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https://gitlab.com/freepascal.org/fpc/source.git
synced 2025-04-14 18:19:54 +02:00
* overloaded statistics functions from Burkhard Carstens, fixed #7236
git-svn-id: trunk@4385 -
This commit is contained in:
florian
parent
22657a363b
commit
d6fe62f0d1
@ -300,12 +300,41 @@ function ldexp(x : float; const p : Integer) : float;
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{ statistical functions }
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function mean(const data : array of Single) : float;
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function sum(const data : array of Single) : float;
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function mean(const data : PSingle; Const N : longint) : float;
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function sum(const data : PSingle; Const N : Longint) : float;
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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function mean(const data : array of double) : float;
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function sum(const data : array of double) : float;
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function mean(const data : PDouble; Const N : longint) : float;
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function sum(const data : PDouble; Const N : Longint) : float;
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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function mean(const data : array of Extended) : float;
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function sum(const data : array of Extended) : float;
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function mean(const data : PExtended; Const N : longint) : float;
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function sum(const data : PExtended; Const N : Longint) : float;
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{$endif FPC_HAS_TYPE_EXTENDED}
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function sumInt(const data : PInt64;Const N : longint) : Int64;
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function sumInt(const data : array of Int64) : Int64;
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function sumofsquares(const data : array of Single) : float;
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function sumofsquares(const data : PSingle; Const N : Integer) : float;
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{ calculates the sum and the sum of squares of data }
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procedure sumsandsquares(const data : array of Single;
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var sum,sumofsquares : float);
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procedure sumsandsquares(const data : PSingle; Const N : Integer;
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var sum,sumofsquares : float);
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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function sumofsquares(const data : array of double) : float;
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function sumofsquares(const data : PDouble; Const N : Integer) : float;
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{ calculates the sum and the sum of squares of data }
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@ -313,14 +342,80 @@ procedure sumsandsquares(const data : array of Double;
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var sum,sumofsquares : float);
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procedure sumsandsquares(const data : PDouble; Const N : Integer;
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var sum,sumofsquares : float);
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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function sumofsquares(const data : array of Extended) : float;
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function sumofsquares(const data : PExtended; Const N : Integer) : float;
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{ calculates the sum and the sum of squares of data }
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procedure sumsandsquares(const data : array of Extended;
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var sum,sumofsquares : float);
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procedure sumsandsquares(const data : PExtended; Const N : Integer;
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var sum,sumofsquares : float);
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{$endif FPC_HAS_TYPE_EXTENDED}
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function minvalue(const data : array of Single) : Single;
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function minvalue(const data : PSingle; Const N : Integer) : Single;
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function maxvalue(const data : array of Single) : Single;
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function maxvalue(const data : PSingle; Const N : Integer) : Single;
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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function minvalue(const data : array of Double) : Double;
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function minvalue(const data : array of integer) : Integer;
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function minvalue(const data : PDouble; Const N : Integer) : Double;
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function MinValue(const Data : PInteger; Const N : Integer): Integer;
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function maxvalue(const data : array of Double) : Double;
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function maxvalue(const data : array of integer) : Integer;
