如何在张量流中使用 scipy.special.expi （指数积分）？

Question

我必须在 tensorflow 中编写代码 scipy.special.expi，但我不知道该怎么做！！！！请有人帮忙因为在 tensorflow 中没有这样的直接代码所以我被困在这里请帮忙！！！

Answer 1

我对这个函数不是很了解，但是基于SciPy中的Fortran实现，scipy/special/specfun/specfun.f中的函数EIX，我整理了一个TensorFlow实现跟随那里的每一步。不过，它仅适用于正值，因为负值的计算包含一个更难矢量化的循环。

import math
import tensorflow as tf

def expi(x):
    x = tf.convert_to_tensor(x)
    # When X is zero
    m_0 = tf.equal(x, 0)
    y_0 = -math.inf + tf.zeros_like(x)
    # When X is negative
    m_neg = x < 0
    # This should be -e1xb(-x) according to ScyPy
    # (negative exponential integral -1)
    # Here it is just left as NaN
    y_neg = math.nan + tf.zeros_like(x)
    # When X is less or equal to 40 - Power series around x = 0
    m_le40 = x <= 40
    k = tf.range(1, 101, dtype=x.dtype)
    r = tf.cumprod(tf.expand_dims(x, -1) * k / tf.square(k + 1), axis=-1)
    ga = tf.constant(0.5772156649015328, dtype=x.dtype)
    y_le40 = ga + tf.log(x) + x * (1 + tf.reduce_sum(r, axis=-1))
    # Otherwise (X is greater than 40) - Asymptotic expansion (the series is not convergent)
    k = tf.range(1, 21, dtype=x.dtype)
    r = tf.cumprod(k / tf.expand_dims(x, -1), axis=-1)
    y_gt40 = tf.exp(x) / x * (1 + tf.reduce_sum(r, axis=-1))
    # Select values
    return tf.where(
        m_0, y_0, tf.where(
        m_neg, y_neg, tf.where(
        m_le40, y_le40, y_gt40)))

小测试

import tensorflow as tf
import scipy.special
import numpy as np

# Test
x = np.linspace(0, 100, 20)
y = scipy.special.expi(x)
with tf.Graph().as_default(), tf.Session() as sess:
    y_tf = sess.run(expi(x))
print(np.allclose(y, y_tf))
# True

但是请注意，这将比 SciPy 占用更多内存，因为它是在内存中展开近似循环而不是一次计算一个步骤。

如何在张量流中使用 scipy.special.expi （指数积分）？

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