[Scipy NNLS](http://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.optimize.nnls.html#scipy.optimize.nnls) perform this:

```
Solve argmin_x || Ax - b ||_2 for x>=0.

```

What's the alternative way to do it if I seek
strictly non-zero solution (i.e. `x > 0`) ?

Here is my LP code using Scipy's NNLS:

```
import numpy as np
from numpy import array
from scipy.optimize import nnls

def by_nnls(A=None, B=None):
    """ Linear programming by NNLS """
    #print "NOF row = ", A.shape[0]
    A = np.nan_to_num(A)
    B = np.nan_to_num(B)

    x, rnorm = nnls(A,B)
    x = x / x.sum()
    # print repr(x)
    return x

B1 = array([  22.133,  197.087,   84.344,    1.466,    3.974,    0.435,
          8.291,   45.059,    5.755,    0.519,    0.   ,   30.272,
         24.92 ,   10.095])
A1 = array([[   46.35,    80.58,    48.8 ,    80.31,   489.01,    40.98,
           29.98,    44.3 ,  5882.96],
       [ 2540.73,    49.53,    26.78,    30.49,    48.51,    20.88,
           19.92,    21.05,    19.39],
       [ 2540.73,    49.53,    26.78,    30.49,    48.51,    20.88,
           19.92,    21.05,    19.39],
       [   30.95,  1482.24,   100.48,    35.98,    35.1 ,    38.65,
           31.57,    87.38,    33.39],
       [   30.95,  1482.24,   100.48,    35.98,    35.1 ,    38.65,
           31.57,    87.38,    33.39],
       [   30.95,  1482.24,   100.48,    35.98,    35.1 ,    38.65,
           31.57,    87.38,    33.39],
       [   15.99,   223.27,   655.79,  1978.2 ,    18.21,    20.51,
           19.  ,    16.19,    15.91],
       [   15.99,   223.27,   655.79,  1978.2 ,    18.21,    20.51,
           19.  ,    16.19,    15.91],
       [   16.49,    20.56,    19.08,    18.65,  4568.97,    20.7 ,
           17.4 ,    17.62,    25.51],
       [   33.84,    26.58,    18.69,    40.88,    19.17,  5247.84,
           29.39,    25.55,    18.9 ],
       [   42.66,    83.59,    99.58,    52.11,    46.84,    64.93,
           43.8 ,  7610.12,    47.13],
       [   42.66,    83.59,    99.58,    52.11,    46.84,    64.93,
           43.8 ,  7610.12,    47.13],
       [   41.63,   204.32,  4170.37,    86.95,    49.92,    87.15,
           51.88,    45.38,    42.89],
       [   81.34,    60.16,   357.92,    43.48,    36.92,    39.13,
         1772.07,    68.43,    38.07]])

```

The usage:

```
In [9]: by_nnls(A=A1,B=B1)
Out[9]:
array([ 0.70089761,  0.        ,  0.06481495,  0.14325696,  0.01218972,
        0.        ,  0.02125942,  0.01906576,  0.03851557]

```

Note the zero solution above.