Cholesky Correlation Matrix Constraint functions

Functions
vector	corr_constrain_lp (vector x)
matrix	cholesky_corr_constrain_lp (vector y, int K)

Detailed Description

Original code is in Stan-math https://github.com/stan-dev/math/blob/develop/stan/math/prim/fun/cholesky_corr_constrain.hpp#L48

 
vector corr_constrain_lp(vector x) {
  int N = num_elements(x);
  vector[N] tanh_x = tanh(x);
  
  target += sum(log1m(square(tanh_x)));
  
  return tanh_x;
}
 
matrix cholesky_corr_constrain_lp(vector y, int K) {
  int k_choose_2 = (K * (K - 1)) %/% 2;
  vector[k_choose_2] z = corr_constrain_lp(y);
  matrix[K, K] x = rep_matrix(0, K, K);
  int iter = 0;
  
  x[1, 1] = 1;
  
  for (i in 2 : K) {
    real sum_sqs;
    iter += 1;
    x[i, 1] = z[iter];
    sum_sqs = square(x[i, 1]);
    if (i > 2) {
      for (j in 2 : i - 1) {
        iter += 1;
        target += 0.5 * log1m(sum_sqs);
        x[i, j] = z[iter] * sqrt(1.0 - sum_sqs);
        sum_sqs += square(x[i, j]);
      }
    }
    x[i, i] = sqrt(1.0 - sum_sqs);
  }
  return x;
}

Function Documentation

cholesky_corr_constrain_lp()

matrix cholesky_corr_constrain_lp	(	vector	y,
		int	K
	)

Cholesky Correlation Matrix Constraint

See https://mc-stan.org/docs/2_27/reference-manual/cholesky-factors-of-correlation-matrices-1.html

Copyright

Sean Pinkney, 2021

Author

Sean Pinkney

Parameters

y	Vector
K	Int

Returns

Cholesky factor of correlation matrix

corr_constrain_lp()

vector corr_constrain_lp

(

vector

x

)

Correlation Constraint

See https://mc-stan.org/docs/2_27/reference-manual/cholesky-factors-of-correlation-matrices-1.html

Copyright

Sean Pinkney, 2021

Author

Sean Pinkney

Parameters

x

Vector

Returns

vector \(\in (-1, 1)\)