def weighted_average_slopes(data, old_start, old_dt, new_start, new_dt,
new_npts, *args, **kwargs):
"""
Implements the weighted average slopes interpolation scheme proposed in
[Wiggins1976]_ for evenly sampled data. The scheme guarantees that there
will be no additional extrema after the interpolation in contrast to
spline interpolation.
The slope :math:`s_i` at each knot is given by a weighted average of the
adjacent linear slopes :math:`m_i` and :math:`m_{i+j}`:
.. math::
s_i = (w_i m_i + w_{i+1} m_{i+1}) / (w_i + w_{i+1})
where
.. math::
w = 1 / max \left\{ \left\| m_i \\right\|, \epsilon \\right\}
The value at each data point and the slope are then plugged into a
piecewise continuous cubic polynomial used to evaluate the interpolated
sample points.
:type data: array_like
:param data: Array to interpolate.
:type old_start: float
:param old_start: The start of the array as a number.
:type old_start: float
:param old_dt: The time delta of the current array.
:type new_start: float
:param new_start: The start of the interpolated array. Must be greater
or equal to the current start of the array.
:type new_dt: float
:param new_dt: The desired new time delta.
:type new_npts: int
:param new_npts: The new number of samples.
"""
old_end, new_end = _validate_parameters(data, old_start, old_dt,
new_start, new_dt, new_npts)
# In almost all cases the unit will be in time.
new_time_array = np.linspace(new_start, new_end, new_npts)
m = np.diff(data) / old_dt
w = np.abs(m)
w = 1.0 / np.clip(w, np.spacing(1), w.max())
slope = np.empty(len(data), dtype=np.float64)
slope[0] = m[0]
slope[1:-1] = (w[:-1] * m[:-1] + w[1:] * m[1:]) / (w[:-1] + w[1:])
slope[-1] = m[-1]
# If m_i and m_{i+1} have opposite signs then set the slope to zero.
# This forces the curve to have extrema at the sample points and not
# in-between.
sign_change = np.diff(np.sign(m)).astype(np.bool)
slope[1:-1][sign_change] = 0.0
derivatives = np.empty((len(data), 2), dtype=np.float64)
derivatives[:, 0] = data
derivatives[:, 1] = slope
# Create interpolated value using hermite interpolation. In this case
# it is directly applicable as the first derivatives are known.
# Using scipy.interpolate.piecewise_polynomial_interpolate() is too
# memory intensive
return_data = np.empty(len(new_time_array), dtype=np.float64)
clibsignal.hermite_interpolation(data, slope, new_time_array, return_data,
len(data), len(return_data), old_dt,
old_start)
return return_data
def weighted_average_slopes(data, old_start, old_dt, new_start, new_dt,
new_npts, *args, **kwargs):
r"""
Implements the weighted average slopes interpolation scheme proposed in
[Wiggins1976]_ for evenly sampled data. The scheme guarantees that there
will be no additional extrema after the interpolation in contrast to
spline interpolation.
The slope :math:`s_i` at each knot is given by a weighted average of the
adjacent linear slopes :math:`m_i` and :math:`m_{i+j}`:
.. math::
s_i = (w_i m_i + w_{i+1} m_{i+1}) / (w_i + w_{i+1})
where
.. math::
w = 1 / max \left\{ \left\| m_i \\right\|, \epsilon \\right\}
The value at each data point and the slope are then plugged into a
piecewise continuous cubic polynomial used to evaluate the interpolated
sample points.
:type data: array_like
:param data: Array to interpolate.
:type old_start: float
:param old_start: The start of the array as a number.
:type old_start: float
:param old_dt: The time delta of the current array.
:type new_start: float
:param new_start: The start of the interpolated array. Must be greater
or equal to the current start of the array.
:type new_dt: float
:param new_dt: The desired new time delta.
:type new_npts: int
:param new_npts: The new number of samples.
"""
old_end, new_end = _validate_parameters(data, old_start, old_dt, new_start,
new_dt, new_npts)
# In almost all cases the unit will be in time.
new_time_array = np.linspace(new_start, new_end, new_npts)
m = np.diff(data) / old_dt
w = np.abs(m)
w = 1.0 / np.clip(w, np.spacing(1), w.max())
slope = np.empty(len(data), dtype=np.float64)
slope[0] = m[0]
slope[1:-1] = (w[:-1] * m[:-1] + w[1:] * m[1:]) / (w[:-1] + w[1:])
slope[-1] = m[-1]
# If m_i and m_{i+1} have opposite signs then set the slope to zero.
# This forces the curve to have extrema at the sample points and not
# in-between.
sign_change = np.diff(np.sign(m)).astype(np.bool)
slope[1:-1][sign_change] = 0.0
derivatives = np.empty((len(data), 2), dtype=np.float64)
derivatives[:, 0] = data
derivatives[:, 1] = slope
# Create interpolated value using hermite interpolation. In this case
# it is directly applicable as the first derivatives are known.
# Using scipy.interpolate.piecewise_polynomial_interpolate() is too
# memory intensive
return_data = np.empty(len(new_time_array), dtype=np.float64)
clibsignal.hermite_interpolation(data, slope, new_time_array, return_data,
len(data), len(return_data), old_dt,
old_start)
return return_data