Hi all,

I need to define a matrix of the following form:

```
Cova_trans = diag_matrix(rep_vector(1, R))- matrix_exp(-deltat[k] * diag_matrix(rep_vector(0.1, R))) * diag_matrix(rep_vector(1, R)) * matrix_exp(-deltat[k] * diag_matrix(rep_vector(0.1, R))');
print(Cova_trans);
xi[k] ~ multi_normal(matrix_exp(-deltat[k] * Gamma) * xi[k-1], Cova_trans);
```

This is a simpler version but just take this one for my question.

By hand calculation, Cova_trans is of the form qI_3 where (0<q<1). (R=3 is provided by data block).

We know that I_3 is positive definite so is qI_3. To be sure, I use R, function is.positive.definite(matrix, tol=1e-1) and obtain the same result of positive definiteness.

However, when I run the code, Stan gives an error:

```
Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: multi_normal_lpdf: LDLT_Factor of covariance parameter is not positive definite. last conditional variance is 0. (in 'model1d881fc227d2_modelALS' at line 170)
Initialization between (-2, 2) failed after 100 attempts.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
[1] "Error in sampler$call_sampler(args_list[[i]]) : Initialization failed."
[1] "error occurred during calling the sampler; sampling not done"
```

I use print function and see that in the console in R I obtain:

```
[[0.999999,0,0],[0,0.999999,0],[0,0,0.999999]]
[[0.999997,0,0],[0,0.999997,0],[0,0,0.999997]]
[[0.999986,0,0],[0,0.999986,0],[0,0,0.999986]]
[[0.834701,0,0],[0,0.834701,0],[0,0,0.834701]]
[[0.834701,0,0],[0,0.834701,0],[0,0,0.834701]]
[[0.997521,0,0],[0,0.997521,0],[0,0,0.997521]]
[[0.996302,0,0],[0,0.996302,0],[0,0,0.996302]]
[[0.993262,0,0],[0,0.993262,0],[0,0,0.993262]]
```

Clearly these matrices are of the form qI_3 and they are positive definite.

So my question is: Why does Stan says that the matrix is not positive definite contradicting with hand calculation. Why does Stan gives error even Stan prints positive definite matrices?

Thank you for reading!

**P/S**: I am sorry that I cannot post the full code. It is not allowed at this moment.