def _generateSubHarmonics(self, numberOfSubHarmonics):
nSub = 3
lowFreqScreen = np.zeros((self._screenSzInPx, self._screenSzInPx),
dtype=np.complex)
freqX = bfft.frequencies_x_map(nSub, 1. / nSub)
freqY = bfft.frequencies_y_map(nSub, 1. / nSub)
freqMod = bfft.frequencies_norm_map(nSub, 1. / nSub)
vv = np.arange(self._screenSzInPx) / self._screenSzInPx
xx = np.tile(vv, (self._screenSzInPx, 1))
yy = xx.T
depth = 0
while depth < numberOfSubHarmonics:
depth += 1
phase = self._randomPhase()
freqMod /= nSub
freqX /= nSub
freqY /= nSub
modul = self._kolmogorovAmplitudeMap(freqMod)
for ix in range(nSub):
for jx in range(nSub):
sh = np.exp(2 * np.pi * 1j *
(xx * freqX[ix, jx] + yy * freqY[ix, jx] +
phase[ix, jx]))
sh0 = sh.sum() / self._screenSzInPx**2
lowFreqScreen += 1. / nSub**depth * modul[ix,
jx] * (sh - sh0)
lowFreqScreen *= np.sqrt(0.0228) * self._screenSzInPx**(5. / 6)
return lowFreqScreen
def testFrequenciesYMap(self):
sizeInPoints = 1022
pixelSize = 0.001
frequenciesMap = bfft.frequencies_y_map(sizeInPoints, pixelSize)
sz2 = int(sizeInPoints / 2)
mostPosFrequency = bfft.most_positive_frequency(
sizeInPoints, pixelSize)
mostNegFrequency = bfft.most_negative_frequency(
sizeInPoints, pixelSize)
self.assertEqual((sizeInPoints, sizeInPoints), frequenciesMap.shape)
self.assertTrue(np.all(0 == frequenciesMap[sz2, :]))
self.assertTrue(np.all(mostNegFrequency == frequenciesMap[0, :]))
self.assertTrue(np.all(mostPosFrequency == frequenciesMap[-1, :]))
def testDirectTransformSinusX(self):
sizeInPoints = 500
pixelSize = 0.2
periodInLengthUnits = 4.0
amplitude = 13.4
phase = 0.8
spatialMap = self._makeSinusMap(sizeInPoints, pixelSize, amplitude,
periodInLengthUnits, phase)
spectralMap = bfft.direct_transform(spatialMap)
freqX = bfft.frequencies_x_map(sizeInPoints, pixelSize)
freqY = bfft.frequencies_y_map(sizeInPoints, pixelSize)
self.assertEqual((sizeInPoints, sizeInPoints), spectralMap.shape)
self.assertEqual(
1.0 / periodInLengthUnits,
np.abs(freqX.flatten()[np.argmax(np.abs(spectralMap))]))
self.assertEqual(
0.0, np.abs(freqY.flatten()[np.argmax(np.abs(spectralMap))]))
self._checkParseval(spatialMap, spectralMap)
def test_direct_sinus_x(self):
sizeInPoints = 500
pixelSize = 0.2
periodInLengthUnits = 4.0
amplitude = 13.4
phase = 0.8
spatialMap = self._makeSinusMap(sizeInPoints, pixelSize, amplitude,
periodInLengthUnits, phase)
xyDomain = DomainXY.from_shape((sizeInPoints, sizeInPoints), pixelSize)
xyFunct = ScalarBidimensionalFunction(spatialMap, domain=xyDomain)
fftFunct = bfft.direct(xyFunct)
spectralMap = fftFunct.values
freqX = bfft.frequencies_x_map(sizeInPoints, pixelSize)
freqY = bfft.frequencies_y_map(sizeInPoints, pixelSize)
self.assertEqual((sizeInPoints, sizeInPoints), spectralMap.shape)
self.assertEqual(
1.0 / periodInLengthUnits,
np.abs(freqX.flatten()[np.argmax(np.abs(spectralMap))]))
self.assertEqual(
0.0, np.abs(freqY.flatten()[np.argmax(np.abs(spectralMap))]))
self._checkParseval(spatialMap, spectralMap)
