I get slightly different results when I repeat a calculation. In a
long simulation the differences snowball and swamp the effects I am
trying to measure.
In the attach script there are three tests.
In test1, I construct matrices x and y and then repeatedly calculate z
= calc(x,y). The result z is the same every time. So this test passes.
In test2, I construct matrices x and y each time before calculating z
= calc(x,y). Sometimes z is slightly different---of the order of 1e-21
to 1e-18. But the x's test to be equal and so do the y's. This test
fails. (It doesn't fail on my friend's windows box; I'm running
linux.)
test3 is the same as test2 but I calculate z like this: z = calc(100*x
,y) / (100 * 100). This test passes.
What is going on?
Here is some sample output:
import repeat
repeat.all()
4 z different 8.47032947254e-22
5 z different 8.47032947254e-22
7 z different 8.47032947254e-22
9 z different 8.47032947254e-22
10 z different 8.47032947254e-22
16 z different 8.47032947254e-22
24 z different 8.47032947254e-22
25 z different 8.47032947254e-22
26 z different 8.47032947254e-22
27 z different 8.47032947254e-22
30 z different 8.47032947254e-22
32 z different 8.47032947254e-22
34 z different 8.47032947254e-22
35 z different 8.47032947254e-22
36 z different 8.47032947254e-22
39 z different 8.47032947254e-22
40 z different 8.47032947254e-22
41 z different 8.47032947254e-22
45 z different 8.47032947254e-22
46 z different 8.47032947254e-22
50 z different 8.47032947254e-22
52 z different 8.47032947254e-22
53 z different 8.47032947254e-22
55 z different 8.47032947254e-22
56 z different 8.47032947254e-22
58 z different 8.47032947254e-22
66 z different 8.47032947254e-22
67 z different 8.47032947254e-22
71 z different 8.47032947254e-22
73 z different 8.47032947254e-22
74 z different 8.47032947254e-22
83 z different 8.47032947254e-22
86 z different 8.47032947254e-22
87 z different 8.47032947254e-22
88 z different 8.47032947254e-22
89 z different 8.47032947254e-22
90 z different 8.47032947254e-22
92 z different 8.47032947254e-22
test1: 0 differences
test2: 38 differences
test3: 0 differences
Repeated runs tend to give me the same number of differences in test2
for several runs. Then I get a new number of differences which last
for severals runs...
import numpy.matlib as M
def load():
# x data
x = M.zeros((3,3))
x[0,0] = 0.00301404794991108
x[0,1] = 0.00264742266711118
x[0,2] = -0.00112705028731085
x[1,0] = 0.0228605377994491
x[1,1] = 0.00337153112741583
x[1,2] = -0.00823674912992519
x[2,0] = 0.00447839875836716
x[2,1] = 0.00274880280576514
x[2,2] = -0.00161133933606597
# y data
y = M.zeros((3,1))
y[0,0] = 0.000885398
y[1,0] = 0.00667193
y[2,0] = 0.000324727
return x, y
def calc(x, y):
return x * (x.T * y)
def test1(nsim=100):
x, y = load()
z0 = calc(x, y)
ndiff = 0
for i in xrange(nsim):
z = calc(x, y)
if (z != z0).any():
ndiff += 1
print i, 'z different', abs(z - z0).max()
return ndiff
def test2(nsim=100):
x0, y0 = load()
z0 = calc(x0, y0)
ndiff = 0
for i in xrange(nsim):
x, y = load()
z = calc(x, y)
if (x != x0).any():
print i, 'x different', abs(x - x0).max()
if (y != y0).any():
print i, 'y different', abs(y - y0).max()
if (z != z0).any():
print i, 'z different', abs(z - z0).max()
ndiff += 1
return ndiff
def test3(nsim=100):
x0, y0 = load()
z0 = calc(100*x0, y0) / (100 * 100)
ndiff = 0
for i in xrange(nsim):
x, y = load()
z = calc(100*x, y) / (100 * 100)
if (x != x0).any():
print i, 'x different', abs(x - x0).max()
if (y != y0).any():
print i, 'y different', abs(y - y0).max()
if (z != z0).any():
print i, 'z different', abs(z - z0).max()
ndiff += 1
return ndiff
def all():
n1 = test1()
n2 = test2()
n3 = test3()
print
print 'test1: ', n1, ' differences'
print 'test2: ', n2, ' differences'
print 'test3: ', n3, ' differences'
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