Equation of the least-squares parabola for data set. (FORTRAN)

Question

Original Question:

To find the equation of the parabola

y = A + Bx + Cx^2

that best fits a set of n data points, the values of A, B, and C must be determined for which the sum of the squares of the deviations of the observed y-values from the predicted y-values using the equation) is as small as possible. These values are found by solving the linear system:

nA + (Ex)B + (E(x^2))C = Ey

(Ex)A + (Ex^2)B + (Ex^3)C = E(xy)

(Ex^2)A + (Ex^3)B + (Ex^4)C = E((x^2)y)

E = sumation notaion = capital sigma

Find the equation of the least-squares parabola for the following set of data points:

DATA X / 0.05, 0.12, 0.15, 0.30, 0.45, 0.70, 0.84, 1.04 /

DATA Y / 0.957,0.851,0.832,0.720,0.583,0.378,0.295,0.156 /

I'm getting a couple errors in my code and I'm just not quite sure where I'm going wrong. I hand calculated the "Data Weights (A, B, C)" from the system of linear equations.

The Error Log is:

--------------------Configuration: FIT - Win32 Debug--------------------

Compiling Fortran...

C:\MSDEV\FIT.f90

C:\MSDEV\FIT.f90(34): warning FOR4265: symbol M referenced but not set

Linking...

FIT.obj : error LNK2001: unresolved external symbol _GAUSS@24

FIT.exe : fatal error LNK1120: 1 unresolved externals

Error executing link.exe.

FIT.exe - 2 error(s), 1 warning(s)

This is my current program code:

        PROGRAM FIT
    REAL X(8),Y(8),LIN,QUAD,WEIGHTS(3)
    EXTERNAL LIN,QUAD
    DATA X / 0.05, 0.12, 0.15, 0.30, 0.45, 0.70, 0.84, 1.04  /
    DATA Y / 0.957,0.851,0.832,0.720,0.583,0.378,0.295,0.156 /
    DATA WEIGHTS / -0.245866582919757, 4.19120539122495, 3.92469397298994 /
    CALL GENLSQ(X,Y,8,LIN,QUAD,WEIGHTS)
    PRINT *,'THE WEIGHTS ARE'
    PRINT *, WEIGHTS
    STOP
    END

    SUBROUTINE GENLSQ(X,Y,N,F,G,WEIGHTS)
    INTEGER N
    REAL X(N), Y(N), MATRIX(3,4),WEIGHTS(3)
    EXTERNAL F,G
    DATA MATRIX / 12*0.0 /
    MATRIX(1,1) = FLOAT(N)
    DO 1 I = 1, M
    MATRIX(1,2) = MATRIX(1,2) + F(X(I))
    MATRIX(1,3) = MATRIX(1,3) + G(X(I))
    MATRIX(1,4) = MATRIX(1,4) + Y(I)
    MATRIX(2,2) = MATRIX(2,2) + F(X(I)) ** 2
    MATRIX(2,3) = MATRIX(2,3) + F(X(I))*G(X(I))
    MATRIX(2,4) = MATRIX(2,4) + F(X(I))*Y(I)
    MATRIX(3,3) = MATRIX(3,3) + G(X(I)) ** 2
    MATRIX(3,4) = MATRIX(3,4) + G(X(I))*Y(I)
1       CONTINUE
    MATRIX(2,1) = MATRIX(1,2)
    MATRIX(3,1) = MATRIX(1,3)
    MATRIX(3,2) = MATRIX(2,3)
    CALL GAUSS(MATRIX,3,4,3,WEIGHTS,SINGUL)
    RETURN
    END

    REAL FUNCTION LIN(X)
    LIN=X
    RETURN
    END

    REAL FUNCTION QUAD(X)
    QUAD=X*X
    RETURN
    END

ANY and ALL help is much appreciated! Thanks, Joe

The subroutine `GAUSS` you call is not defined anywhere. Where should it come from? — Bálint Aradi, Mar 15 '13 at 08:46
Are you learning the language? If yes, be aware you are using really ancient and obsolete constructs. Otherwise Aradi is right. (Or Bállint? With Hungarian names I am never sure.) — Vladimir F Героям слава, Mar 15 '13 at 11:43
@VladimirF: I am using it according to the usual (international) convention, not the Hungarian one, so it's Bálint. :-) — Bálint Aradi, Mar 15 '13 at 14:31

score 0 · Answer 1 · answered Mar 15 '13 at 21:52

0

C:\MSDEV\FIT.f90(34): warning FOR4265: symbol M referenced but not set

AFAICT, you never define your loop limit M. That's sure to cause all kinds of mischief.

answered Mar 15 '13 at 21:52

bob.sacamento

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score 0 · Answer 2 · answered Mar 16 '13 at 02:25

You would do better to use implicit none and to put your procedures into a module and to use that module. Instead of external. The first will cause the compiler to notify you of undeclared variables. The second will enable to the compiler to check consistency of arguments in procedure calls.

module my_subs

implicit none

contains

   SUBROUTINE GENLSQ
   ....
   end SUBROUTINE GENLSQ

   FUNCTION LIN(X)
   real :: LIN
   real, intent (in) :: x
   LIN = X
   end FUNCTION LIN(X)

   FUNCTION QUAD(X)
   real :: QUAD
   real, intent (in) :: x
   QUAD=X*X
   end FUNCTION QUAD

end module my_subs


program fit

use my_subs

implicit none

.....

END program fit

Equation of the least-squares parabola for data set. (FORTRAN)

2 Answers2