Hi,
Oh well, I can see you've now have an implementation (new = False)
that beats mine when clustered :) You can use some of the ideas such
as the out ufunc argument and temporary storage to your advantage
nevertheless. For example you can use the out argument of these
ufuncs even more, replacing:
"""
self.dw_struct[:] = 1.0
self.dw_struct[:] = multiply(self.dw_struct,
tile(asarray(dw).reshape(self.NE, self.NS)[:,:,None,None,None], (1, 1,
self.NM, self.NO, self.ND)), ) * self.disp_struct * self.frqs_a
"""
with:
"""
self.dw_struct[:] = 1.0
multiply(self.dw_struct, tile(asarray(dw).reshape(self.NE,
self.NS)[:,:,None,None,None], (1, 1, self.NM, self.NO, self.ND)),
self.dw_struct)
multiply(self.dw_struct, self.disp_struct, self.dw_struct)
multiply(self.dw_struct, self.frqs_a, self.dw_struct)
"""
That shaves off a few milliseconds by avoiding automatic array
creation and destruction, with before:
"""
('sfrq: ', 600000000.0, 'number of cpmg frq', 15, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58.]))
('sfrq: ', 800000000.0, 'number of cpmg frq', 20, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58., 62., 66., 70., 74., 78.]))
('sfrq: ', 900000000.0, 'number of cpmg frq', 22, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58., 62., 66., 70., 74., 78., 82.,
86.]))
('chi2 cluster:', 0.0)
Wed Jun 11 11:45:42 2014 /tmp/tmpwkhLSr
198252 function calls (197150 primitive calls) in 1.499
seconds
Ordered by: cumulative time
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 1.499 1.499 <string>:1(<module>)
1 0.001 0.001 1.499 1.499
profiling_cr72.py:449(cluster)
1000 0.001 0.000 1.427 0.001
profiling_cr72.py:413(calc)
1000 0.009 0.000 1.425 0.001
relax_disp.py:1020(func_CR72_full)
1000 0.066 0.000 1.409 0.001
relax_disp.py:544(calc_CR72_chi2)
1300 0.903 0.001 1.180 0.001 cr72.py:101(r2eff_CR72)
2300 0.100 0.000 0.222 0.000 numeric.py:2056(allclose)
3000 0.032 0.000 0.150 0.000 shape_base.py:761(tile)
4000 0.104 0.000 0.104 0.000 {method 'repeat' of
'numpy.ndarray' objects}
11828 0.091 0.000 0.091 0.000 {method 'reduce' of
'numpy.ufunc' objects}
1 0.000 0.000 0.071 0.071
profiling_cr72.py:106(__init__)
1 0.010 0.010 0.056 0.056
profiling_cr72.py:173(return_r2eff_arrays)
1000 0.032 0.000 0.048 0.000 chi2.py:72(chi2_rankN)
4609 0.005 0.000 0.045 0.000 fromnumeric.py:1762(any)
2300 0.004 0.000 0.036 0.000 fromnumeric.py:1621(sum)
"""
And after:
"""
('sfrq: ', 600000000.0, 'number of cpmg frq', 15, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58.]))
('sfrq: ', 800000000.0, 'number of cpmg frq', 20, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58., 62., 66., 70., 74., 78.]))
('sfrq: ', 900000000.0, 'number of cpmg frq', 22, array([ 2., 6.,
10., 14., 18., 22., 26., 30., 34., 38., 42.,
46., 50., 54., 58., 62., 66., 70., 74., 78., 82.,
86.]))
