-] Problem 5 Full Width at Half Maximum(FWHM). Distribution width is a very important quantity. It tells you how wide a the distribution is. One way to do that is to use a quantity called full-width half max This is the width of the distribution at half maximum. For example for distribution shown below the maximum is at x=0.0 and y=1.0 The maximum of this distribution is 1.0. So we are interested in the width of the distribution when the value of the distribution is 1.0/2=0.5 The width of the distribution is shown in black line. In this case it's about 2.35 import math def demo(x): 1 2 3 4 x = np.linspace (-3,3) 5 return math.exp(-x**2/2.0) y = [demo(xx) for xx in x] 6 plt.plot(x,y) 7 plt.axhline (0.5, color='red') 8 9 plt.axvline (2.355/2,color='red',linestyle= 'dashed') 10 plt.axvline (-2.355/2, color='red', linestyle= 'dashed') 11 12 plt.grid() 13 plt.annotate( 14 15 16 '', xy=(-2.355/2, 0.4), xycoords='data', xytext=(2.355/2, 0.4), textcoords='data', arrowprops={'arrowstyle': '<->'}) 17 plt.text(0,0.3, 'FWHM',horizontalalignment ='center') 10- 0.8 0.6 0.4 0.2 0.0 -2 FWHM ✓ ✓ 5.1)Find FWHM of the following function. Make sure the bound on error of the FWHM is less than 10-4. 1 import math mu = 2.345 return gamma/((x-mu)**2+gamma**2) 2 def f(x, gamma=3.1): 3 4 5 6 y = [f(xx) for xx in x] x = np.linspace (-10,10,200) [25] 7 plt.plot(x,y) ... ... [] 0.30- 0.25 0.20 0.15 0.10 0.05- -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 5.2) Plot FWHM(y-axis) as a function of (gamma) from y = 0.5... 3. Make sure you have at least 30 points. 1 print(f(1.0, gamma-0.2)) # you may find this useful [26] ... 0.108165114047 [ ] 5.3) (Optional) Prove the relation you found in 5.2) 1
-] Problem 5 Full Width at Half Maximum(FWHM). Distribution width is a very important quantity. It tells you how wide a the distribution is. One way to do that is to use a quantity called full-width half max This is the width of the distribution at half maximum. For example for distribution shown below the maximum is at x=0.0 and y=1.0 The maximum of this distribution is 1.0. So we are interested in the width of the distribution when the value of the distribution is 1.0/2=0.5 The width of the distribution is shown in black line. In this case it's about 2.35 import math def demo(x): 1 2 3 4 x = np.linspace (-3,3) 5 return math.exp(-x**2/2.0) y = [demo(xx) for xx in x] 6 plt.plot(x,y) 7 plt.axhline (0.5, color='red') 8 9 plt.axvline (2.355/2,color='red',linestyle= 'dashed') 10 plt.axvline (-2.355/2, color='red', linestyle= 'dashed') 11 12 plt.grid() 13 plt.annotate( 14 15 16 '', xy=(-2.355/2, 0.4), xycoords='data', xytext=(2.355/2, 0.4), textcoords='data', arrowprops={'arrowstyle': '<->'}) 17 plt.text(0,0.3, 'FWHM',horizontalalignment ='center') 10- 0.8 0.6 0.4 0.2 0.0 -2 FWHM ✓ ✓ 5.1)Find FWHM of the following function. Make sure the bound on error of the FWHM is less than 10-4. 1 import math mu = 2.345 return gamma/((x-mu)**2+gamma**2) 2 def f(x, gamma=3.1): 3 4 5 6 y = [f(xx) for xx in x] x = np.linspace (-10,10,200) [25] 7 plt.plot(x,y) ... ... [] 0.30- 0.25 0.20 0.15 0.10 0.05- -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 5.2) Plot FWHM(y-axis) as a function of (gamma) from y = 0.5... 3. Make sure you have at least 30 points. 1 print(f(1.0, gamma-0.2)) # you may find this useful [26] ... 0.108165114047 [ ] 5.3) (Optional) Prove the relation you found in 5.2) 1
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
%matplotlib inline
import math
import numpy as np
from matplotlib import pyplot as plt
import math
def demo(x):
return math.exp(-x**2/2.0)
x = np.linspace(-3,3)
y = [demo(xx) for xx in x]
plt.plot(x,y)
plt.axhline(0.5, color='red')
plt.axvline(2.355/2,color='red',linestyle='dashed')
plt.axvline(-2.355/2,color='red',linestyle='dashed')
plt.grid()
plt.annotate(
'', xy=(-2.355/2, 0.4), xycoords='data',
xytext=(2.355/2, 0.4), textcoords='data',
arrowprops={'arrowstyle': '<->'})
plt.text(0,0.3,'FWHM',horizontalalignment ='center')
5.1
import math
def f(x, gamma=3.1):
mu = 2.345
return gamma/((x-mu)**2+gamma**2)
x = np.linspace(-10,10,200)
y = [f(xx) for xx in x]
plt.plot(x,y)
5.2
print(f(1.0, gamma=0.2)) # you may find this useful
![-]
Problem 5
Full Width at Half Maximum(FWHM). Distribution width is a very important quantity. It tells you how wide a the distribution is. One way to do that is to use a quantity called full-width half max
This is the width of the distribution at half maximum.
