Functions
void	check_naupd (const int_t aInfo)
	decode the dnaupd / pdnaupd flag, info( gInfoNaupd ).
void	check_neupd (const int_t aInfo)
	decode the dneupd flag, info( gInfoNeupd ).
void	check_saupd (const int_t aInfo)
	decode the dsaupd / pdsaupd flag, info( gInfoNaupd ).
void	check_seupd (const int_t aInfo)
	decode the dseupd / pdseupd flag, info( gInfoNeupd ).
void	arpack_standard_eigen (const int_t n, const int_t nnz, const real values, const int_t indices, const int_t pointers, const int_t job, const int_t nev, const int_t ncvmin, const real tol, const int_t maxit, const real sigma, real lambdareal, real lambdaimag, int_t info)
	serial reverse communication driver around dnaupd / dneupd.
void	arpack_symmetric_eigen (const int_t n, const int_t nnz, const real values, const int_t indices, const int_t pointers, const int_t job, const int_t nev, const int_t ncvmin, const real tol, const int_t maxit, const real sigma, real lambdareal, real lambdaimag, int_t info)
	symmetric counterpart of arpack_standard_eigen: dsaupd / dseupd instead of dnaupd / dneupd.
void	arpack_si_step (int_t ido, const int_t n, const int_t nev, const int_t ncv, real tol, real resid, real vectors, const int_t ldv, int_t iparam, int_t ipntr, real workd, real workl, const int_t lworkl, int_t info)
	ONE step of a shift-invert ( mode 3 ) reverse-communication loop.
void	arpack_si_extract (const real sigma, const int_t n, const int_t nev, const int_t ncv, real tol, real resid, real vectors, const int_t ldv, int_t iparam, int_t ipntr, real workd, real workl, const int_t lworkl, real lambdareal, int_t *info)
	extract the eigenvalues after arpack_si_step returned ido = 99.

Variables
constexpr index_t	gNumInfoEntries = 7
constexpr index_t	gInfoNaupd = 0
	index of the dnaupd flag within that array
constexpr index_t	gInfoNeupd = 1
	index of the dneupd flag within that array
constexpr index_t	gInfoNumConverged = 2
	index of the number of converged Ritz values
constexpr index_t	gInfoNumIterations = 3
	index of the number of restart iterations taken
constexpr index_t	gInfoNumOperations = 4
	index of the number of OP*x operations
constexpr index_t	gInfoNumReorthogonalizations = 5
	index of the number of re-orthogonalizations
constexpr index_t	gInfoSubspaceSize = 6
	index of the Krylov subspace size actually used

Function Documentation

◆ arpack_si_extract()

void belfem::arpack::arpack_si_extract	(	const real *	sigma,
		const int_t *	n,
		const int_t *	nev,
		const int_t *	ncv,
		real *	tol,
		real *	resid,
		real *	vectors,
		const int_t *	ldv,
		int_t *	iparam,
		int_t *	ipntr,
		real *	workd,
		real *	workl,
		const int_t *	lworkl,
		real *	lambdareal,
		int_t *	info )

extract the eigenvalues after arpack_si_step returned ido = 99.

The values come back ALREADY transformed to eigenvalues of A – dseupd applies lambda = 1/theta + sigma itself. Do NOT take a reciprocal afterwards; that would invert them a second time.

lambdareal must hold nev entries. Eigenvalues only: no Ritz vectors are computed

◆ arpack_si_step()

void belfem::arpack::arpack_si_step	(	int_t *	ido,
		const int_t *	n,
		const int_t *	nev,
		const int_t *	ncv,
		real *	tol,
		real *	resid,
		real *	vectors,
		const int_t *	ldv,
		int_t *	iparam,
		int_t *	ipntr,
		real *	workd,
		real *	workl,
		const int_t *	lworkl,
		int_t *	info )

ONE step of a shift-invert ( mode 3 ) reverse-communication loop.

The loop itself lives in C++, because OP = A^-1 needs the sparse solver – see run_shift_invert().

Only numeric arguments cross this boundary: BMAT = 'I' and WHICH = 'LM' stay Fortran-side, so no character descriptor is passed. Every array belongs to the caller and MUST NOT be touched between the last step call and the extract call.

Service the returned ido as: -1 : y = A^-1 * x, x at workd[ ipntr[0] - 1 ] 1 : y = A^-1 * x, x at workd[ ipntr[2] - 1 ] <– ipntr(3)! 2 : y = x ( legal, not expected here ) 99 : done result always to workd[ ipntr[1] - 1 ]. The ipntr values are ONE-based Fortran indices

◆ arpack_standard_eigen()

void belfem::arpack::arpack_standard_eigen	(	const int_t *	n,
		const int_t *	nnz,
		const real *	values,
		const int_t *	indices,
		const int_t *	pointers,
		const int_t *	job,
		const int_t *	nev,
		const int_t *	ncvmin,
		const real *	tol,
		const int_t *	maxit,
		const real *	sigma,
		real *	lambdareal,
		real *	lambdaimag,
		int_t *	info )

serial reverse communication driver around dnaupd / dneupd.

