Description

The implementations of the improved dot_product kernels work like a charm for real vectors but return erroneous results for complex ones. It seems like the complex versions are missing a complex-conjugate operation. See the following code snippet for reproducibility.

program main
   use stdlib_linalg_constants
   use stdlib_intrinsics
   implicit none

   integer(ilp), parameter :: n = 128
   complex(dp), dimension(n) :: x, y
   real(dp), dimension(n, 2) :: z

   call random_number(z); x%re = z(:, 1); x%im = z(:, 2)
   call random_number(z); y%re = z(:, 1); y%im = z(:, 2)

   print *, dot_product(x, y)
   print *, stdlib_dot_product(x, y)
   print *, stdlib_dot_product_kahan(x, y)
end program main

Expected Behaviour

Results between stdlib_dot_product, stdlib_dot_product_kahan and the Fortran intrinsic dot_product should be identical (up to a multiple of the machine precision).

Version of stdlib

latest

Platform and Architecture

Ubuntu 22.04

Additional Information

Ping @perazz, @jalvesz