通过 numba 在 Python 中高效模拟任意动力系统？
Efficient simulation of arbitrary dynamical system in Python via numba?
一段时间以来，我一直想知道在 Python 中模拟任意非线性（随机的确定性）动力系统的最有效方法是什么。我最终做了很多教学或研究。我相信一定有一种简单有效的方法可以做到这一点。
今晚在酒吧里我想到了以下...
def iterate(F, X, T, **params):
"""Iterate a non-linear map F starting from some initial condition X for T periods."""
t = 0
while t < T:
yield X
X = F(X, **params)
t += 1
...使用 Tinkerbell Map...
的测试用例
def tinker_bell_map(X, a, b, c, d):
return [X[0]**2 - X[1]**2 + a * X[0] + b * X[1], 2 * X[0] * X[1] + c * X[0] + d * X[1]]
...产量...
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 26 µs per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 100, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 254 µs per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 1000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 2.36 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 19.6 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 100000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 192 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 1000000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 2.02 s per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10000000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 20.5 s per loop
...我已经为确定性和随机系统尝试了其他几个测试用例，并且上面的作品很有魅力。虽然我认为上面的内容非常好，但我想知道是否可以使用 Numba?
使其更快
这是我一直在尝试的两个暂定解决方案...
@njit
def tinker_bell_map(X, params):
out = [X[0]**2 - X[1]**2 + params[0] * X[0] + params[1] * X[1],
2 * X[0] * X[1] + params[2] * X[0] + params[3] * X[1]]
return out
def simulator_factory(F):
@njit
def simulator(initial_condition, T, params):
"""Iterate a non-linear map starting from some X for T periods."""
X = np.empty((initial_condition.shape[0], T + 1))
X[:, 0] = initial_condition # here is the offending line!
for t in xrange(T):
X[:, t+1] = F(X[:, t], params)
return X
return simulator
def iterator_factory(F):
@njit
def iterator(X, T, params):
"""Iterate a non-linear map starting from some X for T periods."""
t = 0
while t < T:
yield X
X = F(X, params) # this is the offending line!
t += 1
return iterator
...不幸的是两者都不起作用...
In [8]: f(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
---------------------------------------------------------------------------
TypingError Traceback (most recent call last)
<ipython-input-8-d4c0195e7f4e> in <module>()
----> 1 f(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in _compile_for_args(self, *args, **kws)
163 assert not kws
164 sig = tuple([self.typeof_pyval(a) for a in args])
--> 165 return self.compile(sig)
166
167 def inspect_llvm(self, signature=None):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in compile(self, sig)
301 self.py_func,
302 args=args, return_type=return_type,
--> 303 flags=flags, locals=self.locals)
304
305 # Check typing error if object mode is used
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(typingctx, targetctx, func, args, return_type, flags, locals, library)
593 pipeline = Pipeline(typingctx, targetctx, library,
594 args, return_type, flags, locals)
--> 595 return pipeline.compile_extra(func)
596
597
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(self, func)
316 raise e
317
--> 318 return self.compile_bytecode(bc, func_attr=self.func_attr)
319
320 def compile_bytecode(self, bc, lifted=(), lifted_from=None,
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_bytecode(self, bc, lifted, lifted_from, func_attr)
325 self.lifted_from = lifted_from
326 self.func_attr = func_attr
--> 327 return self._compile_bytecode()
328
329 def compile_internal(self, bc, func_attr=DEFAULT_FUNCTION_ATTRIBUTES):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in _compile_bytecode(self)
580
581 pm.finalize()
--> 582 return pm.run(self.status)
583
584
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in run(self, status)
207 # No more fallback pipelines?
