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20010512: array element order

David,

The netCDF library stores on disk an array of in-memory values in the
same order as the values exist in memory, i.e. contiguous memory
locations map to contiguous on-disk locations (with the exception of
arrays whose outermost dimension has been declared as unlimited -- but
this exception may safely be ignored).  Put another way, memory
locations of an array vary most rapidly for the innermost dimension of
the array -- the same holds true for the on-disk locations of the
array.

The C programming language has the outermost dimension in the leftmost
position and the innermost dimension in the rightmost position.
Consequently, the C netCDF API adopts the convention that the outermost
dimension maps to the first element of an index vector and the innermost
dimension maps to the last element.

The Fortran programming language has the outermost dimension in the
rightmost position and the innermost dimension in the leftmost position.
Consequently, the Fortran netCDF API adopts the convention that the
innermost dimension maps to the first element of an vector and the
outermost dimension maps to the last element.  The Fortran interface
layer reverses the order of these vectors and changes the indicies from
1-based to 0-based before invoking the C routines.

Now for your particular example:

> To: address@hidden
> cc: address@hidden
> From: "David C. Fox" <address@hidden>
> Subject: array element order
> Organization: Harvard
> Keywords: 200105121848.f4CImop14346

The above message contained the following:

> The documentation says that multidimensional arrays are stored in the
> same order regardless of the language and can be stored and retrieved by
> programs in different languages.  I assume that means
> that if you create
> 
> real a(3, 5)

In the above, the innermost dimension has length 3 and the outermost
dimension has length 5.  In Fortran, the index vector for the last
element would be

    integer ilast(2) / 3, 5 /

whereas in C it would be

    int ilast[2] = {4, 2};

> in Fortran and store it using the Fortran netCDF interface, the Fortran
> netCDF interfaces uses the Fortran-ordering to retrieve the contents of
> a from memory and then stores it in the file in netCDF order

The "netCDF order" of an array on-disk is the same as the in-memory
order.  It is the left/right ordering of the dimensions that differs
between the C and Fortran languages -- not the order of array elements
in-memory or on disk.

> whereas if you then read it in to a C array
> 
> float a[3][5]

The above declaration would be incorrect for the above "a" array because
it reverses the sizes of the dimensions.  The correct C declaration
would be

    float a[5][3]

because, in C, the leftmost dimension is the outermost and the rightmost
dimension is the innermost.

I hope this explanation helps.  Feel free to contact me if you have
additional questions.

Regards,
Steve Emmerson   <http://www.unidata.ucar.edu>