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function maxvalue(const data : PDouble; Const N : Integer) : Double;
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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function minvalue(const data : array of Extended) : Extended;
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function minvalue(const data : PExtended; Const N : Integer) : Extended;
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function maxvalue(const data : array of Extended) : Extended;
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function maxvalue(const data : PExtended; Const N : Integer) : Extended;
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{$endif FPC_HAS_TYPE_EXTENDED}
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function minvalue(const data : array of integer) : Integer;
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function MinValue(const Data : PInteger; Const N : Integer): Integer;
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function maxvalue(const data : array of integer) : Integer;
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function maxvalue(const data : PInteger; Const N : Integer) : Integer;
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{ returns random values with gaussian distribution }
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function randg(mean,stddev : float) : float;
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{$ifdef FPC_HAS_TYPE_SINGLE}
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{ calculates the standard deviation }
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function stddev(const data : array of Single) : float;
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function stddev(const data : PSingle; Const N : Integer) : float;
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{ calculates the mean and stddev }
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procedure meanandstddev(const data : array of Single;
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var mean,stddev : float);
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procedure meanandstddev(const data : PSingle;
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Const N : Longint;var mean,stddev : float);
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function variance(const data : array of Single) : float;
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function totalvariance(const data : array of Single) : float;
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function variance(const data : PSingle; Const N : Integer) : float;
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function totalvariance(const data : PSingle; Const N : Integer) : float;
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{ I don't know what the following functions do: }
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function popnstddev(const data : array of Single) : float;
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function popnstddev(const data : PSingle; Const N : Integer) : float;
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function popnvariance(const data : PSingle; Const N : Integer) : float;
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function popnvariance(const data : array of Single) : float;
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procedure momentskewkurtosis(const data : array of Single;
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var m1,m2,m3,m4,skew,kurtosis : float);
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procedure momentskewkurtosis(const data : PSingle; Const N : Integer;
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var m1,m2,m3,m4,skew,kurtosis : float);
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{ geometrical function }
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{ returns the euclidean L2 norm }
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function norm(const data : array of Single) : float;
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function norm(const data : PSingle; Const N : Integer) : float;
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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{ calculates the standard deviation }
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function stddev(const data : array of Double) : float;
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function stddev(const data : PDouble; Const N : Integer) : float;
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@ -333,8 +428,6 @@ function variance(const data : array of Double) : float;
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function totalvariance(const data : array of Double) : float;
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function variance(const data : PDouble; Const N : Integer) : float;
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function totalvariance(const data : PDouble; Const N : Integer) : float;
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{ returns random values with gaussian distribution }
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function randg(mean,stddev : float) : float;
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{ I don't know what the following functions do: }
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function popnstddev(const data : array of Double) : float;
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@ -351,6 +444,38 @@ procedure momentskewkurtosis(const data : PDouble; Const N : Integer;
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{ returns the euclidean L2 norm }
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function norm(const data : array of double) : float;
