How do get around this limitation on array size?

R2017a, R2014, different computers, same issue.

1. Why does the computer (I'm pretty sure it's not MATLAB) limit me to arrays of length 32767?
2. How do I circumvent this feature?

For example, in my command window I can enter

v = rand(1000000,1);

and the variable is generated without a problem. However, when I run a script or function designed to generate variables with approximate length 10^6, I become automatically restricted to

>> size(z)

ans =

         32767           1

>> size(Y)

ans =

         32767           3

this doesn't make any sense to me, especially considering

>> whos
  Name           Size             Bytes  Class     Attributes

    T              1x1                  8  double              
    Y          32767x3             786408  double              
    sigma          1x1                  8  double              
    z          32767x1             262136  double              

>> memory
Maximum possible array:        5216 MB (5.470e+09 bytes) *
Memory available for all arrays:        5216 MB (5.470e+09 bytes) *
Memory used by MATLAB:        1180 MB (1.237e+09 bytes)
Physical Memory (RAM):        8124 MB (8.518e+09 bytes)

*  Limited by System Memory (physical + swap file) available.

Note that 32767 = 2^15-1

Complete Code:

clc
clear
close all

% Solve over time interval [0 T] with initial conditions [1,1,1]
% f is set of differential equations
% Y is array containing x, y, and z variables
% t is time variable

sigma = 10;
beta = 8/3;
rho = 28;  
tb = 20;
T = 2000;
% Lorenz system
R = @(Y) ... 
    [   -sigma*Y(1) + sigma*Y(2);       ... 
        rho*Y(1) - Y(2) - Y(1)*Y(3);    ... 
        -beta*Y(3) + Y(1)*Y(2)          ]; 

[t,Y] = rk4lorenz(R,[0 T],[1 1 1]);

z = Y(:,3);  

function [t,Y] = rk4lorenz(f, range, y0)
% RK4 Method for the Lorenz system
% range =  time interval
% y0    =  initial value vector
% h     =  time step

a = range(1)
b = range(2)
h = 1/128;

n = int16((b - a)/h) 
Y = zeros(n+1,3);
t = zeros(n+1,1);
t(1) = a;
Y(1,:) = y0; 

for i = 1:n  
    t(i+1) = t(i) + h;
    Y(i+1,:) = rk4step(Y(i,:),h,f);
end

end

function Y = rk4step(Y,h,f)

Y = Y';
s1 = f(Y);
s2 = f(Y + h * s1/2);
s3 = f(Y + h * s2/2);
s4 = f(Y + h * s3);
Y = Y + h*(f(Y) + 2*s2 + 2*s3 + s4)/6;

end

[James Tursa]

Please post your code.

[Zachary Duff]

Posted

[John D'Errico]

Since we don't see your script, we cannot know. If you show the script, we can try to explain to you what happened.

You can also help if you tell what version of MATLAB you are running.

[Zachary Duff]

R2017a. Just posted the script.

[James Tursa]

What variables or lines of code seem to be the problem for you? I.e., what are you getting and what were you expecting?

Answer 1

[Zachary Duff]

The use of the MATLAB function

int16()

"Y = int16(X) converts the values in X to type int16. Values outside the range [-215,215-1] map to the nearest endpoint."