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

#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/time.h>
#include "adpcg.h"

Macros
#define	adpcg_free(var) do {free((var)); (var) = NULL;} while (0)

Functions
static double	my_clock (void)
	Get time stamp for now. More...

static cgint	cg_prepare_preconditioner (adpcg *cg)
	Prepare pre-conditioner for the CG solver. More...

static cgint	cg_precondition (adpcg cg, void v)
	Apply pre-conditioning. More...

static cgint	cg_decision (adpcg *cg)
	Decide whether to update pre-conditioner. More...

cgint	cg_iteration (adpcg cg, void b, cgint warm)
	Implement conjugate gradinet. More...

void	cg_init (adpcg *cg)
	Initialize the conjugate gradient solver. More...

cgint	cg_alloc (adpcg *cg, cgint n, cgint vsize)
	Allocate internal memory for CG solver. More...

void	cg_register (adpcg cg, void A, void diag, void chol)
	Link pointers to LHS matrix, diagonal, and Cholesky pre-conditioner. More...

void	cg_free (adpcg *cg)
	Free the internal memory of CG solver. More...

void	cg_setparam (adpcg *cg, double tol, cgint reuse, cgint maxiter, cgint restart)
	Set parameters for the CG solver. More...

void	cg_getstats (adpcg cg, cgint status, cgint niter, double rnrm, double avgsvtime, double avgfctime, cgint nused, cgint nmaixter, cgint nfactors, cgint nrounds, cgint nsolverd, cgint nsolves)
	Extract CG statistics after some solve. More...

cgint	cg_start (adpcg *cg)
	Start a round of solves. More...

void	cg_finish (adpcg *cg)
	Finish a round of solve. More...

cgint	cg_solve (adpcg cg, void b, void *x0)
	Solve linear system using adaptive pre-conditioned conjugate gradient with restart. More...

Detailed Description

Header for basic types and routine list.

Solve a sequence of linear systems by either pre-conditioned conjugate gradient or direct solver, which is chosen heuristically based on problem conditioning. The routine also implements an adaptive pre-conditioning mechanism that updates the pre-conditioner automatically. Diagonal and Cholesky pre-conditioners are implemented

Author: Wenzhi Gao, Shanghai University of Finance and Economics

Date: Aug 29th, 2022

Function Documentation

◆ cg_alloc()

cgint cg_alloc	(	adpcg *	cg,
		cgint	n,
		cgint	vsize
	)

Allocate internal memory for CG solver.

Parameters

[in]	cg	Adaptive CG solver
[in]	n	Dimension of the linear system
[in]	vsize	Size of vector structure

Returns: CG_OK if memory is successfully allocated

Allocate the internal memory for the CG solver.

◆ cg_decision()

static cgint cg_decision ( adpcg * cg )

static

Decide whether to update pre-conditioner.

Parameters

[in] cg CG solver

1.If the system is classified as ill-conditioned or indefinite by some user-defined criterion 2.If the diagonal pre-conditioner is used 3.If latesttime > 1.5 average solution time 4.If ADP-CG is asked to perform direct solve 5.If average solution time > average factorization time 6.If the "nused" property of the current pre-conditioner exceeds the user-defined threshold

◆ cg_finish()

void cg_finish ( adpcg * cg )

Finish a round of solve.

Parameters

[in] cg CG solver

At the end of each round,

nused increases by 1
currenttime overwrites latesttime
nsolverd is reset

◆ cg_free()

void cg_free ( adpcg * cg )

Free the internal memory of CG solver.

Parameters

[in] cg CG solver

Free all the internal memory allocated by adaptive CG solver. The solver pointer itself has to be freed by user.

◆ cg_getstats()

void cg_getstats	(	adpcg *	cg,
		cgint *	status,
		cgint *	niter,
		double *	rnrm,
		double *	avgsvtime,
		double *	avgfctime,
		cgint *	nused,
		cgint *	nmaixter,
		cgint *	nfactors,
		cgint *	nrounds,
		cgint *	nsolverd,
		cgint *	nsolves
	)

Extract CG statistics after some solve.