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function norm(const data : PDouble; Const N : Integer) : float;
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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{ calculates the standard deviation }
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function stddev(const data : array of Extended) : float;
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function stddev(const data : PExtended; Const N : Integer) : float;
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{ calculates the mean and stddev }
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procedure meanandstddev(const data : array of Extended;
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var mean,stddev : float);
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procedure meanandstddev(const data : PExtended;
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Const N : Longint;var mean,stddev : float);
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function variance(const data : array of Extended) : float;
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function totalvariance(const data : array of Extended) : float;
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function variance(const data : PExtended; Const N : Integer) : float;
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function totalvariance(const data : PExtended; Const N : Integer) : float;
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{ I don't know what the following functions do: }
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function popnstddev(const data : array of Extended) : float;
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function popnstddev(const data : PExtended; Const N : Integer) : float;
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function popnvariance(const data : PExtended; Const N : Integer) : float;
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function popnvariance(const data : array of Extended) : float;
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procedure momentskewkurtosis(const data : array of Extended;
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var m1,m2,m3,m4,skew,kurtosis : float);
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procedure momentskewkurtosis(const data : PExtended; Const N : Integer;
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var m1,m2,m3,m4,skew,kurtosis : float);
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{ geometrical function }
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{ returns the euclidean L2 norm }
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function norm(const data : array of Extended) : float;
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function norm(const data : PExtended; Const N : Integer) : float;
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{$endif FPC_HAS_TYPE_EXTENDED}
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function ifthen(val:boolean;const iftrue:integer; const iffalse:integer= 0) :integer; {$ifdef MATHINLINE}inline; {$endif}
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function ifthen(val:boolean;const iftrue:int64 ; const iffalse:int64 = 0) :int64; {$ifdef MATHINLINE}inline; {$endif}
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@ -724,10 +849,43 @@ function ldexp(x : float;const p : Integer) : float;
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ldexp:=x*intpower(2.0,p);
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end;
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function mean(const data : array of Single) : float;
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begin
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Result:=Mean(PSingle(@data[0]),High(Data)+1);
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end;
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function mean(const data : PSingle; Const N : longint) : float;
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begin
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mean:=sum(Data,N);
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mean:=mean/N;
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end;
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function sum(const data : array of Single) : float;
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begin
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Result:=Sum(PSingle(@Data[0]),High(Data)+1);
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end;
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function sum(const data : PSingle;Const N : longint) : float;
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var
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i : longint;
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begin
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sum:=0.0;
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for i:=0 to N-1 do
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sum:=sum+data[i];
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end;
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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function mean(const data : array of Double) : float;
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begin
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Result:=Mean(@data[0],High(Data)+1);
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Result:=Mean(PDouble(@data[0]),High(Data)+1);
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end;
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function mean(const data : PDouble; Const N : longint) : float;
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@ -740,7 +898,7 @@ function mean(const data : PDouble; Const N : longint) : float;
