9.8 Linear Algebra Example

FILENAME: example7.cpp

Program:

/*

 * This example shows how to use the class RWGenFact<T>
 * to do linear algebra with double precision matrices.
 */

// Include the RWGenFact<T> class header file:
#include <rw/math/genfact.h>
// Include the double precision matrix header file:
#include <rw/math/genmat.h>
#include <iostream.h>

// Initial data for the vectors:
const double adata[] = {-3.0, 2.0, 1.0, 8.0, -7.0, 
                        9.0, 5.0, 4.0, -6.0};
const double arhs[]  = {6.0, 9.0, 1.0};

main()
{
   // Construct a test matrix and print it out:
   RWGenMat<double> testmat(adata,3,3);
   cout << "test matrix:\n" << testmat << "\n";

   /*
    * Calculate and print the inverse.
    * Note that a type conversion occurs:
    * testmat is converted to type RWGenFact<double>
    * before the inverse is computed.
    */
   cout << "inverse:\n" << inverse(testmat);

   // Now construct an RWGenFact<double> from the matrix:
   RWGenFact<double> LUtest(testmat);

   // Once constructed, LUtest may be reused as required.

   // Find the determinant:
   cout << "\ndeterminant\n" << determinant(LUtest) << endl;

   // Solve the linear system testmat*x = rhs:
   RWMathVec<double> rhs(arhs, 3);
   RWMathVec<double> x = solve(LUtest, rhs);

   cout << "solution:\n" << x << "\n";
}

Sample Input:

None required.

Sample Output (note that the exact numbers depend on machine precision):

test matrix:
3X3
[
-3 8 5
2 -7 4
1 9 -6
]
inverse:
3X3
[
0.025532 0.395745 0.285106
0.068085 0.055319 0.093617
0.106383 0.148936 0.021277
]
determinant:
235
solution:
[
4 1 2
]