convolution

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
tf.compat.v1.reset_default_graph()

x = np.sin(np.linspace(0,3*np.pi,30))+ np.random.randn(30)*0.1
filter = np.sin(np.linspace(np.pi/2-np.pi/6,np.pi/2+np.pi/6,5))

x = np.array([ 0.15056179,  0.30541199,  0.72807816,  0.940651  ,  0.97211703,
        1.01255197,  0.86129876,  0.71344136,  0.56986685,  0.24477384,
       -0.01567925, -0.29397656, -0.7427353 , -0.96051523, -0.92409656,
       -1.09632185, -1.03468747, -0.70415137, -0.43263368, -0.10620422,
        0.00126833,  0.50176941,  0.74617082,  1.01136882,  1.01184374,
        1.02194784,  0.81796091,  0.4132255 ,  0.38143445,  0.07454849])
filter = np.array([0.8660254 , 0.96592583, 1.        , 0.96592583, 0.8660254 ])

x_ = tf.reshape(tf.convert_to_tensor(x),[1,-1,1])
filter_ = tf.reshape(tf.convert_to_tensor(filter),[-1,1,1])

y_ = tf.squeeze(tf.nn.conv1d(x_,filter_,stride=1,padding='VALID'))

sess= tf.Session()
y=sess.run(y_)

z1, = plt.plot(np.arange(30),x,label='data',marker='o')
z2, = plt.plot(np.arange(5),filter*3,label='filter',marker='o')
z3, =plt.plot(np.arange(1,27),y*0.5,label='result',marker='o')

plt.legend(handles=[z1,z2,z3],loc='upper center')

비대칭 filter인 경우, 결과가 일치하는 patten에서 최대치를 형성하지는 않는다.
예를 들어, sin곡선의 앞부분을 filter로 했을 때, 원래 sin곡선보다 약간 왼쪽으로 shift된 결과를 얻는다.

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
tf.compat.v1.reset_default_graph()

x_without_noise = np.array([ 0.00000000e+00,  3.09016994e-01,  5.87785252e-01,  8.09016994e-01,
        9.51056516e-01,  1.00000000e+00,  9.51056516e-01,  8.09016994e-01,
        5.87785252e-01,  3.09016994e-01,  1.22464680e-16, -3.09016994e-01,
       -5.87785252e-01, -8.09016994e-01, -9.51056516e-01, -1.00000000e+00,
       -9.51056516e-01, -8.09016994e-01, -5.87785252e-01, -3.09016994e-01,
       -2.44929360e-16,  3.09016994e-01,  5.87785252e-01,  8.09016994e-01,
        9.51056516e-01,  1.00000000e+00,  9.51056516e-01,  8.09016994e-01,
        5.87785252e-01,  3.09016994e-01,  3.67394040e-16])


x = np.sin(np.linspace(0,3*np.pi,31))+ np.random.randn(31)*0.1
filter = np.sin(np.linspace(np.pi/2-np.pi/6,np.pi/2+np.pi/6,5))
filter = np.sin(np.linspace(np.pi/2,np.pi,5))
x = np.array([-8.17646108e-02,  3.13663973e-01,  3.91689052e-01,  6.67779942e-01,
        8.65920525e-01,  1.20870896e+00,  1.00749242e+00,  9.11470321e-01,
        4.79132615e-01,  3.58446563e-01,  4.25711653e-02, -2.85954410e-01,
       -6.10904871e-01, -8.21197786e-01, -1.04441306e+00, -8.63673798e-01,
       -9.76416769e-01, -7.78509796e-01, -6.09985997e-01, -4.90318041e-01,
       -1.80778486e-01,  2.61383469e-01,  5.55101307e-01,  6.89418144e-01,
        8.06513299e-01,  9.04051245e-01,  8.34397936e-01,  7.39944771e-01,
        5.40850263e-01,  3.35311373e-01,  4.03139922e-04])
#filter = np.array([8.09016994e-01, 5.87785252e-01,  3.09016994e-01,  1.22464680e-16, -3.09016994e-01])
filter = np.array([0.00000000e+00,  3.09016994e-01,  5.87785252e-01,  8.09016994e-01,9.51056516e-01])
x_ = tf.reshape(tf.convert_to_tensor(x),[1,-1,1])
filter_ = tf.reshape(tf.convert_to_tensor(filter),[-1,1,1])

y_ = tf.squeeze(tf.nn.conv1d(x_,filter_,stride=1,padding='VALID'))

sess= tf.Session()
y=sess.run(y_)

z1, = plt.plot(np.arange(31),x,label='data',marker='o')
z2, = plt.plot(np.arange(5),filter+2,label='filter',marker='o')
z3, =plt.plot(np.arange(2,29),y*0.5,label='result',marker='o')

plt.legend(handles=[z1,z2,z3],loc='upper center')

• filter = np.array([0.8660254 , 0.96592583, 1. , 0.96592583, 0.8660254 ])

• filter = np.array([0.00000000e+00, 3.09016994e-01, 5.87785252e-01, 8.09016994e-01,9.51056516e-01])