SimplexAdjJac< N, T > Class Template Reference

Implements operations for the adjoint Jacobian matrix of a simplex. More...

#include <SimplexAdjJac.h>

List of all members.

Public Types
typedef T	Number
	The number type.
typedef ads::SquareMatrix< N, Number >	Matrix
	An NxN matrix.
Public Member Functions
Constructors etc.
	SimplexAdjJac ()
	Default constructor. Un-initialized memory.
	SimplexAdjJac (const SimplexAdjJac &other)
	Copy constructor.
	SimplexAdjJac (const Matrix &jacobian)
	Construct from the Jacobian matrix.
SimplexAdjJac &	operator= (const SimplexAdjJac &other)
	Assignment operator.
	~SimplexAdjJac ()
	Trivial destructor.
Accessors
const Matrix &	getMatrix () const
	Return a const reference to the adjoint Jacobian matrix.
const ads::FixedArray< N, Matrix > &	getGradientMatrix () const
	Return a const reference to the gradient of the adjoint Jacobian matrix.
Manipulators
void	setFunction (const Matrix &jacobian)
	Calculate the adjoint Jacobian matrix.
void	set (const Matrix &jacobian)
	Calculate the adjoint Jacobian matrix and its gradient.

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Detailed Description

template<int N, typename T = double>
class SimplexAdjJac< N, T >

Implements operations for the adjoint Jacobian matrix of a simplex.

Parameters:

	N	is the dimension.
	T	is the number type. By default it is double.

The Adjoint of a Matrix

Consult the documentation of geom::SimplexJac for information on the Jacobian matrix of a simplex. This class implements operations on the adjoint of this matrix. In this context, the adjoint is the scaled inverse of a matrix. The adjoint of a non-singular matrix is . For the general case, we have:

where is the identity matrix.

The adjoint of the Jacobian matrix of a simplex is used in the condition number quality metric. (See geom::SimplexCondNum and geom::SimplexModCondNum.)

Usage

Make a SimplexAdjJac by using the default constructor or the Matrix constructor.

  typedef geom::SimplexJac<3> TetJac;
  typedef geom::SimplexAdjJac<3> TetAdjJac;
  typedef TetJac::Vertex Vertex;
  typedef TetJac::Simplex Tetrahedron;
  // Default constructor.
  TetAdjJac adjoint;

  // Identity tetrahedron
  Tetrahedron t(Vertex(0, 0, 0),
                Vertex(1, 0, 0),
                Vertex(1./2, std::sqrt(3.)/2, 0),
                Vertex(1./2, std::sqrt(3.)/6, std::sqrt(2./3.)));
  // The Jacobian matrix.             
  TetJac jacobian(t);
  // The adjoint of the Jacobian matrix.
  TetAdjJac adjoint(jacobian.getMatrix());

The latter constructor calls the set() member function.

To evaluate the adjoint of the Jacobian, first call the setFunction() manipulator and then use the getMatrix() accessor.

  adjoint.setFunction(jacobian.getMatrix());
  std::cout << "Adjoint = \n"
            << adjoint.getMatrix() << '\n';

To evaluate the adjoint of the Jacobian and its gradient, first call the set() manipulator and then use the getMatrix() and getGradientMatrix() accessors.

  adjoint.set(jacobian.getMatrix());
  std::cout << "Adjoint = \n"
            << adjoint.getMatrix()
            << "\nGradient of adjoint = \n"
            << adjoint.getGradientMatrix() << '\n';

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The documentation for this class was generated from the following file:

• SimplexAdjJac.h