def initialisation(self):
# Get the streamline parameter in a single array.
self.parameterisedStreamline = self.streamlineCoordinates[:, 0, 3]
# Calculate the velocity along the streamline
streamlineVelocity = np.linalg.norm(self.streamlineData[:, 2:4], axis=1)
inverseStreamlineVelocity = 1./streamlineVelocity
# Fit a cubic spline to the streamline velocity
# Need this to calculate velocity derivatives
self.parameterisedVelocity = interpolate.CubicSpline(self.parameterisedStreamline, streamlineVelocity, extrapolate=1)
self.parameterisedInverseVelocity = interpolate.CubicSpline(self.parameterisedStreamline, inverseStreamlineVelocity, extrapolate=1)
# Calculate the first derivative
self.parameterisedInverseVelocityPrime = self.parameterisedInverseVelocity.derivative(nu=1)
# Calculate the second derivative
self.parameterisedInverseVelocityDoublePrime = self.parameterisedInverseVelocity.derivative(nu=2)
return self.parameterisedStreamline, streamlineVelocity, self.parameterisedVelocity, self.parameterisedInverseVelocityPrime, self.parameterisedInverseVelocityDoublePrime
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