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Added fplot to Axes subclass. #737

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dmcdougall wants to merge 12 commits into from
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Added fplot to Axes subclass. #737

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1df29a3
Merge branch 'trisurf'
dmcdougall Mar 15, 2012
e4d7a9e
Merge remote-tracking branch 'upstream/master'
dmcdougall Mar 15, 2012
8673b07
Merge remote-tracking branch 'upstream/master'
dmcdougall Mar 17, 2012
22d5e09
Merge remote-tracking branch 'upstream/master'
dmcdougall Mar 22, 2012
241ab8a
Merge remote-tracking branch 'upstream/master'
dmcdougall Mar 28, 2012
646989d
Added fplot to Axes subclass.
dmcdougall Mar 2, 2012
a04f581
Added docstring to Axes.fplot
dmcdougall Mar 17, 2012
d0b01d5
Scaled minimum step size with domain length.
dmcdougall Mar 22, 2012
c6c8b31
Small changes to the algorithm to reduce run time.
dmcdougall Mar 28, 2012
f04c2ab
Updated kwargs popping.
dmcdougall Mar 28, 2012
04bb1a0
Speed up computation when f is expensive.
dmcdougall Mar 29, 2012
90af9c9
Account for singularities in f.
dmcdougall Mar 29, 2012
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Small changes to the algorithm to reduce run time. 
The old method computed 'left' and 'right' gradients. These are the same
for a linear approximation, which is what Line2D is anyway.

I have also stored some function values that are used later in the
algorithm. This is good if f is expensive to compute.

The above changes to reduce computation time by 20%.
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@dmcdougall
dmcdougall committed Mar 28, 2012
commit c6c8b3130e3bed7e6280f53001a42c9c185034d5
20 changes: 11 additions & 9 deletions lib/matplotlib/fplot.py
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Expand Up @@ -74,20 +74,22 @@ def fplot(axes, f, limits, *args, **kwargs):
#
# If the function values are too close, the payoff is
# negligible, so skip them.
if np.abs(x_new - x[i]) < min_step or np.abs(f(x_new) - f(x[i])) < min_step:
f_new = f(x_new) # Used later, so store it
f_i = f(x[i]) # Used later, so store it
if abs(x_new - x[i]) < min_step or abs(f_new - f_i) < min_step:
continue

# Compute gradient
# FIXME: What if f(x[i]) is nan?
grad = (f(x[i+1]) - f(x[i])) / (x[i+1] - x[i])
# Compare gradients of actual f and linear approximation
# FIXME: What if f(x[i]) or f(x[i+1]) is nan?
dx = abs(x[i+1] - x[i])
f_interp = (f(x[i+1]) + f_i)

# Compute gradients to the left and right of x_new
grad_right = (f(x[i+1]) - f(x_new)) / (x[i+1] - x_new)
grad_left = (f(x_new) - f(x[i])) / (x_new - x[i])
# This line is the absolute error of the gradient
grad_error = np.abs(f_interp - 2.0 * f_new) / dx

# If the new gradients are not within the tolerance, store
# If the new gradient is not within the tolerance, store
# the subdivision point for merging later
if np.abs(grad_right - grad) > tol or np.abs(grad_left - grad) > tol:
if grad_error > tol:
within_tol = False
new_pts.append(x_new)

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