---------------------------------------------------------------------------------------------------------------
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>
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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