Module garoupa.algebra.npmath
Operations using numpy
Expand source code
# Copyright (c) 2021. Davi Pereira dos Santos
# This file is part of the garoupa project.
# Please respect the license - more about this in the section (*) below.
#
# garoupa is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# garoupa is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with garoupa. If not, see <http://www.gnu.org/licenses/>.
#
# (*) Removing authorship by any means, e.g. by distribution of derived
# works or verbatim, obfuscated, compiled or rewritten versions of any
# part of this work is illegal and is unethical regarding the effort and
# time spent here.
"""Operations using numpy"""
import numpy as np
def bytes2bm(bs):
m = np.eye(17)
m[0, 1] = float(bs[15] & 1)
m[0, 2] = float(bs[15] >> 1 & 1)
m[0, 3] = float(bs[15] >> 2 & 1)
m[0, 5] = float(bs[15] >> 3 & 1)
m[0, 6] = float(bs[15] >> 4 & 1)
m[0, 7] = float(bs[15] >> 5 & 1)
m[0, 8] = float(bs[15] >> 6 & 1)
m[0, 9] = float(bs[15] >> 7 & 1)
m[0, 10] = float(bs[14] & 1)
m[0, 11] = float(bs[14] >> 1 & 1)
m[0, 12] = float(bs[14] >> 2 & 1)
m[0, 13] = float(bs[14] >> 3 & 1)
m[0, 14] = float(bs[14] >> 4 & 1)
m[0, 15] = float(bs[14] >> 5 & 1)
m[0, 16] = float(bs[14] >> 6 & 1)
m[1, 2] = float(bs[14] >> 7 & 1)
m[1, 3] = float(bs[13] & 1)
m[1, 5] = float(bs[13] >> 1 & 1)
m[1, 6] = float(bs[13] >> 2 & 1)
m[1, 7] = float(bs[13] >> 3 & 1)
m[1, 8] = float(bs[13] >> 4 & 1)
m[1, 9] = float(bs[13] >> 5 & 1)
m[1, 10] = float(bs[13] >> 6 & 1)
m[1, 11] = float(bs[13] >> 7 & 1)
m[1, 12] = float(bs[12] & 1)
m[1, 13] = float(bs[12] >> 1 & 1)
m[1, 14] = float(bs[12] >> 2 & 1)
m[1, 15] = float(bs[12] >> 3 & 1)
m[1, 16] = float(bs[12] >> 4 & 1)
m[2, 3] = float(bs[12] >> 5 & 1)
m[2, 5] = float(bs[12] >> 6 & 1)
m[2, 6] = float(bs[12] >> 7 & 1)
m[2, 7] = float(bs[11] & 1)
m[2, 8] = float(bs[11] >> 1 & 1)
m[2, 9] = float(bs[11] >> 2 & 1)
m[2, 10] = float(bs[11] >> 3 & 1)
m[2, 11] = float(bs[11] >> 4 & 1)
m[2, 12] = float(bs[11] >> 5 & 1)
m[2, 13] = float(bs[11] >> 6 & 1)
m[2, 14] = float(bs[11] >> 7 & 1)
m[2, 15] = float(bs[10] & 1)
m[2, 16] = float(bs[10] >> 1 & 1)
m[3, 5] = float(bs[10] >> 2 & 1)
m[3, 6] = float(bs[10] >> 3 & 1)
m[3, 7] = float(bs[10] >> 4 & 1)
m[3, 8] = float(bs[10] >> 5 & 1)
m[3, 9] = float(bs[10] >> 6 & 1)
m[3, 10] = float(bs[10] >> 7 & 1)
m[3, 11] = float(bs[9] & 1)
m[3, 12] = float(bs[9] >> 1 & 1)
m[3, 13] = float(bs[9] >> 2 & 1)
m[3, 14] = float(bs[9] >> 3 & 1)
m[3, 15] = float(bs[9] >> 4 & 1)
m[3, 16] = float(bs[9] >> 5 & 1)
m[4, 5] = float(bs[9] >> 6 & 1)
m[4, 6] = float(bs[9] >> 7 & 1)
