Initialization failed for complicated code

My stan code involves a sequence of matrix multiplication (to transform rotation angle vector into Givens matrix). There is error:

Chain 1: Initialization between (-2, 2) failed after 100 attempts.
[1] “Error in sampler$call_sampler(args_list[[i]]) : Initialization failed.”
[1] “error occurred during calling the sampler; sampling not done”

I wonder: Can Stan compute the analytical log-posterior and its gradient for such complex code?

Below are the Stan code and the print you may refer to.

Thank you.

Stan code:

functions{
matrix theta2U(real[] theta1, real[] theta_ge2, int TT){
matrix[TT,TT] U;
real cos1;
real sin1;
row_vector[TT] linear1;
row_vector[TT] linear2;
int index;
index=1;
for(j in 2:TT){
cos1=cos(theta1[j-1]);
sin1=sin(theta1[j-1]);
linear1=cos1U[1,:]-sin1U[j,:];
linear2=sin1U[1,:]+cos1U[j,:];
U[1,:]=linear1;
U[j,:]=linear2;
}
for(i in 2:(TT-1)){
for(j in (i+1):TT){
cos1=cos(theta_ge2[index]);
sin1=sin(theta_ge2[index]);
linear1=cos1U[i,:]-sin1U[j,:];
linear2=sin1U[i,:]+cos1U[j,:];
U[i,:]=linear1;
U[j,:]=linear2;
index+=1;
// print(“i=”,i,", j=",j,", index=",index);
}
}
// print(“theta1=”,theta1);
// print(“theta_ge2=”,theta_ge2);
// print(“U=”,U);
return U;
}
}
data {
int<lower=0> V; // number of data points
int<lower=0> TT; // dimensionality
int<lower=0> C; // number of GMM components
matrix[TT,V] X; // prewhitened data matrix: Notice that each column is a sample
int<lower=0,upper=C> z[V,TT];
vector<lower=0>[C] alpha_w;
real<lower=0> sd_prior_mu_prime; //mu’~N(0,sd_prior_mu_prime^2)
real<lower=0> shape_gamma_prime;
real<lower=0> scale_gamma_prime;
}
parameters {
simplex[C] w[TT];
vector[C] mu_prime[TT];
vector<lower=0>[C] sigma_prime_sq[TT];
real<lower=0,upper=2pi()> theta1[TT-1]; //theta[1,j]: j=2,…,TT
real<lower=0,upper=pi()> theta_ge2[(TT-2)
(TT-1)/2]; //theta[i,j]: i=2,…,TT, j=i+1,…,TT
}
transformed parameters {
vector[C] mu[TT];
vector[C] mu_prime_prime[TT];
vector<lower=0>[C] sigma[TT];
real sd1;
matrix[TT,TT] U;

for(q in 1:TT){
mu_prime_prime[q]=mu_prime[q]-sum(w[q] .* mu_prime[q]);
sd1=sqrt(sum(w[q] .* (mu_prime_prime[q] .* mu_prime_prime[q]+sigma_prime_sq[q])));
mu[q]=mu_prime_prime[q]/sd1;
sigma[q]=sqrt(sigma_prime_sq[q])/sd1;
}
U=theta2U(theta1,theta_ge2,TT);
}
model {
print(“initial lp outside for loop=”,target());
theta1~uniform(0,2*pi()); //theta[1,j]: j=2,…,TT
theta_ge2~uniform(0,pi()); //theta[i,j]: i=2,…,TT, j=i+1,…,TT
print(“lp outside for loop after theta_ge2=”,target());

for(q in 1:TT){
print(“initial lp in for loop=”,target());
w[q] ~ dirichlet(alpha_w);
// print(“q=”,q);
// print(“w=”,w);
print(“lp after w=”,target());

mu_prime[q] ~ normal(0,sd_prior_mu_prime);
// print("mu_prime=",mu_prime);
print("lp after mu'=",target());

sigma_prime_sq[q] ~ inv_gamma(shape_gamma_prime,scale_gamma_prime);
// print("sigma_prime_sq=",sigma_prime_sq);
print("lp after sigma'=",target());

z[,q] ~ categorical(w[q]);
// target += categorical_lpmf(z | w);
print("lp after z=",target());

target += normal_lpdf(U[q,]*X | mu[q][z[,q]],sigma[q][z[,q]]);
// print("U[q,]=",U[q,]);
// print("mu=",mu);
// print("sigma=",sigma);
print("Final lp=",target());

}
}

R code:

MH=sampling(object=GMM.stan.model,data=list(V=V,TT=TT,C=Ck.max,X=t(x.prewhiten),z=z.mid,

  •                                         alpha_w=rep(0.02,Ck.max),sd_prior_mu_prime=2,
    
  •                                         shape_gamma_prime=1,scale_gamma_prime=1),
    
  •         init=list(list(w=array(1/Ck.max,c(TT,Ck.max)),mu_prime=array(0,c(TT,Ck.max)),
    
  •                        sigma_prime_sq=array(1,c(TT,Ck.max)),
    
  •                        theta1=rep(pi/3,TT-1),theta_ge2=rep(pi,(TT-2)*(TT-1)/2))),
    
  •         iter=10, warmup=5, chains = 1, control=list(adapt_delta=0.9),verbose=FALSE)
    

R console output:

SAMPLING FOR MODEL ‘GMMBLCAdesign20181030_standardize_withZ_redundant_1level’ NOW (CHAIN 1).
Chain 1: initial lp outside for loop=-inf
lp outside for loop after theta_ge2=-inf
initial lp in for loop=-inf
lp after w=-inf
lp after mu’=-inf
lp after sigma’=-inf
lp after z=-inf

…(these repeats many times)

Chain 1: initial lp outside for loop=-inf
lp outside for loop after theta_ge2=-inf
initial lp in for loop=-inf
lp after w=-inf
lp after mu’=-inf
lp after sigma’=-inf
lp after z=-inf

Chain 1: Initialization between (-2, 2) failed after 100 attempts.
[1] “Error in sampler$call_sampler(args_list[[i]]) : Initialization failed.”
[1] “error occurred during calling the sampler; sampling not done”

Yes, although it is just the differentiable log-posterior kernel that needs to be defined by the Stan program and then you can, in principle, differentiate it algorithmically. But the Discourse markdown messed up your code. Can you use the attach functionality to provide the Stan program and R code?