('chi2 cluster:', 0.0)
Wed Jun 11 11:49:29 2014 /tmp/tmpML9Lx5
198252 function calls (197150 primitive calls) in 1.462
seconds
Ordered by: cumulative time
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 1.462 1.462 <string>:1(<module>)
1 0.001 0.001 1.462 1.462
profiling_cr72.py:449(cluster)
1000 0.001 0.000 1.393 0.001
profiling_cr72.py:413(calc)
1000 0.009 0.000 1.392 0.001
relax_disp.py:1022(func_CR72_full)
1000 0.056 0.000 1.376 0.001
relax_disp.py:544(calc_CR72_chi2)
1300 0.887 0.001 1.158 0.001 cr72.py:101(r2eff_CR72)
2300 0.097 0.000 0.217 0.000 numeric.py:2056(allclose)
3000 0.031 0.000 0.148 0.000 shape_base.py:761(tile)
4000 0.103 0.000 0.103 0.000 {method 'repeat' of
'numpy.ndarray' objects}
11828 0.090 0.000 0.090 0.000 {method 'reduce' of
'numpy.ufunc' objects}
1 0.000 0.000 0.068 0.068
profiling_cr72.py:106(__init__)
1 0.010 0.010 0.053 0.053
profiling_cr72.py:173(return_r2eff_arrays)
1000 0.031 0.000 0.047 0.000 chi2.py:72(chi2_rankN)
4609 0.006 0.000 0.044 0.000 fromnumeric.py:1762(any)
2300 0.004 0.000 0.036 0.000 fromnumeric.py:1621(sum)
"""
The additional suggestions I didn't specify before was to use these
ufuncs with the out argument in the lib.dispersion modules themselves.
You don't need to create R2eff here, just pack it into back_calc!
Regards,
Edward
On 11 June 2014 11:55, Troels Emtekær Linnet <tlinnet@xxxxxxxxxxxxx>
wrote:
Hi Edward.
Some timings.
Per spin, you have a faster method.
But I win per cluster.
1000 iterations
1 / 100 spins
Edward
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 0.523 0.523 <string>:1(<module>)
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 3.875 3.875 <string>:1(<module>)
Troels Tile
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 0.563 0.563 <string>:1(<module>)
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 2.102 2.102 <string>:1(<module>)
Troels Outer
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 0.546 0.546 <string>:1(<module>)
ncalls tottime percall cumtime percall
filename:lineno(function)
1 0.000 0.000 1.974 1.974 <string>:1(<module>)
2014-06-11 11:46 GMT+02:00 Troels Emtekær Linnet
<tlinnet@xxxxxxxxxxxxx>:
Hi Edward.
This is a really god page!
http://docs.scipy.org/doc/numpy/reference/ufuncs.html
""
Tip
The optional output arguments can be used to help you save memory for
large calculations. If your arrays are large, complicated expressions
can take longer than absolutely necessary due to the creation and
(later) destruction of temporary calculation spaces. For example, the
expression G = a * b + c is equivalent to t1 = A * B; G = T1 + C; del
t1. It will be more quickly executed as G = A * B; add(G, C, G) which
is the same as G = A * B; G += C.
""
2014-06-10 23:08 GMT+02:00 Edward d'Auvergne <edward@xxxxxxxxxxxxx>:
Note that masks and numpy.ma.multiply() and numpy.ma.add() may speed
this up even more. However due to overheads in the numpy masking,
there is a chance that this also makes the dw and R20 data structure
construction slower.
Regards,
Edward
On 10 June 2014 22:36, Edward d'Auvergne <edward@xxxxxxxxxxxxx>
wrote:
Hi Troels,
To make things even simpler, here is what needs to be done for R20,
R20A and R20B:
"""
from numpy import abs, add, array, float64, multiply, ones, sum,
zeros
# Init mimic.
#############
# Values from
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster.
NE = 1
NS = 2
NM = 2
NO = 1
ND = 8
R20A = array([ 9.984626320294867, 11.495327724693091,
12.991028416082928, 14.498419290021163])
shape = (NE, NS, NM, NO, ND)
# Final structure for lib.dispersion.
R20A_struct = zeros(shape, float64)
# Temporary storage to avoid memory allocations and garbage
collection.
R20A_temp = zeros(shape, float64)
# The structure for multiplication with R20A to piecewise build up
the
full R20A structure.
R20A_mask = zeros((NS*NM,) + shape, float64)
for si in range(NS):
for mi in range(NM):
R20A_mask[si*NM+mi, :, si, mi] = 1.0
print(R20A_mask)
print("\n\n")
# Values to be found (again taken directly from
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster - as a
printout of dw_frq_a).
