Class that calculates the solution to a nonlinear system. More...

#include <NonlinearSolver.h>

Collaboration diagram for NonlinearSolver:

Public Member Functions
	NonlinearSolver (ResidJacEval *func)
	Default constructor.

	NonlinearSolver (const NonlinearSolver &right)
	Copy Constructor for the ThermoPhase object.

	~NonlinearSolver ()
	Destructor.

NonlinearSolver &	operator= (const NonlinearSolver &right)
	Assignment operator.

void	createSolnWeights (const doublereal *const y)
	Create solution weights for convergence criteria.

doublereal	solnErrorNorm (const doublereal const delta_y, const char title=0, int printLargest=0, const doublereal dampFactor=1.0) const
	L2 norm of the delta of the solution vector.

doublereal	residErrorNorm (const doublereal const resid, const char title=0, const int printLargest=0, const doublereal *const y=0) const
	L2 norm of the residual of the equation system.

int	doResidualCalc (const doublereal time_curr, const int typeCalc, const doublereal const y_curr, const doublereal const ydot_curr, const ResidEval_Type_Enum evalType=Base_ResidEval) const
	Compute the current residual.

int	doNewtonSolve (const doublereal time_curr, const doublereal const y_curr, const doublereal const ydot_curr, doublereal *const delta_y, GeneralMatrix &jac)
	Compute the undamped Newton step.

int	doAffineNewtonSolve (const doublereal const y_curr, const doublereal const ydot_curr, doublereal *const delta_y, GeneralMatrix &jac)
	Compute the newton step, either by direct newton's or by solving a close problem that is represented by a Hessian (.

doublereal	trustRegionLength () const
	Calculate the length of the current trust region in terms of the solution error norm.

void	setDefaultDeltaBoundsMagnitudes ()
	Set default deulta bounds amounts.

void	adjustUpStepMinimums ()
	Adjust the step minimums.

void	setDeltaBoundsMagnitudes (const doublereal *const deltaBoundsMagnitudes)
	Set the delta Bounds magnitudes by hand.

doublereal	boundStep (const doublereal const y, const doublereal const step0)
	Bound the step.

void	setBoundsConstraints (const doublereal const y_low_bounds, const doublereal const y_high_bounds)
	Set bounds constraints for all variables in the problem.

std::vector< doublereal > &	lowBoundsConstraintVector ()
	Return an editable vector of the low bounds constraints.

std::vector< doublereal > &	highBoundsConstraintVector ()
	Return an editable vector of the high bounds constraints.

void	calc_ydot (const int order, const doublereal const y_curr, doublereal const ydot_curr) const
	Internal function to calculate the time derivative of the solution at the new step.

int	beuler_jac (GeneralMatrix &J, doublereal const f, doublereal time_curr, doublereal CJ, doublereal const y, doublereal *const ydot, int num_newt_its)
	Function called to evaluate the jacobian matrix and the current residual vector at the current time step.

doublereal	filterNewStep (const doublereal timeCurrent, const doublereal const ybase, doublereal const step0)
	Apply a filtering process to the step.

doublereal	filterNewSolution (const doublereal timeCurrent, doublereal const y_current, doublereal const ydot_current)
	Apply a filter to the solution.

doublereal	deltaBoundStep (const doublereal const y, const doublereal const step0)
	Return the factor by which the undamped Newton step 'step0' must be multiplied in order to keep the update within the bounds of an accurate jacobian.

int	dampStep (const doublereal time_curr, const doublereal const y_n_curr, const doublereal const ydot_n_curr, doublereal const step_1, doublereal const y_n_1, doublereal const ydot_n_1, doublereal step_2, doublereal &stepNorm_2, GeneralMatrix &jac, bool writetitle, int &num_backtracks)
	Find a damping coefficient through a look-ahead mechanism.

int	solve_nonlinear_problem (int SolnType, doublereal const y_comm, doublereal const ydot_comm, doublereal CJ, doublereal time_curr, GeneralMatrix &jac, int &num_newt_its, int &num_linear_solves, int &num_backtracks, int loglevelInput)
	Find the solution to F(X) = 0 by damped Newton iteration.

void	setColumnScaling (bool useColScaling, const double *const scaleFactors=0)
	Set the column scaling that are used for the inversion of the matrix.

void	setRowScaling (bool useRowScaling)
	Set the rowscaling that are used for the inversion of the matrix.

void	scaleMatrix (GeneralMatrix &jac, doublereal const y_comm, doublereal const ydot_comm, doublereal time_curr, int num_newt_its)
	Scale the matrix.

void	print_solnDelta_norm_contrib (const doublereal const step_1, const char const stepNorm_1, const doublereal const step_2, const char const stepNorm_2, const char const title, const doublereal const y_n_curr, const doublereal *const y_n_1, doublereal damp, size_t num_entries)
	Print solution norm contribution.

void	computeResidWts ()
	Compute the Residual Weights.

void	getResidWts (doublereal *const residWts) const
	Return the residual weights.

int	convergenceCheck (int dampCode, doublereal s1)
	Check to see if the nonlinear problem has converged.

void	setAtol (const doublereal *const atol)
	Set the absolute tolerances for the solution variables.

void	setRtol (const doublereal rtol)
	Set the relative tolerances for the solution variables.

void	setResidualTols (double residRtol, double *residATol, int residNormHandling=2)
	Set the relative and absolute tolerances for the Residual norm comparisons, if used.

void	setMaxNewtIts (const int maxNewtIts)
	Set the value of the maximum # of newton iterations.

void	calcSolnToResNormVector ()
	Calculate the scaling factor for translating residual norms into solution norms.

doublereal	doCauchyPointSolve (GeneralMatrix &jac)
	Calculate the steepest descent direction and the Cauchy Point where the quadratic formulation of the nonlinear problem expects a minimum along the descent direction.

void	descentComparison (doublereal time_curr, doublereal ydot0, doublereal ydot1, int &numTrials)
	This is a utility routine that can be used to print out the rates of the initial residual decline.

void	setupDoubleDogleg ()
	Setup the parameters for the double dog leg.

int	lambdaToLeg (const doublereal lambda, doublereal &alpha) const
	Change the global lambda coordinate into the (leg,alpha) coordinate for the double dogleg.

int	calcTrustIntersection (doublereal trustVal, doublereal &lambda, doublereal &alpha) const
	Given a trust distance, this routine calculates the intersection of the this distance with the double dogleg curve.

void	initializeTrustRegion ()
	Initialize the size of the trust vector.

void	setTrustRegionInitializationMethod (int method, doublereal factor)
	Set Trust region initialization strategy.

int	dampDogLeg (const doublereal time_curr, const doublereal y_n_curr, const doublereal ydot_n_curr, std::vector< doublereal > &step_1, doublereal const y_n_1, doublereal const ydot_n_1, doublereal &stepNorm_1, doublereal &stepNorm_2, GeneralMatrix &jac, int &num_backtracks)
	Damp using the dog leg approach.

int	decideStep (const doublereal time_curr, int leg, doublereal alpha, const doublereal const y_n_curr, const doublereal const ydot_n_curr, const std::vector< doublereal > &step_1, const doublereal const y_n_1, const doublereal const ydot_n_1, doublereal trustDeltaOld)
	Decide whether the current step is acceptable and adjust the trust region size.

doublereal	expectedResidLeg (int leg, doublereal alpha) const
	Calculated the expected residual along the double dogleg curve.

void	residualComparisonLeg (const doublereal time_curr, const doublereal *const ydot0, int &legBest, doublereal &alphaBest) const
	Here we print out the residual at various points along the double dogleg, comparing against the quadratic model in a table format.

void	setPrintLvl (int printLvl)
	Set the print level from the nonlinear solver.

void	setSolverScheme (int doDogLeg, int doAffineSolve)
	Parameter to turn on solution solver schemes.

Static Public Attributes
static bool	s_TurnOffTiming
	Turn off printing of time.

static bool	s_print_NumJac
	Turn on or off printing of the Jacobian.

static bool	s_print_DogLeg
	Turn on extra printing of dogleg information.

static bool	s_doBothSolvesAndCompare
	Turn on solving both the Newton and Hessian systems and comparing the results.

static bool	s_alwaysAssumeNewtonGood
	This toggle turns off the use of the Hessian when it is warranted by the condition number.

Protected Member Functions
void	readjustTrustVector ()
	Readjust the trust region vectors.

void	fillDogLegStep (int leg, doublereal alpha, std::vector< doublereal > &deltaX) const
	Fill a dogleg solution step vector.

doublereal	calcTrustDistance (std::vector< doublereal > const &deltaX) const
	Calculate the trust distance of a step in the solution variables.

Private Member Functions
void	calcColumnScales ()
	Set the column scales.

Private Attributes
ResidJacEval *	m_func
	Pointer to the residual and jacobian evaluator for the function.

int	solnType_
	Solution type.

size_t	neq_
	Local copy of the number of equations.

std::vector< doublereal >	m_ewt
	Soln error weights.

int	m_manualDeltaStepSet
	Boolean indicating whether a manual delta bounds has been input.

std::vector< doublereal >	m_deltaStepMinimum
	Soln Delta bounds magnitudes.

std::vector< doublereal >	m_deltaStepMaximum
	Value of the delta step magnitudes.

std::vector< doublereal >	m_y_n_curr
	Vector containing the current solution vector within the nonlinear solver.

std::vector< doublereal >	m_ydot_n_curr
	Vector containing the time derivative of the current solution vector within the nonlinear solver (where applicable)

std::vector< doublereal >	m_y_nm1
	Vector containing the solution at the previous time step.

std::vector< doublereal >	m_y_n_1
	Vector containing the solution at the previous time step.

std::vector< doublereal >	m_ydot_n_1
	Value of the solution time derivative at the new point that is to be considered.

std::vector< doublereal >	m_step_1
	Value of the step to be taken in the solution.

std::vector< doublereal >	m_colScales
	Vector of column scaling factors.

std::vector< doublereal >	m_rowScales
	Weights for normalizing the values of the residuals.

std::vector< doublereal >	m_rowWtScales
	Weights for normalizing the values of the residuals.

std::vector< doublereal >	m_resid
	Value of the residual for the nonlinear problem.

std::vector< doublereal >	m_wksp
	Workspace of length neq_.

std::vector< doublereal >	m_wksp_2
	Workspace of length neq_.

