Introduction

Header of the lineal algebra routines used in the CuikSuite.

This file includes high level routines which require LU or QR decompositions, and similar procedures.

See also: algebra.c

Definition in file algebra.h.

Data Structures
struct	TBroyden
	Broyden method. More...

Macros
#define	DAMPED_NEWTON 0
	Damped Newton process. More...

#define	DN_F 0.1
	Damping Newton initial factor. More...

#define	DN_MF 0.95
	Damping Newton maximum factor. More...

#define	DN_W 0.25
	Damping Newton update ratio. More...

Functions
int	MatrixDeterminantSgn (double epsilon, unsigned int n, double *A)
	Sign of the determinant of a matrix. More...

double	MatrixDeterminant (unsigned int n, double *A)
	Determinant of a matrix. More...

unsigned int	MatrixExponential (unsigned int m, double A, double t, double eA)
	Exponential of a matrix. More...

unsigned int	MatrixExponentialVector (unsigned int m, double A, double t, double v)
	Exponential of a matrix and product by a vector. More...

unsigned int	FindRank (double epsilon, unsigned int nr, unsigned int nc, double *mT)
	Determines the row-rank of a matrix. More...

unsigned int	FindKernel (unsigned int nr, unsigned int nc, double mT, unsigned int dof, boolean check, double epsilon, double *T)
	Computes the kernel of a matrix. More...

unsigned int	FindKernelAndRank (unsigned int nr, unsigned int nc, double mT, unsigned int rank, double epsilon, double **T)
	Computes the kernel and the rank of a matrix. More...

unsigned int	FindKernelAndIndependentRows (unsigned int nr, unsigned int nc, double mT, unsigned int dof, double epsilon, boolean singular, boolean IR, double T)
	Computes the kernel of a matrix and determines the independent rows of this matrix. More...

unsigned int	FindIndependentRows (unsigned int nr, unsigned int nc, double mT, unsigned int dof, double epsilon, boolean singular, boolean **IR)
	Computes the independent rows of this matrix. More...

boolean	InvertMatrix (unsigned int nr, double *A)
	Inverse of a matrix. More...

void	InitNewton (unsigned int nr, unsigned int nc, TNewton *n)
	Defines a Newton structure. More...

double *	GetNewtonMatrixBuffer (TNewton *n)
	Buffer to store the Newton matrix. More...

double *	GetNewtonRHBuffer (TNewton *n)
	Buffer to store the Newton right hand. More...

void	NewtonSetMatrix (unsigned int i, unsigned int j, double v, TNewton *n)
	Defines the matrix being used in a Newton step. More...

void	NewtonSetRH (unsigned int i, double v, TNewton *n)
	Defines the vector being used in a Newton step. More...

int	NewtonStep (double nullSingularValue, double x, double dif, TNewton *n)
	One step in a Newton iteration. More...

void	DeleteNewton (TNewton *n)
	Releases a Newton structure. More...

void	InitBroyden (unsigned int nr, unsigned int nc, TBroyden *b)
	Defines a Broyden structure. More...

void	ResetBroyden (TBroyden *b)
	Resets a Broyden structure. More...

double *	GetBroydenMatrixBuffer (TBroyden *b)
	Buffer to store the Broyden matrix. More...

double *	GetBroydenRHBuffer (TBroyden *b)
	Buffer to store the Broyden right hand. More...

int	BroydenStep (double epsilon, unsigned int tp, double x, TBroyden *b)
	One step in a Broyden iteration. More...

void	BroydenUpdateJacobian (double epsilon, TBroyden *b)
	Updates the approximated Jacobian. More...

void	DeleteBroyden (TBroyden *b)
	Releases a Broyden structure. More...

void	InitLS (unsigned int nr, unsigned int nc, unsigned int nrh, TLinearSystem *ls)
	Defines a linear system structure. More...

double *	GetLSMatrixBuffer (TLinearSystem *ls)
	Buffer to store the A matrix. More...

double *	GetLSRHBuffer (TLinearSystem *ls)
	Buffer to store the linear system right hand (RH). More...

double *	GetLSSolutionBuffer (TLinearSystem *ls)
	Buffer to store the linear system solution. More...

void	LSSetMatrix (unsigned int i, unsigned int j, double v, TLinearSystem *ls)
	Defines the matrix being used in a linear system. More...

void	LSSetRH (unsigned int i, unsigned int j, double v, TLinearSystem *ls)
	Defines the vector being used in a linear system. More...

int	LSSolve (TLinearSystem *ls)
	Solves the linear sytem. More...

int	LSSolveCond (double rcond, TLinearSystem ls)
	Solves the linear sytem. More...

void	DeleteLS (TLinearSystem *ls)
	Releases a linear system structure. More...