R20A_final = array([[[[[ 9.984626320294867, 9.984626320294867,
9.984626320294867,
9.984626320294867, 9.984626320294867,
9.984626320294867,
9.984626320294867, 9.984626320294867]],
[[ 11.495327724693091, 11.495327724693091,
11.495327724693091,
11.495327724693091, 11.495327724693091,
11.495327724693091,
11.495327724693091,
11.495327724693091]]],
[[[ 12.991028416082928, 12.991028416082928,
12.991028416082928,
12.991028416082928, 12.991028416082928,
12.991028416082928,
12.991028416082928, 12.991028416082928]],
[[ 14.498419290021163, 14.498419290021163,
14.498419290021163,
14.498419290021163, 14.498419290021163,
14.498419290021163,
14.498419290021163,
14.498419290021163]]]]])
# Target function.
##################
# Loop over the R20A elements (one per spin).
for r20_index in range(NS*NM):
# First multiply the spin specific R20A with the spin specific
frequency mask, using temporary storage.
multiply(R20A[r20_index], R20A_mask[r20_index], R20A_temp)
# The add to the total.
add(R20A_struct, R20A_temp, R20A_struct)
# Show that the structure is reproduced perfectly.
print(R20A_struct)
print(R20A_struct - R20A_final)
print(sum(abs(R20A_struct - R20A_final)))
"""
You may notice one simplification compared to my previous example
for
the dw parameter
(http://thread.gmane.org/gmane.science.nmr.relax.devel/6135/focus=6154).
The values here too come from the
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster system
test.
Regards,
Edward
On 10 June 2014 21:31, Edward d'Auvergne <edward@xxxxxxxxxxxxx>
wrote:
Hi Troels,
No need for an example. Here is the code to add to your
infrastructure which will make the analytic dispersion models
insanely
fast:
"""
from numpy import add, array, float64, multiply, ones, zeros
# Init mimic.
#############
# Values from
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster.
NE = 1
NS = 2
NM = 2
NO = 1
ND = 8
dw = array([ 1.847792726895652, 0.193719379085542])
frqs = [-382.188861036982701, -318.479128911056137]
shape = (NE, NS, NM, NO, ND)
# Final structure for lib.dispersion.
dw_struct = zeros(shape, float64)
# Temporary storage to avoid memory allocations and garbage
collection.
dw_temp = zeros((NS,) + shape, float64)
# The structure for multiplication with dw to piecewise build up
the
full dw structure.
dw_mask = zeros((NS,) + shape, float64)
for si in range(NS):
for mi in range(NM):
dw_mask[si, :, si, mi] = frqs[mi]
print(dw_mask)
# Values to be found (again taken directly from
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster - as a
printout of dw_frq_a).
dw_final = array([[[[[-706.205797724669765, -706.205797724669765,
-706.205797724669765, -706.205797724669765,
-706.205797724669765, -706.205797724669765,
-706.205797724669765,
-706.205797724669765]],
[[-588.483418069912318, -588.483418069912318,
-588.483418069912318, -588.483418069912318,
-588.483418069912318, -588.483418069912318,
-588.483418069912318,
-588.483418069912318]]],
[[[ -74.03738885349469 , -74.03738885349469 ,
-74.03738885349469 , -74.03738885349469 ,
-74.03738885349469 , -74.03738885349469 ,
-74.03738885349469 , -74.03738885349469
]],
[[ -61.69557910435401 , -61.69557910435401 ,
-61.69557910435401 , -61.69557910435401 ,
-61.69557910435401 , -61.69557910435401 ,
-61.69557910435401 , -61.69557910435401
]]]]])
# Target function.
##################
# Loop over the dw elements (one per spin).
for si in range(NS):
# First multiply the spin specific dw with the spin specific
frequency mask, using temporary storage.
multiply(dw[si], dw_mask[si], dw_temp[si])
# The add to the total.
add(dw_struct, dw_temp[si], dw_struct)
# Show that the structure is reproduced perfectly.
print(dw_struct - dw_final)
"""
As mentioned in the comments, the structures come from the
Relax_disp.test_cpmg_synthetic_ns3d_to_cr72_noise_cluster. I just
added a check of "if len(dw) > 1: asdfasd" to kill the test, and
added
printouts to obtain dw, frq_a, dw_frq_a, etc. This is exactly the
implementation I described. Although there might be an even
faster
way, this will eliminate all numpy array creation and deletion via
Python garbage collection in the target functions (when used for
R20
as well).
