Encountered invalid value when I use pearsonr

Maybe I made a mistake. If so, I am sorry to ask this.

I want to calculate Pearson's correlation coefficent by using scipy's pearsonr function.

from scipy.stats.stats import pearsonr

X = [4, 4, 4, 4, 4, 4]
Y = [4, 5, 5, 4, 4, 4]

pearsonr(X, Y)

I get an error below

RuntimeWarning: invalid value encountered in double_scalars ###

The reason why I get an error is E[X] = 4 (Excepted Value of X is 4)

I look at the code of pearsonr function in scpy.stats.stats.py. Some part of the pearsonr function is as follows.

mx = x.mean() # which is 4
my = y.mean() # not necessary
xm, ym = x-mx, y-my # xm = [0 0 0 0 0 0]
r_num = n*(np.add.reduce(xm*ym)) #r_num = 0, because xm*ym 1x6 Zero Vector.
r_den = n*np.sqrt(ss(xm)*ss(ym)) #r_den = 0
r = (r_num / r_den) # Invalid value encountered in double_scalars

At the end, pearsonr returns (nan, 1.0)

Should pearsonr return (0, 1.0)?

I think if a vector has same value for every row/column, covariance should be zero. Thus Pearson's Correleation Coefficient should also be zero by the definition of PCC.

Pearson's correlation coefficient between two variables is defined as the covari开发者_StackOverflow社区ance of the two variables divided by the product of their standard deviations.

Is it bug or where do I make a mistake?

Pearson's correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviations.

So it's the covariance over

• the standard deviation of [4, 5, 5, 4, 4, 4] times
• the standard deviation of [4, 4, 4, 4, 4, 4].

The standard deviation of [4, 4, 4, 4, 4, 4] is zero.

So it's the covariance over

• the standard deviation of [4, 5, 5, 4, 4, 4] times
• zero.

So it's the covariance over

• zero.

Anything divided by zero is nan. The value of the covariance is irrelevant.