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Solve a linear system of equations with bounds using LSQR/LSMR SciPy

Question is quite straight forward. I have an overdetermined system I am attempting to use SciPy LSQR (or LSMR) to solve. However, I cannot find anywhere in the docs on how to set restraints for the minimization.

E.G. Let’s say this is the output:

The matrix A has 469 rows and 3 columns
damp = 0.00000000000000e+00

atol = 1.00e-06                 conlim = 1.00e+08

btol = 1.00e-06             maxiter =        3

 
   itn      x(1)       norm r    norm Ar  compatible   LS      norm A   cond A
     0  0.00000e+00  1.150e-01  2.291e-02   1.0e+00  1.7e+00
     1  3.33741e-01  9.411e-03  5.359e-05   8.2e-02  2.8e-02  2.0e-01  5.0e+00
     2  2.73042e-01  8.440e-03  3.281e-06   7.3e-02  1.9e-03  2.0e-01  7.8e+01
     3 -1.70218e-01  8.332e-03  3.197e-12   7.2e-02  1.9e-09  2.0e-01  4.1e+02
 
LSMR finished
The least-squares solution is good enough, given atol     
istop =       2    normr = 8.3e-03
    normA = 2.0e-01    normAr = 3.2e-12
itn   =       3    condA = 4.1e+02
    normx = 8.7e-01
     3 -1.70218e-01   8.332e-03  3.197e-12
   7.2e-02  1.9e-09   2.0e-01  4.1e+02

We can see the solution arrive to -0.1, which is great. However, I’d like to set bounds such that x(1) >= 0. Therefore, the iteration would stop when x(1) = 0.27. I cannot find anywhere on the documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.lsqr.html regarding how to do this.

Any help would greatly be appreciated!

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Answer

The functions lsqr and lsmr in scipy.sparse.linalg do not have options for adding constraints. You might be able to use scipy.optimize.lsq_linear instead.

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