In [1]:
from pycalphad import Database, Model
from pycalphad.core.utils import make_callable
import pycalphad.variables as v
import numba
import numpy as np
In [2]:
dbf = Database('Al-Ni/Al-Ni-Dupin-2001.tdb')
mod = Model(dbf, ['AL', 'NI', 'VA'], 'FCC_L12')
In [3]:
from sympy import lambdify
from pycalphad.core.utils import NumPyPrinter
@numba.jit('float64(boolean, float64, float64)', nopython=True, nogil=True)
def where(condition, x, y):
if condition:
return x
else:
return y
In [4]:
x1 = np.random.rand(5, 1, 1)*2000
x2 = np.random.rand(5, 5, 1)
x3 = np.random.rand(5, 5, 1)
x4 = np.random.rand(5, 5, 6000)
x5 = np.random.rand(5, 5, 6000)
x6 = np.random.rand(5, 5, 6000)
#np.testing.assert_allclose(vec_func(x1, x2, x3, x4, x5, x6), pure_func(x1, x2, x3, x4, x5, x6))
#%timeit vec_func(x1, x2, x3, x4, x5, x6)
In [5]:
from sympy import lambdify, count_ops
import numba
def make_gradient_from_graph(graph, wrt):
wrt = tuple(wrt)
grads = np.empty((len(wrt)), dtype=object)
hess_indices = []
namespace = {}
for i in range(len(wrt)):
grads[i] = graph.diff(wrt[i])
#print('------------------------------------')
#print(grads[i])
for j in range(i, len(wrt)):
hess_elem = grads[i].diff(wrt[j])
hess_elem_func = lambdify(tuple(wrt), hess_elem, dummify=True,\
modules=[{'where': where}, 'numpy'], printer=NumPyPrinter)
namespace['hess_{0}{1}'.format(i, j)] = numba.jit('float64({})'.format(','.join(['float64'] * len(wrt))),
nopython=True, nogil=True)(hess_elem_func)
hess_indices.append((i, j))
grad_elem_func = lambdify(tuple(wrt), grads[i], dummify=True,\
modules=[{'where': where}, 'numpy'], printer=NumPyPrinter)
namespace['grad_{0}'.format(i)] = numba.jit('float64({})'.format(','.join(['float64'] * len(wrt))),
nopython=True, nogil=True)(grad_elem_func)
# Build the gradient and Hessian using compile() and exec
# We do this because Numba needs "static" information about the arguments and functions
call_args = ','.join(['_x{0}'.format(i) for i in range(len(wrt))])
call_passed_args = ','.join(['_x{0}[0]'.format(i) for i in range(len(wrt))])
grad_code = 'def grad_func({0}, lengthfix, result):'.format(call_args)
grad_list = [' result[..., {0}] = grad_{0}({1})'.format(i, call_passed_args) for i in range(len(wrt))]
grad_code = grad_code + '\n' + '\n'.join(grad_list)
#print(grad_code)
grad_code = compile(grad_code, '<string>', 'exec')
try:
exec grad_code in namespace
except SyntaxError:
exec(grad_code, namespace)
# Now construct the Hessian
hess_code = 'def hess_func({0}, lengthfix, result):'.format(call_args)
hess_list = [' result[{0},{1}] = result[{1}, {0}] = hess_{0}{1}({2})'.format(i, j, call_passed_args) \
for i, j in hess_indices]
hess_code = hess_code + '\n' + '\n'.join(hess_list)
#print(hess_code)
hess_code = compile(hess_code, '<string>', 'exec')
try:
exec hess_code in namespace
except SyntaxError:
exec(hess_code, namespace)
grad_func = numba.guvectorize([','.join(['float64[:]'] * (len(wrt)+2))],
','.join(['()'] * len(wrt)) + ',(n)->(n)', nopython=True)(namespace['grad_func'])
hess_func = None
hess_func = numba.guvectorize([','.join(['float64[:]'] * (len(wrt)+1)) + ',float64[:,:]'],
','.join(['()'] * len(wrt)) + ',(n)->(n,n)', nopython=True)(namespace['hess_func'])
return grad_func, hess_func
In [6]:
