The following seems to work, for switching at run-time in Julia 1.7.
No need to restart.
julia> using LinearAlgebra
julia> BLAS.get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries:
└ [ILP64] libopenblas64_.so
julia> using MKL
julia> BLAS.get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries:
└ [ILP64] libmkl_rt.so
julia> LinearAlgebra.__init__()
julia> BLAS.get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries:
└ [ILP64] libopenblas64_.so
julia> MKL.__init__()
4770
julia> BLAS.get_config()
LinearAlgebra.BLAS.LBTConfig
Libraries:
└ [ILP64] libmkl_rt.so
Credits to @giordano (though he also warned this might not be proper way to switch).