CoCalc -- Lecture 11.ipynb

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Kernel: Unknown Kernel

In [1]:

x = float(raw_input('Enter a number: '))

Out[1]:

Enter a number: seven

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-1-61ced4682ade> in <module>()
----> 1 x = float(raw_input('Enter a number: '))

ValueError: could not convert string to float: seven

In [1]:

try:
    s = raw_input('Enter a number: ')
    x = float(s)
except ValueError:
    print("%s cannot be converted to floating point number." % s)

Out[1]:

Enter a number: seven
seven cannot be converted to floating point number.

In [2]:

list = [1,2,3,4]
print(list[4])

Out[2]:

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-2-8d9c2d533693> in <module>()
      1 list = [1,2,3,4]
----> 2 print(list[4])

IndexError: list index out of range

In [3]:

from math import sqrt
sqrt(-2)

Out[3]:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-3-03202d5db7db> in <module>()
      1 from math import sqrt
----> 2 sqrt(-2)

ValueError: math domain error

In [4]:

x = 0
y = 2
a = y/x

Out[4]:

---------------------------------------------------------------------------
ZeroDivisionError                         Traceback (most recent call last)
<ipython-input-4-bb76b55e818d> in <module>()
      1 x = 0
      2 y = 2
----> 3 a = y/x

ZeroDivisionError: integer division or modulo by zero

In [5]:

a = 2
print(A)

Out[5]:

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-5-23441cc05d89> in <module>()
      1 a = 2
----> 2 print(A)

NameError: name 'A' is not defined

In [6]:

a =* 2

Out[6]:

  File "<ipython-input-6-d6ea3953da97>", line 1
    a =* 2
       ^
SyntaxError: invalid syntax

In [9]:

a = '2'
b = 3.0
try:
    print(a*b)
except TypeError:
    print('Please do not multiply strings by floats.')

Out[9]:

Please do not multiply strings by floats.

In [8]:

a = 'abc'
b = 10
print(a*b)

Out[8]:

abcabcabcabcabcabcabcabcabcabc

In [1]:

value = 0
counter = 0
while value is 0 and counter < 3:
    try:
        value = float(raw_input("Enter a number: "))
    except ValueError:
        print('That\'s not a number.')
        counter += 1
print(value)

Out[1]:

Enter a number: seven
That's not a number.
Enter a number: aardvaark
That's not a number.
Enter a number: seven aardvaarks
That's not a number.
0

In [2]:

def leftInt(f,a,b,n=100):
    if type(a) != float:
        a = float(a) #Will raise an exception if a cannot be converted to float.
    if type(b) != float:
        b = float(b) #Will raise an exception if b cannot be converted to float.
    if (type(n) != int) or (n <= 0):
        raise ValueError("number of rectangles must be a positive integer") #We don't want to convert n into an int...if the user passed in a non-int or negative, there clearly is a problem.
    deltax = (b-a)/n
    x = a
    sum = 0
    for i in range(n):
        try:
            sum += f(x)
        except TypeError:
            raise TypeError("integrand is not a valid function") #Sometimes we want to catch a particular exception and re-raise it with a more specific error message.
        x += deltax
    return deltax*sum

In [3]:

def f(x):
    return 3*x**2

leftInt(f,0,4,3.5)

Out[3]:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-3-1f37c601bc1e> in <module>()
      2     return 3*x**2
      3 
----> 4 leftInt(f,0,4,3.5)

<ipython-input-2-b28beb750b2d> in leftInt(f, a, b, n)
      5         b = float(b) #Will raise an exception if b cannot be converted to float.
      6     if (type(n) != int) or (n <= 0):
----> 7         raise ValueError("number of rectangles must be a positive integer") #We don't want to convert n into an int...if the user passed in a non-int or negative, there clearly is a problem.
      8     deltax = (b-a)/n
      9     x = a
ValueError: number of rectangles must be a positive integer

In [4]:

def g(x):
    return "You're a jerk!"

leftInt(g,0,4,3)

Out[4]:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-2b6f8aa6e3b6> in <module>()
      2     return "You're a jerk!"
      3 
----> 4 leftInt(g,0,4,3)