Regards,
Edward
On 10 June 2014 21:09, Edward d'Auvergne <edward@xxxxxxxxxxxxx>
wrote:
If you have a really complicated example of your current
'dw_frq_a'
data structure for multiple spins and multiple fields, that
could help
to construct an example.
Cheers,
Edward
On 10 June 2014 20:57, Edward d'Auvergne <edward@xxxxxxxxxxxxx>
wrote:
Hi,
I'll have a look tomorrow but, as you've probably seen, some of
the
fine details such as indices to be used need to be sorted out
when
implementing this.
Regards,
Edward
On 10 June 2014 20:49, Troels Emtekær Linnet
<tlinnet@xxxxxxxxxxxxx> wrote:
What ever I do, I cannot get this to work?
Can you show an example ?
2014-06-10 16:29 GMT+02:00 Edward d'Auvergne
<edward@xxxxxxxxxxxxx>:
Here is an example of avoiding automatic numpy data structure
creation
and then garbage collection:
"""
from numpy import add, ones, zeros
a = zeros((5, 4))
a[1] = 1
a[:,1] = 2
b = ones((5, 4))
add(a, b, a)
print(a)
"""
The result is:
[[ 1. 3. 1. 1.]
[ 2. 3. 2. 2.]
[ 1. 3. 1. 1.]
[ 1. 3. 1. 1.]
[ 1. 3. 1. 1.]]
The out argument for numpy.add() is used here to operate in a
similar
way to the Python "+=" operation. But it avoids the
temporary numpy
data structures that the Python "+=" operation will create.
This will
save a lot of time in the dispersion code.
Regards,
Edward
On 10 June 2014 15:56, Edward d'Auvergne
<edward@xxxxxxxxxxxxx> wrote:
Hi Troels,
Here is one suggestion, of many that I have, for
significantly
improving the speed of the analytic dispersion models in your
'disp_spin_speed' branch. The speed ups you have currently
achieved
for spin clusters are huge and very impressive. But now
that you have
the infrastructure in place, you can advance this much more!
The suggestion has to do with the R20, R20A, and R20B numpy
data
structures. They way they are currently handled is
relatively
inefficient, in that they are created de novo for each
function call.
This means that memory allocation and Python garbage
collection
happens for every single function call - something which
should be
avoided at almost all costs.
A better way to do this would be to have a self.R20_struct,
self.R20A_struct, and self.R20B_struct created in
__init__(), and then
to pack in the values from the parameter vector into these
structures.
You could create a special structure in __init__() for this.
It would
have the dimensions [r20_index][ei][si][mi][oi], where the
first
dimension corresponds to the different R20 parameters. And
for each
r20_index element, you would have ones at the
[ei][si][mi][oi]
positions where you would like R20 to be, and zeros
elsewhere. The
key is that this is created at the target function start up,
and not
for each function call.
This would be combined with the very powerful 'out' argument
set to
self.R20_struct with the numpy.add() and numpy.multiply()
functions to
prevent all memory allocations and garbage collection.
Masks could be
used, but I think that that would be much slower than having
special
numpy structures with ones where R20 should be and zeros
elsewhere.
For just creating these structures, looping over a single
r20_index
loop and multiplying by the special
[r20_index][ei][si][mi][oi]
one/zero structure and using numpy.add() and
numpy.multiply() with out
arguments would be much, much faster than masks or the
current
R20_axis logic. It will also simplify the code.
Regards,
Edward
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Re: Speed up suggestion for task #7807.