157 lines
3.9 KiB
Python
157 lines
3.9 KiB
Python
''' mbinary
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#########################################################################
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# File : vector_norm.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.xyz
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# Github: https://github.com/mbinary
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# Created Time: 2018-10-02 21:14
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# Description:
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#########################################################################
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'''
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from random import randint, random
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import numpy as np
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from operator import neg, and_
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from functools import reduce
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class obj():
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def __init__(self, data):
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self.data = np.array(data)
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def __add__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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return self.__class__(self.data + data)
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def __radd__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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return self.__class__(data + self.data)
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def __iadd__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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self.data += data
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def __mul__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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return self.__class__(self.data * data)
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def __imul__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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self.data *= data
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def __rmul__(self, x):
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data = x.data if self.__class__ == x.__class__ else x
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return self.__class__(data * self.data)
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def __neg__(self):
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return neg(self)
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def __abs__(self):
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return abs(self.data)
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'''
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@property
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def data(self):
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return self.data
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@data.setter
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def data(self,s):
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self.data = s
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'''
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def norm(self, n=0):
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'''the default is +oo norm'''
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absolute = abs(self.data)
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if n < 1:
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return max(absolute)
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return (sum(absolute**n))**(1/n)
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def hasNorm(self):
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'''check norm's three necessary conditions:
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1. not neg
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2. homogenious (qici)
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3. triangle inequlity
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there is much probably wrong
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'''
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bl = reduce(and_, [self.norm(i) >= 0 for i in range(3)])
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if bl:
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n = randint(2, 100)
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bl = reduce(and_, [n*(self.norm(i)) == (n*self).norm(i)
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for i in range(3)])
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if bl:
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another = self*randint(2, 10)-randint(1, 100)
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return reduce(and_, [(another+self).norm(i) <= another.norm(i)+self.norm(i) for i in range(3)])
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return False
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class vector(obj):
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def __init__(self, arr):
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''' arr: iterable'''
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self.data = np.array(arr)
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def innerProduct(self, x):
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return sum(self.data*x)
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def outerProduct(self, x):
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pass
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class matrix(obj):
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def __init__(self, s):
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'''s is a list of lists'''
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self.data = np.mat(s)
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self.T = None
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self. I = None
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'''
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@property
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def T(self):
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if self.T==None:self.T = self.data.T
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return self.T
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@T.setter
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def T(self,s):
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self.T = s
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@property
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def I(self):
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if self.I == None: self.I = self.data.I
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return self.I
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@I.setter
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def I(self,s):
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self.I = s
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'''
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def E(self, n=None):
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if n is None:
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n = self.data.shape[0]
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return np.eye(n)
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def norm(self, n=0):
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absolute = abs(self.data)
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if n < 1:
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# max of one row sum
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return max([sum(i) for i in absolute])
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if n == 1:
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return self.norm1()
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elif n == 2:
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return self.norm2()
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def norm1(self):
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''' max of sum of cols'''
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absolute = abs(self.data)
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return max(absolute.sum(axis=0))
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def norm2(self):
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''' max of sum of rows'''
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absolute = abs(self.data)
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return max(absolute.sum(axis=1))
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def norm_f(self):
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return sum((self.data**2).sum(axis=1))**0.5
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if __name__ == '__main__':
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v1 = vector([1, -2, 3, 4])
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v2 = vector([0, 2, 0, 5])
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m1 = matrix([v1, v2, v2, v1])
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print([v1.norm(i) for i in range(3)])
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