void copy(const QString &src, const QString &dest)
{
QFile copyInput(src);
QFile copyOutput(dest);
if(!copyInput.open(QIODevice::ReadOnly)) {
kWarning(1212) << "Couldn't open " << src ;
return;
}
if(!copyOutput.open(QIODevice::WriteOnly)) {
kWarning(1212) << "Couldn't open " << dest ;
copyInput.close();
return;
}
while(!copyInput.atEnd()) {
copyOutput.putch(copyInput.getch());
}
copyInput.close();
copyOutput.close();
}
/**
* Execute smoothing of a single spectrum.
* @param inputWS :: A workspace to pick a spectrum from.
* @param wsIndex :: An index of a spectrum to smooth.
* @return :: A single-spectrum workspace with the smoothed data.
*/
API::MatrixWorkspace_sptr
WienerSmooth::smoothSingleSpectrum(API::MatrixWorkspace_sptr inputWS,
size_t wsIndex) {
size_t dataSize = inputWS->blocksize();
// it won't work for very small workspaces
if (dataSize < 4) {
g_log.debug() << "No smoothing, spectrum copied." << std::endl;
return copyInput(inputWS, wsIndex);
}
// Due to the way RealFFT works the input should be even-sized
const bool isOddSize = dataSize % 2 != 0;
if (isOddSize) {
// add a fake value to the end to make size even
inputWS = copyInput(inputWS, wsIndex);
wsIndex = 0;
auto &X = inputWS->dataX(wsIndex);
auto &Y = inputWS->dataY(wsIndex);
auto &E = inputWS->dataE(wsIndex);
double dx = X[dataSize - 1] - X[dataSize - 2];
X.push_back(X.back() + dx);
Y.push_back(Y.back());
E.push_back(E.back());
}
// the input vectors
auto &X = inputWS->readX(wsIndex);
auto &Y = inputWS->readY(wsIndex);
auto &E = inputWS->readE(wsIndex);
// Digital fourier transform works best for data oscillating around 0.
// Fit a spline with a small number of break points to the data.
// Make sure that the spline passes through the first and the last points
// of the data.
// The fitted spline will be subtracted from the data and the difference
// will be smoothed with the Wiener filter. After that the spline will be
// added to the smoothed data to produce the output.
// number of spline break points, must be smaller than the data size but
// between 2 and 10
size_t nbreak = 10;
if (nbreak * 3 > dataSize)
nbreak = dataSize / 3;
// NB. The spline mustn't fit too well to the data. If it does smoothing
// doesn't happen.
// TODO: it's possible that the spline is unnecessary and a simple linear
// function will
// do a better job.
g_log.debug() << "Spline break points " << nbreak << std::endl;
// define the spline
API::IFunction_sptr spline =
API::FunctionFactory::Instance().createFunction("BSpline");
auto xInterval = getStartEnd(X, inputWS->isHistogramData());
spline->setAttributeValue("StartX", xInterval.first);
spline->setAttributeValue("EndX", xInterval.second);
spline->setAttributeValue("NBreak", static_cast<int>(nbreak));
// fix the first and last parameters to the first and last data values
spline->setParameter(0, Y.front());
spline->fix(0);
size_t lastParamIndex = spline->nParams() - 1;
spline->setParameter(lastParamIndex, Y.back());
spline->fix(lastParamIndex);
// fit the spline to the data
auto fit = createChildAlgorithm("Fit");
fit->initialize();
fit->setProperty("Function", spline);
fit->setProperty("InputWorkspace", inputWS);
fit->setProperty("WorkspaceIndex", static_cast<int>(wsIndex));
fit->setProperty("CreateOutput", true);
fit->execute();
// get the fit output workspace; spectrum 2 contains the difference that is to
// be smoothed
API::MatrixWorkspace_sptr fitOut = fit->getProperty("OutputWorkspace");
// Fourier transform the difference spectrum
auto fourier = createChildAlgorithm("RealFFT");
fourier->initialize();
fourier->setProperty("InputWorkspace", fitOut);
fourier->setProperty("WorkspaceIndex", 2);
// we don't require bin linearity as we don't need the exact transform
fourier->setProperty("IgnoreXBins", true);
fourier->execute();
API::MatrixWorkspace_sptr fourierOut =
fourier->getProperty("OutputWorkspace");
// spectrum 2 of the transformed workspace has the transform modulus which is
// a square
// root of the power spectrum
