...
1
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1answer
98 views

2-norm and infinty norm of a system in controls

How to compute 2-norm or infinity norm of following system? i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...
3
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1answer
81 views

Type of computer used for computation

In some scientific papers I see that authors provide what type of simulation tool and what type of computer was used for computation. For example: The computations were performed using MATLAB in ...
1
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0answers
17 views

How can this attempt to implement a Milstein numerical approximation for an Ito process of multiple components be fixed?

I have been reading Kloeden and Platen's Numerical Solution of Stochastic Differential Equations, and have more or less been trying to systematically complete the various exercises therein as I go ...
1
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1answer
187 views

Prescribing variables as an excitation in Runge-Kutta method

I am using Runge-Kutta to solve a $3 \times 3$ 2nd order linear ODE $$M x'' + C x' + K x = 0$$ and initial conditions are all zeros. Then I prescribe the 2nd variable to follow a given path. As for ...
3
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1answer
2k views

2D cross section from 3D surface

I am trying to apply the "restoring force surface" method to a dynamic linear system. The idea behind this method is that, knowing acceleration, displacement, velocity and input force it is possible ...
0
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1answer
35 views

Best search algorithm for optimal weight factor in SOR method

I had written an algorithm that searches for the optimal weight parameter to be implemented in the successive-over relaxation (SOR) method which worked cleanly by vectorizing the interval and for ...
1
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1answer
115 views

Reason behind different outputs for Fast Fourier Transform in Numpy and Matlab

Here is the output of Numpy np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary Here is the output of Matlab ...
1
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1answer
212 views

What is difference between L2 norm and H2 Norm?

When someone refers 2-norm of system,L2 and H2 are used interchangeably by author and is rather confusing. Even the matlab has different functions for H-infinity norm and L-infinity norm. as shown in ...
6
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6answers
5k views

What is the difference between MATLAB and FORTRAN?

In our university some Ph.D students for computational methods prefer FORTRAN over MATLAB. I can't understand why? What is the difference between them when are used in computational methods like ...
-1
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1answer
30 views

relres in gmres MATLAB

I think the relres in MATLABis the form that relres = norm(M(b-Ax))/norm(M\b),when it smaller than tol then stop the iteration. I want to know how to change relres to norm((b-Ax))/norm(b). Or use ...
2
votes
2answers
463 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 ...
1
vote
2answers
177 views

Continuation of solution to $-\nabla\cdot (k(x,y)\nabla u)=f$

I'm trying to solve the following problem, I had previously opened another discussion for the implementation and well, it seems that it has turned out well, it can be found here. I need to calculate ...
0
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2answers
343 views

Implementing routine for $-\nabla\cdot (k(x,y) \nabla u)=f$ in Matlab

I am solving the Poisson Equation for 2D given by the following expression: $$-\nabla\cdot (k(x,y) \nabla u)=f$$ in a rectangle with Dirichlet conditions on the boundary using Matlab. In principle I ...
2
votes
1answer
88 views

Vectorization Matlab/Octave of Markov Matrix Powers

I have just created a code snippet in Octave/Matlab that aims to create a plot which shows the accuracy of an initial probability vector $\vec{\pi}$ derived from the transition probability matrix $\...
3
votes
1answer
102 views

How can I extract the banded or block diagonal part of a sparse matrix in MATLAB?

Given a large sparse (square) matrix in MATLAB, how can I extract the banded or the block-diagonal parts (of fixed size) of it efficiently? These are useful operations when prototyping and testing ...
0
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1answer
121 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 ...
1
vote
1answer
157 views

What is the use of arrayfun if a for loop is faster?

This may not be so much of a scientific computing question but more of a MATLAB question, if that is the case, please feel free to close or migrate the question. Root-finding problems are commonly ...
0
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1answer
45 views

Efficient solution to linear system involving Kronecker sum in MATLAB

High dimensional finite difference problems often lead to linear systems of the form $$ A x = b, \qquad A = B_1 \oplus B_2 \oplus \cdots \oplus B_d, $$ where $\oplus$ denotes the Kronecker sum. $B_i \...
7
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3answers
241 views

Converting from planar polynomial domain to planar polygon

Let's assume we have a planar domain whose boundary can be described with a polynomial curve (like Bezier curves). Now assume that you want to produce a discretization of the boundary, i.e. you want ...
5
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2answers
552 views

Specifying ode solver options to speed up compute time

I'm specifying the 'JPattern', sparsity_pattern in the ode options to speed up the compute time of my actual system. I am sharing a sample code below to show how I ...
0
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0answers
66 views

Path constraints for state variables - fmincon, ODE45

My problem lies in constraining state variables (look for 23,24,25). I am currently using ODE45 to solve equations and fmincon to find best control variable.How would you go about solving this? Here ...
4
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1answer
97 views

How are Matrices Stored in MATLAB?

I have this simple question but I am trying to figure out why: Are matrices stored column-wise in MATLAB? If so then why? I theorize that they are stored column-wise because the memory does not have ...
0
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0answers
53 views

Can I get a symbolic solution for these coupled ODEs?

