API: change the dot patterns

[tacaswell]

• change the dotted pattern to [[1.1, 1.1]]
• change scale floor to a lw of 2.0

These settings were discussed with @efiring and @jenshnielsen

Some of the test images (+ source) are below.

---

import numpy as np
import matplotlib.pyplot as plt
from cycler import cycler
import matplotlib

th = np.linspace(0, 2*np.pi)
fig, ax = plt.subplots()
dot_styles = [[1.2, .6],
              [1.2, 1.2],
              [0.8, 1.2]]

cy = cycler(matplotlib.rcParams['axes.prop_cycle'])
for j, (ds, sty) in enumerate(zip(dot_styles, cy)):
    for k in range(1, 10):
        ax.plot(th, j*np.ones(50) + .1 * k, linestyle=(0, ds),
                label=str((ds, k)), lw=k, **sty)
ax.legend()

import numpy as np
import matplotlib.pyplot as plt
from cycler import cycler
import matplotlib

th = np.linspace(0, 32)
fig, ax = plt.subplots()

dot_size = [.9, 1, 1.1, 1.2]
cy = cycler(matplotlib.rcParams['axes.prop_cycle'])
for j, (ds, sty) in enumerate(zip(dot_size, cy)):
    for lw in np.linspace(.5, 10, 10):
        ax.plot(th, j*np.ones(50) + .1 * lw, linestyle=(0, [ds, ds]),
                label=str((ds, lw)), lw=lw, **sty)

ax.legend()

[afvincent]

How does the new scale floor of lw=2 impact the other dash styles (dashed and dashdot)? With this new behavior, because default lw=1.5, they will now appear doubled compared to what was shown in #5926, won't they? Is it what was wanted?

[jenshnielsen]

It's only 0.5/1.5 = 1/3 larger at 1.5? But you are right that we should check all of the default patterns.
This should give us some idea

import numpy as np
import matplotlib.pyplot as plt
from cycler import cycler
import matplotlib

th = np.linspace(0, 32)
fig, ax = plt.subplots()

lins_styles = ['dashed', 'dotted', 'dashdot']
cy = cycler(matplotlib.rcParams['axes.prop_cycle'])
for j, (ls, sty) in enumerate(zip(lins_styles, cy)):
    for lw in np.linspace(.5, 10, 10):
        ax.plot(th, j*np.ones(50) + .1 * lw, linestyle=ls,
                label=str((ls, lw)), lw=lw, **sty)

ax.legend()

[afvincent]

@jenshnielsen You're right, I didn't take into account that previously the scale was already 1.5. So indeed the impact of the new PR shouldn't be that important.

[efiring]

In the line above, I expect the second half of the dashdot pattern should match the dot pattern, or if anything, should be even a little more stretched out along the line. The 0.8 can go to 1.2.

[afvincent]

If it is still time to propose a cosmetic enhancement about the named dash styles, I would like to note that something I find a bit ugly about the current dash style defaults is that there are not very congruent. Because of that, they appear a bit not "homogeneous" in the legend: the dash handle doesn't seem to have the same length as the dotted one (one finishes with ink while the other does with blank), as well as the dotted one vs the dashdot one. Here is a small picture of what I mean by congruent patterns:

I'm not saying this should be the main criterium to define the dash styles, but IMHO, it might be nice to have default dash styles that are L-congruent (L a length to define), and a default handle length for the legend that shows exactly L or 2*L (with default linewidth).

For the record, here is the code used to find congruent sequence and plot the example. Please note that the constraints I used for the demo might not be the best ones (especially the dash in dashdot is significantly shorter than the current one)...

import matplotlib.pyplot as plt
import numpy as np

"""
*More or less* the current pattern styles
"""
default_lengths = {'blank': 1.2, 'dot': 1.2, 'dash': 2.8, 'long_dash': 4.8,
                   'short_dot': 1.2}

"""
Solve a set of constraints on pattern lengths for a better congruence
"""
# col0: blank (common to all styles)
# col1: simple dot (from 'dotted')
# col2: simple dash (from 'dashed')
# col3: long dash (from 'dashdot')
# col4: short dot (from 'dashdot')
# with L a common length for the three default patterns
L = 100.0  # percent
AA = np.array([[2.,  3.,  0.,  0.,  0.],  # dot - blank - dot - blank - dot = L
               [1.,  0.,  2.,  0.,  0.],  # dash - blank - dash = L
               [1.,  0.,  0.,  1.,  1.],  # long_dash - blank - short_dot = L
               [1., -1.,  0.,  0.,  0.],  # blank = dot
               [0.,  0.,  0.,  1., -3]])  # long_dash = 4 * short_dot
bb = np.array([L, L, L, 0, 0])
xx = np.linalg.solve(AA, bb)
print(xx)  # DEBUG

ref_scale = default_lengths['blank']
patterns_lengths = {key: val for key, val in zip(
                    ('blank', 'dot', 'dash', 'long_dash', 'short_dot'),
                    list(ref_scale * xx / xx.min()))}


def add_pattern(ax, ink_length, blank_length, xinit, yval, color='Black'):
    """ Plot one pattern (ink, empty) """
    # Ink
    ax.plot([xinit, xinit + ink_length], [yval, yval], color=color, lw=2)
    # Blank
    xfinal = xinit + ink_length + blank_length
    return ax, xfinal


