# Trouble setting up QR

I am implementing the QR reparametrization of section 9.2. However, my model calls for an array of matrices.

``````data {
int<lower=0> N;
int T; // number of days in campaign
int K; // number of predictors

matrix[N, K] x[T];
vector[N] y[T];
}
``````

So for the transformed data block I want to set up T Q_ast matrices with the modification that each QR parameter is a array of dimension T.

``````	for (t in 1:T){
Q_ast[t] = qr_Q(z[t])[, 1:K] * sqrt(N - 1);
R_ast[t] = qr_R(z[t])[1:K, ] / sqrt(N - 1);
R_ast_inverse[t] = inverse(R_ast[t]);
}
``````

However, I am not sure how I would recover beta using the formula from the manual.

`beta = R_ast_inverse * theta`

since in my case both R_ast_inverse and theta are arrays of dimension T, I will end up with T sets of betas. Do I take the average?

1 Like

I am trying the QR technique out. I ran into non-invertible matrix problem

`````` Q_ast = qr_Q(x)[, 1:K] * sqrt(N - 1);
R_ast = qr_R(x)[1:K, ] / sqrt(N - 1);
R_ast_inverse = inverse(R_ast);
``````

But because my data contains most 0’s, the inverse calculation fails

Q_ast = [[0.154673,0,-0.0379848,-0.121529,0.00411132],[-0,3,-0,0,0],[-0,0,3.53977e-06,0.0282982,-0.324708],[0.12117,0,-0.0297572,2.99507,0.0032208],[-0,0,0.324708,0.00306288,2.96485],[0.719883,0,2.89347,-0.000357266,-0.313177],[-0,0,1.13273e-06,1.06847e-08,-1.22602e-07],[5.82244e-05,0,0.10423,0.000980936,-0.0112814],[2.45722,0,-0.603449,-0.100074,0.0653149],[1.55087,0,-0.380866,-0.0631614,0.0412234]]

R_ast = [[0.648872,-0,0.0799872,-0,-0],[0,0,0,0,9.26125e-36],[-0,-0,0.325705,-0,-0],[0,0,0,0,0],[0,0,0,0,0]]

R_ast_inverse = [[nan,nan,nan,nan,nan],[nan,nan,nan,nan,nan],[nan,nan,nan,nan,nan],[nan,nan,nan,nan,nan],[nan,nan,nan,nan,inf]]

Does any one have tricks to get around this problem in order to still leverage QR?

I wrote a lower triangular inversion function recently, perhaps that helps? edit: no probably not, but will leave it here anyway!

``````matrix inverse_lowtri(matrix l, int unitdiag){ //inverse of lower triangular matrix
matrix[rows(l),rows(l)] b ;
matrix[rows(l),rows(l)] x;
x = diag_matrix(rep_vector(1,rows(l)));
b = x;

for(j in 1:cols(x)){
if(unitdiag != 1) x[j,j] = b[j,j] / l[1,1];

if(rows(x)>1){
for(m in 2:rows(x)){
x[m,j]  =  (b[m,j] - (l[m,1:(m-1)] * x[1:(m-1),j]) ) / l[m,m];
}
}
}
return x;
}
``````

[edit: added triple back ticks before and after code to format it]