m[4, 7] = float(bs[8] & 1)
m[4, 8] = float(bs[8] >> 1 & 1)
m[4, 9] = float(bs[8] >> 2 & 1)
m[4, 10] = float(bs[8] >> 3 & 1)
m[4, 11] = float(bs[8] >> 4 & 1)
m[4, 12] = float(bs[8] >> 5 & 1)
m[4, 13] = float(bs[8] >> 6 & 1)
m[4, 14] = float(bs[8] >> 7 & 1)
m[4, 15] = float(bs[7] & 1)
m[4, 16] = float(bs[7] >> 1 & 1)
m[5, 6] = float(bs[7] >> 2 & 1)
m[5, 7] = float(bs[7] >> 3 & 1)
m[5, 8] = float(bs[7] >> 4 & 1)
m[5, 9] = float(bs[7] >> 5 & 1)
m[5, 10] = float(bs[7] >> 6 & 1)
m[5, 11] = float(bs[7] >> 7 & 1)
m[5, 12] = float(bs[6] & 1)
m[5, 13] = float(bs[6] >> 1 & 1)
m[5, 14] = float(bs[6] >> 2 & 1)
m[5, 15] = float(bs[6] >> 3 & 1)
m[5, 16] = float(bs[6] >> 4 & 1)
m[6, 7] = float(bs[6] >> 5 & 1)
m[6, 8] = float(bs[6] >> 6 & 1)
m[6, 9] = float(bs[6] >> 7 & 1)
m[6, 10] = float(bs[5] & 1)
m[6, 11] = float(bs[5] >> 1 & 1)
m[6, 12] = float(bs[5] >> 2 & 1)
m[6, 13] = float(bs[5] >> 3 & 1)
m[6, 14] = float(bs[5] >> 4 & 1)
m[6, 15] = float(bs[5] >> 5 & 1)
m[6, 16] = float(bs[5] >> 6 & 1)
m[7, 8] = float(bs[5] >> 7 & 1)
m[7, 9] = float(bs[4] & 1)
m[7, 10] = float(bs[4] >> 1 & 1)
m[7, 11] = float(bs[4] >> 2 & 1)
m[7, 12] = float(bs[4] >> 3 & 1)
m[7, 13] = float(bs[4] >> 4 & 1)
m[7, 14] = float(bs[4] >> 5 & 1)
m[7, 15] = float(bs[4] >> 6 & 1)
m[7, 16] = float(bs[4] >> 7 & 1)
m[8, 9] = float(bs[3] & 1)
m[8, 10] = float(bs[3] >> 1 & 1)
m[8, 11] = float(bs[3] >> 2 & 1)
m[8, 12] = float(bs[3] >> 3 & 1)
m[8, 13] = float(bs[3] >> 4 & 1)
m[8, 14] = float(bs[3] >> 5 & 1)
m[8, 15] = float(bs[3] >> 6 & 1)
m[8, 16] = float(bs[3] >> 7 & 1)
m[9, 10] = float(bs[2] & 1)
m[9, 11] = float(bs[2] >> 1 & 1)
m[9, 12] = float(bs[2] >> 2 & 1)
m[9, 13] = float(bs[2] >> 3 & 1)
m[9, 14] = float(bs[2] >> 4 & 1)
m[9, 15] = float(bs[2] >> 5 & 1)
m[9, 16] = float(bs[2] >> 6 & 1)
m[10, 11] = float(bs[2] >> 7 & 1)
m[10, 12] = float(bs[1] & 1)
m[10, 13] = float(bs[1] >> 1 & 1)
m[10, 14] = float(bs[1] >> 2 & 1)
m[10, 15] = float(bs[1] >> 3 & 1)
m[10, 16] = float(bs[1] >> 4 & 1)
m[11, 12] = float(bs[1] >> 5 & 1)
m[11, 13] = float(bs[1] >> 6 & 1)
m[11, 14] = float(bs[1] >> 7 & 1)
m[11, 15] = float(bs[0] & 1)
m[11, 16] = float(bs[0] >> 1 & 1)
m[13, 14] = float(bs[0] >> 2 & 1)
m[13, 15] = float(bs[0] >> 3 & 1)
m[13, 16] = float(bs[0] >> 4 & 1)
m[14, 15] = float(bs[0] >> 5 & 1)
m[14, 16] = float(bs[0] >> 6 & 1)
m[15, 16] = float(bs[0] >> 7 & 1)
return m
def int2bm(n):
return bytes2bm(n.to_bytes(16, byteorder="big"))
def bmm(a, b, mod):
"""unitriangular matrix (modulo) multiplication"""
return (a @ b) % mod
def bm2int(m):
n = 0
b = 0
for i in range(12):
if i < 3:
