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# ftcurvpi

Calculates an integral of an interpolatory spline between two specified points.

## Prototype

```	function ftcurvpi (
xl  : numeric,
xr  : numeric,
p   : numeric,
xi     : numeric,
yi     : numeric
)

return_val  :  float or double
```

## Arguments

xl

A scalar value containing the lower limit of the integration.

xr

A scalar value containing the upper limit of the integration.

p

A scalar value specifying the period of the input function; the value must not be less than xi(npts-1) - xi(0).

xi

An array containing the abscissae for the input function, with rightmost dimension npts. If xi is multi-dimensional, it must have the same dimension sizes as yi.

yi

An array of any dimensionality, whose rightmost dimension is npts, containing the functional values of the input function. That is, yi(...,k) is the functional value at xi(...,k) for k=0,npts-1.

## Return value

The integral of the interpolated function from xl to xr - a scalar if yi is a one-dimensional array, otherwise an array with the same dimensions as all but the last dimension of yi.

The output value will be of type double if any of the input is double, and float otherwise.

## Description

ftcurvpi is in the Fitgrid package - a package containing 1D and 2D interpolators using cubic splines under tension.

There are some parameters that can alter the behavior of ftcurvpi. These parameters all have reasonable default values. However, users may change any of these parameters by invoking ftsetp prior to calling ftcurvpi. ftcurvpi is called after all of the desired values for control parameters have been set.

The only control parameter that applies to ftcurvpi is: sig.

The value for the parameter sig specifies the tension factor. Values near zero result in a cubic spline; large values (e.g. 50) result in nearly a polygonal line. A typical value is 1. (the default).

You can extrapolate values with ftcurvpi (that is, calculate interpolated values for abscissae outside of the domain of the input), but these values are, in general, unreliable.

## Examples

```begin
xi = (/  0.00,   2.00,   5.00,   8.00,  10.00,  13.00,     \
15.00,  18.00,  21.00,  23.00,  30.00         /)
yi = (/  1.00,   0.81,   0.00,  -0.81,  -1.00,  -0.84,     \
-0.56,   0.04,   0.73,   1.18,   2.0          /)

integral = ftcurvpi(10., 30., 31., xi, yi)
end
```