c - Expanding the QR Decomposition of square matrices to tall matrices

Question

I'm trying to convert the QR Decomposition from "Numerical Recipes in C" to work with skinny (tall) matrices. Does anyone know how to do this? I believe the problem lies in how the householder is multiplied with the A but I am unable to figure it out.

void qrdcmp(float **a, int n, float *c, float *d, int *sing)
{
    int i,j,k;
    float scale,sigma,sum,tau;
        *sing=0;

    for (k = 1; k < n; k++) {
        scale = 0.0;
        for (i = k; i <= n; i++) scale = FMAX(scale, fabs(a[i][k]));
        if (scale == 0.0) { // Singular case.
            *sing = 1;
            c[k] = d[k] = 0.0;
        } else { // Form Qk and Qk · A.
            for (i = k; i <= n; i++) a[i][k] /= scale;
            for (sum = 0.0, i = k; i <= n; i++) sum += SQR(a[i][k]);
            sigma = SIGN(sqrt(sum), a[k][k]);
            a[k][k] += sigma;
            c[k] = sigma * a[k][k];
            d[k] = -scale * sigma;
            for (j = k + 1; j <= n; j++) {
                for (sum = 0.0, i = k; i <= n; i++) sum += a[i][k] * a[i][j];
                tau = sum / c[k];
                for (i = k; i <= n; i++) a[i][j] -= tau * a[i][k];
            }
        }
    }

    d[n] = a[n][n];
    if (d[n] == 0.0) *sing=1;
}