auto &powerSpec = fourierOut->dataY(2);
// convert the modulus to power spectrum wich is the base of the Wiener filter
std::transform(powerSpec.begin(), powerSpec.end(), powerSpec.begin(),
PowerSpectrum());
// estimate power spectrum's noise as the average of its high frequency half
size_t n2 = powerSpec.size();
double noise =
std::accumulate(powerSpec.begin() + n2 / 2, powerSpec.end(), 0.0);
noise /= static_cast<double>(n2);
// index of the maximum element in powerSpec
const size_t imax = static_cast<size_t>(std::distance(
powerSpec.begin(), std::max_element(powerSpec.begin(), powerSpec.end())));
if (noise == 0.0) {
noise = powerSpec[imax] / guessSignalToNoiseRatio;
}
g_log.debug() << "Maximum signal " << powerSpec[imax] << std::endl;
g_log.debug() << "Noise " << noise << std::endl;
// storage for the Wiener filter, initialized with 0.0's
std::vector<double> wf(n2);
// The filter consists of two parts:
// 1) low frequency region, from 0 until the power spectrum falls to the
// noise level, filter is calculated
// from the power spectrum
// 2) high frequency noisy region, filter is a smooth function of frequency
// decreasing to 0
// the following code is an adaptation of a fortran routine
// noise starting index
size_t i0 = 0;
// intermediate variables
double xx = 0.0;
double xy = 0.0;
double ym = 0.0;
// low frequency filter values: the higher the power spectrum the closer the
// filter to 1.0
for (size_t i = 0; i < n2; ++i) {
double cd1 = powerSpec[i] / noise;
if (cd1 < 1.0 && i > imax) {
i0 = i;
break;
}
double cd2 = log(cd1);
wf[i] = cd1 / (1.0 + cd1);
double j = static_cast<double>(i + 1);
xx += j * j;
xy += j * cd2;
ym += cd2;
}
// i0 should always be > 0 but in case something goes wrong make a check
if (i0 > 0) {
g_log.debug() << "Noise start index " << i0 << std::endl;
// high frequency filter values: smooth decreasing function
double ri0f = static_cast<double>(i0 + 1);
double xm = (1.0 + ri0f) / 2;
ym /= ri0f;
double a1 = (xy - ri0f * xm * ym) / (xx - ri0f * xm * xm);
double b1 = ym - a1 * xm;
g_log.debug() << "(a1,b1) = (" << a1 << ',' << b1 << ')' << std::endl;
const double dblev = -20.0;
// cut-off index
double ri1 = floor((dblev / 4 - b1) / a1);
if (ri1 < static_cast<double>(i0)) {
g_log.warning() << "Failed to build Wiener filter: no smoothing."
<< std::endl;
ri1 = static_cast<double>(i0);
}
size_t i1 = static_cast<size_t>(ri1);
if (i1 > n2)
i1 = n2;
for (size_t i = i0; i < i1; ++i) {
double s = exp(a1 * static_cast<double>(i + 1) + b1);
wf[i] = s / (1.0 + s);
}
// wf[i] for i1 <= i < n2 are 0.0
g_log.debug() << "Cut-off index " << i1 << std::endl;
} else {
g_log.warning() << "Power spectrum has an unexpected shape: no smoothing"
<< std::endl;
return copyInput(inputWS, wsIndex);
}
// multiply the fourier transform by the filter
auto &re = fourierOut->dataY(0);
auto &im = fourierOut->dataY(1);
std::transform(re.begin(), re.end(), wf.begin(), re.begin(),
std::multiplies<double>());
std::transform(im.begin(), im.end(), wf.begin(), im.begin(),
std::multiplies<double>());
// inverse fourier transform
fourier = createChildAlgorithm("RealFFT");
fourier->initialize();
fourier->setProperty("InputWorkspace", fourierOut);
fourier->setProperty("IgnoreXBins", true);
fourier->setPropertyValue("Transform", "Backward");
fourier->execute();
API::MatrixWorkspace_sptr out = fourier->getProperty("OutputWorkspace");
auto &background = fitOut->readY(1);
auto &y = out->dataY(0);
if (y.size() != background.size()) {
throw std::logic_error("Logic error: inconsistent arrays");
}
// add the spline "background" to the smoothed data
std::transform(y.begin(), y.end(), background.begin(), y.begin(),
std::plus<double>());
// copy the x-values and errors from the original spectrum
// remove the last values for odd-sized inputs
if (isOddSize) {
out->dataX(0).assign(X.begin(), X.end() - 1);
out->dataE(0).assign(E.begin(), E.end() - 1);
out->dataY(0).resize(Y.size() - 1);
} else {
out->setX(0, X);
out->dataE(0).assign(E.begin(), E.end());
}
return out;
}
