问题
I have the following code:
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
def f(arrA, arrB):
""" Check if two matrices overlap"""
return not set(map(tuple, arrA)).isdisjoint(map(tuple, arrB))
Basically it runs Linear Programing by using NNLS. By taking matrix A and vector B. And I have two sets of those: A1 B1 and A2 B2.
And A1 is subset of A2, and B1 is subset of B2.
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]])
B2=array([ 5.144, 30.771, 22.133, 0. , 0.427, 0. ,
1.329, 197.087, 84.344, 1.466, 3.974, 0.435,
8.291, 45.059, 5.755, 0.519, 21.662, 41.665,
5.544, 0.482, 1.953, 4.214, 0.576, 0. ,
30.272, 2.262, 24.92 , 30.32 , 0.948, 1.107, 10.095])
A2 = array([[ 29.95, 36.96, 51.68, 35.95, 34.18, 49.8 ,
30.47, 4565.08, 34.25],
[ 29.95, 36.96, 51.68, 35.95, 34.18, 49.8 ,
30.47, 4565.08, 34.25],
[ 46.35, 80.58, 48.8 , 80.31, 489.01, 40.98,
29.98, 44.3 , 5882.96],
[ 26. , 151.76, 2850.8 , 64.88, 29.08, 110.99,
23.67, 23.69, 25.84],
[ 26. , 151.76, 2850.8 , 64.88, 29.08, 110.99,
23.67, 23.69, 25.84],
[ 26. , 151.76, 2850.8 , 64.88, 29.08, 110.99,
23.67, 23.69, 25.84],
[ 19.33, 23.2 , 28.65, 22.05, 5271.38, 24.4 ,
20.88, 20.28, 23.45],
[ 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 ],
[ 21.18, 4213.22, 1172.23, 39.19, 33.68, 32.09,
17.48, 47.11, 26.52],
[ 21.18, 4213.22, 1172.23, 39.19, 33.68, 32.09,
17.48, 47.11, 26.52],
[ 23.61, 28.03, 22.92, 27.01, 24.62, 27.2 ,
23.86, 23.1 , 925.26],
[ 23.61, 28.03, 22.92, 27.01, 24.62, 27.2 ,
23.86, 23.1 , 925.26],
[ 23.61, 28.03, 22.92, 27.01, 24.62, 27.2 ,
23.86, 23.1 , 925.26],
[ 111.35, 24.3 , 42.06, 23.83, 118.74, 21.12,
1464.47, 86.8 , 157.35],
[ 111.35, 24.3 , 42.06, 23.83, 118.74, 21.12,
1464.47, 86.8 , 157.35],
[ 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],
[ 21.01, 14.49, 9.62, 19.74, 10.73, 2396.79,
15.9 , 11.78, 10.06],
[ 41.63, 204.32, 4170.37, 86.95, 49.92, 87.15,
51.88, 45.38, 42.89],
[ 2500.99, 60.14, 59. , 64.74, 72.4 , 61.48,
64.68, 51.07, 51.89],
[ 62.61, 121.71, 161.71, 2949.63, 74.98, 82.22,
63.01, 719.7 , 72.93],
[ 62.61, 121.71, 161.71, 2949.63, 74.98, 82.22,
63.01, 719.7 , 72.93],
[ 81.34, 60.16, 357.92, 43.48, 36.92, 39.13,
1772.07, 68.43, 38.07]])
Then I find something strange. The solution of a particular point exist in A1 but it becomes 0 in A2. This is how it looks:
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])
In [10]: by_nnls(A=A2,B=B2)
Out[10]:
array([ 0.72020358, 0.0992065 , 0.04161968, 0.04371648, 0.00698775,
0. , 0. , 0.03533024, 0.05293576])
Sixth (0-based) solution of A1 gives 0.02125942 but in B2 yield 0.
Why is that? How can I resolve this issue?
My understanding is that as you add more evidence (i.e. rows) the value should increase. Perhaps that intuition was wrong?
If you'd like to verify whether A1 is subset of A2:
In [15]: f(A1,A2)
Out[15]: True
来源：https://stackoverflow.com/questions/35405183/stability-of-scipy-nnls-solution-on-two-overlapping-a-matrices