Why would the square of a real number ever be negative? I believe the "quirk" in python is just operator precedence, as the power gets evaluated before applying the unary "-"
On Sun, Oct 8, 2017 at 11:34 AM Joel Nothman <joel.noth...@gmail.com> wrote: > (normalize(X) * normalize(X)).sum(axis=1) works fine here. > > But I was unaware of these quirks in Python's implementation of pow: > > Numpy seems to be consistent in returning nan when a negative float is > raised to a non-integer (or equivalent float) power. By only calculating > integer powers of negative floats, the absolute value is returned in > suqareing. I assume this follows C conventions? > > Python, on the other hand, seems to do strange things: > > Numpy: > >>> np.array(-.6) ** 2.1 > nan > >>> np.array(-.6+0j) ** 2.1 > (0.32532987876940411+0.10570608538524294j) > > Python 3.6.2 returns the norm of the complex power: > >>> -.6 ** 2.1 > -0.3420720779420435 > >>> (-.6 + 0j) ** 2.1 > (0.3253298787694041+0.10570608538524294j) > >>> (((-.6 + 0j) ** 2.1).real ** 2 + ((-.6 + 0j) ** 2.1).imag ** 2) ** .5 > 0.3420720779420434 > > Very strangely, putting the LHS in parentheses performs complex power in > Python. > > >>> (-.6) ** 2.1 > (0.3253298787694041+0.10570608538524294j) > > At https://docs.python.org/3/reference/expressions.html: > > Raising a negative number to a fractional power results in a complex > <https://docs.python.org/3/library/functions.html#complex> number. (In > earlier versions it raised a ValueError > <https://docs.python.org/3/library/exceptions.html#ValueError>.) > > By "in earlier versions" it means Python 2. I don't know why this should > only be the case where the LHS is parenthesised. Seems like a CPython bug! > > On 8 October 2017 at 16:08, Christopher Pfeifer < > chrispfeifer8...@gmail.com> wrote: > >> I am attempting to validate the output of an L2 normalization function: >> >> *data_l2 = preprocessing.normalize(data, norm='l2') * # raw data >> is below at end of this email >> >> output: >> >> array([[ 0.57649683, 0.53806371, 0.61492995], >> [-0.53806371, -0.57649683, -0.61492995], >> [ 0.3359268 , 0.90089461, -0.2748492 ], >> [ 0.6676851 , -0.39566524, -0.63059148], >> [-0.70710678, 0. , 0.70710678], >> [-0.63116874, 0.45083482, 0.63116874]]) >> >> >> Each row being a set of three features of an observation >> >> >> I am under the belief that the sum of the 'squared' values of an instance >> (row) should be virtually equal to 1 (normalized). >> >> >> *Problem - 1:* >> >> the np.square() function is returning the absolute value of the sum of the >> three features, even when the sum of the squares is clearly negative. >> >> np.square(-0.53806371) returns 0.28951255601896408 however, >> (-0.53806371**2) returns -0.2895125560189641 >> >> The correct square of -0.53806371 is -0.2895125560189641 (a negative >> number), even my 10 year old calculator gets it right. >> >> I can find nothing in the numpy documentation that indicates np.square() >> always returns the absolute value, instead of the correctly signed value. >> >> *Question:* >> >> Is there a way to force np.square() to return the correctly signed square >> value not the absolute value? >> >> >> *Problem - 2:* >> >> For some of the observations (rows), the sum of the squared values (which >> should be virtually 1), are nowhere near 1. >> >> >> print 0.57649683**2 + 0.53806371**2 + 0.61492995**2 row 1 >> >> 0.9999999944260154 (this is virtually 1) >> >> >> print -0.63116874**2 + 0.45083482**2 + 0.63116874**2 row 6 >> >> 0.203252034924 (*this is nowhere near 1*) >> >> >> sum of the 'squared' values of an instance (row) should be virtually equal >> to 1. >> >> >> *Question:* >> >> Is the preprocessing.normalize(data, norm='l2') messing up, or is my raw >> data being fed into the normalization routine to unrealistic (I made it up >> of both positive and negative numbers. >> >> >> *Raw Data* >> >> array([[ 1.5, 1.4, 1.6], >> [-1.4, -1.5, -1.6], >> [ 2.2, 5.9, -1.8], >> [ 5.4, -3.2, -5.1], >> [-1.4, 0. , 1.4], >> [-1.4, 1. , 1.4]]) >> >> Thanks: Chris >> >> >> P.S.: Not a real world problem, just trying to understand the functionality >> of scikit-learn. Have only been working with the package for two weeks. >> >> >> _______________________________________________ >> scikit-learn mailing list >> scikit-learn@python.org >> https://mail.python.org/mailman/listinfo/scikit-learn >> >> > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn >
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