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function sum(const data : array of Double) : float;
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begin
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Result:=Sum(@Data[0],High(Data)+1);
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Result:=Sum(PDouble(@Data[0]),High(Data)+1);
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end;
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function sum(const data : PDouble;Const N : longint) : float;
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@ -753,6 +911,39 @@ function sum(const data : PDouble;Const N : longint) : float;
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for i:=0 to N-1 do
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sum:=sum+data[i];
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end;
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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function mean(const data : array of Extended) : float;
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begin
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Result:=Mean(PExtended(@data[0]),High(Data)+1);
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end;
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function mean(const data : PExtended; Const N : longint) : float;
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begin
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mean:=sum(Data,N);
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mean:=mean/N;
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end;
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function sum(const data : array of Extended) : float;
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begin
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Result:=Sum(PExtended(@Data[0]),High(Data)+1);
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end;
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function sum(const data : PExtended;Const N : longint) : float;
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var
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i : longint;
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begin
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sum:=0.0;
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for i:=0 to N-1 do
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sum:=sum+data[i];
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end;
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{$endif FPC_HAS_TYPE_EXTENDED}
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function sumInt(const data : PInt64;Const N : longint) : Int64;
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@ -771,10 +962,55 @@ function sumInt(const data : array of Int64) : Int64;
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Result:=SumInt(@Data[0],High(Data)+1);
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end;
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function sumofsquares(const data : array of Single) : float;
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begin
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Result:=sumofsquares(PSingle(@data[0]),High(Data)+1);
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end;
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function sumofsquares(const data : PSingle; Const N : Integer) : float;
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var
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i : longint;
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begin
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sumofsquares:=0.0;
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for i:=0 to N-1 do
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sumofsquares:=sumofsquares+sqr(data[i]);
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end;
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procedure sumsandsquares(const data : array of Single;
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var sum,sumofsquares : float);
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begin
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sumsandsquares (PSingle(@Data[0]),High(Data)+1,Sum,sumofsquares);
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end;
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procedure sumsandsquares(const data : PSingle; Const N : Integer;
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var sum,sumofsquares : float);
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var
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i : Integer;
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temp : float;
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begin
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sumofsquares:=0.0;
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sum:=0.0;
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for i:=0 to N-1 do
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begin
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temp:=data[i];
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sumofsquares:=sumofsquares+sqr(temp);
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sum:=sum+temp;
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end;
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end;
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{$endif FPC_HAS_TYPE_SINGLE}
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{$ifdef FPC_HAS_TYPE_DOUBLE}
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function sumofsquares(const data : array of Double) : float;
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begin
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Result:=sumofsquares(@data[0],High(Data)+1);