Macro Definition Documentation

◆ DAMPED_NEWTON

#define DAMPED_NEWTON 0

If 1, the Newton correction step is damped: it is multiplied by a factor alpha in [0,1] to reduce overshooting and to improve converged.

The alpha factor is initialized to DN_F and increased towards DN_MF using the DN_W weight at each step.

Only experimental. Not actually used.

Definition at line 37 of file algebra.h.

◆ DN_F

#define DN_F 0.1

Initial value for the constant used to damp the Newton step.

Definition at line 44 of file algebra.h.

◆ DN_MF

#define DN_MF 0.95

Maximum value for the constant used to damp the Newton step.

Definition at line 51 of file algebra.h.

◆ DN_W

#define DN_W 0.25

Factor used to damp the Newton step.

The update rule is alpha=alpha+DM_W*(DM_MF-alpha) with alpha initialized to DN_F.

Definition at line 61 of file algebra.h.

Function Documentation

◆ MatrixDeterminantSgn()

int MatrixDeterminantSgn	(	double	epsilon,
		unsigned int	n,
		double *	A
	)

Sign of the determinant of a squared matrix.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

epsilon	Numerical accuracy.
n	Number of rows/columsn of the matrix.
A	The matrix.

Returns: The matrix determinant sign (-1,0,1).

Referenced by GetChartDegree().

◆ MatrixDeterminant()

double MatrixDeterminant	(	unsigned int	n,
		double *	A
	)

Determinant of a squared matrix.

This function must be used with caution (only for small matrices) since the determinant can easily overflow.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

n	Number of rows/columsn of the matrix.
A	The matrix.

Returns: The matrix determinant.

Referenced by CompareTangentSpaces().

◆ MatrixExponential()

unsigned int MatrixExponential	(	unsigned int	m,
		double *	A,
		double	t,
		double *	eA
	)

Computes the exponential of a matrix (at a given time step).

For a constant matrix A, the error of this function grows with the time 't'. Use with caution for large t's (i.e., 5, 10, is already large).

Parameters

m	Number of rows/columsn of the matrix.
A	The matrix.
t	The time.
eA	The exponential of the matrix: exp(A*t).

Returns: 1 if the process was succesful.

Definition at line 1583 of file algebra.c.

References dgpadm_(), IdentityMatrix(), and NEW.

Referenced by dGt(), and LQRPolicy().

◆ MatrixExponentialVector()

unsigned int MatrixExponentialVector	(	unsigned int	m,
		double *	A,
		double	t,
		double *	v
	)

Computes the product of the exponential of a matrix with a vector at a given time step.

For a constant matrix A, the error of this function grows with the time 't'. Use with caution for large t's because the error in this case scales much faster than when using MatrixExponential. In this case the error can be significative just for t=1. If accuracy is required (over speed) just use MatrixExponential and multiply the result by vector v.

Parameters

m	Number of rows/columsn of the matrix.
A	The matrix.
t	The time.
v	The input vector. Re-used to store the output: exp(At)v.

Returns: 1 if the process was succesful.

Definition at line 1660 of file algebra.c.

References dgchbv_(), and NEW.

◆ FindRank()

unsigned int FindRank	(	double	epsilon,
		unsigned int	nr,
		unsigned int	nc,
		double *	mT
	)

Determines the rank of a matrix, i.e. the dimension of the space spanned by the rows/column of the matrix.

For a given problem, the number of variables minus the rank of the Jacobian gives the dimensionality of the solution space, assuming that the Jacobian is evaluated in a regular point. The dimensionality of the solution space is the same as that of its tangent space.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

epsilon	Numerical accuracy.
nr	Number of rows of the matrix (no transposed).
nc	Number of columns of the matrix (no transposed).
mT	The TRANSPOSED matrix. This matrix is overwriten inside this function!!

Returns: The rank of the matrix. NO_UINT if the rank can not be computed.

Definition at line 1724 of file algebra.c.

References AnalyzeKernel(), FALSE, and TRUE.

Referenced by ManifoldDimension().

