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)))
小测验
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
我对这个函数了解不多,但是基于SciPy中的Fortran实现,^{} 中的函数
EIX
,我在那里的每个步骤后面都放了一个TensorFlow实现。不过,这只适用于正值,因为负值的计算包含了一个更难矢量化的循环。你知道吗小测验
但是请注意,这将比SciPy占用更多的内存,因为它在内存中展开近似循环,而不是一次计算一步。你知道吗
相关问题 更多 >
编程相关推荐