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## 6.7 Indexing

Stan arrays, matrices, vectors, and row vectors are all accessed using the same array-like notation. For instance, if x is a variable of type array [] real (a one-dimensional array of reals) then x[1] is the value of the first element of the array.

Subscripting has higher precedence than any of the arithmetic operations. For example, alpha * x[1] is equivalent to alpha * (x[1]).

Multiple subscripts may be provided within a single pair of square brackets. If x is of type array[,] real, a two-dimensional array, then x[2, 501] is of type real.

### Accessing subarrays

The subscripting operator also returns subarrays of arrays. For example, if x is of type array[,,] real, then x[2] is of type array[,] real, and x[2, 3] is of type array[] real. As a result, the expressions x[2, 3] and x[2][3] have the same meaning.

### Accessing matrix rows

If Sigma is a variable of type matrix, then Sigma[1] denotes the first row of Sigma and has the type row_vector.

### Mixing array and vector/matrix indexes

Stan supports mixed indexing of arrays and their vector, row vector or matrix values. For example, if m is of type matrix[ , ], a two-dimensional array of matrices, then m[1] refers to the first row of the array, which is a one-dimensional array of matrices. More than one index may be used, so that m[1, 2] is of type matrix and denotes the matrix in the first row and second column of the array. Continuing to add indices, m[1, 2, 3] is of type row_vector and denotes the third row of the matrix denoted by m[1, 2]. Finally, m[1, 2, 3, 4] is of type real and denotes the value in the third row and fourth column of the matrix that is found at the first row and second column of the array m.