Data Structures
struct	UnitRange
	Represents a range of consecutive integers. More...

struct	BinaryNode_s

struct	OrderedBinaryTree
	The binary tree for the rsLQR solver. More...

struct	NdLqrCholeskyFactors
	Stores a list of CholeskyInfo structs for the rsLQR solver. More...

struct	NdFactor
	A chunk of memory for a single time step. More...

struct	NdData
	Core storage container for the rsLQR solver. More...

struct	NdLqrProfile
	A struct describing how long each part of the solve took, in milliseconds. More...

struct	NdLqrSolver
	Main solver for rsLQR. More...

Typedefs
typedef struct BinaryNode_s	BinaryNode
	One of the nodes in the binary tree for the rsLQR solver. More...

Functions
OrderedBinaryTree	ndlqr_BuildTree (int N)
	Construct a new binary tree for a horizon of length `N`. More...

int	ndlqr_FreeTree (OrderedBinaryTree *tree)
	Frees the data in `tree`. More...

int	ndlqr_GetIndexFromLeaf (const OrderedBinaryTree *tree, int leaf, int level)
	Get the knot point index given the leaf index at a given level. More...

int	ndlqr_GetIndexLevel (const OrderedBinaryTree *tree, int index)
	Get the level for a given knot point index. More...

int	ndlqr_GetIndexAtLevel (const OrderedBinaryTree *tree, int index, int level)
	Get the index in `level` that corresponds to `index`. More...

NdLqrCholeskyFactors *	ndlqr_NewCholeskyFactors (int depth, int nhorizon)
	Initialize a new NdLqrCholeskyFactors object. More...

int	ndlqr_FreeCholeskyFactors (NdLqrCholeskyFactors *cholfacts)
	Free the memory of a CholeskyFactors object. More...

int	ndlqr_GetQFactorizon (NdLqrCholeskyFactors cholfacts, int index, CholeskyInfo *cholfact)
	Get the CholeskyInfo for the matrix Q at index `index`. More...

int	ndlqr_GetRFactorizon (NdLqrCholeskyFactors cholfacts, int index, CholeskyInfo *cholfact)
	Get the CholeskyInfo for the matrix R at index `index`. More...

int	ndlqr_GetSFactorization (NdLqrCholeskyFactors cholfacts, int leaf, int level, CholeskyInfo *cholfact)
	Get the CholeskyInfo for the output of ndlqr_SolveCholeskyFactor(). More...

Matrix	ndlqr_GetLambdaFactor (NdFactor *factor)

Matrix	ndlqr_GetStateFactor (NdFactor *factor)

Matrix	ndlqr_GetInputFactor (NdFactor *factor)

NdData *	ndlqr_NewNdData (int nstates, int ninputs, int nhorizon, int width)
	Initialize the NdData structure. More...

int	ndlqr_FreeNdData (NdData *nddata)
	Frees the memory allocated in an NdData structure. More...

int	ndlqr_GetNdFactor (NdData nddata, int index, int level, NdFactor *factor)
	Retrieve an individual NdFactor out of the NdData. More...

void	ndlqr_ResetNdData (NdData *nddata)
	Resets all of the memory for an NdData to zero. More...

int	ndlqr_SolveLeaf (NdLqrSolver *solver, int index)
	Solve all the equations for the lowest-level diagonal blocks, by timestep. More...

int	ndlqr_SolveLeaves (NdLqrSolver *solver)

int	ndlqr_FactorInnerProduct (NdData data, NdData fact, int index, int data_level, int fact_level)
	Calculates one of the inner products needed at level `data_level`. More...

int	ndlqr_SolveCholeskyFactor (NdData fact, CholeskyInfo cholinfo, int index, int level, int upper_level)
	Use the precomputed Cholesky factorization to solve for y at each parent level. More...

bool	ndlqr_ShouldCalcLambda (OrderedBinaryTree *tree, int index, int i)
	Determines if the $ \Lambda $ should be updated during ndlqr_UpdateSchurFactor() More...

int	ndlqr_UpdateShurFactor (NdData fact, NdData soln, int index, int i, int level, int upper_level, bool calc_lambda)
	Calculates $ x $ and $ z $ to complete the factorization at the current level. More...

int	ndlqr_ComputeShurCompliment (NdLqrSolver *solver, int index, int level, int upper_level)

int	ndlqr_Solve (NdLqrSolver *solver)
	Solve an LQR problem using rsLQR. More...