%time grad_func, hess_func = make_gradient_from_graph(mod.ast, mod.variables)
CPU times: user 2min 29s, sys: 634 ms, total: 2min 29s
Wall time: 2min 29s
In [7]:
%time grad_func(x1, x2, x3, x4, x5, x6, np.empty(6), np.zeros(x6.shape + (6,)))
CPU times: user 339 ms, sys: 1 ms, total: 340 ms
Wall time: 341 ms
Out[7]:
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-2.15679967e+05, -2.13877602e+05, -1.05044323e+05],
[ 8.26747974e+03, -1.86298718e+05, -1.88219434e+05,
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[ 4.48969994e+03, -5.06844260e+04, -4.18993567e+04,
-2.19473838e+05, -2.18247066e+05, -9.76418382e+04]],
[[ 4.37914804e+03, -4.63043151e+04, -3.90873039e+04,
-2.09495892e+05, -2.15212803e+05, -9.81782582e+04],
[ 4.54172648e+36, -1.35586793e+41, -1.05445632e+41,
-4.51955976e+40, -3.51485439e+40, -5.00661178e+40],
[ 7.88590998e+03, -1.77029639e+05, -1.49025663e+05,
-4.65675050e+05, -4.27099097e+05, -2.49132062e+05],
...,
[ 1.18678643e+21, -1.98188736e+25, -1.22423271e+25,
-6.60629121e+24, -4.08077571e+24, -2.75604360e+24],
[ 3.25749055e+17, -3.78220758e+21, -2.60098244e+21,
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[ 5.79295584e+03, -9.58459367e+04, -8.55759181e+04,
-3.07685339e+05, -3.00815764e+05, -1.43340059e+05]],
[[ 5.98568323e+03, -9.27482064e+04, -1.26820082e+05,
-2.97117052e+05, -3.09492993e+05, -1.01075790e+05],
[ 5.88431341e+03, -9.39373776e+04, -1.10257918e+05,
-2.98227626e+05, -3.00213311e+05, -9.14230215e+04],
[ 4.53298401e+03, -4.95417034e+04, -5.89423929e+04,
-2.21804365e+05, -2.18317273e+05, -6.12594135e+04],
...,
[ 7.50068457e+03, -1.58203963e+05, -2.00657555e+05,
-3.81817399e+05, -3.95806969e+05, -1.85746395e+05],
[ 4.34871724e+03, -4.32063710e+04, -5.26177458e+04,
-2.06082860e+05, -2.06381868e+05, -7.43750029e+04],
[ 7.09900271e+03, -1.36714708e+05, -1.94576706e+05,
-3.55051518e+05, -3.70490255e+05, -1.74351856e+05]],
[[ 5.06284990e+03, -7.85870208e+04, -6.62883140e+04,
-2.54503682e+05, -2.51580905e+05, -1.29199800e+05],
[ 5.20079980e+03, -9.31670857e+04, -7.39672577e+04,
-2.62363174e+05, -2.59849105e+05, -1.57421517e+05],
[ 6.07702188e+03, -1.24389013e+05, -1.05212042e+05,
-3.18580805e+05, -3.15140305e+05, -1.84612394e+05],
...,
[ 4.48953792e+03, -4.88486330e+04, -4.49140945e+04,
-2.16717289e+05, -2.22969380e+05, -8.78170133e+04],
[ 4.67578442e+03, -5.61892217e+04, -5.30571845e+04,
-2.27149092e+05, -2.30328336e+05, -1.07692158e+05],
[ 5.08102047e+03, -7.02333981e+04, -6.93949793e+04,
-2.52346257e+05, -2.55923528e+05, -1.25291650e+05]]],
[[[ 7.69682357e+02, -8.38898923e+03, -3.51918635e+04,
-1.76466334e+05, -1.84708703e+05, -2.17295533e+04],
[ 6.48277604e+02, -6.37644381e+03, -1.14452462e+04,
-1.49848321e+05, -1.51051898e+05, -2.05221803e+04],
[ 8.75835285e+02, -9.59403528e+03, -4.88355741e+04,
-2.01454554e+05, -2.13907837e+05, -2.34617368e+04],
...,
[ 8.00615531e+02, -7.05880649e+03, -2.94644033e+04,
-1.85989085e+05, -1.92231547e+05, -1.29951367e+04],
[ 8.98399188e+02, -1.41274066e+04, -3.95873607e+04,
-2.09666940e+05, -2.23320388e+05, -3.13678805e+04],
[ 8.50978814e+02, -1.14210881e+04, -4.34050178e+04,
-1.96269577e+05, -2.08829992e+05, -2.79010272e+04]],
[[ 7.29226322e+02, -1.53552096e+04, -1.57701202e+04,
-1.68518904e+05, -1.68718742e+05, -7.30576732e+03],
[ 1.21190214e+03, -2.08548328e+04, -5.82659161e+04,
