Numpy.dot bug? Inconsistent NaN behavior

Question

I noticed an inconsistent behavior in numpy.dot when nans and zeros are involved.

Can anybody make sense of it? Is this a bug? Is this specific to the dot function?

I'm using numpy v1.6.1, 64bit, running on linux (also tested on v1.6.2). I also tested on v1.8.0 on windows 32bit (so I can't tell if the differences are due to the version or OS or arch).

from numpy import *
0*nan, nan*0
=> (nan, nan)  # makes sense

#1
a = array([[0]])
b = array([[nan]])
dot(a, b)
=> array([[ nan]])  # OK

#2 -- adding a value to b. the first value in the result is
#     not expected to be affected.
a = array([[0]])
b = array([[nan, 1]])
dot(a, b)
=> array([[ 0.,  0.]])  # EXPECTED : array([[ nan,  0.]])
# (also happens in 1.6.2 and 1.8.0)
# Also, as @Bill noted, a*b works as expected, but not dot(a,b)

#3 -- changing a from 0 to 1, the first value in the result is
#     not expected to be affected.
a = array([[1]])
b = array([[nan, 1]])
dot(a, b)
=> array([[ nan,   1.]])  # OK

#4 -- changing shape of a, changes nan in result
a = array([[0],[0]])
b = array([[ nan, 1.]])
dot(a, b)
=> array([[ 0.,  0.], [ 0.,  0.]])  # EXPECTED : array([[ nan,  0.], [ nan,  0.]])
# (works as expected in 1.6.2 and 1.8.0)

Case #4 seems to be working correctly in v1.6.2 and v1.8.0, but not case #2...

---

EDIT: @seberg pointed out this is a blas issue, so here is the info about the blas installation I found by running from numpy.distutils.system_info import get_info; get_info('blas_opt'):

1.6.1 linux 64bit
/usr/lib/python2.7/dist-packages/numpy/distutils/system_info.py:1423: UserWarning: 
    Atlas (http://math-atlas.sourceforge.net/) libraries not found.
    Directories to search for the libraries can be specified in the
    numpy/distutils/site.cfg file (section [atlas]) or by setting
    the ATLAS environment variable.
  warnings.warn(AtlasNotFoundError.__doc__)
{'libraries': ['blas'], 'library_dirs': ['/usr/lib'], 'language': 'f77', 'define_macros': [('NO_ATLAS_INFO', 1)]}

1.8.0 windows 32bit (anaconda)
c:\Anaconda\Lib\site-packages\numpy\distutils\system_info.py:1534: UserWarning:
   Blas (http://www.netlib.org/blas/) sources not found.
   Directories to search for the sources can be specified in the
   numpy/distutils/site.cfg file (section [blas_src]) or by setting
   the BLAS_SRC environment variable.
 warnings.warn(BlasSrcNotFoundError.__doc__)
{}

(I personally don't know what to make of it)

Answer 1

I think, as seberg suggested, this is an issue with the BLAS library used. If you look at how numpy.dot is implemented here and here you'll find a call to cblas_dgemm() for the double-precision matrix-times-matrix case.

This C program, which reproduces some of your examples, gives the same output when using "plain" BLAS, and the right answer when using ATLAS.

#include <stdio.h>
#include <math.h>

#include "cblas.h"

void onebyone(double a11, double b11, double expectc11)
{
  enum CBLAS_ORDER order=CblasRowMajor;
  enum CBLAS_TRANSPOSE transA=CblasNoTrans;
  enum CBLAS_TRANSPOSE transB=CblasNoTrans;
  int M=1;
  int N=1;
  int K=1;
  double alpha=1.0;
  double A[1]={a11};
  int lda=1;
  double B[1]={b11};
  int ldb=1;
  double beta=0.0;
  double C[1];
  int ldc=1;

  cblas_dgemm(order, transA, transB,
              M, N, K,
              alpha,A,lda,
              B, ldb,
              beta, C, ldc);

  printf("dot([ %.18g],[%.18g]) -> [%.18g]; expected [%.18g]\n",a11,b11,C[0],expectc11);
}

void onebytwo(double a11, double b11, double b12,
              double expectc11, double expectc12)
{
  enum CBLAS_ORDER order=CblasRowMajor;
  enum CBLAS_TRANSPOSE transA=CblasNoTrans;
  enum CBLAS_TRANSPOSE transB=CblasNoTrans;
  int M=1;
  int N=2;
  int K=1;
  double alpha=1.0;
  double A[]={a11};
  int lda=1;
  double B[2]={b11,b12};
  int ldb=2;
  double beta=0.0;
  double C[2];
  int ldc=2;

  cblas_dgemm(order, transA, transB,
              M, N, K,
              alpha,A,lda,
              B, ldb,
              beta, C, ldc);

  printf("dot([ %.18g],[%.18g, %.18g]) -> [%.18g, %.18g]; expected [%.18g, %.18g]\n",
         a11,b11,b12,C[0],C[1],expectc11,expectc12);
}

int
main()
{
  onebyone(0, 0, 0);
  onebyone(2, 3, 6);
  onebyone(NAN, 0, NAN);
  onebyone(0, NAN, NAN);
  onebytwo(0, 0,0, 0,0);
  onebytwo(2, 3,5, 6,10);
  onebytwo(0, NAN,0, NAN,0);
  onebytwo(NAN, 0,0, NAN,NAN);
  return 0;
}

Output with BLAS:

dot([ 0],[0]) -> [0]; expected [0]
dot([ 2],[3]) -> [6]; expected [6]
dot([ nan],[0]) -> [nan]; expected [nan]
dot([ 0],[nan]) -> [0]; expected [nan]
dot([ 0],[0, 0]) -> [0, 0]; expected [0, 0]
dot([ 2],[3, 5]) -> [6, 10]; expected [6, 10]
dot([ 0],[nan, 0]) -> [0, 0]; expected [nan, 0]
dot([ nan],[0, 0]) -> [nan, nan]; expected [nan, nan]

Output with ATLAS:

dot([ 0],[0]) -> [0]; expected [0]
dot([ 2],[3]) -> [6]; expected [6]
dot([ nan],[0]) -> [nan]; expected [nan]
dot([ 0],[nan]) -> [nan]; expected [nan]
dot([ 0],[0, 0]) -> [0, 0]; expected [0, 0]
dot([ 2],[3, 5]) -> [6, 10]; expected [6, 10]
dot([ 0],[nan, 0]) -> [nan, 0]; expected [nan, 0]
dot([ nan],[0, 0]) -> [nan, nan]; expected [nan, nan]

BLAS seems to have expected behaviour when the first operand has a NaN, and the wrong when the first operand is zero and the second has a NaN.

Anyway, I don't think this bug is in the Numpy layer; it's in BLAS. It appears to be possible to workaround by using ATLAS instead.

Above generated on Ubuntu 14.04, using Ubuntu-provided gcc, BLAS, and ATLAS.