def draw_dashed(ax, yval, xstart=0., nb_patterns=12, color='Black',
                p_lengths=patterns_lengths):
    """ Plot a given amount of dash patterns """
    x = xstart
    for j in range(nb_patterns):
        ax, x = add_pattern(ax, p_lengths['dash'], p_lengths['blank'],
                            x, yval, color=color)
    return ax


def draw_dotted(ax, yval, xstart=0., nb_patterns=18, color='Black',
                p_lengths=patterns_lengths):
    """ Plot a given amount of dotted patterns """
    x = xstart
    for j in range(nb_patterns):
        ax, x = add_pattern(ax, p_lengths['dot'], p_lengths['blank'],
                            x, yval, color=color)
    return ax


def draw_dashdot(ax, yval, xstart=0., nb_patterns=6, color='Black',
                 p_lengths=patterns_lengths):
    """ Plot a given amount of dashdot patterns """
    x = xstart
    for j in range(nb_patterns):
        ax, x = add_pattern(ax, p_lengths['long_dash'], p_lengths['blank'],
                            x, yval, color=color)
        ax, x = add_pattern(ax, p_lengths['short_dot'], p_lengths['blank'],
                            x, yval, color=color)
    return ax


def plot_example_set(ax, p_lengths, color='Black', yoffset=0.0, title=""):
    """ Plot an example showing all the named dash styles """
    ax = draw_dotted(ax, 0.25 + yoffset, p_lengths=p_lengths, color=color)
    ax = draw_dashed(ax, 0.50 + yoffset, p_lengths=p_lengths, color=color)
    ax = draw_dashdot(ax, 0.75 + yoffset, p_lengths=p_lengths, color=color)

    # What the handle length of legend entry should at least show
    default_handlelength = (p_lengths['long_dash'] +
                            p_lengths['blank'] +
                            p_lengths['short_dot'])
    ax.axvline(0.0, color='0.5')
    ax.axvline(default_handlelength, color='0.5')

    ax.set_ylim([0, 1])
    ax.set_title(title)
    return ax


if __name__ == '__main__':

    fig, (ax0, ax1) = plt.subplots(nrows=2, num='Demo', sharex=True)
    ax0 = plot_example_set(ax0, default_lengths, color='Crimson',
                           title='~ current default (poor congruence)')
    ax1 = plot_example_set(ax1, patterns_lengths, color='CornFlowerBlue',
                           title='Possible solution for congruent patterns')

[tacaswell]

@afvincent That seems like a reasonable approach to me. One concern is that the pattern now scales with linewidth so picking the length for the legend gets tricky.

[WeatherGod]

That said... if the problem about the scaling the pattern to the linewidth
could be solved, then this would also solve the problem we are having with
the lines in the legend not always showing the entire dot pattern.

On Thu, Jun 9, 2016 at 8:26 AM, Thomas A Caswell notifications@github.com
wrote:

@afvincent https://github.com/afvincent That seems like a reasonable
approach to me. One concern is that the pattern now scales with linewidth
so picking the length for the legend gets tricky.

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[tacaswell]

We could scale the length of each handle also by lw, but then if you have
mixed lw in your legend your handle sizes will be mixed which seems worse
to me.

On Thu, Jun 9, 2016, 09:35 Benjamin Root notifications@github.com wrote:

That said... if the problem about the scaling the pattern to the linewidth
could be solved, then this would also solve the problem we are having with
the lines in the legend not always showing the entire dot pattern.

On Thu, Jun 9, 2016 at 8:26 AM, Thomas A Caswell <notifications@github.com

wrote:

@afvincent https://github.com/afvincent That seems like a reasonable
approach to me. One concern is that the pattern now scales with linewidth
so picking the length for the legend gets tricky.

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[afvincent]

My genuine proposition was simply to have a set of name "dash" styles that are congruent, and show an integer number of "patterns¹" with the default linewidth. Doing that, people that play only with the colors and the markers would have more regular legend handles. And for the others who play also with the named dash styles, they could simply increase the handle length to match something better (like for example the "lowest common multiple" of "patterns"), if they want to. And for the hardcore ones who also use user-defined dash styles, well the new situation wouldn't be worse or better than before...

For the record, my first guess was that a default handle length of 2 "patterns" would be nice, because I was thinking that if lw=1 corresponds to N=2 "patterns", then lw=2 would be OK for N=1 "pattern" with the same handle length. But then I saw that the default lw is 1.5 and the new scale floor is lw=2 so this cannot work this way...

I didn't even bother trying to propose something about tuning the length of the handle, as I expect that a consensus about what would be the better default behavior may be difficult to achieve.

¹ : beware it's not really a "pattern" (meaning a period)! It's just that I find that the case were the handles have ink on both ends more pleasant to the eye. So for example the handle for the dashdot would have a length of N*(dash + blank + dot).

[efiring]

dot: 1.2, 1.2
dash: 2.4, 1.2
dash-dot: 3.6, 1.2, 1.2, 1.2

[efiring]

This will address #6515.

[tacaswell]

Updated to use the patterns @efiring listed.

Re-running @jenshnielsen 's

[mdboom]

👍 from me. This all seems very well-reasoned. Closed/opened to force Travis to rerun -- not sure why that one failure only on Python 2.7 is appearing.

[WeatherGod]

similar failures in py2.7, 3.4 and 3.5. A whole bunch of them, too.

[tacaswell]

Restored the masking for non-'classic' style sheet, will update the images in another PR.

[QuLogic]

will update the images in another PR.

Does this still need to be done?

[tacaswell]

That is #6757 which is failing and I have not sorted out why yet.