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Result:=sumofsquares(PDouble(@data[0]),High(Data)+1);
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end;
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function sumofsquares(const data : PDouble; Const N : Integer) : float;
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@ -792,7 +1028,7 @@ procedure sumsandsquares(const data : array of Double;
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var sum,sumofsquares : float);
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begin
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sumsandsquares (@Data[0],High(Data)+1,Sum,sumofsquares);
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sumsandsquares (PDouble(@Data[0]),High(Data)+1,Sum,sumofsquares);
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end;
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procedure sumsandsquares(const data : PDouble; Const N : Integer;
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@ -812,13 +1048,224 @@ procedure sumsandsquares(const data : PDouble; Const N : Integer;
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sum:=sum+temp;
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end;
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end;
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{$endif FPC_HAS_TYPE_DOUBLE}
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{$ifdef FPC_HAS_TYPE_EXTENDED}
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function sumofsquares(const data : array of Extended) : float;
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begin
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Result:=sumofsquares(PExtended(@data[0]),High(Data)+1);
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end;
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function sumofsquares(const data : PExtended; Const N : Integer) : float;
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var
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i : longint;
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begin
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sumofsquares:=0.0;
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for i:=0 to N-1 do
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sumofsquares:=sumofsquares+sqr(data[i]);
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end;
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procedure sumsandsquares(const data : array of Extended;
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var sum,sumofsquares : float);
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begin
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sumsandsquares (PExtended(@Data[0]),High(Data)+1,Sum,sumofsquares);
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end;
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procedure sumsandsquares(const data : PExtended; Const N : Integer;
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var sum,sumofsquares : float);
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var
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i : Integer;
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temp : float;
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begin
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sumofsquares:=0.0;
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sum:=0.0;
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for i:=0 to N-1 do
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begin
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temp:=data[i];
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sumofsquares:=sumofsquares+sqr(temp);
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sum:=sum+temp;
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end;
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end;
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{$endif FPC_HAS_TYPE_EXTENDED}
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function randg(mean,stddev : float) : float;
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Var U1,S2 : Float;
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begin
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repeat
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u1:= 2*random-1;
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S2:=Sqr(U1)+sqr(2*random-1);
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until s2<1;
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randg:=Sqrt(-2*ln(S2)/S2)*u1*stddev+Mean;
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end;
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{$ifdef FPC_HAS_TYPE_SINGLE}
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function stddev(const data : array of Single) : float;
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begin
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Result:=Stddev(PSingle(@Data[0]),High(Data)+1)
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end;
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function stddev(const data : PSingle; Const N : Integer) : float;
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begin
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StdDev:=Sqrt(Variance(Data,N));
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end;
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procedure meanandstddev(const data : array of Single;
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var mean,stddev : float);
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begin
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Meanandstddev(PSingle(@Data[0]),High(Data)+1,Mean,stddev);
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end;
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procedure meanandstddev(const data : PSingle;
