Header for basic types and routine list. More...

#include <stddef.h>

Macros
#define	id "%d"

#define	sperr(x) printf(x);

#define	SP_EIGS_OK (0)

#define	SP_EIGS_ERR (1)

#define	MATRIX_TYPE_ZERO (0)

#define	MATRIX_TYPE_SPARSE (1)

#define	MATRIX_TYPE_GENERAL (2)

#define	MATRIX_TYPE_RANKONE (3)

#define	MATRIX_TYPE_DIAG (4)

#define	MATRIX_TYPE_TWOTWO (5)

#define	SPEIG_VER (1)

Typedefs
typedef int32_t	spint

Functions
spint	speigs_analyze (spint Ap, spint Ai, double Ax, spint dim, spint iwork, spint liwork, double work, spint lwork, spint type, spint sn, double tol, double gthresh)
	Perform the analysis phase of sparse eigen-value factorization. More...

spint	speigs_factorize (spint Ap, spint Ai, double Ax, spint dim, spint aiwork, double awork, spint type, spint sn, spint iwork, spint liwork, double work, spint lwork, double evals, double evecs, spint *rank, double tol)
	Perform the analysis phase of sparse eigen-value factorization. More...

Detailed Description

Header for basic types and routine list.

Implement the eigen-decomposition algorithm from DSDP5.8 by Steve Benson.

Given a real symmetric matrix A, the routine explores special structures within and computes the full eigen-decomposition of the matrix. In the backend the routine calls Lapack dsyev (or Netlib Eispack) to decompose the pre-processed system.

This routine is also employed in HDSDP solver for SDP.

Author: Wenzhi Gao, Shanghai University of Finance and Economics

Date: Aug, 24th, 2022

Function Documentation

◆ speigs_analyze()

spint speigs_analyze	(	spint *	Ap,
		spint *	Ai,
		double *	Ax,
		spint *	dim,
		spint *	iwork,
		spint *	liwork,
		double *	work,
		spint *	lwork,
		spint *	type,
		spint *	sn,
		double	tol,
		double	gthresh
	)

Perform the analysis phase of sparse eigen-value factorization.

Parameters

[in]	Ap	CSC format column pointer
[in]	Ai	CSC format row index
[in]	Ax	CSC format matrix nonzero entries
[in]	dim	Dimension of the matrix
[out]	iwork	Integer working array for the analysis phase
[in]	liwork	Length of "iwork" or the expected length of integer working array
[out]	work	Double working array for the analysis phase
[in]	lwork	Length of "lwork" or the expected length of double working array
[out]	type	Type of the matrix
[out]	sn	Size of the submatrix
[in]	tol	Tolerance to classify if a matrix is rank-one by $\|\|A - a a^T\|\|_F \leq tol$
[in]	gthresh	Threshold of (submatrix size / dim) classifying a matrix as general or sparse

Returns: retcode Status of the analysis phase

Perform the analysis phase of the sparse eigen-value factorization.

If all the necessary memories are allocated, on exit, "work" and "iwork" are filled by the intermediate information which can be used in the factorization phase; "type" is filled by one of the five types; "sn" is filled by size of the submatrix.

If "dim" is supplied and the rest of the working array is incomplete, "lwork" and "work" will be respectively filled by the expected length of the double and integer working arrays

◆ speigs_factorize()

spint speigs_factorize	(	spint *	Ap,
		spint *	Ai,
		double *	Ax,
		spint *	dim,
		spint *	aiwork,
		double *	awork,
		spint *	type,
		spint *	sn,
		spint *	iwork,
		spint *	liwork,
		double *	work,
		spint *	lwork,
		double *	evals,
		double *	evecs,
		spint *	rank,
		double	tol
	)