Cholesky Correlation Angles Matrix Constraint functions

Functions
matrix	angle2chol (matrix angle_mat)
matrix	angle_vec2angle_mat (vector angle, int K)

Detailed Description

 
matrix angle2chol(matrix angle_mat) {
  int N = rows(angle_mat);
  matrix[N, N] inv_mat = identity_matrix(N);
  
  inv_mat[ : , 1] = cos(angle_mat[ : , 1]);
  
  for (i in 2 : N) {
    inv_mat[i, i] = prod(sin(angle_mat[i, 1 : (i - 1)]));
    if (i > 2) {
      for (j in 2 : (i - 1)) {
        inv_mat[i, j] = cos(angle_mat[i, j]) * prod(sin(angle_mat[i, 1 : (j - 1)]));
      }
    }
  }
  return inv_mat;
}
 
matrix angle_vec2angle_mat(vector angle, int K) {
  int N = num_elements(angle);
  matrix[K, K] mat = add_diag(identity_matrix(K), rep_vector(-1, K));
  int count = K - 1;
  int pos = 1;
  
  for (k in 1 : K - 1) {
    mat[k + 1 : K, k] = segment(angle, pos, count);
    pos += count;
    count -= 1;
  }
  
  return mat;
}

Function Documentation

angle2chol()

matrix angle2chol

(

matrix

angle_mat

)

Angles matrix to Cholesky correlation

Copyright 2021, Sean Pinkney

Peter J. Rousseeuw & Geert Molenberghs (1993) Transformation of non positive semidefinite correlation matrices, Communications in Statistics - Theory and Methods, 22:4, 965-984, DOI: 10.1080/03610928308831068

Parameters

angle_mat	Matrix of angles
Cholesky	factor of correlation matrix

angle_vec2angle_mat()

matrix angle_vec2angle_mat	(	vector	angle,
		int	K
	)

Angle svector to angle matrix

Copyright 2021, Sean Pinkney

Parameters

angle	Vector of angles length of the number of elements of the lower triangle elemements n/ of the output angle matrix. If the size of the output matrix is K x K then the n/ length is K * (K - 1) / 2
angle	matrix