Consider floating point accuracy for system specs checks (#270)

* - when checked for system violations of sequence, floating point accuracy is  considered

* - changed >= to >
- added eps to avoid floating point rounding issues

---------

Co-authored-by: Patrick Schuenke <37338697+schuenke@users.noreply.github.com>

Author: h3lg3

src/pypulseq/make_arbitrary_grad.py

@@ -3,6 +3,7 @@
 
 import numpy as np
 
+from pypulseq import eps
 from pypulseq.opts import Opts
 from pypulseq.utils.tracing import trace, trace_enabled
 
@@ -76,9 +77,9 @@ def make_arbitrary_grad(
         raise ValueError(f'Invalid channel. Must be one of x, y or z. Passed: {channel}')
 
     slew_rate = np.diff(waveform) / system.grad_raster_time
-    if max(abs(slew_rate)) >= max_slew:
+    if max(abs(slew_rate)) > max_slew + eps:
         raise ValueError(f'Slew rate violation {max(abs(slew_rate)) / max_slew * 100}')
-    if max(abs(waveform)) >= max_grad:
+    if max(abs(waveform)) > max_grad + eps:
         raise ValueError(f'Gradient amplitude violation {max(abs(waveform)) / max_grad * 100}')
 
     if first is None:

src/pypulseq/make_extended_trapezoid_area.py

@@ -3,6 +3,7 @@
 
 import numpy as np
 
+from pypulseq import eps
 from pypulseq.make_extended_trapezoid import make_extended_trapezoid
 from pypulseq.opts import Opts
 from pypulseq.utils.cumsum import cumsum
@@ -87,7 +88,7 @@ def _find_solution(duration: int) -> Union[None, Tuple[int, int, int, float]]:
 
         # Check if gradient amplitude exceeds max_grad, if so, adjust ramp
         # times for a trapezoidal gradient with maximum slew rate.
-        if grad_start + ramp_up_time * max_slew * raster_time > max_grad:
+        if grad_start + ramp_up_time * max_slew * raster_time > max_grad + eps:
             ramp_up_time = round(_calc_ramp_time(grad_start, max_grad) / raster_time)
             ramp_down_time = round(_calc_ramp_time(grad_end, max_grad) / raster_time)
         else:
@@ -105,7 +106,7 @@ def _find_solution(duration: int) -> Union[None, Tuple[int, int, int, float]]:
 
         # Check if gradient amplitude exceeds -max_grad, if so, adjust ramp
         # times for a trapezoidal gradient with maximum slew rate.
-        if grad_start - ramp_up_time * max_slew * raster_time < -max_grad:
+        if grad_start - ramp_up_time * max_slew * raster_time < -max_grad - eps:
             ramp_up_time = round(_calc_ramp_time(grad_start, -max_grad) / raster_time)
             ramp_down_time = round(_calc_ramp_time(grad_end, -max_grad) / raster_time)
         else:

src/pypulseq/make_trapezoid.py

@@ -20,7 +20,7 @@ def calculate_shortest_params_for_area(area: float, max_slew: float, max_grad: f
     effective_time = rise_time
 
     # Adjust for max gradient constraint
-    if abs(amplitude) > max_grad:
+    if abs(amplitude) > max_grad + eps:
         effective_time = math.ceil(abs(area) / max_grad / grad_raster_time) * grad_raster_time
         amplitude = area / effective_time
         rise_time = math.ceil(abs(amplitude) / max_slew / grad_raster_time) * grad_raster_time
@@ -225,15 +225,15 @@ def make_trapezoid(
     if rise_time is None and fall_time is None:
         rise_time = fall_time = calculate_shortest_rise_time(amplitude2, max_slew, system.grad_raster_time)
 
-    if abs(amplitude2) > max_grad:
+    if abs(amplitude2) > max_grad + eps:
         raise ValueError(f'Refined amplitude ({abs(amplitude2):0.0f} Hz/m) is larger than max ({max_grad:0.0f} Hz/m).')
 
-    if abs(amplitude2) / rise_time > max_slew:
+    if abs(amplitude2) / rise_time > max_slew + eps:
         raise ValueError(
             f'Refined slew rate ({abs(amplitude2) / rise_time:0.0f} Hz/m/s) for ramp up is larger than max ({max_slew:0.0f} Hz/m/s).'
         )
 
-    if abs(amplitude2) / fall_time > max_slew:
+    if abs(amplitude2) / fall_time > max_slew + eps:
         raise ValueError(
             f'Refined slew rate ({abs(amplitude2) / fall_time:0.0f} Hz/m/s) for ramp down is larger than max ({max_slew:0.0f} Hz/m/s).'
         )