Array Arguments

Each two-dimensional array argument is immediately followed in the argument list by its leading dimension, whose name has the form LD<array-name>. For example:

A

(input/output) REAL/COMPLEX array, dimension (LDA,N)
...

LDA

(input) INTEGER
The leading dimension of the array A. LDA $\geq$ max(1,M).

It should be assumed, unless stated otherwise, that vectors and matrices are stored in one- and two-dimensional arrays in the conventional manner. That is, if an array X of dimension (N) holds a vector x, then X(i) holds x_i for $i = 1, \ldots, n$. If a two-dimensional array A of dimension (LDA,N) holds an m-by-n matrix A, then A(i,j) holds a_ij for $i = 1, \ldots, m$ and $j = 1, \ldots, n$ (LDA must be at least m). See Section 5.3 for more about storage of matrices.

Note that array arguments are usually declared in the software as assumed-size arrays (last dimension *), for example:

      REAL A( LDA, * )

although the documentation gives the dimensions as (LDA,N). The latter form is more informative since it specifies the required minimum value of the last dimension. However an assumed-size array declaration has been used in the software, in order to overcome some limitations in the Fortran 77 standard. In particular it allows the routine to be called when the relevant dimension (N, in this case) is zero. However actual array dimensions in the calling program must be at least 1 (LDA in this example).