On 11/14/2012 06:59 AM, platane wrote:
In Sage 5.4 determinant for dense matrix is very slow. For the following Hankel
determinant calculation, Sage 4.6.1 is 100000 time more fast than Sage 5.4 (!!):
Sage 5.4, Sparse = False, Time=117.49
Sage 4.6.1, Sparse=False, Time=0.0011
# --------------------
import time
def test(K, SP):
n=100
f=taylor(prod((1-x**i) for i in range(1,n)),x,0,n)
A=[f.coefficient(x,i) for i in range(n)]
cf= [[A[i+j] for i in range(K)] for j in range(K)]
m= matrix(ZZ, cf, sparse=SP)
#
t0=time.time()
print " K =", K, ", result =", m.det()
t_det= time.time()-t0
print " ",version()
print " sparse= ", SP
print " time = ", t_det
KK=30
test(KK, True)
print
test(KK, False)
# --------------------
It happened some time in between 4.7.2 and 4.8: (det.sage) is the above
code.
----------------------------------------------------------------------
| Sage Version 4.7.2, Release Date: 2011-10-29 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: attach det.sage
K = 30 , result = -9
Sage Version 4.7.2, Release Date: 2011-10-29
sparse= True
time = 0.260323047638
K = 30 , result = -9
Sage Version 4.7.2, Release Date: 2011-10-29
sparse= False
time = 0.026487827301
sage:
Exiting Sage (CPU time 0m1.77s, Wall time 0m29.31s).
Exiting spawned Gap process.
----------------------------------------------------------------------
| Sage Version 4.8, Release Date: 2012-01-20 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: attach det.sage
K = 30 , result = -9
Sage Version 4.8, Release Date: 2012-01-20
sparse= True
time = 0.011904001236
K = 30 , result = -9
Sage Version 4.8, Release Date: 2012-01-20
sparse= False
time = 122.02807498
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