
import numpy as np
vector_row = np.array([[1, -5, 3, 2, 4]])
vector_column = np.array([[1], 
                          [2], 
                          [3], 
                          [4]])
print(vector_row.shape)
print(vector_column.shape)


print(vector_row)
print(vector_column)


import sys
sys.float_info

sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)


import numpy as np

# Spacing tells us how far "next largest/smallest" number is
np.spacing(100_000_000)

1.4901161193847656e-08


np.spacing(100.2)  # notice smaller spacing at this point

1.4210854715202004e-14


print(  np.spacing(1e4)  )
print(  np.spacing(1e-4)  )

1.8189894035458565e-12
1.3552527156068805e-20


num = 1e9
# num = 100.0
spacing = np.spacing(num)
print(num)
print(spacing)

num_next = num + spacing
print(num_next)
print("Next is same:    ", num == num_next)

num_closer = num + (spacing/2)
print(num_closer)
print("Closer is same:  ", num == num_closer)

1000000000.0
1.1920928955078125e-07
1000000000.0000001
Next is same:     False
1000000000.0
Closer is same:   True


sys.float_info.max

1.7976931348623157e+308


sys.float_info.min

2.2250738585072014e-308


# Reading assignment: Chop-off and Round-off


import numpy as np 
num_1 = 2e12
sp_1 = np.spacing(num_1)
num_2 = 15.22
sp_2 = np.spacing(num_2)
print(sp_1, "       ", sp_2)

0.000244140625         1.7763568394002505e-15

Set Name	Symbol	Description
Naturals	$\mathbb{N}$	${\mathbb{N}} = \{1, 2, 3, 4, \cdots\}$
Wholes	$\mathbb{W}$	${\mathbb{W}} = \mathbb{N} \cup \{0\}$
Integers	$\mathbb{Z}$	${\mathbb{Z}} = \mathbb{W} \cup \{-1, -2, -3, \cdots\}$
Rationals	$\mathbb{Q}$	${\mathbb{Q}} = \{\frac{p}{q} : p\in {\mathbb{Z}}, q\in {\mathbb{Z}} \backslash \{0\}\}$
Irrationals	$\mathbb{I}$	${\mathbb{I}}$ is the set of real numbers not expressible as a fraction of integers.
Reals	$\mathbb{R}$	${\mathbb{R}} = \mathbb{Q} \cup \mathbb{I}$
Complex Numbers	$\mathbb{C}$	${\mathbb{C}} = \{a + bi : a,b\in {\mathbb{R}}, i = \sqrt{-1}\}$

Numbers and Types¶

Floating Point Numbers¶