I have a numpy 2d array [medium/large sized - say 500x500]. I want to find the eigenvalues of the element-wise exponent of it. The problem is that some of the values are quite negative (-800,-1000, etc), and their exponents underflow (meaning they are so close to zero, so that numpy treats them as zero). Is there anyway to use arbitrary precision in numpy?
The way I dream it:
import numpy as np
np.set_precision('arbitrary') # <--- Missing part
a = np.array([[-800.21,-600.00],[-600.00,-1000.48]])
ex = np.exp(a) ## Currently warns about underflow
eigvals, eigvecs = np.linalg.eig(ex)
I have searched for a solution with gmpy and mpmath to no avail. Any idea will be welcome.
SymPy can calculate arbitrary precision:
from sympy import exp, N, S
from sympy.matrices import Matrix
data = [[S("-800.21"),S("-600.00")],[S("-600.00"),S("-1000.48")]]
m = Matrix(data)
ex = m.applyfunc(exp).applyfunc(lambda x:N(x, 100))
vecs = ex.eigenvects()
print vecs[0][0] # eigen value
print vecs[1][0] # eigen value
print vecs[0][2] # eigen vect
print vecs[1][2] # eigen vect
output:
-2.650396553004310816338679447269582701529092549943247237903254759946483528035516341807463648841185335e-261
2.650396553004310816338679447269582701529092549943247237903254759946483528035516341807466621962539464e-261
[[-0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999994391176386872]
[ 1]]
[[1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000560882361313]
[ 1]]
you can change 100 in N(x, 100) to other precision, but, as I tried 1000, the calculation of eigen vect failed.