Matrix	ndlqr_GetSolution (NdLqrSolver *solver)
	Return the solution vector. More...

int	ndlqr_CopySolution (NdLqrSolver solver, double soln)
	Copies the solution vector to a user-supplied array. More...

NdLqrProfile	ndlqr_NewNdLqrProfile ()
	Create a profile initialized with zeros.

void	ndlqr_ResetProfile (NdLqrProfile *prof)
	Reset the profile to its initialized state. More...

void	ndlqr_CopyProfile (NdLqrProfile dest, NdLqrProfile src)
	Copy the profile information to a new profile. More...

void	ndlqr_PrintProfile (NdLqrProfile *profile)
	Print a summary fo the profile. More...

void	ndlqr_CompareProfile (NdLqrProfile base, NdLqrProfile prof)
	Compare two profiles, printing the comparison to stdout. More...

NdLqrSolver *	ndlqr_NewNdLqrSolver (int nstates, int ninputs, int nhorizon)
	Create a new solver, allocating all the required memory. More...

int	ndlqr_FreeNdLqrSolver (NdLqrSolver *solver)
	Deallocates the memory for the solver. More...

int	ndlqr_InitializeWithLQRProblem (const LQRProblem lqrprob, NdLqrSolver solver)
	Initialize the solver with data from an LQR Problem. More...

void	ndlqr_ResetSolver (NdLqrSolver *solver)
	Resets the rsLQR solver. More...

void	ndlqr_PrintSolveSummary (NdLqrSolver *solver)
	Prints a summary of the solve. More...

int	ndlqr_GetNumVars (NdLqrSolver *solver)
	Gets the total number of decision variables for the problem. More...

int	ndlqr_SetNumThreads (NdLqrSolver *solver, int num_threads)
	Set the number of threads to be used during the solve. More...

int	ndlqr_GetNumThreads (NdLqrSolver *solver)
	Get the number of threads used during the rsLQR solve. More...

int	ndlqr_PrintSolveProfile (NdLqrSolver *solver)
	Prints a summary of how long individual components took. More...

NdLqrProfile	ndlqr_GetProfile (NdLqrSolver *solver)
	Ge the internal profile data from a solve. More...

Detailed Description

Typedef Documentation

◆ BinaryNode

typedef struct BinaryNode_s BinaryNode

One of the nodes in the binary tree for the rsLQR solver.

Function Documentation

◆ ndlqr_BuildTree()

OrderedBinaryTree ndlqr_BuildTree ( int N )

Construct a new binary tree for a horizon of length N.

Must be paired with a corresponding call to ndlqr_FreeTree().

Parameters

N	horizon length. Must be a power of 2.

Returns: A new binary tree

◆ ndlqr_CompareProfile()

void ndlqr_CompareProfile	(	NdLqrProfile *	base,
		NdLqrProfile *	prof
	)

Compare two profiles, printing the comparison to stdout.

Parameters

base	The baseline profile
prof	The "new" profile

◆ ndlqr_CopyProfile()

void ndlqr_CopyProfile	(	NdLqrProfile *	dest,
		NdLqrProfile *	src
	)

Copy the profile information to a new profile.

Parameters

dest	New location for data. Existing data will be overwritten.
src	Data to be copied.

◆ ndlqr_CopySolution()

int ndlqr_CopySolution	(	NdLqrSolver *	solver,
		double *	soln
	)

Copies the solution vector to a user-supplied array.

See ndlqr_GetSolution() for variable order.

Precondition: ndlqr_Solve() has already been called

Parameters

solver	The solver with the solution.
soln	Output location for the solution vector. Should have length at least equal to the output of ndlqr_GetNumVars().

Returns

◆ ndlqr_FactorInnerProduct()

int ndlqr_FactorInnerProduct	(	NdData *	data,
		NdData *	fact,
		int	index,
		int	data_level,
		int	fact_level
	)

Calculates one of the inner products needed at level data_level.

