Arange
Arange : arange
import numpy as np
X = np.arange(10)
X
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
X-1.0
array([-1., 0., 1., 2., 3., 4., 5., 6., 7., 8.])
10+X
array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19])
np.arange(3,12)
array([ 3, 4, 5, 6, 7, 8, 9, 10, 11])
np.arange(1,10,2)
array([1, 3, 5, 7, 9])
np.arange(10,11,0.01)
array([10. , 10.01, 10.02, 10.03, 10.04, 10.05, 10.06, 10.07, 10.08,
10.09, 10.1 , 10.11, 10.12, 10.13, 10.14, 10.15, 10.16, 10.17,
10.18, 10.19, 10.2 , 10.21, 10.22, 10.23, 10.24, 10.25, 10.26,
10.27, 10.28, 10.29, 10.3 , 10.31, 10.32, 10.33, 10.34, 10.35,
10.36, 10.37, 10.38, 10.39, 10.4 , 10.41, 10.42, 10.43, 10.44,
10.45, 10.46, 10.47, 10.48, 10.49, 10.5 , 10.51, 10.52, 10.53,
10.54, 10.55, 10.56, 10.57, 10.58, 10.59, 10.6 , 10.61, 10.62,
10.63, 10.64, 10.65, 10.66, 10.67, 10.68, 10.69, 10.7 , 10.71,
10.72, 10.73, 10.74, 10.75, 10.76, 10.77, 10.78, 10.79, 10.8 ,
10.81, 10.82, 10.83, 10.84, 10.85, 10.86, 10.87, 10.88, 10.89,
10.9 , 10.91, 10.92, 10.93, 10.94, 10.95, 10.96, 10.97, 10.98,
10.99])
Application : Plot multi-functions
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
sns.set()
Gaussian Distribution
len(np.arange(-4,4,0.01))
800
xs = np.arange(-4,4,0.01)
plt.figure(figsize = [10,2])
sigma =1.0
mu = 0.0
N = 1/np.sqrt(2*np.pi*sigma**2)
fx = N*np.exp(-(xs-mu)**2/(2*sigma**2))
plt.plot(xs,fx)
plt.xlabel('x',fontsize =20)
plt.ylabel('probability')
plt.show()
xs = np.arange(-10,10,0.01)
plt.figure(figsize = [10,6])
sigmas = [ 1.0,1.5,2.0,2.5,3.0,3.5,4.0]
mus = [0.0,1.0,1.5,2.0,2.5,3.0,3.5]
for s,m in zip(sigmas,mus):
N = 1/np.sqrt(2*np.pi*s**2)
fx = N*np.exp(-(xs-m)**2/(2*s**2))
plt.plot(xs,fx, label = "mu="+str(m)+",sigma="+str(s))
plt.xlabel('x')
plt.ylabel('probability')
plt.show()
xs = np.arange(-10,10,0.01)
plt.figure(figsize = [14,16])
sigmas = [ 1.0,1.5,2.0,2.5,3.0,3.5,4.0]
mus = [0.0,1.0,1.5,2.0,2.5,3.0,3.5]
k = 1
for s,m in zip(sigmas,mus):
plt.subplot(4,2,k)
N = 1/np.sqrt(2*np.pi*s**2)
fx = N*np.exp(-(xs-m)**2/(2*s**2))
plt.plot(xs,fx, label = "mu="+str(m)+",sigma="+str(s))
plt.xlabel('x',fontsize =20)
plt.ylabel('prabability')
plt.legend()
k = k+1
plt.show()
List Comprehension with arange
xs = np.arange(0,3.14,0.1)
np.sin(xs)
array([0. , 0.09983342, 0.19866933, 0.29552021, 0.38941834,
0.47942554, 0.56464247, 0.64421769, 0.71735609, 0.78332691,
0.84147098, 0.89120736, 0.93203909, 0.96355819, 0.98544973,
0.99749499, 0.9995736 , 0.99166481, 0.97384763, 0.94630009,
0.90929743, 0.86320937, 0.8084964 , 0.74570521, 0.67546318,
0.59847214, 0.51550137, 0.42737988, 0.33498815, 0.23924933,
0.14112001, 0.04158066])
np.cos(xs)
array([ 1. , 0.99500417, 0.98006658, 0.95533649, 0.92106099,
0.87758256, 0.82533561, 0.76484219, 0.69670671, 0.62160997,
0.54030231, 0.45359612, 0.36235775, 0.26749883, 0.16996714,
