Skip to content

Instantly share code, notes, and snippets.

@shmalex

shmalex/sum_of_matrix.py

Last active August 15, 2023 13:29
Show Gist options

  • Select an option

    Learn more about clone URLs
  • Save shmalex/34acb9b1af72f41174c0c8192983c429 to your computer and use it in GitHub Desktop.

Select an option

Learn more about clone URLs
Save shmalex/34acb9b1af72f41174c0c8192983c429 to your computer and use it in GitHub Desktop.
Download ZIP

Revisions

  1. shmalex revised this gist Aug 15, 2023. No changes.
  2. shmalex revised this gist Aug 15, 2023. 1 changed file with 36 additions and 2 deletions.
    38 changes: 36 additions & 2 deletions sum_of_matrix.py
    View file
    Original file line number Diff line number Diff line change
    @@ -1,6 +1,6 @@
    import numpy as np
    def sum_of_bins_greater_then(n):
    print("N:",n)
    print("n =",n)
    left = []
    for i in range(2**n):
    left += [sum(int(x) for x in bin(i)[2:])]
    @@ -15,10 +15,14 @@ def sum_of_bins_greater_then(n):
    m[li,ui]=int(l<u)
    # print(f"{0:1}", int(m[li,ui]), end=' ')
    twopowertwoN = 2**(2*n)
    print('')
    print('2^(2*n)=', twopowertwoN)
    print('Matrix sum', int(np.sum(m)))
    print("Equals?",twopowertwoN==np.sum(m))
    print('')

    # Main Run ~5 minutes
    for i in range(15):
    sum_of_bins_greater_then(i)

    """
    OUTPUT
    @@ -81,6 +85,36 @@ def sum_of_bins_greater_then(n):
    2^(2*n)= 262144
    Matrix sum 262144
    Equals? True
    n = 10
    Matrix shape 1024 x 2048
    2^(2*n)= 1048576
    Matrix sum 1048576
    Equals? True
    n = 11
    Matrix shape 2048 x 4096
    2^(2*n)= 4194304
    Matrix sum 4194304
    Equals? True
    n = 12
    Matrix shape 4096 x 8192
    2^(2*n)= 16777216
    Matrix sum 16777216
    Equals? True
    n = 13
    Matrix shape 8192 x 16384
    2^(2*n)= 67108864
    Matrix sum 67108864
    Equals? True
    n = 14
    Matrix shape 16384 x 32768
    2^(2*n)= 268435456
    Matrix sum 268435456
    Equals? True
    """


  3. shmalex created this gist Aug 15, 2023.
    86 changes: 86 additions & 0 deletions sum_of_matrix.py
    View file
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,86 @@
    import numpy as np
    def sum_of_bins_greater_then(n):
    print("N:",n)
    left = []
    for i in range(2**n):
    left += [sum(int(x) for x in bin(i)[2:])]
    up = []
    for i in range(2**(n+1)):
    up += [sum(int(x) for x in bin(i)[2:])]
    print("Matrix shape", len(left),'x',len(up))
    m = np.zeros((2**n, 2**(n+1)))-1
    for li, l in enumerate(left):
    # print('')
    for ui, u in enumerate(up):
    m[li,ui]=int(l<u)
    # print(f"{0:1}", int(m[li,ui]), end=' ')
    twopowertwoN = 2**(2*n)
    print('')
    print('2^(2*n)=', twopowertwoN)
    print('Matrix sum', int(np.sum(m)))
    print("Equals?",twopowertwoN==np.sum(m))

    """
    OUTPUT
    n = 0
    Matrix shape 1 x 2
    2^(2*n)= 1
    Matrix sum 1
    Equals? True
    n = 1
    Matrix shape 2 x 4
    2^(2*n)= 4
    Matrix sum 4
    Equals? True
    n = 2
    Matrix shape 4 x 8
    2^(2*n)= 16
    Matrix sum 16
    Equals? True
    n = 3
    Matrix shape 8 x 16
    2^(2*n)= 64
    Matrix sum 64
    Equals? True
    n = 4
    Matrix shape 16 x 32
    2^(2*n)= 256
    Matrix sum 256
    Equals? True
    n = 5
    Matrix shape 32 x 64
    2^(2*n)= 1024
    Matrix sum 1024
    Equals? True
    n = 6
    Matrix shape 64 x 128
    2^(2*n)= 4096
    Matrix sum 4096
    Equals? True
    n = 7
    Matrix shape 128 x 256
    2^(2*n)= 16384
    Matrix sum 16384
    Equals? True
    n = 8
    Matrix shape 256 x 512
    2^(2*n)= 65536
    Matrix sum 65536
    Equals? True
    n = 9
    Matrix shape 512 x 1024
    2^(2*n)= 262144
    Matrix sum 262144
    Equals? True
    """