Calculates the following:

\[ \bar{\Lambda_{k+1}^{(p)}} = \bar{\Lambda_k^{(p)}}S + \langle X_k^{(j)}, \bar{X}_k^{(p)} \rangle + \langle U_k^{(j)}, \bar{U}_k^{(p)} \rangle + \langle X_{k+1}^{(j)}, \bar{X}_{k+1}^{(p)} \rangle + \langle U_{k+1}^{(j)}, \bar{U}_{k+1}^{(p)} \rangle \]

where $ j $ is data_level, $ p $ is fact_level, and $ k $ is index.

Parameters

data	The data for the original KKT matrix
fact	The current data for the factorization
index	Knot point index
data_level	Level index for the original data, or equivalently the current level being processed by the outer solve
fact_level	Level index for the factorization data, or equivalently the parent or upper level. `fact_level` >= `data_level`.

Returns: 0 if successful

◆ ndlqr_FreeCholeskyFactors()

int ndlqr_FreeCholeskyFactors ( NdLqrCholeskyFactors * cholfacts )

Free the memory of a CholeskyFactors object.

Parameters

cholfacts An initialized NdLqrCholeskyFactors object

Postcondition: cholfacts = NULL

Returns: 0 if successful

◆ ndlqr_FreeNdData()

int ndlqr_FreeNdData ( NdData * nddata )

Frees the memory allocated in an NdData structure.

Parameters

nddata Initialized NdData structure

Returns: 0 if successful

◆ ndlqr_FreeNdLqrSolver()

int ndlqr_FreeNdLqrSolver ( NdLqrSolver * solver )

Deallocates the memory for the solver.

Parameters

solver An initialized solver.

Returns: 0 if successful.

Postcondition: solver == NULL

◆ ndlqr_FreeTree()

int ndlqr_FreeTree ( OrderedBinaryTree * tree )

Frees the data in tree.

Parameters

tree	An initialized binary tree

Returns: 0 if successful

◆ ndlqr_GetIndexAtLevel()

int ndlqr_GetIndexAtLevel	(	const OrderedBinaryTree *	tree,
		int	index,
		int	level
	)

Get the index in level that corresponds to index.

If the level is higher than the level of the given index, it's simply the parent at that level. If it's lower, then it's the index that's closest to the given one, with ties broken by choosing the left (or smaller) of the two.

Parameters

tree	Precomputed binary tree
index	Start index of the search. The result will be the index closest to this index.
level	The level in which the returned index should belong to.

Returns: int The index closest to the provided one, in the given level. -1 if unsucessful.

◆ ndlqr_GetIndexFromLeaf()

int ndlqr_GetIndexFromLeaf	(	const OrderedBinaryTree *	tree,
		int	leaf,
		int	level
	)

Get the knot point index given the leaf index at a given level.

Parameters

tree	An initialized binary tree for the problem horizon
leaf	Leaf index
level	Level of tree from which to get the index

Returns

◆ ndlqr_GetIndexLevel()

int ndlqr_GetIndexLevel	(	const OrderedBinaryTree *	tree,
		int	index
	)

Get the level for a given knot point index.

Parameters

tree	An initialized binary tree for the problem horizon
index	Knot point index

Returns: The level for the given index

◆ ndlqr_GetNdFactor()

int ndlqr_GetNdFactor	(	NdData *	nddata,
		int	index,
		int	level,
		NdFactor **	factor
	)

Retrieve an individual NdFactor out of the NdData.

Retrieves a block of memory out of NdData, stored as an NdFactor. Typical usage will look like:

NdData* ndata = ndlqr_NewNdData(nstates, ninputs, nhorizon, nstates);
NdFactor* factor;
int index = 0;  // set to desired index
int level = 1;  // set to desired level
ndlqr_GetNdFactor(nddata, index, level, &factor);

Parameters

nddata	Storage location for the desired block of memory
index	Time step of the factor to extract
level	Level (or column in the NdData) of the desired factor
factor	Storage location for the factor.

Returns: 0 if successful

◆ ndlqr_GetNumThreads()

int ndlqr_GetNumThreads ( NdLqrSolver * solver )

Get the number of threads used during the rsLQR solve.

Parameters

solver A solver which has already been initialized and solved

Returns: number of OpenMP threads used the by solver

◆ ndlqr_GetNumVars()

int ndlqr_GetNumVars ( NdLqrSolver * solver )

Gets the total number of decision variables for the problem.

Parameters

solver

◆ ndlqr_GetProfile()

NdLqrProfile ndlqr_GetProfile ( NdLqrSolver * solver )

Ge the internal profile data from a solve.