208 if is_final_pipeline:
--> 209 raise patched_exception
210 # Go to next fallback pipeline
211 else:
TypingError: Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 710, in type_inference_stage
infer.propagate()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 408, in propagate
self.constrains.propagate(self.context, self.typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 113, in propagate
loc=constrain.loc)
TypingError: Internal error at <numba.typeinfer.CallConstrain object at 0x10c5a7d50>:
Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 709, in type_inference_stage
infer.build_constrain()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 395, in build_constrain
self.constrain_statement(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 519, in constrain_statement
self.typeof_assign(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 555, in typeof_assign
self.typeof_expr(inst, inst.target, value)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 672, in typeof_expr
raise NotImplementedError(type(expr), expr)
NotImplementedError: (<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
File "sandbox.py", line 45
Failed at nopython (nopython frontend)
Internal error at <numba.typeinfer.CallConstrain object at 0x10c5a7d50>:
Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 709, in type_inference_stage
infer.build_constrain()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 395, in build_constrain
self.constrain_statement(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 519, in constrain_statement
self.typeof_assign(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 555, in typeof_assign
self.typeof_expr(inst, inst.target, value)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 672, in typeof_expr
raise NotImplementedError(type(expr), expr)
NotImplementedError: (<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
File "sandbox.py", line 45
...以及模拟器工厂...
In [10]: s = simulator_factory(tinker_bell_map)
In [11]: s(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
---------------------------------------------------------------------------
TypingError Traceback (most recent call last)
<ipython-input-11-049d0797e27e> in <module>()
----> 1 s(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in _compile_for_args(self, *args, **kws)
163 assert not kws
164 sig = tuple([self.typeof_pyval(a) for a in args])
--> 165 return self.compile(sig)
166
167 def inspect_llvm(self, signature=None):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in compile(self, sig)
301 self.py_func,
302 args=args, return_type=return_type,
--> 303 flags=flags, locals=self.locals)
304
305 # Check typing error if object mode is used
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(typingctx, targetctx, func, args, return_type, flags, locals, library)
593 pipeline = Pipeline(typingctx, targetctx, library,
594 args, return_type, flags, locals)
--> 595 return pipeline.compile_extra(func)
596
597
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(self, func)
316 raise e
317
--> 318 return self.compile_bytecode(bc, func_attr=self.func_attr)
319
320 def compile_bytecode(self, bc, lifted=(), lifted_from=None,
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_bytecode(self, bc, lifted, lifted_from, func_attr)
325 self.lifted_from = lifted_from
326 self.func_attr = func_attr
--> 327 return self._compile_bytecode()
328
329 def compile_internal(self, bc, func_attr=DEFAULT_FUNCTION_ATTRIBUTES):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in _compile_bytecode(self)
580
581 pm.finalize()
--> 582 return pm.run(self.status)
583
584
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in run(self, status)
207 # No more fallback pipelines?
208 if is_final_pipeline:
--> 209 raise patched_exception
210 # Go to next fallback pipeline
211 else:
TypingError: Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 710, in type_inference_stage
infer.propagate()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 408, in propagate
self.constrains.propagate(self.context, self.typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 107, in propagate
constrain(context, typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 304, in __call__
(ty, it, vt), loc=self.loc)
TypingError: Cannot resolve setitem: array(float64, 2d, C)[(slice3_type, int32)] = array(float64, 1d, C)
File "sandbox.py", line 29
Failed at nopython (nopython frontend)
Cannot resolve setitem: array(float64, 2d, C)[(slice3_type, int32)] = array(float64, 1d, C)
File "sandbox.py", line 29
```
这里的问题似乎与我尝试将数组分配给切片有关。
目前发现 Numba 有点令人沮丧...