for j in range(i + 1, 4):
n += int(m[i, j]) << b
b += 1
for j in range(max(5, i + 1), 17):
n += int(m[i, j]) << b
b += 1
for i in range(13, 17):
for j in range(max(12, i + 1), 17):
n += int(m[i, j]) << b
b += 1
return n
def bminv(m):
return np.uint8(np.linalg.inv(m) % 2)
def int2bm6(n):
m = np.eye(6)
m[0, 1] = float(n >> 14 & 1)
m[0, 2] = float(n >> 13 & 1)
m[0, 3] = float(n >> 12 & 1)
m[0, 4] = float(n >> 11 & 1)
m[0, 5] = float(n >> 10 & 1)
m[1, 2] = float(n >> 9 & 1)
m[1, 3] = float(n >> 8 & 1)
m[1, 4] = float(n >> 7 & 1)
m[1, 5] = float(n >> 6 & 1)
m[2, 3] = float(n >> 5 & 1)
m[2, 4] = float(n >> 4 & 1)
m[2, 5] = float(n >> 3 & 1)
m[3, 4] = float(n >> 2 & 1)
m[3, 5] = float(n >> 1 & 1)
m[4, 5] = float(n & 1)
return m
def bm2int6(m):
n = (int(m[0, 1]) << 14) + (int(m[0, 2]) << 13) + (int(m[0, 3]) << 12) + (int(m[0, 4]) << 11) + (int(m[0, 5]) << 10)
n += (int(m[1, 2]) << 9) + (int(m[1, 3]) << 8) + (int(m[1, 4]) << 7) + (int(m[1, 5]) << 6)
n += (int(m[2, 3]) << 5) + (int(m[2, 4]) << 4) + (int(m[2, 5]) << 3)
n += (int(m[3, 4]) << 2) + (int(m[3, 5]) << 1)
n += int(m[4, 5])
return n
def int2bm8bit(n):
m = np.eye(5)
m[0, 2] = float(n >> 7 & 1)
m[0, 3] = float(n >> 6 & 1)
m[0, 4] = float(n >> 5 & 1)
m[1, 2] = float(n >> 4 & 1)
m[1, 3] = float(n >> 3 & 1)
m[1, 4] = float(n >> 2 & 1)
m[2, 3] = float(n >> 1 & 1)
m[2, 4] = float(n & 1)
return m
def bm2int8bit(m):
n = (int(m[0, 2]) << 7) + (int(m[0, 3]) << 6) + (int(m[0, 4]) << 5)
n += (int(m[1, 2]) << 4) + (int(m[1, 3]) << 3) + (int(m[1, 4]) << 2)
n += (int(m[2, 3]) << 1) + int(m[2, 4])
return n
def int2bml(n, l, bits):
m = np.eye(l)
b = bits - 1
for i in range(l - 1):
for j in range(i + 1, l):
m[i, j] = float(n >> b & 1)
b -= 1
return m
def bm2intl(m, bits):
n = 0
l = len(m)
b = bits - 1
for i in range(l - 1):
for j in range(i + 1, l):
n += int(m[i, j]) << b
b -= 1
return n
def int2ml(n, o, l):
"""
Usage:
>>> from numpy import uint64
>>> int2ml(4095, 4, 5)
array([[1, 3, 3, 3, 3],
[0, 1, 3, 3, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, 0, 1]], dtype=uint64)
"""
m = np.eye(l, dtype=np.uint64)
for i in range(l - 1):
for j in range(i + 1, l):
n, rem = divmod(n, o)
m[i, j] = rem
return m
def m2intl(m, o):
"""
Usage:
>>> from numpy import array, uint8
>>> m = array([[1, 3, 3, 3, 3],
... [0, 1, 3, 3, 0],
... [0, 0, 1, 0, 0],
... [0, 0, 0, 1, 0],
... [0, 0, 0, 0, 1]], dtype=np.uint64)
>>> m2intl(m, 4)
4095
"""
n = 0
l = len(m)
exp = 1
for i in range(l - 1):
for j in range(i + 1, l):
n += int(m[i, j]) * exp
exp *= o
return n
#########################################