std::vector< doublereal >	m_residWts
	Vector of residual weights.

doublereal	m_normResid_0
	Norm of the residual at the start of each nonlinear iteration.

doublereal	m_normResid_Bound
	Norm of the residual after it has been bounded.

doublereal	m_normResid_1
	Norm of the residual at the end of the first leg of the current iteration.

doublereal	m_normResid_full
	Norm of the residual at the end of the first leg of the current iteration.

doublereal	m_normDeltaSoln_Newton
	Norm of the solution update created by the iteration in its raw, undamped form, using the solution norm.

doublereal	m_normDeltaSoln_CP
	Norm of the distance to the cauchy point using the solution norm.

doublereal	m_normResidTrial
	Norm of the residual for a trial calculation which may or may not be used.

doublereal	m_normResidPoints [15]
	Vector of the norm.

bool	m_resid_scaled
	Boolean indicating whether we should scale the residual.

std::vector< doublereal >	m_y_high_bounds
	Bounds vector for each species.

std::vector< doublereal >	m_y_low_bounds
	Lower bounds vector for each species.

doublereal	m_dampBound
	Damping factor imposed by hard bounds and by delta bounds.

doublereal	m_dampRes
	Additional damping factor due to bounds on the residual and solution norms.

doublereal	delta_t_n
	Delta t for the current step.

int	m_nfe
	Counter for the total number of function evaluations.

int	m_colScaling
	The type of column scaling used in the matrix inversion of the problem.

int	m_rowScaling
	int indicating whether row scaling is turned on (1) or not (0)

int	m_numTotalLinearSolves
	Total number of linear solves taken by the solver object.

int	m_numLocalLinearSolves
	Number of local linear solves done during the current iteration.

int	m_numTotalNewtIts
	Total number of newton iterations.

int	m_min_newt_its
	Minimum number of newton iterations to use.

int	maxNewtIts_
	Maximum number of newton iterations.

int	m_jacFormMethod
	Jacobian formation method.

int	m_nJacEval
	Number of Jacobian evaluations.

doublereal	time_n
	Current system time.

int	m_matrixConditioning
	Boolean indicating matrix conditioning.

int	m_order
	Order of the time step method = 1.

doublereal	rtol_
	value of the relative tolerance to use in solving the equation set

doublereal	atolBase_
	Base value of the absolute tolerance.

doublereal *	m_ydot_nm1
	Pointer containing the solution derivative at the previous time step.

std::vector< doublereal >	atolk_
	absolute tolerance in the solution unknown

std::vector< doublereal >	userResidAtol_
	absolute tolerance in the unscaled solution unknowns

doublereal	userResidRtol_
	absolute tolerance in the unscaled solution unknowns

int	checkUserResidualTols_
	Check the residual tolerances explictly against user input.

int	m_print_flag
	Determines the level of printing for each time step.

doublereal	m_ScaleSolnNormToResNorm
	Scale factor for turning residual norms into solution norms.

Cantera::GeneralMatrix *	jacCopyPtr_
	Copy of the jacobian that doesn't get overwritten when the inverse is determined.

Cantera::GeneralMatrix *	HessianPtr_
	Hessian.

std::vector< doublereal >	deltaX_CP_
	Steepest descent direction. This is also the distance to the Cauchy Point.

std::vector< doublereal >	deltaX_Newton_
	Newton Step - This is the newton step determined from the straight Jacobian.

doublereal	residNorm2Cauchy_
	Expected value of the residual norm at the Cauchy point if the quadratic model were valid.

int	dogLegID_
	Current leg.

doublereal	dogLegAlpha_
	Current Alpha param along the leg.

doublereal	RJd_norm_
	Residual dot Jd norm.

doublereal	lambdaStar_
	Value of lambdaStar_ which is used to calculate the Cauchy point.

std::vector< doublereal >	Jd_
	Jacobian times the steepest descent direction in the normalized coordinates.

std::vector< doublereal >	deltaX_trust_
	Vector of trust region values.

doublereal	norm_deltaX_trust_
	Current norm of the vector deltaX_trust_ in terms of the solution norm.

doublereal	trustDelta_
	Current value of trust radius.

int	trustRegionInitializationMethod_
	Method for handling the trust region initialization.

doublereal	trustRegionInitializationFactor_
	Factor used to set the initial trust region.

doublereal	Nuu_
	Relative distance down the Newton step that the second dogleg starts.

doublereal	dist_R0_
	Distance of the zeroeth leg of the dogleg in terms of the solution norm.

doublereal	dist_R1_
	Distance of the first leg of the dogleg in terms of the solution norm.

doublereal	dist_R2_
	Distance of the second leg of the dogleg in terms of the solution norm.

doublereal	dist_Total_
	Distance of the sum of all legs of the doglegs in terms of the solution norm.

doublereal	JdJd_norm_
	Dot product of the Jd_ variable defined above with itself.

doublereal	normTrust_Newton_
	Norm of the Newton Step wrt trust region.

doublereal	normTrust_CP_
	Norm of the Cauchy Step direction wrt trust region.

int	doDogLeg_
	General toggle for turning on dog leg damping.

int	doAffineSolve_
	General toggle for turning on Affine solve with Hessian.

doublereal	m_conditionNumber
	Condition number of the matrix.

doublereal	CurrentTrustFactor_
	Factor indicating how much trust region has been changed this iteration - output variable.

doublereal	NextTrustFactor_
	Factor indicating how much trust region has been changed next iteration - output variable.

bool	ResidWtsReevaluated_
	Boolean indicating that the residual weights have been reevaluated this iteration - output variable.

doublereal	ResidDecreaseSDExp_
	Expected DResid_dS for the steepest descent path - output variable.

doublereal	ResidDecreaseSD_
	Actual DResid_dS for the steepest descent path - output variable.

doublereal	ResidDecreaseNewtExp_
	Expected DResid_dS for the Newton path - output variable.

doublereal	ResidDecreaseNewt_
	Actual DResid_dS for the newton path - output variable.

Detailed Description

Class that calculates the solution to a nonlinear system.

This is a small nonlinear solver that can solve highly nonlinear problems that must use a dense matrix to relax the system.

Newton's method is used.

Damping is used extensively when relaxing the system.

The basic idea is that we predict a direction that is parameterized by an overall coordinate value, beta, from zero to one, This may or may not be the same as the value, damp, depending upon whether the direction is straight.

TIME STEP TYPE

The code solves a nonlinear problem. Frequently the nonlinear problem is created from time-dependent residual. Whenever you change the solution vector, you are also changing the derivative of the solution vector. Therefore, the code has the option of altering ydot, a vector of time derivatives of the solution in tandem with the solution vector and then feeding a residual and Jacobian routine with the time derivatives as well as the solution. The code has support for a backwards euler method and a second order Adams-Bashforth or Trapezoidal Rule.

In order to use these methods, the solver must be initialized with delta_t and m_y_nm1[i] to specify the conditions at the previous time step. For second order methods, the time derivative at t_nm1 must also be supplied, m_ydot_nm1[i]. Then the solution type NSOLN_TYPE_TIME_DEPENDENT may be used to solve the problem.

For steady state problem whose residual doesn't have a solution time derivative in it, you should use the NSOLN_TYPE_STEADY_STATE problem type.

We have a NSOLN_TYPE_PSEUDO_TIME_DEPENDENT defined. However, this is not implemented yet. This would be a pseudo time dependent calculation, where an optional time derivative could be added in order to help equilibrate a nonlinear steady state system. The time transient is not important in and of itself. Many physical systems have a time dependence to them that provides a natural way to relax the nonlinear system.

MATRIX SCALING

NonlinearSolver *nls = new NonlinearSolver(&r1);
int solnType =       NSOLN_TYPE_STEADY_STATE ;
nls->setDeltaBoundsMagnitudes(deltaBounds);
nls->solve_nonlinear_problem(solnType, y_comm, ydot_comm, CJ, time_curr, jac,
                              num_newt_its,  num_linear_solves, numBacktracks,
                             loglevelInput);

Definition at line 133 of file NonlinearSolver.h.

Constructor & Destructor Documentation

NonlinearSolver ( ResidJacEval * func )

Default constructor.

Parameters

func	Residual and jacobian evaluator function object

Definition at line 92 of file NonlinearSolver.cpp.

NonlinearSolver ( const NonlinearSolver & right )

Copy Constructor for the ThermoPhase object.

Parameters

right Item to be copied

Definition at line 215 of file NonlinearSolver.cpp.

References NonlinearSolver::operator=().

~NonlinearSolver ( )

Destructor.

Definition at line 305 of file NonlinearSolver.cpp.

References NonlinearSolver::HessianPtr_, and NonlinearSolver::jacCopyPtr_.

Member Function Documentation

NonlinearSolver & operator= ( const NonlinearSolver & right )

Assignment operator.

This is NOT a virtual function.

Parameters

right Reference to NonlinearSolver object to be copied into the current one.

Definition at line 315 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::NonlinearSolver().

void createSolnWeights ( const doublereal *const y )

Create solution weights for convergence criteria.

We create soln weights from the following formula

wt[i] = rtol * abs(y[i]) + atol[i]

The program always assumes that atol is specific to the solution component

Parameters

y	vector of the current solution values

Definition at line 430 of file NonlinearSolver.cpp.

References NonlinearSolver::atolk_, NonlinearSolver::m_ewt, NonlinearSolver::neq_, and NonlinearSolver::rtol_.

Referenced by NonlinearSolver::solve_nonlinear_problem().

doublereal solnErrorNorm	(	const doublereal *const	delta_y,
		const char *	title = `0`,
		int	printLargest = `0`,
		const doublereal	dampFactor = `1.0`
	)		const

L2 norm of the delta of the solution vector.

calculate the norm of the solution vector. This will involve the column scaling of the matrix

The third argument has a default of false. However, if true, then a table of the largest values is printed out to standard output.

Parameters

delta_y	Vector to take the norm of
title	Optional title to be printed out
printLargest	int indicating how many specific lines should be printed out
dampFactor	Current value of the damping factor. Defaults to 1. only used for printout out a table.

Returns: Returns the L2 norm of the delta

Definition at line 483 of file NonlinearSolver.cpp.

References Cantera::error(), Cantera::int2str(), NonlinearSolver::m_ewt, NonlinearSolver::m_print_flag, NonlinearSolver::m_y_n_curr, NonlinearSolver::neq_, Cantera::npos, and Cantera::print_line().

