This is Ruby/Numo::NArray version of 100 numpy exercises (Repository)

1. Import the numpy package under the name np (★☆☆)

Python:

import numpy as np

Ruby:

In [1]:
require "numo/narray"
Out[1]:
true

2. Print the numpy version and the configuration (★☆☆)

Python:

print(np.__version__)
np.show_config()

Ruby:

In [2]:
p Numo::NArray::VERSION
"0.9.0.3"
Out[2]:
"0.9.0.3"

3. Create a null vector of size 10 (★☆☆)

Python:

Z = np.zeros(10)
print(Z)

Ruby:

In [3]:
z = Numo::DFloat.zeros(10)
p z
Numo::DFloat#shape=[10]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Out[3]:
Numo::DFloat#shape=[10]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

4. How to find the memory size of any array (★☆☆)

Python:

Z = np.zeros((10,10))
print("%d bytes" % (Z.size * Z.itemsize))

Ruby:

In [4]:
z = Numo::DFloat.zeros(10,10)
printf "%d bytes", z.byte_size
800 bytes

5. How to get the documentation of the numpy add function from the command line? (★☆☆)

Python:

$ python -c "import numpy; numpy.info(numpy.add)"

Ruby:

In [5]:
ri 'Numo::DFloat#+'
Numo::DFloat#+

(from gem numo-narray-0.9.0.3)
Implementation from DFloat
------------------------------------------------------------------------------
  +(p1)

------------------------------------------------------------------------------

Binary add. @overload + other @param [Numo::NArray,Numeric] other @return
[Numo::NArray] self + other


6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆)

Python:

Z = np.zeros(10)
Z[4] = 1
print(Z)

Ruby:

In [6]:
z = Numo::DFloat.zeros(10)
z[4] = 1
p z
Numo::DFloat#shape=[10]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0]
Out[6]:
Numo::DFloat#shape=[10]
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0]

7. Create a vector with values ranging from 10 to 49 (★☆☆)

Python:

Z = np.arange(10,50)
print(Z)

Ruby:

In [7]:
z = Numo::DFloat[10..49]
p z
Numo::DFloat#shape=[40]
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, ...]
Out[7]:
Numo::DFloat#shape=[40]
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, ...]

8. Reverse a vector (first element becomes last) (★☆☆)

Python:

Z = np.arange(50)
Z = Z[::-1]
print(Z)

Ruby:

In [9]:
z = Numo::Int32.new(50).seq
z = z.reverse
Out[9]:
Numo::Int32(view)#shape=[50]
[49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, ...]

9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)

Python:

Z = np.arange(9).reshape(3,3)
print(Z)

Ruby:

In [10]:
z = Numo::Int32.new(3,3).seq
p z
Numo::Int32#shape=[3,3]
[[0, 1, 2], 
 [3, 4, 5], 
 [6, 7, 8]]
Out[10]:
Numo::Int32#shape=[3,3]
[[0, 1, 2], 
 [3, 4, 5], 
 [6, 7, 8]]

10. Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)

Python:

nz = np.nonzero([1,2,0,0,4,0])
print(nz)

Ruby:

In [11]:
nz = Numo::NArray[1,2,0,0,4,0].ne(0).where
p nz
Numo::Int32#shape=[3]
[0, 1, 4]
Out[11]:
Numo::Int32#shape=[3]
[0, 1, 4]

11. Create a 3x3 identity matrix (★☆☆)

Python:

Z = np.eye(3)
print(Z)

Ruby:

In [12]:
z = Numo::DFloat.eye(3)
p z
Numo::DFloat#shape=[3,3]
[[1, 0, 0], 
 [0, 1, 0], 
 [0, 0, 1]]
Out[12]:
Numo::DFloat#shape=[3,3]
[[1, 0, 0], 
 [0, 1, 0], 
 [0, 0, 1]]

12. Create a 3x3x3 array with random values (★☆☆)

Python:

Z = np.random.random((3,3,3))
print(Z)

Ruby:

In [13]:
z = Numo::DFloat.new(3,3,3).rand
p z
Numo::DFloat#shape=[3,3,3]
[[[0.0617545, 0.373067, 0.794815], 
  [0.201042, 0.116041, 0.344032], 
  [0.539948, 0.737815, 0.165089]], 
 [[0.0508827, 0.108065, 0.0687079], 
  [0.904121, 0.478644, 0.342969], 
  [0.164541, 0.74603, 0.138994]], 
 [[0.411576, 0.292532, 0.869421], 
  [0.0854984, 0.688965, 0.159977], 
  [0.279215, 0.625155, 0.676329]]]
Out[13]:
Numo::DFloat#shape=[3,3,3]
[[[0.0617545, 0.373067, 0.794815], 
  [0.201042, 0.116041, 0.344032], 
  [0.539948, 0.737815, 0.165089]], 
 [[0.0508827, 0.108065, 0.0687079], 
  [0.904121, 0.478644, 0.342969], 
  [0.164541, 0.74603, 0.138994]], 
 [[0.411576, 0.292532, 0.869421], 
  [0.0854984, 0.688965, 0.159977], 
  [0.279215, 0.625155, 0.676329]]]

13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)

Python:

Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()
print(Zmin, Zmax)

Ruby:

In [14]:
z = Numo::DFloat.new(10,10).rand
zmin, zmax = z.minmax
p zmin, zmax
0.0007664325967829586
0.995590771731077
Out[14]:
[0.0007664325967829586, 0.995590771731077]

14. Create a random vector of size 30 and find the mean value (★☆☆)

Python:

Z = np.random.random(30)
m = Z.mean()
print(m)

Ruby:

In [15]:
z = Numo::DFloat.new(30).rand
m = z.mean
p m
0.5609149765660713
Out[15]:
0.5609149765660713

15. Create a 2d array with 1 on the border and 0 inside (★☆☆)

Python:

Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)

Ruby:

In [16]:
z = Numo::DFloat.ones(10,10)
z[1..-2,1..-2] = 0
p z
Numo::DFloat#shape=[10,10]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]
Out[16]:
Numo::DFloat#shape=[10,10]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 
 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

16. How to add a border (filled with 0's) around an existing array? (★☆☆)

Python:

Z = np.ones((5,5))
Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
print(Z)

Ruby:

# todo: pad

17. What is the result of the following expression? (★☆☆)

Python:

print(0 * np.nan)
print(np.nan == np.nan)
print(np.inf > np.nan)
print(np.nan - np.nan)
print(0.3 == 3 * 0.1)

Ruby:

In [17]:
0 * Float::NAN
Float::NAN == Float::NAN
Float::INFINITY > Float::NAN
Float::NAN - Float::NAN
0.3 == 3 * 0.1
Out[17]:
false

18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)

Python:

Z = np.diag(1+np.arange(4),k=-1)
print(Z)

Ruby:

In [18]:
z = Numo::Int32.zeros(5,5)
z.diagonal(-1)[] = Numo::Int32[1..4]
p z
Numo::Int32#shape=[5,5]
[[0, 0, 0, 0, 0], 
 [1, 0, 0, 0, 0], 
 [0, 2, 0, 0, 0], 
 [0, 0, 3, 0, 0], 
 [0, 0, 0, 4, 0]]
Out[18]:
Numo::Int32#shape=[5,5]
[[0, 0, 0, 0, 0], 
 [1, 0, 0, 0, 0], 
 [0, 2, 0, 0, 0], 
 [0, 0, 3, 0, 0], 
 [0, 0, 0, 4, 0]]

19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)

Python:

Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)

Ruby:

In [19]:
# todo: rangewithstep
x = Numo::Int32.new(1,8).seq
y = Numo::Int32.new(8,1).seq
z = (x+y)%2
p z
Numo::Int32#shape=[8,8]
[[0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0]]
Out[19]:
Numo::Int32#shape=[8,8]
[[0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0], 
 [0, 1, 0, 1, 0, 1, 0, 1], 
 [1, 0, 1, 0, 1, 0, 1, 0]]

20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element?