#########################################
#########################################
def m4m(a, b, mod):
"""unitriangular matrix (modulo) multiplication"""
return (a @ b) % mod
def m42int(m, o):
"""
Usage:
>>> from numpy import array, uint8
>>> m = array([[1, 3, 3, 3, 3],
... [0, 1, 3, 3, 0],
... [0, 0, 1, 0, 0],
... [0, 0, 0, 1, 0],
... [0, 0, 0, 0, 1]], dtype=np.uint64)
>>> m42int(m, 4)
4095
"""
n = 0
l = len(m)
exp = 1
for i in range(l - 1):
for j in range(i + 1, l):
n += int(m[i, j]) * exp
exp *= o
return n
def int2m4(n, o, l=4):
"""
Usage:
>>> int2m4(4095, 4, 5)
array([[1, 3, 3, 3, 3],
[0, 1, 3, 3, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, 0, 1]], dtype=uint64)
"""
m = np.eye(l, dtype=np.uint64)
for i in range(l - 1):
for j in range(i + 1, l):
n, rem = divmod(n, o)
m[i, j] = rem
return m
def m4inv(m, o):
# if o < 257:
# return np.uint8(np.linalg.inv(m) % o)
return np.linalg.inv(m) % oFunctions
def bm2int(m)-
Expand source code
def bm2int(m): n = 0 b = 0 for i in range(12): if i < 3: for j in range(i + 1, 4): n += int(m[i, j]) << b b += 1 for j in range(max(5, i + 1), 17): n += int(m[i, j]) << b b += 1 for i in range(13, 17): for j in range(max(12, i + 1), 17): n += int(m[i, j]) << b b += 1 return n def bm2int6(m)-
Expand source code
def bm2int6(m): n = (int(m[0, 1]) << 14) + (int(m[0, 2]) << 13) + (int(m[0, 3]) << 12) + (int(m[0, 4]) << 11) + (int(m[0, 5]) << 10) n += (int(m[1, 2]) << 9) + (int(m[1, 3]) << 8) + (int(m[1, 4]) << 7) + (int(m[1, 5]) << 6) n += (int(m[2, 3]) << 5) + (int(m[2, 4]) << 4) + (int(m[2, 5]) << 3) n += (int(m[3, 4]) << 2) + (int(m[3, 5]) << 1) n += int(m[4, 5]) return n def bm2int8bit(m)-
Expand source code
def bm2int8bit(m): n = (int(m[0, 2]) << 7) + (int(m[0, 3]) << 6) + (int(m[0, 4]) << 5) n += (int(m[1, 2]) << 4) + (int(m[1, 3]) << 3) + (int(m[1, 4]) << 2) n += (int(m[2, 3]) << 1) + int(m[2, 4]) return n def bm2intl(m, bits)-
Expand source code
def bm2intl(m, bits): n = 0 l = len(m) b = bits - 1 for i in range(l - 1): for j in range(i + 1, l): n += int(m[i, j]) << b b -= 1 return n def bminv(m)-
Expand source code
def bminv(m): return np.uint8(np.linalg.inv(m) % 2) def bmm(a, b, mod)-
unitriangular matrix (modulo) multiplication
Expand source code
def bmm(a, b, mod): """unitriangular matrix (modulo) multiplication""" return (a @ b) % mod def bytes2bm(bs)-
Expand source code
