linalg_abstract.h File Reference

This file is the bottom of the LinAlg include hierarchy. More...

#include <complex>
#include <iostream>

Include dependency graph for linalg_abstract.h:

This graph shows which files directly or indirectly include this file:

Classes
class	linalg_traits< T >
	Helper class defining relationships between numerical types; e.g. of what type is norm(T)? More...
struct	interval
	A class to define index-sets, specifically for subvectors and submatrices. More...
class	Vector< T >
	The abstract base class for vectors; provides size and element access. More...
class	Matrix< T >
	The abstract base class for matrices; provides size/shape and element access. More...
Typedefs
typedef std::complex< double >	complex
	A convenient synonym for std::complex<double>, complex is one of LinAlg's most important datatypes.
typedef unsigned int	itype
	The type of all index variables that run from 0 to N.
Enumerations
enum	MatrixStorageType {   Dense, UpperTri, LowerTri, Banded,   Sparse, PermScale, Other }
	An enumerated list of all the types of matrices we expect to support (someday), including "other".
Functions
void	ThrowError (char *errstring, bool fatal=false)
	A routine for easily printing an error string, and aborting if necessary.
void	Profile (char *methodname, int p1, int p2, double p3)
	Prints methodname, p1, p2, and p3 to "profile.log".
Variables
std::ofstream *	ProfileStream
	Output stream, used by Profile(), which opens it to "profile.log".
const complex	I
	Defined in linalg.cpp as std::complex<double>(0,1).
const double	Pi
	Defined in linalg.cpp as M_PI.

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Detailed Description

This file is the bottom of the LinAlg include hierarchy.

It defines two abstract linear algebra classes (Vector and Matrix), and some helper classes.

The abstract Vector<T> class provides the interface that a Vector must have:

• it provides its size [Size()]
• it provides reference [T& operator()] and const [T operator() const] access to its elements
• it provides an output function [print( std::ostream )]

The abstract Matrix<T> class provides the interface that a Matrix must have:

• it provides its size [Size()], and dimensions [Rows(), Columns()].
• it provides reference [T& operator()] and const [T operator() const] access to its elements
• it provides an output function [print( std::ostream )]

We define three simple types:

• "complex" is a synonym for std::complex<double>
• "itype", the type that indices take, is a synonym for "unsigned int".
  • MatrixStorageType is an enumerated type.

We define two helper classes.

Class linalg_traits<T> is a fundamental class containing typedefs which define (for various datatypes T) how the data type behaves under: Conjugation, Norm, Abs, Eigenvalue, Eigenvector. By default, these are all the same as the original type, but (for instance), (1) real matrices have complex eigenvalues, and (2) complex numbers have real norms.

Class interval is intended to simplify definition of subvectors and submatrices. It defines an interval of integers [start,end]. It can be constructed from a single integer: interval(i) = [i,i]. It can also be constructed from a pair of integers: interval(i,j) = [i,j].

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