Working with matrices, accelerate framework, iOS - ios

Question

I have two matrices: A and B.
How can I store them?
How can I calculate the inverse matrix of matrix A using the Accelerate framework?
How can find the product of A*B?
How can I transpose matrix A using the Accelerate framework?
Thank you for answering my questions!
Helper file
#import <Foundation/Foundation.h>
#include <Accelerate/Accelerate.h>
#interface Working_with_matrices : NSObject
-(int)invert_matrix:(int) N andWithMatrix:(double*) matrix;
#end
Implementation file
#import "Working_with_matrices.h"
#include <Accelerate/Accelerate.h>
#implementation Working_with_matrices
-(int) matrix_invert:(int) N andWithMatrix:(double*)matrix
{
int error=0;
int *pivot = malloc(N*N*sizeof(int));
double *workspace = malloc(N*sizeof(double));
dgetrf_(&N, &N, matrix, &N, pivot, &error);
if (error != 0) {
NSLog(#"Error 1");
return error;
}
dgetri_(&N, matrix, &N, pivot, workspace, &N, &error);
if (error != 0) {
NSLog(#"Error 2");
return error;
}
free(pivot);
free(workspace);
return error;
}
Call my code from main function
#import <Foundation/Foundation.h>
#import "Working_with_matrices.h"
int main(int argc, const char * argv[])
{
int N = 3;
double A[9];
Working_with_matrices* wm=[[Working_with_matrices alloc]init];
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;
[wm invert_matrix:N andWithMatrix:A];
// [ -1.25 -1.0 3.25 ]
// A^-1 = [ 0.5 1.0 -1.5 ]
// [ 0.25 0.0 -0.25 ]
for (int i=0; i<9; i++)
{
NSLog(#"%f", A[i]);
}
return 0;
}

Answer 1

I'm still kinda new to using the accelerate framework but I'll answer what I can.
The accelerate framework expects the matrices to be passed in as a
1D array. So if you have a 4x4 matrix, the first row would be placed
in indexes 0-3 of your array, the second rouw would be placed in
indexes 4-7 and so on.
I've never done it but this answer looks like a good starting point. https://stackoverflow.com/a/11321499/385017
The method you'll want to use is vDSP_mmul for single precision or vDSP_mmulD for double precision. You might want to look at the documentation for it to get a better unerstanding of how to use it but heres an example to get you started.
float *matrixA; //set by you
float *matrixB; //set by you
float *matrixAB; //the matrix that the answer will be stored in
vDSP_mmul( matrixA, 1, matrixB, 1, matrixAB, 1, 4, 4, 4 );
// the 1s should be left alone in most situations
// The 4s in order are:
// the number of rows in matrix A
// the number of columns in matrix B
// the number of columns in matrix A and the number of rows in matrix B.