◆ FindKernel()

unsigned int FindKernel	(	unsigned int	nr,
		unsigned int	nc,
		double *	mT,
		unsigned int	dof,
		boolean	check,
		double	epsilon,
		double **	T
	)

Defines a basis of the null space of a matrix.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

nr	Number of rows of the matrix (no transposed).
nc	Numbe of columns of the matrix (no transposed).
mT	The TRANSPOSED matrix stored as a vector. This matrix is overwriten inside this function!!
dof	Expected dimension of the kernel.
check	If TRUE the function introduces some consistancy checks (whether the kernel dimensionality is larger or smaller than the expected one).
epsilon	Values below epsilon are taken as zero.
T	The output kernel. This is a (nc x dof) matrix (stored as a vector). The space for this matrix is allocated in this function but must be de-allocated externally.

Returns: 0 if all the operations are correct, 1 if there the kernel is too large (i.e., the given point is singular), 2 if the chart could not be defined since the kernel is too small at the given point, and 3 if there is an error while performing QR decomposition. These outputs come directly from AnalyzeKernel.

Definition at line 1738 of file algebra.c.

References AnalyzeKernel(), FALSE, and TRUE.

Referenced by FindRightNullVector(), and RefineSingularPoint().

◆ FindKernelAndRank()

unsigned int FindKernelAndRank	(	unsigned int	nr,
		unsigned int	nc,
		double *	mT,
		unsigned int *	rank,
		double	epsilon,
		double **	T
	)

Defines a basis of the null space of a matrix, without any clue about the dimension of this null space. The returne rank is actually the number of variables minus the dimension of such space.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

nr	Number of rows of the matrix (no transposed).
nc	Numbe of columns of the matrix (no transposed).
mT	The TRANSPOSED matrix stored as a vector. This matrix is overwriten inside this function!!
rank	The rank of the input matrix: number of variables (columns) minus dimension of the output null space (num columns of the matrix representing the matrix).
epsilon	Values below epsilon are taken as zero.
T	The output kernel. This is a (nc x dof) matrix (stored as a vector). The space for this matrix is allocated in this function but must be de-allocated externally.

Returns: 0 if all the operations are correct and 3 if there is an error while performing QR decomposition. These outputs come directly from AnalyzeKernel.

Definition at line 1752 of file algebra.c.

References AnalyzeKernel(), FALSE, and TRUE.

◆ FindKernelAndIndependentRows()

unsigned int FindKernelAndIndependentRows	(	unsigned int	nr,
		unsigned int	nc,
		double *	mT,
		unsigned int	dof,
		double	epsilon,
		boolean *	singular,
		boolean **	IR,
		double **	T
	)

Defines a basis of the null space of a matrix and determines a subset of the rows of the matrix that are independent.

This is useful because in our case most (all?) the matrices have redundancy (i.e., rows that are linearly dependent on other rows). However, for some purposes we need to determine a subset of the rows that are linearly independent.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

nr	Number of rows of the matrix (no transposed).
nc	Numbe of columns of the matrix (no transposed).
mT	The TRANSPOSED matrix stored as a vector. This matrix is overwriten inside this function!!
dof	Expected dimension of the kernel. If zero, the function tries to determine the rank automatically.
epsilon	Values below epsilon are taken as zero.
singular	TRUE if the matrix is singular (has more null eigen values than the expected ones). Output.
IR	The set of independent rows as a boolean vector with as many entriees as rows in the input matrix and TRUE for the independent rows. The space for this vector is allocated here but must be deallocated externally. If the matrix is singular this contains the most likely basis of the matrix (up to the numerical accuracy). Caution must be taken to use this output in this case.
T	The output kernel. This is a (nc x dof) matrix (stored as a vector). The space for this matrix is allocated in this function but must be de-allocated externally.

Returns: 0 if all the operations are correct, 1 if there the kernel is too large (i.e., the given point is singular), 2 if the chart could not be defined since the kernel is too small at the given point, and 3 if there is an error while performing QR decomposition. These outputs come directly from AnalyzeKernel.

Definition at line 1765 of file algebra.c.

References AnalyzeKernel(), FALSE, and TRUE.

Referenced by ComputeJacobianKernelBasis().

