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Cosine Regression - Eddie W. Shore - 07-28-2017 10:21 PM
Introduction
The program COSREG attempts to fit data to the curve:
Y = A*cos(C*(X-D)) +B
The user will provide the x-data, y-data, and the period of the data. Radians mode will be used.
HP Prime Program: COSREG
Arguments x list, y list, estimated period
Code:
EXPORT COSREG(L1,L2,P)
BEGIN
// EWS 2017-07-25
// x list, y list, period
// Estimated Cosine Regression
// Y = A*COS(C(X-D))+B
// Radians mode
HAngle:=0;
LOCAL C:=2*π/P;
LOCAL I:=POS(L2,MAX(L2));
LOCAL D:=L1(I);
LOCAL S:=SIZE(L1);
LOCAL L0:=MAKELIST(1,X,1,S);
L1:=COS(C*L1-D);
LOCAL M1,M2,M3;
M1:=list2mat(CONCAT(L0,L1),S);
M1:=TRN(M1);
M2:=list2mat(L2,S);
M2:=TRN(M2);
M3:=CAS.LSQ(M1,M2);
LOCAL A:=M3[2,1];
LOCAL B:=M3[1,1];
RETURN {"A*COS(C(X-D))+B",
A,C,D,B};
END;The coefficients are returned in a list.
Cosine Regression: Y = A * COS(C*(X – D)) + B
Example 1
X = {0, π/4, π/2, 3π/4 ,1}
Y = {5, 2, -1, 2, 5}
Period: π
Results:
A = 3
C = 2
D = 0
B = 2
(Y = 2 COS(2X) + 3)