# Different results when using sparse vs non-sparse matrices in Matlab

Hi,
thanks for the great forum first of all. I am fairly new to the use of OSQP, so I fear this could be a duplicate of another question or something obvious, but I could not find an answer to my problem until now…

I am working on a simple problem of the form

min 1/2*x’Px
s.t. Ax=b
lb<=x<=ub

I have three implementations of the problem: one in Python, and 2 in Matlab (in the first, I have defined P and A_eq to be `sparse`, in the second they are just normal Matlab matrices).
To ensure reproducibility of the optimal solution found, I have set `adaptive_rho_interval=50` (as suggested in other posts like this one).
However,I observe that:

• the solution obtained in Python is exactly the same as the one found in Matlab without the use of the sparse matrices
• the solution found in Matlab using the sparse matrices is different.

Is there any reason for this to be happening?

I copy my two scripts in the following, to reproduce the issue. To make the code more readable, I specify the values of the vectors/matrices used at the bottom of the question.

Thank you very much in advance.

Matlab code:

``````
w = [ones(1,33), 0.01*ones(1,8), 10*ones(1,9)];

lb = [zeros(1,33), -6*ones(1,17)];
ub = [ones(1,33), 6*ones(1,17)];

%% use OSQP without sparse matrices
% rewrite the cost function as x'Px
P = diag(2*w);
prob = osqp;

A_eq_osqp = [A_eq; eye(50)];
lb_osqp = [B_eq; lb'];
ub_osqp = [B_eq; ub'];

% Setup workspace
prob.setup(P, [], A_eq_osqp, lb_osqp, ub_osqp, 'verbose', 0, 'adaptive_rho_interval', 50);

% Solve problem
res = prob.solve();
x_osqp = res.x;

%% then use OSQP with sparse matrixes
% rewrite the cost function as x'Px
P = sparse(diag(2*w));
prob = osqp;

A_eq_osqp = sparse([A_eq; eye(50)]);
lb_osqp = [B_eq; lb'];
ub_osqp = [B_eq; ub'];

% Setup workspace
prob.setup(P, [], A_eq_osqp, lb_osqp, ub_osqp, 'verbose', 0, 'adaptive_rho_interval', '50');

% Solve problem
res_sparse = prob.solve();
x_osqp_sparse = res_sparse.x;

%% Plot the comparison
h = figure;
set(gca,'fontsize',15,'LineWidth',2)
hold on
plot(x_osqp, 'LineWidth',2)
plot(x_osqp_sparse, 'LineWidth',2)
legend( "OSQP","OSQP sparse")
xlabel("optimization variables")
grid on
``````

Python code:

``````
import numpy as np
import osqp
from scipy import sparse

lb = np.concatenate((np.zeros((1, 33)), -6*np.ones((1, 17))), axis=1)
ub = np.concatenate((np.ones((1, 33)), 6*np.ones((1, 17))), axis=1)

## SOLVE with OSQP
w = np.concatenate((np.ones((1, 33)), 0.01*np.ones((1, 8)), 10*np.ones((1, 9))), axis=1)
P = sparse.csc_matrix(2*np.diagflat(w))
A_eq_osqp = sparse.csc_matrix(np.concatenate((A_eq, np.eye(50)), axis=0))
lb_osqp = np.concatenate((np.transpose(np.atleast_2d(B_eq)), np.transpose(lb)), axis=0)
ub_osqp = np.concatenate((np.transpose(np.atleast_2d(B_eq)), np.transpose(ub)), axis=0)

prob = osqp.OSQP()
prob.setup(P=P, A=A_eq_osqp, l=lb_osqp, u=ub_osqp, verbose=False, adaptive_rho_interval=50)
res = prob.solve()
x_opt = res.x
``````

