Linear algebra

Collaboration diagram for Linear algebra:

Macros
#define	SVDMAXITER   1000

Functions
int	AllocateMatrix (double **Matrix, long Lines, long Columns, int *Status)
int	AllocateVector (double *(Vector[]), long Lines, int *Status)
int	FreeMatrix (double **Matrix)
int	FreeVector (double *(Vector[]))
int	FrobeniusNorm (double *A, double *Norm, long Lines, long Columns)
int	GetIdentitySquareMatrix (double *A, long Size)
int	LinearLeastSquares (double *A, long Lines, long Columns, double B[], double X[], double Tolerance, int *Status)
int	MatrixAdd (double *A, double *B, double *X, long Lines, long Columns)
int	MatrixConditionNumber (double *A, long Lines, long Columns, double *ConditionNumber, double Tolerance, long MaxIterations, int *Status)
int	MatrixGramSchmidtOrthonormalize (double *A, double *B, long Lines, long Columns, double Tolerance)
int	MatrixMinor (double *A, double *B, long Lines, long Columns, long i, long j)
int	MatrixMultiply (double *A, double *B, double *X, long Lines, long CommonSize, long Columns)
int	MatrixRank (double *A, long Lines, long Columns, long *Rank, double Tolerance, long MaxIterations, int *Status)
int	MatrixSubtract (double *A, double *B, double *X, long Lines, long Columns)
int	MatrixTimesVector (double *A, double *B, double *X, long Lines, long Columns)
int	MatrixTranspose (double *A, double *At, long Lines, long Columns)
int	multiply_3Matrices (double *A, double *B, double *C, double *X, long Lines, long CommonSizeH, long CommonSizeW, long Columns)
int	multiply_4Matrices (double *A, double *B, double *C, double *D, double *X, long Lines, long CommonSizeH1, long CommonSizeW1, long CommonSizeW2, long Columns)
int	multiply_5Matrices (double *A, double *B, double *C, double *D, double *E, double *X, long Lines, long CommonSizeH1, long CommonSizeW1, long CommonSizeW2, long CommonSizeH2, long Columns)
int	QRdecomposition (double *Q, double *R, long Lines, long Columns, double Tolerance, int *Status)
int	SingularValueBackSubstitution (double *U, double W[], double *V, long Lines, long Columns, double B[], double X[], int *Status)
int	SingularValueDecomposition (double *U, long Lines, long Columns, double W[], double *V, long MaxIterations, int *Status)
int	SquareMatrixDeterminant (double *A, long Size, double *Determinant, int *Status)
int	SquareMatrixInvertGauss (double *Direct, double *Inverse, long Size, double Tolerance, int *Status)
int	SquareMatrixSquareRoot (double *A, double *B, long Size, double Tolerance, long MaxIterations, int *Status)
int	SquareMatrixTrace (double *A, double *Trace, long Size)
int	Vector3DcrossProduct (double A[], double B[], double X[])
int	VectorAdd (double A[], double B[], double X[], long Lines)
int	VectorAngle (double A[], double B[], double *Angle, long Lines, double Tolerance)
int	VectorHomogenize (double A[], double X[], long Lines, double Tolerance)
int	VectorNorm (double A[], double *Norm, long Lines)
int	VectorNormalize (double A[], double X[], long Lines)
int	VectorScalarProduct (double A[], double B[], double *X, long Lines)
int	VectorScale (double A[], double X[], double Scale, long Lines)
int	VectorSubtract (double A[], double B[], double X[], long Lines)

Detailed Description

Macro Definition Documentation

SVDMAXITER

#define SVDMAXITER   1000

Definition at line 257 of file linearalgebra.h.

