Calculate the determinant of a matrix that includes quadratic expressions.

Answered

Bohao Li

• October 25, 2024 08:34

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

0

• 

  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

   

  0
• 

  Bohao Li

  • October 26, 2024 08:01

  

  

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

  0

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