-2.82009841e+05, -2.84493432e+05, -1.47751035e+04],
[ 6.43483707e+02, -9.22593307e+03, -9.27472679e+03,
-1.48219408e+05, -1.48534088e+05, -5.88275259e+03],
...,
[ 8.31332876e+02, -1.93529661e+04, -1.28100619e+04,
-1.94155738e+05, -1.92630935e+05, -6.02945605e+03],
[ 7.05180975e+02, -1.56613063e+04, -1.42254741e+04,
-1.62777614e+05, -1.62906567e+05, -7.55569304e+03],
[ 6.89430905e+02, -1.27126437e+04, -1.17419945e+04,
-1.59400989e+05, -1.59368579e+05, -6.21657106e+03]],
[[ 1.01145807e+03, -9.68617009e+03, -6.39559514e+04,
-2.32574180e+05, -2.40873763e+05, -6.96446290e+03],
[ 1.12109192e+03, -2.50072028e+04, -7.05463102e+04,
-2.55853250e+05, -2.73421447e+05, -2.57139343e+04],
[ 7.90321962e+02, -8.07068294e+03, -1.71480979e+04,
-1.83021527e+05, -1.88102718e+05, -5.54351947e+03],
...,
[ 6.47796571e+02, -6.19163313e+03, -1.37923177e+04,
-1.49318911e+05, -1.50452794e+05, -4.68479785e+03],
[ 8.93095776e+02, -9.00053371e+03, -3.12993077e+04,
-2.06032414e+05, -2.14439726e+05, -6.35522138e+03],
[ 8.77258388e+02, -8.28996123e+03, -2.26954140e+04,
-2.02810954e+05, -2.11635010e+05, -5.30387894e+03]],
[[ 9.77566821e+02, -9.43123747e+04, -1.35772267e+05,
-2.18504970e+05, -2.47823521e+05, -1.59481730e+05],
[ 2.69557993e+04, -2.04793698e+07, -2.90519056e+07,
-7.07013147e+06, -9.93500984e+06, -8.45805567e+06],
[ 8.29031306e+12, -3.98479034e+15, -1.23724523e+16,
-1.32826345e+15, -4.12415078e+15, -8.24135477e+15],
...,
[ 6.14726049e+14, -3.16029873e+18, -2.16250659e+18,
-1.05343291e+18, -7.20835529e+17, -1.88366076e+17],
[ 6.62846603e+07, -2.29738947e+10, -6.58586625e+10,
-7.65813278e+09, -2.19530597e+10, -5.61747531e+10],
[ 1.26531942e+03, -1.37795774e+05, -1.11016030e+05,
-3.37351566e+05, -3.47134759e+05, -1.40395227e+05]],
[[ 9.60691579e+02, -2.98612085e+04, -2.85754477e+04,
-2.30349682e+05, -2.31844968e+05, -2.46059521e+04],
[ 6.61045932e+02, -8.42816640e+03, -7.36312834e+03,
-1.54844812e+05, -1.53989896e+05, -7.85407716e+03],
[ 8.75419830e+02, -3.21453661e+04, -3.58734702e+04,
-2.04971166e+05, -2.09648097e+05, -3.22177235e+04],
...,
[ 9.32664251e+02, -4.59715396e+04, -2.14984462e+04,
-2.26935173e+05, -2.23860393e+05, -2.69236749e+04],
[ 8.71145707e+02, -2.15092095e+04, -2.36258428e+04,
-2.07158570e+05, -2.08543664e+05, -2.01236343e+04],
[ 6.33501181e+02, -7.32837591e+03, -7.51521195e+03,
-1.46430389e+05, -1.46713895e+05, -1.52345415e+04]]]])
In [8]:
result = np.zeros(x6.shape + (6,6))
%time hess_func(x1, x2, x3, x4, x5, x6, np.empty(6), result)
print(result)
CPU times: user 1.02 s, sys: 10 ms, total: 1.03 s
Wall time: 1.03 s
[[[[[ 1.45361401e+03 -2.29986420e+01 -1.73589195e+01 -1.02005939e+04
-1.01999411e+04 2.74441554e+03]
[ -2.29986420e+01 -4.74392218e+04 -6.93471628e+04 -1.77374376e+05
-4.11677105e+05 -9.88653984e+04]
[ -1.73589195e+01 -6.93471628e+04 -5.72915605e+04 -3.96437720e+05
-2.04358468e+05 -1.53607366e+05]
[ -1.02005939e+04 -1.77374376e+05 -3.96437720e+05 -2.46217342e+05
-5.19359773e+05 -5.35529146e+05]
[ -1.01999411e+04 -4.11677105e+05 -2.04358468e+05 -5.19359773e+05
-2.68361172e+05 -5.56156449e+05]
[ 2.74441554e+03 -9.88653984e+04 -1.53607366e+05 -5.35529146e+05
-5.56156449e+05 -1.31204415e+05]]
[[ 1.24397101e+03 -1.36274063e+01 -1.09969754e+01 -8.72771452e+03
-8.72540495e+03 2.18926887e+03]
