2-6 ARRAY STORAGE ORDER
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Array elements are stored in memory one after the other, if you
have a one-dimensional array, everything is simple, higher array
indices correspond to higher memory addresses.
With multi-dimensional arrays it is more complicated, there are
two practical possibilities: the COLUMN MAJOR ORDER used in FORTRAN,
and ROW MAJOR ORDER used in C.
Let's examine a small matrix:
A11 A12 A13
A21 A22 A23
A31 A32 A33
We can store the elements in memory like this:
A11 A21 A31 A12 A22 A32 A13 A23 A33 ---> Higher addresses
This is FORTRAN's Column major order, the first array index
varies most rapidly.
The alternative method is:
A11 A12 A13 A21 A22 A23 A31 A32 A33 ---> Higher addresses
That is C row major order, the last array index varies most rapidly.
By the way, if the matrix is symmetric the values stored in memory
will be the same in both methods.
Whole array operations
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When you WRITE an array in FORTRAN using just the array name,
you will get the elements written in FORTRAN's order - the
transpose of the mathematical order, the small 3x3 array:
A11 A12 A13
A21 A22 A23
A31 A32 A33
Will be written (with a format that allows 3 numbers per line):
A11 A21 A31
A12 A22 A32
A13 A23 A33
Try this small program:
PROGRAM ARRELM
C ------------------------------------------------------------------
INTEGER
* I, J,
* ARRAY(9,9)
C ------------------------------------------------------------------
DO I=1,9
DO J=1,9
ARRAY(I,J) = 10*I + J
ENDDO
ENDDO
C ------------------------------------------------------------------
WRITE(UNIT=*,'(1X,9I4)') ARRAY
C ------------------------------------------------------------------
END
If you always reference array elements using array indexes, and pass
whole arrays to subprograms, the memory order doesn't matter, except
when optimizing program memory use.
More 'sophisticated' (and worse) programs may depend on tricks based
on the internal memory order.

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