python - how to add two matrices with production rules -


i have 2 matrices, 1 2 x 3 dimensions , other 1 3 x 2. 

a = [[1, 0, 1],         [1, 0, 1]]  b = [[1, 0],         [1, 0],      [1, 0]]

i return 2x2 matrix c that's sum of element-wise logical or operation between , b.

so result be

c = [[3,2]      [3,2]]

are there packages out there these operations efficiently? large matrices hundreds of thousands of dimensions, looping through elements/vectors slow.

this relatively easy return 2x2 matrix d result of addition of element-wise logical and operation between , b.

d = np.dot(a,b) accomplish this. i'm wondering if there packages counterparts of np.dot logic or instead.

is object oriented approach acceptable ? 

#!/usr/bin/env python  __future__ import absolute_import __future__ import print_function import numpy   class pseudobinary(object):     def __init__(self,i):         self.i =      def __mul__(self,rhs):         return pseudobinary(self.i or rhs.i)      __rmul__ = __mul__     __imul__ = __mul__      def __add__(self,rhs):         return pseudobinary(self.i + rhs.i)      __radd__ = __add__     __iadd__ = __add__      def __str__(self):         return str(self.i)      __repr__ = __str__    = [[pseudobinary(1), pseudobinary(0), pseudobinary(1)],      [pseudobinary(1), pseudobinary(0), pseudobinary(1)]]  b = [[pseudobinary(1), pseudobinary(0)],      [pseudobinary(1), pseudobinary(0)],      [pseudobinary(1), pseudobinary(0)]]  c = numpy.dot(a,b) print(c)

prints 

[[3 2]  [3 2]]

i have spent time measuring, understanding performance of approach. long story short: numpy.dot custom objects several orders of magnitude slower regular matrix multiplication of integers.

i not 100% sure of root cause of difference. have asked specific question reasons of slowness.

the performance graph following: enter image description here

in plot red curve (base) base measurement of numpy.dot(..,..) call integer matrixes. blue curve (setor) approach suggested in @vortex's answer. green curve numpy.dot() performance using matrixes of custom objects. can see numpy.dot custom objects very slow. got these numbers in macbook air (13-inch, 2014), 1.7 ghz intel core i7, 8 gb 1600 mhz ddr3

the code executes performance measurement , prints plot this: (tested in python 2.7.10) 

#!/usr/bin/env python  # possible answer , performance analysis stackoverflow # question. https://stackoverflow.com/q/45682641/5771861  __future__ import absolute_import __future__ import print_function import numpy import time import matplotlib mpl import matplotlib.pyplot plt import matplotlib.dates mdates import matplotlib.ticker tick import random import datetime import timeit  class pseudobinary(object):     def __init__(self,i):         self.i =      def __mul__(self,rhs):         return pseudobinary(self.i or rhs.i)      __rmul__ = __mul__     __imul__ = __mul__      def __add__(self,rhs):     return pseudobinary(self.i + rhs.i)      __radd__ = __add__     __iadd__ = __add__      def __str__(self):         return "p"+str(self.i)      __repr__ = __str__  class testcase(object):     def __init__(self,n):         self.n = n          # use square matrixes         rows = self.n         cols = self.n      self.base = numpy.array([[random.getrandbits(1) x in range(cols)] \         y in range(rows)])     self.pseudo = numpy.array(         [[pseudobinary(v) v in row] row in self.base])      @staticmethod     def printmatrix(m):         row in m:             v in row:                 print(v,end=" ")             print("")      def print(self):         print("base")         testcase.printmatrix(self.base)         print("pseudo")         testcase.printmatrix(self.pseudo)  class testres(object):     def __init__(self):       self.res = []     def append(self,v):       self.res.append(v)     def mean(self):       return sum(self.res)/float(len(self.res))  def runwithtime(f,count,msg):     start = time.time()     in xrange(count):        f()     end = time.time()     elapsed = end-start     print(msg,"took",str(datetime.timedelta(seconds=end-start)),"seconds")     return elapsed  def measureandprint(execcount):    random.seed(1)     print("start initialize test data")    start = time.time()    sizes = [1, 4, 8, 16, 32]    testcases = [testcase(n) n in sizes]    end = time.time()    print("test data initialization complete in ",       str(datetime.timedelta(seconds=end-start)))     meascount = 4     baseresults = {}    pseudoresults = {}    setorresults = {}     tc in testcases:        print("test case for",tc.n)         def base():        rv = numpy.dot(tc.base,tc.base)        return rv         res = testres()        in xrange(meascount):       t = runwithtime(base,execcount,"base")       res.append(t)        baseresults[tc.n] = res         def pseudo():       rv = numpy.dot(tc.pseudo,tc.pseudo)       return rv         res = testres()        in xrange(meascount):       t = runwithtime(pseudo,execcount,"pseudo")       res.append(t)        pseudoresults[tc.n] = res         ones = numpy.ones(tc.n)        dotinput = ones-tc.base        def setor():       rv = ones*tc.n-numpy.dot(dotinput,dotinput)       return rv         res = testres()        in xrange(meascount):       t = runwithtime(setor,execcount,"setor")       res.append(t)        setorresults[tc.n] = res     return baseresults,pseudoresults,setorresults  def isclose(a, b, rel_tol=1e-09, abs_tol=0.0):     # https://stackoverflow.com/a/33024979/5771861     return abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)  def formatseconds(s):     # concise printer time duration in millisecond accuracy.     # example 3 d 12 h 4 m 5 s 234 mi     def maybestr(fmt,x):         # if x non-zero return formatted string x         if isclose(x,0):             return ""         else:             return fmt.format(x)      seconds, fraction = divmod(s, 1)     days, seconds = divmod(seconds, 86400)     hours, seconds = divmod(seconds, 3600)     minutes, seconds = divmod(seconds, 60)     milli = int(fraction * 1000)      rv = maybestr("{} d ",days) \        + maybestr("{} h ",hours) \        + maybestr("{} m ",minutes) \        + maybestr("{} s ",seconds) \        + maybestr("{} millis ",milli) \      if rv=="":         return "0"     else:         return rv  def plotresults(results,color,label):    # key , values in same order.    res = sorted(results.items())    xx = [x (x,y) in res]    yy = [y.mean() (x,y) in res]    plt.semilogy(xx,yy,color,label=label)    plt.scatter(xx,yy,c=color)     # add annotation each measurement data point.    x,y in res:       yvalue = y.mean()       plt.annotate(str(formatseconds(yvalue)),(x,yvalue))  multiplicationcount = 1000 baseresults,pseudoresults,setorresults = measureandprint(multiplicationcount)  plotresults(baseresults,"r","base") plotresults(pseudoresults,"g","pseudo") plotresults(setorresults,"b","setor") plt.legend(loc="upper left") plt.title("numpy.dot() performance measurements") plt.ylabel("mean seconds taken {} multiplications".format(multiplicationcount)) plt.xlabel("dimension of square matrix")  def yfmt(val,pos):    return formatseconds(val)  axes = plt.gca() yaxis = axes.get_yaxis() yaxis.set_major_formatter(tick.funcformatter(yfmt))  plt.show()

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