def bytes2bm(bs): m = np.eye(17) m[0, 1] = float(bs[15] & 1) m[0, 2] = float(bs[15] >> 1 & 1) m[0, 3] = float(bs[15] >> 2 & 1) m[0, 5] = float(bs[15] >> 3 & 1) m[0, 6] = float(bs[15] >> 4 & 1) m[0, 7] = float(bs[15] >> 5 & 1) m[0, 8] = float(bs[15] >> 6 & 1) m[0, 9] = float(bs[15] >> 7 & 1) m[0, 10] = float(bs[14] & 1) m[0, 11] = float(bs[14] >> 1 & 1) m[0, 12] = float(bs[14] >> 2 & 1) m[0, 13] = float(bs[14] >> 3 & 1) m[0, 14] = float(bs[14] >> 4 & 1) m[0, 15] = float(bs[14] >> 5 & 1) m[0, 16] = float(bs[14] >> 6 & 1) m[1, 2] = float(bs[14] >> 7 & 1) m[1, 3] = float(bs[13] & 1) m[1, 5] = float(bs[13] >> 1 & 1) m[1, 6] = float(bs[13] >> 2 & 1) m[1, 7] = float(bs[13] >> 3 & 1) m[1, 8] = float(bs[13] >> 4 & 1) m[1, 9] = float(bs[13] >> 5 & 1) m[1, 10] = float(bs[13] >> 6 & 1) m[1, 11] = float(bs[13] >> 7 & 1) m[1, 12] = float(bs[12] & 1) m[1, 13] = float(bs[12] >> 1 & 1) m[1, 14] = float(bs[12] >> 2 & 1) m[1, 15] = float(bs[12] >> 3 & 1) m[1, 16] = float(bs[12] >> 4 & 1) m[2, 3] = float(bs[12] >> 5 & 1) m[2, 5] = float(bs[12] >> 6 & 1) m[2, 6] = float(bs[12] >> 7 & 1) m[2, 7] = float(bs[11] & 1) m[2, 8] = float(bs[11] >> 1 & 1) m[2, 9] = float(bs[11] >> 2 & 1) m[2, 10] = float(bs[11] >> 3 & 1) m[2, 11] = float(bs[11] >> 4 & 1) m[2, 12] = float(bs[11] >> 5 & 1) m[2, 13] = float(bs[11] >> 6 & 1) m[2, 14] = float(bs[11] >> 7 & 1) m[2, 15] = float(bs[10] & 1) m[2, 16] = float(bs[10] >> 1 & 1) m[3, 5] = float(bs[10] >> 2 & 1) m[3, 6] = float(bs[10] >> 3 & 1) m[3, 7] = float(bs[10] >> 4 & 1) m[3, 8] = float(bs[10] >> 5 & 1) m[3, 9] = float(bs[10] >> 6 & 1) m[3, 10] = float(bs[10] >> 7 & 1) m[3, 11] = float(bs[9] & 1) m[3, 12] = float(bs[9] >> 1 & 1) m[3, 13] = float(bs[9] >> 2 & 1) m[3, 14] = float(bs[9] >> 3 & 1) m[3, 15] = float(bs[9] >> 4 & 1) m[3, 16] = float(bs[9] >> 5 & 1) m[4, 5] = float(bs[9] >> 6 & 1) m[4, 6] = float(bs[9] >> 7 & 1) m[4, 7] = float(bs[8] & 1) m[4, 8] = float(bs[8] >> 1 & 1) m[4, 9] = float(bs[8] >> 2 & 1) m[4, 10] = float(bs[8] >> 3 & 1) m[4, 11] = float(bs[8] >> 4 & 1) m[4, 12] = float(bs[8] >> 5 & 1) m[4, 13] = float(bs[8] >> 6 & 1) m[4, 14] = float(bs[8] >> 7 & 1) m[4, 15] = float(bs[7] & 1) m[4, 16] = float(bs[7] >> 1 & 1) m[5, 6] = float(bs[7] >> 2 & 1) m[5, 7] = float(bs[7] >> 3 & 1) m[5, 8] = float(bs[7] >> 4 & 1) m[5, 9] = float(bs[7] >> 5 & 1) m[5, 10] = float(bs[7] >> 6 & 1) m[5, 11] = float(bs[7] >> 7 & 1) m[5, 12] = float(bs[6] & 1) m[5, 13] = float(bs[6] >> 1 & 1) m[5, 14] = float(bs[6] >> 2 & 1) m[5, 15] = float(bs[6] >> 3 & 1) m[5, 16] = float(bs[6] >> 4 & 1) m[6, 7] = float(bs[6] >> 5 & 1) m[6, 8] = float(bs[6] >> 6 & 1) m[6, 9] = float(bs[6] >> 7 & 1) m[6, 10] = float(bs[5] & 1) m[6, 11] = float(bs[5] >> 1 & 1) m[6, 12] = float(bs[5] >> 2 & 1) m[6, 13] = float(bs[5] >> 3 & 1) m[6, 14] = float(bs[5] >> 4 & 1) m[6, 15] = float(bs[5] >> 5 & 1) m[6, 16] = float(bs[5] >> 6 & 1) m[7, 8] = float(bs[5] >> 7 & 1) m[7, 9] = float(bs[4] & 1) m[7, 10] = float(bs[4] >> 1 & 1) m[7, 11] = float(bs[4] >> 2 & 1) m[7, 12] = float(bs[4] >> 3 & 1) m[7, 13] = float(bs[4] >> 4 & 1) m[7, 14] = float(bs[4] >> 5 & 1) m[7, 15] = float(bs[4] >> 6 & 1) m[7, 16] = float(bs[4] >> 7 & 1) m[8, 9] = float(bs[3] & 1) m[8, 10] = float(bs[3] >> 1 & 1) m[8, 11] = float(bs[3] >> 2 & 1) m[8, 12] = float(bs[3] >> 3 & 1) m[8, 13] = float(bs[3] >> 4 & 1) m[8, 14] = float(bs[3] >> 5 & 1) m[8, 15] = float(bs[3] >> 6 & 1) m[8, 16] = float(bs[3] >> 7 & 1) m[9, 10] = float(bs[2] & 1) m[9, 11] = float(bs[2] >> 1 & 1) m[9, 12] = float(bs[2] >> 2 & 1) m[9, 13] = float(bs[2] >> 3 & 1) m[9, 14] = float(bs[2] >> 4 & 1) m[9, 15] = float(bs[2] >> 5 & 1) m[9, 16] = float(bs[2] >> 6 & 1) m[10, 11] = float(bs[2] >> 7 & 1) m[10, 12] = float(bs[1] & 1) m[10, 13] = float(bs[1] >> 1 & 1) m[10, 14] = float(bs[1] >> 2 & 1) m[10, 15] = float(bs[1] >> 3 & 1) m[10, 16] = float(bs[1] >> 4 & 1) m[11, 12] = float(bs[1] >> 5 & 1) m[11, 13] = float(bs[1] >> 6 & 1) m[11, 14] = float(bs[1] >> 7 & 1) m[11, 15] = float(bs[0] & 1) m[11, 16] = float(bs[0] >> 1 & 1) m[13, 14] = float(bs[0] >> 2 & 1) m[13, 15] = float(bs[0] >> 3 & 1) m[13, 16] = float(bs[0] >> 4 & 1) m[14, 15] = float(bs[0] >> 5 & 1) m[14, 16] = float(bs[0] >> 6 & 1) m[15, 16] = float(bs[0] >> 7 & 1) return m def int2bm(n)-
Expand source code
def int2bm(n): return bytes2bm(n.to_bytes(16, byteorder="big")) def int2bm6(n)-
Expand source code
def int2bm6(n): m = np.eye(6) m[0, 1] = float(n >> 14 & 1) m[0, 2] = float(n >> 13 & 1) m[0, 3] = float(n >> 12 & 1) m[0, 4] = float(n >> 11 & 1) m[0, 5] = float(n >> 10 & 1) m[1, 2] = float(n >> 9 & 1) m[1, 3] = float(n >> 8 & 1) m[1, 4] = float(n >> 7 & 1) m[1, 5] = float(n >> 6 & 1) m[2, 3] = float(n >> 5 & 1) m[2, 4] = float(n >> 4 & 1) m[2, 5] = float(n >> 3 & 1) m[3, 4] = float(n >> 2 & 1) m[3, 5] = float(n >> 1 & 1) m[4, 5] = float(n & 1) return m def int2bm8bit(n)-
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def int2bm8bit(n): m = np.eye(5) m[0, 2] = float(n >> 7 & 1) m[0, 3] = float(n >> 6 & 1) m[0, 4] = float(n >> 5 & 1) m[1, 2] = float(n >> 4 & 1) m[1, 3] = float(n >> 3 & 1) m[1, 4] = float(n >> 2 & 1) m[2, 3] = float(n >> 1 & 1) m[2, 4] = float(n & 1) return m def int2bml(n, l, bits)-
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def int2bml(n, l, bits): m = np.eye(l) b = bits - 1 for i in range(l - 1): for j in range(i + 1, l): m[i, j] = float(n >> b & 1) b -= 1 return m def int2m4(n, o, l=4)-