[ -1.36274063e+01 -3.68949488e+04 -7.54660758e+04 -1.48501843e+05
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[ -8.72771452e+03 -1.48501843e+05 -3.43304270e+05 -2.07171698e+05
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[ -8.72540495e+03 -3.56051190e+05 -1.73638770e+05 -4.51677800e+05
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[ 2.18926887e+03 -1.21523230e+05 -1.16823966e+05 -4.29167244e+05
-4.48037086e+05 -1.03622666e+05]]
[[ 9.53279161e+02 -5.66636813e+00 -4.55636513e+00 -6.68638714e+03
-6.68600689e+03 1.50980181e+03]
[ -5.66636813e+00 -4.42902651e+04 -2.16535591e+04 -1.17707253e+05
-2.53816749e+05 -5.45086612e+04]
[ -4.55636513e+00 -2.16535591e+04 -4.85660333e+04 -2.49732928e+05
-1.24734292e+05 -6.40426305e+04]
[ -6.68638714e+03 -1.17707253e+05 -2.49732928e+05 -1.65582623e+05
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[ -6.68600689e+03 -2.53816749e+05 -1.24734292e+05 -3.45019555e+05
-1.72310900e+05 -3.02308698e+05]
[ 1.50980181e+03 -5.45086612e+04 -6.40426305e+04 -2.93230374e+05
-3.02308698e+05 -3.90631733e+04]]
...,
[[ 1.33916110e+03 -1.93165092e+01 -1.43190028e+01 -9.39670012e+03
-9.39611170e+03 2.43400559e+03]
[ -1.93165092e+01 -4.74069910e+04 -5.83454104e+04 -1.62707000e+05
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[ -9.39670012e+03 -1.62707000e+05 -3.62411821e+05 -2.27430021e+05
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[ -9.39611170e+03 -3.75368799e+05 -1.86403969e+05 -4.78569219e+05
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[ 2.43400559e+03 -8.67296845e+04 -1.35450058e+05 -4.72420101e+05
-4.91101667e+05 -1.06068419e+05]]
[[ 8.63977313e+02 -2.93790967e+00 -2.47910185e+00 -6.05923245e+03
-6.06064497e+03 1.32329718e+03]
[ -2.93790967e+00 -4.60651234e+04 -1.01162842e+04 -1.08268606e+05
-2.21637200e+05 -2.80272973e+04]
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[ 1.32329718e+03 -2.80272973e+04 -4.49433550e+04 -2.57911700e+05
-2.61747105e+05 -2.14238783e+04]]
[[ 8.57888782e+02 -2.76938475e+00 -2.11818965e+00 -6.01621185e+03
-6.01634254e+03 1.30797317e+03]
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[ 1.30797317e+03 -4.38408921e+04 -5.72508900e+04 -2.51576276e+05
-2.60064563e+05 -3.00202859e+04]]]
[[[ 1.41225594e+03 -1.80861453e+01 -1.81222589e+01 -9.91174043e+03
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-5.14375931e+05 -1.09022690e+05]]
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-7.59624381e+03 1.80384564e+03]
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[ 1.80384564e+03 -5.74308664e+04 -6.05779901e+04 -3.58583457e+05
-3.56080311e+05 -4.36089702e+04]]
...,
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[ 2.30068822e+03 -1.27909734e+05 -5.03259791e+04 -4.75634794e+05
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In [9]:
from pycalphad.core.autograd_utils import build_functions
%time obj, ag_grad_func, ag_hess_func = build_functions(mod.ast, tuple(mod.variables))
%time ag_grad_func(x1, x2, x3, x4, x5, x6)
CPU times: user 284 ms, sys: 7 ms, total: 291 ms
Wall time: 269 ms
CPU times: user 977 ms, sys: 335 ms, total: 1.31 s
Wall time: 1.31 s
Out[9]:
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Content source: richardotis/pycalphad-sandbox
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