Function Documentation

AllocateMatrix()

int AllocateMatrix	(	double **	Matrix,
		long	Lines,
		long	Columns,
		int *	Status
	)

AllocateVector()

int AllocateVector	(	double *	Vector[],
		long	Lines,
		int *	Status
	)

FreeMatrix()

int FreeMatrix

(

double **

Matrix

)

FreeVector()

int FreeVector

(

double *

Vector[]

)

FrobeniusNorm()

int FrobeniusNorm	(	double *	A,
		double *	Norm,
		long	Lines,
		long	Columns
	)

Compute the Frobenius norm of the matrix A. The size of A is (Lines x Columns). success: return(!ERROR); failure: return(ERROR)

GetIdentitySquareMatrix()

int GetIdentitySquareMatrix	(	double *	A,
		long	Size
	)

LinearLeastSquares()

int LinearLeastSquares	(	double *	A,
		long	Lines,
		long	Columns,
		double	B[],
		double	X[],
		double	Tolerance,
		int *	Status
	)

MatrixAdd()

int MatrixAdd	(	double *	A,
		double *	B,
		double *	X,
		long	Lines,
		long	Columns
	)

MatrixConditionNumber()

int MatrixConditionNumber	(	double *	A,
		long	Lines,
		long	Columns,
		double *	ConditionNumber,
		double	Tolerance,
		long	MaxIterations,
		int *	Status
	)

Compute the condition number of the matrix A. The size of A is (Lines x Columns). ConditionNumber = -1.0 indicates a singular matrix.

success: return(!ERROR); failure: return(ERROR)

MatrixGramSchmidtOrthonormalize()

int MatrixGramSchmidtOrthonormalize	(	double *	A,
		double *	B,
		long	Lines,
		long	Columns,
		double	Tolerance
	)

Orthonormalize a matrix. The size of A and B is (Lines x Columns). The orthogonalization proceeds row-wise.

success: return(!ERROR); failure: return(ERROR)

MatrixMinor()

int MatrixMinor	(	double *	A,
		double *	B,
		long	Lines,
		long	Columns,
		long	i,
		long	j
	)

Extract a minor matrix B from the major matrix A. The size of A is (Lines x Columns). The size of B is ((Lines - 1) x (Columns - 1)). The line to delete is i (indexing starts from 0). The column to delete is j (indexing starts from 0).

success: return(!ERROR); failure: return(ERROR)

MatrixMultiply()

int MatrixMultiply	(	double *	A,
		double *	B,
		double *	X,
		long	Lines,
		long	CommonSize,
		long	Columns
	)

MatrixRank()

int MatrixRank	(	double *	A,
		long	Lines,
		long	Columns,
		long *	Rank,
		double	Tolerance,
		long	MaxIterations,
		int *	Status
	)

Compute the rank of the matrix A. The size of A is (Lines x Columns).

success: return(!ERROR); failure: return(ERROR)

MatrixSubtract()

int MatrixSubtract	(	double *	A,
		double *	B,
		double *	X,
		long	Lines,
		long	Columns
	)

MatrixTimesVector()

int MatrixTimesVector	(	double *	A,
		double *	B,
		double *	X,
		long	Lines,
		long	Columns
	)

MatrixTranspose()

int MatrixTranspose	(	double *	A,
		double *	At,
		long	Lines,
		long	Columns
	)

multiply_3Matrices()

int multiply_3Matrices	(	double *	A,
		double *	B,
		double *	C,
		double *	X,
		long	Lines,
		long	CommonSizeH,
		long	CommonSizeW,
		long	Columns
	)

Multiply 3 Matrices. X=A*B*C; A is of size Lines x CommonSizeH, B is of size CommonSizeH x CommonSizeW, C is of size CommonSizeW x Columns. Finally, X is of size Lines x Columns.