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::residualComparisonLeg(), NonlinearSolver::setupDoubleDogleg(), NonlinearSolver::solve_nonlinear_problem(), and NonlinearSolver::trustRegionLength().

doublereal residErrorNorm	(	const doublereal *const	resid,
		const char *	title = `0`,
		const int	printLargest = `0`,
		const doublereal *const	y = `0`
	)		const

L2 norm of the residual of the equation system.

Calculate the norm of the residual vector. This may involve using the row sum scaling from the matrix problem.

The second argument has a default of false. However, if true, then a table of the largest values is printed out to standard output.

Parameters

resid	Vector of the residuals
title	Optional title to be printed out
printLargest	Number of specific entries to be printed
y	Current value of y - only used for printouts

Returns: Returns the L2 norm of the delta

Definition at line 565 of file NonlinearSolver.cpp.

References mdp::checkFinite(), Cantera::error(), Cantera::int2str(), NonlinearSolver::m_print_flag, NonlinearSolver::m_residWts, NonlinearSolver::neq_, Cantera::npos, and Cantera::print_line().

Referenced by NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

int doResidualCalc	(	const doublereal	time_curr,
		const int	typeCalc,
		const doublereal *const	y_curr,
		const doublereal *const	ydot_curr,
		const ResidEval_Type_Enum	evalType = `Base_ResidEval`
	)		const

Compute the current residual.

The current value of the residual is stored in the internal work array m_resid, which is defined as mutable

Parameters

time_curr	Value of the time
typeCalc	Type of the calculation
y_curr	Current value of the solution vector
ydot_curr	Current value of the time derivative of the solution vector
evalType	Base evaluation type Defaults to Base_ResidEval

Returns: Returns a flag to indicate that operation is successful. 1 Means a successful operation -0 or neg value Means an unsuccessful operation

Definition at line 729 of file NonlinearSolver.cpp.

References DATA_PTR, NonlinearSolver::delta_t_n, ResidJacEval::evalResidNJ(), NonlinearSolver::m_func, NonlinearSolver::m_nfe, NonlinearSolver::m_resid, and NonlinearSolver::m_resid_scaled.

Referenced by NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

int doNewtonSolve	(	const doublereal	time_curr,
		const doublereal *const	y_curr,
		const doublereal *const	ydot_curr,
		doublereal *const	delta_y,
		GeneralMatrix &	jac
	)

Compute the undamped Newton step.

Compute the undamped Newton step. The residual function is evaluated at the current time, t_n, at the current values of the solution vector, m_y_n, and the solution time derivative, m_ydot_n. The Jacobian is not recomputed.

A factored jacobian is reused, if available. If a factored jacobian is not available, then the jacobian is factored. Before factoring, the jacobian is row and column-scaled. Column scaling is not recomputed. The row scales are recomputed here, after column scaling has been implemented.

Parameters

time_curr	Current value of the time
y_curr	Current value of the solution
ydot_curr	Current value of the solution derivative.
delta_y	return value of the raw change in y
jac	Jacobian

Returns: Returns the result code from lapack. A zero means success. Anything else indicates a failure.

Definition at line 964 of file NonlinearSolver.cpp.

References DATA_PTR, NonlinearSolver::m_colScales, NonlinearSolver::m_colScaling, NonlinearSolver::m_numLocalLinearSolves, NonlinearSolver::m_numTotalLinearSolves, NonlinearSolver::m_resid, NonlinearSolver::m_resid_scaled, NonlinearSolver::m_rowScales, NonlinearSolver::m_rowScaling, NonlinearSolver::neq_, and GeneralMatrix::solve().

Referenced by NonlinearSolver::dampStep(), and NonlinearSolver::solve_nonlinear_problem().

int doAffineNewtonSolve	(	const doublereal *const	y_curr,
		const doublereal *const	ydot_curr,
		doublereal *const	delta_y,
		GeneralMatrix &	jac
	)

Compute the newton step, either by direct newton's or by solving a close problem that is represented by a Hessian (.

This is algorith A.6.5.1 in Dennis / Schnabel

Compute the QR decomposition

Compute the undamped Newton step. The residual function is evaluated at the current time, t_n, at the current values of the solution vector, m_y_n, and the solution time derivative, m_ydot_n. The Jacobian is not recomputed.

A factored jacobian is reused, if available. If a factored jacobian is not available, then the jacobian is factored. Before factoring, the jacobian is row and column-scaled. Column scaling is not recomputed. The row scales are recomputed here, after column scaling has been implemented.

Parameters

y_curr	Current value of the solution
ydot_curr	Current value of the solution derivative.
delta_y	return value of the raw change in y
jac	Jacobian

Internal input

internal m_resid Stored residual is used as input

Returns: Returns the result code from lapack. A zero means success. Anything else indicates a failure.

Definition at line 1056 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::solve_nonlinear_problem().

doublereal trustRegionLength ( ) const

Calculate the length of the current trust region in terms of the solution error norm.

We carry out a norm of deltaX_trust_ first. Then, we multiply that value by trustDelta_

Definition at line 1979 of file NonlinearSolver.cpp.

References DATA_PTR, NonlinearSolver::deltaX_trust_, NonlinearSolver::norm_deltaX_trust_, NonlinearSolver::solnErrorNorm(), and NonlinearSolver::trustDelta_.

Referenced by NonlinearSolver::dampDogLeg(), and NonlinearSolver::decideStep().

void setDefaultDeltaBoundsMagnitudes ( )

Set default deulta bounds amounts.

Delta bounds are set to 0.01 for all unknowns arbitrarily and capriciously Then, for each call to the nonlinear solver Then, they are increased to 1000 x atol then, they are increased to 0.1 fab(y[i])

Definition at line 1985 of file NonlinearSolver.cpp.

References NonlinearSolver::atolk_, NonlinearSolver::m_deltaStepMinimum, NonlinearSolver::m_y_n_curr, ckr::max(), and NonlinearSolver::neq_.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void adjustUpStepMinimums ( )

Adjust the step minimums.

Definition at line 1993 of file NonlinearSolver.cpp.

References NonlinearSolver::deltaX_trust_, NonlinearSolver::m_deltaStepMinimum, NonlinearSolver::neq_, and NonlinearSolver::trustDelta_.

Referenced by NonlinearSolver::decideStep().

void setDeltaBoundsMagnitudes ( const doublereal *const deltaBoundsMagnitudes )

Set the delta Bounds magnitudes by hand.

Parameters

deltaBoundsMagnitudes set the deltaBoundsMagnitude vector

Definition at line 2004 of file NonlinearSolver.cpp.

References NonlinearSolver::m_deltaStepMinimum, NonlinearSolver::m_manualDeltaStepSet, and NonlinearSolver::neq_.

void readjustTrustVector ( )

protected

Readjust the trust region vectors.

The trust region is made up of the trust region vector calculation and the trustDelta_ value We periodically recalculate the trustVector_ values so that they renormalize to the correct length. We change the trustDelta_ values regularly

The trust region calculate is based on

|| delta_x   dot  1/trustDeltaX_ ||   <= trustDelta_

Definition at line 2134 of file NonlinearSolver.cpp.

References DATA_PTR, NonlinearSolver::deltaX_trust_, NonlinearSolver::doDogLeg_, NonlinearSolver::m_deltaStepMaximum, NonlinearSolver::m_deltaStepMinimum, NonlinearSolver::m_ewt, NonlinearSolver::m_print_flag, NonlinearSolver::m_y_n_curr, NonlinearSolver::neq_, NonlinearSolver::norm_deltaX_trust_, NonlinearSolver::solnErrorNorm(), and NonlinearSolver::trustDelta_.

Referenced by NonlinearSolver::initializeTrustRegion(), and NonlinearSolver::solve_nonlinear_problem().

void fillDogLegStep	(	int	leg,
		doublereal	alpha,
		std::vector< doublereal > &	deltaX
	)		const

protected

Fill a dogleg solution step vector.

Previously, we have filled up deltaX_Newton_[], deltaX_CP_[], and Nuu_, so that this routine is straightforward.

Parameters

leg	Leg of the dog leg you are on (0, 1, or 2)
alpha	Relative length along the dog length that you are on.
deltaX	Vector to be filled up

Definition at line 2254 of file NonlinearSolver.cpp.

References NonlinearSolver::deltaX_CP_, NonlinearSolver::deltaX_Newton_, NonlinearSolver::neq_, and NonlinearSolver::Nuu_.

Referenced by NonlinearSolver::dampDogLeg().

doublereal calcTrustDistance ( std::vector< doublereal > const & deltaX ) const

protected

Calculate the trust distance of a step in the solution variables.

The trust distance is defined as the length of the step according to the norm wrt to the trust region. We calculate the trust distance by the following method.

trustDist =  || delta_x   dot  1/trustDeltaX_ ||

Parameters

deltaX Current value of deltaX

Definition at line 2280 of file NonlinearSolver.cpp.

References NonlinearSolver::deltaX_trust_, NonlinearSolver::neq_, and NonlinearSolver::trustDelta_.

Referenced by NonlinearSolver::initializeTrustRegion(), NonlinearSolver::setupDoubleDogleg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal boundStep	(	const doublereal *const	y,
		const doublereal *const	step0
	)

Bound the step.

Return the factor by which the undamped Newton step 'step0' must be multiplied in order to keep all solution components in all domains between their specified lower and upper bounds. Other bounds may be applied here as well.

Currently the bounds are hard coded into this routine:

Minimum value for all variables: - 0.01 * m_ewt[i] Maximum value = none.

Thus, this means that all solution components are expected to be numerical greater than zero in the limit of time step truncation errors going to zero.

Delta bounds: The idea behind these is that the Jacobian couldn't possibly be representative if the variable is changed by a lot. (true for nonlinear systems, false for linear systems) Maximum increase in variable in any one newton iteration: factor of 2 Maximum decrease in variable in any one newton iteration: factor of 5

Parameters

y	Current solution value of the old step
step0	Proposed step change in the solution

Returns: Returns the damping factor determined by the bounds calculation

Definition at line 2366 of file NonlinearSolver.cpp.

