How to perform matrix inverse operation using the accelerate framework? - osx-lion

Question

I would like to find the inverse of a matrix.
I know this involves first LU factorisation then the inversion step but I cannot find the required function by searching apple's docs of 10.7!
This seems like a useful post Symmetric Matrix Inversion in C using CBLAS/LAPACK, pointing out that the sgetrf_ and sgetri_ functions should be used. However searching these terms I find nothing in Xcode docs.
Does anybody have boiler plate code for this matrix operation?

Answer 1

Apple does not document the LAPACK code at all, I guess because they just implement the standard interface from netlib.org. It's a shame that you cannot search the these function names from the built-in Xcode docs, however the solution is fairly straight forward: just specify the function name in the URL e.g. for dgetrf_() go to, http://www.netlib.org/clapack/what/double/dgetrf.c.
To invert a matrix two LAPACK function are need: dgetrf_(), which performs LU factorisation, and dgetri_() which takes the output of the previous function and does the actual inversion.
I created a standard Application Project using Xcode, added the Accelerate Framework, create two C files: matinv.h, matinv.c and edited the main.m file to remove Cocoa things:
// main.m
#import "matinv.h"
int main(int argc, char *argv[])
{
int N = 3;
double A[N*N];
A[0] = 1; A[1] = 1; A[2] = 7;
A[3] = 1; A[4] = 2; A[5] = 1;
A[6] = 1; A[7] = 1; A[8] = 3;
matrix_invert(N, A);
// [ -1.25 -1.0 3.25 ]
// A^-1 = [ 0.5 1.0 -1.5 ]
// [ 0.25 0.0 -0.25 ]
return 0;
}
Now the header file,
// matinv.h
int matrix_invert(int N, double *matrix);
and then source file,
int matrix_invert(int N, double *matrix) {
int error=0;
int *pivot = malloc(N*sizeof(int)); // LAPACK requires MIN(M,N), here M==N, so N will do fine.
double *workspace = malloc(N*sizeof(double));
/* LU factorisation */
dgetrf_(&N, &N, matrix, &N, pivot, &error);
if (error != 0) {
NSLog(#"Error 1");
free(pivot);
free(workspace);
return error;
}
/* matrix inversion */
dgetri_(&N, matrix, &N, pivot, workspace, &N, &error);
if (error != 0) {
NSLog(#"Error 2");
free(pivot);
free(workspace);
return error;
}
free(pivot);
free(workspace);
return error;
}