SURFACE_VALUES

This rank-2 array function returns a tensor product array result, given two arrays of independent variable values. Use the optional input argument for the covariance matrix when the square root of the variance function is evaluated. The result will be a scalar value when the input independent variable is scalar.

Required Arguments

DERIVATIVE = DERIVATIVE(1:2) (Input)
The indices of the partial derivative evaluated. Use non-negative integer values. For the function itself use the array (/0,0/).

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

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

KNOTSX = KNOTSX (Input)
The derived type ?_spline_knots, used when the array coeffs(:,:)was obtained with the function SURFACE_FITTING. This contains the polynomial spline degree and the number of knots and the knots themselves, in the x dimension.

KNOTSY = KNOTSY (Input)
The derived type ?_spline_knots, used when the array coeffs(:,:) was obtained with the function SURFACE_FITTING. This contains the polynomial spline degree and the number of knots and the knots themselves, in the y dimension.

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

 

These result from the fitting process or array assignment C=SURFACE_FITTING(...), defined below.

The values M = size (C,1) and N = size (C,2) satisfies the respective identities
N -1 + spline_degree = size (?_knotsx), and M -1 + spline_degree = size (?_knotsy) , where the two right-most quantities in both equations refer to components of the arguments knotsx and knotsy. The same value of spline_degree must be used for both knotsx and knotsy.

Optional Arguments

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

e(x,y) = (b(x,y)TGb(x,y))1/2

where

b(x,y) = [B1(x)B1(y),…,BN(x)BN(y),…]T

 

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

c = [c11,…,cN1,…]T

The argument G is an optional output from SURFACE_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 SURFACE_VALUES (DERIVATIVE, VARIABLESX, VARIABLESY, KNOTSX, KNOTSY, COEFFS [, …])

Specific: The specific interface names are S_SURFACE_VALUES and D_SURFACE_VALUES.