gramschmidt.h File Reference

Routines for orthogonalizing column vectors via classical and modified gram-schmidt. More...

#include <myramath/MYRAMATH_EXPORT.h>
#include <myramath/utility/Number.h>

Include dependency graph for gramschmidt.h:

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Classes
class	myra::Matrix< Number >
	Tabulates an IxJ matrix. Allows random access, has column major layout to be compatible with BLAS/LAPACK. More...
class	myra::Vector< Number >
	Tabulates a vector of length N, allows random access. More...
class	myra::MatrixRange< Number >
	Represents a mutable MatrixRange. More...
class	myra::VectorRange< Number >
	Represents a mutable VectorRange. More...
class	myra::CMatrixRange< Number >
	Represents a const MatrixRange. More...
class	myra::CVectorRange< Number >
	Represents a const VectorRange. More...

Functions
NumberS	myra::cgs_inplace (const CVectorRange< NumberS > &q, const VectorRange< NumberS > &v)
	Orthogonalize v against q via classical gram-schmidt, v = (I-qq')*v, returns q'v.
NumberD	myra::cgs_inplace (const CVectorRange< NumberD > &q, const VectorRange< NumberD > &v)
	Orthogonalize v against q via classical gram-schmidt, v = (I-qq')*v, returns q'v.
NumberC	myra::cgs_inplace (const CVectorRange< NumberC > &q, const VectorRange< NumberC > &v)
	Orthogonalize v against q via classical gram-schmidt, v = (I-qq')*v, returns q'v.
NumberZ	myra::cgs_inplace (const CVectorRange< NumberZ > &q, const VectorRange< NumberZ > &v)
	Orthogonalize v against q via classical gram-schmidt, v = (I-qq')*v, returns q'v.
Vector< NumberS >	myra::cgs_inplace (const CMatrixRange< NumberS > &Q, const VectorRange< NumberS > &v)
	Orthogonalizes v against Q via classical gram-schmidt, v = (I-QQ')*v, returns Q'v.
Vector< NumberD >	myra::cgs_inplace (const CMatrixRange< NumberD > &Q, const VectorRange< NumberD > &v)
	Orthogonalizes v against Q via classical gram-schmidt, v = (I-QQ')*v, returns Q'v.
Vector< NumberC >	myra::cgs_inplace (const CMatrixRange< NumberC > &Q, const VectorRange< NumberC > &v)
	Orthogonalizes v against Q via classical gram-schmidt, v = (I-QQ')*v, returns Q'v.
Vector< NumberZ >	myra::cgs_inplace (const CMatrixRange< NumberZ > &Q, const VectorRange< NumberZ > &v)
	Orthogonalizes v against Q via classical gram-schmidt, v = (I-QQ')*v, returns Q'v.
Matrix< NumberS >	myra::cgs_inplace (const CMatrixRange< NumberS > &Q, const MatrixRange< NumberS > &V)
	Orthogonalizes V against Q via classical gram-schmidt, V = (I-QQ')*V, returns Q'V.
Matrix< NumberD >	myra::cgs_inplace (const CMatrixRange< NumberD > &Q, const MatrixRange< NumberD > &V)
	Orthogonalizes V against Q via classical gram-schmidt, V = (I-QQ')*V, returns Q'V.
Matrix< NumberC >	myra::cgs_inplace (const CMatrixRange< NumberC > &Q, const MatrixRange< NumberC > &V)
	Orthogonalizes V against Q via classical gram-schmidt, V = (I-QQ')*V, returns Q'V.
Matrix< NumberZ >	myra::cgs_inplace (const CMatrixRange< NumberZ > &Q, const MatrixRange< NumberZ > &V)
	Orthogonalizes V against Q via classical gram-schmidt, V = (I-QQ')*V, returns Q'V.
void	myra::mgs_inplace (const MatrixRange< NumberS > &A, const MatrixRange< NumberS > &R)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Ovewrites R such that A=Q*R.
void	myra::mgs_inplace (const MatrixRange< NumberD > &A, const MatrixRange< NumberD > &R)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Ovewrites R such that A=Q*R.
void	myra::mgs_inplace (const MatrixRange< NumberC > &A, const MatrixRange< NumberC > &R)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Ovewrites R such that A=Q*R.
void	myra::mgs_inplace (const MatrixRange< NumberZ > &A, const MatrixRange< NumberZ > &R)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Ovewrites R such that A=Q*R.
Matrix< NumberS >	myra::mgs_inplace (const MatrixRange< NumberS > &A)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Returns R such that A=Q*R.
Matrix< NumberD >	myra::mgs_inplace (const MatrixRange< NumberD > &A)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Returns R such that A=Q*R.
Matrix< NumberC >	myra::mgs_inplace (const MatrixRange< NumberC > &A)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Returns R such that A=Q*R.
Matrix< NumberZ >	myra::mgs_inplace (const MatrixRange< NumberZ > &A)
	Overwrites A with orthonormal columns Q via modified gram-schmidt. Returns R such that A=Q*R.
std::pair< Matrix< NumberS >, Matrix< NumberS > >	myra::mgs (const CMatrixRange< NumberS > &A)
	Factors A = Q*R, where Q is orthogonal and R is upper triangular.
std::pair< Matrix< NumberD >, Matrix< NumberD > >	myra::mgs (const CMatrixRange< NumberD > &A)
	Factors A = Q*R, where Q is orthogonal and R is upper triangular.
std::pair< Matrix< NumberC >, Matrix< NumberC > >	myra::mgs (const CMatrixRange< NumberC > &A)
	Factors A = Q*R, where Q is orthogonal and R is upper triangular.
std::pair< Matrix< NumberZ >, Matrix< NumberZ > >	myra::mgs (const CMatrixRange< NumberZ > &A)
	Factors A = Q*R, where Q is orthogonal and R is upper triangular.

Detailed Description

Routines for orthogonalizing column vectors via classical and modified gram-schmidt.