[Octave-bug-tracker] [bug #56582] [octave forge] (optim) lsqlin produces unexpected error on linearly dependent inputs

[Nicholas Jankowski]

Follow-up Comment #1, bug #56582 (project octave):

checking full Matlab output for compatibility. #2 is odd:

1. Matlab:

>> C = [1,2,3;2,4,6;2,4,5];
>> D = [4 8 5]';
>> [X, RESNORM, RESIDUAL, EXITFLAG, OUTPUT, LAMBDA]=lsqlin(C,D,[],[])

X =

   NaN
   NaN
     3


RESNORM =

   NaN


RESIDUAL =

   NaN
   NaN
   NaN


EXITFLAG =

     1


OUTPUT = 

  struct with fields:

         iterations: 0
          algorithm: 'mldivide'
      firstorderopt: []
    constrviolation: []
       cgiterations: []
       linearsolver: []
            message: ''


LAMBDA = 

  struct with fields:

      lower: []
      upper: []
    ineqlin: []
      eqlin: []

Octave error:

error: __qp__: operator *: nonconformant arguments (op1 is 1x1, op2 is 3x1)
error: called from
    quadprog at line 352 column 36
    lsqlin at line 123 column 21


2. Matlab:

>> C=[1 2 3;4 5 6; 2 4 6];
>> D=[4 5 8]';
>> [X, RESNORM, RESIDUAL, EXITFLAG, OUTPUT, LAMBDA]=lsqlin(C,D,[],[])

X =

   NaN
   NaN
   NaN


RESNORM =

   NaN


RESIDUAL =

   NaN
   NaN
   NaN


EXITFLAG =

     1


OUTPUT = 

  struct with fields:

         iterations: 0
          algorithm: 'mldivide'
      firstorderopt: []
    constrviolation: []
       cgiterations: []
       linearsolver: []
            message: ''


LAMBDA = 

  struct with fields:

      lower: []
      upper: []
    ineqlin: []
      eqlin: []

Octave output:

X =

  -3.2660
   6.5320
  -3.2660

RESNORM =  105.00
RESIDUAL =

  -4.0000
  -8.0000
  -5.0000

EXITFLAG = 0
OUTPUT =

  scalar structure containing the fields:

    iterations =  200

LAMBDA = [](0x0)


3. Matlab:

>> C = [1 2 3; 4 5 6];
>> D = [4 5]';
>> A = [1 1 1;2 2 2];
>> B = [1 2]';
>> [X, RESNORM, RESIDUAL, EXITFLAG, OUTPUT,
LAMBDA]=lsqlin(C,D,[],[],A,B,[],[])

Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint
tolerance.

<stopping criteria details>

X =

   -0.1667
    0.3333
    0.8333


RESNORM =

     2


RESIDUAL =

   -1.0000
    1.0000


EXITFLAG =

     1


OUTPUT = 

  struct with fields:

            message: '↵Minimum found that satisfies the
constraints.↵↵Optimization completed because the objective function is
non-decreasing in ↵feasible directions, to within the value of the
optimality tolerance,↵and constraints are satisfied to within the value of
the constraint tolerance.↵↵<stopping criteria details>↵↵Optimization
completed: The relative dual feasibility, 9.259951e-13,↵is less than
options.OptimalityTolerance = 1.000000e-08, the complementarity
measure,↵0.000000e+00, is less than options.OptimalityTolerance, and the
relative maximum constraint↵violation, 0.000000e+00, is less than
options.ConstraintTolerance = 1.000000e-08.↵↵'
          algorithm: 'interior-point'
      firstorderopt: 4.1670e-11
    constrviolation: 0
         iterations: 1
       linearsolver: 'dense'
       cgiterations: []


LAMBDA = 

  struct with fields:

    ineqlin: [0×1 double]
      eqlin: [2×1 double]
      lower: [3×1 double]
      upper: [3×1 double]


Octave error:

error: quadprog: equality constraint matrix must be full row rank
error: called from
    quadprog at line 283 column 11
    lsqlin at line 123 column 21


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