Parameters

solver A solver which has already been initialized and solved

Returns: A profile object containing timing information about the solve See NdLqrProfile for more info.

◆ ndlqr_GetQFactorizon()

int ndlqr_GetQFactorizon	(	NdLqrCholeskyFactors *	cholfacts,
		int	index,
		CholeskyInfo **	cholfact
	)

Get the CholeskyInfo for the matrix Q at index index.

Parameters

[in]	cholfacts	All the stored info for the Cholesky solves
[in]	index	Knot point index
[out]	cholfact	Location for the retrieved CholeskyInfo

Returns: 0 if successful

◆ ndlqr_GetRFactorizon()

int ndlqr_GetRFactorizon	(	NdLqrCholeskyFactors *	cholfacts,
		int	index,
		CholeskyInfo **	cholfact
	)

Get the CholeskyInfo for the matrix R at index index.

Parameters

[in]	cholfacts	All the stored info for the Cholesky solves
[in]	index	Knot point index
[out]	cholfact	Location for the retrieved CholeskyInfo

Returns: 0 if successful

◆ ndlqr_GetSFactorization()

int ndlqr_GetSFactorization	(	NdLqrCholeskyFactors *	cholfacts,
		int	leaf,
		int	level,
		CholeskyInfo **	cholfact
	)

Get the CholeskyInfo for the output of ndlqr_SolveCholeskyFactor().

Gets the CholeskyInfo for $ \bar{B}_i^{(j)} $.

Parameters

[in]	cholfacts	All the stored info for the Cholesky solves
[in]	leaf	The leaf index for the desired factor
[in]	level	The level of the binary tree for the factor
[out]	cholfact	Location for the retrieved CholeskyInfo

Returns: 0 if successful

◆ ndlqr_GetSolution()

Matrix ndlqr_GetSolution ( NdLqrSolver * solver )

Return the solution vector.

Returns the solution vector as a Matrix object, which is a simple wrapper around a raw pointer which points to the data actually stored by the solver. The user must not free the data, as it is owned by the solver. To get a solution vector owned by the caller, use ndlqr_CopySolution() instead.

Variable Ordering

The variables are ordered in the solution vector as follows:

\[ \begin{bmatrix} \lambda_1^T & x_1^T & u_1^T & \lambda_2^T & \dots & x_{N-1}^T & u_{N-1}^T & \lambda_N^T & x_N^T \end{bmatrix}^T \]

Precondition: ndlqr_Solve() has already been called

Parameters

solver

Returns

◆ ndlqr_InitializeWithLQRProblem()

int ndlqr_InitializeWithLQRProblem	(	const LQRProblem *	lqrprob,
		NdLqrSolver *	solver
	)

Initialize the solver with data from an LQR Problem.

Precondition: Solver has already been initialized via ndlqr_NewNdLqrSolver()

Parameters

lqrprob	An initialized LQR problem with the data to be be solved.
solver	An initialized solver.

Returns: 0 if successful

◆ ndlqr_NewCholeskyFactors()

NdLqrCholeskyFactors* ndlqr_NewCholeskyFactors	(	int	depth,
		int	nhorizon
	)

Initialize a new NdLqrCholeskyFactors object.

Must be paired with a call to ndlqr_FreeCholeskyFactors().

Parameters

depth	Depth of the binary tree
nhorizon	Length of the time horizon. `log2`(@depth) = `nhorizon`.

Returns: An initialized NdLqrCholeskyFactors object.

◆ ndlqr_NewNdData()

NdData* ndlqr_NewNdData	(	int	nstates,
		int	ninputs,
		int	nhorizon,
		int	width
	)

Initialize the NdData structure.

Note this allocates a large block of memory. This should be followed by a single call to ndlqr_FreeNdData().

Parameters

nstates	Number of variables in the state vector
ninputs	Number of control inputs
nhorizon	Length of the time horizon
width	With of each factor. Should be `nstates` for KKT matrix data, or 1 for the right-hand side vector.

Returns: The initialized NdData structure

◆ ndlqr_NewNdLqrSolver()

NdLqrSolver* ndlqr_NewNdLqrSolver	(	int	nstates,
		int	ninputs,
		int	nhorizon
	)

Create a new solver, allocating all the required memory.

Must be followed by a later call to ndlqr_FreeNdLqrSolver().

