Calculate the determinant of a matrix that includes quadratic expressions.

Answered

Bohao Li

October 25, 2024 08:34

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Hi,

I'm calculating the determinant of a Gram matrix of a matrix variable using the code in the link below. However, the following error occurs. Is there a way to resolve this issue?

https://support.gurobi.com/hc/en-us/community/posts/23265737046417-How-to-maximize-the-determinant-of-a-N-by-N-Matrix-variable 

My code

def det(A):
    v = m.addVar(lb=-float("inf")) 
    if A.shape == (2,2):
        m.addConstr(v == A[0,0]*A[1,1]-A[1,0]*A[0,1]) # TODO
        return v
    expr = gp.QuadExpr() 
    cofactor = 1 
    for i in range(A.shape[1]):
        cols = [c for c in range(A.shape[1]) if c != i]
        expr += cofactor * A[0,i] * det(A[1:][:,cols]) # TODO
        cofactor = -cofactor
    m.addConstr(v == expr)
    return v

Xe = m.addMVar((ne,me),lb=0, ub=1, vtype=GRB.CONTINUOUS)
aux5 = det(Xe @ Xe.T)

Error

Traceback (most recent call last):
  File "/data/bhli/dspf-parser-0.3.0/gurobi2.py", line 116, in <module>
    aux4 = det(Xv @ Xv.T)
  File "/data/bhli/dspf-parser-0.3.0/gurobi2.py", line 22, in det
    expr += cofactor * A[0,i] * det(A[1:][:,cols]) # TODO
  File "/data/bhli/dspf-parser-0.3.0/gurobi2.py", line 22, in det
    expr += cofactor * A[0,i] * det(A[1:][:,cols]) # TODO
  File "/data/bhli/dspf-parser-0.3.0/gurobi2.py", line 22, in det
    expr += cofactor * A[0,i] * det(A[1:][:,cols]) # TODO
  [Previous line repeated 38 more times]
  File "/data/bhli/dspf-parser-0.3.0/gurobi2.py", line 16, in det
    m.addConstr(v == A[0,0]*A[1,1]-A[1,0]*A[0,1].item()) # TODO
TypeError: unsupported operand type(s) for *: 'MQuadExpr' and 'MQuadExpr'

Related to

• Matrix API

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:09 Edited

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  Riley Clement

  • Gurobi Staff

  October 25, 2024 23:01

  Hi Bohao,

  The code you linked is intended to be used with a matrix of variables (MVar) but you are passing it a matrix of quadratic expressions (MQuadExpr).  The easiest solution here is to define a MVar for the gram matrix, e.g.

  Xe = m.addMVar((ne,me),lb=0, ub=1, vtype=GRB.CONTINUOUS)
  Xe_gram = m.addMVar((ne,ne),lb=0, ub=me, vtype=GRB.CONTINUOUS)
  m.addConstr(Xe @ Xe.T == Xe_gram)
  aux5 = det(Xe_gram)

  - Riley

   

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• 

  Bohao Li

  October 26, 2024 08:01

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  Thank you very much for your help, Riley. Have a wonderful day!

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