Optional Arguments

AXIS1=ascending-value-list

specifies a list of numeric values to assign to the first (y) variable in the grid request for the output data set. Numbers that you specify with this option determine the number of values for y, and override a value that you specify with the NAXIS1= option. The ascending-value-list must be arranged in ascending order. The value list can be in any of the following forms:

• n <...n>
• n TO n <BY increment>
• n <...n> TO n <BY increment > <n <...n> >

Examples:Using the Default Interpolation Method

Spline Interpolation

AXIS2=ascending-value-list

specifies a list of numeric values to assign to the second (x) variable in the grid request for the output data set. Numbers that you specify with this option determine the number of values for x and override a value that you specify with the NAXIS2= option. The ascending-value-list must be arranged in ascending order. The value list can be in any of the following forms:

• n <...n>
• n TO n <BY increment>
• n <...n> TO n <BY increment > <n <...n> >

Examples:Using the Default Interpolation Method

Spline Interpolation

JOIN

uses a linear interpolation within a set of triangular regions that are formed from the input data set. This interpolation method creates values in the range of the initial values of the vertical variable, but the resulting interpolated surface might not be smooth.

NAXIS1=n

specifies the number of values for the first (y) variable in the grid request for the output data set. You can determine the actual values used for y by taking the minimum and the maximum values of y and dividing the range into n- one equal sections.

A value specified with NAXIS1= is ignored if values are also specified with AXIS1=.

Default:11

NAXIS2=n

specifies the number of values for the second (x) variable in the grid request for the output data set. You can determine the actual values that are used for x by taking the minimum value and the maximum value of x, and dividing the range into n- one equal sections.

A value specified with NAXIS2= is ignored if values are also specified with AXIS2=.

Default:11

NEAR=n

specifies the number of the nearest data points to use for computing the estimates of the first derivative, and the second derivative. As NEAR= values become larger, time and computation costs increase significantly. NEAR= is ignored if you specify SPLINE. The value of n must be greater than or equal to 3.

If the number of input data points is insufficient for the number that you specify with NEAR=, a smaller number of data points is used.

Default:3

Example:Partial Spline Interpolation

NOSCALE

specifies that the x and y variables not be scaled to the same range before interpolation. By default, the interpolation is performed after both variables are similarly scaled because the interpolation methods assume that the scales of x and y are comparable.

Default:SCALE

PARTIAL

specifies that a spline be used to estimate the derivatives for the biquintic polynomial interpolation. A bivariate spline is fit to the nearest neighbors, and is used to estimate the needed derivatives. This option produces results that are less smooth than those produced by the SPLINE option and uses fewer computer resources. However, the results produced by PARTIAL are smoother than those that are produced by the default. If you use both the PARTIAL option and the SPLINE option, the PARTIAL option is ignored.

Example:Partial Spline Interpolation

SCALE

specifies that the x and y variables be scaled to the same range before interpolation. The interpolation is performed after both variables are similarly scaled because the interpolation methods assume that the scales of x and y are comparable.

Default:SCALE

SMOOTH=ascending-value-list

specifies a list of numbers for smoothing parameters. Use the SMOOTH= option only when you also use the SPLINE option. The ascending-value-list must be arranged in ascending order. The value list can be in any of the following forms:

• n <...n>
• n TO n <BY increment>
• n <...n> TO n <BY increment > <n <...n> >

For each value λ of the smoothing parameter, a function u (x, y) is formed that minimizes

datapoints, and the pairs (x_j, y_j ) are the available points, with corresponding function values z_j (Wahba 1990).

The higher the value of the smoothing parameter, the smoother the resulting interpolation. The lower the smoothing parameter, the closer the resulting surface is to the original data points. A smoothing parameter of 0 produces the same results as the SPLINE option without the SMOOTH= option.

This procedure repeats for each value of the smoothing parameter. The output data set that you specify in the OUT= option contains:

• the interpolated values
• the values of the grid points
• the values of the smoothing parameter in the variable _SMTH_
• a separate grid for each value of the smoothing parameter

Example:Spline and Smoothing Interpolations

SPLINE

specifies the use of a bivariate spline (Harder and Desmarais 1972, Meinguet 1979, Green and Silverman 1994) to interpolate, or to form a smoothed estimate, if you also use the SMOOTH= option. The SPLINE option results in the use of an order n³ algorithm, where n is the number of input data points. Consequently, this method can be time-consuming. If you use more than 100 input points, the procedure can use excessive time.

Examples:Spline and Smoothing Interpolations

Spline Interpolation