Integration of values in a buffer with Delphi - delphi

Question

Following on from my question on differentiation:
Differentiation of a buffer with Delphi
I'm now looking at doing the integration. I can't quite get my head around this one. The situation is that I receive a buffer of data periodically that contains a number of values that are a fixed distance in time apart. I need to differentiate them. It is soo long since I did calculus at school ....
What I have come up with is this:
procedure IntegrateBuffer(ABuffer: TDoubleDynArray;
var AOutBuffer: TDoubleDynArray;
AVPS: integer);
const
SumSum: double = 0.0;
LastValue: double = NaN;
var
i: integer;
dt, aa, hl, hr: double;
begin
// protect from divide by zero
if (AVPS < 1) then exit;
dt := 1 / AVPS;
for i := 0 to high(ABuffer) do begin
if (i = 0) then begin
if (IsNaN(LastValue)) then begin
hl := ABuffer[0];
hr := ABuffer[0];
end else begin
hl := LastValue;
hr := ABuffer[i];
end;
end else begin
hl := ABuffer[i -1];
hr := ABuffer[i];
end;
aa := 0.5 * dt * (hl + hr);
SumSum := SumSum + aa;
AOutBuffer[i] := SumSum;
end;
// remember the last value for next time
LastValue := ABuffer[high(ABuffer)];
end;
I'm using the trapezium rule, hl and hr ar the left and right heights of the trapezium. dt is the base.
AVPS is values per second. A typical value for this would be between 10 and 100. The length of the buffers would typically be 500 to 1000 values.
I call the buffer time after time with new data which is continuous with the previous block of data, hence keeping the last value of the block for next time.
Is what I have done correct? ie, will it integrate the values properly?
Thank you.

Answer 1

Looks like you need some help with testing the code. Here, as discussed in comments, is a very simple test.
{$APPTYPE CONSOLE}
uses
SysUtils, Math;
type
TDoubleDynArray = array of Double;
var
SumSum: double;
LastValue: double;
procedure Clear;
begin
SumSum := 0.0;
LastValue := NaN;
end;
procedure IntegrateBuffer(
ABuffer: TDoubleDynArray;
var AOutBuffer: TDoubleDynArray;
AVPS: integer
);
var
i: integer;
dt, aa, hl, hr: double;
begin
// protect from divide by zero
if (AVPS < 1) then exit;
dt := 1 / AVPS;
for i := 0 to high(ABuffer) do begin
if (i = 0) then begin
if (IsNaN(LastValue)) then begin
hl := ABuffer[0];
hr := ABuffer[0];
end else begin
hl := LastValue;
hr := ABuffer[i];
end;
end else begin
hl := ABuffer[i -1];
hr := ABuffer[i];
end;
aa := 0.5 * dt * (hl + hr);
SumSum := SumSum + aa;
AOutBuffer[i] := SumSum;
end;
// remember the last value for next time
LastValue := ABuffer[high(ABuffer)];
end;
var
Buffer: TDoubleDynArray;
OutBuffer: TDoubleDynArray;
begin
// test y = 1 for a single call, expected output = 1, actual output = 2
Clear;
Buffer := TDoubleDynArray.Create(1.0, 1.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Writeln(OutBuffer[high(OutBuffer)]);
Readln;
end.
I'm integrating the function y(x) = 1 over the range [0..1]. So, the expected output is 1. But the actual output is 2.
So, what's wrong? You can work it out in the debugger, but it's easy enough to see by inspecting the code. You are summing a triangle on the very first sample. When IsNaN(LastValue) is true then you should not make a contribution to the integral. At that point you've not covered any distance on the x axis.
So to fix the code, let's try this:
....
if (IsNaN(LastValue)) then begin
hl := 0.0;//no contribution to sum
hr := 0.0;
end else begin
hl := LastValue;
hr := ABuffer[i];
end;
....
That fixes the problem.
Now let's extend the test a little and test y(x) = x:
// test y = x, expected output = 12.5
Clear;
Buffer := TDoubleDynArray.Create(0.0, 1.0, 2.0, 3.0, 4.0, 5.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Writeln(OutBuffer[high(OutBuffer)]);
So, that looks good.
OK, what about multiple calls:
// test y = x for multiple calls, expected output = 18
Clear;
Buffer := TDoubleDynArray.Create(0.0, 1.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Buffer := TDoubleDynArray.Create(2.0, 3.0, 4.0, 5.0, 6.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Writeln(OutBuffer[high(OutBuffer)]);
And how about one value at a time?
// test y = x for multiple calls, one value at a time, expected 0.5
Clear;
Buffer := TDoubleDynArray.Create(0.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Buffer := TDoubleDynArray.Create(1.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Writeln(OutBuffer[high(OutBuffer)]);
What about passing an empty array?
// test y = x for multiple calls, some empty arrays, expected 0.5
Clear;
Buffer := TDoubleDynArray.Create(0.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Buffer := nil;
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Buffer := TDoubleDynArray.Create(1.0);
SetLength(OutBuffer, Length(Buffer));
IntegrateBuffer(Buffer, OutBuffer, 1);
Writeln(OutBuffer[high(OutBuffer)]);
Uh, oh, access violation. Better protect that by simply skipping the function at the start if the buffer is empty:
if (AVPS < 1) then exit;
if (Length(ABuffer) = 0) then exit;
OK, now that last test passes
Hopefully you get the idea now. I've just used noddy Writeln based testing but that does not scale. Get yourself a unit test framework (I recommend DUnitX) and build proper test cases. This will also force you to factor your code so that it is well designed. One of the often unexpected benefits of making code testable is that it usually results in the design of the interface being improved.
For your next question, I request that you supply an SSCCE with the test code! ;-)
Some comments on the code:
Pass dynamic arrays by const or by var. In your case you want to pass the input buffer by const.
Don't use writeable typed constants. Use either parameters, or some other more sane state management.
Again, as I said in the previous question, write tests to prove code, as well as checking it by eye. The key to writing tests is to start with the very simplest thing you can possibly think of. Something so simple that you know for 100% sure the answer. Then, once you get that to work, expand the testing to more complex cases.