Linear algebra functions and classes

Functions
bool	gcgInverseMatrix2 (MATRIX2 inverse, MATRIX2 matrix)
	Computes the inverse of a 2x2 matrix by the direct method. It is suitable for fast inverse computation in bidimensional spaces. In this version, both input and output matrices are C vectors of 4 floats in row first order. More...
bool	gcgInverseMatrix3 (MATRIX3 inverse, MATRIX3 matrix)
	Computes the inverse of a 3x3 matrix by the direct method. It is suitable for fast inverse computation in tridimensional spaces. More...
bool	gcgInverseMatrix4 (MATRIX4 inverse, MATRIX4 matrix)
	Computes the inverse of a 4x4 matrix by the direct method. It is suitable for fast inverse computation in homogeneous spaces in computer graphics. In this version, both input and output matrices are C vectors of 16 floats in row first order. More...
bool	gcgInverseMatrix2 (MATRIX2d inverse, MATRIX2d matrix)
	Computes the inverse of a 2x2 matrix by the direct method. It is suitable for fast inverse computation in bidimensional spaces. In this version, both input and output matrices are C vectors of 4 doubles in row first order. More...
bool	gcgInverseMatrix3 (MATRIX3d inverse, MATRIX3d matrix)
	Computes the inverse of a 3x3 matrix by the direct method. It is suitable for fast inverse computation in tridimensional spaces. More...
bool	gcgInverseMatrix4 (MATRIX4d inverse, MATRIX4d matrix)
	Computes the inverse of a 4x4 matrix by the direct method. It is suitable for fast inverse computation in homogeneous spaces in computer graphics. In this version, both input and output matrices are C vectors of 16 doubles in row first order. More...
bool	gcgEigenSymmetric (int norder, float matrix[], float eigenvectors[], float eigenvalues[])
	Computes the eigensystem decomposition of a symmetric matrix matrix with arbitraty order. The resulted eigenvectors are stored as rows in a matrix eigenvectors with norder x norder elements. Their respective norder eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of norder x norder floats in row first order. More...
bool	gcgEigenSymmetric (int norder, double matrix[], double eigenvectors[], double eigenvalues[])
	Computes the eigensystem decomposition of a symmetric matrix matrix with arbitraty order. The resulted eigenvectors are stored as rows in a matrix eigenvectors with norder x norder elements. Their respective norder eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of norder x norder doubles in row first order. More...
bool	gcgEigenSymmetricMatrix3 (MATRIX3 matrix, MATRIX3 eigenvectors, VECTOR3 eigenvalues)
	Computes the eigensystem decomposition of a symmetric 3 x 3 matrix matrix. The resulted eigenvectors are stored as rows in a matrix eigenvectors with 3 x 3 elements. Their respective three eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of 3 x 3 floats in row first order. More...
bool	gcgEigenSymmetricMatrix3 (MATRIX3d matrix, MATRIX3d eigenvectors, VECTOR3d eigenvalues)
	Computes the eigensystem decomposition of a symmetric 3 x 3 matrix matrix. The resulted eigenvectors are stored as rows in a matrix eigenvectors with 3 x 3 elements. Their respective three eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of 3 x 3 doubles in row first order. More...

Detailed Description

GCGlib provides a minimum linear algebra functionality which serves as basis for several methods. It is the core of important computer vision and computer geometry algorithms.

Function Documentation

gcgEigenSymmetric() [1/2]

bool gcgEigenSymmetric	(	int	norder,
		float	matrix[],
		float	eigenvectors[],
		float	eigenvalues[]
	)

Computes the eigensystem decomposition of a symmetric matrix matrix with arbitraty order. The resulted eigenvectors are stored as rows in a matrix eigenvectors with norder x norder elements. Their respective norder eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of norder x norder floats in row first order.