The whole matrix lives on the calling rank.

info must have gNumInfoEntries entries and is filled with 0 : dnaupd flag, or a driver code >= 100 ( see check_naupd ) 1 : dneupd flag 2 : NCONV, number of converged Ritz values 3 : MXITER, restart iterations taken 4 : NUMOP, number of OP*x operations 5 : NUMREO, number of re-orthogonalizations 6 : NCV, Krylov subspace size actually used

lambdareal and lambdaimag must have nev + 1 entries. Eigenvalues only – the driver does not compute Ritz vectors.

◆ arpack_symmetric_eigen()

void belfem::arpack::arpack_symmetric_eigen	(	const int_t *	n,
		const int_t *	nnz,
		const real *	values,
		const int_t *	indices,
		const int_t *	pointers,
		const int_t *	job,
		const int_t *	nev,
		const int_t *	ncvmin,
		const real *	tol,
		const int_t *	maxit,
		const real *	sigma,
		real *	lambdareal,
		real *	lambdaimag,
		int_t *	info )

symmetric counterpart of arpack_standard_eigen: dsaupd / dseupd instead of dnaupd / dneupd.

Same argument list, same info layout, same fold argument – and the SAME BUFFER SIZES, so a caller can switch between the two on the strength of the matrix alone.

lambdaimag comes back as exact zeros: the spectrum of a symmetric matrix is real.

The flags in info are decoded by check_saupd / check_seupd, NOT by the nonsymmetric pair – the error tables differ.

◆ check_naupd()

void belfem::arpack::check_naupd ( const int_t aInfo )

decode the dnaupd / pdnaupd flag, info( gInfoNaupd ).

throws on a negative flag except -9999 ( no Arnoldi factorization could be built ), which is reported like the non-converged exits and left to the converged count; warns on a non-converged exit.

Flags >= 100 are raised by the BELFEM drivers rather than by ARPACK, and mean nothing was computed: 100 unexpected reverse communication request 101 the local row blocks do not sum to the global row count, or the global row count differs between ranks 102 at least one rank owns no rows 103 the local nonzero count contradicts the row pointers 104 the job flag is neither 0 nor 1 105 an MPI call failed while the row map was built 101-105 can only come from the distributed driver.

◆ check_neupd()

void belfem::arpack::check_neupd ( const int_t aInfo )

decode the dneupd flag, info( gInfoNeupd ).

dnaupd and dneupd do NOT share an error table, so they must not share a decoder either

◆ check_saupd()

void belfem::arpack::check_saupd ( const int_t aInfo )

decode the dsaupd / pdsaupd flag, info( gInfoNaupd ).

dsaupd does NOT share dnaupd's table, which is why this exists: -5 admits 'LA', 'SA' and 'BE' that the nonsymmetric routine rejects, -13 means something different. info = 3 ( no shifts applied ) is documented by both and decoded as a warning here as well. Decoding a symmetric run with check_naupd would misreport.

The driver codes >= 100 have the same meaning as in check_naupd.

◆ check_seupd()

void belfem::arpack::check_seupd ( const int_t aInfo )

decode the dseupd / pdseupd flag, info( gInfoNeupd ).

Separate from check_neupd for the same reason check_saupd is separate from check_naupd

Variable Documentation

◆ gInfoNaupd

index_t belfem::arpack::gInfoNaupd = 0

constexpr

index of the dnaupd flag within that array

◆ gInfoNeupd

index_t belfem::arpack::gInfoNeupd = 1

constexpr

index of the dneupd flag within that array

◆ gInfoNumConverged

index_t belfem::arpack::gInfoNumConverged = 2

constexpr

index of the number of converged Ritz values

◆ gInfoNumIterations

index_t belfem::arpack::gInfoNumIterations = 3

constexpr

index of the number of restart iterations taken

◆ gInfoNumOperations

index_t belfem::arpack::gInfoNumOperations = 4

constexpr

index of the number of OP*x operations

◆ gInfoNumReorthogonalizations

index_t belfem::arpack::gInfoNumReorthogonalizations = 5

constexpr

index of the number of re-orthogonalizations

◆ gInfoSubspaceSize

index_t belfem::arpack::gInfoSubspaceSize = 6

constexpr

index of the Krylov subspace size actually used

◆ gNumInfoEntries

index_t belfem::arpack::gNumInfoEntries = 7

constexpr

number of entries the info array of the eigen drivers expects. arpacktools.f90 and parpacktools.f90 share this layout on purpose, so check_naupd() / check_neupd() decode both

Functions

Variables

Function Documentation

◆ arpack_si_extract()

◆ arpack_si_step()

◆ arpack_standard_eigen()

◆ arpack_symmetric_eigen()

◆ check_naupd()

◆ check_neupd()

◆ check_saupd()

◆ check_seupd()

Variable Documentation

◆ gInfoNaupd

◆ gInfoNeupd

◆ gInfoNumConverged

◆ gInfoNumIterations

◆ gInfoNumOperations

◆ gInfoNumReorthogonalizations

◆ gInfoSubspaceSize

◆ gNumInfoEntries