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Description
triu and tril
tril - lower triangular part of an array
triu - upper triangular part of an array
Return a copy of the lower/upper triangular part of a rank-2 array. The elements below/above the k-th diagonal are replaced with zeroes (default k=0)
Useful to recover the lower or upper part of a matrix factorization.
Interface
interface tril
module function tril_rsp(A) result(L)
real(sp), intent(in) :: A(:,:)
real(sp) :: L(size(A,1),size(A,2))
end function
module function tril_k_rsp(A,k) result(L)
real(sp), intent(in) :: A(:,:)
integer, intent(in) :: k
real(sp) :: L(size(A,1),size(A,2))
end function
! .. repeat for all real and integer kinds ..
end interfaceAnalogous interface for triu. The interfaces would go to the file stdlib_experimental_linalg.f90. Implementations would go to the submodule stdlib_experimental_linalg_trilu.f90.
Point for discussion: two separate functions (without or with diagonal) as shown above or only a single interface using the present intrinsic?
Other languages
Julia
- tril: https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.tril
- triu: https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.triu
MATLAB
- tril: https://de.mathworks.com/help/matlab/ref/tril.html
- triu: https://de.mathworks.com/help/matlab/ref/triu.html
Python (NumPy)
- tril: https://numpy.org/doc/stable/reference/generated/numpy.tril.html
- triu: https://numpy.org/doc/stable/reference/generated/numpy.triu.html
C++
- (Eigen) Triangular view: https://eigen.tuxfamily.org/dox/group__QuickRefPage.html#title14 (since matrices are classes, this gives a triangular view of a dense matrix with specialized operations)
- (Armadillo) trimatu/trimatl: http://arma.sourceforge.net/docs.html#trimat
Other
- Would we like a subroutine version which works in-place? In Julia they use the
tril!(M)andtriu!(M)syntax for this purpose.