Python:

print(np.unravel_index(100,(6,7,8)))

Ruby:

In [22]:
# NArray allows unraveled index access
z = Numo::Int32.new(6,7,8).seq
p z[100]
100
Out[22]:
100

21. Create a checkerboard 8x8 matrix using the tile function (★☆☆)

Python:

Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)

Ruby:

# todo: tile

22. Normalize a 5x5 random matrix (★☆☆)

Python:

Z = np.random.random((5,5))
Zmax, Zmin = Z.max(), Z.min()
Z = (Z - Zmin)/(Zmax - Zmin)
print(Z)

Ruby:

In [23]:
z = Numo::DFloat.new(5,5).rand
zmin, zmax = z.minmax
z = (z - zmin)/(zmax - zmin)
p z
Numo::DFloat#shape=[5,5]
[[0.766088, 0.769435, 0.641326, 0.836021, 0.287046], 
 [0.838608, 0.290923, 0.0930798, 0.235153, 0.57146], 
 [0.167737, 0.548881, 1, 0.771149, 0.683695], 
 [0.766882, 0.486607, 0.942667, 0, 0.45248], 
 [0.801575, 0.23934, 0.267108, 0.536452, 0.382229]]
Out[23]:
Numo::DFloat#shape=[5,5]
[[0.766088, 0.769435, 0.641326, 0.836021, 0.287046], 
 [0.838608, 0.290923, 0.0930798, 0.235153, 0.57146], 
 [0.167737, 0.548881, 1, 0.771149, 0.683695], 
 [0.766882, 0.486607, 0.942667, 0, 0.45248], 
 [0.801575, 0.23934, 0.267108, 0.536452, 0.382229]]

23. Create a custom dtype that describes a color as four unisgned bytes (RGBA) (★☆☆)

Python:

color = np.dtype([("r", np.ubyte, 1),
                  ("g", np.ubyte, 1),
                  ("b", np.ubyte, 1),
                  ("a", np.ubyte, 1)])

Ruby:

In [24]:
# todo: record
color = Numo::Struct.new do
  uint8 "r"
  uint8 "g"
  uint8 "b"
  uint8 "a"
end
Out[24]:
#<Class:0x007f8cfab26a68>

24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)

Python:

Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)

Ruby:

In [25]:
x = Numo::DFloat.ones(5,3)
y = Numo::DFloat.ones(3,2)
z = x.dot y
p z
Numo::DFloat#shape=[5,2]
[[3, 3], 
 [3, 3], 
 [3, 3], 
 [3, 3], 
 [3, 3]]
Out[25]:
Numo::DFloat#shape=[5,2]
[[3, 3], 
 [3, 3], 
 [3, 3], 
 [3, 3], 
 [3, 3]]

25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)

Python:

# Author: Evgeni Burovski

Z = np.arange(11)
Z[(3 < Z) & (Z <= 8)] *= -1
print(Z)

Ruby:

In [27]:
z = Numo::Int32.new(11).seq
z[(3 < z) & (z <= 8)] *= -1
p z
Numo::Int32#shape=[11]
[0, 1, 2, 3, -4, -5, -6, -7, -8, 9, 10]
Out[27]:
Numo::Int32#shape=[11]
[0, 1, 2, 3, -4, -5, -6, -7, -8, 9, 10]

26. What is the output of the following script? (★☆☆)

Python:

# Author: Jake VanderPlas

print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))

Ruby:

In [15]:
p [*0...5,-1].inject(:+)
p Numo::Int32[0...5].sum(-1)
9
10
Out[15]:
10

27. Consider an integer vector Z, which of these expressions are legal? (★☆☆)

Python:

Z = np.arange(5)
Z**Z
2 << Z >> 2
Z <- Z
1j*Z
Z/1/1
Z<Z>Z

Ruby:

In [16]:
z = Numo::Int32.new(5).seq
z**z
2 << z >> 2
z <- z
1i*z
z/1/1
z<z>z
TypeError: no implicit conversion of Numo::Int32 into Integer
(pry):51:in `<<'
(pry):51:in `<main>'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `evaluate_ruby'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:323:in `handle_line'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:243:in `block (2 levels) in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `block in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:65:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:12:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:87:in `execute_request'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:47:in `dispatch'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:37:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:70:in `run_kernel'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:34:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/bin/iruby:5:in `<top (required)>'
/usr/local/bin/iruby:22:in `load'
/usr/local/bin/iruby:22:in `<main>'

28. What are the result of the following expressions?

Python:

print(np.array(0) / np.array(0))
print(np.array(0) // np.array(0))
print(np.array([np.nan]).astype(int).astype(float))

Ruby:

In [17]:
p Numo::Int32[0] / Numo::Int32[0]
p Numo::DFloat[Float::NAN].cast_to(Numo::Int32).cast_to(Numo::DFloat)
ZeroDivisionError: error in NArray operation
(pry):56:in `/'
(pry):56:in `<main>'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `evaluate_ruby'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:323:in `handle_line'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:243:in `block (2 levels) in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `block in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:65:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:12:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:87:in `execute_request'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:47:in `dispatch'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:37:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:70:in `run_kernel'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:34:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/bin/iruby:5:in `<top (required)>'
/usr/local/bin/iruby:22:in `load'
/usr/local/bin/iruby:22:in `<main>'

29. How to round away from zero a float array ? (★☆☆)

Python:

# Author: Charles R Harris

Z = np.random.uniform(-10,+10,10)
print (np.trunc(Z + np.copysign(0.5, Z)))

Ruby:

In [18]:
z = Numo::DFloat.new(10).rand(-10,+10)
p (z + (0.5*z.sign)).trunc
# todo: copysign
Numo::DFloat#shape=[10]
[-7, -0, 10, -5, -7, -1, -10, -3, -1, -5]
Out[18]:
Numo::DFloat#shape=[10]
[-7, -0, 10, -5, -7, -1, -10, -3, -1, -5]

30. How to find common values between two arrays? (★☆☆)

Python:

Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(np.intersect1d(Z1,Z2))

Ruby:

In [19]:
# todo: intersect1d

35. How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)

Python:

A = np.ones(3)*1
B = np.ones(3)*2
np.add(A,B,out=B)
np.divide(A,2,out=A)
np.negative(A,out=A)
np.multiply(A,B,out=A)

Ruby:

In [3]:
a = Numo::DFloat.new(3).fill(1)
b = Numo::DFloat.new(3).fill(2)
p (a+b)*(-a/2)
(a+b.inplace)*(-a.inplace/2)
p b
Numo::DFloat#shape=[3]
[-1.5, -1.5, -1.5]
Numo::DFloat#shape=[3]
[-1.5, -1.5, -1.5]
Out[3]:
Numo::DFloat#shape=[3]
[-1.5, -1.5, -1.5]

36. Extract the integer part of a random array using 5 different methods (★★☆)

Python:

Z = np.random.uniform(0,10,10)

print (Z - Z%1)
print (np.floor(Z))
print (np.ceil(Z)-1)
print (Z.astype(int))
print (np.trunc(Z))

Ruby:

In [4]:
z = Numo::DFloat.new(10).rand(10)

p z - z%1
p z.floor
p z.ceil - 1
p z.cast_to(Numo::Int32)
p z.trunc
Numo::DFloat#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]
Numo::DFloat#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]
Numo::DFloat#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]
Numo::Int32#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]
Numo::DFloat#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]
Out[4]:
Numo::DFloat#shape=[10]
[0, 3, 7, 2, 1, 3, 5, 7, 1, 0]

37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)

Python:

Z = np.zeros((5,5))
Z += np.arange(5)
print(Z)

Ruby:

In [5]:
z = Numo::DFloat.zeros(5,5)
z += Numo::Int32.new(5).seq
p z
Numo::DFloat#shape=[5,5]
[[0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4]]
Out[5]:
Numo::DFloat#shape=[5,5]
[[0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4], 
 [0, 1, 2, 3, 4]]

39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)

Python:

Z = np.linspace(0,1,12,endpoint=True)[1:-1]
print(Z)

Ruby:

In [6]:
z = Numo::DFloat.linspace(0,1,12)[1..-2]
p z
Numo::DFloat(view)#shape=[10]
[0.0909091, 0.181818, 0.272727, 0.363636, 0.454545, 0.545455, 0.636364, ...]
Out[6]:
Numo::DFloat(view)#shape=[10]
[0.0909091, 0.181818, 0.272727, 0.363636, 0.454545, 0.545455, 0.636364, ...]

40. Create a random vector of size 10 and sort it (★★☆)

Python:

Z = np.random.random(10)
Z.sort()
print(Z)

Ruby:

In [7]:
z = Numo::DFloat.new(10).rand
z = z.sort
p z
Numo::DFloat#shape=[10]
[0.0687079, 0.108065, 0.138994, 0.164541, 0.292532, 0.342969, 0.411576, ...]
Out[7]:
Numo::DFloat#shape=[10]
[0.0687079, 0.108065, 0.138994, 0.164541, 0.292532, 0.342969, 0.411576, ...]

43. Make an array immutable (read-only) (★★☆)

Python:

Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1

Ruby:

In [3]:
z = Numo::DFloat.zeros(10)
z.freeze
z[0] = 1
RuntimeError: cannot write to frozen NArray.
(pry):7:in `[]='
(pry):7:in `<main>'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:355:in `evaluate_ruby'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:323:in `handle_line'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:243:in `block (2 levels) in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:242:in `block in eval'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `catch'
/var/lib/gems/2.1.0/gems/pry-0.10.4/lib/pry/pry_instance.rb:241:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:65:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/backend.rb:12:in `eval'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:87:in `execute_request'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:47:in `dispatch'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/kernel.rb:37:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:70:in `run_kernel'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/lib/iruby/command.rb:34:in `run'
/var/lib/gems/2.1.0/gems/iruby-0.2.9/bin/iruby:5:in `<top (required)>'
/usr/local/bin/iruby:22:in `load'
/usr/local/bin/iruby:22:in `<main>'

44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)

Python:

Z = np.random.random((10,2))
X,Y = Z[:,0], Z[:,1]
R = np.sqrt(X**2+Y**2)
T = np.arctan2(Y,X)
print(R)
print(T)

Ruby:

In [4]:
z = Numo::DFloat.new(10,2).rand
x,y = z[true,0], z[true,1]
r = Numo::NMath.sqrt(x**2+y**2)
t = Numo::NMath.atan2(y,x)
p r
p t
Numo::DFloat#shape=[10]
[0.378143, 0.819847, 0.363075, 0.914284, 0.172752, 0.128057, 1.023, ...]
Numo::DFloat#shape=[10]
[1.40675, 0.247746, 1.24548, 0.939032, 0.298976, 0.566331, 0.486892, ...]
Out[4]:
Numo::DFloat#shape=[10]
[1.40675, 0.247746, 1.24548, 0.939032, 0.298976, 0.566331, 0.486892, ...]

45. Create random vector of size 10 and replace the maximum value by 0 (★★☆)

Python:

Z = np.random.random(10)
Z[Z.argmax()] = 0
print(Z)

Ruby:

In [5]:
z = Numo::DFloat.new(10).rand
z[z.max_index] = 0
p z
Numo::DFloat#shape=[10]
[0, 0.0854984, 0.688965, 0.159977, 0.279215, 0.625155, 0.676329, ...]
Out[5]:
Numo::DFloat#shape=[10]
[0, 0.0854984, 0.688965, 0.159977, 0.279215, 0.625155, 0.676329, ...]

50. How to find the closest value (to a given scalar) in an array? (★★☆)

Python:

Z = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(Z-v)).argmin()
print(Z[index])

Ruby:

In [3]:
z = Numo::Int32.new(100).seq
v = rand*100
index = (z-v).abs.min_index
p z[index]
86
Out[3]:
86

54. How to read the following file? (★★☆)

Python:

from io import StringIO

# Fake file
s = StringIO("""1, 2, 3, 4, 5\n
                6,  ,  , 7, 8\n
                 ,  , 9,10,11\n""")
Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
print(Z)

Ruby:

In [4]:
require "stringio"
s = StringIO.new("1, 2, 3, 4, 5
                  6,  ,  , 7, 8
                   ,  , 9,10,11")
z = Numo::NArray[*s.readlines.map{|l| l.split(",").map{|x| x.strip.empty? ? Float::NAN : x.to_f}}]
Out[4]:
Numo::DFloat#shape=[3,5]
[[1, 2, 3, 4, 5], 
 [6, nan, nan, 7, 8], 
 [nan, nan, 9, 10, 11]]

55. What is the equivalent of enumerate for numpy arrays? (★★☆)

Python:

Z = np.arange(9).reshape(3,3)
for index, value in np.ndenumerate(Z):
    print(index, value)
for index in np.ndindex(Z.shape):
    print(index, Z[index])

Ruby:

In [5]:
z = Numo::Int32.new(3,3).seq
z.each_with_index{|x,*i| p [i,x]}
[[0, 0], 0]
[[0, 1], 1]
[[0, 2], 2]
[[1, 0], 3]
[[1, 1], 4]
[[1, 2], 5]
[[2, 0], 6]
[[2, 1], 7]
[[2, 2], 8]
Out[5]:
Numo::Int32#shape=[3,3]
[[0, 1, 2], 
 [3, 4, 5], 
 [6, 7, 8]]

56. Generate a generic 2D Gaussian-like array (★★☆)

Python:

X, Y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
D = np.sqrt(X*X+Y*Y)
sigma, mu = 1.0, 0.0
G = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
print(G)

Ruby:

In [6]:
x = Numo::DFloat.linspace(-1,1,10)
y = Numo::DFloat.linspace(-1,1,10).expand_dims(1)
d = Numo::NMath.sqrt(x*x+y*y)
sigma, mu = 1.0, 0.0
g = Numo::NMath.exp(-( (d-mu)**2 / ( 2.0 * sigma**2 ) ) )
p g
Numo::DFloat#shape=[10,10]
[[0.367879, 0.448221, 0.519795, 0.573753, 0.602798, 0.602798, 0.573753, ...], 
 [0.448221, 0.546108, 0.633313, 0.699056, 0.734444, 0.734444, 0.699056, ...], 
 [0.519795, 0.633313, 0.734444, 0.810684, 0.851723, 0.851723, 0.810684, ...], 
 [0.573753, 0.699056, 0.810684, 0.894839, 0.940138, 0.940138, 0.894839, ...], 
 [0.602798, 0.734444, 0.851723, 0.940138, 0.98773, 0.98773, 0.940138, ...], 
 [0.602798, 0.734444, 0.851723, 0.940138, 0.98773, 0.98773, 0.940138, ...], 
 [0.573753, 0.699056, 0.810684, 0.894839, 0.940138, 0.940138, 0.894839, ...], 
 [0.519795, 0.633313, 0.734444, 0.810684, 0.851723, 0.851723, 0.810684, ...], 
 [0.448221, 0.546108, 0.633313, 0.699056, 0.734444, 0.734444, 0.699056, ...], 
 [0.367879, 0.448221, 0.519795, 0.573753, 0.602798, 0.602798, 0.573753, ...]]
Out[6]:
Numo::DFloat#shape=[10,10]
[[0.367879, 0.448221, 0.519795, 0.573753, 0.602798, 0.602798, 0.573753, ...], 
 [0.448221, 0.546108, 0.633313, 0.699056, 0.734444, 0.734444, 0.699056, ...], 
 [0.519795, 0.633313, 0.734444, 0.810684, 0.851723, 0.851723, 0.810684, ...], 
 [0.573753, 0.699056, 0.810684, 0.894839, 0.940138, 0.940138, 0.894839, ...], 
 [0.602798, 0.734444, 0.851723, 0.940138, 0.98773, 0.98773, 0.940138, ...], 
 [0.602798, 0.734444, 0.851723, 0.940138, 0.98773, 0.98773, 0.940138, ...], 
 [0.573753, 0.699056, 0.810684, 0.894839, 0.940138, 0.940138, 0.894839, ...], 
 [0.519795, 0.633313, 0.734444, 0.810684, 0.851723, 0.851723, 0.810684, ...], 
 [0.448221, 0.546108, 0.633313, 0.699056, 0.734444, 0.734444, 0.699056, ...], 
 [0.367879, 0.448221, 0.519795, 0.573753, 0.602798, 0.602798, 0.573753, ...]]

58. Subtract the mean of each row of a matrix (★★☆)

Python:

# Author: Warren Weckesser

X = np.random.rand(5, 10)

# Recent versions of numpy
Y = X - X.mean(axis=1, keepdims=True)

# Older versions of numpy
Y = X - X.mean(axis=1).reshape(-1, 1)

print(Y)

Ruby:

In [7]:
x = Numo::DFloat.new(5, 10).rand
y = x - x.mean(1).expand_dims(1)
Out[7]:
Numo::DFloat#shape=[5,10]
[[-0.276694, 0.0346182, 0.456367, -0.137406, -0.222408, 0.00558358, ...], 
 [-0.257554, -0.29691, 0.538503, 0.113026, -0.0226486, -0.201077, ...], 
 [0.49633, -0.287593, 0.315874, -0.213114, -0.0938766, 0.252064, 0.303238, ...], 
 [-0.0359266, -0.116908, 0.508809, 0.423319, -0.309937, -0.404925, ...], 
 [-0.168796, -0.165424, 0.464085, -0.0274508, 0.0251129, 0.0339921, ...]]

59. How to I sort an array by the nth column? (★★☆)

Python:

# Author: Steve Tjoa

Z = np.random.randint(0,10,(3,3))
print(Z)
print(Z[Z[:,1].argsort()])

Ruby:

In [8]:
z = Numo::Int32.new(3,3).rand(10)
p z
p z[z[true,1].sort_index,true]
Numo::Int32#shape=[3,3]
[[7, 3, 0], 
 [2, 5, 0], 
 [2, 7, 7]]
Numo::Int32(view)#shape=[3,3]
[[7, 3, 0], 
 [2, 5, 0], 
 [2, 7, 7]]
Out[8]:
Numo::Int32(view)#shape=[3,3]
[[7, 3, 0], 
 [2, 5, 0], 
 [2, 7, 7]]

60. How to tell if a given 2D array has null columns? (★★☆)

Python:

# Author: Warren Weckesser

Z = np.random.randint(0,3,(3,10))
print((~Z.any(axis=0)).any())

Ruby:

In [2]:
z = Numo::Int32.new(3,10).rand(3)
(~z.ne(0).any?(0)).any?
Out[2]:
true

61. Find the nearest value from a given value in an array (★★☆)

Python:

Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print(m)

Ruby:

In [3]:
z = Numo::DFloat.new(10).rand
x = 0.5
m = z[(z - x).abs.min_index]
p m
0.4115760120668863
Out[3]:
0.4115760120668863

66. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★)

Python:

# Author: Nadav Horesh

w,h = 16,16
I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
F = I[...,0]*256*256 + I[...,1]*256 +I[...,2]
n = len(np.unique(F))
print(np.unique(I))

Ruby:

In [4]:
# todo: unique
w,h = 16,16
i = Numo::UInt32.new(h,w,3).rand(2)
f = i[false,0]*256*256 + i[false,1]*256 +i[false,2]
p f.flatten.sort.to_a.uniq
[0, 1, 256, 257, 65536, 65793, 65792, 65537]
Out[4]:
[0, 1, 256, 257, 65536, 65793, 65792, 65537]

67. Considering a four dimensions array, how to get sum over the last two axis at once? (★★★)

Python:

A = np.random.randint(0,10,(3,4,3,4))
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print(sum)

Ruby:

In [5]:
a = Numo::Int32.new(3,4,3,4).rand(10)
sum = a.sum(-2,-1)
p sum
Numo::Int32#shape=[3,4]
[[80, 51, 48, 48], 
 [51, 58, 56, 43], 
 [59, 61, 73, 54]]
Out[5]:
Numo::Int32#shape=[3,4]
[[80, 51, 48, 48], 
 [51, 58, 56, 43], 
 [59, 61, 73, 54]]

68. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices? (★★★)

Python:

# Author: Jaime Fernández del Río

D = np.random.uniform(0,1,100)
S = np.random.randint(0,10,100)
D_sums = np.bincount(S, weights=D)
D_counts = np.bincount(S)
D_means = D_sums / D_counts
print(D_means)

Ruby:

# todo: bincount

69. How to get the diagonal of a dot product? (★★★)

Python:

# Author: Mathieu Blondel

A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))

# Slow version
np.diag(np.dot(A, B))

# Fast version
np.sum(A * B.T, axis=1)

# Faster version
np.einsum("ij,ji->i", A, B)

Ruby:

In [6]:
a = Numo::DFloat.new(3,3).seq
b = Numo::DFloat.new(3,3).seq
p a.mulsum(b.transpose,1)
# speed?
Numo::DFloat#shape=[3]
[15, 54, 111]
Out[6]:
Numo::DFloat#shape=[3]
[15, 54, 111]

70. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)

Python:

# Author: Warren Weckesser

Z = np.array([1,2,3,4,5])
nz = 3
Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
Z0[::nz+1] = Z
print(Z0)

Ruby:

In [7]:
z = Numo::NArray[1,2,3,4,5]
nz = 3
z0 = Numo::Int32.zeros(z.size + (z.size-1)*(nz))
# todo: rangewithstep
# z0[(0..-1).step(nz+1)] = z
# p z0
Out[7]:
Numo::Int32#shape=[17]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)

Python:

A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print(A * B[:,:,None])

Ruby:

In [8]:
a = Numo::Int32.ones(5,5,3)
b = Numo::Int32.new(5,5).fill(2)
p a * b[:*,:*,:-]
Numo::Int32#shape=[5,5,3]
[[[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 ...
Out[8]:
Numo::Int32#shape=[5,5,3]
[[[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 [[2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2], 
  [2, 2, 2]], 
 ...

72. How to swap two rows of an array? (★★★)

Python:

# Author: Eelco Hoogendoorn

A = np.arange(25).reshape(5,5)
A[[0,1]] = A[[1,0]]
print(A)

Ruby:

In [9]:
a = Numo::Int32.new(5,5).seq
a[[0,1],true] = a[[1,0],true].copy
p a
# todo: identity check between read/write array
Numo::Int32#shape=[5,5]
[[5, 6, 7, 8, 9], 
 [0, 1, 2, 3, 4], 
 [10, 11, 12, 13, 14], 
 [15, 16, 17, 18, 19], 
 [20, 21, 22, 23, 24]]
Out[9]:
Numo::Int32#shape=[5,5]
[[5, 6, 7, 8, 9], 
 [0, 1, 2, 3, 4], 
 [10, 11, 12, 13, 14], 
 [15, 16, 17, 18, 19], 
 [20, 21, 22, 23, 24]]

73. Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)

Python:

# Author: Nicolas P. Rougier

faces = np.random.randint(0,100,(10,3))
F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
F = F.reshape(len(F)*3,2)
F = np.sort(F,axis=1)
G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
G = np.unique(G)
print(G)

Ruby:

# todo: roll

74. Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C? (★★★)

Python:

# Author: Jaime Fernández del Río

C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print(A)

Ruby:

# todo: bincount, repeat

75. How to compute averages using a sliding window over an array? (★★★)

Python:

# Author: Jaime Fernández del Río

def moving_average(a, n=3) :
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret[n - 1:] / n
Z = np.arange(20)
print(moving_average(Z, n=3))

Ruby:

In [2]:
def moving_average(a, n=3)
  ret = a.cumsum
  ret[n..-1] = ret[n..-1] - ret[0..-n-1]
  ret[n-1..-1] / n
end
z = Numo::DFloat.new(20).seq
p moving_average(z, 3)
Numo::DFloat#shape=[18]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
Out[2]:
Numo::DFloat#shape=[18]
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]

76. Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1]) (★★★)

Python:

# Author: Joe Kington / Erik Rigtorp
from numpy.lib import stride_tricks

def rolling(a, window):
    shape = (a.size - window + 1, window)
    strides = (a.itemsize, a.itemsize)
    return stride_tricks.as_strided(a, shape=shape, strides=strides)
Z = rolling(np.arange(10), 3)
print(Z)

Ruby:

# no module: stride_tricks

77. How to negate a boolean, or to change the sign of a float inplace? (★★★)

Python:

# Author: Nathaniel J. Smith

Z = np.random.randint(0,2,100)
np.logical_not(Z, out=Z)

Z = np.random.uniform(-1.0,1.0,100)
np.negative(Z, out=Z)

Ruby:

In [3]:
# todo: logical_not
z = Numo::Int32.new(100).rand(2)
p z
z.inplace ^ 1
p z

z = Numo::DFloat.new(100).rand(-1,1)
p z
-z.inplace
p z
Numo::Int32#shape=[100]
[0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, ...]
Numo::Int32#shape=[100]
[1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...]
Numo::DFloat#shape=[100]
[-0.00105903, 0.140595, -0.671175, 0.782669, 0.406039, -0.54762, 0.86998, ...]
Numo::DFloat#shape=[100]
[0.00105903, -0.140595, 0.671175, -0.782669, -0.406039, 0.54762, -0.86998, ...]
Out[3]:
Numo::DFloat#shape=[100]
[0.00105903, -0.140595, 0.671175, -0.782669, -0.406039, 0.54762, -0.86998, ...]

78. Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to compute distance from p to each line i (P0[i],P1[i])? (★★★)

Python:

def distance(P0, P1, p):
    T = P1 - P0
    L = (T**2).sum(axis=1)
    U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
    U = U.reshape(len(U),1)
    D = P0 + U*T - p
    return np.sqrt((D**2).sum(axis=1))

P0 = np.random.uniform(-10,10,(10,2))
P1 = np.random.uniform(-10,10,(10,2))
p  = np.random.uniform(-10,10,( 1,2))
print(distance(P0, P1, p))

Ruby:

In [4]:
def distance(p0, p1, p)
  t = p1 - p0
  l = (t**2).sum(1)
  u = -((p0[true,0]-p[false,0])*t[true,0] + (p0[true,1]-p[false,1])*t[true,1]) / l
  u = u.reshape(u.size,1)
  d = p0 + u*t - p
  return Numo::NMath.sqrt((d**2).sum(1))
end

p0 = Numo::DFloat.new(10,2).rand(-10,10)
p1 = Numo::DFloat.new(10,2).rand(-10,10)
p  = Numo::DFloat.new( 1,2).rand(-10,10)
p distance(p0, p1, p)
Numo::DFloat#shape=[10]
[4.40292, 8.02008, 14.77, 16.1336, 16.0784, 7.29705, 9.79877, 10.7509, ...]
Out[4]:
Numo::DFloat#shape=[10]
[4.40292, 8.02008, 14.77, 16.1336, 16.0784, 7.29705, 9.79877, 10.7509, ...]

