elpa_gener...igenvalues(3)

🌸 NAME 🌸

okay so bestie, welcome to elpa_gener...igenvalues(3) from the Library Functions Manual — this is the page for elpa_generalized_eigenvalues, and it computes all eigenvalues of a generalized eigenvalue problem, A*Q = λ*B*Q, for real symmetric or complex hermitian matrices A, B. iconic behavior, honestly. 💅✨

There are also variations of this routine that can accept not only host but also device pointers as input/output. Names of these routines explicitly contain the corresponding datatypes:

• elpa_generalized_eigenvalues_double
• elpa_generalized_eigenvalues_float
• elpa_generalized_eigenvalues_double_complex
• elpa_generalized_eigenvalues_float_complex

✨ SYNOPSIS ✨

🧚 FORTRAN INTERFACE 🧚

use elpa
class(elpa_t), pointer :: elpa_handle

call elpa_handle%generalized_eigenvalues (a, b, ev,
       is_already_decomposed, error)

With the definitions of the input and output variables:

• class(elpa_t) :: elpa_handle — an instance of the ELPA object. main character handle energy.
• datatype :: a — the local matrix a for which the eigenvalues should be computed. The dimensions of matrix a must be set BEFORE with the methods elpa_set(3) and elpa_setup(3). The datatype of the matrix can be one of "real(kind=c_double)", "real(kind=c_float)", "complex(kind=c_double)", or "complex(kind=c_float)".
• datatype :: b — the local matrix b defining the generalized eigenvalue problem. The dimensions and datatype of matrix b has to be the same as for matrix a.
• datatype_real :: ev — the array where the eigenvalues λ will be stored in ascending order. The datatype_real of the vector ev can be either "real(kind=c_double)" or "real(kind=c_float)", depending on the datatype of the matrix. Note that complex hermitian matrices also have real eigenvalues.
• logical :: is_already_decomposed — has to be set to .false. for the first call with a given b and .true. for each subsequent call with the same b, since b then already contains decomposition and thus the decomposing step is skipped. iykyk.
• 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_generalized_eigenvalues(elpa_t elpa_handle, datatype *a,
       datatype *b, datatype_real *ev, int is_already_decomposed, int *error);

With the definitions of the input and output variables:

• elpa_t elpa_handle; — the handle to the ELPA object.
• datatype *a; — the local matrix a for which the eigenvalues should be computed. The dimensions of the matrix must be set BEFORE with the methods elpa_set(3) and elpa_setup(3). The datatype can be one of "double", "float", "double complex"/"std::complex<double>", "float complex"/"std::complex<float>" for C/C++.
• datatype * b; — the matrix b defining the generalized eigenvalue problem. The dimensions and the datatype of matrix b must be the same as matrix a.
• datatype_real *ev; — the array where the eigenvalues λ will be stored in ascending order. The datatype_real can be either "double" or "float". Note that the eigenvalues of complex hermitian matrices are also real.
• int is_already_decomposed; — has to be set to 0 for the first call with a given b and 1 for each subsequent call with the same b, since b then already contains decomposition and thus the decomposing step is skipped.
• 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 generalized eigenvalues for a real symmetric or complex hermitian generalized eigenproblem. The functions elpa_init(3), elpa_allocate(3), elpa_set(3), and elpa_setup(3) must be called BEFORE elpa_generalized_eigenvalues can be called. No skipping the prequel, bestie.

Unlike in the case of ordinary eigenvalue problem, the generalized problem calls some external ScaLAPACK routines. The user is responsible for initialization of the BLACS context, which then has to be passed to elpa by elpa_set(3) BEFORE elpa_generalized_eigenvalues can be called. That part is on you, fr fr. periodt.

🎀 SEE ALSO 🎀

okay bestie, go give these their flowers too:

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

with all the 💖 from the ELPA girlies — source/version ELPA, date Thu Nov 28 2024, page elpa_gener...igenvalues(3) 🫶✨