Computing the inverse of a matrix using lapack in C

Question

I would like to be able to compute the inverse of a general NxN matrix in C/C++ using lapack.

My understanding is that the way to do an inversion in lapack is by using the dgetri function, however, I can't figure out what all of its arguments are supposed to be.

Here is the code I have:

void dgetri_(int* N, double* A, int* lda, int* IPIV, double* WORK, int* lwork, int* INFO);

int main(){

    double M [9] = {
        1,2,3,
        4,5,6,
        7,8,9
    };

    return 0;
}

How would you complete it to obtain the inverse of the 3x3 matrix M using dgetri_?

Answer 1

Here is the working code for computing the inverse of a matrix using lapack in C/C++:

#include <cstdio>

extern "C" {
    // LU decomoposition of a general matrix
    void dgetrf_(int* M, int *N, double* A, int* lda, int* IPIV, int* INFO);

    // generate inverse of a matrix given its LU decomposition
    void dgetri_(int* N, double* A, int* lda, int* IPIV, double* WORK, int* lwork, int* INFO);
}

void inverse(double* A, int N)
{
    int *IPIV = new int[N];
    int LWORK = N*N;
    double *WORK = new double[LWORK];
    int INFO;

    dgetrf_(&N,&N,A,&N,IPIV,&INFO);
    dgetri_(&N,A,&N,IPIV,WORK,&LWORK,&INFO);

    delete[] IPIV;
    delete[] WORK;
}

int main(){

    double A [2*2] = {
        1,2,
        3,4
    };

    inverse(A, 2);

    printf("%f %f\n", A[0], A[1]);
    printf("%f %f\n", A[2], A[3]);

    return 0;
}