79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)

Python:

# Author: Italmassov Kuanysh

# based on distance function from previous question
P0 = np.random.uniform(-10, 10, (10,2))
P1 = np.random.uniform(-10,10,(10,2))
p = np.random.uniform(-10, 10, (10,2))
print(np.array([distance(P0,P1,p_i) for p_i in p]))

Ruby:

In [5]:
p0 = Numo::DFloat.new(10,2).rand(-10,10)
p1 = Numo::DFloat.new(10,2).rand(-10,10)
p  = Numo::DFloat.new(10,2).rand(-10,10)
p a = p.shape[0].times.map{|i| distance(p0, p1, p.slice(i,true))}
# todo: concat narray
[Numo::DFloat#shape=[10]
[4.02299, 3.7767, 7.22074, 2.65235, 4.03999, 0.0493129, 5.89712, 0.821607, ...], Numo::DFloat#shape=[10]
[4.06287, 10.2757, 5.22386, 9.17308, 3.49263, 6.51912, 12.1396, 6.87145, ...], Numo::DFloat#shape=[10]
[12.2731, 4.95469, 14.9322, 6.10746, 12.3248, 8.71038, 4.51429, 8.38228, ...], Numo::DFloat#shape=[10]
[7.29208, 11.2986, 5.80238, 9.93285, 11.5081, 9.4783, 9.65492, 10.33, ...], Numo::DFloat#shape=[10]
[7.42679, 14.6827, 6.16027, 13.4397, 8.20325, 10.8814, 16.0162, 11.3742, ...], Numo::DFloat#shape=[10]
[8.90535, 14.3727, 6.22079, 12.941, 13.1026, 11.9889, 13.0645, 12.8597, ...], Numo::DFloat#shape=[10]
[10.121, 14.4822, 11.257, 13.8115, 7.24394, 11.2893, 17.1786, 11.2277, ...], Numo::DFloat#shape=[10]
[9.10298, 2.80676, 12.3148, 3.95976, 7.48986, 5.13894, 6.17195, 4.37329, ...], Numo::DFloat#shape=[10]
[0.720696, 7.46437, 3.14777, 6.04, 4.88395, 4.03443, 8.16959, 4.84799, ...], Numo::DFloat#shape=[10]
[2.82967, 10.3413, 0.872794, 8.92055, 6.33658, 6.80721, 10.889, 7.56309, ...]]
Out[5]:
[Numo::DFloat#shape=[10]
[4.02299, 3.7767, 7.22074, 2.65235, 4.03999, 0.0493129, 5.89712, 0.821607, ...], Numo::DFloat#shape=[10]
[4.06287, 10.2757, 5.22386, 9.17308, 3.49263, 6.51912, 12.1396, 6.87145, ...], Numo::DFloat#shape=[10]
[12.2731, 4.95469, 14.9322, 6.10746, 12.3248, 8.71038, 4.51429, 8.38228, ...], Numo::DFloat#shape=[10]
[7.29208, 11.2986, 5.80238, 9.93285, 11.5081, 9.4783, 9.65492, 10.33, ...], Numo::DFloat#shape=[10]
[7.42679, 14.6827, 6.16027, 13.4397, 8.20325, 10.8814, 16.0162, 11.3742, ...], Numo::DFloat#shape=[10]
[8.90535, 14.3727, 6.22079, 12.941, 13.1026, 11.9889, 13.0645, 12.8597, ...], Numo::DFloat#shape=[10]
[10.121, 14.4822, 11.257, 13.8115, 7.24394, 11.2893, 17.1786, 11.2277, ...], Numo::DFloat#shape=[10]
[9.10298, 2.80676, 12.3148, 3.95976, 7.48986, 5.13894, 6.17195, 4.37329, ...], Numo::DFloat#shape=[10]
[0.720696, 7.46437, 3.14777, 6.04, 4.88395, 4.03443, 8.16959, 4.84799, ...], Numo::DFloat#shape=[10]
[2.82967, 10.3413, 0.872794, 8.92055, 6.33658, 6.80721, 10.889, 7.56309, ...]]

80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary) (★★★)

Python:

# Author: Nicolas Rougier

Z = np.random.randint(0,10,(10,10))
shape = (5,5)
fill  = 0
position = (1,1)

R = np.ones(shape, dtype=Z.dtype)*fill
P  = np.array(list(position)).astype(int)
Rs = np.array(list(R.shape)).astype(int)
Zs = np.array(list(Z.shape)).astype(int)

R_start = np.zeros((len(shape),)).astype(int)
R_stop  = np.array(list(shape)).astype(int)
Z_start = (P-Rs//2)
Z_stop  = (P+Rs//2)+Rs%2

R_start = (R_start - np.minimum(Z_start,0)).tolist()
Z_start = (np.maximum(Z_start,0)).tolist()
R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
Z_stop = (np.minimum(Z_stop,Zs)).tolist()

r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
R[r] = Z[z]
print(Z)
print(R)

Ruby:

# todo: minimum, maximum

81. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]]? (★★★)

Python:

# Author: Stefan van der Walt

Z = np.arange(1,15,dtype=np.uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print(R)

Ruby:

# no moudle: stride_tricks

82. Compute a matrix rank (★★★)

Python:

# Author: Stefan van der Walt

Z = np.random.uniform(0,1,(10,10))
U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
rank = np.sum(S > 1e-10)
print(rank)

Ruby:

# todo: svd

83. How to find the most frequent value in an array?

Python:

Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())

Ruby:

# todo: bincount

84. Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)

Python:

# Author: Chris Barker

Z = np.random.randint(0,5,(10,10))
n = 3
i = 1 + (Z.shape[0]-3)
j = 1 + (Z.shape[1]-3)
C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)
print(C)

Ruby:

# no module: stride_tricks

85. Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)

Python:

# Author: Eric O. Lebigot
# Note: only works for 2d array and value setting using indices

class Symetric(np.ndarray):
    def __setitem__(self, index, value):
        i,j = index
        super(Symetric, self).__setitem__((i,j), value)
        super(Symetric, self).__setitem__((j,i), value)

def symetric(Z):
    return np.asarray(Z + Z.T - np.diag(Z.diagonal())).view(Symetric)

S = symetric(np.random.randint(0,10,(5,5)))
S[2,3] = 42
print(S)

Ruby:

In [6]:
module Symetric
  def []=(i,j,value)
    super(i,j,value)
    super(j,i,value) if i != j
  end
end

def symetric(z)
  y = z + z.transpose
  y.diagonal.store(z.diagonal)
  y.extend(Symetric)
end

s = symetric(Numo::Int32.new(5,5).rand(10))
s[2,3] = 42
p s
Numo::Int32#shape=[5,5]
[[8, 6, 5, 8, 12], 
 [6, 7, 9, 11, 10], 
 [5, 9, 5, 42, 6], 
 [8, 11, 42, 3, 16], 
 [12, 10, 6, 16, 0]]
Out[6]:
Numo::Int32#shape=[5,5]
[[8, 6, 5, 8, 12], 
 [6, 7, 9, 11, 10], 
 [5, 9, 5, 42, 6], 
 [8, 11, 42, 3, 16], 
 [12, 10, 6, 16, 0]]

86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)

Python:

# Author: Stefan van der Walt

p, n = 10, 20
M = np.ones((p,n,n))
V = np.ones((p,n,1))
S = np.tensordot(M, V, axes=[[0, 2], [0, 1]])
print(S)

# It works, because:
# M is (p,n,n)
# V is (p,n,1)
# Thus, summing over the paired axes 0 and 0 (of M and V independently),
# and 2 and 1, to remain with a (n,1) vector.