◆ FindIndependentRows()

unsigned int FindIndependentRows	(	unsigned int	nr,
		unsigned int	nc,
		double *	mT,
		unsigned int	dof,
		double	epsilon,
		boolean *	singular,
		boolean **	IR
	)

Determines a subset of the rows of a matrix that are independent.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

nr	Number of rows of the matrix (no transposed).
nc	Numbe of columns of the matrix (no transposed).
mT	The TRANSPOSED matrix stored as a vector. This matrix is overwriten inside this function!!
dof	Expected dimension of the kernel. If zero, the function tries to determine the rank automatically.
epsilon	Values below epsilon are taken as zero.
singular	TRUE if the matrix is singular (has more null eigen values than the expected ones). Output.
IR	The set of independent rows as a boolean vector with as many entriees as rows in the input matrix and TRUE for the independent rows. The space for this vector is allocated here but must be deallocated externally. If the matrix is singular this contains the most likely basis of the matrix (up to the numerical accuracy). Caution must be taken to use this output in this case.

Returns: 0 if all the operations are correct, 1 if there the kernel is too large (i.e., the given point is singular), 2 if the chart could not be defined since the kernel is too small at the given point, and 3 if there is an error while performing QR decomposition. These outputs come directly from AnalyzeKernel.

Definition at line 1779 of file algebra.c.

References AnalyzeKernel(), FALSE, and TRUE.

Referenced by GetPositionJacobian().

◆ InvertMatrix()

boolean InvertMatrix	(	unsigned int	nr,
		double *	A
	)

Computes the inverse of a matrix.

Parameters

nr	Number of rows (and columns) of the matrix.
A	A square matrix.

Returns: TRUE if the inverse is computed correctly.

◆ InitNewton()

void InitNewton	(	unsigned int	nr,
		unsigned int	nc,
		TNewton *	n
	)

Initializes the structure to be used in a iterative Newton process.

Note that the dimensionality of the solution set can be deduced at each Newton step (using the QR with pivoting) but it is more efficient if we know it beforehand.

Parameters

nr	Number of rows.
nc	Number of columns.
n	The Newton structure to initialize.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ GetNewtonMatrixBuffer()

double* GetNewtonMatrixBuffer ( TNewton * n )

inline

Buffer to store the Newton matrix.

This buffer must be accessed using the RC2INDEX macro since the matrix can be stored row major or column major depending on the underlying lineal algebra library being used.

Parameters

n	The Newton structure.

Returns: A pointer to the buffer where to store the matrix.

Definition at line 1794 of file algebra.c.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ GetNewtonRHBuffer()

double* GetNewtonRHBuffer ( TNewton * n )

inline

Buffer to store the Newton RH.

Parameters

n	The Newton structure.

Returns: A pointer to the buffer where to store the RH.

Definition at line 1799 of file algebra.c.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ NewtonSetMatrix()

void NewtonSetMatrix	(	unsigned int	i,
		unsigned int	j,
		double	v,
		TNewton *	n
	)

inline

Sets one element of the matrix to be used in one Newton step. This matrix is typically initilized externally, but here we provide a mehtod to set it.

Parameters

i	The row.
j	The column.
v	The new value.
n	The Newton structure to set.

Definition at line 1804 of file algebra.c.

References RC2INDEX.

Referenced by CuikNewtonInBox().

◆ NewtonSetRH()

void NewtonSetRH	(	unsigned int	i,
		double	v,
		TNewton *	n
	)

inline

Sets one element of the vector to be used in one Newton step. This vector is typically initilized externally, but here we provide a mehtod to set it.

Parameters

i	The index in the vector.
v	The new value.
n	The Newton structure to set.

Definition at line 1809 of file algebra.c.

Referenced by CuikNewtonInBox().

◆ NewtonStep()

int NewtonStep	(	double	nullSingularValue,
		double *	x,
		double *	dif,
		TNewton *	n
	)

Computes and applies the correction in one step of a Newton iteration.

This function allows to easily apply Newton processes just defining the input data (A, b), setting the initial value for x, and allocating space for the process. The space for the process is not allocated inside this function to avoid continous malloc/free calls since this function is typically used many times in a row.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

nullSingularValue	Singular values below this are set to zero.
x	The current approximation to the system solution. This is updated internally.
dif	Norm of the change applied to x.
n	The Newton information.

Returns: 0 if no error is encountered in the Newton step.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ DeleteNewton()

void DeleteNewton ( TNewton * n )

Releases the memory allocated for a Newton step.

Parameters

n	A Newton structure.

Referenced by CuikNewtonInBox(), CuikNewtonSimp(), Newton2ManifoldPlane(), and RefineSingularPoint().