References NonlinearSolver::deltaBoundStep(), Cantera::int2str(), NonlinearSolver::m_print_flag, NonlinearSolver::m_y_high_bounds, NonlinearSolver::m_y_low_bounds, ckr::min(), NonlinearSolver::neq_, and Cantera::npos.

Referenced by NonlinearSolver::dampDogLeg(), and NonlinearSolver::dampStep().

void setBoundsConstraints	(	const doublereal *const	y_low_bounds,
		const doublereal *const	y_high_bounds
	)

Set bounds constraints for all variables in the problem.

Parameters

y_low_bounds	Vector of lower bounds
y_high_bounds	Vector of high bounds

Definition at line 443 of file NonlinearSolver.cpp.

References NonlinearSolver::m_y_high_bounds, NonlinearSolver::m_y_low_bounds, and NonlinearSolver::neq_.

std::vector< doublereal > & lowBoundsConstraintVector ( )

Return an editable vector of the low bounds constraints.

Definition at line 458 of file NonlinearSolver.cpp.

References NonlinearSolver::m_y_low_bounds.

std::vector< doublereal > & highBoundsConstraintVector ( )

Return an editable vector of the high bounds constraints.

Definition at line 463 of file NonlinearSolver.cpp.

References NonlinearSolver::m_y_high_bounds.

void calc_ydot	(	const int	order,
		const doublereal *const	y_curr,
		doublereal *const	ydot_curr
	)		const

Internal function to calculate the time derivative of the solution at the new step.

Previously, the user must have supplied information about the previous time step for this routine to work as intended.

Parameters

order	of the BDF method
y_curr	current value of the solution
ydot_curr	Calculated value of the solution derivative that is consistent with y_curr

Definition at line 3969 of file NonlinearSolver.cpp.

References NonlinearSolver::delta_t_n, NonlinearSolver::m_y_nm1, NonlinearSolver::m_ydot_nm1, and NonlinearSolver::neq_.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

int beuler_jac	(	GeneralMatrix &	J,
		doublereal *const	f,
		doublereal	time_curr,
		doublereal	CJ,
		doublereal *const	y,
		doublereal *const	ydot,
		int	num_newt_its
	)

Function called to evaluate the jacobian matrix and the current residual vector at the current time step.

Parameters

J	Jacobian matrix to be filled in
f	Right hand side. This routine returns the current value of the rhs (output), so that it does not have to be computed again.
time_curr	Current time
CJ	inverse of the value of deltaT
y	value of the solution vector
ydot	value of the time derivative of the solution vector
num_newt_its	Number of newton iterations

Returns: Returns a flag to indicate that operation is successful. 1 Means a successful operation 0 Means an unsuccessful operation

Definition at line 3690 of file NonlinearSolver.cpp.

References ResidJacEval::calcDeltaSolnVariables(), GeneralMatrix::checkColumns(), GeneralMatrix::checkRows(), GeneralMatrix::clearFactorFlag(), GeneralMatrix::copyData(), DATA_PTR, NonlinearSolver::delta_t_n, ResidJacEval::evalJacobian(), ResidJacEval::evalResidNJ(), Cantera::int2str(), Cantera::JacBase_ResidEval, NonlinearSolver::jacCopyPtr_, Cantera::JacDelta_ResidEval, NonlinearSolver::m_ewt, NonlinearSolver::m_func, NonlinearSolver::m_jacFormMethod, NonlinearSolver::m_nfe, NonlinearSolver::m_nJacEval, NonlinearSolver::m_print_flag, NonlinearSolver::m_wksp, GeneralMatrix::matrixType_, mdp::mdp_alloc_dbl_1(), mdp::mdp_safe_free(), NonlinearSolver::neq_, GeneralMatrix::nRowsAndStruct(), NSOLN_JAC_ANAL, NSOLN_TYPE_STEADY_STATE, GeneralMatrix::ptrColumn(), NonlinearSolver::s_print_NumJac, NonlinearSolver::solnType_, and Cantera::subtractRD().

Referenced by NonlinearSolver::solve_nonlinear_problem().

doublereal filterNewStep	(	const doublereal	timeCurrent,
		const doublereal *const	ybase,
		doublereal *const	step0
	)

Apply a filtering process to the step.

Parameters

timeCurrent	Current value of the time
ybase	current value of the solution
step0	Proposed step change in the solution

Returns: Returns the norm of the value of the amount filtered

Definition at line 4003 of file NonlinearSolver.cpp.

References ResidJacEval::filterNewStep(), and NonlinearSolver::m_func.

Referenced by NonlinearSolver::solve_nonlinear_problem().

doublereal filterNewSolution	(	const doublereal	timeCurrent,
		doublereal *const	y_current,
		doublereal *const	ydot_current
	)

Apply a filter to the solution.

Parameters

timeCurrent	Current value of the time
y_current	current value of the solution
ydot_current	Current value of the solution derivative.

Returns: Returns the norm of the value of the amount filtered

Definition at line 4018 of file NonlinearSolver.cpp.

References ResidJacEval::filterSolnPrediction(), and NonlinearSolver::m_func.

Referenced by NonlinearSolver::solve_nonlinear_problem().

double deltaBoundStep	(	const doublereal *const	y,
		const doublereal *const	step0
	)

Return the factor by which the undamped Newton step 'step0' must be multiplied in order to keep the update within the bounds of an accurate jacobian.

The idea behind these is that the Jacobian couldn't possibly be representative, if the variable is changed by a lot. (true for nonlinear systems, false for linear systems) Maximum increase in variable in any one newton iteration: factor of 1.5 Maximum decrease in variable in any one newton iteration: factor of 2

Parameters

y	Initial value of the solution vector
step0	initial proposed step size

Returns: returns the damping factor

Definition at line 2030 of file NonlinearSolver.cpp.

References Cantera::int2str(), NonlinearSolver::m_deltaStepMinimum, NonlinearSolver::m_print_flag, ckr::max(), and NonlinearSolver::neq_.

Referenced by NonlinearSolver::boundStep().

int dampStep	(	const doublereal	time_curr,
		const doublereal *const	y_n_curr,
		const doublereal *const	ydot_n_curr,
		doublereal *const	step_1,
		doublereal *const	y_n_1,
		doublereal *const	ydot_n_1,
		doublereal *	step_2,
		doublereal &	stepNorm_2,
		GeneralMatrix &	jac,
		bool	writetitle,
		int &	num_backtracks
	)

Find a damping coefficient through a look-ahead mechanism.

On entry, step_1 must contain an undamped Newton step for the solution y_n_curr. This method attempts to find a damping coefficient such that all components stay in bounds, and the next undamped step would have a norm smaller than that of step_1. If successful, the new solution after taking the damped step is returned in y_n_1, and the undamped step at y_n_1 is returned in step_2.

Parameters

time_curr	Current physical time
y_n_curr	Base value of the solution before any steps are taken
ydot_n_curr	Base value of the time derivative of the solution
step_1	Initial step suggested.
y_n_1	Value of y1, the suggested solution after damping
ydot_n_1	Value of the time derivative of the solution at y_n_1
step_2	Value of the step change from y_n_1 to y_n_2
stepNorm_2	norm of the step change in going from y_n_1 to y_n_2
jac	Jacobian
writetitle	Write a title line
num_backtracks	Number of backtracks taken

Returns: returns an integer indicating what happened.

Definition at line 2442 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::solve_nonlinear_problem().

int solve_nonlinear_problem	(	int	SolnType,
		doublereal *const	y_comm,
		doublereal *const	ydot_comm,
		doublereal	CJ,
		doublereal	time_curr,
		GeneralMatrix &	jac,
		int &	num_newt_its,
		int &	num_linear_solves,
		int &	num_backtracks,
		int	loglevelInput
	)

Find the solution to F(X) = 0 by damped Newton iteration.

On entry, x0 contains an initial estimate of the solution. On successful return, x1 contains the converged solution.

SolnType = TRANSIENT -> we will assume we are relaxing a transient equation system for now. Will make it more general later, if an application comes up.

Parameters

SolnType	Solution type
y_comm	Initial value of the solution. On return this is the converged value of the solution
ydot_comm	Initial value of the solution derivative. On return this is the converged value of the solution derivative.
CJ	Inverse of the value of deltaT
time_curr	Current value of the time
jac	Matrix that will be used to store the jacobian
num_newt_its	Number of newton iterations taken
num_linear_solves	Number of linear solves taken
num_backtracks	Number of backtracking steps taken
loglevelInput	Input log level determines the amount of printing.

Returns: A positive value indicates a successful convergence -1 Failed convergence

Definition at line 3031 of file NonlinearSolver.cpp.

void calcColumnScales ( )

private

Set the column scales.

Definition at line 702 of file NonlinearSolver.cpp.

References ResidJacEval::calcSolnScales(), DATA_PTR, NonlinearSolver::m_colScales, NonlinearSolver::m_colScaling, NonlinearSolver::m_ewt, NonlinearSolver::m_func, NonlinearSolver::m_y_n_curr, NonlinearSolver::m_y_nm1, NonlinearSolver::neq_, and NonlinearSolver::time_n.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void setColumnScaling	(	bool	useColScaling,
		const double *const	scaleFactors = `0`
	)

Set the column scaling that are used for the inversion of the matrix.

There are three ways to do this.

The first method is to set the bool useColScaling to true, leaving the scaling factors unset. Then, the column scales will be set to the solution error weighting factors. This has the effect of ensuring that all delta variables will have the same order of magnitude at convergence end.

The second way is the explicity set the column factors in the second argument of this function call.

The final way to input the scales is to override the ResidJacEval member function call,

calcSolnScales(double time_n, const double *m_y_n_curr, const double *m_y_nm1, double *m_colScales)

Overriding this function call will trump all other ways to specify the column scaling factors.

Parameters

useColScaling	Turn this on if you want to use column scaling in the calculations
scaleFactors	A vector of doubles that specifies the column factors.

Definition at line 667 of file NonlinearSolver.cpp.

References NonlinearSolver::m_colScales, NonlinearSolver::m_colScaling, and NonlinearSolver::neq_.

void setRowScaling ( bool useRowScaling )

Set the rowscaling that are used for the inversion of the matrix.

Row scaling is set here. Right now the row scaling is set internally in the code.

Parameters

useRowScaling Turn row scaling on or off.

Definition at line 692 of file NonlinearSolver.cpp.

