traj_to_grad

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traj_to_grad#

pypulseqpp.traj_to_grad()[source]#

Convert a k-space trajectory to gradient and slew-rate waveforms.

By default, samples describe geometry and MRArbGrad chooses the timing within vector gradient and slew limits; output length can differ from input length. With time_optimal=False, samples already lie on the raster and are differentiated without limit enforcement.

Parameters:

  • k (numpy.ndarray) – K-space trajectory, time last: shape (n,), (2, n) or (3, n), in 1/m.

  • raster_time (float, default=None) – Gradient raster (s). Defaults to the system’s.

  • time_optimal (bool, default=True) – Re-parameterise the path within the limits rather than differentiate it.

  • system (pypulseqpp.Opts, default=None) – System limits; supplies max_grad, max_slew and the raster.

  • oversampling (int, default=8) – Path-resampling factor the solver works at.

  • start_at_zero (bool, default=True) – Ramp the waveform up from and back down to zero amplitude.

  • end_at_zero (bool, default=True) – Ramp the waveform up from and back down to zero amplitude.

Returns:

  • g (numpy.ndarray) – Gradient waveform (Hz/m), same axis convention as k.

  • slew (numpy.ndarray) – Slew rate (Hz/m/s), one value per gradient sample.

Examples

An analytic spiral becomes a playable gradient:

>>> import numpy as np
>>> import pypulseqpp as pp
>>> system = pp.Opts(max_grad=40, grad_unit="mT/m", max_slew=150, slew_unit="T/m/s")
>>> theta = np.linspace(0, 8 * np.pi, 2000)
>>> radius = np.linspace(0, 250.0, 2000)
>>> k = np.stack([radius * np.cos(theta), radius * np.sin(theta)])
>>> g, slew = pp.traj_to_grad(k, system=system)
>>> bool(np.abs(np.linalg.norm(g, axis=0)).max() <= system.max_grad * 1.001)
True

Then hand it to a factory per axis:

gx = pp.make_arbitrary_grad("x", g[0], system=system)

Differentiating instead, for a path already on the raster:

>>> g, slew = pp.traj_to_grad(k, system=system, time_optimal=False)
>>> g.shape[1] == k.shape[1] - 1
True

See also

make_arbitrary_grad

wrap one axis of the result as an event.

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