◆ InitBroyden()

void InitBroyden	(	unsigned int	nr,
		unsigned int	nc,
		TBroyden *	b
	)

Initializes the structure to be used in a iterative Broyden process.

Note that the dimensionality of the solution set can be deduced at each Broyden step (using the QR with pivoting) but it is more efficient if we know it beforehand.

Parameters

nr	Number of rows.
nc	Number of columns.
b	The Broyden structure to initialize.

Definition at line 1839 of file algebra.c.

References Error(), GetLSMatrixBuffer(), GetLSRHBuffer(), GetLSSolutionBuffer(), InitLS(), and NEW.

Referenced by InitDynamicSpace().

◆ ResetBroyden()

void ResetBroyden ( TBroyden * b )

inline

Resets the Broyden structure (the internal iteration) without releasing memory.

Parameters

b	The Broyden structure to initialize.

Definition at line 1862 of file algebra.c.

Referenced by NextDynamicState().

◆ GetBroydenMatrixBuffer()

double* GetBroydenMatrixBuffer ( TBroyden * b )

inline

Buffer to store the Broyden matrix.

This buffer must be accessed using the RC2INDEX macro since the matrix can be stored row major or column major depending on the underlying lineal algebra library being used.

Parameters

b	The Broyden structure.

Returns: A pointer to the buffer where to store the matrix.

Definition at line 1867 of file algebra.c.

References Error().

Referenced by InitDynamicSpace().

◆ GetBroydenRHBuffer()

double* GetBroydenRHBuffer ( TBroyden * b )

inline

Buffer to store the Broyden RH.

Parameters

b	The Broyden structure.

Returns: A pointer to the buffer where to store the RH.

Definition at line 1874 of file algebra.c.

Referenced by InitDynamicSpace().

◆ BroydenStep()

int BroydenStep	(	double	epsilon,
		unsigned int *	tp,
		double *	x,
		TBroyden *	b
	)

Computes and applies the correction in one step of a Broyden iteration. Calls the Newton iteration with the current Jacobian matrix and updates this matrix.

The result is stored in the right-hand side buffer.

Parameters

epsilon	Numerical accuracy.
tp	Topology of the variables.
x	The current approximation to the system solution. This is updated internally.
b	The Broyden information.

Returns: 0 if no error is encountered in the Broyden step.

Definition at line 1879 of file algebra.c.

References LSSolve(), NEW, Norm(), PI2PI, PrintMatrix(), PrintVector(), and TOPOLOGY_S.

Referenced by NextDynamicState().

◆ BroydenUpdateJacobian()

void BroydenUpdateJacobian	(	double	epsilon,
		TBroyden *	b
	)

Applies the Broyden's Jacobian update procedure. This can only be used after using BroydenStep at least once.

Parameters

epsilon	The numerical accuracy.
b	The Broyden structure.

Definition at line 1952 of file algebra.c.

References AccumulateVector(), DifferenceVector(), GeneralDotProduct(), MatrixVectorProduct(), and RankOneUpdate().

Referenced by NextDynamicState().

◆ DeleteBroyden()

void DeleteBroyden ( TBroyden * b )

Releases the memory allocated for a Broyden step.

Parameters

b	A Broyden structure.

Definition at line 1987 of file algebra.c.

References DeleteLS().

Referenced by DeleteDynamicSpace().

◆ InitLS()

void InitLS	(	unsigned int	nr,
		unsigned int	nc,
		unsigned int	nrh,
		TLinearSystem *	ls
	)

Initializes the structure to be used when solving a linear system.

Parameters

nr	Number of rows.
nc	Number of columns.
nrh	Number of right hand terms.
ls	The linear system structure to initialize.

Referenced by Chart2Manifold(), InitBroyden(), InitDynamicSpace(), and SetLinearizedDynamics().

◆ GetLSMatrixBuffer()

double* GetLSMatrixBuffer ( TLinearSystem * ls )

inline

Buffer to store the A matrix.

This buffer must be accessed using the RC2INDEX macro since the matrix can be stored row major or column major depending on the underlying lineal algebra library being used.

Parameters

ls	The linear system structure.

Returns: A pointer to the buffer where to store the matrix.

Definition at line 1814 of file algebra.c.

Referenced by Chart2Manifold(), InitBroyden(), InitDynamicSpace(), and SetLinearizedDynamics().

◆ GetLSRHBuffer()

double* GetLSRHBuffer ( TLinearSystem * ls )

inline

Buffer to store the linear system RH.

