| Member Functions | |||
| condition() determinant() factor() |
fail() good() inverse() |
isSingular() order() 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, RWBoolean 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.
RWBoolean fail() const;
Returns TRUE if the factorization fails, perhaps due to singularity, otherwise returns FALSE.
void factor(const RWGenMat<T>& m, RWBoolean ce = TRUE);
Recalculates the factorization, this time using the matrix m. If the argument ce is TRUE, a condition number is also calculated.
RWBoolean 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.
©Copyright 1999, Rogue Wave Software, Inc.
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