References NonlinearSolver::m_rowScaling.

void scaleMatrix	(	GeneralMatrix &	jac,
		doublereal *const	y_comm,
		doublereal *const	ydot_comm,
		doublereal	time_curr,
		int	num_newt_its
	)

Scale the matrix.

Parameters

jac	Jacobian
y_comm	Current value of the solution vector
ydot_comm	Current value of the time derivative of the solution vector
time_curr	current value of the time
num_newt_its	Current value of the number of newt its

Definition at line 745 of file NonlinearSolver.cpp.

References GeneralMatrix::begin(), NonlinearSolver::computeResidWts(), GeneralMatrix::factored(), NonlinearSolver::m_colScales, NonlinearSolver::m_colScaling, NonlinearSolver::m_ewt, NonlinearSolver::m_rowScales, NonlinearSolver::m_rowScaling, NonlinearSolver::m_rowWtScales, GeneralMatrix::matrixType_, NonlinearSolver::neq_, GeneralMatrix::nRowsAndStruct(), and GeneralMatrix::ptrColumn().

Referenced by NonlinearSolver::solve_nonlinear_problem().

void print_solnDelta_norm_contrib	(	const doublereal *const	step_1,
		const char *const	stepNorm_1,
		const doublereal *const	step_2,
		const char *const	stepNorm_2,
		const char *const	title,
		const doublereal *const	y_n_curr,
		const doublereal *const	y_n_1,
		doublereal	damp,
		size_t	num_entries
	)

Print solution norm contribution.

Prints out the most important entries to the update to the solution vector for the current step

Parameters

step_1	Raw update vector for the current nonlinear step
stepNorm_1	Norm of the vector step_1
step_2	Raw update vector for the next solution value based on the old matrix
stepNorm_2	Norm of the vector step_2
title	title of the printout
y_n_curr	Old value of the solution
y_n_1	New value of the solution after damping corrections
damp	Value of the damping factor
num_entries	Number of entries to print out

Definition at line 3589 of file NonlinearSolver.cpp.

References Cantera::error(), Cantera::int2str(), NonlinearSolver::m_ewt, NonlinearSolver::neq_, Cantera::npos, and Cantera::print_line().

Referenced by NonlinearSolver::dampStep().

void computeResidWts ( )

Compute the Residual Weights.

The residual weights are defined here to be equal to the inverse of the row scaling factors used to row scale the matrix, after column scaling is used. They are multiplied by 10-3 because the column weights are also multiplied by that same quantity.

The basic idea is that a change in the solution vector on the order of the convergence tolerance multiplied by [RJC] which is of order one after row scaling should give you the relative weight of the row. Values of the residual for that row can then be normalized by the value of this weight. When the tolerance in delta x is achieved, the tolerance in the residual is also achieved.

Definition at line 4038 of file NonlinearSolver.cpp.

References NonlinearSolver::atolBase_, NonlinearSolver::checkUserResidualTols_, NonlinearSolver::m_residWts, NonlinearSolver::m_rowWtScales, NonlinearSolver::m_ScaleSolnNormToResNorm, ckr::min(), NonlinearSolver::neq_, NonlinearSolver::ResidWtsReevaluated_, NonlinearSolver::userResidAtol_, and NonlinearSolver::userResidRtol_.

Referenced by NonlinearSolver::calcSolnToResNormVector(), and NonlinearSolver::scaleMatrix().

void getResidWts ( doublereal *const residWts ) const

Return the residual weights.

Parameters

residWts Vector of length neq_

Definition at line 4069 of file NonlinearSolver.cpp.

References NonlinearSolver::m_residWts, and NonlinearSolver::neq_.

int convergenceCheck	(	int	dampCode,
		doublereal	s1
	)

Check to see if the nonlinear problem has converged.

Parameters

dampCode	Code from the damping routine
s1	Value of the norm of the step change

Returns: integer is returned. If positive, then the problem has converged 1 Successful step was taken: Next step's norm is less than 1.0. The final residual norm is less than 1.0. 2 Successful step: Next step's norm is less than 0.8. This step's norm is less than 1.0. The residual norm can be anything. 3 Success: The final residual is less than 1.0 The predicted deltaSoln is below 1.0. 0 Not converged yet

Definition at line 4090 of file NonlinearSolver.cpp.

References NonlinearSolver::m_dampBound, NonlinearSolver::m_dampRes, NonlinearSolver::m_normDeltaSoln_Newton, and NonlinearSolver::m_normResidTrial.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void setAtol ( const doublereal *const atol )

Set the absolute tolerances for the solution variables.

Set the absolute tolerances used in the calculation

Parameters

atol	Vector of length neq_ that contains the tolerances to be used for the solution variables

Definition at line 4143 of file NonlinearSolver.cpp.

References NonlinearSolver::atolk_, and NonlinearSolver::neq_.

void setRtol ( const doublereal rtol )

Set the relative tolerances for the solution variables.

Set the relative tolerances used in the calculation

Parameters

rtol	single double

Definition at line 4156 of file NonlinearSolver.cpp.

References NonlinearSolver::rtol_.

void setResidualTols	(	double	residRtol,
		double *	residATol,
		int	residNormHandling = `2`
	)

Set the relative and absolute tolerances for the Residual norm comparisons, if used.

Residual norms are used to calculate convergence within the nonlinear solver, since these are the norms that are associated with convergence proofs, especially for ill-conditioned systems. Usually the residual weights for each row are calculated by the program such that they correlate with the convergence requirements on the solution variables input by the user using the routines setAtol() and setRtol(). The residual weights are essentially calculated from the value

 residWeightNorm[i]  = m_ScaleSolnNormToResNorm  * sum_j ( fabs(A_i,j) ewt(j))

The factor, m_ScaleSolnNormToResNorm, is computed periodically to ensure that the solution norms and the residual norms are converging at the same time and thus accounts for some-illconditioning issues but not all.

The user specified tolerance for the residual is given by the following quantity

residWeightNorm[i] = residAtol[i] + residRtol * m_rowWtScales[i] / neq

Parameters

residNormHandling Parameter that sets the default handling of the residual norms 0 The residual weighting vector is calculated to make sure that the solution norms are roughly 1 when the residual norm is roughly 1. This is the default if this routine is not called. 1 Use the user residual norm specified by the parameters in this routine 2 Use the minimum value of the residual weights calculcated by method 1 and 2. This is the default if this routine is called and this parameter isn't specified.

Definition at line 4174 of file NonlinearSolver.cpp.

References NonlinearSolver::checkUserResidualTols_, NonlinearSolver::neq_, NonlinearSolver::userResidAtol_, and NonlinearSolver::userResidRtol_.

void setMaxNewtIts ( const int maxNewtIts )

Set the value of the maximum # of newton iterations.

Parameters

maxNewtIts Maximum number of newton iterations

void calcSolnToResNormVector ( )

Calculate the scaling factor for translating residual norms into solution norms.

This routine calls computeResidWts() a couple of times in the calculation of m_ScaleSolnNormToResNorm. A more sophisticated routine may do more with signs to get a better value. Perhaps, a series of calculations with different signs attached may be in order. Then, m_ScaleSolnNormToResNorm would be calculated as the minimum of a series of calculations.

Definition at line 892 of file NonlinearSolver.cpp.

References NonlinearSolver::atolBase_, NonlinearSolver::checkUserResidualTols_, NonlinearSolver::computeResidWts(), Cantera::error(), GeneralMatrix::factored(), NonlinearSolver::jacCopyPtr_, NonlinearSolver::m_ewt, NonlinearSolver::m_residWts, NonlinearSolver::m_rowWtScales, NonlinearSolver::m_ScaleSolnNormToResNorm, NonlinearSolver::m_wksp, ckr::min(), NonlinearSolver::neq_, NonlinearSolver::userResidAtol_, and NonlinearSolver::userResidRtol_.

doublereal doCauchyPointSolve ( GeneralMatrix & jac )

Calculate the steepest descent direction and the Cauchy Point where the quadratic formulation of the nonlinear problem expects a minimum along the descent direction.

Parameters

jac	Jacobian matrix: must be unfactored.

Returns: Returns the norm of the solution update

Definition at line 1404 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void descentComparison	(	doublereal	time_curr,
		doublereal *	ydot0,
		doublereal *	ydot1,
		int &	numTrials
	)

This is a utility routine that can be used to print out the rates of the initial residual decline.

The residual**2 decline for various directions is printed out. The rate of decline of the square of the residuals multiplied by the number of equations along each direction is printed out This quantity can be directly related to the theory, and may be calculated from derivatives at the original point.

( (r)**2 * neq - (r0)**2 * neq ) / distance

What's printed out:

The theoretical linearized residual decline The actual residual decline in the steepest descent direction determined by numerical differencing The actual residual decline in the newton direction determined by numerical differencing

This routine doesn't need to be called for the solution of the nonlinear problem.

Parameters

time_curr	Current time
ydot0	INPUT Current value of the derivative of the solution vector
ydot1	INPUT Time derivatives of solution at the conditions which are evaluated for success
numTrials	OUTPUT Counter for the number of residual evaluations

Definition at line 1534 of file NonlinearSolver.cpp.

References Cantera::Base_LaggedSolutionComponents, DATA_PTR, NonlinearSolver::deltaX_CP_, NonlinearSolver::deltaX_Newton_, NonlinearSolver::doDogLeg_, NonlinearSolver::doResidualCalc(), NonlinearSolver::lambdaStar_, NonlinearSolver::m_normResid_0, NonlinearSolver::m_print_flag, NonlinearSolver::m_resid, NonlinearSolver::m_wksp, NonlinearSolver::m_y_n_curr, NonlinearSolver::neq_, NSOLN_TYPE_STEADY_STATE, NonlinearSolver::ResidDecreaseNewt_, NonlinearSolver::ResidDecreaseNewtExp_, NonlinearSolver::ResidDecreaseSD_, NonlinearSolver::ResidDecreaseSDExp_, NonlinearSolver::residErrorNorm(), NonlinearSolver::RJd_norm_, NonlinearSolver::s_print_DogLeg, NonlinearSolver::solnErrorNorm(), and NonlinearSolver::solnType_.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void setupDoubleDogleg ( )

Setup the parameters for the double dog leg.

The calls to the doCauchySolve() and doNewtonSolve() routines are done at the main level. This routine comes after those calls. We calculate the point Nuu_ here, the distances of the dog-legs, and the norms of the CP and Newton points in terms of the trust vectors.