我认为这可能与 njit 装饰器 非常 严格关于 nopython 的含义有关。创建新矩阵和切片分配在 njit 中似乎都失败了。此外，代码中 tinker_bell_map 的 njit 编辑副本 returns 是一个列表（python 对象）而不是数组。
将示例重构回最基本的结构，看来只要进行足够的按摩，numba 就做得非常出色。 （numpy 1.9.2 和 numba 0.14）
import numba
from numba import *
from numpy import *
import numpy as np
@njit
def simulator(initial_condition, params, X):
a = params[0]
b = params[1]
c = params[2]
d = params[3]
X[0, 0] = initial_condition[0]
X[1, 0] = initial_condition[1]
for t in range(1, X.shape[1]):
u = X[0, t-1]
v = X[1, t-1]
X[0, t] = u**2 - v**2 + a * u + b * v
X[1, t] = 2 * u * v + c * u + d * v
return X
时间
x0 = np.array([-0.72, -0.64])
params = np.array([0.9, -0.6013, 2.0,0.5])
xs = np.zeros((2, 10000000 ))
%timeit -n 1 -r 3 simulator(x0, params, xs)
1 loops, best of 3: 70.7 ms per loop
xs = np.zeros((2, 100000000 ))
%timeit -n 1 -r 3 simulator(x0, params, xs)
1 loops, best of 3: 715 ms per loop
例子更接近原文
@njit
def tinker_bell_map(X, params, out):
out[0] = X[0]**2 - X[1]**2 + params[0] * X[0] + params[1] * X[1]
out[1] = 2 * X[0] * X[1] + params[2] * X[0] + params[3] * X[1]
def simulator_factory(f):
def simulator(x0, params, x):
for i in xrange(2):
x[i,0] = x0[i]
for t in xrange(1, x.shape[1]):
f(x[:,t-1], params, x[:,t])
return x
return njit(simulator)
xs = np.zeros((2, 10))
sim = simulator_factory(tinker_bell_map)
print sim(x0, params, xs)
更新时间：
xs = np.zeros((2, 10000000 ))
%timeit -n 1 -r 3 sim(x0, params, xs)
1 loops, best of 3: 272 ms per loop
xs = np.zeros((2, 100000000 ))
%timeit -n 1 -r 3 sim(x0, params, xs)
1 loops, best of 3: 2.73 s per loop
一段时间以来，我一直想知道在 Python 中模拟任意非线性（随机的确定性）动力系统的最有效方法是什么。我最终做了很多教学或研究。我相信一定有一种简单有效的方法可以做到这一点。
今晚在酒吧里我想到了以下...
def iterate(F, X, T, **params):
"""Iterate a non-linear map F starting from some initial condition X for T periods."""
t = 0
while t < T:
yield X
X = F(X, **params)
t += 1
...使用 Tinkerbell Map...
的测试用例def tinker_bell_map(X, a, b, c, d):
return [X[0]**2 - X[1]**2 + a * X[0] + b * X[1], 2 * X[0] * X[1] + c * X[0] + d * X[1]]
...产量...
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 26 µs per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 100, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 254 µs per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 1000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 2.36 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 19.6 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 100000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 192 ms per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 1000000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 2.02 s per loop
%timeit -n 1 -r 3 [X for X in iterate(tinker_bell_map, [-0.72, -0.64], 10000000, a=0.9, b=-0.6013, c=2.0, d=0.5)]
1 loops, best of 3: 20.5 s per loop
...我已经为确定性和随机系统尝试了其他几个测试用例，并且上面的作品很有魅力。虽然我认为上面的内容非常好，但我想知道是否可以使用 Numba?
使其更快这是我一直在尝试的两个暂定解决方案...
@njit
def tinker_bell_map(X, params):
out = [X[0]**2 - X[1]**2 + params[0] * X[0] + params[1] * X[1],
2 * X[0] * X[1] + params[2] * X[0] + params[3] * X[1]]
return out
def simulator_factory(F):
@njit
def simulator(initial_condition, T, params):
"""Iterate a non-linear map starting from some X for T periods."""
X = np.empty((initial_condition.shape[0], T + 1))
X[:, 0] = initial_condition # here is the offending line!
for t in xrange(T):
X[:, t+1] = F(X[:, t], params)
return X
return simulator
def iterator_factory(F):
@njit
def iterator(X, T, params):
"""Iterate a non-linear map starting from some X for T periods."""
t = 0
while t < T:
yield X
X = F(X, params) # this is the offending line!
t += 1
return iterator
...不幸的是两者都不起作用...
In [8]: f(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
---------------------------------------------------------------------------
TypingError Traceback (most recent call last)
<ipython-input-8-d4c0195e7f4e> in <module>()
----> 1 f(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in _compile_for_args(self, *args, **kws)
163 assert not kws
164 sig = tuple([self.typeof_pyval(a) for a in args])
--> 165 return self.compile(sig)
166
167 def inspect_llvm(self, signature=None):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in compile(self, sig)
301 self.py_func,
302 args=args, return_type=return_type,
--> 303 flags=flags, locals=self.locals)
304
305 # Check typing error if object mode is used
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(typingctx, targetctx, func, args, return_type, flags, locals, library)
593 pipeline = Pipeline(typingctx, targetctx, library,
594 args, return_type, flags, locals)
--> 595 return pipeline.compile_extra(func)
596
597
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(self, func)
316 raise e
317
--> 318 return self.compile_bytecode(bc, func_attr=self.func_attr)
319
320 def compile_bytecode(self, bc, lifted=(), lifted_from=None,
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_bytecode(self, bc, lifted, lifted_from, func_attr)
325 self.lifted_from = lifted_from
326 self.func_attr = func_attr
--> 327 return self._compile_bytecode()
328
329 def compile_internal(self, bc, func_attr=DEFAULT_FUNCTION_ATTRIBUTES):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in _compile_bytecode(self)
580
581 pm.finalize()
--> 582 return pm.run(self.status)
583
584
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in run(self, status)
207 # No more fallback pipelines?
208 if is_final_pipeline:
--> 209 raise patched_exception
210 # Go to next fallback pipeline
211 else:
TypingError: Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 710, in type_inference_stage
infer.propagate()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 408, in propagate
self.constrains.propagate(self.context, self.typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 113, in propagate
loc=constrain.loc)
TypingError: Internal error at <numba.typeinfer.CallConstrain object at 0x10c5a7d50>:
Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 709, in type_inference_stage
infer.build_constrain()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 395, in build_constrain
self.constrain_statement(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 519, in constrain_statement
self.typeof_assign(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 555, in typeof_assign
self.typeof_expr(inst, inst.target, value)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 672, in typeof_expr
raise NotImplementedError(type(expr), expr)
NotImplementedError: (<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
File "sandbox.py", line 45
Failed at nopython (nopython frontend)
Internal error at <numba.typeinfer.CallConstrain object at 0x10c5a7d50>:
Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 709, in type_inference_stage
infer.build_constrain()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 395, in build_constrain
self.constrain_statement(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 519, in constrain_statement
self.typeof_assign(inst)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 555, in typeof_assign
self.typeof_expr(inst, inst.target, value)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 672, in typeof_expr
raise NotImplementedError(type(expr), expr)
NotImplementedError: (<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var([=15=].27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var([=15=].52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
File "sandbox.py", line 45
...以及模拟器工厂...
In [10]: s = simulator_factory(tinker_bell_map)
In [11]: s(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
---------------------------------------------------------------------------
TypingError Traceback (most recent call last)
<ipython-input-11-049d0797e27e> in <module>()
----> 1 s(np.array([-0.72, -0.64]), 10, np.array([0.9, -0.6013, 2.0, 0.5]))
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in _compile_for_args(self, *args, **kws)
163 assert not kws
164 sig = tuple([self.typeof_pyval(a) for a in args])
--> 165 return self.compile(sig)
166
167 def inspect_llvm(self, signature=None):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/dispatcher.pyc in compile(self, sig)
301 self.py_func,
302 args=args, return_type=return_type,
--> 303 flags=flags, locals=self.locals)
304
305 # Check typing error if object mode is used
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(typingctx, targetctx, func, args, return_type, flags, locals, library)
593 pipeline = Pipeline(typingctx, targetctx, library,
594 args, return_type, flags, locals)
--> 595 return pipeline.compile_extra(func)
596
597
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_extra(self, func)
316 raise e
317
--> 318 return self.compile_bytecode(bc, func_attr=self.func_attr)
319
320 def compile_bytecode(self, bc, lifted=(), lifted_from=None,
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in compile_bytecode(self, bc, lifted, lifted_from, func_attr)
325 self.lifted_from = lifted_from
326 self.func_attr = func_attr
--> 327 return self._compile_bytecode()
328
329 def compile_internal(self, bc, func_attr=DEFAULT_FUNCTION_ATTRIBUTES):
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in _compile_bytecode(self)
580
581 pm.finalize()
--> 582 return pm.run(self.status)
583
584
/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.pyc in run(self, status)
207 # No more fallback pipelines?
208 if is_final_pipeline:
--> 209 raise patched_exception
210 # Go to next fallback pipeline
211 else:
TypingError: Caused By:
Traceback (most recent call last):
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 201, in run
res = stage()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 415, in stage_nopython_frontend
self.locals)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/compiler.py", line 710, in type_inference_stage
infer.propagate()
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 408, in propagate
self.constrains.propagate(self.context, self.typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 107, in propagate
constrain(context, typevars)
File "/Users/drpugh/anaconda/lib/python2.7/site-packages/numba/typeinfer.py", line 304, in __call__
(ty, it, vt), loc=self.loc)
TypingError: Cannot resolve setitem: array(float64, 2d, C)[(slice3_type, int32)] = array(float64, 1d, C)
File "sandbox.py", line 29
Failed at nopython (nopython frontend)
Cannot resolve setitem: array(float64, 2d, C)[(slice3_type, int32)] = array(float64, 1d, C)
File "sandbox.py", line 29
```
这里的问题似乎与我尝试将数组分配给切片有关。
目前发现 Numba 有点令人沮丧...
我认为这可能与 njit 装饰器 非常 严格关于 nopython 的含义有关。创建新矩阵和切片分配在 njit 中似乎都失败了。此外，代码中 tinker_bell_map 的 njit 编辑副本 returns 是一个列表（python 对象）而不是数组。
将示例重构回最基本的结构，看来只要进行足够的按摩，numba 就做得非常出色。 （numpy 1.9.2 和 numba 0.14）
import numba
from numba import *
from numpy import *
import numpy as np
@njit
def simulator(initial_condition, params, X):
a = params[0]
b = params[1]
c = params[2]
d = params[3]
X[0, 0] = initial_condition[0]
X[1, 0] = initial_condition[1]
for t in range(1, X.shape[1]):
u = X[0, t-1]
v = X[1, t-1]
X[0, t] = u**2 - v**2 + a * u + b * v
X[1, t] = 2 * u * v + c * u + d * v
return X
时间
x0 = np.array([-0.72, -0.64])
params = np.array([0.9, -0.6013, 2.0,0.5])
xs = np.zeros((2, 10000000 ))
%timeit -n 1 -r 3 simulator(x0, params, xs)
1 loops, best of 3: 70.7 ms per loop
xs = np.zeros((2, 100000000 ))
%timeit -n 1 -r 3 simulator(x0, params, xs)
1 loops, best of 3: 715 ms per loop
例子更接近原文
@njit
def tinker_bell_map(X, params, out):
out[0] = X[0]**2 - X[1]**2 + params[0] * X[0] + params[1] * X[1]
out[1] = 2 * X[0] * X[1] + params[2] * X[0] + params[3] * X[1]
def simulator_factory(f):
def simulator(x0, params, x):
for i in xrange(2):
x[i,0] = x0[i]
for t in xrange(1, x.shape[1]):
f(x[:,t-1], params, x[:,t])
return x
return njit(simulator)
xs = np.zeros((2, 10))
sim = simulator_factory(tinker_bell_map)
print sim(x0, params, xs)
更新时间：
xs = np.zeros((2, 10000000 ))
%timeit -n 1 -r 3 sim(x0, params, xs)
1 loops, best of 3: 272 ms per loop
xs = np.zeros((2, 100000000 ))
%timeit -n 1 -r 3 sim(x0, params, xs)
1 loops, best of 3: 2.73 s per loop