使用scipy.integrate.quad_vec和Tensorflow进行数值积分

我试图应用以下问题答案中的代码： 解决我的问题。 为了更简单，我想集成三个分别包含1、2和3次勒让德多项式的二维数组

from scipy.special import legendre
import numpy as np
import warnings
with warnings.catch_warnings():
    warnings.filterwarnings("ignore",category=FutureWarning)
    import tensorflow.compat.v1 as tf
    tf.disable_v2_behavior()
 

def f_2(n):
    def f_3(a):
        return np.arange(11, 20).reshape(3, 3) * legendre(n)(a) * legendre(n)(a) + np.ones((3, 3))
    return f_3


with tf.Session() as sess:
    def integrated(f, n):
        return tf.map_fn(fn=lambda x: tf.py_function(func=lambda z: integrate.quad_vec(f(z), 0.0, 4.0)[0],
                                                     #func=integrate.quad_vec(f, 0.0, 4.0)[0],
                                                     inp=[x],
                                                     Tout=tf.float64),
                         elems=n,
                         dtype=(tf.float64))
    res = sess.run(integrated(f_2, tf.constant([1, 2, 3], dtype = tf.int32)))
    print("res 1: ",  res )

这会引发错误：ValueError:n必须是正整数

> [[{{node map/while/EagerPyFunc}}]]
> 
> During handling of the above exception, another exception occurred:
> 
> Traceback (most recent call last):   File
> "C:/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 178, in <module>
>     res = sess.run(integrated(f_2, tf.constant([1, 2], dtype = tf.int32)))   File
> "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\client\session.py",
> line 950, in run
>     run_metadata_ptr)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\client\session.py",
> line 1173, in _run
>     feed_dict_tensor, options, run_metadata)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\client\session.py",
> line 1350, in _do_run
>     run_metadata)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\client\session.py",
> line 1370, in _do_call
>     raise type(e)(node_def, op, message) tensorflow.python.framework.errors_impl.InvalidArgumentError:
> ValueError: n must be a positive integer. Traceback (most recent call
> last):
> 
>   File
> "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\script_ops.py",
> line 207, in __call__
>     return func(device, token, args)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\script_ops.py",
> line 109, in __call__
>     ret = self._func(*args)   File "C:/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 159, in <lambda>
>     func=lambda z: integrate.quad_vec(f(z), 0.0, 4.0)[0],   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\scipy\integrate\_quad_vec.py",
> line 305, in quad_vec
>     ig, err, rnd = _quadrature(x1, x2, f, norm_func)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\scipy\integrate\_quad_vec.py",
> line 582, in _quadrature_gk21
>     return _quadrature_gk(a, b, f, norm_func, x, w, v)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\scipy\integrate\_quad_vec.py",
> line 483, in _quadrature_gk
>     ff = f(c + h*x[i])   File "C:/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 137, in f_3
>     return np.arange(11, 20).reshape(3, 3) * legendre(n)(a) * legendre(n)(a) + np.ones((3, 3))   File
> "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\scipy\special\orthogonal.py",
> line 2077, in legendre
>     x, w, mu0 = roots_legendre(n1, mu=True)   File "C:\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\scipy\special\orthogonal.py",
> line 2021, in roots_legendre
>     raise ValueError("n must be a positive integer.")
> 
> ValueError: n must be a positive integer.
> 
> 
>    [[node map/while/EagerPyFunc (defined at
> /Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py:162)
> ]]
> 
> Errors may have originated from an input operation. Input Source
> operations connected to node map/while/EagerPyFunc: 
> map/while/TensorArrayReadV3 (defined at
> /Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py:165)
> 
> Original stack trace for 'map/while/EagerPyFunc':   File
> "/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 178, in <module>
>     res = sess.run(integrated(f_2, tf.constant([1, 2], dtype = tf.int32)))   File
> "/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 165, in integrated
>     dtype=(tf.float64)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\map_fn.py",
> line 268, in map_fn
>     maximum_iterations=n)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\control_flow_ops.py", line 2727, in while_loop
>     return_same_structure)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\control_flow_ops.py", line 2238, in BuildLoop
>     pred, body, original_loop_vars, loop_vars, shape_invariants)   File
> "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\control_flow_ops.py", line 2163, in _BuildLoop
>     body_result = body(*packed_vars_for_body)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\control_flow_ops.py", line 2682, in <lambda>
>     body = lambda i, lv: (i + 1, orig_body(*lv))   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\map_fn.py",
> line 257, in compute
>     packed_fn_values = fn(packed_values)   File "/Users/Enot/PycharmProjects/GPU-DL/cython_integral/test_tf_integral.py",
> line 162, in <lambda>
>     Tout=tf.float64   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\script_ops.py",
> line 392, in eager_py_func
>     return _internal_py_func(func=func, inp=inp, Tout=Tout, eager=True, name=name)   File
> "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\script_ops.py",
> line 281, in _internal_py_func
>     input=inp, token=token, Tout=Tout, name=name)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\ops\gen_script_ops.py",
> line 74, in eager_py_func
>     "EagerPyFunc", input=input, token=token, Tout=Tout, name=name)   File
> "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\framework\op_def_library.py",
> line 788, in _apply_op_helper
>     op_def=op_def)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\util\deprecation.py",
> line 507, in new_func
>     return func(*args, **kwargs)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\framework\ops.py",
> line 3296, in create_op
>     op_def=op_def)   File "\Users\Enot\PycharmProjects\GPU-DL\venv\lib\site-packages\tensorflow\python\framework\ops.py",
> line 1692, in __init__
>     self._traceback = tf_stack.extract_stack()

