E208: Least Squares Polynomial Fit

Author(s): E. Keil	Library: KERNLIB
Submitter: B. Schorr	Submitted: 01.12.1969
Language: Fortran	Revised: 27.11.1984

Subroutine LSQ fits a polynomial of degree m-1 to n equally-weighted data points ( ). The computed coefficients of the fitted polynomial have values which minimize

For the case m=2 (straight line fit), subroutine LLSQ is faster and easier to use than LSQ.

Meaningful results can usually be obtained only for small values of m (typically less than 10).

Structure:

SUBROUTINE subprograms
User Entry Names: LSQ, LLSQ
Files Referenced: Printer
External References: RVSUM, RSEQN, DSEQN, KERMTR, ABEND

Usage:

    CALL LSQ(N,X,Y,M,A)
    CALL LLSQ(N,X,Y,A1,A2,IFAIL)

N

(INTEGER) Number n of data points.

X

(REAL) One-dimensional array. X(i) must be equal to the data coordinate ,
.

Y

(REAL) One-dimensional array. Y(i) must be equal to the observed value ,
.

M

(INTEGER) On entry, M must be equal to the number m of coefficients of the polynomial to be fitted. On exit, the value of M may differ from this (see Error Handling).

A

(REAL) One-dimensional array. On exit from LSQ, A(j) is equal to the coefficient of in the fitted polynomial, .

A1,A2

(REAL) On exit from LLSQ, A1 and A2 are equal to the coefficients of the fitted straight line .

IFAIL

(INTEGER) On exit from LLSQ, IFAIL is equal to -2 if , to -1 if the matrix of normal equations is numerically singular, and to zero otherwise.

Method:

Normal equations.

Error handling:

Error E208.1: or or (subroutine LSQ). M is replaced by zero.
Error E208.2: The normal equations matrix is numerically singular (subroutine LSQ).
For each error, a message is printed unless subroutine KERSET (N001) has been called.

Notes:

On computers other than Cray and CDC double-precision arithmetic is used internally.