Parameters

nstates	Number of elements in the state vector
ninputs	Number of control inputs
nhorizon	Length of the time horizon. Must be a power of 2.

Returns: A pointer to the new solver

◆ ndlqr_PrintProfile()

void ndlqr_PrintProfile ( NdLqrProfile * profile )

Print a summary fo the profile.

Parameters

profile

◆ ndlqr_PrintSolveProfile()

int ndlqr_PrintSolveProfile ( NdLqrSolver * solver )

Prints a summary of how long individual components took.

Precondition: ndlqr_Solve() has already been called

Parameters

solver A solver which has already been initialized and solved

Returns: 0 if successful

◆ ndlqr_PrintSolveSummary()

void ndlqr_PrintSolveSummary ( NdLqrSolver * solver )

Prints a summary of the solve.

Prints solve time, the residual norm, and the number of theads.

Precondition: ndlqr_Solve() has already been called

Parameters

solver

◆ ndlqr_ResetNdData()

void ndlqr_ResetNdData ( NdData * nddata )

Resets all of the memory for an NdData to zero.

Parameters

nddata Initialized NdData structure

◆ ndlqr_ResetProfile()

void ndlqr_ResetProfile ( NdLqrProfile * prof )

Reset the profile to its initialized state.

Parameters

prof A profile

◆ ndlqr_ResetSolver()

void ndlqr_ResetSolver ( NdLqrSolver * solver )

Resets the rsLQR solver.

Resets all of the data in the solver to how it was when it was first initialized.

Parameters

solver

◆ ndlqr_SetNumThreads()

int ndlqr_SetNumThreads	(	NdLqrSolver *	solver,
		int	num_threads
	)

Set the number of threads to be used during the solve.

Does not guarantee that the specified number of threads will be used. To query the actual number of threads used during the solve, use the ndlqr_GetNumThreads() function after the solve.

Parameters

solver	rsLQR solver
num_threads	requested number of threads

Returns: 0 if successful

◆ ndlqr_ShouldCalcLambda()

bool ndlqr_ShouldCalcLambda	(	OrderedBinaryTree *	tree,
		int	index,
		int	i
	)

Determines if the $ \Lambda $ should be updated during ndlqr_UpdateSchurFactor()

Basically checks to see if the $ \Lambda $ for the given index is a $B_i^{(p)}$ for any level greater than or equal to the current level.

Parameters

tree	Binary tree with cached information about the structure of the problem
index	Knot point index calculated using ndlqr_GetIndexAtLevel()
i	Knot point index being processed

Returns: 0 if successful

◆ ndlqr_Solve()

int ndlqr_Solve ( NdLqrSolver * solver )

Solve an LQR problem using rsLQR.

This is the main method of the package. Using the data already allocated in the solver, this first calculates the factorization of the matrix data and then solves for solution vector. Note that calling this method twice will not result in the same data since it replaces the original right-hand-side data with the solution vector.

Extracting the solution

The solution can be retrieved after the solve by calling either ndlqr_GetSolution() or ndlqr_CopySolution().

Calling solve multiple times

If you want to call this method multiple times on the same data (e.g. when benchmarking solve times), use ndlqr_ResetNdData() between solves to reset the factorization data. Then re-initialize the solver with the problem data via ndlqr_InitializeWithLQRProblem().

Parameters

solver An nsLQR solver that has been initialized with the desired problem data.

Returns: 0 if successful.

◆ ndlqr_SolveCholeskyFactor()

int ndlqr_SolveCholeskyFactor	(	NdData *	fact,
		CholeskyInfo *	cholinfo,
		int	index,
		int	level,
		int	upper_level
	)

Use the precomputed Cholesky factorization to solve for y at each parent level.

Solve the following linear system of equations, overwriting the right-hand-side.

\[ \bar{\Lambda}_{k+1}^{(j)} y = \bar{\Lambda}_{k+1}^{(p)} \]

where $ j $ is level, $ p $ is upper_level, and $ k $ is index.

This is the same as solving

\[ -\bar{B}_i^{(j)} y_i^{(j,p)} = \bar{b}_i^{(j,p)} \]

using the notation from the paper.

