Linear Algebraic Equations
We will cover only Gauss Jordan and summarize the remainder
AX = b and Gauss Jordan Elimination
The data files //note that you have to type them
Notes
The main function is xgaussj and it uses gaussj along with the file matrx1.dat
Be sure to save the .dat file as a text file and check to see that it has a .dat extension
The name for the main program does not matter but it must be a source file
The name for the implementation file (also a source file) must be xgaussj
Input File (matrx1.dat - a text file)
MATRICES FOR INPUT TO TEST ROUTINES
Size of matrix (NxN), Number of solutions:
3 2
Matrix A:
1.0 0.0 0.0
0.0 2.0 0.0
0.0 0.0 3.0
Solution vectors:
1.0 0.0 0.0
1.0 1.0 1.0
Code for reading the data files (in examples)
int j,k,l,m,n;
string dummy;
//string to store things
ifstream fp("matrx1.dat"); //open
file and use fp alias
if (fp.fail())
NR::nrerror("Data file matrx1.dat not found");
//in case file is not found
cout << fixed << setprecision(6); //for
formatting
getline(fp,dummy); //reads the
first line ("MATRICES FOR ...)
while (!fp.eof())
{
getline(fp,dummy); //reads the second line
("Size of matrix...)
fp >> n >> m;
//reads the number of rows (n) and columns (m)
fp.get();
getline(fp,dummy);
Mat_DP a(n,n),u(n,n),b(n,m),t(n,m);
for (k=0;k<n;k++)
for (l=0;l<n;l++) fp >> a[k][l];
fp.get();
getline(fp,dummy);
for (l=0;l<m;l++)
for (k=0;k<n;k++) fp >> b[k][l];
fp.get();
getline(fp,dummy);
// save matrices for later testing of results
Mat_DP ai=a;
Mat_DP x=b;
Output
Notes
The inverse is a matrix (listed as inverse of matrix a below) that, when multiplied by the original,
results in the identity matrix (listed as a times a-inverse beow).
The identity matrix is a matrix with 1s along the diagonal and 0s elsewhere.
The code then checks to ensure that the original matrix multiplied by the solution vector
(Ax) equals the original right hand side vector (b). Below this is listed as matrix*sol'n and is
shown to be equal to the original vectors (listed as 0 and 1)
Data File (matrix1.dat - a text file)
NEXT PROBLEM
Size of matrix (NxN), Number of solutions:
3 2
Matrix A:
1.0 2.0 3.0
2.0 2.0 3.0
3.0 3.0 3.0
Solution vectors:
1.0 1.0 1.0
1.0 2.0 3.0
Output
The main function is xludcmp.cpp - it uses ludcmp
MATRICES FOR INPUT TO TEST ROUTINES
Size of matrix (NXN), Number of solutions;
3 2
Matrix A:
1.0 0.0 0.0
0.0 2.0 0.0
0.0 0.0 3.0
Solution vectors:
1.0 0.0 0.0
1.0 1.0 1.0
Note: You can either place the input file in the same project or modify the code as follows
ifstream fp("c:\\matrx1.dat"); //location of file, note the \, first is escape character
Output
Program uses ludcmp.cpp, lubksb.cpp, and the driver xlubksb.cpp
Input file is matrix1.dat as above
