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nfolib

Section: C Library Functions (3)
Updated: 7 October 1999
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NAME

least_squares, spline, lsq_fgen, lint, splint, trapspl, Simpson_spl, Milne_diff, Brent, golden

SYNOPSIS

void least_squares
(
       int fit,

       int n_pts,

       double x_arr[],

       double y_arr[],

       double *r1,

       double *r2,

       double lsq_coeff[]

);
void spline
(
       double x[],

       double y[],

       int n,

       double yp1,

       double ypn,

       double y2[]

);
double lsq_fgen
(
       double tr,

       int fit,

       double lsq_coeff[]

);
double lint
(
       double xa[],

       double ya[],

       int n,

       double x

);
double splint
(
       double xa[],

       double ya[],

       double y2a[],

       int n,

       double x

);
double trapspl
(
       double t_1,

       double t_2,

       double h,

       double y[],

       double y2[],

       double x[],

       int n_pts

);
double Simpson_spl
(
       double from,

       double to,

       double step,

       double y_table[],

       double yd_table[],

       double x_table[],

       int n_pts

);
double Milne_diff
(
       int el,

       double h,

       double y_arr[]

);
double Brent
(
       double ax,

       double bx,

       double cx,

       double (*f)(void),

       double tol,

       double *xmin

);

double golden
(
       double ax,

       double bx,

       double cx,

       double (*f)(void),

       double tol,

       double *xmin

);

PARAMETERS

int fit: Type of fit required.
int n_pts (least_squares): Number of data points.
double x_arr[]: Array of X data.
double y_arr[]: Array of Y data.
double *r1: Goodness of fit.
double *r2: Coeff of determination.
double lsq_coeff[]: Least squares coeffs.
double x[] (spline): Array of X values.
double y[]: Array of Y values.
int n: Number of points.
double yp1: Boundary condition 1.
double ypn: Boundary condition 2.
double y2[] (spline): Array of Y derivatives dy/dx.
double tr: Not Documented.
double xa[]: Array of X values.
double ya[]: Array of Y values.
double x: Point to interpolate.
double y2a[]: Array of derivatives dy/dx.
double t_1: Integral lower limit.
double t_2: Integral upper limit.
double h: Trapezium size h.
double y2[] (trapspl): Array of derivatives dy/dx.
double x[] (trapspl): Array of Y values.
int n_pts (trapspl): Number of pts in num function.
double from: Integral lower limit.
double to: Integral upper limit.
double step: Simpson step length.
double y_table[]: Array of Y values.
double yd_table[]: Array of derivatives.
double x_table[]: Array of X values.
int n_pts (Simpson_spl): Number of pts in function.
int el: Not Documented.
double ax (Brent): Bracket 1.
double bx (Brent): Bracket 2.
double cx (Brent): Bracket 3.
double (*f)(void) (Brent): Function to be minimised.
double tol (Brent): Relaxation tolerance.
double *xmin (Brent): X co-ordinate of minimum.
double ax (golden): Guess [bracket 1 co-ordinate].
double bx (golden): Guess [bracket 2 co-ordinate].
double cx (golden): Guess [bracket 3 co-ordinate].
double (*f)(void) (golden): Function to be bracketed.
double tol (golden): Bracket tolerance.
double *xmin (golden): Co-ordinate of minimum.

DESCRIPTION

least_squares

Least squares regression package.

Linear, Inverse, Log, Power and Exponential least squares fits. See Micro User, Educational suppliment for further details.

spline

Routine to generate a cubic interpolation table ...

lsq_fgen

Routine to generate fitted function from least squares parameters ...

lint

Linear interpolation routine ...

splint

Cubic spline interpolation. For further details see "Numerical Recipes in C" pp96-97 ...

trapspl

Routine to integrate a numerical function using the Trapezium rule ...

Simpson_spl

Integration routine using Simpsons rule ...

Milne_diff

Routine to differentiate using Milnes' method ...

Brent

Routine to minimise a linear function using Brent's method ...

golden

Find the minimum of a function of one dimension using the Golden section search ...

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