Function to average elements of any array in Delphi - arrays

Question

How can we implement a function to average all elements of a dynamic multidimensional array in Delphi 6? Such as:
Function Average(arr:any_array):extended;
Where arr is a dynamic array and may have 1 or more dimensions.
Linked question: how can we linearize a multidimension array? Do you have any example?
I ask this because I have many different arrays which I must average, if possible, with the one same function.

Answer 1

If you have one dimensional array you can simply use Mean function located in Math unit.
But for multidimensional array I'm afraid there is no already available function. The main reason is that Delphi treats multidimensional arrays in a rather specific way.
While in many other programming languages multidimensional array are in fact just one dimensional array with modified mechanism for accessing array elements which works something like this:
Actual Array Item Index = First parameter + (Second parameter * Size of first dimension)
In Delphi multidimensional arrays are represented as multiple one dimensional array referenced by another array like so:
Array of One Dimensional Array
EDIT 2: As mentioned by David in his comment these type of arrays are also known as Jagged arrays or Ragged arrays.
Why is this so different? Why is it so important? Because those One Dimensional Arrays that from multidimensional array in Delphi don't need to be of the same size. So data in your multidimensional array can actually look like this (where each X represents one array item):
XXXX
XXXXXXX
XXXX
XXXXX
So I'm afraid you will have to write your own function for this. But that should not be so hard.
All you need is a mechanism to iterate through every item in your arrays (I bet you have this already implemented in your code somewhere) so you can sum up the value of all elements in your arrays. And then you divide that sum with the number of elements in your arrays in order to get the arithmetical average of all items.
EDIT 3: I'm not sure if you could have single code to iterate through all of your dynamic arrays. I mean at least you need to know how many dimensions does your array have. This is required because for iterating through multiple dimensions of an array you actually need to recursively iterate through each separate array that represents separate dimensions.
The code for summing up elements in a 3D dynamic array would look like this:
type
TDyn3Darray = array of array of array of Single;
implementation
function SumOf3DArray(Dyn3DArray: TDyn3DArray): Single;
var X,Y,Z, a: Integer;
ArrItem: Single;
begin
Result := 0;
SetLength(Dyn3Darray,5,8,40);
for X := Low(Dyn3Darray) to High(Dyn3Darray) do
begin
for Y := Low(Dyn3Darray[X]) to High(Dyn3Darray[X]) do
begin
for Z := Low(Dyn3Darray[X,Y]) to High(Dyn3Darray[X,Y]) do
begin
Result := Result + Dyn3Darray[X,Y,Z];
end;
end;
end;
end;
I believe you will be capable to modify the code accordingly for different number of dimensions yourself.
EDIT 1: As for linearizing of multidimensional arrays in which I believe you mean changing the multidimensional array in one dimensional array you would just copy elements of separate dimensions and add them into one dimensional array.
But doing that just in order to get average value of all elements would not be practical because for first you would need double the amount of memory and as second in order to copy all the elements from multiple dimension into one you would probably have to iterate through every element in the first place. And then whatever method would you use for calculating average value would also have to iterate through all those copied elements again and thus just slowing down the process for no good reason.
And if you are interested in replacing multidimensional arrays with one dimensional arrays while still threating its elements as if they are in multidimensional array check my explanation of how some other programming languages treat multidimensional array.
NOTE that this would require you accessing all items of such arrays through special methods and will thus result in large changes of your code where you interact with these arrays. Unless if you would wrap these arrays in a class with default multi indexed property that will allow you accessing the array items. Such approach would require additional code for initialization and finalization of such classes and require a slightly modified approach when resizing of such arrays.

Answer 2

Delphi does not provide easy ways for you to inspect the dimensions of an arbitrary dynamic array. Indeed it provides no means for you to pass around an arbitrary dynamic array. However, in practice, you will encounter one and two dimensional arrays commonly, and seldom anything of higher dimensions. So you need to write only a handful of functions:
type
TDoubleArray1 = array of Double;
TDoubleArray2 = array of TDoubleArray1;
TDoubleArray3 = array of TDoubleArray2;
function Mean(const arr: TDoubleArray1): Double; overload;
function Mean(const arr: TDoubleArray2): Double; overload;
function Mean(const arr: TDoubleArray3): Double; overload;
Implement like this:
function Mean(const arr: TDoubleArray1): Double;
var
i: Integer;
begin
Result := 0.0;
for i := low(arr) to high(arr) do
Result := Result + arr[i];
Result := Result / Length(arr);
end;
function Mean(const arr: TDoubleArray2): Double;
var
i, j, N: Integer;
begin
Result := 0.0;
N := 0;
for i := low(arr) to high(arr) do
for j := low(arr[i]) to high(arr[i]) do
begin
Result := Result + arr[i,j];
inc(N);
end;
Result := Result / N;
end;
function Mean(const arr: TDoubleArray3): Double;
var
i, j, k, N: Integer;
begin
Result := 0.0;
N := 0;
for i := low(arr) to high(arr) do
for j := low(arr[i]) to high(arr[i]) do
for k := low(arr[i,j]) to high(arr[i,j]) do
begin
Result := Result + arr[i,j,k];
inc(N);
end;
Result := Result / N;
end;
It would astound me if you really needed higher dimensions than this, but it is easy to add.
Some points:
I'm using Double rather than Extended for reasons of performance, as the latter has a size of 10 which leads to a lot of mis-aligned memory access. If you cannot bring yourself to avoid Extended you can readily adapt the code above.
You could probably find low-level methods using RTTI to write a single function that iterates over any dynamic array, however, the RTTI would likely impact performance. I personally don't see any point in going that route. Use a handful of functions like this and be done.