Parameters

[in]	norder	order of the input square matrix.
[in]	matrix	pointer to a square matrix of norder x norder elements stored in row first order.
[out]	eigenvectors	pointer to a square matrix of norder x norder elements that will receive the norder eigenvectors of the input matrix arranged by row first order.
[out]	eigenvalues	pointer to a vector of norder elements that will receive the eigenvalues of the input matrix. They are stored by decreasing eigenvalues and their positions are respective to the eigenvectors positions in the matrix eigenvectors.

Returns

true if the eigensystem was correctly computed. If it returns false, the results returned in eigenvectors and eigenvalues are undefined. Check GCG_REPORT_MESSAGE(gcgGetReport()) for knowing the problem.

See also

gcgEigenSymmetricMatrix3

Since

0.01.0

gcgEigenSymmetric() [2/2]

bool gcgEigenSymmetric	(	int	norder,
		double	matrix[],
		double	eigenvectors[],
		double	eigenvalues[]
	)

Computes the eigensystem decomposition of a symmetric matrix matrix with arbitraty order. The resulted eigenvectors are stored as rows in a matrix eigenvectors with norder x norder elements. Their respective norder eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of norder x norder doubles in row first order.

Parameters

[in]	norder	order of the input square matrix.
[in]	matrix	pointer to a square matrix of norder x norder elements stored in row first order.
[out]	eigenvectors	pointer to a square matrix of norder x norder elements that will receive the norder eigenvectors of the input matrix arranged by row first order.
[out]	eigenvalues	pointer to a vector of norder elements that will receive the eigenvalues of the input matrix. They are stored by decreasing eigenvalues and their positions are respective to the eigenvectors positions in the matrix eigenvectors.

Returns

true if the eigensystem was correctly computed. If it returns false, the results returned in eigenvectors and eigenvalues are undefined. Check GCG_REPORT_MESSAGE(gcgGetReport()) for knowing the problem.

See also

gcgEigenSymmetricMatrix3

Since

0.01.0

gcgEigenSymmetricMatrix3() [1/2]

bool gcgEigenSymmetricMatrix3	(	MATRIX3	matrix,
		MATRIX3	eigenvectors,
		VECTOR3	eigenvalues
	)

Computes the eigensystem decomposition of a symmetric 3 x 3 matrix matrix. The resulted eigenvectors are stored as rows in a matrix eigenvectors with 3 x 3 elements. Their respective three eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of 3 x 3 floats in row first order.

Parameters

[in]	matrix	pointer to a square matrix of 3 x 3 elements stored in row first order.
[out]	eigenvectors	pointer to a square matrix of 3 x 3 elements that will receive the three eigenvectors of the input matrix arranged by row first order.
[out]	eigenvalues	pointer to a vector of three elements that will receive the eigenvalues of the input matrix. They are stored by decreasing eigenvalues and their positions are respective to the eigenvectors positions in the matrix eigenvectors.

Returns

true if the eigensystem was correctly computed. If it returns false, the results returned in eigenvectors and eigenvalues are undefined. Check GCG_REPORT_MESSAGE(gcgGetReport()) for knowing the problem.

See also

gcgEigenSymmetricMatrix

Since

0.01.0

gcgEigenSymmetricMatrix3() [2/2]

bool gcgEigenSymmetricMatrix3	(	MATRIX3d	matrix,
		MATRIX3d	eigenvectors,
		VECTOR3d	eigenvalues
	)

Computes the eigensystem decomposition of a symmetric 3 x 3 matrix matrix. The resulted eigenvectors are stored as rows in a matrix eigenvectors with 3 x 3 elements. Their respective three eigenvalues are stored in the vector eigenvalues. The eigenvectors and eigenvalues are ordered by decreasing eigenvalues. Version adapted from the public domain Java Matrix library JAMA. In this version, the input and output matrices are C vectors of 3 x 3 doubles in row first order.

