I prepare a matrix of random numbers, calculate its inverse and matrix multiply it with the original matrix. This, in theory, gives the unit matrix. How can I let numpy
do that for me?
import numpy
A = numpy.zeros((100,100))
E = numpy.zeros((100,100))
size = 100
for i in range(size):
for j in range(size):
A[i][j]+=numpy.random.randint(10)
if i == j:
E[i][j]+=1
A_inv = numpy.linalg.linalg.inv(A)
print numpy.dot(A, A_inv)
Running the code produces
[me]machine @ numeric $ python rand_diag.py
[[ 1.00000000e+00 -7.99360578e-15 -1.14491749e-16 ..., 3.81639165e-17
-4.42701431e-15 1.17961196e-15]
[ -5.55111512e-16 1.00000000e+00 -2.22044605e-16 ..., -3.88578059e-16
1.33226763e-15 -8.32667268e-16]
It's evident the result is a unit matrix, but not precisely, so print numpy.dot(A, A_inv) == E
evidently gives False
. I'm doing this for practicing linear algebra and trying to find the size of the matrix for which my machine arrives at its limits. Getting a True
would be didactically appealing.
Edit:
Setting size=10000
, I run out of memory
[me]machine @ numeric $ Python(794) malloc:
***mmap(size=800002048) failed (error code=12)
*** error: can't allocate region
*** set a breakpoint in malloc_error_break to debug
Traceback (most recent call last):
File "rand_diag.py", line 14, in <module> A_inv = numpy.linalg.linalg.inv(A)
File "/Library/Frameworks/Python.framework/Versions/7.2/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 445, in inv
return wrap(solve(a, identity(a.shape[0], dtype=a.dtype)))
File "/Library/Frameworks/Python.framework/Versions/7.2/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 323, in solve
a, b = _fastCopyAndTranspose(t, a, b)
File "/Library/Frameworks/Python.framework/Versions/7.2/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 143, in _fastCopyAndTranspose
cast_arrays = cast_arrays + (_fastCT(a),)
MemoryError
[1]+ Exit 1 python rand_diag.py
How can I allocate more memory and how can I run this in parallel (I have 4 cores)?
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