<ipython-input-2-b28beb750b2d> in leftInt(f, a, b, n)
     13             sum += f(x)
     14         except TypeError:
---> 15             raise TypeError("integrand is not a valid function") #Sometimes we want to catch a particular exception and re-raise it with a more specific error message.
     16         x += deltax
     17     return deltax*sum
TypeError: integrand is not a valid function

In [1]:

import L11approximations
def f(x):
    return x**3 + 2*x

a = 0
b = 4
print(L11approximations.leftInt(f,0,4,10))
print(L11approximations.rightInt(f,0,4,10))
print(L11approximations.trapInt(f,0,4,10))

Out[1]:

24
04
64

In [3]:

from L11approximations import *
print(leftInt(f,0,4,100))

Out[3]:

78.5664

In [4]:

import numpy as np
dataList = [1,2,3,4,5,6]
dataArray = np.array(dataList)
print(dataArray)

Out[4]:

[1 2 3 4 5 6]

In [5]:

dataList = [1,2,3.1,4,5,6]
dataArray = np.array(dataList)
print(dataArray)

Out[5]:

[ 1.   2.   3.1  4.   5.   6. ]

In [6]:

[1,2,3]+[4,5,6]

Out[6]:

[1, 2, 3, 4, 5, 6]

In [7]:

dataArray2 = np.array([1,2,3,4,5.0,6.2])
dataArray = dataArray + dataArray2
print(dataArray)

Out[7]:

[  2.    4.    6.1   8.   10.   12.2]

In [8]:

zeroArray = np.zeros(12)
print(zeroArray)

Out[8]:

[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]

In [10]:

intervalArray = np.linspace(1,5,20)
print(intervalArray)

Out[10]:

[ 1.          1.21052632  1.42105263  1.63157895  1.84210526  2.05263158
26315789  2.47368421  2.68421053  2.89473684  3.10526316  3.31578947
52631579  3.73684211  3.94736842  4.15789474  4.36842105  4.57894737
78947368  5.        ]

In [11]:

def g(x):
    return x**3

print(g(intervalArray))

Out[11]:

[   1.            1.77387374    2.8696603     4.34334451    6.25091121
64834524   11.59163143   15.13675463   19.33969966   24.25645138
94299461   36.45531419   43.84939496   52.18122175   61.50677941
88205278   83.36302668   96.00568596  109.86601545  125.        ]

In [12]:

from numpy import *
print(exp(intervalArray))

Out[12]:

[   2.71828183    3.35525011    4.1414776     5.11193983    6.30980809
78836987    9.61339939   11.86608357   14.64663368   18.07874325
31509059   27.54413077   33.99847904   41.96525883   51.79887449
93677707   78.91892444   97.41180148  120.23806881  148.4131591 ]

In [13]:

print(cos(pi*intervalArray))

Out[13]:

[-1.         -0.78914051 -0.24548549  0.40169542  0.87947375  0.9863613
  0.67728157  0.08257935 -0.54694816 -0.94581724 -0.94581724 -0.54694816
  0.08257935  0.67728157  0.9863613   0.87947375  0.40169542 -0.24548549
 -0.78914051 -1.        ]

In [15]:

print(dot(intervalArray,intervalArray))
print(dot(np.array([1,2,3,4]), np.array([1,1,1,1])))

Out[15]:

209.473684211
10

In [16]:

print(cross(array([1,2,3]),array([2,5,7])))

Out[16]:

[-1 -1  1]

In [17]:

A = array([[1,2,3],[3,-4,5],[5,6,7]])
print(A)

Out[17]:

[[ 1  2  3]
 [ 3 -4  5]
 [ 5  6  7]]

In [18]:

eigenvalues, eigenvectors = linalg.eig(A)
print(eigenvalues)
print(eigenvectors)

Out[18]:

[ 11.25664784  -0.89351035  -6.36313749]
[[ 0.32531663  0.85160988  0.09637145]
 [ 0.35164354 -0.02060987 -0.92099553]
 [ 0.87779036 -0.5237708   0.37746494]]

In [19]:

linalg.det(A)

Out[19]:

63.999999999999979

In [20]:

print(A*A)

Out[20]:

[[ 1  4  9]
 [ 9 16 25]
 [25 36 49]]

In [21]:

print(dot(A,A))

Out[21]:

[[22 12 34]
 [16 52 24]
 [58 28 94]]

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