Help Using Lapack for Getting Least Squares Fit Polynomial Coefficients

Hello all,

I am a first time MKL user trying to use the library to fit a 3rd-order 2-d polynomial function to f(x,y). This algorithm works using pretty much the same exact approach in Python so I believe it to be conceptually sound.

I'm trying to use LAPACKE_dgelsy but my program dies whenever it's called, and I'm sure my function arguments are incorrect.

I created my A matrix to be  10 x 60,000, with each of the 10 rows representing a coefficient for {1,x,y,x²,xy,y²,etc..} at each index of data, and B[i] = f(x[i],y[i]) (B is size 1 x 60,000). dgelsy only takes a single pointer, so I've had "a" take the form of the array: 

double * a = new double[n * 10];

and I just concatenated each row of data one after the other into this array. I'm under the impression that dgelsy's argument values "LAPACK_ROW_MAJOR","m", "n", and "nrhs" will order the data in a more typical A*x=B, m x n, matrix form for all the calculations (at least conceptually, not in actual memory). Do I have the dimensions and input form correct in this?

The rest of the code looks like this so far:

lapack_int matrixLayout = LAPACK_ROW_MAJOR;
lapack_int n = 60000;
lapack_int lda = n;
lapack_int ldb = n;
m = 10;
lapack_int nrhs = n;
int *jpvt = new int[n];//No idea what this is
lapack_int rcond = -1; //This either
int *rank = new int[n]; // This is supposed to be an output variable, how should I initialize it?
int LapackResult = LAPACKE_dgelsy(matrixLayout, m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank);

It crashes the program at the last line obviously. I've looked at all the documentation and I can't figure out what it wants for the arguments: jpvt, rcond, and rank. Could anyone give me more info about what these mean?

Finally, if WHEN I do get dgelsy to work, how can I interpret the output (i.e. rank pointer) to find the coefficients of my fitted polynomial?

Sorry if I'm coming at this completely wrong. I've gotten the IPP library to work very well for me so I've been taking some of the things I learned there and trying to apply them here to no avail. 

I appreciate any help you can offer!