elpa_solve_tridiagonal(3)

🌈 elpa_solve_tridiagonal 🌈

okay so bestie, this page lives in the Library Functions Manual, and the main character is elpa_solve_tridiagonal. it's giving “tiny tridiagonal matrix, huge eigenvalue energy” 💅✨

✨ NAME ✨

elpa_solve_tridiagonal — computes the eigenvalue problem for real symmetric tridiagonal matrix. like, it computes all eigenvalues λ and all eigenvectors for a real symmetric tridiagonal matrix: T*Q = λ*Q. periodt. 👑

🎀 SYNOPSIS 🎀

💖 FORTRAN INTERFACE 💖

use elpa
class(elpa_t), pointer :: elpa_handle

call elpa_handle%solve_tridiagonal (d, e, q, error)

with the definitions of the input and output variables:

• class(elpa_t) :: elpa_handle — an instance of the ELPA object. she's the handle, she's the moment.
• datatype_real :: d — the diagonal elements of matrix T. d is a gloabal array of size elpa_handle%na, replicated on all MPI ranks. The dimensions of the matrix must be set BEFORE with elpa_setup(3). On exit the eigenvalues are stored in d. The datatype_real of the diagonal elements can either be "real(kind=c_double)" or "real(kind=c_float)".
• datatype_real :: e — the offdiagonal elements of matrix T. e is a gloabal array of size elpa_handle%na-1, replicated on all MPI ranks. The datatype_real of the diagonal elements can either be "real(kind=c_double)" or "real(kind=c_float)". (yes, the page says “diagonal elements” here too — not me fixing it, bestie 💀)
• datatype_real :: q — the storage space for the computed eigenvectors Q. The datatype_real of the matrix can be either "real(kind=c_double)" or "real(kind=c_float)".
• integer, optional :: error — the return error code of the function. Should be "ELPA_OK". The error code can be queried with the function elpa_strerr(3).

🦋 C/C++ INTERFACE 🦋

#include <elpa/elpa.h>
elpa_t elpa_handle;

void elpa_solve_tridiagonal(elpa_t elpa_handle, datatype_real *d,
datatype_real *e, datatype_real *q, int *error);

with the definitions of the input and output variables:

• elpa_t elpa_handle; — the handle to the ELPA object.
• datatype_real *d; — the diagonal elements of matrix T. d is a gloabal array of size na, replicated on all MPI ranks. The dimensions of the matrix must be set BEFORE with elpa_setup(3). On exit the eigenvalues are stored in d. The datatype_real can be one of "double" or "float".
• datatype_real *e; — the offdiagonal elements of matrix T. ev is a gloabal array of size na-1, replicated on all MPI ranks. The datatype_real can be one of "double" or "float". (the page says ev here, not e; iconic, keeping it fr fr)
• datatype_real *q; — the storage space for the computed eigenvectors Q. The datatype_real can be one of "double" or "float".
• int *error; — the error code of the function. Should be "ELPA_OK". The error codes can be queried with elpa_strerr(3).

🌸 DESCRIPTION 🌸

computes the eigenvalue problem of a real symmetric tridiagonal matrix. The functions elpa_init(3), elpa_allocate(3), elpa_set(3), and elpa_setup(3) must be called BEFORE elpa_solve_tridiagonal can be called. that's the whole vibe check, no cap 🫶

🦋 SEE ALSO 🦋

• elpa2_print_kernels(1)
• elpa_init(3)
• elpa_allocate(3)
• elpa_set(3)
• elpa_setup(3)
• elpa_strerr(3)
• elpa_eigenvalues(3)
• elpa_cholesky(3)
• elpa_invert_triangular(3)
• elpa_hermitian_multiply(3)
• elpa_uninit(3)
• elpa_deallocate(3)

sign-off from the footer: source/version ELPA, date Thu Nov 28 2024, page elpa_solve_tridiagonal(3) — bye bestie, go get those eigenvalues 💖✨💅