Parameters

[in]	matrix	pointer to a square matrix of 3 x 3 elements stored in row first order.
[out]	eigenvectors	pointer to a square matrix of 3 x 3 elements that will receive the three eigenvectors of the input matrix arranged by row first order.
[out]	eigenvalues	pointer to a vector of three elements that will receive the eigenvalues of the input matrix. They are stored by decreasing eigenvalues and their positions are respective to the eigenvectors positions in the matrix eigenvectors.

Returns

true if the eigensystem was correctly computed. If it returns false, the results returned in eigenvectors and eigenvalues are undefined. Check GCG_REPORT_MESSAGE(gcgGetReport()) for knowing the problem.

See also

gcgEigenSymmetricMatrix

Since

0.01.0

gcgInverseMatrix2() [1/2]

bool gcgInverseMatrix2	(	MATRIX2	inverse,
		MATRIX2	matrix
	)

Computes the inverse of a 2x2 matrix by the direct method. It is suitable for fast inverse computation in bidimensional spaces. In this version, both input and output matrices are C vectors of 4 floats in row first order.

Parameters

[out]	inverse	Points to the 2x2 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint.
[in]	matrix	The input 2x2 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix3

gcgInverseMatrix4

Since

0.01.0

gcgInverseMatrix2() [2/2]

bool gcgInverseMatrix2	(	MATRIX2d	inverse,
		MATRIX2d	matrix
	)

Computes the inverse of a 2x2 matrix by the direct method. It is suitable for fast inverse computation in bidimensional spaces. In this version, both input and output matrices are C vectors of 4 doubles in row first order.

Parameters

[out]	inverse	Points to the 2x2 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint.
[in]	matrix	The input 2x2 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix3

gcgInverseMatrix4

Since

0.01.0

gcgInverseMatrix3() [1/2]

bool gcgInverseMatrix3	(	MATRIX3	inverse,
		MATRIX3	matrix
	)

Computes the inverse of a 3x3 matrix by the direct method. It is suitable for fast inverse computation in tridimensional spaces.

Parameters

[out]	inverse	Points to the 3x3 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint. In this version, both input and output matrices are C vectors of 9 floats in row first order.
[in]	matrix	The input 3x3 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix2

gcgInverseMatrix4

Since

0.01.0

gcgInverseMatrix3() [2/2]

bool gcgInverseMatrix3	(	MATRIX3d	inverse,
		MATRIX3d	matrix
	)

Computes the inverse of a 3x3 matrix by the direct method. It is suitable for fast inverse computation in tridimensional spaces.

Parameters

[out]	inverse	Points to the 3x3 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint. In this version, both input and output matrices are C vectors of 9 doubles in row first order.
[in]	matrix	The input 3x3 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix2

gcgInverseMatrix4

Since

0.01.0

gcgInverseMatrix4() [1/2]

bool gcgInverseMatrix4	(	MATRIX4	inverse,
		MATRIX4	matrix
	)

Computes the inverse of a 4x4 matrix by the direct method. It is suitable for fast inverse computation in homogeneous spaces in computer graphics. In this version, both input and output matrices are C vectors of 16 floats in row first order.

Parameters

[out]	inverse	Points to the 4x4 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint.
[in]	matrix	The input 4x4 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix2

gcgInverseMatrix3

Since

0.01.0

gcgInverseMatrix4() [2/2]

bool gcgInverseMatrix4	(	MATRIX4d	inverse,
		MATRIX4d	matrix
	)

Computes the inverse of a 4x4 matrix by the direct method. It is suitable for fast inverse computation in homogeneous spaces in computer graphics. In this version, both input and output matrices are C vectors of 16 doubles in row first order.

Parameters

[out]	inverse	Points to the 4x4 matrix that receives the inverted matrix of matrix parameter. If it is a singular matrix, it receives its adjoint.
[in]	matrix	The input 4x4 matrix to be inverted.

Returns

true if inverse exists and, in that case, the inverse parameter receives the inverted matrix. If returns false, the input matrix is singular and the inverse parameter receives its adjoint matrix.

See also

gcgInverseMatrix2

gcgInverseMatrix3

Since

0.01.0