C++ Armadillo :: pseudo-inverse
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Description::
This is the basic C++ program of C++ armadillo library which shows how to find psuedo inverse of the given matrix. It can be carried out by the help of inbuilt function "pinv" in armadillo library.
- The computation is based on singular value decomposition
- The tolerance argument is optional
- The default tolerance is max(m,n)*max_sv*datum::eps, where:
- m = number of rows and n = number of columns in A
- max_sv = maximal singular value of A
- datum::eps = difference between 1 and the least value greater than 1 that is representable
- Any singular values less than tolerance are treated as zero
- The method argument is optional; method is either
"dc"or"std""dc"indicates divide-and-conquer method (default setting)"std"indicates standard method- the divide-and-conquer method provides slightly different results than the standard method, but is considerably faster for large matrices
- If the decomposition fails:
- B = pinv(A) resets B and throws a std::runtime_error exception
- pinv(B,A) resets B and returns a bool set to false (exception is not thrown)
Source:http://arma.sourceforge.net
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Program::
#include <iostream>
#include <armadillo>using namespace std;
using namespace arma;
int main()
{ //initialize the random generator
//Create a 4 x 5 random matrix and printing it
mat A = randu<mat>(4,5); //random matrix of size 4x5 (generared by this syntax)
mat B = pinv(A); // use default tolerance
mat C = pinv(A, 0.01); // set tolerance to 0.01
cout << "Matrix A::\n"<<endl;
cout<< A << endl;
cout << "Matrix B(p-Inverse)::\n"<<endl;
cout << B << endl;
cout << "Matrix C::\n"<<endl;
cout << C << endl;
return 0;
}
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Commands to run program on terminal::
$ g++ filename.cpp -o objectname -O2 -larmadillo
$ ./objectname
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Output::
Matrix A::
0.7868 0.0193 0.5206 0.1400 0.4998
0.2505 0.4049 0.3447 0.5439 0.4194
0.7107 0.2513 0.2742 0.5219 0.7443
0.9467 0.0227 0.5610 0.8571 0.2492
Matrix B(p-Inverse)::
0.2018 -1.2532 0.6697 0.4844
0.1658 1.5798 -0.4228 -0.5809
1.9145 1.9283 -2.4930 -0.0942
-1.5113 0.1178 0.4900 0.9748
0.1057 -0.1299 1.4217 -0.9153
Matrix C::
0.2018 -1.2532 0.6697 0.4844
0.1658 1.5798 -0.4228 -0.5809
1.9145 1.9283 -2.4930 -0.0942
-1.5113 0.1178 0.4900 0.9748
0.1057 -0.1299 1.4217 -0.9153
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