/** Executes the algorithm
*
*/
void SplineBackground::exec()
{
API::MatrixWorkspace_sptr inWS = getProperty("InputWorkspace");
int spec = getProperty("WorkspaceIndex");
if (spec > static_cast<int>(inWS->getNumberHistograms()))
throw std::out_of_range("WorkspaceIndex is out of range.");
const MantidVec& X = inWS->readX(spec);
const MantidVec& Y = inWS->readY(spec);
const MantidVec& E = inWS->readE(spec);
const bool isHistogram = inWS->isHistogramData();
const int ncoeffs = getProperty("NCoeff");
const int k = 4; // order of the spline + 1 (cubic)
const int nbreak = ncoeffs - (k - 2);
if (nbreak <= 0)
throw std::out_of_range("Too low NCoeff");
gsl_bspline_workspace *bw;
gsl_vector *B;
gsl_vector *c, *w, *x, *y;
gsl_matrix *Z, *cov;
gsl_multifit_linear_workspace *mw;
double chisq;
int n = static_cast<int>(Y.size());
bool isMasked = inWS->hasMaskedBins(spec);
std::vector<int> masked(Y.size());
if (isMasked)
{
for(API::MatrixWorkspace::MaskList::const_iterator it=inWS->maskedBins(spec).begin();it!=inWS->maskedBins(spec).end();++it)
masked[it->first] = 1;
n -= static_cast<int>(inWS->maskedBins(spec).size());
}
if (n < ncoeffs)
{
g_log.error("Too many basis functions (NCoeff)");
throw std::out_of_range("Too many basis functions (NCoeff)");
}
/* allocate a cubic bspline workspace (k = 4) */
bw = gsl_bspline_alloc(k, nbreak);
B = gsl_vector_alloc(ncoeffs);
x = gsl_vector_alloc(n);
y = gsl_vector_alloc(n);
Z = gsl_matrix_alloc(n, ncoeffs);
c = gsl_vector_alloc(ncoeffs);
w = gsl_vector_alloc(n);
cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
mw = gsl_multifit_linear_alloc(n, ncoeffs);
/* this is the data to be fitted */
int j = 0;
for (MantidVec::size_type i = 0; i < Y.size(); ++i)
{
if (isMasked && masked[i]) continue;
gsl_vector_set(x, j, (isHistogram ? (0.5*(X[i]+X[i+1])) : X[i])); // Middle of the bins, if a histogram
gsl_vector_set(y, j, Y[i]);
gsl_vector_set(w, j, E[i]>0.?1./(E[i]*E[i]):0.);
++j;
}
if (n != j)
{
gsl_bspline_free(bw);
gsl_vector_free(B);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_free(Z);
gsl_vector_free(c);
gsl_vector_free(w);
gsl_matrix_free(cov);
gsl_multifit_linear_free(mw);
throw std::runtime_error("Assertion failed: n != j");
}
double xStart = X.front();
double xEnd = X.back();
/* use uniform breakpoints */
gsl_bspline_knots_uniform(xStart, xEnd, bw);
/* construct the fit matrix X */
for (int i = 0; i < n; ++i)
{
double xi=gsl_vector_get(x, i);
/* compute B_j(xi) for all j */
gsl_bspline_eval(xi, B, bw);
/* fill in row i of X */
for (j = 0; j < ncoeffs; ++j)
{
double Bj = gsl_vector_get(B, j);
gsl_matrix_set(Z, i, j, Bj);
}
}
/* do the fit */
gsl_multifit_wlinear(Z, w, y, c, cov, &chisq, mw);
/* output the smoothed curve */
API::MatrixWorkspace_sptr outWS = WorkspaceFactory::Instance().create(inWS,1,X.size(),Y.size());
{
outWS->getAxis(1)->setValue(0, inWS->getAxis(1)->spectraNo(spec));
double xi, yi, yerr;
for (MantidVec::size_type i=0;i<Y.size();i++)
{
xi = X[i];
gsl_bspline_eval(xi, B, bw);
gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
outWS->dataY(0)[i] = yi;
outWS->dataE(0)[i] = yerr;
}
outWS->dataX(0) = X;
}
gsl_bspline_free(bw);
gsl_vector_free(B);
gsl_vector_free(x);
gsl_vector_free(y);
gsl_matrix_free(Z);
gsl_vector_free(c);
gsl_vector_free(w);
gsl_matrix_free(cov);
gsl_multifit_linear_free(mw);
setProperty("OutputWorkspace",outWS);
}
/**
* 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;
}