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Const N : Longint;var mean,stddev : float);
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Var I : longint;
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begin
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Mean:=0;
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StdDev:=0;
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For I:=0 to N-1 do
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begin
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Mean:=Mean+Data[i];
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StdDev:=StdDev+Sqr(Data[i]);
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end;
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Mean:=Mean/N;
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StdDev:=(StdDev-N*Sqr(Mean));
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If N>1 then
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StdDev:=Sqrt(Stddev/(N-1))
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else
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StdDev:=0;
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end;
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function variance(const data : array of Single) : float;
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begin
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Variance:=Variance(PSingle(@Data[0]),High(Data)+1);
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end;
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function variance(const data : PSingle; Const N : Integer) : float;
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begin
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If N=1 then
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Result:=0
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else
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Result:=TotalVariance(Data,N)/(N-1);
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end;
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function totalvariance(const data : array of Single) : float;
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begin
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Result:=TotalVariance(PSingle(@Data[0]),High(Data)+1);
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end;
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|
||||
function totalvariance(const data : PSingle;Const N : Integer) : float;
|
||||
|
||||
var S,SS : Float;
|
||||
|
||||
begin
|
||||
If N=1 then
|
||||
Result:=0
|
||||
else
|
||||
begin
|
||||
SumsAndSquares(Data,N,S,SS);
|
||||
Result := SS-Sqr(S)/N;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
function popnstddev(const data : array of Single) : float;
|
||||
|
||||
begin
|
||||
PopnStdDev:=Sqrt(PopnVariance(PSingle(@Data[0]),High(Data)+1));
|
||||
end;
|
||||
|
||||
function popnstddev(const data : PSingle; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
PopnStdDev:=Sqrt(PopnVariance(Data,N));
|
||||
end;
|
||||
|
||||
function popnvariance(const data : array of Single) : float;
|
||||
|
||||
begin
|
||||
popnvariance:=popnvariance(PSingle(@data[0]),high(Data)+1);
|
||||
end;
|
||||
|
||||
function popnvariance(const data : PSingle; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
PopnVariance:=TotalVariance(Data,N)/N;
|
||||
end;
|
||||
|
||||
procedure momentskewkurtosis(const data : array of Single;
|
||||
var m1,m2,m3,m4,skew,kurtosis : float);
|
||||
|
||||
begin
|
||||
momentskewkurtosis(PSingle(@Data[0]),High(Data)+1,m1,m2,m3,m4,skew,kurtosis);
|
||||
end;
|
||||
|
||||
procedure momentskewkurtosis(const data : PSingle; Const N : Integer;
|
||||
var m1,m2,m3,m4,skew,kurtosis : float);
|
||||
|
||||
Var S,SS,SC,SQ,invN,Acc,M1S,S2N,S3N,temp : Float;
|
||||
I : Longint;
|
||||
|
||||
begin
|
||||
invN:=1.0/N;
|
||||
s:=0;
|
||||
ss:=0;
|
||||
sq:=0;
|
||||
sc:=0;
|
||||
for i:=0 to N-1 do
|
||||
begin
|
||||
temp:=Data[i]; { faster }
|
||||
S:=S+temp;
|
||||
acc:=sqr(temp);
|
||||
ss:=ss+acc;
|
||||
Acc:=acc*temp;
|
||||
Sc:=sc+acc;
|
||||
acc:=acc*temp;
|
||||
sq:=sq+acc;
|
||||
end;
|
||||
M1:=s*invN;
|
||||
M1S:=sqr(M1);
|
||||
S2N:=SS*invN;
|
||||
S3N:=SC*invN;
|
||||
M2:=S2N-M1S;
|
||||
M3:=S3N-(M1*3*S2N) + 2*M1S*M1;
|
||||
M4:=SQ*invN - (M1 * 4 * S3N) + (M1S*6*S2N-3*Sqr(M1S));
|
||||
Skew:=M3*power(M2,-3/2);
|
||||
Kurtosis:=M4 / Sqr(M2);
|
||||
end;
|
||||
|
||||
function norm(const data : array of Single) : float;
|
||||
|
||||
begin
|
||||
norm:=Norm(PSingle(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function norm(const data : PSingle; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
norm:=sqrt(sumofsquares(data,N));
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_SINGLE}
|
||||
|
||||
{$ifdef FPC_HAS_TYPE_DOUBLE}
|
||||
function stddev(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
Result:=Stddev(@Data[0],High(Data)+1)
|
||||
Result:=Stddev(PDouble(@Data[0]),High(Data)+1)
|
||||
end;
|
||||
|
||||
function stddev(const data : PDouble; Const N : Integer) : float;
|
||||
@ -831,7 +1278,7 @@ procedure meanandstddev(const data : array of Double;
|
||||
var mean,stddev : float);
|
||||
|
||||
begin
|
||||
Meanandstddev(@Data[0],High(Data)+1,Mean,stddev);
|
||||
Meanandstddev(PDouble(@Data[0]),High(Data)+1,Mean,stddev);
|
||||
end;
|
||||
|
||||
procedure meanandstddev(const data : PDouble;
|
||||
@ -858,7 +1305,7 @@ end;
|
||||
function variance(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
Variance:=Variance(@Data[0],High(Data)+1);
|
||||
Variance:=Variance(PDouble(@Data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function variance(const data : PDouble; Const N : Integer) : float;
|
||||
@ -873,7 +1320,7 @@ function variance(const data : PDouble; Const N : Integer) : float;
