Compute the power spectral density of a real function.

## Usage

call SHPowerSpectrumDensity (cilm, lmax, pspectrum, exitstatus)

## Parameters

cilm : input, real*8, dimension (2, lmaxin+1, lmaxin+1)
The real function expressed in real spherical harmonics.
lmax : input, integer
The maximum spherical harmonic degree used in calculating the power spectrum. This must be less than or equal to lmaxin.
pspectrum : output, real*8, dimension (lmax+1)
The power spectral density of the function.
exitstatus : output, optional, integer
If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

## Description

SHPowerSpectrumDensity will calculate the power spectral density of a function expressed in real 4-pi normalized spherical harmonics. For a given spherical harmonic degree l, this is explicitly calculated as:

pspectrum(l) = Sum_{i=1}^2 Sum_{m=0}^l cilm(i, l+1, m+1)**2 / (2l + 1).