Parameters

ls	The linear system structure.

Returns: A pointer to the buffer where to store the RH.

Definition at line 1819 of file algebra.c.

Referenced by Chart2Manifold(), InitBroyden(), InitDynamicSpace(), and SetLinearizedDynamics().

◆ GetLSSolutionBuffer()

double* GetLSSolutionBuffer ( TLinearSystem * ls )

inline

Buffer to store the linear sytem solution. Note that this maybe the same as the buffer for the rhs.

Parameters

ls	The linear system structure.

Returns: A pointer to the buffer where to store the solution.

Definition at line 1824 of file algebra.c.

Referenced by Chart2Manifold(), ComputeAcceleration(), InitBroyden(), InitDynamicSpace(), and SetLinearizedDynamics().

◆ LSSetMatrix()

void LSSetMatrix	(	unsigned int	i,
		unsigned int	j,
		double	v,
		TLinearSystem *	ls
	)

inline

Sets one element of the matrix to be used in a linear system.

Parameters

i	The row.
j	The column.
v	The new value.
ls	The linear system structure.

Definition at line 1829 of file algebra.c.

References RC2INDEX.

◆ LSSetRH()

void LSSetRH	(	unsigned int	i,
		unsigned int	j,
		double	v,
		TLinearSystem *	ls
	)

inline

Sets one element of the right hand vector of a linear system.

Parameters

i	The row index.
j	The column index.
v	The new value.
ls	The linear system structure.

Definition at line 1834 of file algebra.c.

References RC2INDEX.

◆ LSSolve()

int LSSolve ( TLinearSystem * ls )

Computes the solution of a linear system.

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

ls	The linear system to solve.

Returns: 0 if no error is encountered when solving the system.

Referenced by BroydenStep(), Chart2Manifold(), ComputeAcceleration(), ComputeInverseDynamics(), and SetLinearizedDynamics().

◆ LSSolveCond()

int LSSolveCond	(	double *	rcond,
		TLinearSystem *	ls
	)

Computes the solution of a linear system only and returns the the reciprocal of the condition number of the system matrix. This provides information about the confidence in the solution (solutions with low condition number are not reliable).

Since we compute 1 / ( norm(A) * norm(inv(A)) ), we only implement this option for squared systems (otherwise inv(A) would not be defined).

IMPORTANT: The intput matrix may be modified inside this function. The caller CAN NOT assume that it remains unchanged.

Parameters

rcond	The condition number. Returned mainly for debugging purposes.
ls	The linear system to solve.

Returns: 0 if no error is encountered when solving the system.

Referenced by LQRComputePolicy(), and LQRComputePolicy_t().

◆ DeleteLS()

void DeleteLS ( TLinearSystem * ls )

Releases the memory allocated for a linear system.

Parameters

ls	A linear system structure.

Referenced by Chart2Manifold(), DeleteBroyden(), DeleteDynamicSpace(), and SetLinearizedDynamics().

Institut de Robòtica i Informàtica Industrial

Introduction

Data Structures

Macros

Functions

Macro Definition Documentation

◆ DAMPED_NEWTON

◆ DN_F

◆ DN_MF

◆ DN_W

Function Documentation

◆ MatrixDeterminantSgn()

◆ MatrixDeterminant()

◆ MatrixExponential()

◆ MatrixExponentialVector()

◆ FindRank()

◆ FindKernel()

◆ FindKernelAndRank()

◆ FindKernelAndIndependentRows()

◆ FindIndependentRows()

◆ InvertMatrix()

◆ InitNewton()

◆ GetNewtonMatrixBuffer()

◆ GetNewtonRHBuffer()

◆ NewtonSetMatrix()

◆ NewtonSetRH()

◆ NewtonStep()

◆ DeleteNewton()

◆ InitBroyden()

◆ ResetBroyden()

◆ GetBroydenMatrixBuffer()

◆ GetBroydenRHBuffer()

◆ BroydenStep()

◆ BroydenUpdateJacobian()

◆ DeleteBroyden()

◆ InitLS()

◆ GetLSMatrixBuffer()

◆ GetLSRHBuffer()

◆ GetLSSolutionBuffer()

◆ LSSetMatrix()

◆ LSSetRH()

◆ LSSolve()

◆ LSSolveCond()

◆ DeleteLS()

Institut de Robòtica
i Informàtica Industrial