Solving a System of Equations
The most basic problem of linear algebra is to solve a system of equations. Here is a simple program to do this, using float precision and general square matrices:
#include <iostream> // 1
#include <rw/math/genfact.h>
int main()
{
RWGenMat<float> A; // 2
RWMathVec<float> b;
std::cin >> A >> b; // 3
RWMathVec<float> x = solve(A,b); // 4
std::cout << x << std::endl;
return 0;
}
Here is a line-by-line description of what this program does:
//1 The first #include statement allows the use of iostreams. The second #include statement includes the header file genfact.h, which declares the float general factorization type RWGenFact<float>.
//2 Here the variable A is defined as a general floating point matrix, RWGenMat<float>, and b is defined as a floating point vector, RWMathVec<float>.
//3 The variables A and b are read in from the standard input. Here is a possible input file showing the format:
2x2
[ 4 5
1 3 ]
[ 2 1 ]
In this case, the 2 x 2 matrix:
and the two-element long vector (2, 1) are read in.
//4 This is the key statement in the program. The vector x which satisfies the equation Ax=b is returned by the solve() function. We will discuss how this works in more detail later.
At this point, you notice that the factorization class, RWGenFact<float>, is not used in the program! Or is it? If you look in the header file genfact.h, you can see that the solve function is declared to take an argument of type const RWGenFact<float>&. The C++ compiler constructed a temporary variable of type RWGenFact<float> for you. This temporary variable was constructed using the RWGenFact<float>(const RWGenMat<float>&) constructor and then passed to the solve function. Class RWGenFact<float> was used after all!
