How to formulate matrix multiplication and inverse using constraint program?

回答済み

Sanket Yenare

2023年10月17日 09:58 編集済み

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Hello, I want to formulate a Matrix multiplication and inverse using a strictly integer constraint program, and I don't know how to proceed with it. 

G = [  [-4, 2, 1],
       [-2, 2, 1],
       [-1, 1, 1]
    ]

C = [ [-2],
      [2],
      [1)
    ]

and I want to find W vector such as:

W = G(G⊺G)^−1 C

That is, G(G transpose G)inverse C

is this matrix multiplication and most importantly the INVERSE of the multiplication is possible to formulate

Help will be appreciated :)

 

0

• 

  Riley Clement

  • Gurobi Staff

  2023年10月17日 23:29

  Hi Sanket,

  This isn't an optimization problem, it just requires matrix arithmetic, which can be achieved with Python and numpy for example:

  import numpy as np
  
  G = np.array([
      [-4, 2, 1],
      [-2, 2, 1],
      [-1, 1, 1]
  ])
  
  C = np.array([-2,2,1])
  
  W = G@np.linalg.inv(G.transpose()@G)@C

  Then W = array([1.55431223e-15, 1.00000000e+00, 4.44089210e-16])

  - Riley

  1

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