### C++ Armadillo :: Log Determinant

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Description::
This is the basic C++ program of C++ armadillo library which shows how to shift particular element of column of the given matrix by some particular number. It can be carried out by the help of inbuilt function "log_det" in armadillo library.
• Log determinant of square matrix A
• If A is not square sized, a std::logic_error exception is thrown
• form 1: store the calculated log determinant in val and sign
the determinant is equal to exp(val)*sign
• form 2: return the complex log determinant
• if matrix A is real and the determinant is positive:
• the real part of the result is the log determinant
• the imaginary part is zero
• if matrix A is real and the determinant is negative:
• the real part of the result is the log of the absolute value of the determinant
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Program::

#include <iostream>
using namespace std;
using namespace arma;

int main()
{
//initialize the random generator
//Create a 5 x 5 random matrix and printing it
mat A(5,5,fill::randu); //random matrix of size 5x5 (generared by this syntax)
double val; double sign; log_det(val, sign, A); //form 1 cx_double result = log_det(A); //form 2
cout << "Matrix A::\n"<<endl;
cout<< A << endl;
cout << "Sign::" << endl;
cout << sign << endl; cout << "Val::" << endl;
cout << val << endl; cout << "result" << endl;
cout << result << 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 0.4049 0.2742 0.8571 0.2393 0.2505 0.2513 0.5610 0.4998 0.3201 0.7107 0.0227 0.1400 0.4194 0.9105 0.9467 0.5206 0.5439 0.7443 0.1648 0.0193 0.3447 0.5219 0.2492 0.2455 Sign:: -1 Val:: -3.62033 result: (-3.62033,3.14159)

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