SPLINE_VALUES

This rank-1 array function returns an array result, given an array of input. Use the optional argument for the covariance matrix when the square root of the variance function is required. The result will be a scalar value when the input variable is scalar.

Required Arguments

DERIVATIVE = DERIVATIVE (Input)
The index of the derivative evaluated. Use non-negative integer values. For the function itself use the value 0.

VARIABLES = VARIABLES (Input)
The independent variable values where the spline or its derivatives are evaluated. Either a rank-1 array or a scalar can be used as this argument.

KNOTS = KNOTS (Input)
The derived type ?_spline_knots, defined as the array COEFFS was obtained with the function SPLINE_FITTING. This contains the polynomial spline degree and the number of knots and the knots themselves for this spline function.

COEFFS = C (Input)
The coefficients in the representation for the spline function,

 

These result from the fitting process or array assignment C=SPLINE_FITTING(...), defined below. The value N = size(C) satisfies the identity N - 1 + spline_degree = size (?_knots), where the two right-most quantities refer to components of the argument knots.

Optional Arguments

COVARIANCE = G (Input)
This argument, when present, results in the evaluation of the square root of the variance function

e(x) = (b(x)TGb(x))1/2

where

b(x) = [B1(x),…,BN(x)]T

 

and G is the covariance matrix associated with the coefficients of the spline

c = [c1,…,cN]T

 

The argument G is an optional output parameter from the function SPLINE_FITTING, described below. When the square root of the variance function is computed, the arguments DERIVATIVE and C are not used.

IOPT = IOPT (Input)
This optional argument, of derived type ?_options, is not used in this release.

FORTRAN 90 Interface

Generic: CALL SPLINE_VALUES (DERIVATIVE, VARAIBLES, KNOTS, COEFFS [, …])

Specific: The specific interface names are S_SPLINE_VALUES and D_SPLINE_VALUES.