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coefficients: cleanup and refactor some code into CoefficientSource
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@ -46,7 +46,7 @@ class UnivariateMultiSparseSpline(UnivariateMultiSpline):
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def pad_const(x, n, axis=0):
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"""Prefix and postfix the array `x` by `n` repetitions of the first and
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last vlaue along `axis`.
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last value along `axis`.
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"""
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a = np.repeat(x.take([0], axis), n, axis)
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b = np.repeat(x.take([-1], axis), n, axis)
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@ -86,9 +86,9 @@ class CoefficientSource:
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def crop_x(self, start, stop, num=2):
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"""Return an array of valid sample positions.
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This function needs to be implemented only if this
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`CoefficientSource` does not support sampling at arbitrary
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positions.
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This method needs to be overloaded if this `CoefficientSource`
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does not support sampling at arbitrary positions or at arbitrary
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density.
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:param start: First sample position.
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:param stop: Last sample position.
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@ -99,15 +99,23 @@ class CoefficientSource:
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return np.linspace(start, stop, num)
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def scale_x(self, x, scale):
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# TODO: This could be moved to the the Driver/Mediator code as it is
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# device-specific.
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"""Scale and round sample positions.
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The sample times may need to be changed and/or decimated if
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incompatible with hardware requirements.
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:param x: Input sample positions in data space.
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:param scale: Data space position to cycles conversion scale,
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in units of x-units per clock cycle.
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:return: `x_sample`, the rounded sample positions and `durations`, the
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integer durations of the individual samples in cycles.
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"""
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raise NotImplementedError
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t = np.rint(x/scale)
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x_sample = t*scale
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durations = np.diff(t).astype(np.int)
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return x_sample, durations
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def __call__(self, x, **kwargs):
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"""Perform sampling and return coefficients.
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@ -118,25 +126,18 @@ class CoefficientSource:
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raise NotImplementedError
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def get_segment_data(self, start, stop, scale, cutoff=1e-12,
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min_duration=1, min_length=20,
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target="bias", variable="amplitude"):
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"""Build wavesynth segment data.
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:param start: see `crop_x()`.
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:param stop: see `crop_x()`.
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:param scale: see `scale_x()`.
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:param num: see `crop_x()`.
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:param cutoff: coefficient cutoff towards zero to compress data.
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:param min_duration: Minimum duration of a line.
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:param min_length: Minimum segment length to space triggers.
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"""
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x = self.crop_x(start, stop)
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x_sample, durations = self.scale_x(x, scale)
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coefficients = self(x_sample)
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np.clip(np.fabs(durations), min_duration, None, out=durations)
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if len(durations) == 1:
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durations[0] = max(durations[0], min_length)
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if start == stop:
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if len(x_sample) == 1 and start == stop:
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coefficients = coefficients[:1]
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# rescale coefficients accordingly
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coefficients *= (scale*np.sign(durations))**np.arange(
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@ -146,12 +147,14 @@ class CoefficientSource:
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return build_segment(durations, coefficients, target=target,
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variable=variable)
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def extend_segment(self, segment, *args, **kwargs):
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def extend_segment(self, segment, trigger=True, *args, **kwargs):
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"""Extend a wavesynth segment.
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See `get_segment()` for arguments.
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"""
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for line in self.get_segment_data(*args, **kwargs):
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for i, line in enumerate(self.get_segment_data(*args, **kwargs)):
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if i == 0:
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line["trigger"] = True
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segment.add_line(**line)
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@ -183,36 +186,42 @@ class SplineSource(CoefficientSource):
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x = self.x[ia:ib]
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return np.r_[start, x, stop]
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def scale_x(self, x, scale, nudge=1e-9):
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def scale_x(self, x, scale, min_duration=1, min_length=20):
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"""
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Due to minimum duration and/or minimum segment length constraints
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this method may drop samples from `x_sample` or adjust `durations` to
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comply. But `x_sample` and `durations` should be kept consistent.
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:param min_duration: Minimum duration of a line.
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:param min_length: Minimum segment length to space triggers.
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"""
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# We want to only sample a spline at t_knot + epsilon
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# where the highest order derivative has just jumped
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# and is valid at least up to the next knot after t_knot.
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#
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# To ensure that we are on the right side of a knot:
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# To ensure that we are on the correct side of a knot:
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# * only ever increase t when rounding (for increasing t)
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# * or only ever decrease it (for decreasing t)
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#
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# The highest derivative is discontinuous at t
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# and the correct value for a segment is obtained
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# for t_int >= t_float == t_knot (and v.v. for t decreasing).
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x = x/scale
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inc = np.diff(x) >= 0
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t = x/scale
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inc = np.diff(t) >= 0
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inc = np.r_[inc, inc[-1]]
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x = np.where(inc, np.ceil(x + nudge), np.floor(x - nudge))
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if len(x) > 1 and x[0] == x[1]:
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x = x[1:]
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if len(x) > 1 and x[-2] == x[-1]:
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x = x[:-1]
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x_sample = x[:-1]*scale
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durations = np.diff(x.astype(np.int))
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return x_sample, durations
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t = np.where(inc, np.ceil(t), np.floor(t))
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dt = np.diff(t.astype(np.int))
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valid = np.absolute(dt) >= min_duration
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dt = dt[valid]
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t = t[np.r_[True, valid]]
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if dt.shape[0] == 1:
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dt[0] = max(dt[0], min_length)
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x_sample = t[:-1]*scale
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return x_sample, dt
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def __call__(self, x):
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return self.spline(x)
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class ComposingSplineSource(SplineSource):
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# TODO
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# TODO: verify, test, document
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def __init__(self, x, y, components, order=4, pad_dx=1.):
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self.x = np.asanyarray(x)
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assert self.x.ndim == 1
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@ -236,18 +245,18 @@ class ComposingSplineSource(SplineSource):
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components, self.x, order)
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def __call__(self, t, gain={}, offset={}):
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der = list((set(self.components.n) | set(offset)) & set(self.der))
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der = list((set(self.components.n) | set(offset))
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& set(range(len(self.splines))))
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u = np.zeros((self.splines[0].order, len(self.splines[0].s), len(t)))
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# der, order, ele, t
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p = np.array([self.splines[i](t) for i in der])
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# order, der, None, t
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s = self.components(t)
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s_gain = np.array([gain.get(_, 1.) for _ in self.components.n])
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s = s[:, :, None, :]*s_gain[None, :, None, None]
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# order, der, None, t
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s = self.components(t)[:, :, None, :]*s_gain[None, :, None, None]
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for k, v in offset.items():
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if v and k in self.der:
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u += v*p[self.der.index(k)]
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ps = p[[self.der.index(_) for _ in self.shims.der]]
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if v:
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u += v*p[k]
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ps = p[self.shims.n]
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for i in range(u.shape[1]):
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for j in range(i + 1):
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u[i] += binom(i, j)*(s[j]*ps[:, i - j]).sum(0)
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