loos::Math Namespace Reference

Namespace for math and math-related things in loos. More...

Classes
class	ColMajor
	Class for storing a matrix in column-major order. More...
class	Matrix
	Simple matrix template class using policy classes to determine behavior. More...
class	RowMajor
	Class for storing a matrix in row-major order... More...
class	SharedArray
	Storage policy for a block of memory wrapped in a boost::shared_array pointer. More...
class	SparseArray
	Storage policy for a sparse matrix (see important note in the detailed documentation). More...
class	Triangular
	Class for storing a symmetric triangular matrix. More...

Typedefs
typedef std::pair< uint, uint >	Range
	Specify a range for columns/rows [first,second)

Functions
greal	angle (const GCoord &, const GCoord &, const GCoord &, const GCoord *=NULL)
	Compute the angle in degrees assuming the middle is the vertex.
greal	angle (const pAtom &a, const pAtom &b, const pAtom &c, const GCoord *=NULL)
	Compute the angle in degrees assuming the middle is the vertex.
greal	torsion (const GCoord &a, const GCoord &b, const GCoord &c, const GCoord &d, const GCoord *=NULL)
	Compute the torsion in degrees.
greal	torsion (const pAtom &a, const pAtom &b, const pAtom &c, const pAtom &d, const GCoord *=NULL)
	Compute the torsion in degrees.
template<typename T , template< typename > class S>
Matrix< T, RowMajor, S >	reinterpretOrder (const Matrix< T, ColMajor, S > &)
template<typename T , template< typename > class S>
Matrix< T, ColMajor, S >	reinterpretOrder (const Matrix< T, RowMajor, S > &)
template<typename T , class P , template< typename > class S>
std::ostream &	operator<< (std::ostream &os, const Matrix< T, P, S > &M)
DoubleMatrix	eigenDecomp (DoubleMatrix &M)
	Compute eigendecomposition of M.
boost::tuple< RealMatrix, RealMatrix, RealMatrix >	svd (RealMatrix &M)
	Compute the SVD of a single precision matrix.
RealMatrix	MMMultiply (const RealMatrix &A, const RealMatrix &B, const bool transa=false, const bool transb=false)
	Matrix-matrix multiply (using BLAS)
RealMatrix	invert (RealMatrix &A, const float eps=1e-5)
	Pseudo-inverse of a matrix using the SVD.
DoubleMatrix	invert (DoubleMatrix &A, const double eps)
void	operator+= (RealMatrix &A, const RealMatrix &B)
	Overloaded operators for RealMatrix matrices (see important note below)
RealMatrix	operator+ (const RealMatrix &A, const RealMatrix &B)
void	operator-= (RealMatrix &A, const RealMatrix &B)
RealMatrix	operator- (const RealMatrix &A, const RealMatrix &B)
void	operator*= (RealMatrix &A, const float d)
RealMatrix	operator* (const RealMatrix &A, const float d)
void	operator*= (RealMatrix &A, const RealMatrix &B)
RealMatrix	operator* (const RealMatrix &A, const RealMatrix &B)
void	operator*= (DoubleMatrix &A, const double d)
DoubleMatrix	operator* (const DoubleMatrix &A, const double d)
RealMatrix	operator- (RealMatrix &A)
void	normalizeColumns (loos::DoubleMatrix &A)
	Normalizes each column as a column-vector.
DoubleMatrix	deye (const uint n)
template<typename T >
T	eye (const uint n)
	An identity matrix of size n.
template<typename T >
T	submatrix (const T &M, const Range &rows, const Range &cols)
	Extracts a submatrix.
template<typename T >
T	permuteColumns (const T &A, const std::vector< uint > &indices)
	Returns a copy of the matrix with the columns permuted by the indices.
template<typename T >
T	permuteRows (const T &A, const std::vector< uint > &indices)
	Returns a copy of the matrix with the rows permuted by the indices.
template<typename T >
T	transpose (const T &A)
	Transposes a matrix.
template<typename T >
T	shuffleColumns (const T &A)
	Randomly shuffle the columns of a matrix.
template<typename T >
T	shuffleColumnVector (const T &v)
	! Randomly shuffle the rows of a single column vector
template<typename T >
void	reverseColumns (T &A)
template<typename T >
void	reverseRows (T &A)
template<typename T >
double	subspaceOverlap (const T &A, const T &B, uint nmodes=0)
template<typename T >
double	covarianceOverlap (const T &lamA, const T &UA, const T &lamB, const T &UB)
	Computes the covariance overlap between two subspaces.
template<typename T >
boost::tuple< double, double, double >	zCovarianceOverlap (const T &lamA, const T &UA, const T &lamB, const T &UB, const uint tries)
template<class T1 , class P1 , template< typename > class S1, class T2 , class P2 , template< typename > class S2>
void	copyMatrix (Matrix< T1, P1, S1 > &A, const Matrix< T2, P2, S2 > &M)
	Copy one matrix into another, converting order/storage along the way.
template<class T1 , class P1 , class T2 , class P2 >
void	copyMatrix (Matrix< T1, P1, SparseArray > &A, const Matrix< T2, P2, SparseArray > &M)
	Overload for copying a sparse matrix that preserves the original.
template<typename T , class P , template< typename > class S>
std::vector< T >	getRow (const Matrix< T, P, S > &M, const uint j)
	Extract a row from a matrix as a vector of T.
template<typename T , class P , template< typename > class S>
std::vector< T >	getCol (const Matrix< T, P, S > &M, const uint i)
	Extract a column from a matrix as a vector of T.

