Gekko Error: Matrix Is Structurally Singular. How Can Solve It?

I am trying to follow the suggestions from: How to apply m.connection from Gekko using arrays? and now I am getting these errors: Error return from MC23A because matrix is structur

Solution 1:

To run the script, I uncommented this region of the code:

hocl=m.Array(m.Var,2)
nh3=m.Array(m.Var,2)
nh2cl=m.Array(m.Var,2,lb=1e-10)
nh2cl_meas=m.Array(m.Param,2)
nhcl2=m.Array(m.Var,2,lb=1e-10)
h=m.Array(m.Var,2)
oh=m.Array(m.Var,2)
I=m.Array(m.Var,2,lb=1e-10)
ocl=m.Array(m.Var,2)
nh4=m.Array(m.Var,2)
h2co3=m.Array(m.Var,2)
hco3=m.Array(m.Var,2)
co32=m.Array(m.Var,2)
alk=m.Array(m.Var,2)
DOC1=m.Array(m.Var,2)
DOC2=m.Array(m.Var,2)
cnh3=m.Array(m.Var,2)
cnh2cl=m.Array(m.Var,2)

The code runs but gives suspicious results with negative concentrations or rates.

The error Structurally Singular means that there are problems with finding the search direction from solving the Ax=b equation with linear solver in IPOPT. A singular matrix is not invertible. A matrix is singular if its determinant is zero or for numerical solutions if the A matrix has particular properties that prevent the Ax=b solution. There is more information on how that Ax=b linear solve is used in the Interior Point algorithm. For your problem, it is likely because the problem is numerically difficult to solve or that a variable swap in degrees of freedom does not have an associated equation or objective to determine that variable.