Matrices (in Python format):

``````B_eq = np.array([-4.18274179e+00,  1.56056756e+01, -1.67703208e+00,  2.02253004e+00,
1.02790865e+01, -2.01405712e+00, -3.32916514e+02, -1.75742282e+02,
1.15009521e+02,  4.65990026e+01,  1.47867987e+03, -2.88275491e+02,
-3.45840577e+03, -1.02597422e+03,  3.26288535e+03,  2.15487771e+02,
4.83631402e+02])
A_eq = np.array([[ 5.59696010e+01,  1.50303950e+02, -1.45080962e+01,
2.42435057e+01, -3.82537529e+01, -1.74936497e+01,
-1.67269744e+01,  3.02613145e+01,  4.94917744e+01,
3.89645168e+01,  7.09048417e+00,  5.96168902e-01,
-3.68276595e+01,  6.75212395e+00, -3.33314640e+00,
-1.14602731e+01, -2.54238971e+00,  7.14121399e+00,
-6.43876344e+01, -2.35359455e+01, -1.96299142e+01,
-5.77662614e+01, -4.17765699e+01, -5.76682147e+01,
-2.15573061e+01,  2.54067375e+01,  2.92530478e+01,
2.91631734e+01,  1.14630510e+00,  1.51251526e+01,
-3.23904168e+01,  1.25577904e+01,  1.32951586e+01,
0.00000000e+00,  8.16171599e+00,  3.78787898e-01,
6.93423802e-02, -3.28678201e+00,  4.69479355e+00,
-1.04163405e+01, -5.20524024e+00,  7.47774401e-01,
-7.28333260e-01,  1.02762678e+00, -1.25265004e+00,
1.52868387e-01, -6.24779521e-01,  3.34824541e+00,
-3.38433639e-01, -1.25840458e+00],
[ 9.09582169e+01,  1.63531562e+02,  6.76170202e+01,
1.33191732e+01, -2.25146109e+01, -5.07062625e+01,
-2.53086586e+01,  1.52858727e+01,  8.91711589e+00,
-4.85496152e+00,  2.74820618e-01, -2.67000408e+01,
2.70874680e+01, -2.57143726e+01,  9.40861332e+00,
6.22547423e+00, -1.60467598e+00, -2.00925151e+01,
-8.72455807e+01, -7.72219459e+01,  3.12429213e+01,
1.00761797e+00, -2.93258428e+00, -4.31498382e+01,
1.65764127e+00,  5.06411469e-01,  1.19956345e+00,
5.12911789e+00, -3.93200936e+00, -8.94446923e+00,
3.04401658e+01, -1.48532904e+01, -4.05740054e+00,
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7.69915963e-01, -3.60953781e-01, -3.05457080e+00,
-3.11945796e-01,  2.93483957e+00],
[-2.64304368e+01, -3.75791071e+01, -4.32392637e+01,
-1.64330601e+00, -2.29284875e+01,  6.91498438e+00,
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0.00000000e+00,  8.62533437e-01,  3.89261632e+01,
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-8.51544134e-01,  1.70608004e-01,  1.34644497e-01,
8.78530619e-01, -5.63808869e-01],
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-2.31293472e-03,  1.67533989e-01, -5.63923553e-01,
2.51754003e-01,  3.36401086e-01],
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1.77543950e+03,  1.62077993e+03, -2.17391055e+03,
1.15598418e+03,  1.60315553e+03,  9.68504357e+02,
2.68076381e+02, -7.59436193e+02, -8.16528029e+02,
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0.00000000e+00, -6.40965175e+01,  2.37080945e+01,
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5.67130918e+02, -3.54120459e+02,  3.93475236e+00,
6.10210565e+01,  1.75290056e+01,  5.73721147e+01,
-9.81246585e+01,  2.08877083e+01,  1.20108050e+02,
8.03968723e+01, -1.66980834e+02],
[-3.44918148e+02,  4.15357569e+02, -2.42169445e+03,
2.04760396e+02, -2.40330272e+03, -3.72517496e+02,
1.33098258e+02,  9.33406447e+02,  2.46563911e+03,
1.89174479e+03, -3.98073573e+02,  3.61226707e+02,
-8.86123781e+02,  2.11321131e+03, -1.20762754e+02,
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