|
||||
function totalvariance(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
Result:=TotalVariance(@Data[0],High(Data)+1);
|
||||
Result:=TotalVariance(PDouble(@Data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function totalvariance(const data : PDouble;Const N : Integer) : float;
|
||||
@ -890,22 +1337,11 @@ function totalvariance(const data : PDouble;Const N : Integer) : float;
|
||||
end;
|
||||
end;
|
||||
|
||||
function randg(mean,stddev : float) : float;
|
||||
|
||||
Var U1,S2 : Float;
|
||||
|
||||
begin
|
||||
repeat
|
||||
u1:= 2*random-1;
|
||||
S2:=Sqr(U1)+sqr(2*random-1);
|
||||
until s2<1;
|
||||
randg:=Sqrt(-2*ln(S2)/S2)*u1*stddev+Mean;
|
||||
end;
|
||||
|
||||
function popnstddev(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
PopnStdDev:=Sqrt(PopnVariance(@Data[0],High(Data)+1));
|
||||
PopnStdDev:=Sqrt(PopnVariance(PDouble(@Data[0]),High(Data)+1));
|
||||
end;
|
||||
|
||||
function popnstddev(const data : PDouble; Const N : Integer) : float;
|
||||
@ -917,7 +1353,7 @@ function popnstddev(const data : PDouble; Const N : Integer) : float;
|
||||
function popnvariance(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
popnvariance:=popnvariance(@data[0],high(Data)+1);
|
||||
popnvariance:=popnvariance(PDouble(@data[0]),high(Data)+1);
|
||||
end;
|
||||
|
||||
function popnvariance(const data : PDouble; Const N : Integer) : float;
|
||||
@ -930,7 +1366,7 @@ procedure momentskewkurtosis(const data : array of Double;
|
||||
var m1,m2,m3,m4,skew,kurtosis : float);
|
||||
|
||||
begin
|
||||
momentskewkurtosis(@Data[0],High(Data)+1,m1,m2,m3,m4,skew,kurtosis);
|
||||
momentskewkurtosis(PDouble(@Data[0]),High(Data)+1,m1,m2,m3,m4,skew,kurtosis);
|
||||
end;
|
||||
|
||||
procedure momentskewkurtosis(const data : PDouble; Const N : Integer;
|
||||
@ -949,7 +1385,7 @@ procedure momentskewkurtosis(const data : PDouble; Const N : Integer;
|
||||
begin
|
||||
temp:=Data[i]; { faster }
|
||||
S:=S+temp;
|
||||
acc:=temp*temp;
|
||||
acc:=sqr(temp);
|
||||
ss:=ss+acc;
|
||||
Acc:=acc*temp;
|
||||
Sc:=sc+acc;
|
||||
@ -957,7 +1393,7 @@ procedure momentskewkurtosis(const data : PDouble; Const N : Integer;
|
||||
sq:=sq+acc;
|
||||
end;
|
||||
M1:=s*invN;
|
||||
M1S:=M1*M1;
|
||||
M1S:=sqr(M1);
|
||||
S2N:=SS*invN;
|
||||
S3N:=SC*invN;
|
||||
M2:=S2N-M1S;
|
||||
@ -970,7 +1406,7 @@ procedure momentskewkurtosis(const data : PDouble; Const N : Integer;
|
||||
function norm(const data : array of Double) : float;
|
||||
|
||||
begin
|
||||
norm:=Norm(@data[0],High(Data)+1);
|
||||
norm:=Norm(PDouble(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function norm(const data : PDouble; Const N : Integer) : float;
|
||||
@ -978,6 +1414,162 @@ function norm(const data : PDouble; Const N : Integer) : float;
|
||||
begin
|
||||
norm:=sqrt(sumofsquares(data,N));
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_DOUBLE}
|
||||
|
||||
{$ifdef FPC_HAS_TYPE_EXTENDED}
|
||||
function stddev(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
Result:=Stddev(PExtended(@Data[0]),High(Data)+1)
|
||||
end;
|
||||
|
||||
function stddev(const data : PExtended; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
StdDev:=Sqrt(Variance(Data,N));
|
||||
end;
|
||||
|
||||
procedure meanandstddev(const data : array of Extended;
|
||||
var mean,stddev : float);
|
||||
|
||||
begin
|
||||
Meanandstddev(PExtended(@Data[0]),High(Data)+1,Mean,stddev);
|
||||
end;
|
||||
|
||||
procedure meanandstddev(const data : PExtended;
|
||||
Const N : Longint;var mean,stddev : float);
|
||||
|
||||
Var I : longint;
|
||||
|
||||
begin
|
||||
Mean:=0;
|
||||
StdDev:=0;
|
||||
For I:=0 to N-1 do
|
||||
begin
|
||||
Mean:=Mean+Data[i];
|
||||
StdDev:=StdDev+Sqr(Data[i]);
|
||||
end;
|
||||
Mean:=Mean/N;
|
||||
StdDev:=(StdDev-N*Sqr(Mean));
|
||||
If N>1 then
|
||||
StdDev:=Sqrt(Stddev/(N-1))
|
||||
else
|
||||
StdDev:=0;
|
||||
end;
|
||||
|
||||
function variance(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
Variance:=Variance(PExtended(@Data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function variance(const data : PExtended; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
If N=1 then
|
||||
Result:=0
|
||||
else
|
||||
Result:=TotalVariance(Data,N)/(N-1);
|
||||
end;
|
||||
|
||||
function totalvariance(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
Result:=TotalVariance(PExtended(@Data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function totalvariance(const data : PExtended;Const N : Integer) : float;
|
||||
|
||||
var S,SS : Float;
|
||||
|
||||
begin
|
||||
If N=1 then
|
||||
Result:=0
|
||||
else
|
||||
begin
|
||||
SumsAndSquares(Data,N,S,SS);
|
||||
Result := SS-Sqr(S)/N;
|
||||
end;
|
||||
end;
|
||||
|
||||
|
||||
function popnstddev(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
PopnStdDev:=Sqrt(PopnVariance(PExtended(@Data[0]),High(Data)+1));
|
||||
end;
|
||||
|
||||
function popnstddev(const data : PExtended; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
PopnStdDev:=Sqrt(PopnVariance(Data,N));
|
||||
end;
|
||||
|
||||
function popnvariance(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
popnvariance:=popnvariance(PExtended(@data[0]),high(Data)+1);
|
||||
end;
|
||||
|
||||
function popnvariance(const data : PExtended; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
PopnVariance:=TotalVariance(Data,N)/N;
|
||||
end;
|
||||
|
||||
procedure momentskewkurtosis(const data : array of Extended;
|
||||
var m1,m2,m3,m4,skew,kurtosis : float);
|
||||
|
||||
begin
|
||||
momentskewkurtosis(PExtended(@Data[0]),High(Data)+1,m1,m2,m3,m4,skew,kurtosis);
|
||||
end;
|
||||
|
||||
procedure momentskewkurtosis(const data : PExtended; Const N : Integer;
|
||||
var m1,m2,m3,m4,skew,kurtosis : float);
|
||||
|
||||