multiply_4Matrices()

int multiply_4Matrices	(	double *	A,
		double *	B,
		double *	C,
		double *	D,
		double *	X,
		long	Lines,
		long	CommonSizeH1,
		long	CommonSizeW1,
		long	CommonSizeW2,
		long	Columns
	)

multiply_5Matrices()

int multiply_5Matrices	(	double *	A,
		double *	B,
		double *	C,
		double *	D,
		double *	E,
		double *	X,
		long	Lines,
		long	CommonSizeH1,
		long	CommonSizeW1,
		long	CommonSizeW2,
		long	CommonSizeH2,
		long	Columns
	)

QRdecomposition()

int QRdecomposition	(	double *	Q,
		double *	R,
		long	Lines,
		long	Columns,
		double	Tolerance,
		int *	Status
	)

Decompose the (Lines x Columns) input matrix Q into an orthonormal. Output matrix Q of same size (Lines x Columns) and an upper-diagonal. Square matrix R of size (Columns x Columns), such that the matrix. Product (Q * R) gives the input matrix, and such that the matrix. Product (Q^T * Q) gives the identity.

requirement: Columns <= Lines

success: return(!ERROR); failure: return(ERROR)

SingularValueBackSubstitution()

int SingularValueBackSubstitution	(	double *	U,
		double	W[],
		double *	V,
		long	Lines,
		long	Columns,
		double	B[],
		double	X[],
		int *	Status
	)

SingularValueDecomposition()

int SingularValueDecomposition	(	double *	U,
		long	Lines,
		long	Columns,
		double	W[],
		double *	V,
		long	MaxIterations,
		int *	Status
	)

SquareMatrixDeterminant()

int SquareMatrixDeterminant	(	double *	A,
		long	Size,
		double *	Determinant,
		int *	Status
	)

SquareMatrixInvertGauss()

int SquareMatrixInvertGauss	(	double *	Direct,
		double *	Inverse,
		long	Size,
		double	Tolerance,
		int *	Status
	)

SquareMatrixSquareRoot()

int SquareMatrixSquareRoot	(	double *	A,
		double *	B,
		long	Size,
		double	Tolerance,
		long	MaxIterations,
		int *	Status
	)

Compute one out of the 2^Size square roots B of a matrix A such that B.B = A. The size of the matrices A and B is (Size x Size). B must provide an initial solution.

success: return(!ERROR); failure: return(ERROR)

SquareMatrixTrace()

int SquareMatrixTrace	(	double *	A,
		double *	Trace,
		long	Size
	)

Perform the vector cross product X = A x B. The size of A is (Size x Size)

success: return(!ERROR); failure: return(ERROR)

Vector3DcrossProduct()

int Vector3DcrossProduct	(	double	A[],
		double	B[],
		double	X[]
	)

VectorAdd()

int VectorAdd	(	double	A[],
		double	B[],
		double	X[],
		long	Lines
	)

VectorAngle()

int VectorAngle	(	double	A[],
		double	B[],
		double *	Angle,
		long	Lines,
		double	Tolerance
	)

Compute the angle between two vectors *(n-D). The size of A and B is (Lines x 1). The angle unit is radian.

success: return(!ERROR); failure: return(ERROR)

VectorHomogenize()

int VectorHomogenize	(	double	A[],
		double	X[],
		long	Lines,
		double	Tolerance
	)

Convert a vector from non-homogenous to homogenous coordinates. Satisfy (Vout = a * Vin) such that (Vout[last] = 1.0). The size of A and X is (Lines x 1).

success: return(!ERROR); failure: return(ERROR)

VectorNorm()

int VectorNorm	(	double	A[],
		double *	Norm,
		long	Lines
	)

VectorNormalize()

int VectorNormalize	(	double	A[],
		double	X[],
		long	Lines
	)

VectorScalarProduct()

int VectorScalarProduct	(	double	A[],
		double	B[],
		double *	X,
		long	Lines
	)

VectorScale()

int VectorScale	(	double	A[],
		double	X[],
		double	Scale,
		long	Lines
	)

VectorSubtract()

int VectorSubtract	(	double	A[],
		double	B[],
		double	X[],
		long	Lines
	)