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我正在试验 stan 和 Gaussian Processes。在一些错误之后，我发现一切的根源是函数的奇怪行为cov_exp_quad。
特别是我不明白为什么它返回一个不对称的矩阵。
这里是 stan 脚本：

data {
  int<lower=1> N;
  real x[N];
  real y[N];
}

transformed data {
  matrix[N,N] K = cov_exp_quad(x, y, 1, 1);
  }

generated quantities {
  matrix[N, N] Cov = K;
}

这里是R代码：

library(rstan)

x <- seq(0, 1, length.out = 3)

X <- expand.grid(x, x)

data_stan <- list(N = dim(X)[1],
                  x = X[, 1],
                  y = X[, 2])

fit <- stan(file = "./stan_script.stan",
            data = data_stan,
            algorithm = "Fixed_param",
            warmup = 0,
            chains = 1,
            iter = 1)

samples <- rstan::extract(fit)

drop(samples$Cov)

这是，而不是输出

> drop(samples$Cov)
           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]      [,9]
 [1,] 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969 0.6065307 0.6065307 0.6065307
 [2,] 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969
 [3,] 0.6065307 0.6065307 0.6065307 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000
 [4,] 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969 0.6065307 0.6065307 0.6065307
 [5,] 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969
 [6,] 0.6065307 0.6065307 0.6065307 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000
 [7,] 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969 0.6065307 0.6065307 0.6065307
 [8,] 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000 0.8824969 0.8824969 0.8824969
 [9,] 0.6065307 0.6065307 0.6065307 0.8824969 0.8824969 0.8824969 1.0000000 1.0000000 1.0000000

为什么这不是对称的？谢谢

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