linalg: Cholesky factorization

[perazz]

Compute the Cholesky factorization of a real or complex matrix: $A = L \cdot L^T $, or $A = U^T \cdot U$, where $A$ is symmetric or complex Hermitian, and $L$, $U$ are lower- or upper-triangular, respectively.
Based on LAPACK Cholesky factorization (*POTRF) routines.

• base implementation
• tests
• exclude unsupported xdp
• documentation
• submodule
• examples
• all pure subroutine interfaces

Prior art

• Numpy: L = cholesky(a, /, *, upper=False)
• Scipy: L = cholesky(a, lower=False, overwrite_a=False, check_finite=True)

Proposed implementation

• call cholesky(A, lower [, other_zeroed] [, err]) : inplace pure subroutine interface

• call cholesky(A, chol, lower, [, other_zeroed] [, err]): non-inplace pure subroutine interface

• L = chol(A, lower [, other_zeroed]): pure function interface

• Only $L$ or $U$ is returned. The unused triangular region is zeroed out by default. However, if the user wants to save time, they can set the other_zeroed=.false. argument. In this case, the unused region will not be accessed at all, and will in general contain garbage. This option is to be used with caution part of the expert interface.

cc: @fortran-lang/stdlib @jalvesz @jvdp1

[jvdp1]

Overall LGTM. Thank you.