Parameters

[in]	cg	CG solver
[out]	status	CG solution status
[out]	niter	Number of CG iterations
[out]	rnrm	Residual norm
[out]	avgsvtime	Current avarage solution time
[out]	avgfctime	Current average factorization time
[out]	nused	Current number of iterations the pre-conditioner is used
[out]	nmaixter	Number of iterations CG fails to solve the system
[out]	nfactors	Number of factorizations
[out]	nrounds	Number of rounds
[out]	nsolverd	Number of solves in the current round
[out]	nsolves	Number of solves

Collect different CG statistics. If some statistic is not needed, just let it be NULL.

◆ cg_init()

void cg_init ( adpcg * cg )

Initialize the conjugate gradient solver.

Parameters

[in] cg Adaptive CG solver Initlaize all the pointers to NULL and values to 0

◆ cg_iteration()

cgint cg_iteration	(	adpcg *	cg,
		void *	b,
		cgint	warm
	)

Implement conjugate gradinet.

Parameters

[in]	cg	CG solver
[in]	b	RHS vector
[in]	warm	If there is warm start?

Implement pre-conditioned CG with restart

◆ cg_precondition()

static cgint cg_precondition	(	adpcg *	cg,
		void *	v
	)

static

Apply pre-conditioning.

Parameters

[in]	cg	CG solver
[in]	v	Overwritten by P \ v

Returns: CG_OK if pre-conditioning is done successfully

◆ cg_prepare_preconditioner()

static cgint cg_prepare_preconditioner ( adpcg * cg )

static

Prepare pre-conditioner for the CG solver.

Parameters

[in] cg CG solver

Returns: CG_OK if the pre-conditioner is successfully collected

The method invokes internal preparation routine of pre-conditioner. The time computing pre-conditioner is counted into avgsvtime

◆ cg_register()

void cg_register	(	adpcg *	cg,
		void *	A,
		void *	diag,
		void *	chol
	)

Link pointers to LHS matrix, diagonal, and Cholesky pre-conditioner.

Parameters

[in]	cg	CG Solver
[in]	A	Left hand side matrix
[in]	diag	Diagonal matrix
[in]	chol	Cholesky factor

Register pointers for coefficient data, diagonal matrix and Cholesky factor

◆ cg_setparam()

void cg_setparam	(	adpcg *	cg,
		double	tol,
		cgint	reuse,
		cgint	maxiter,
		cgint	restart
	)

Set parameters for the CG solver.

Parameters

[in]	cg	CG solver
[in]	tol	Relative solution tolerance
[in]	reuse	The maximum reuse number
[in]	maxiter	Maximum of iteration
[in]	restart	Restart frequency of CG. -1 if automatically decided

Set CG parameters

◆ cg_solve()

cgint cg_solve	(	adpcg *	cg,
		void *	b,
		void *	x0
	)

Solve linear system using adaptive pre-conditioned conjugate gradient with restart.

Parameters

[in]	cg	CG Solver
[in]	b	RHS vector. Overwritten when solved
[in]	x0	Initial point

Solve the linear system by adaptive pre-conditioning and restart.

◆ cg_start()

cgint cg_start ( adpcg * cg )

Start a round of solves.

Parameters

[in] cg CG solver

Several rules decide whether to update the current pre-conditioner

◆ my_clock()

static double my_clock ( void )

static

Get time stamp for now.

Returns: Current time stamp

Macros

Functions

Detailed Description

Function Documentation

◆ cg_alloc()

◆ cg_decision()

◆ cg_finish()

◆ cg_free()

◆ cg_getstats()

◆ cg_init()

◆ cg_iteration()

◆ cg_precondition()

◆ cg_prepare_preconditioner()

◆ cg_register()

◆ cg_setparam()

◆ cg_solve()

◆ cg_start()

◆ my_clock()