For example for distribution shown below the maximum is at x=0.0 and y=1.0
The maximum of this distribution is 1.0. So we are interested in the width of the distribution when the value of the distribution is 1.0/2=0.5
The width of the distribution is shown in black line. In this case it's about 2.35
import math
def demo(x):
1
2
3
4
x = np.linspace (-3,3)
5
return math.exp(-x**2/2.0)
y = [demo(xx) for xx in x]
6 plt.plot(x,y)
7 plt.axhline (0.5, color='red')
8
9 plt.axvline (2.355/2,color='red',linestyle= 'dashed')
10 plt.axvline (-2.355/2, color='red', linestyle= 'dashed')
11
12 plt.grid()
13 plt.annotate(
14
15
16
'', xy=(-2.355/2, 0.4), xycoords='data',
xytext=(2.355/2, 0.4), textcoords='data',
arrowprops={'arrowstyle': '<->'})
17 plt.text(0,0.3, 'FWHM',horizontalalignment ='center')
<matplotlib.text.Text at 0x107045fd0>
10-
0.8
0.6
0.4
0.2
0.0
-2
FWHM](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff97c0725-689e-40d7-87a0-46553d65cfc3%2F5bd205f8-1084-4f78-ae89-c4e684487017%2Fsez0sf_processed.png&w=3840&q=75)
Transcribed Image Text:-]
Problem 5
Full Width at Half Maximum(FWHM). Distribution width is a very important quantity. It tells you how wide a the distribution is. One way to do that is to use a quantity called full-width half max
This is the width of the distribution at half maximum.
For example for distribution shown below the maximum is at x=0.0 and y=1.0
The maximum of this distribution is 1.0. So we are interested in the width of the distribution when the value of the distribution is 1.0/2=0.5
The width of the distribution is shown in black line. In this case it's about 2.35
import math
def demo(x):
1
2
3
4
x = np.linspace (-3,3)
5
return math.exp(-x**2/2.0)
y = [demo(xx) for xx in x]
6 plt.plot(x,y)
7 plt.axhline (0.5, color='red')
8
9 plt.axvline (2.355/2,color='red',linestyle= 'dashed')
10 plt.axvline (-2.355/2, color='red', linestyle= 'dashed')
11
12 plt.grid()
13 plt.annotate(
14
15
16
'', xy=(-2.355/2, 0.4), xycoords='data',
xytext=(2.355/2, 0.4), textcoords='data',
arrowprops={'arrowstyle': '<->'})
17 plt.text(0,0.3, 'FWHM',horizontalalignment ='center')
<matplotlib.text.Text at 0x107045fd0>
10-
0.8
0.6
0.4
0.2
0.0
-2
FWHM
![✓ ✓
5.1)Find FWHM of the following function. Make sure the bound on error of the FWHM is less than 10-4.
1 import math
mu = 2.345
return gamma/((x-mu)**2+gamma**2)
2
def f(x, gamma=3.1):
3
4
5
6
y = [f(xx) for xx in x]
x = np.linspace (-10,10,200)
[25]
7 plt.plot(x,y)
...
...
[<matplotlib.lines. Line2D at 0x106fd2050>]
0.30-
0.25
0.20
0.15
0.10
0.05-
-10.0 -7.5 -5.0 -2.5 0.0
2.5 5.0 7.5 10.0
5.2) Plot FWHM(y-axis) as a function of (gamma) from y = 0.5... 3. Make sure you have at least 30 points.
1 print(f(1.0, gamma-0.2)) # you may find this useful
[26]
...
0.108165114047
[ ]
5.3) (Optional) Prove the relation you found in 5.2)
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff97c0725-689e-40d7-87a0-46553d65cfc3%2F5bd205f8-1084-4f78-ae89-c4e684487017%2Ff8j1baj_processed.png&w=3840&q=75)
Transcribed Image Text:✓ ✓
5.1)Find FWHM of the following function. Make sure the bound on error of the FWHM is less than 10-4.
1 import math
mu = 2.345
return gamma/((x-mu)**2+gamma**2)
2
def f(x, gamma=3.1):
3
4
5
6
y = [f(xx) for xx in x]
x = np.linspace (-10,10,200)
[25]
7 plt.plot(x,y)
...
...
[<matplotlib.lines. Line2D at 0x106fd2050>]
0.30-
0.25
0.20
0.15
0.10
0.05-
-10.0 -7.5 -5.0 -2.5 0.0
2.5 5.0 7.5 10.0
5.2) Plot FWHM(y-axis) as a function of (gamma) from y = 0.5... 3. Make sure you have at least 30 points.
1 print(f(1.0, gamma-0.2)) # you may find this useful
[26]
...
0.108165114047
[ ]
5.3) (Optional) Prove the relation you found in 5.2)
1
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