RWGenFact<T>

Module:  Essential Math    Group:  LU Factorization classes

Does not inherit

• Local Index
• Synopsis
• Description
• Public Constructors
• Public Member Functions
• Related Global Functions

Members

condition() factor()

fail() good()

isSingular() order()

RWGenFact()

Non-Members

condition()

determinant()

inverse()

solve()

#include <rw/math/genfact.h>
#include <rw/math/genmat.h>
RWGenMat<T> matrix;
template <class T>
RWGenFact<T> LUFactor(matrix);

Class RWGenFact<T> is a templatized LU factorization class. This class holds the LU factorization of a general square matrix of type T. Once such a factorization is built, it can be used to invert a matrix, calculate its determinant, or solve a set of simultaneous linear equations.

Optionally, a condition number can be calculated and then recovered via member function condition(), which returns the reciprocal of the standard definition for the condition number of a matrix.

The result is in the range [0,1]. The closer the result is to 0, the closer the matrix is to being singular. See Dongarra et al. (1979) for additional information.

RWGenFact();

Sets up an empty LU factorization. Member function factor() can then be used to actually calculate the factorization.

RWGenFact(const RWGenMat<T>& m, bool ce = true);

Constructs an LU factorization from the matrix m. If the argument ce is true, a condition number is also calculated. Setting ce to false saves some time (perhaps 20%), but gives you less information about how ill-conditioned the matrix is. If the matrix m is not square, an exception with value LPAK_NOTSQUARE occurs. This constructor also serves as a type conversion from RWGenMat<T> to RWGenFact<T>.

RWGenFact(const RWGenFact<T>&);

Copy constructor. Reference semantics are used; that is, a shallow copy of the argument is made.

double
condition() const;

An exception with value LPAK_NOCONDITION occurs if the condition number is not calculated.

bool
fail() const;

Returns true if the factorization fails, perhaps due to singularity, otherwise returns false.

void
factor(const RWGenMat<T>& m, bool ce = true);

Recalculates the factorization, this time using the matrix m. If the argument ce is true, a condition number is also calculated.

bool
good() const;

Returns true if the factorization succeeds.

int
isSingular() const;

Checks to see if the matrix is singular. If isSingular() returns a non-zero value, the matrix is singular. Note that the LU factorization is still defined; however, an attempt to use it to compute the matrix inverse fails.

unsigned
order() const;

Returns the order of the matrix from which the LU factorization is constructed.

double 
condition(const RWGenFact<T>& m);
double 
condition(const RWGenMat<T>& A);

Returns the inverse condition number of matrix A or of the matrix whose LU factorization is m.

T
determinant(const RWGenFact<T>& m);

Returns the determinant of the matrix from which an LU factorization m is constructed.

RWGenMat<T>
inverse(const RWGenFact<T>& m);
RWGenMat<T>
inverse(const RWGenMat<T>& A);

Calculates the inverse of the matrix from which an existing LU factorization m is constructed.

RWMathVec<T>
solve(const RWGenFact<T>& m, const RWMathVec<T>& b);
RWGenMat<T>
solve(const RWGenFact<T>& m, const RWGenMat<T>& b);
RWMathVec<T>
solve(const RWGenMat<T>& A, const RWMathVec<T>& b);
RWGenMat<T>
solve(const RWGenMat<T>& A, const RWGenMat<T>& b);

Calculates the solution to A*x = b, where m is an LU factorization constructed from the RWGenMat<T> A.

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