Add LogSumExp functions #34
Description
LogSumExp
LogSumExp or LSE for a sequence x1,...,xn is is defined as the logarithm of the sum of the exponentials of the arguments:
LSE(x1,...,xn) = log(exp(x1) + ... + exp(xn))
Source: Wikipedia
function LSE(const A: array of Extended): Extended;
begin
var Sum: Extended := 0.0;
for var X in A do
Sum := Sum + Exp(X):
Result := Ln(Sum);
end;Strictly Convex LogSumExp
Source: Wikipedia
Since exp(0) = e^0 = 1, we have
LSE(0, x1,...,xn) = log(exp(0) + exp(x1) + ... + exp(xn))
= log(1 + exp(x1) + ... + exp(xn)),
So, in Pascal we can have:
function ConvexLSE(const A: array of Extended): Extended;
begin
var Sum: Extended := 1.0; // for additional Exp(0) term
for var X in A do
Sum := Sum + Exp(X):
Result := Ln(Sum);
end;This issue was extracted from issue #16
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