Computational Science Asked on February 28, 2021
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 code in which I am trying to set up the jpattern in
odeset
for a toy model in MATLAB.
global mat1 mat2
mat1=[
1 -2 1 0 0 0 0 0 0 0;
0 1 -2 1 0 0 0 0 0 0;
0 0 1 -2 1 0 0 0 0 0;
0 0 0 1 -2 1 0 0 0 0;
0 0 0 0 1 -2 1 0 0 0;
0 0 0 0 0 1 -2 1 0 0;
0 0 0 0 0 0 1 -2 1 0;
0 0 0 0 0 0 0 1 -2 1;
];
mat2 = [
1 -1 0 0 0 0 0 0 0 0;
0 1 -1 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 1 -1 0 0 0 0 0;
0 0 0 0 1 -1 0 0 0 0;
0 0 0 0 0 1 -1 0 0 0;
0 0 0 0 0 0 1 -1 0 0;
0 0 0 0 0 0 0 1 -1 0;
];
x0 = [1 0 0 0 0 0 0 0 0 0]';
tspan = 0:0.01:5;
f0 = fun(0, x0);
joptions = struct('diffvar', 2, 'vectvars', 1, 'thresh', 1e-8, 'fac', []);
J = odenumjac(@fun,{0 x0}, f0, joptions);
sparsity_pattern = sparse(J~=0.);
options = odeset('Stats', 'on', 'JPattern', sparsity_pattern);
ttic = tic();
[t, sol] = ode15s(@(t,x) fun(t,x), tspan , x0); %, options);
ttoc = toc(ttic)
fprintf('runtime %f seconds ...n', ttoc)
plot(t, sol)
function f = fun(t,x)
global mat1 mat2
fprintf('size of x: %d %dn', size(x))
f(1,1) = 0;
f(2:9,1) = mat1*x + mat2*x;
f(10,1) = 2*(x(end-1) - x(end));
end
When I run the code, I notice that the size of the vector x
in fun
changes for the second iteration
because of which an error occurs.
size of x: 10 1
size of x: 10 10
Error:
Unable to perform assignment because the size of the left side is 8-by-1 and the size of the right side is 8-by-10.
Error in Untitled>fun (line 47)
f(2:9,1) = mat1*x + mat2*x;
Error in odenumjac (line 143)
Fdel = feval(F,Fargs_expanded{:});
Error in Untitled (line 31)
J = odenumjac(@fun,{0 x0}, f0, joptions);
Suggestions on how to fix this error will be really helpful.
EDIT:
I’ve tried to vectorize f
in fun
and also set vectvars
=2 to vectorize the jacobian calculation.
global mat1 mat2
mat1=[
1 -2 1 0 0 0 0 0 0 0;
0 1 -2 1 0 0 0 0 0 0;
0 0 1 -2 1 0 0 0 0 0;
0 0 0 1 -2 1 0 0 0 0;
0 0 0 0 1 -2 1 0 0 0;
0 0 0 0 0 1 -2 1 0 0;
0 0 0 0 0 0 1 -2 1 0;
0 0 0 0 0 0 0 1 -2 1;
];
mat2 = [
1 -1 0 0 0 0 0 0 0 0;
0 1 -1 0 0 0 0 0 0 0;
0 0 1 -1 0 0 0 0 0 0;
0 0 0 1 -1 0 0 0 0 0;
0 0 0 0 1 -1 0 0 0 0;
0 0 0 0 0 1 -1 0 0 0;
0 0 0 0 0 0 1 -1 0 0;
0 0 0 0 0 0 0 1 -1 0;
];
x0 = [1 0 0 0 0 0 0 0 0 0]';
tspan = 0:0.01:5;
f0 = fun(0, x0);
joptions = struct('diffvar', 2, 'vectvars', 2, 'thresh', 1e-8, 'fac', []);
J = odenumjac(@fun,{0 x0}, f0, joptions);
sparsity_pattern = sparse(J~=0.);
options = odeset('Stats', 'on', 'JPattern', sparsity_pattern, 'Vectorized', 'on');
ttic = tic();
[t, sol] = ode15s(@(t,x) fun(t,x), tspan , x0, options);
ttoc = toc(ttic)
fprintf('runtime %f seconds ...n', ttoc)
plot(t, sol)
function f = fun(t,x)
global mat1 mat2
f(1,:) = 0;
f(2:9,:) = mat1*x + mat2*x;
f(10,:) = 2*(x(end-1) - x(end));
end
However, there is a problem again when vectvars
= 2 in joptions and/or ‘Vectorized’, ‘on’ in options defined for ode15s.
Unable to perform assignment because the size of the left side is 8-by-1 and the size of the right side is 8-by-10.
Error in cse_11_5_20>fun (line 44)
f(2:9,:) = mat1*x + mat2*x;
Error in odenumjac (line 143)
Fdel = feval(F,Fargs_expanded{:});
Error in cse_11_5_20 (line 31)
J = odenumjac(@fun,{0 x0}, f0, joptions);
odenumjac
calls your function in a vectorized manner it seems, and your function is not vectorized. You can easily change that by changing the second index of f in your function to :
instead of 1
, for instance:
f(10,:) = 2*(x(end-1,:) - x(end,:));
I thought the setting joptions.vectvars=1
would not allow the vectorised call (see one of your other questions). I realize that this is actually not the case, you should instead set it to []
(empty). If you want to vectorize the Jacobian calculation, set it to 2
. You can type open odenumjac
in the Matlab console to access the function file and read its documentation.
More info on vectorization can be found here: https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html
Correct answer by Laurent90 on February 28, 2021
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