E201: Least Squares Polynomial Fit

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 01.12.1994
Language: Fortran	Revised:

Subroutine subprograms RLSQPM and DLSQPM fit a polynomial

of degree m to n equally-weighted data points ( ). The calculated coefficients are such that

Subroutine subprograms RLSQP1 and DLSQP1 fit a straight line to n such points.

Subroutine subprograms RLSQP2 and DLSQP2 fit a parabola to n such points.

An estimate of the standard deviation is calculated.

On CDC and Cray computers, the double-precision versions DLSQPM, DLSQP1 and DLSQP2 are not available.

Structure:

SUBROUTINE subprograms
User Entry Names: RLSQPM, RLSQP1, RLSQP2, DLSQPM, DLSQP1, DLSQP2
External References: RVSET, DVSET, DVSUM, DVMPY, DSEQN

Usage:

For (type REAL), (type DOUBLE PRECISION),

    CALL tLSQPM(N,X,Y,M,A,SD,IFAIL)
    CALL tLSQP1(N,X,Y,A0,A1,SD,IFAIL)
    CALL tLSQP2(N,X,Y,A0,A1,A2,SD,IFAIL)

N

(INTEGER) Number n of data points.

X

(type according to t) One-dimensional array of length . On entry, X(i) contains the abscissas .

Y

(type according to t) One-dimensional array of length . On entry, Y(i) contains the ordinates .

M

(INTEGER) Degree m of the polynomial to be fitted.

A

(type according to t) One-dimensional array of dimension (0:d), where . Contains, on exit, in A(j) the coefficients .

A0,A1,A2

(type according to t) Contain, on exit, the coefficients , for or for , respectively.

SD

(type according to t) Contains, on exit, the estimate s.

IFAIL

(INTEGER) Error flag.
Normal case,
or or or ,
The matrix of normal equations is numerically singular.

In the case : , and on exit.

Method:

The normal equations are solved. On computers other than CDC or Cray, double-precision mode arithmetic is used internally for RLSQPM, RLSQP1 and RLSQP2.

Notes:

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

References:

1. D.H. Menzel, Fundamental formulas of physics, v. 1, (Dover, New York 1960) 116-122.