---

有什么想法吗？

好的，根据您对问题的更新，下面是希望对您有用的代码（已测试）。我省略了“I”，积分从0.0开始。。。10.0，但您可以修改以包含该内容。其主要思想是，如果要在python函数中使用张量值，首先需要通过

numpy（）

方法将其转换为其值

from scipy.special import legendre
from scipy import integrate
import numpy as np
import warnings
with warnings.catch_warnings():
    warnings.filterwarnings("ignore",category=FutureWarning)
    import tensorflow.compat.v1 as tf
    tf.disable_v2_behavior()

def integrated( n ):
    return tf.map_fn(fn=lambda x: tf.py_function(func=lambda z: integrate.quad( legendre( z.numpy() ), 0.0, 10.0 )[0],
                                                inp=[x],
                                                Tout=tf.float64 ),
                     elems=n,
                     fn_output_signature = tf.float64 )
input_tensor = tf.compat.v1.placeholder( tf.int32 )
integrated_tensor = integrated( input_tensor )

with tf.Session() as sess:
    print( 'input' )
    input = np.arange(1, 10).astype( np.int32 )
    print( input )
    res = sess.run( integrated_tensor, feed_dict= { input_tensor: input } )
    print("res 1: ",  res.reshape( 3, 3 ) )

这将输出：

输入

[123456789]

决议1:[5.00000000e+014.95000000e+026.17500000e+03]

[8.6253750E+04 1.29071875e+06 2.02334344e+07]

[3.27986609e+08 5.45295453e+09 9.24706365e+10]]

---

希望这就是你想要的。

我需要迭代的不是积分的上限，而是多项式次数。

from scipy.special import legendre
from scipy import integrate
import numpy as np
import warnings
with warnings.catch_warnings():
    warnings.filterwarnings("ignore",category=FutureWarning)
    import tensorflow.compat.v1 as tf
    tf.disable_v2_behavior()

def integrated( n ):
    return tf.map_fn(fn=lambda x: tf.py_function(func=lambda z: integrate.quad( legendre( z.numpy() ), 0.0, 10.0 )[0],
                                                inp=[x],
                                                Tout=tf.float64 ),
                     elems=n,
                     fn_output_signature = tf.float64 )
input_tensor = tf.compat.v1.placeholder( tf.int32 )
integrated_tensor = integrated( input_tensor )

with tf.Session() as sess:
    print( 'input' )
    input = np.arange(1, 10).astype( np.int32 )
    print( input )
    res = sess.run( integrated_tensor, feed_dict= { input_tensor: input } )
    print("res 1: ",  res.reshape( 3, 3 ) )