[PYTHON] I tried to find an alternating series with tensorflow
I recently started studying tensorflow, so I asked for an alternating series. If you make a mistake, please comment.
Purpose
\sum^{\infty}_{n=1}(-1)^{n-1}/n\ \But\log{2}\I want to know if it converges to.
This formula can be proved by using the quadrature method. (See Resources for details)
Execution environment
- os: windows10(Docker) --docker image: b.gcr.io/tensorflow/tensorflow:latest-devel
- python: 2.7 --virtualbox (docker machine): Memory 4gb (I think 1gb is fine), Processor 4 (I think 1 is fine)
Execution method
$ docker run -v [Directory with code you want to run on windows]:/app -it b.gcr.io/tensorflow/tensorflow:latest-devel bash
# cd /app
# python alternating_sum.py
You can share the container file with the host with the -v option. For more information, please read Docker Official.
Implementation
alternating_sum.py
# coding:utf-8
import tensorflow as tf
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
N = 50000
#For graphs
figy = np.zeros([21])
figdif = np.zeros([21])
#Settings such as variables
y = tf.Variable(tf.cast(0, tf.float32))
x = tf.placeholder(tf.float32)
#operation
update_y = tf.assign(y, tf.add(y, tf.div(tf.cast(1, tf.float32), x)))
#Error with log2
dif = tf.sub(tf.log(tf.cast(2, tf.float32)), y)
#session initialization
sess = tf.Session()
sess.run(tf.initialize_all_variables())
#Start calculation
i = 0
for _ in range(N):
i += 1
tmp = -i if i % 2 == 0 else i
sess.run(update_y, feed_dict={x: tmp})
if i <= 20:
figy[i] = sess.run(y)
figdif[i] = sess.run(dif)
if i % 10 == 0:
print('STEP: %d, RES: %f, DIF: %f' %(i, sess.run(y), sess.run(dif)))
#Creating a graph
plt.plot(figy, label = "result")
plt.plot(figdif, label = "dif")
plt.legend()
plt.ylim([-2,2])
plt.savefig("result.png ")
Description
y = tf.Variable(tf.cast(0, tf.float32))
The initial variable is 0. Without tf.cast, it will cause a TypeError.
x = tf.placeholder(tf.float32)
x can be a value such as
1or-2.
update_y = tf.assign(y, tf.add(y, tf.div(tf.cast(1, tf.float32), x)))
Find 1 / x with tf.div and y + tf.div with tf.add. It will be one line that assigns that value to y with tf.assign. That is,
y = y + 1 / x. Think of update_y as the operator that does that.
dif = tf.sub(tf.log(tf.cast(2, tf.float32)), y)
The difference between log2 and y is taken. The value of log2 uses the function of tensorflow.
sess.run(tf.initialize_all_variables())
Initializing each variable.
for statement
You will actually do the calculations in sess.run. If you pass a variable such as
yas an argument here, the current value ofywill be returned. I am trying to put a value in x declared earlier in feed_dict.
From the above, we are looking for the result of the desired formula. Read Resources for graphs.
result
Image result
Output result to terminal
Slightly modified to make it easier to see. I haven't messed with the numbers.
STEP: 1, RES: 1.000000, DIF: -0.306853
STEP: 2, RES: 0.500000, DIF: 0.193147
STEP: 3, RES: 0.833333, DIF: -0.140186
STEP: 4, RES: 0.583333, DIF: 0.109814
STEP: 5, RES: 0.783333, DIF: -0.090186
STEP: 6, RES: 0.616667, DIF: 0.076481
STEP: 7, RES: 0.759524, DIF: -0.066377
STEP: 8, RES: 0.634524, DIF: 0.058623
STEP: 9, RES: 0.745635, DIF: -0.052488
STEP: 10, RES: 0.645635, DIF: 0.047512
STEP: 100, RES: 0.688172, DIF: 0.004975
STEP: 1000, RES: 0.692646, DIF: 0.000501
STEP: 10000, RES: 0.693092, DIF: 0.000055
STEP: 50000, RES: 0.693129, DIF: 0.000018
Finally
I think that tensorflow is often used in deep running etc., but this time I did a simple numerical calculation. There were some stumbling blocks, but I enjoyed making it with tensorflow. tensorflow is good!
References
the Internet
-Introduction to TensorFlow --Summary of four arithmetic operations and basic mathematical functions -Understanding TensorFlow by Arithmetic -Tensorflow Official Document -Proof of alternating series that converges on log2 -Introduction to matplotlib -Meeting Python for Machine Learning -Data science with Python
Books
-[TensorFlow started practice! Latest Google Machine Learning (Next Publishing)](https://www.amazon.co.jp/TensorFlow%E3%81%AF%E3%81%98%E3%82%81%E3%81%BE%E3%81 % 97% E3% 81% 9F-% E5% AE% 9F% E8% B7% B5% EF% BC% 81% E6% 9C% 80% E6% 96% B0Google% E3% 83% 9E% E3% 82% B7% E3% 83% B3% E3% 83% A9% E3% 83% BC% E3% 83% 8B% E3% 83% B3% E3% 82% B0-NextPublishing-% E6% 9C% 89% E5% B1 % B1-% E5% 9C% AD% E4% BA% 8C-ebook / dp / B01IT509EY) -[Introduction to deep learning learned with TensorFlow-Thorough explanation of convolutional neural network](https://www.amazon.co.jp/TensorFlow%E3%81%A7%E5%AD%A6%E3%81%B6%E3%] 83% 87% E3% 82% A3% E3% 83% BC% E3% 83% 97% E3% 83% A9% E3% 83% BC% E3% 83% 8B% E3% 83% B3% E3% 82% B0% E5% 85% A5% E9% 96% 80% EF% BD% 9E% E7% 95% B3% E3% 81% BF% E8% BE% BC% E3% 81% BF% E3% 83% 8B% E3% 83% A5% E3% 83% BC% E3% 83% A9% E3% 83% AB% E3% 83% 8D% E3% 83% 83% E3% 83% 88% E3% 83% AF% E3% 83% BC% E3% 82% AF% E5% BE% B9% E5% BA% 95% E8% A7% A3% E8% AA% AC-% E4% B8% AD% E4% BA% 95-% E6% 82% A6% E5% 8F% B8-ebook / dp / B01MAWJJOW / ref = sr_1_2? s = digital-text & ie = UTF8 & qid = 1479886851 & sr = 1-2 & keywords = tensorflow)
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