0.0707372 , -0.02919952, -0.12884449, -0.22720209, -0.32328957,
-0.41614684, -0.5048461 , -0.58850112, -0.66627602, -0.73739372,
-0.80114362, -0.85688875, -0.90407214, -0.94222234, -0.97095817,
-0.9899925 , -0.99913515])
Sum of sin(x)+cos(x)
np.sin(xs)+ np.cos(xs)
array([ 1. , 1.09483758, 1.17873591, 1.2508567 , 1.31047934,
1.3570081 , 1.38997809, 1.40905987, 1.4140628 , 1.40493688,
1.38177329, 1.34480348, 1.29439684, 1.23105701, 1.15541687,
1.06823219, 0.97037408, 0.86282032, 0.74664554, 0.62301052,
0.49315059, 0.35836326, 0.21999529, 0.07942919, -0.06193053,
-0.20267147, -0.34138738, -0.47669226, -0.60723419, -0.73170884,
-0.84887249, -0.95755449])
List including array for cos(x), cos(2x), cos(3x), cos(4x)
[np.cos(n*xs) for n in range(1,5)]
[array([ 1. , 0.99500417, 0.98006658, 0.95533649, 0.92106099,
0.87758256, 0.82533561, 0.76484219, 0.69670671, 0.62160997,
0.54030231, 0.45359612, 0.36235775, 0.26749883, 0.16996714,
0.0707372 , -0.02919952, -0.12884449, -0.22720209, -0.32328957,
-0.41614684, -0.5048461 , -0.58850112, -0.66627602, -0.73739372,
-0.80114362, -0.85688875, -0.90407214, -0.94222234, -0.97095817,
-0.9899925 , -0.99913515]),
array([ 1. , 0.98006658, 0.92106099, 0.82533561, 0.69670671,
0.54030231, 0.36235775, 0.16996714, -0.02919952, -0.22720209,
-0.41614684, -0.58850112, -0.73739372, -0.85688875, -0.94222234,
-0.9899925 , -0.99829478, -0.96679819, -0.89675842, -0.79096771,
-0.65364362, -0.49026082, -0.30733287, -0.11215253, 0.08749898,
0.28366219, 0.46851667, 0.63469288, 0.77556588, 0.88551952,
0.96017029, 0.9965421 ]),
array([ 1. , 0.95533649, 0.82533561, 0.62160997, 0.36235775,
0.0707372 , -0.22720209, -0.5048461 , -0.73739372, -0.90407214,
-0.9899925 , -0.98747977, -0.89675842, -0.7259323 , -0.49026082,
-0.2107958 , 0.08749898, 0.37797774, 0.63469288, 0.83471278,
0.96017029, 0.99985864, 0.95023259, 0.8157251 , 0.60835131,
0.34663532, 0.05395542, -0.24354415, -0.51928865, -0.74864665,
-0.91113026, -0.99222533]),
array([ 1. , 0.92106099, 0.69670671, 0.36235775, -0.02919952,
-0.41614684, -0.73739372, -0.94222234, -0.99829478, -0.89675842,
-0.65364362, -0.30733287, 0.08749898, 0.46851667, 0.77556588,
0.96017029, 0.99318492, 0.86939749, 0.60835131, 0.25125984,
-0.14550003, -0.51928865, -0.81109301, -0.97484362, -0.98468786,
-0.83907153, -0.56098426, -0.19432991, 0.20300486, 0.56828963,
0.84385396, 0.9861923 ])]
Sum of cos(x)+cos(2x)+cos(3x)+cos(4x)
sum([np.cos(n*xs) for n in range(1,5)])
array([ 4. , 3.85146823, 3.4231699 , 2.76463983, 1.95092594,
1.07247523, 0.22309756, -0.51225912, -1.0681813 , -1.40642268,
-1.51948065, -1.42971764, -1.18429539, -0.84680556, -0.48695014,
-0.16988081, 0.0531896 , 0.15173255, 0.11908368, -0.02828465,
-0.2551202 , -0.51453694, -0.75669441, -0.93754707, -1.02623127,
-1.00991764, -0.89540092, -0.70725333, -0.48294025, -0.26579566,
-0.09709851, -0.00862608])