I found this IPython notebook called ‘Roller Coaster’ from", "numfys.net, where they model the movement of a ball over a path described by a third-degree polynomial $y(x)$ with slope $\...
1
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1answer
177 views

MATLAB : find an algorithm to inverse quickly a large matrix of symbolic variables

I have to solve the equality between 2 matrixes 12x12 containing a lot of symbolic variables and with which I perform inversion of matrix. There is only one unknown called "...
0
votes
1answer
44 views

Round-off error step choice

In the Numerical Recipes in section 5.7.- Numerical derivatives the choice of the step size $h$ in the numerical derivative should lead to a difference between $x$ and $x+h$ representable by an exact ...
1
vote
1answer
139 views

temperature profile on axial direction of a chamber

I have a task to plot average temperature profile at each cross-section in the axial direction of a combustion chamber. I have $x$, $y$, $z$ coordinates data in excel as well as the corresponding ...
2
votes
1answer
264 views

Minimal surface finite differences problem - Matlab assemble

I face to the following problem: $$(1+u_x^2)u_{yy} - 2u_xu_yu_{xy} + (1+u_y^2)u_{xx}=0.$$ Problem needs to be discretized and assembled. Does anybody know how to proceed in Matlab?
0
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0answers
36 views

Using event function to shift between 2 sets of ODE

I have a bunch of ODEs I am trying to solve using ode45 in MATLAB. I have hidden the details of the equations to keep it simple (so as to build a general algorithm)! \[\frac{dR}{dt}= F_{1}(R,N) \quad\...
2
votes
0answers
33 views

Problem with Numerical DAE Implementation of Nernst-Planck Equations

I write to you all today in order to clarify if I implemented my model correctly into MATLAB. I will outline the following: analytical governing equations, my discretization for the equations and ...
6
votes
2answers
812 views

Complex Eigenvalues using eig (Matlab)

I wanted to find and plot the eigenvalues of large matrices (around1000x1000). But discovered when using the eig function in matlab, it gives complex eigenvalues when it shouldn't. For example, in the ...
1
vote
2answers
169 views

How can I learn Scientific Python?

I am an intermediate user of Matlab and Mathematica, but I would really love to start learning Python language for scientific purposes (I am interested in Maths and Physics). Could please someone ...
0
votes
0answers
94 views

Error $L_{2}$ convergence in Finite Element for Poisson Equation

I have written a Matlab code to solve the equation $-u'' = f$ with conditions $u(0) = u'(1) = 0$ on the domain $x \in [0,1]$. I tested the code with $f(x) = -2, \forall x\in [0,1]$. I check the plot ...
0
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1answer
42 views

Rem function in Octave showing wrong result

I am trying to write an if statement that checks if 2 numbers are divisible before running some commands. The problem is, the rem function is giving some wrong results for certain number (2 is ...
-1
votes
1answer
48 views

How to reduce computational time in DDE simulation on Matlab

I need to simulate a network of nodes. The weights of the edges are being given in a matrix . Due to the non-zero distances between the nodes, we consider time-delays, which are computed given the ...
-1
votes
1answer
96 views

ODE45 and a variable that assumes multiple values during the timespan

I have tried in different ways to see what happens to voltage V and gating conductances m, n and h when, at time step x, current I switched from 0 to 0.1, and then at time step x + n it gets back to 0....
0
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2answers
3k views

FEM Stiffness Matrix is always close to Singular or Badly Scaled

I am making a code for an 18-node (3x3x2) 3D element FEM. However, even though I am (pretty) sure that all the shape functions are correct and whatnot, whenever I try and invert the stiffness matrix ...
0
votes
1answer
26 views

Software to find zero divisors of a ring

Are there some programs with packages that help to list all zero-divisors of the ring we desired? especially for the ring of Gaussian integers modulo $n$, $\mathbb{z}_n[i]$. Also want to find which of ...
-1
votes
1answer
129 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 ...
2
votes
2answers
1k views

Solving DAE with higher index

I want to solve 7 coupled differential equations in MATLAB. I used the method of lines (MOL) to convert them to a system of DAEs. I then attempted to solve this system using ode15s. Unfortunately an ...
3
votes
4answers
327 views

How does gmres method iteration behave for this non-diagonalizable matrix?

Recently, I have been studied my lessons about gmres iteration, probably the most popular iteration method for general large sparse linear system of equations Ax=b. And the convergence is obtained ...
8
votes
1answer
10k views

Matlab solution for implicit finite difference heat equation with kinetic reactions

I am trying to model heat conduction within a wood cylinder using implicit finite difference methods. The general heat equation that I'm using for cylindrical and spherical shapes is: Where p is the ...
0
votes
1answer
88 views

Visualize a mesh from list of 3D point and faces

I have a list of vertices and faces. Now, I want to create a mesh using the given points and faces list and visualize it. Also, I want to play with the mesh by adding an extra point on the faces. Can ...
1
vote
0answers
78 views

C.S.R method in finite element matrix assembly

I have solved the 2D Poisson equation using finite element method with simplex triangular element in MATLAB. First, I generated the triangular mesh using pdetool in ...
-2
votes
1answer
42 views

Solving differential equation by setting vectorization `on` in MATLAB

This is a follow up to my previous question posted here. I've set up an ode system in MATLAB and I'm trying to vectorize the code to increase the speed of computation. The follow is the code for my ...
1
vote
2answers
391 views

How to set up the differential equation system to speed up computation?

I've set up a system of differential equations, obtained after discretizing pde, in the following way ...
0
votes
1answer
75 views

Solving differential equation by specifying jacobian pattern

This is a follow up to my previous question posted here I'm trying to construct the sparsity pattern of the jacobian matrix to speed up the computation of a large system of odes. The following is the ...

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