Matrix Inversion in CBLAS/LAPACK vs Python - numpy

Question

The matrix I am trying to invert is:
[ 1 0 1]
A = [ 2 0 1]
[-1 1 1]
The true inverse is:
[-1 1 0]
A^-1 = [-3 2 1]
[ 2 -1 0]
Using Python's numpy.linalg.inv, I get the correct answer. One of my routines for matrix inverse uses dgetri_, it is:
void compute_matrix_inverse_dbl( double* matrix,
int order,
double * inverse )
{
int N, lwork;
int success;
int *pivot;
double* workspace;
//===Allocate Space===//
pivot = malloc(order * order * order * sizeof(*pivot));
workspace = malloc(order * order * sizeof(*workspace));
//===Run Setup===//
N = order;
copy_array_dbl(matrix, order*order, inverse);
lwork = order*order;
//===Factor Matrix===//
dgetrf_(&N,&N,inverse,&N,pivot,&success);
//===Compute Inverse===//
dgetri_(&N, inverse, &N, pivot, workspace, &lwork, &success);
//===Clean Up===//
free(workspace);
free(pivot);
return;
}
Using this routine, I get:
[-1 1 +-e1 ]
A^-1 = [-3 2 1 ]
[ 2 -1 +-e2 ]
Where e1 and e2 and small numbers on the order of machine precision 1e-16. Now perhaps dgetri_ is not the best to use. However, when I invert using QR decomposition via zgeqrf_ and zungqr_, I get a similar answer. When I use dgesvd_ for inverse using SVD, I get a similar answer as well.
Python seems to use a routine called _umath_linalg.inv. So I have a few questions:
What does that routine do?
What CBLAS/LAPACK routine can I use to invert this matrix and get a result like CBLAS/LAPACK (such that the e1 and e2 get replaced by proper zeros)?

Answer 1

It seems that numpy.linalg.inv is a lite version of the scipy.linalg.inv as per the description:
This module is a lite version of the linalg.py module in SciPy which
contains high-level Python interface to the LAPACK library.
Looking at scipy.linalg.inv, it does a call to getrf, then getri.