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/***********************************************/
/**
* @file powerSpectralDensity2CovarianceFunction.cpp
*
* @brief Covariance functions from Power Spectral Density (PSD).
*
* @author Matthias Ellmer
* @date 2013-08-27
*/
/***********************************************/
// Latex documentation
#define DOCSTRING docstring
static const char *docstring = R"(
Covariance function from Power Spectral Density (PSD).
The \configFile{inputfilePSD}{matrix} contains in the first column the frequency $[Hz]$, followed by (possibly multiple) PSDs $[unit^2/Hz]$.
The output is a \file{matrix}{matrix}, the first column containing time lag $[s]$ and the other columns the covariance functions $[unit^2]$.
Conversion between PSD $p_j$ and covariance function $c_k$ is performed by discrete cosine transformation:
\begin{equation}
c_k = \frac{1}{4\Delta t (n-1)}\left(p_0 + p_{n-1} (-1)^k + \sum_{j=1}^{n-2} 2 p_j \cos(\pi jk/(n-1))\right).
\end{equation}
See also \program{CovarianceFunction2PowerSpectralDensity}.
)";
/***********************************************/
#include "programs/program.h"
#include "base/fourier.h"
#include "files/fileMatrix.h"
/***** CLASS ***********************************/
/** @brief Covariance functions from Power Spectral Density (PSD).
* @ingroup programsGroup */
class PowerSpectralDensity2CovarianceFunction
{
public:
void run(Config &config, Parallel::CommunicatorPtr comm);
};
GROOPS_REGISTER_PROGRAM(PowerSpectralDensity2CovarianceFunction, SINGLEPROCESS, "Covariance functions from Power Spectral Density (PSD).", Covariance)
GROOPS_RENAMED_PROGRAM(CovariancePsd2CovarianceFunction, PowerSpectralDensity2CovarianceFunction, date2time(2020, 5, 24))
/***********************************************/
void PowerSpectralDensity2CovarianceFunction::run(Config &config, Parallel::CommunicatorPtr /*comm*/)
{
try
{
FileName fileNameCov, fileNamePsd;
readConfig(config, "outputfileCovarianceFunction", fileNameCov, Config::MUSTSET, "", "first column: time steps [seconds], following columns: covariance functions");
readConfig(config, "inputfilePSD", fileNamePsd, Config::MUSTSET, "", "first column: frequency [Hz], following columns PSD [unit^2/Hz]");
if(isCreateSchema(config)) return;
logStatus<<"read PSD file <"<<fileNamePsd<<">"<<Log::endl;
Matrix psd;
readFileMatrix(fileNamePsd, psd);
Matrix cov(psd.rows(), psd.columns());
const Double dt = 1./(2*psd(psd.rows()-1, 0));
for(UInt i=0; i<cov.rows(); i++)
cov(i,0) = i*dt;
for(UInt k=1; k<cov.columns(); k++)
copy(Fourier::psd2covariance(psd.column(k), dt), cov.column(k));
logStatus<<"write covariance file <"<<fileNameCov<<">"<<Log::endl;
writeFileMatrix(fileNameCov, cov);
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
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