Usage:
>>> int2m4(4095, 4, 5) array([[1, 3, 3, 3, 3], [0, 1, 3, 3, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]], dtype=uint64)Expand source code
def int2m4(n, o, l=4): """ Usage: >>> int2m4(4095, 4, 5) array([[1, 3, 3, 3, 3], [0, 1, 3, 3, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]], dtype=uint64) """ m = np.eye(l, dtype=np.uint64) for i in range(l - 1): for j in range(i + 1, l): n, rem = divmod(n, o) m[i, j] = rem return m def int2ml(n, o, l)-
Usage:
>>> from numpy import uint64 >>> int2ml(4095, 4, 5) array([[1, 3, 3, 3, 3], [0, 1, 3, 3, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]], dtype=uint64)Expand source code
def int2ml(n, o, l): """ Usage: >>> from numpy import uint64 >>> int2ml(4095, 4, 5) array([[1, 3, 3, 3, 3], [0, 1, 3, 3, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]], dtype=uint64) """ m = np.eye(l, dtype=np.uint64) for i in range(l - 1): for j in range(i + 1, l): n, rem = divmod(n, o) m[i, j] = rem return m def m2intl(m, o)-
Usage:
>>> from numpy import array, uint8 >>> m = array([[1, 3, 3, 3, 3], ... [0, 1, 3, 3, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 1, 0], ... [0, 0, 0, 0, 1]], dtype=np.uint64) >>> m2intl(m, 4) 4095Expand source code
def m2intl(m, o): """ Usage: >>> from numpy import array, uint8 >>> m = array([[1, 3, 3, 3, 3], ... [0, 1, 3, 3, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 1, 0], ... [0, 0, 0, 0, 1]], dtype=np.uint64) >>> m2intl(m, 4) 4095 """ n = 0 l = len(m) exp = 1 for i in range(l - 1): for j in range(i + 1, l): n += int(m[i, j]) * exp exp *= o return n def m42int(m, o)-
Usage:
>>> from numpy import array, uint8 >>> m = array([[1, 3, 3, 3, 3], ... [0, 1, 3, 3, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 1, 0], ... [0, 0, 0, 0, 1]], dtype=np.uint64) >>> m42int(m, 4) 4095Expand source code
def m42int(m, o): """ Usage: >>> from numpy import array, uint8 >>> m = array([[1, 3, 3, 3, 3], ... [0, 1, 3, 3, 0], ... [0, 0, 1, 0, 0], ... [0, 0, 0, 1, 0], ... [0, 0, 0, 0, 1]], dtype=np.uint64) >>> m42int(m, 4) 4095 """ n = 0 l = len(m) exp = 1 for i in range(l - 1): for j in range(i + 1, l): n += int(m[i, j]) * exp exp *= o return n def m4inv(m, o)-
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def m4inv(m, o): # if o < 257: # return np.uint8(np.linalg.inv(m) % o) return np.linalg.inv(m) % o def m4m(a, b, mod)-
unitriangular matrix (modulo) multiplication
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def m4m(a, b, mod): """unitriangular matrix (modulo) multiplication""" return (a @ b) % mod