nmrIsOrthonormal.h File Reference

Declaration of functions nmrIsOrthonormal. More...

#include <cisstVector/vctFixedSizeMatrix.h>
#include <cisstVector/vctDynamicMatrix.h>

Go to the source code of this file.

Classes
class	nmrIsOrthonormalDynamicData< _elementType >
	Data (workspace) for nmrIsOrthonormal (Dynamic). More...
class	nmrIsOrthonormalDynamicData< _elementType >::Friend
class	nmrIsOrthonormalFixedSizeData< _elementType, _rows >
	Data for nmrIsOrthonormal (Fixed size). More...
class	nmrIsOrthonormalFixedSizeData< _elementType, _rows >::Friend

Functions
nmrIsOrthonormal: Check if a matrix is orthonormal
This function computes the product of the matrix with its transpose then subtracts the identity and verifies that all elements are null within some tolerance. This function is overloaded to be used with either a fixed size or a dynamic matrix (see vctFixedSizeMatrix and vctDynamicMatrix). Furthermore, it is possible to provide a workspace to store the product of the matrix and its transpose and avoid any undesired memory allocation: The workspace can be provided using the dedicated classes nmrIsOrthonormalDynamicData and nmrIsOrthonormalFixedSizeData. The user has to create the data based on the matrix to be tested and then pass it to nmrIsOrthonormal: vctDynamicMatrix<double> A(9, 9); nmrIsOrthonormalDynamicData<double> data(A); int i; bool result; for (i = 0; i < 100; i++) { vctRandom(A, -10.0, 10.0); result = nmrIsOrthonormal(A, data); ... } The workspace can be provided as a dynamic vector (vctDynamicVector) large enough to store the product of the matrix with its transpose: vctDynamicMatrix<double> A(12, 12); vctRandom(A, -10.0, 10.0); vctDynamicVector<double> workspace(500); // we need at least 12x12 bool result = nmrIsOrthonormal(A, workspace); If no workspace is provided the nmrIsOrthonormal function will allocate one for you. This might be more convenient for most users but one must be aware that a memory allocation has to be performed (stack allocation for fixed size matrices, dynamic allocation for dynamic matrices): vctFixedSizeMatrix<double, 5, 5> A; vctRandom(A, -10.0, 10.0); bool result = nmrIsOrthonormal(A); Note For a dynamic matrix, the function will throw an exception is the matrix is not square (std::runtime_error). The workspace needs to be compact and large enough otherwise nmrIsOrthonormal will throw an exception (std::runtime_error). See Also nmrIsOrthonormalDynamicData nmrIsOrthonormalFixedSizeData
template<vct::size_type _size, vct::stride_type _rowStride, vct::stride_type _colStride, typename _elementType , class _dataPtrType >
bool	nmrIsOrthonormal (const vctFixedSizeConstMatrixBase< _size, _size, _rowStride, _colStride, _elementType, _dataPtrType > &A, nmrIsOrthonormalFixedSizeData< _elementType, _size > &data, _elementType tolerance=cmnTypeTraits< _elementType >::Tolerance())
template<vct::size_type _size, vct::stride_type _rowStride, vct::stride_type _colStride, typename _elementType , class _dataPtrType >
bool	nmrIsOrthonormal (const vctFixedSizeConstMatrixBase< _size, _size, _rowStride, _colStride, _elementType, _dataPtrType > &A, _elementType tolerance=cmnTypeTraits< _elementType >::Tolerance())
template<class _matrixOwnerTypeA , class _elementType >
bool	nmrIsOrthonormal (const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &A, nmrIsOrthonormalDynamicData< _elementType > &data, _elementType tolerance=cmnTypeTraits< _elementType >::Tolerance()) throw (std::runtime_error)
template<class _matrixOwnerTypeA , typename _elementType >
bool	nmrIsOrthonormal (const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &A, _elementType tolerance=cmnTypeTraits< _elementType >::Tolerance()) throw (std::runtime_error)
template<class _matrixOwnerTypeA , class _vectorOwnerTypeWorkspace , typename _elementType >
bool	nmrIsOrthonormal (const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &A, vctDynamicVectorBase< _vectorOwnerTypeWorkspace, _elementType > &workspace, _elementType tolerance=cmnTypeTraits< _elementType >::Tolerance()) throw (std::runtime_error)

Detailed Description

Declaration of functions nmrIsOrthonormal.

Function Documentation

template<vct::size_type _size, vct::stride_type _rowStride, vct::stride_type _colStride, typename _elementType , class _dataPtrType >

bool nmrIsOrthonormal	(	const vctFixedSizeConstMatrixBase< _size, _size, _rowStride, _colStride, _elementType, _dataPtrType > &	A,
		nmrIsOrthonormalFixedSizeData< _elementType, _size > &	data,
		_elementType	tolerance = cmnTypeTraits<_elementType>::Tolerance()
	)

This function checks if a fixed size matrix is orthonormal. It uses a data (see nmrIsOrthonormalFixedSizeData) to store the temporary product of the matrix with its transpose.

Parameters

A	A square fixed size matrix
data	Workspace used to compute the product
tolerance	Tolerance used to compare the product with identity

template<vct::size_type _size, vct::stride_type _rowStride, vct::stride_type _colStride, typename _elementType , class _dataPtrType >

bool nmrIsOrthonormal	(	const vctFixedSizeConstMatrixBase< _size, _size, _rowStride, _colStride, _elementType, _dataPtrType > &	A,
		_elementType	tolerance = cmnTypeTraits<_elementType>::Tolerance()
	)

This function checks if a fixed size matrix is orthonormal. It creates a data on the stack to store the temporary product of the matrix with its transpose.

Parameters

A	A square fixed size matrix
tolerance	Tolerance used to compare the product with identity

template<class _matrixOwnerTypeA , class _elementType >

bool nmrIsOrthonormal	(	const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &	A,
		nmrIsOrthonormalDynamicData< _elementType > &	data,
		_elementType	tolerance = cmnTypeTraits<_elementType>::Tolerance()
	)
throw	(	std::runtime_error
	)

This function checks if a dynamic matrix is orthonormal. It uses a data (see nmrIsOrthonormalDynamicData) to store the temporary product of the matrix with its transpose.

Parameters

A	A square dynamic matrix
data	Workspace used to compute the product
tolerance	Tolerance used to compare the product with identity

template<class _matrixOwnerTypeA , typename _elementType >

bool nmrIsOrthonormal	(	const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &	A,
		_elementType	tolerance = cmnTypeTraits<_elementType>::Tolerance()
	)
throw	(	std::runtime_error
	)

This function checks if a dynamic matrix is orthonormal. It dynamically allocates a data to store the temporary product of the matrix with its transpose.

Parameters

A	A square dynamic matrix
tolerance	Tolerance used to compare the product with identity

template<class _matrixOwnerTypeA , class _vectorOwnerTypeWorkspace , typename _elementType >

bool nmrIsOrthonormal	(	const vctDynamicConstMatrixBase< _matrixOwnerTypeA, _elementType > &	A,
		vctDynamicVectorBase< _vectorOwnerTypeWorkspace, _elementType > &	workspace,
		_elementType	tolerance = cmnTypeTraits<_elementType>::Tolerance()
	)
throw	(	std::runtime_error
	)

This function checks if a dynamic matrix is orthonormal. It uses a user allocated workspace to store the temporary product of the matrix with its transpose.

Parameters

A	A square dynamic matrix
workspace	Workspace used to compute the product
tolerance	Tolerance used to compare the product with identity