DQM Example

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  David J  (Report)

  September 23, 2023 05:19

  Hello,

  I am having a little trouble understanding exactly what you would like to do.
  Could you please provide a little clarification?

  It sounds like you want to have the Z variables (z0, z1, z2,..) be discrete values from the set z_valid.

  With the code example you have above, each variable can only be one of the values in the c array.
  This could be an indexing issue, as you have c[i]. If you were to set this to c[j], then each of the z variables could be one of the values in the c array.

  Example:

  >>>dqm.get_linear("z0")
  array([0.        , 0.4958104 , 0.47840023, 0.43096018, 0.35200113,
         0.31345015, 0.31345015, 0.28250982, 0.24629329, 0.23308393])

  This does not take into account valid_z in any way. I am not sure how that fits in just, yet but hopefully you can provide a little clarification.

  With the above example, calling dqm.getlinear() on any of the z variables will return the same array, as these are the discrete values that z0-z10 can be selected from, based on the loop in the code example you provided.

  Please let us know if this helps to resolve your problem. 
  I look forward to receiving further details.

  For future code examples, please be sure to provide a complete example that can be copied and pasted directly into a Python interpreter. This will help make the process a bit quicker and easier.

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  Amir P  (Report)

  September 26, 2023 11:29

  Hello David, thanks for looking into my query.

  Sorry things were not clear enough. You may ignore my codes now, as I know this is not what it should be. I just try to clarify my goal here.

  I have a linear function to minimise: f=c1z1+c2z2+...c10z10

  Each z_i can only be chosen from the set valid_z written above. The size of valid_z set is eventually 10 but could be any other size.

  I am looking to know how this can be coded in DQM. A sample source code will be highly appreciated.

  Thanks again.

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  David J  (Report)

  September 27, 2023 22:26 (Edited September 27, 2023 22:27)

  Hello,

  Just so I am understanding correctly, let me state the problem.
  You have a problem:
  f=c1*z1+c2z2+...c10z10
  Where c values are constants and z values are DQM variables with n cases each.
  You would like to multiply the constant c by the value of the z case. Correct?

  The values of the z cases are essentially just labels, and would not take part in the calculation at all.
  They would evaluate to 1 or 0. The z variable has n cases and acts as a one-hot constraint.
  This means that one of the cases will evaluate to 1 and the rest to 0.

  In order to accomplish the behaviour you are interested in, you would need to precalculate the values of c1*z1_case1, c1*z1_case2... up to c10*z10_case10.
  Then you would set the linear values for each of the cases for each of the variables.

  It would look something like:

  #Create the dqm
  dqm = dimod.DiscreteQuadraticModel()
  z=["z1","z2","z3"]
  #Set the constants
  c = [1,2,3]
  #Set the valid cases for z
  valid_z = [1,2,3,4,5,6,7,8,9,10]
  #Add the variables z_1 through z_n with number of valid cases being 10
  for i in range(len(z)):
     dqm.add_variable(len(valid_z), label=z[i])
  #Compute the linear terms for all of the cases for all of the variables
  for i in range(len(c)):
     z_biases[i] = c[i]*valid_z
  #Set the linear biases for all cases of all variables
  for i in range(len(c)):
     dqm.set_linear(z[i], z_biases[i])

  Alternatively you can set the linear case terms one-by-one:

  dqm.set_linear_case(z1, "case_1", c1*valid_z["case_1"])

  Hopefully this is helpful.
  Please let us know if you have any questions.

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