Variables
const double	DEGREES = 180 / M_PI

Detailed Description

Namespace for math and math-related things in loos.

Note: the operator overloads presented for DoubleMatrix are not going to be efficient. They are only provided as a convenience for working with matrices in LOOS. If you need to perform more serious linear algebra operations, you are encouraged to use a 3rd party library for your tool.

Function Documentation

angle() [1/2]

greal loos::Math::angle	(	const GCoord &	a,
		const GCoord &	b,
		const GCoord &	c,
		const GCoord *	box = NULL )

Compute the angle in degrees assuming the middle is the vertex.

If you pass a pointer to a GCoord specifying the box size, this function will correctly handle periodicity

angle() [2/2]

greal loos::Math::angle	(	const pAtom &	a,
		const pAtom &	b,
		const pAtom &	c,
		const GCoord *	box = NULL )

Compute the angle in degrees assuming the middle is the vertex.

If you pass a pointer to a GCoord specifying the box size, this function will correctly handle periodicity

copyMatrix() [1/2]

template<class T1 , class P1 , template< typename > class S1, class T2 , class P2 , template< typename > class S2>

void loos::Math::copyMatrix	(	Matrix< T1, P1, S1 > &	A,
		const Matrix< T2, P2, S2 > &	M )

Copy one matrix into another, converting order/storage along the way.

Scans over all elements of a matrix. This may not behave as intended with sparse matrices...

copyMatrix() [2/2]

template<class T1 , class P1 , class T2 , class P2 >

void loos::Math::copyMatrix	(	Matrix< T1, P1, SparseArray > &	A,
		const Matrix< T2, P2, SparseArray > &	M )

Overload for copying a sparse matrix that preserves the original.

Note: static null_value SHOULD match what's in MatrixStorage, but this probably isn't guaranteed Note: Overloading templated functions is dangerous. If this needs to be expanded, better to use an Impl class...

covarianceOverlap()

template<typename T >

double loos::Math::covarianceOverlap	(	const T &	lamA,
		const T &	UA,
		const T &	lamB,
		const T &	UB )

Computes the covariance overlap between two subspaces.

This function expects a set of eigenpairs for comparison. The eigenvalues are stored in a Matrix-vector (i.e. an nx1 matrix). The eigenvectors are stored in the columns of the respective matrices.

Note: Be sure that the eigenvalues are scaled appropriately. For example, when comparing PCA and ENM, the ENM eigenvalues are inversely proportional to the PCA eigenvalues while the PCA "eigenvalues" are actually the singular values (and hence the square-root of the eigenvalues of AA'

Note: It is possible for double sum to be slightly greater than 2x the sum of the eigenvalues, which results in trying to take the square root of a negative number. To prevent this, we actually use the absolute value of the difference.

Note: Due to rounding errors in single precision, it is possible that the covariance overlap of a set of eigenpairs against itself will not come out to be exactly 1, but will be close (i.e. to within 1e-3).

eigenDecomp()

RealMatrix loos::Math::eigenDecomp

(

DoubleMatrix &

M

)

Compute eigendecomposition of M.

Internally, this function uses dsyev from ATLAS/LAPACK. The passed matrix, M, will be overwritten by the eigenvectors. The ordering of eigenpairs is from smallest magnitude to largest.

svd()

boost::tuple< DoubleMatrix, DoubleMatrix, DoubleMatrix > loos::Math::svd

(

DoubleMatrix &

M

)

Compute the SVD of a single precision matrix.

Compute the SVD of a double precision matrix.

The SVD functions will overwrite the source matrix

• M

torsion() [1/2]

greal loos::Math::torsion	(	const GCoord &	a,
		const GCoord &	b,
		const GCoord &	c,
		const GCoord &	d,
		const GCoord *	box = NULL )

Compute the torsion in degrees.

If you pass a pointer to a GCoord specifying the box size, this function will correctly handle periodicity

torsion() [2/2]

greal loos::Math::torsion	(	const pAtom &	a,
		const pAtom &	b,
		const pAtom &	c,
		const pAtom &	d,
		const GCoord *	box = NULL )

Compute the torsion in degrees.

If you pass a pointer to a GCoord specifying the box size, this function will correctly handle periodicity