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Ensure streamplot Euler step is always called when going out of bounds. #11947

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Merged
merged 5 commits into from
Sep 3, 2019
Merged

Ensure streamplot Euler step is always called when going out of bounds. #11947

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e6926e6
FIX: Ensure Euler step is always called when going out of bounds.
tomflannaghan Aug 27, 2018
f924361
Remove unused code
tomflannaghan Aug 27, 2018
e00e512
Improve the OutOfBounds logic in the integration.
tomflannaghan Sep 3, 2018
91c6718
TST: push up the tolerance on mac
tacaswell Sep 1, 2019
4f1c54e
STY: add whitespace
tacaswell Sep 3, 2019
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55 changes: 35 additions & 20 deletions lib/matplotlib/streamplot.py
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Original file line number Diff line number Diff line change
Expand Up @@ -133,7 +133,7 @@ def streamplot(axes, x, y, u, v, density=1, linewidth=None, color=None,
line_kw['zorder'] = zorder
arrow_kw['zorder'] = zorder

## Sanity checks.
# Sanity checks.
if u.shape != grid.shape or v.shape != grid.shape:
raise ValueError("'u' and 'v' must match the shape of 'Grid(x, y)'")

Expand All @@ -156,8 +156,8 @@ def streamplot(axes, x, y, u, v, density=1, linewidth=None, color=None,

# Check if start_points are outside the data boundaries
for xs, ys in sp2:
if not (grid.x_origin <= xs <= grid.x_origin + grid.width
and grid.y_origin <= ys <= grid.y_origin + grid.height):
if not (grid.x_origin <= xs <= grid.x_origin + grid.width and
grid.y_origin <= ys <= grid.y_origin + grid.height):
raise ValueError("Starting point ({}, {}) outside of data "
"boundaries".format(xs, ys))

Expand Down Expand Up @@ -263,8 +263,8 @@ def __init__(self, grid, mask):
self.grid = grid
self.mask = mask
# Constants for conversion between grid- and mask-coordinates
self.x_grid2mask = (mask.nx - 1) / grid.nx
self.y_grid2mask = (mask.ny - 1) / grid.ny
self.x_grid2mask = (mask.nx - 1) / (grid.nx - 1)
self.y_grid2mask = (mask.ny - 1) / (grid.ny - 1)

self.x_mask2grid = 1. / self.x_grid2mask
self.y_mask2grid = 1. / self.y_grid2mask
Expand Down Expand Up @@ -413,19 +413,21 @@ class TerminateTrajectory(Exception):


# Integrator definitions
#========================
# =======================

def get_integrator(u, v, dmap, minlength, maxlength, integration_direction):

# rescale velocity onto grid-coordinates for integrations.
u, v = dmap.data2grid(u, v)

# speed (path length) will be in axes-coordinates
u_ax = u / dmap.grid.nx
v_ax = v / dmap.grid.ny
u_ax = u / (dmap.grid.nx - 1)
v_ax = v / (dmap.grid.ny - 1)
speed = np.ma.sqrt(u_ax ** 2 + v_ax ** 2)

def forward_time(xi, yi):
if not dmap.grid.within_grid(xi, yi):
raise OutOfBounds
ds_dt = interpgrid(speed, xi, yi)
if ds_dt == 0:
raise TerminateTrajectory()
Expand Down Expand Up @@ -480,6 +482,10 @@ def integrate(x0, y0):
return integrate


class OutOfBounds(IndexError):
pass


def _integrate_rk12(x0, y0, dmap, f, maxlength):
"""2nd-order Runge-Kutta algorithm with adaptive step size.

Expand Down Expand Up @@ -523,18 +529,28 @@ def _integrate_rk12(x0, y0, dmap, f, maxlength):
xf_traj = []
yf_traj = []

while dmap.grid.within_grid(xi, yi):
xf_traj.append(xi)
yf_traj.append(yi)
while True:
try:
if dmap.grid.within_grid(xi, yi):
xf_traj.append(xi)
yf_traj.append(yi)
else:
raise OutOfBounds

# Compute the two intermediate gradients.
# f should raise OutOfBounds if the locations given are
# outside the grid.
k1x, k1y = f(xi, yi)
k2x, k2y = f(xi + ds * k1x,
yi + ds * k1y)
except IndexError:
# Out of the domain on one of the intermediate integration steps.
# Take an Euler step to the boundary to improve neatness.
ds, xf_traj, yf_traj = _euler_step(xf_traj, yf_traj, dmap, f)
stotal += ds
k2x, k2y = f(xi + ds * k1x, yi + ds * k1y)

except OutOfBounds:
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If all of the raising logic is here it might be clearer to just use if and else statements.

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The raising logic is all here directly within the try block, including line 529 as well (so can't simply be put in the else). I can rewrite it using a flag variable like so. What do you think? Happy to update if you prefer it.

        try:
            out_of_bounds = False
            if dmap.grid.within_grid(xi, yi):
                xf_traj.append(xi)
                yf_traj.append(yi)

                k1x, k1y = f(xi, yi)

                if dmap.grid.within_grid(xi + ds * k1x, yi + ds * k1y):
                    k2x, k2y = f(xi + ds * k1x, yi + ds * k1y)
                else:
                    out_of_bounds = True
            else:
                out_of_bounds = True

            if out_of_bounds:
                # Out of the domain during this step.
                # Take an Euler step to the boundary to improve neatness
                # unless the trajectory is currently empty.
                if xf_traj:
                    ds, xf_traj, yf_traj = _euler_step(xf_traj, yf_traj,
                                                       dmap, f)
                    stotal += ds
                break

        except TerminateTrajectory:
            break

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Another simple approach could be to move the bounds check and raise OutOfbounds into f. Would simplify the logic in the interpolator.

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I've pushed a change to the PR moving the raise OutOfBounds into f. I tried quite a few things and I think this is the clearest.

# Out of the domain during this step.
# Take an Euler step to the boundary to improve neatness
# unless the trajectory is currently empty.
if xf_traj:
ds, xf_traj, yf_traj = _euler_step(xf_traj, yf_traj,
dmap, f)
stotal += ds
break
except TerminateTrajectory:
break
Expand All @@ -546,7 +562,7 @@ def _integrate_rk12(x0, y0, dmap, f, maxlength):

nx, ny = dmap.grid.shape
# Error is normalized to the axes coordinates
error = np.hypot((dx2 - dx1) / nx, (dy2 - dy1) / ny)
error = np.hypot((dx2 - dx1) / (nx - 1), (dy2 - dy1) / (ny - 1))

# Only save step if within error tolerance
if error < maxerror:
Expand Down Expand Up @@ -651,7 +667,6 @@ def _gen_starting_points(shape):
x, y = 0, 0
direction = 'right'
for i in range(nx * ny):

yield x, y

if direction == 'right':
Expand Down
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