Definition at line 1668 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::solve_nonlinear_problem().

int lambdaToLeg	(	const doublereal	lambda,
		doublereal &	alpha
	)		const

Change the global lambda coordinate into the (leg,alpha) coordinate for the double dogleg.

Parameters

lambda	Global value of the distance along the double dogleg
alpha	relative value along the particular leg

Returns: Returns the leg number ( 0, 1, or 2).

Definition at line 1732 of file NonlinearSolver.cpp.

References NonlinearSolver::dist_R0_, NonlinearSolver::dist_R1_, NonlinearSolver::dist_R2_, and NonlinearSolver::dist_Total_.

int calcTrustIntersection	(	doublereal	trustVal,
		doublereal &	lambda,
		doublereal &	alpha
	)		const

Given a trust distance, this routine calculates the intersection of the this distance with the double dogleg curve.

Parameters

trustVal	(INPUT) Value of the trust distance
lambda	(OUTPUT) Returns the internal coordinate of the double dogleg
alpha	(OUTPUT) Returns the relative distance along the appropriate leg

Returns: leg (OUTPUT) Returns the leg ID (0, 1, or 2)

Definition at line 2300 of file NonlinearSolver.cpp.

References NonlinearSolver::deltaX_CP_, NonlinearSolver::deltaX_Newton_, NonlinearSolver::deltaX_trust_, NonlinearSolver::dist_R0_, NonlinearSolver::dist_R1_, NonlinearSolver::dist_R2_, NonlinearSolver::dist_Total_, NonlinearSolver::neq_, NonlinearSolver::normTrust_CP_, NonlinearSolver::normTrust_Newton_, and NonlinearSolver::Nuu_.

Referenced by NonlinearSolver::dampDogLeg().

void initializeTrustRegion ( )

Initialize the size of the trust vector.

The algorithm we use is to set it equal to the length of the Distance to the Cauchy point.

Definition at line 2201 of file NonlinearSolver.cpp.

References NonlinearSolver::calcTrustDistance(), NonlinearSolver::deltaX_CP_, NonlinearSolver::deltaX_Newton_, NonlinearSolver::deltaX_trust_, NonlinearSolver::doDogLeg_, NonlinearSolver::m_ewt, NonlinearSolver::m_normDeltaSoln_CP, NonlinearSolver::m_normDeltaSoln_Newton, NonlinearSolver::m_print_flag, NonlinearSolver::neq_, NonlinearSolver::readjustTrustVector(), NonlinearSolver::trustDelta_, NonlinearSolver::trustRegionInitializationFactor_, and NonlinearSolver::trustRegionInitializationMethod_.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void setTrustRegionInitializationMethod	(	int	method,
		doublereal	factor
	)

Set Trust region initialization strategy.

The default is use method 2 with a factor of 1. Then, on subsequent invocations of solve_nonlinear_problem() the strategy flips to method 0.

Parameters

method	Method to set the strategy 0 No strategy - Use the previous strategy 1 Factor of the solution error weights 2 Factor of the first Cauchy Point distance 3 Factor of the first Newton step distance
factor	Factor to use in combination with the method

int dampDogLeg	(	const doublereal	time_curr,
		const doublereal *	y_n_curr,
		const doublereal *	ydot_n_curr,
		std::vector< doublereal > &	step_1,
		doublereal *const	y_n_1,
		doublereal *const	ydot_n_1,
		doublereal &	stepNorm_1,
		doublereal &	stepNorm_2,
		GeneralMatrix &	jac,
		int &	num_backtracks
	)

Damp using the dog leg approach.

Parameters

time_curr	INPUT Current value of the time
y_n_curr	INPUT Current value of the solution vector
ydot_n_curr	INPUT Current value of the derivative of the solution vector
step_1	INPUT First trial step for the first iteration
y_n_1	INPUT First trial value of the solution vector
ydot_n_1	INPUT First trial value of the derivative of the solution vector
stepNorm_1	OUTPUT Norm of the vector step_1
stepNorm_2	OUTPUT Estimated norm of the vector step_2
jac	INPUT jacobian
num_backtracks	OUTPUT number of backtracks taken in the current damping step

Returns: 1 Successful step was taken. The predicted residual norm is less than one 2 Successful step: Next step's norm is less than 0.8 3 Success: The final residual is less than 1.0 A predicted deltaSoln1 is not produced however. s1 is estimated. 4 Success: The final residual is less than the residual from the previous step. A predicted deltaSoln1 is not produced however. s1 is estimated. 0 Uncertain Success: s1 is about the same as s0 -2 Unsuccessful step.

Definition at line 2674 of file NonlinearSolver.cpp.

Referenced by NonlinearSolver::solve_nonlinear_problem().

int decideStep	(	const doublereal	time_curr,
		int	leg,
		doublereal	alpha,
		const doublereal *const	y_n_curr,
		const doublereal *const	ydot_n_curr,
		const std::vector< doublereal > &	step_1,
		const doublereal *const	y_n_1,
		const doublereal *const	ydot_n_1,
		doublereal	trustDeltaOld
	)

Decide whether the current step is acceptable and adjust the trust region size.

This is an extension of algorithm 6.4.5 of Dennis and Schnabel.

Here we decide whether to accept the current step At the end of the calculation a new estimate of the trust region is calculated

Parameters

time_curr	INPUT Current value of the time
leg	INPUT Leg of the dogleg that we are on
alpha	INPUT Distance down that leg that we are on
y_n_curr	INPUT Current value of the solution vector
ydot_n_curr	INPUT Current value of the derivative of the solution vector
step_1	INPUT Trial step
y_n_1	OUTPUT Solution values at the conditions which are evaluated for success
ydot_n_1	OUTPUT Time derivatives of solution at the conditions which are evaluated for success
trustDeltaOld	INPUT Value of the trust length at the old conditions

Returns: This function returns a code which indicates whether the step will be accepted or not. 3 Step passed with flying colors. Try redoing the calculation with a bigger trust region. 2 Step didn't pass deltaF requirement. Decrease the size of the next trust region for a retry and return 0 The step passed. -1 The step size is now too small (||d || < 0.1). A really small step isn't decreasing the function. This is an error condition. -2 Current value of the solution vector caused a residual error in its evaluation. Step is a failure, and the step size must be reduced in order to proceed further.

Definition at line 2850 of file NonlinearSolver.cpp.

References NonlinearSolver::adjustUpStepMinimums(), Cantera::Base_LaggedSolutionComponents, NonlinearSolver::CurrentTrustFactor_, DATA_PTR, NonlinearSolver::deltaX_CP_, NonlinearSolver::dogLegAlpha_, NonlinearSolver::dogLegID_, NonlinearSolver::doResidualCalc(), NonlinearSolver::expectedResidLeg(), NonlinearSolver::lambdaStar_, NonlinearSolver::m_dampBound, NonlinearSolver::m_normDeltaSoln_Newton, NonlinearSolver::m_normResid_0, NonlinearSolver::m_normResid_1, NonlinearSolver::m_normResidTrial, NonlinearSolver::m_print_flag, NonlinearSolver::m_resid, NonlinearSolver::neq_, NonlinearSolver::NextTrustFactor_, NSOLN_TYPE_STEADY_STATE, NonlinearSolver::residErrorNorm(), NonlinearSolver::RJd_norm_, NonlinearSolver::rtol_, NonlinearSolver::solnErrorNorm(), NonlinearSolver::solnType_, NonlinearSolver::trustDelta_, and NonlinearSolver::trustRegionLength().

Referenced by NonlinearSolver::dampDogLeg().

doublereal expectedResidLeg	(	int	leg,
		doublereal	alpha
	)		const

Calculated the expected residual along the double dogleg curve.

Parameters

leg	0, 1, or 2 representing the curves of the dogleg
alpha	Relative distance along the particular curve.

Returns: Returns the expected value of the residual at that point according to the quadratic model. The residual at the newton point will always be zero.

Definition at line 1754 of file NonlinearSolver.cpp.

References NonlinearSolver::lambdaStar_, NonlinearSolver::m_normResid_0, NonlinearSolver::neq_, NonlinearSolver::Nuu_, and NonlinearSolver::RJd_norm_.

Referenced by NonlinearSolver::decideStep(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::setupDoubleDogleg().

void residualComparisonLeg	(	const doublereal	time_curr,
		const doublereal *const	ydot0,
		int &	legBest,
		doublereal &	alphaBest
	)		const

Here we print out the residual at various points along the double dogleg, comparing against the quadratic model in a table format.

Parameters

time_curr	INPUT current time
ydot0	INPUT Current value of the derivative of the solution vector for non-time dependent determinations
legBest	OUTPUT leg of the dogleg that gives the lowest residual
alphaBest	OUTPUT distance along dogleg for best result.

Definition at line 1818 of file NonlinearSolver.cpp.

References Cantera::Base_LaggedSolutionComponents, NonlinearSolver::calc_ydot(), DATA_PTR, NonlinearSolver::deltaX_CP_, NonlinearSolver::deltaX_Newton_, NonlinearSolver::doDogLeg_, NonlinearSolver::doResidualCalc(), NonlinearSolver::expectedResidLeg(), NonlinearSolver::m_order, NonlinearSolver::m_print_flag, NonlinearSolver::m_resid, NonlinearSolver::m_wksp, NonlinearSolver::m_wksp_2, NonlinearSolver::m_y_n_curr, NonlinearSolver::neq_, NSOLN_TYPE_STEADY_STATE, NonlinearSolver::Nuu_, NonlinearSolver::residErrorNorm(), NonlinearSolver::s_print_DogLeg, NonlinearSolver::solnErrorNorm(), and NonlinearSolver::solnType_.

Referenced by NonlinearSolver::solve_nonlinear_problem().

void setPrintLvl ( int printLvl )

Set the print level from the nonlinear solver.

0 -> absolutely nothing is printed for a single time step. 1 -> One line summary per solve_nonlinear call 2 -> short description, points of interest: Table of nonlinear solve - one line per iteration 3 -> Table is included -> More printing per nonlinear iteration (default) that occurs during the table 4 -> Summaries of the nonlinear solve iteration as they are occurring -> table no longer printed 5 -> Algorithm information on the nonlinear iterates are printed out 6 -> Additional info on the nonlinear iterates are printed out 7 -> Additional info on the linear solve is printed out. 8 -> Info on a per iterate of the linear solve is printed out.