Parameters

fact	Data for the factorization
cholinfo	Cached Cholesky factorization for $ \bar{\Lambda}_{k+1}^{(j)} $.
index	Knot point index. Should be calculated using ndlqr_GetIndexFromLeaf().
level	Level index for the level currently being processed by the upper-level solve.
upper_level	Level index for the right-hand-side. `upper_level` > `level`.

Returns: 0 if successful

◆ ndlqr_SolveLeaf()

int ndlqr_SolveLeaf	(	NdLqrSolver *	solver,
		int	index
	)

Solve all the equations for the lowest-level diagonal blocks, by timestep.

Called at the beginning of the solve, this method calculates the initial pieces of the factorization needed to start the recursion up through the rest of the levels. For and LQR problem, it calculates

\[ Q_k^{-1} A_k^T Q_k^{-1} q_k R_k^{-1} B_k^T R_k^{-1} r_k \]

for each index $ k $, with special-casing applied to the first and last indices.

Parameters

solver	An initialized rsLQR solver
index	Knotpoint index

Returns: 0 if successful

◆ ndlqr_UpdateShurFactor()

int ndlqr_UpdateShurFactor	(	NdData *	fact,
		NdData *	soln,
		int	index,
		int	i,
		int	level,
		int	upper_level,
		bool	calc_lambda
	)

Calculates $ x $ and $ z $ to complete the factorization at the current level.

Calculates the following

\[ \bar{\Lambda}_k^{(p)} = \bar{\Lambda}_k^{(p)} - \bar{\Lambda}_k^{(j)} \bar{\Lambda}_{k_\text{sep}}^{(p)} \bar{X}_k^{(p)} = \bar{X}_k^{(p)} - \bar{X}_k^{(j)} \bar{\Lambda}_{k_\text{sep}}^{(p)} \bar{U}_k^{(p)} = \bar{U}_k^{(p)} - \bar{U}_k^{(j)} \bar{\Lambda}_{k_\text{sep}}^{(p)} \]

where $ \bar{\Lambda}_{k_\text{sep}}^{(p)} $ is equivalent to $y_i^{(j,p)}$ from the paper and is the result of the ndlqr_SolveCholeskyFactor() for index, level, and upper_level.

Parameters

fact	NdData for the factorization data
soln	NdData for the factorization data or solution vector
index	Knot point index of the "separator" at level `level`. Should be calculated using ndlqr_GetIndexAtlevel().
i	Knot point index to be processed
level	Level index for the level currently being processed
upper_level	Level index of the upper level. `upper_level` > `level`
calc_lambda	Whether the $ \Lambda $ factor should be updated. This should be calculated using ndlqr_ShouldCalcLambda().

Returns

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ BinaryNode

Function Documentation

◆ ndlqr_BuildTree()

◆ ndlqr_CompareProfile()

◆ ndlqr_CopyProfile()

◆ ndlqr_CopySolution()

◆ ndlqr_FactorInnerProduct()

◆ ndlqr_FreeCholeskyFactors()

◆ ndlqr_FreeNdData()

◆ ndlqr_FreeNdLqrSolver()

◆ ndlqr_FreeTree()

◆ ndlqr_GetIndexAtLevel()

◆ ndlqr_GetIndexFromLeaf()

◆ ndlqr_GetIndexLevel()

◆ ndlqr_GetNdFactor()

◆ ndlqr_GetNumThreads()

◆ ndlqr_GetNumVars()

◆ ndlqr_GetProfile()

◆ ndlqr_GetQFactorizon()

◆ ndlqr_GetRFactorizon()

◆ ndlqr_GetSFactorization()

◆ ndlqr_GetSolution()

Variable Ordering

◆ ndlqr_InitializeWithLQRProblem()

◆ ndlqr_NewCholeskyFactors()

◆ ndlqr_NewNdData()

◆ ndlqr_NewNdLqrSolver()

◆ ndlqr_PrintProfile()

◆ ndlqr_PrintSolveProfile()

◆ ndlqr_PrintSolveSummary()

◆ ndlqr_ResetNdData()

◆ ndlqr_ResetProfile()

◆ ndlqr_ResetSolver()

◆ ndlqr_SetNumThreads()

◆ ndlqr_ShouldCalcLambda()

◆ ndlqr_Solve()

Extracting the solution

Calling solve multiple times

◆ ndlqr_SolveCholeskyFactor()

◆ ndlqr_SolveLeaf()

◆ ndlqr_UpdateShurFactor()