## 1D vector example

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Vec1dex.m % Written by Ebenezer P Gnanamanickam% Dec 2006. % DISCLAIMER - I do not claim to be an expert on MATLAB but what little I % have learned during the course of grad school here at Purdue University % I want to share. If it's useful GREAT if not sorry. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % This script gives an idea of how to carry out vector operations in MATLAB % using Blasius boundary layer profile as an example. Here delta =f(x). That is % the boundary layer profile is plotted at different x locations for a single % freestream velocity. You can choose between four ways of doing this % (i) for loop operations - the standard C/Fortan method of doing it - This % is extremely slow. PLEASE, I repeat PLEASE do not use for loops for % anything more than a 1000 points without variable declarations/ memory % allocation. The reason is that MATLAB evaluates for loops line by line % and allocates memory as the vector grows. one word - NO!!!!! % (ii) Vectorized operations for which MATLAB is optimized to work % (iii) For loop operations with variable declaration (memory % allocation) - this as it turns out is almost as efficient as the % vectorized option % (iv) Using variable declaration as well as vectorized operations - no real % advantage here clc; % clears the command window clear all; % clears all the variables close all; % close all existing windows tstart=clock; % starts the clock to calculate the run time %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUTS n=100000; % number of points method=1; % choose the method you want to use %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mu=1.73e-5*10e-5; % in N-s/m^2 rho=1.229; % in kg/m^3 U_inf=20;% in m/s switch (method) case 1 x=linspace(0,10,n);% in m for (i=1:1:length(x)) delta(i)=3.5*sqrt(mu*x(i)/rho/U_inf); end smethod='for loop operations'; case 2 x=linspace(0,10,n);% in m delta=3.5.*sqrt(mu.*x./rho/U_inf); smethod='vectorized operations'; case 3 x=zeros(1,n); delta=zeros(1,n); x=linspace(0,10,n);% in m for (i=1:1:length(x)) delta(i)=3.5*sqrt(mu*x(i)/rho/U_inf); end smethod='for loop operations with variable decleration'; case 4 x=zeros(1,n); delta=zeros(1,n); x=linspace(0,10,n);% in m delta=3.5.*sqrt(mu.*x./rho/U_inf); smethod='vectorized operations with variable declerations'; end figure plot(x,delta) xlabel('x in m') ylabel('\delta_{99} in m'); title('Blasius - Boundary layer thickness on flat plate'); legend('\delta_{99}',4); grid; tfinish=clock; % end run time runtime=etime(tfinish,tstart); % estimates the runtimes s1=['number of points = ' num2str(n)] s2=['method = ' smethod] s3=['run time = ' num2str(runtime)]