Var S,SS,SC,SQ,invN,Acc,M1S,S2N,S3N,temp : Float;
|
||||
I : Longint;
|
||||
|
||||
begin
|
||||
invN:=1.0/N;
|
||||
s:=0;
|
||||
ss:=0;
|
||||
sq:=0;
|
||||
sc:=0;
|
||||
for i:=0 to N-1 do
|
||||
begin
|
||||
temp:=Data[i]; { faster }
|
||||
S:=S+temp;
|
||||
acc:=sqr(temp);
|
||||
ss:=ss+acc;
|
||||
Acc:=acc*temp;
|
||||
Sc:=sc+acc;
|
||||
acc:=acc*temp;
|
||||
sq:=sq+acc;
|
||||
end;
|
||||
M1:=s*invN;
|
||||
M1S:=sqr(M1);
|
||||
S2N:=SS*invN;
|
||||
S3N:=SC*invN;
|
||||
M2:=S2N-M1S;
|
||||
M3:=S3N-(M1*3*S2N) + 2*M1S*M1;
|
||||
M4:=SQ*invN - (M1 * 4 * S3N) + (M1S*6*S2N-3*Sqr(M1S));
|
||||
Skew:=M3*power(M2,-3/2);
|
||||
Kurtosis:=M4 / Sqr(M2);
|
||||
end;
|
||||
|
||||
function norm(const data : array of Extended) : float;
|
||||
|
||||
begin
|
||||
norm:=Norm(PExtended(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function norm(const data : PExtended; Const N : Integer) : float;
|
||||
|
||||
begin
|
||||
norm:=sqrt(sumofsquares(data,N));
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_EXTENDED}
|
||||
|
||||
|
||||
function MinIntValue(const Data: array of Integer): Integer;
|
||||
@ -989,6 +1581,15 @@ begin
|
||||
If Data[I] < Result Then Result := Data[I];
|
||||
end;
|
||||
|
||||
function MaxIntValue(const Data: array of Integer): Integer;
|
||||
var
|
||||
I: Integer;
|
||||
begin
|
||||
Result := Data[Low(Data)];
|
||||
For I := Succ(Low(Data)) To High(Data) Do
|
||||
If Data[I] > Result Then Result := Data[I];
|
||||
end;
|
||||
|
||||
function MinValue(const Data: array of Integer): Integer;
|
||||
|
||||
begin
|
||||
@ -1004,54 +1605,6 @@ begin
|
||||
If Data[I] < Result Then Result := Data[I];
|
||||
end;
|
||||
|
||||
|
||||
function minvalue(const data : array of Double) : Double;
|
||||
|
||||
begin
|
||||
Result:=minvalue(PDouble(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function minvalue(const data : PDouble; Const N : Integer) : Double;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
minvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]<minvalue then
|
||||
minvalue:=data[i];
|
||||
end;
|
||||
|
||||
function MaxIntValue(const Data: array of Integer): Integer;
|
||||
var
|
||||
I: Integer;
|
||||
begin
|
||||
Result := Data[Low(Data)];
|
||||
For I := Succ(Low(Data)) To High(Data) Do
|
||||
If Data[I] > Result Then Result := Data[I];
|
||||
end;
|
||||
|
||||
function maxvalue(const data : array of Double) : Double;
|
||||
|
||||
begin
|
||||
Result:=maxvalue(PDouble(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function maxvalue(const data : PDouble; Const N : Integer) : Double;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
maxvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]>maxvalue then
|
||||
maxvalue:=data[i];
|
||||
end;
|
||||
|
||||
function MaxValue(const Data: array of Integer): Integer;
|
||||
|
||||
begin
|
||||
@ -1071,6 +1624,129 @@ begin
|
||||
maxvalue:=data[i];
|
||||
end;
|
||||
|
||||
{$ifdef FPC_HAS_TYPE_SINGLE}
|
||||
function minvalue(const data : array of Single) : Single;
|
||||
|
||||
begin
|
||||
Result:=minvalue(PSingle(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function minvalue(const data : PSingle; Const N : Integer) : Single;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
minvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]<minvalue then
|
||||
minvalue:=data[i];
|
||||
end;
|
||||
|
||||
|
||||
function maxvalue(const data : array of Single) : Single;
|
||||
|
||||
begin
|
||||
Result:=maxvalue(PSingle(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function maxvalue(const data : PSingle; Const N : Integer) : Single;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
maxvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]>maxvalue then
|
||||
maxvalue:=data[i];
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_SINGLE}
|
||||
|
||||
{$ifdef FPC_HAS_TYPE_DOUBLE}
|
||||
function minvalue(const data : array of Double) : Double;
|
||||
|
||||
begin
|
||||
Result:=minvalue(PDouble(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function minvalue(const data : PDouble; Const N : Integer) : Double;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
minvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]<minvalue then
|
||||
minvalue:=data[i];
|
||||
end;
|
||||
|
||||
|
||||
function maxvalue(const data : array of Double) : Double;
|
||||
|
||||
begin
|
||||
Result:=maxvalue(PDouble(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function maxvalue(const data : PDouble; Const N : Integer) : Double;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
maxvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]>maxvalue then
|
||||
maxvalue:=data[i];
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_DOUBLE}
|
||||
|
||||
{$ifdef FPC_HAS_TYPE_EXTENDED}
|
||||
function minvalue(const data : array of Extended) : Extended;
|
||||
|
||||
begin
|
||||
Result:=minvalue(PExtended(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function minvalue(const data : PExtended; Const N : Integer) : Extended;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
minvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]<minvalue then
|
||||
minvalue:=data[i];
|
||||
end;
|
||||
|
||||
|
||||
function maxvalue(const data : array of Extended) : Extended;
|
||||
|
||||
begin
|
||||
Result:=maxvalue(PExtended(@data[0]),High(Data)+1);
|
||||
end;
|
||||
|
||||
function maxvalue(const data : PExtended; Const N : Integer) : Extended;
|
||||
|
||||
var
|
||||
i : longint;
|
||||
|
||||
begin
|
||||
{ get an initial value }
|
||||
maxvalue:=data[0];
|
||||
for i:=1 to N-1 do
|
||||
if data[i]>maxvalue then
|
||||
maxvalue:=data[i];
|
||||
end;
|
||||
{$endif FPC_HAS_TYPE_EXTENDED}
|
||||
|
||||
|
||||
function Min(a, b: Integer): Integer;inline;
|
||||
begin
|
||||
|
||||
Loading…
Reference in New Issue
Block a user