FIX: linprog_simplex: Fix bug in Phase 1

[oyamad]

Fix #725

Simplified instance:

c = np.array([-1,  1])
A_ub = np.array([[-2, -1], [1, 1]])
b_ub = np.array([-2, 1])
linprog_simplex(c=c, A_ub=A_ub, b_ub=b_ub)

Pre-bugfix version:

SimplexResult(x=array([0., 1.]), lambd=array([0., 1.]), fun=1.0, success=True, status=0, num_iter=4)

This bugfix version:

SimplexResult(x=array([ 1., -0.]), lambd=array([2., 3.]), fun=-1.0, success=True, status=0, num_iter=4)

Instances reported in #725:

c = np.array([-392.62555556, 1260.73744444])
A_ub = np.array([[1, 0.1], [-1, -0.1], [1, 1]])
b_ub = np.array([10,-10,10])
linprog_simplex(c=c, A_ub=A_ub, b_ub=b_ub)

SimplexResult(x=array([10., -0.]), lambd=array([   0.        , 1837.07      , 1444.44444444]), fun=-3926.2555556, success=True, status=0, num_iter=5)

c = np.array([-4.09555556,  4.59044444])
A_ub = np.array([[1, 0.1], [-1, -0.1], [1, 1]])
b_ub = np.array([9.1,-0.1,0.1])
linprog_simplex(c=c, A_ub=A_ub, b_ub=b_ub)

SimplexResult(x=array([ 0.1, -0. ]), lambd=array([0.        , 9.65111111, 5.55555555]), fun=-0.40955555600000004, success=True, status=0, num_iter=5)

[coveralls]

coverage: 93.041% (+0.009%) from 93.032%
when pulling 85ca2a1 on fix-linprog
into d7c2f52 on main.

[oyamad]

@mmcky It would be great if you could make a new release when you have time.. Thanks!

[mmcky]

thanks @oyamad -- will look at this now. 👍