Ruby:

In [7]:
p, n = 10, 20
m = Numo::DFloat.ones(p,n,n)
v = Numo::DFloat.ones(p,n,1)
s = m.transpose(0,2,1).mulsum(v,0,1)
p s
# todo: tensordot?
Numo::DFloat#shape=[20]
[200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, ...]
Out[7]:
Numo::DFloat#shape=[20]
[200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, ...]

87. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)

Python:

# Author: Robert Kern

Z = np.ones((16,16))
k = 4
S = np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),
                                       np.arange(0, Z.shape[1], k), axis=1)
print(S)

Ruby:

In [8]:
n, k = 16, 4
z = Numo::DFloat.ones(n,n)
s = z.reshape(n/k,k,n/k,k).sum(1,3)
# todo: reduceat?
Out[8]:
Numo::DFloat#shape=[4,4]
[[16, 16, 16, 16], 
 [16, 16, 16, 16], 
 [16, 16, 16, 16], 
 [16, 16, 16, 16]]

88. How to implement the Game of Life using numpy arrays? (★★★)

Python:

# Author: Nicolas Rougier

def iterate(Z):
    # Count neighbours
    N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +
         Z[1:-1,0:-2]                + Z[1:-1,2:] +
         Z[2:  ,0:-2] + Z[2:  ,1:-1] + Z[2:  ,2:])

    # Apply rules
    birth = (N==3) & (Z[1:-1,1:-1]==0)
    survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)
    Z[...] = 0
    Z[1:-1,1:-1][birth | survive] = 1
    return Z

Z = np.random.randint(0,2,(50,50))
for i in range(100): Z = iterate(Z)
print(Z)

Ruby:

In [9]:
def iterate(z)
  # Count neighbours
  n = z[0..-3,0..-3] + z[0..-3,1..-2] + z[0..-3,2..-1] +
      z[1..-2,0..-3]                  + z[1..-2,2..-1] +
      z[2..-1,0..-3] + z[2..-1,1..-2] + z[2..-1,2..-1]

  # Apply rules
  birth = n.eq(3) & z[1..-2,1..-2].eq(0)
  survive = (n.eq(2) | n.eq(3)) & z[1..-2,1..-2].eq(1)
  z[] = 0
  #z[1..-2,1..-2][birth | survive] = 1
  y = z[0..-3,0..-3].copy
  y[birth | survive] = 1
  z[1..-2,1..-2] = y
end

z = Numo::Int32.new(50,50).rand(2)
100.times{ iterate(z) }
p z
Numo::Int32#shape=[50,50]
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 ...
Out[9]:
Numo::Int32#shape=[50,50]
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, ...], 
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...], 
 ...

89. How to get the n largest values of an array (★★★)

Python:

Z = np.arange(10000)
np.random.shuffle(Z)
n = 5

# Slow
print (Z[np.argsort(Z)[-n:]])

# Fast
print (Z[np.argpartition(-Z,n)[:n]])

Ruby:

In [10]:
z = Numo::DFloat.new(10000).rand
n = 5
p z[z.sort_index[-n..-1]]
# todo: shuffle, argpartition
Numo::DFloat(view)#shape=[5]
[0.999617, 0.999781, 0.999866, 0.999873, 0.999884]
Out[10]:
Numo::DFloat(view)#shape=[5]
[0.999617, 0.999781, 0.999866, 0.999873, 0.999884]

90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)

Python:

# Author: Stefan Van der Walt

def cartesian(arrays):
    arrays = [np.asarray(a) for a in arrays]
    shape = (len(x) for x in arrays)

    ix = np.indices(shape, dtype=int)
    ix = ix.reshape(len(arrays), -1).T

    for n, arr in enumerate(arrays):
        ix[:, n] = arrays[n][ix[:, n]]

    return ix

print (cartesian(([1, 2, 3], [4, 5], [6, 7])))

Ruby:

In [11]:
def cartesian(*arrays)
  arrays = arrays.map{|a| Numo::Int32.cast(a)}
  shape = arrays.map{|x| x.size}
  asz = arrays.size

  ix = Numo::Int32.zeros(*shape, asz)
  arrays.each_with_index do |arr,n|
    s = [1]*asz
    s[n] = arr.size
    ix[false,n] = arr.reshape(*s)
  end
  return ix.reshape(ix.size/asz,asz)
end

p cartesian([1, 2, 3], [4, 5], [6, 7])
Numo::Int32#shape=[12,3]
[[1, 4, 6], 
 [1, 4, 7], 
 [1, 5, 6], 
 [1, 5, 7], 
 [2, 4, 6], 
 [2, 4, 7], 
 [2, 5, 6], 
 [2, 5, 7], 
 [3, 4, 6], 
 [3, 4, 7], 
 [3, 5, 6], 
 [3, 5, 7]]
Out[11]:
Numo::Int32#shape=[12,3]
[[1, 4, 6], 
 [1, 4, 7], 
 [1, 5, 6], 
 [1, 5, 7], 
 [2, 4, 6], 
 [2, 4, 7], 
 [2, 5, 6], 
 [2, 5, 7], 
 [3, 4, 6], 
 [3, 4, 7], 
 [3, 5, 6], 
 [3, 5, 7]]

91. How to create a record array from a regular array? (★★★)

Python:

Z = np.array([("Hello", 2.5, 3),
              ("World", 3.6, 2)])
R = np.core.records.fromarrays(Z.T,
                               names='col1, col2, col3',
                               formats = 'S8, f8, i8')
print(R)

Ruby:

# todo: record

92. Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)

Python:

# Author: Ryan G.

x = np.random.rand(5e7)

%timeit np.power(x,3)
%timeit x*x*x
%timeit np.einsum('i,i,i->i',x,x,x)

Ruby:

In [2]:
x = Numo::DFloat.new(5e7).rand
x**3 # probably fast
Out[2]:
Numo::DFloat#shape=[50000000]
[0.000235508, 0.051923, 0.50211, 0.00812571, 0.00156255, 0.040719, ...]

93. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A that contain elements of each row of B regardless of the order of the elements in B? (★★★)

Python:

# Author: Gabe Schwartz

A = np.random.randint(0,5,(8,3))
B = np.random.randint(0,5,(2,2))

C = (A[..., np.newaxis, np.newaxis] == B)
rows = (C.sum(axis=(1,2,3)) >= B.shape[1]).nonzero()[0]
print(rows)

Ruby:

In [3]:
a = Numo::Int32.new(8,3).rand(5)
b = Numo::Int32.new(2,2).rand(5)
c = a[false,:new,:new].eq b
rows = (c.count_true(1,2,3) >= b.shape[1]).where
p rows
Numo::Int32#shape=[6]
[0, 1, 2, 5, 6, 7]
Out[3]:
Numo::Int32#shape=[6]
[0, 1, 2, 5, 6, 7]

94. Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)

Python:

# Author: Robert Kern

Z = np.random.randint(0,5,(10,3))
E = np.logical_and.reduce(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print(Z)
print(U)

Ruby:

In [4]:
z = Numo::Int32.new(10,3).rand(5)
e = (z[true,1..-1].eq z[true,0..-2]).all?(1)
u = z[(~e).where,true]
p z
p u
Numo::Int32#shape=[10,3]
[[0, 2, 1], 
 [3, 1, 0], 
 [3, 1, 2], 
 [2, 4, 4], 
 [0, 3, 0], 
 [4, 3, 3], 
 [4, 3, 2], 
 [2, 0, 2], 
 [2, 3, 2], 
 [2, 3, 4]]
Numo::Int32(view)#shape=[10,3]
[[0, 2, 1], 
 [3, 1, 0], 
 [3, 1, 2], 
 [2, 4, 4], 
 [0, 3, 0], 
 [4, 3, 3], 
 [4, 3, 2], 
 [2, 0, 2], 
 [2, 3, 2], 
 [2, 3, 4]]
Out[4]:
Numo::Int32(view)#shape=[10,3]
[[0, 2, 1], 
 [3, 1, 0], 
 [3, 1, 2], 
 [2, 4, 4], 
 [0, 3, 0], 
 [4, 3, 3], 
 [4, 3, 2], 
 [2, 0, 2], 
 [2, 3, 2], 
 [2, 3, 4]]

95. Convert a vector of ints into a matrix binary representation (★★★)

Python:

# Author: Warren Weckesser

I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
B = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)
print(B[:,::-1])

# Author: Daniel T. McDonald

I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)
print(np.unpackbits(I[:, np.newaxis], axis=1))

Ruby:

# todo: bit

96. Given a two dimensional array, how to extract unique rows? (★★★)

Python:

# Author: Jaime Fernández del Río

Z = np.random.randint(0,2,(6,3))
T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))
_, idx = np.unique(T, return_index=True)
uZ = Z[idx]
print(uZ)

Ruby:

# todo: unique row

97. Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)

Python:

# Author: Alex Riley
# Make sure to read: http://ajcr.net/Basic-guide-to-einsum/

A = np.random.uniform(0,1,10)
B = np.random.uniform(0,1,10)

np.einsum('i->', A)       # np.sum(A)
np.einsum('i,i->i', A, B) # A * B
np.einsum('i,i', A, B)    # np.inner(A, B)
np.einsum('i,j', A, B)    # np.outer(A, B)

Ruby:

In [5]:
# no method: einsum
a = Numo::DFloat.new(10).rand(0,1)
b = Numo::DFloat.new(10).rand(0,1)

a.sum           # np.sum(A)
a*b             # A * B
a.mulsum(b)     # np.inner(A, B)
a[false,:new]*b # np.outer(A, B)
Out[5]:
Numo::DFloat#shape=[10,10]
[[0.418361, 0.252631, 0.168549, 0.367414, 0.0409535, 0.365022, 0.22084, ...], 
 [0.369513, 0.223134, 0.148869, 0.324515, 0.0361717, 0.322402, 0.195055, ...], 
 [0.575741, 0.347666, 0.231954, 0.505629, 0.0563594, 0.502337, 0.303916, ...], 
 [0.423199, 0.255553, 0.170498, 0.371663, 0.0414271, 0.369243, 0.223394, ...], 
 [0.0554262, 0.0334696, 0.02233, 0.0486766, 0.00542569, 0.0483596, ...], 
 [0.285368, 0.172322, 0.114968, 0.250617, 0.0279347, 0.248985, 0.150637, ...], 
 [0.398275, 0.240502, 0.160457, 0.349775, 0.0389873, 0.347497, 0.210238, ...], 
 [0.21605, 0.130464, 0.0870418, 0.18974, 0.0211492, 0.188505, 0.114046, ...], 
 [0.343856, 0.20764, 0.138532, 0.301982, 0.0336601, 0.300016, 0.181511, ...], 
 [0.0467036, 0.0282024, 0.0188159, 0.0410162, 0.00457183, 0.0407492, ...]]

98. Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)?

Python:

# Author: Bas Swinckels

phi = np.arange(0, 10*np.pi, 0.1)
a = 1
x = a*phi*np.cos(phi)
y = a*phi*np.sin(phi)

dr = (np.diff(x)**2 + np.diff(y)**2)**.5 # segment lengths
r = np.zeros_like(x)
r[1:] = np.cumsum(dr)                # integrate path
r_int = np.linspace(0, r.max(), 200) # regular spaced path
x_int = np.interp(r_int, r, x)       # integrate path
y_int = np.interp(r_int, r, y)

Ruby:

# todo: interp

99. Given an integer n and a 2D array X, select from X the rows which can be interpreted as draws from a multinomial distribution with n degrees, i.e., the rows which only contain integers and which sum to n. (★★★)

Python:

# Author: Evgeni Burovski

X = np.asarray([[1.0, 0.0, 3.0, 8.0],
                [2.0, 0.0, 1.0, 1.0],
                [1.5, 2.5, 1.0, 0.0]])
n = 4
M = np.logical_and.reduce(np.mod(X, 1) == 0, axis=-1)
M &= (X.sum(axis=-1) == n)
print(X[M])

Ruby:

100. Compute bootstrapped 95% confidence intervals for the mean of a 1D array X (i.e., resample the elements of an array with replacement N times, compute the mean of each sample, and then compute percentiles over the means). (★★★)

Python:

# Author: Jessica B. Hamrick

X = np.random.randn(100) # random 1D array
N = 1000 # number of bootstrap samples
idx = np.random.randint(0, X.size, (N, X.size))
means = X[idx].mean(1)
confint = np.percentile(means, [2.5, 97.5])
print(confint)

Ruby:

In [2]:
x = Numo::DFloat.new(100).rand
n = 1000 # number of bootstrap samples
idx = Numo::Int32.new(n, x.size).rand(x.size)
means = x[idx].mean(1)
confint = means[means.sort_index[means.size/100.0*Numo::DFloat[2.5, 97.5]]]
p confint
# todo: percentile, rand_norm
Numo::DFloat(view)#shape=[2]
[0.345385, 0.449567]
Out[2]:
Numo::DFloat(view)#shape=[2]
[0.345385, 0.449567]
In [ ]: