有一段时间我一直想知道在Python中模拟任意非线性(确定性随机)动力系统的最有效方法。我最终在教学或研究方面做了很多。我确信必须有一种简单而有效的方法。
今晚在酒吧,我想出了以下内容......
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,上面的工作就像一个魅力。虽然我认为以上情况非常好,但我想知道使用Numba是否可以更快地制作它?
以下是我一直在玩的两个尝试性解决方案......
@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......
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($0.27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var($0.52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var($0.27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var($0.52, /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($0.27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var($0.52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
Failed at nopython (nopython frontend)
(<class 'numba.ir.Expr'>, build_list(items=[Var($0.27, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (18)), Var($0.52, /Users/drpugh/Research/python-dev/ramseyPy/sandbox.py (19))]))
File "sandbox.py", line 45
......还有模拟器工厂......
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
```
这里的问题似乎是我尝试将数组分配给切片。
目前发现Numba有点令人沮丧......
答案 0 :(得分:4)
我认为这可能与njit
装饰者关于nopython意味着什么非常严格相关。在njit中,创建新矩阵和切片分配似乎都失败了。此外,代码中的njit
- 版本的tinker_bell_map返回一个列表(一个python对象)而不是一个数组。
将这个例子重新修改为裸骨,似乎给予足够的按摩,numba做得很好。 (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
计时
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
靠近原始
的示例@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