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TSUM

TSUM

## Purpose

Trapezoidal summation of the area under a curve.

## Explanation

Adapted from the procedure INTEG in the IUE procedure library.

## Calling Sequence

Result = TSUM(y)
or
Result = TSUM( x, y, [ imin, imax, /nan ] )

## Inputs

x = array containing monotonic independent variable. If omitted, then
x is assumed to contain the index of the y variable.
x = lindgen( N_elements(y) ).
y = array containing dependent variable y = f(x)

## Optional Inputs

imin = scalar index of x array at which to begin the integration
If omitted, then summation starts at x[0].
imax = scalar index of x value at which to end the integration
If omitted then the integration ends at x[npts-1].
nan: If set cause the routine to check for occurrences of the IEEE
floating-point values NaN or Infinity in the input data.
Elements with the value NaN or Infinity are treated as missing data

## Outputs

result = area under the curve y=f(x) between x[imin] and x[imax].

## Example

IDL> x = [0.0,0.1,0.14,0.3]
IDL> y = sin(x)
IDL> print,tsum(x,y) ===> 0.0445843

In this example, the exact curve can be computed analytically as
1.0 - cos(0.3) = 0.0446635

## Procedure

The area is determined of individual trapezoids defined by x[i],
x[i+1], y[i] and y[i+1].
If the data is known to be at all smooth, then a more accurate
integration can be found by interpolation prior to the trapezoidal
sums, for example, by the standard IDL User Library int_tabulated.pro.

## Modification History

Written, W.B. Landsman, STI Corp. May 1986
Modified so X is not altered in a one parameter call Jan 1990
Converted to IDL V5.0 W. Landsman September 1997
Allow non-integer values of imin and imax W. Landsman April 2001
Fix problem if only 1 parameter supplied W. Landsman June 2002
Added /nan keyword. Julio Castro/WL May 2014

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