Question

I have a Fortran subroutine which uses BLAS' subroutines dgemm, dgemv and ddot, which calculate matrix * matrix, matrix * vector and vector * vector. I have m * m matrices and m * 1 vectors. In some cases m=1. It seems that those subroutines doesn't work well in those cases. They doesn't give errors, but there seems to be some numerical unstability in results. So I have to write something like:

if(m>1) then 
  vtuni(i,t) = yt(i,t) - ct(i,t) - ddot(m, zt(i,1:m,(t-1)*tvar(3)+1), 1, arec, 1)
else 
   vtuni(i,t) = yt(i,t) - ct(i,t) - zt(i,1,(t-1)*tvar(3)+1)*arec(1)

So my actual question is, am I right that those BLAS' subroutines doesn't work properly when m=1 or is there just something wrong in my code? Can the compiler affect this? I'm using gfortran.

Was it helpful?

Solution

BLAS routines are supposed to behave correctly with objects of size 1. I don't think it can depend on compiler, but it could possible depend on the implementation of BLAS you're relying on (though I'd consider it a bug of the implementation). The reference (read: not target-optimised) implementation of BLAS, which can be found on Netlib, handles that case fine.

I've done some testing on both arrays of size 1, and size-1 slices of larger array (as in your own code), and they both work fine:

 $ cat a.f90 
 implicit none
 double precision :: u(1), v(1)
 double precision, external :: ddot
 u(:) = 2
 v(:) = 3
 print *, ddot(1, u, 1, v, 1)
 end
 $ gfortran a.f90 -lblas && ./a.out
  6.0000000000000000     

 $ cat b.f90                       
 implicit none
 double precision, allocatable :: u(:,:,:), v(:)
 double precision, external :: ddot
 integer :: i, j
 allocate(u(3,1,3),v(1))
 u(:,:,:) = 2
 v(:) = 3
 i = 2
 j = 2
 print *, ddot(1, u(i,1:1,j), 1, v, 1)
 end
 $ gfortran b.f90 -lblas && ./a.out
  6.0000000000000000     

Things I'd consider to debug this problem further:

  • Check that your ddot definition is correct
  • Substitute the reference BLAS to your optimised one, to check if it changes anything (you can just compile and link in the ddot.f file I linked to earlier in my answer)
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