Parameters

printLvl integer value

Definition at line 4195 of file NonlinearSolver.cpp.

References NonlinearSolver::m_print_flag.

void setSolverScheme	(	int	doDogLeg,
		int	doAffineSolve
	)

Parameter to turn on solution solver schemes.

Parameters

doDogLeg	Parameter to turn on the double dog leg scheme Default is to always use a damping scheme in the Newton Direction. When this is nonzero, a model trust region approach is used using a double dog leg with the steepest descent direction used for small step sizes.
doAffineSolve	Parameter to turn on or off the solution of the system using a Hessian if the matrix has a bad condition number.

Definition at line 452 of file NonlinearSolver.cpp.

References NonlinearSolver::doAffineSolve_, and NonlinearSolver::doDogLeg_.

Member Data Documentation

ResidJacEval* m_func

private

Pointer to the residual and jacobian evaluator for the function.

See ResidJacEval.h for an evaluator.

Definition at line 922 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::calcColumnScales(), NonlinearSolver::doResidualCalc(), NonlinearSolver::filterNewSolution(), NonlinearSolver::filterNewStep(), NonlinearSolver::NonlinearSolver(), and NonlinearSolver::operator=().

int solnType_

private

Solution type.

Definition at line 925 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

size_t neq_

private

Local copy of the number of equations.

Definition at line 928 of file NonlinearSolver.h.

std::vector<doublereal> m_ewt

private

Soln error weights.

Definition at line 931 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::calcColumnScales(), NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::createSolnWeights(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::print_solnDelta_norm_contrib(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::scaleMatrix(), and NonlinearSolver::solnErrorNorm().

int m_manualDeltaStepSet

private

Boolean indicating whether a manual delta bounds has been input.

Definition at line 934 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), NonlinearSolver::setDeltaBoundsMagnitudes(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_deltaStepMinimum

private

Soln Delta bounds magnitudes.

Definition at line 937 of file NonlinearSolver.h.

Referenced by NonlinearSolver::adjustUpStepMinimums(), NonlinearSolver::deltaBoundStep(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::setDefaultDeltaBoundsMagnitudes(), and NonlinearSolver::setDeltaBoundsMagnitudes().

std::vector<doublereal> m_deltaStepMaximum

private

Value of the delta step magnitudes.

Definition at line 940 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), and NonlinearSolver::readjustTrustVector().

std::vector<doublereal> m_y_n_curr

private

Vector containing the current solution vector within the nonlinear solver.

Definition at line 943 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcColumnScales(), NonlinearSolver::descentComparison(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::residualComparisonLeg(), NonlinearSolver::setDefaultDeltaBoundsMagnitudes(), NonlinearSolver::solnErrorNorm(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_ydot_n_curr

private

Vector containing the time derivative of the current solution vector within the nonlinear solver (where applicable)

Definition at line 947 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_y_nm1

private

Vector containing the solution at the previous time step.

Definition at line 950 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calc_ydot(), NonlinearSolver::calcColumnScales(), NonlinearSolver::NonlinearSolver(), and NonlinearSolver::operator=().

std::vector<doublereal> m_y_n_1

private

Vector containing the solution at the previous time step.

Definition at line 953 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_ydot_n_1

private

Value of the solution time derivative at the new point that is to be considered.

Definition at line 956 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_step_1

private

Value of the step to be taken in the solution.

Definition at line 959 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_colScales

private

Vector of column scaling factors.

Definition at line 962 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcColumnScales(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::scaleMatrix(), and NonlinearSolver::setColumnScaling().

std::vector<doublereal> m_rowScales

private

Weights for normalizing the values of the residuals.

These are computed if row scaling, m_rowScaling, is turned on. They are calculated currently as the sum of the absolute values of the rows of the jacobian.

Definition at line 969 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::scaleMatrix().

std::vector<doublereal> m_rowWtScales

private

Weights for normalizing the values of the residuals.

They are calculated as the sum of the absolute values of the jacobian multiplied by the solution weight function. This is carried out in scaleMatrix().

Definition at line 977 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::scaleMatrix().

std::vector<doublereal> m_resid

mutableprivate

Value of the residual for the nonlinear problem.

Definition at line 980 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::doResidualCalc(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_wksp

mutableprivate

Workspace of length neq_.

Definition at line 983 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::descentComparison(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::setupDoubleDogleg().

std::vector<doublereal> m_wksp_2

mutableprivate

Workspace of length neq_.

Definition at line 986 of file NonlinearSolver.h.

Referenced by NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

std::vector<doublereal> m_residWts

private

Vector of residual weights.

These are used to establish useful and informative weighted norms of the residual vector.

Definition at line 995 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::getResidWts(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::residErrorNorm().

doublereal m_normResid_0

private

Norm of the residual at the start of each nonlinear iteration.

Definition at line 998 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::expectedResidLeg(), NonlinearSolver::operator=(), NonlinearSolver::setupDoubleDogleg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normResid_Bound

private

Norm of the residual after it has been bounded.

Definition at line 1001 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normResid_1

private

Norm of the residual at the end of the first leg of the current iteration.

Definition at line 1004 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normResid_full

private

Norm of the residual at the end of the first leg of the current iteration.

Definition at line 1007 of file NonlinearSolver.h.

Referenced by NonlinearSolver::solve_nonlinear_problem().

doublereal m_normDeltaSoln_Newton

private

Norm of the solution update created by the iteration in its raw, undamped form, using the solution norm.

Definition at line 1010 of file NonlinearSolver.h.

Referenced by NonlinearSolver::convergenceCheck(), NonlinearSolver::decideStep(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), NonlinearSolver::setupDoubleDogleg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normDeltaSoln_CP

private

Norm of the distance to the cauchy point using the solution norm.

Definition at line 1013 of file NonlinearSolver.h.

Referenced by NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), NonlinearSolver::setupDoubleDogleg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normResidTrial

private

Norm of the residual for a trial calculation which may or may not be used.

Definition at line 1016 of file NonlinearSolver.h.

Referenced by NonlinearSolver::convergenceCheck(), NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_normResidPoints[15]

private

Vector of the norm.

Definition at line 1019 of file NonlinearSolver.h.

bool m_resid_scaled

mutableprivate

Boolean indicating whether we should scale the residual.

Definition at line 1022 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::doResidualCalc(), and NonlinearSolver::operator=().

std::vector<doublereal> m_y_high_bounds

private

Bounds vector for each species.

Definition at line 1029 of file NonlinearSolver.h.

Referenced by NonlinearSolver::boundStep(), NonlinearSolver::highBoundsConstraintVector(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::setBoundsConstraints().

std::vector<doublereal> m_y_low_bounds

private

Lower bounds vector for each species.

Definition at line 1032 of file NonlinearSolver.h.

Referenced by NonlinearSolver::boundStep(), NonlinearSolver::lowBoundsConstraintVector(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::setBoundsConstraints().

doublereal m_dampBound

private

Damping factor imposed by hard bounds and by delta bounds.

Definition at line 1035 of file NonlinearSolver.h.

Referenced by NonlinearSolver::convergenceCheck(), NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_dampRes

private

Additional damping factor due to bounds on the residual and solution norms.

Definition at line 1038 of file NonlinearSolver.h.

Referenced by NonlinearSolver::convergenceCheck(), NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal delta_t_n

private

Delta t for the current step.

Definition at line 1041 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::calc_ydot(), NonlinearSolver::doResidualCalc(), and NonlinearSolver::operator=().

int m_nfe

mutableprivate

Counter for the total number of function evaluations.

Definition at line 1044 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::doResidualCalc(), and NonlinearSolver::operator=().

int m_colScaling

private

The type of column scaling used in the matrix inversion of the problem.

If 1 then colScaling = m_ewt[] If 2 then colScaling = user set if 0 then colScaling = 1.0

Definition at line 1056 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcColumnScales(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::operator=(), NonlinearSolver::scaleMatrix(), and NonlinearSolver::setColumnScaling().

int m_rowScaling

private

int indicating whether row scaling is turned on (1) or not (0)

Definition at line 1059 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::operator=(), NonlinearSolver::scaleMatrix(), and NonlinearSolver::setRowScaling().

int m_numTotalLinearSolves

private

Total number of linear solves taken by the solver object.

Definition at line 1062 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doNewtonSolve(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

int m_numLocalLinearSolves

private

Number of local linear solves done during the current iteration.

Definition at line 1065 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doNewtonSolve(), and NonlinearSolver::solve_nonlinear_problem().

int m_numTotalNewtIts

private

Total number of newton iterations.

Definition at line 1068 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

int m_min_newt_its

private

Minimum number of newton iterations to use.

Definition at line 1071 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

int maxNewtIts_

private

Maximum number of newton iterations.

Definition at line 1074 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

int m_jacFormMethod

private

Jacobian formation method.

1 = numerical (default) 2 = analytical

Definition at line 1081 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), and NonlinearSolver::operator=().

int m_nJacEval

private

Number of Jacobian evaluations.

Definition at line 1084 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), and NonlinearSolver::operator=().

doublereal time_n

private

Current system time.

Note, we assume even for steady state problems that the residual is a function of a system time.

Definition at line 1091 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcColumnScales(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

int m_matrixConditioning

private

Boolean indicating matrix conditioning.

Definition at line 1094 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=().

int m_order

private

Order of the time step method = 1.

Definition at line 1097 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::dampStep(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal rtol_

private

value of the relative tolerance to use in solving the equation set

Definition at line 1100 of file NonlinearSolver.h.

Referenced by NonlinearSolver::createSolnWeights(), NonlinearSolver::decideStep(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), and NonlinearSolver::setRtol().

doublereal atolBase_

private

Base value of the absolute tolerance.

Definition at line 1103 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::NonlinearSolver(), and NonlinearSolver::operator=().

doublereal* m_ydot_nm1

private

Pointer containing the solution derivative at the previous time step.

Definition at line 1106 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calc_ydot().

std::vector<doublereal> atolk_

private

absolute tolerance in the solution unknown

This is used to evaluating the weighting factor

Definition at line 1112 of file NonlinearSolver.h.

