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{ ******************************************************************
Polynomial regression : Y = B(0) + B(1) * X + B(2) * X^2 + ...
****************************************************************** }
unit upolfit;
interface
uses
utypes, ulineq;
procedure PolFit(X, Y : PVector;
Lb, Ub, Deg : Integer;
B : PVector;
V : PMatrix);
{ ------------------------------------------------------------------
Unweighted polynomial regression
------------------------------------------------------------------
Input parameters: X, Y = point coordinates
Lb, Ub = array bounds
Deg = degree of polynomial
Output parameters: B = regression parameters
V = inverse matrix
------------------------------------------------------------------ }
procedure WPolFit(X, Y, S : PVector;
Lb, Ub, Deg : Integer;
B : PVector;
V : PMatrix);
{ ------------------------------------------------------------------
Weighted polynomial regression
------------------------------------------------------------------
Additional input parameter:
S = standard deviations of observations
------------------------------------------------------------------ }
implementation
procedure PolFit(X, Y : PVector;
Lb, Ub, Deg : Integer;
B : PVector;
V : PMatrix);
var
I, I1, J, K, D1 : Integer;
XI, Det : Float;
begin
if Ub - Lb < Deg then
begin
SetErrCode(MatErrDim);
Exit;
end;
{ Initialize }
for I := 0 to Deg do
begin
for J := 0 to Deg do
V^[I]^[J] := 0.0;
B^[I] := 0.0;
end;
V^[0]^[0] := Ub - Lb + 1;
for K := Lb to Ub do
begin
XI := X^[K]; { x^i }
B^[0] := B^[0] + Y^[K];
V^[0]^[1] := V^[0]^[1] + XI;
B^[1] := B^[1] + XI * Y^[K];
for I := 2 to Deg do
begin
XI := XI * X^[K];
V^[0]^[I] := V^[0]^[I] + XI; { First line of matrix: 1 --> x^d }
B^[I] := B^[I] + XI * Y^[K]; { Constant vector: y --> x^d.y }
end;
for I := 1 to Deg do
begin
XI := XI * X^[K];
V^[I]^[Deg] := V^[I]^[Deg] + XI; { Last col. of matrix: x^d --> x^2d }
end;
end;
{ Fill lower matrix }
D1 := Deg - 1;
for I := 1 to Deg do
begin
I1 := I - 1;
for J := 0 to D1 do
V^[I]^[J] := V^[I1]^[J + 1];
end;
{ Solve system }
LinEq(V, B, 0, Deg, Det);
end;
procedure WPolFit(X, Y, S : PVector;
Lb, Ub, Deg : Integer;
B : PVector;
V : PMatrix);
var
I, I1, J, K, D1 : Integer;
W, WXI, Det : Float;
begin
if Ub - Lb < Deg then
begin
SetErrCode(MatErrDim);
Exit;
end;
{ Initialize }
for I := 0 to Deg do
begin
for J := 0 to Deg do
V^[I]^[J] := 0.0;
B^[I] := 0.0;
end;
for K := Lb to Ub do
begin
if S^[K] <= 0.0 then
begin
SetErrCode(MatSing);
Exit;
end;
W := 1.0 / Sqr(S^[K]);
WXI := W * X^[K]; { w.x^i }
V^[0]^[0] := V^[0]^[0] + W;
B^[0] := B^[0] + W * Y^[K];
V^[0]^[1] := V^[0]^[1] + WXI;
B^[1] := B^[1] + WXI * Y^[K];
for I := 2 to Deg do
begin
WXI := WXI * X^[K];
V^[0]^[I] := V^[0]^[I] + WXI; { First line of matrix: w --> w.x^d }
B^[I] := B^[I] + WXI * Y^[K]; { Constant vector: w.y --> w.x^d.y }
end;
for I := 1 to Deg do
begin
WXI := WXI * X^[K];
V^[I]^[Deg] := V^[I]^[Deg] + WXI; { Last col. of matrix: w.x^d --> w.x^2d }
end;
end;
{ Fill lower matrix }
D1 := Deg - 1;
for I := 1 to Deg do
begin
I1 := I - 1;
for J := 0 to D1 do
V^[I]^[J] := V^[I1]^[J + 1];
end;
{ Solve system }
LinEq(V, B, 0, Deg, Det);
end;
end.
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