Referenced by NonlinearSolver::createSolnWeights(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::setAtol(), and NonlinearSolver::setDefaultDeltaBoundsMagnitudes().

std::vector<doublereal> userResidAtol_

private

absolute tolerance in the unscaled solution unknowns

Definition at line 1115 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::operator=(), and NonlinearSolver::setResidualTols().

doublereal userResidRtol_

private

absolute tolerance in the unscaled solution unknowns

Definition at line 1118 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::operator=(), and NonlinearSolver::setResidualTols().

int checkUserResidualTols_

private

Check the residual tolerances explictly against user input.

0 Don't calculate residual weights from residual tolerance inputs 1 Calculate residual weights from residual tolerance inputs only 2 Calculate residual weights from a minimum of the solution error weights process and the direct residual tolerance inputs

Definition at line 1126 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), NonlinearSolver::operator=(), and NonlinearSolver::setResidualTols().

int m_print_flag

private

Determines the level of printing for each time step.

0 -> absolutely nothing is printed for a single time step. 1 -> One line summary per solve_nonlinear call 2 -> short description, points of interest: Table of nonlinear solve - one line per iteration 3 -> Table is included -> More printing per nonlinear iteration (default) that occurs during the table 4 -> Summaries of the nonlinear solve iteration as they are occurring -> table no longer printed 5 -> Algorithm information on the nonlinear iterates are printed out 6 -> Additional info on the nonlinear iterates are printed out 7 -> Additional info on the linear solve is printed out. 8 -> Info on a per iterate of the linear solve is printed out.

Definition at line 1140 of file NonlinearSolver.h.

doublereal m_ScaleSolnNormToResNorm

private

Scale factor for turning residual norms into solution norms.

Definition at line 1143 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::computeResidWts(), and NonlinearSolver::operator=().

Cantera::GeneralMatrix* jacCopyPtr_

private

Copy of the jacobian that doesn't get overwritten when the inverse is determined.

The jacobian stored here is the raw matrix, before any row or column scaling is carried out

Definition at line 1149 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac(), NonlinearSolver::calcSolnToResNormVector(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::operator=(), NonlinearSolver::solve_nonlinear_problem(), and NonlinearSolver::~NonlinearSolver().

Cantera::GeneralMatrix* HessianPtr_

private

Hessian.

Definition at line 1152 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::operator=(), and NonlinearSolver::~NonlinearSolver().

std::vector<doublereal> deltaX_CP_

private

Steepest descent direction. This is also the distance to the Cauchy Point.

Definition at line 1159 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::fillDogLegStep(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::setupDoubleDogleg().

std::vector<doublereal> deltaX_Newton_

private

Newton Step - This is the newton step determined from the straight Jacobian.

Definition at line 1165 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::descentComparison(), NonlinearSolver::fillDogLegStep(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), NonlinearSolver::setupDoubleDogleg(), and NonlinearSolver::solve_nonlinear_problem().

doublereal residNorm2Cauchy_

private

Expected value of the residual norm at the Cauchy point if the quadratic model were valid.

Definition at line 1169 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doCauchyPointSolve(), and NonlinearSolver::operator=().

int dogLegID_

private

Current leg.

Definition at line 1172 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal dogLegAlpha_

private

Current Alpha param along the leg.

Definition at line 1175 of file NonlinearSolver.h.

Referenced by NonlinearSolver::dampDogLeg(), NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal RJd_norm_

private

Residual dot Jd norm.

This is equal to R_hat dot J_hat d_y_descent

Definition at line 1181 of file NonlinearSolver.h.

Referenced by NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::expectedResidLeg(), and NonlinearSolver::operator=().

doublereal lambdaStar_

private

Value of lambdaStar_ which is used to calculate the Cauchy point.

Definition at line 1184 of file NonlinearSolver.h.

Referenced by NonlinearSolver::decideStep(), NonlinearSolver::descentComparison(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::expectedResidLeg(), and NonlinearSolver::operator=().

std::vector<doublereal> Jd_

private

Jacobian times the steepest descent direction in the normalized coordinates.

This is equal to [ Jhat d^y_{descent} ] in the notes, Eqn. 18.

Definition at line 1190 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::NonlinearSolver(), and NonlinearSolver::operator=().

std::vector<doublereal> deltaX_trust_

private

Vector of trust region values.

Definition at line 1193 of file NonlinearSolver.h.

Referenced by NonlinearSolver::adjustUpStepMinimums(), NonlinearSolver::calcTrustDistance(), NonlinearSolver::calcTrustIntersection(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::NonlinearSolver(), NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::solve_nonlinear_problem(), and NonlinearSolver::trustRegionLength().

doublereal norm_deltaX_trust_

mutableprivate

Current norm of the vector deltaX_trust_ in terms of the solution norm.

Definition at line 1196 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::solve_nonlinear_problem(), and NonlinearSolver::trustRegionLength().

doublereal trustDelta_

private

Current value of trust radius.

This is used with deltaX_trust_ to calculate the max step size.

Definition at line 1200 of file NonlinearSolver.h.

Referenced by NonlinearSolver::adjustUpStepMinimums(), NonlinearSolver::calcTrustDistance(), NonlinearSolver::dampDogLeg(), NonlinearSolver::decideStep(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::solve_nonlinear_problem(), and NonlinearSolver::trustRegionLength().

int trustRegionInitializationMethod_

private

Method for handling the trust region initialization.

Then, on subsequent invocations of solve_nonlinear_problem() the strategy flips to method 0.

method Method to set the strategy 0 No strategy - Use the previous strategy 1 Factor of the solution error weights 2 Factor of the first Cauchy Point distance 3 Factor of the first Newton step distance

Definition at line 1212 of file NonlinearSolver.h.

Referenced by NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal trustRegionInitializationFactor_

private

Factor used to set the initial trust region.

Definition at line 1215 of file NonlinearSolver.h.

Referenced by NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal Nuu_

private

Relative distance down the Newton step that the second dogleg starts.

Definition at line 1218 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::expectedResidLeg(), NonlinearSolver::fillDogLegStep(), NonlinearSolver::operator=(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::setupDoubleDogleg().

doublereal dist_R0_

private

Distance of the zeroeth leg of the dogleg in terms of the solution norm.

Definition at line 1221 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::lambdaToLeg(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

doublereal dist_R1_

private

Distance of the first leg of the dogleg in terms of the solution norm.

Definition at line 1224 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::lambdaToLeg(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

doublereal dist_R2_

private

Distance of the second leg of the dogleg in terms of the solution norm.

Definition at line 1227 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::lambdaToLeg(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

doublereal dist_Total_

private

Distance of the sum of all legs of the doglegs in terms of the solution norm.

Definition at line 1230 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::lambdaToLeg(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

doublereal JdJd_norm_

private

Dot product of the Jd_ variable defined above with itself.

Definition at line 1233 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doCauchyPointSolve(), and NonlinearSolver::operator=().

doublereal normTrust_Newton_

private

Norm of the Newton Step wrt trust region.

Definition at line 1236 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::dampDogLeg(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

doublereal normTrust_CP_

private

Norm of the Cauchy Step direction wrt trust region.

Definition at line 1239 of file NonlinearSolver.h.

Referenced by NonlinearSolver::calcTrustIntersection(), NonlinearSolver::operator=(), and NonlinearSolver::setupDoubleDogleg().

int doDogLeg_

private

General toggle for turning on dog leg damping.

Definition at line 1242 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::doAffineNewtonSolve(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::initializeTrustRegion(), NonlinearSolver::operator=(), NonlinearSolver::readjustTrustVector(), NonlinearSolver::residualComparisonLeg(), NonlinearSolver::setSolverScheme(), and NonlinearSolver::solve_nonlinear_problem().

int doAffineSolve_

private

General toggle for turning on Affine solve with Hessian.

Definition at line 1245 of file NonlinearSolver.h.

Referenced by NonlinearSolver::operator=(), NonlinearSolver::setSolverScheme(), and NonlinearSolver::solve_nonlinear_problem().

doublereal m_conditionNumber

private

Condition number of the matrix.

Definition at line 1248 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve(), and NonlinearSolver::solve_nonlinear_problem().

doublereal CurrentTrustFactor_

private

Factor indicating how much trust region has been changed this iteration - output variable.

Definition at line 1251 of file NonlinearSolver.h.

Referenced by NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal NextTrustFactor_

private

Factor indicating how much trust region has been changed next iteration - output variable.

Definition at line 1254 of file NonlinearSolver.h.

Referenced by NonlinearSolver::decideStep(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

bool ResidWtsReevaluated_

private

Boolean indicating that the residual weights have been reevaluated this iteration - output variable.

Definition at line 1257 of file NonlinearSolver.h.

Referenced by NonlinearSolver::computeResidWts(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal ResidDecreaseSDExp_

private

Expected DResid_dS for the steepest descent path - output variable.

Definition at line 1260 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal ResidDecreaseSD_

private

Actual DResid_dS for the steepest descent path - output variable.

Definition at line 1263 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal ResidDecreaseNewtExp_

private

Expected DResid_dS for the Newton path - output variable.

Definition at line 1266 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

doublereal ResidDecreaseNewt_

private

Actual DResid_dS for the newton path - output variable.

Definition at line 1269 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::operator=(), and NonlinearSolver::solve_nonlinear_problem().

bool s_TurnOffTiming

static

Turn off printing of time.

Necessary to do for test suites

Definition at line 1280 of file NonlinearSolver.h.

Referenced by NonlinearSolver::solve_nonlinear_problem().

bool s_print_NumJac

static

Turn on or off printing of the Jacobian.

Definition at line 1283 of file NonlinearSolver.h.

Referenced by NonlinearSolver::beuler_jac().

bool s_print_DogLeg

static

Turn on extra printing of dogleg information.

Definition at line 1286 of file NonlinearSolver.h.

Referenced by NonlinearSolver::descentComparison(), NonlinearSolver::doCauchyPointSolve(), NonlinearSolver::residualComparisonLeg(), and NonlinearSolver::solve_nonlinear_problem().

bool s_doBothSolvesAndCompare

static

Turn on solving both the Newton and Hessian systems and comparing the results.

This is off by default

Definition at line 1292 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve().

bool s_alwaysAssumeNewtonGood

static

This toggle turns off the use of the Hessian when it is warranted by the condition number.

This is a debugging option.

Definition at line 1298 of file NonlinearSolver.h.

Referenced by NonlinearSolver::doAffineNewtonSolve().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Internal input

Member Data Documentation