Matplotlib axis with two scales shared origin

Question

I need two overlay two datasets with different Y-axis scales in Matplotlib. The data contains both positive and negative values. I want the two axes to share one origin, but Matplotlib does not align the two scales by default.

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax1 = fig.add_subplot(111)
ax2 = ax1.twinx()

ax1.bar(range(6), (2, -2, 1, 0, 0, 0))
ax2.plot(range(6), (0, 2, 8, -2, 0, 0))
plt.show()

I suppose it is possible to perform some computation with .get_ylim() and .set_ylim() two align the two scales. Is there an easier solution?

Answer 1

use the align_yaxis() function:

import numpy as np
import matplotlib.pyplot as plt

def align_yaxis(ax1, v1, ax2, v2):
    """adjust ax2 ylimit so that v2 in ax2 is aligned to v1 in ax1"""
    _, y1 = ax1.transData.transform((0, v1))
    _, y2 = ax2.transData.transform((0, v2))
    inv = ax2.transData.inverted()
    _, dy = inv.transform((0, 0)) - inv.transform((0, y1-y2))
    miny, maxy = ax2.get_ylim()
    ax2.set_ylim(miny+dy, maxy+dy)


fig = plt.figure()
ax1 = fig.add_subplot(111)
ax2 = ax1.twinx()

ax1.bar(range(6), (2, -2, 1, 0, 0, 0))
ax2.plot(range(6), (0, 2, 8, -2, 0, 0))

align_yaxis(ax1, 0, ax2, 0)
plt.show()

Answer 2

In order to ensure that the y-bounds are maintained (so no data points are shifted off the plot), and to balance adjustment of both y-axes, I made some additions to @HYRY's answer:

def align_yaxis(ax1, v1, ax2, v2):
    """adjust ax2 ylimit so that v2 in ax2 is aligned to v1 in ax1"""
    _, y1 = ax1.transData.transform((0, v1))
    _, y2 = ax2.transData.transform((0, v2))
    adjust_yaxis(ax2,(y1-y2)/2,v2)
    adjust_yaxis(ax1,(y2-y1)/2,v1)

def adjust_yaxis(ax,ydif,v):
    """shift axis ax by ydiff, maintaining point v at the same location"""
    inv = ax.transData.inverted()
    _, dy = inv.transform((0, 0)) - inv.transform((0, ydif))
    miny, maxy = ax.get_ylim()
    miny, maxy = miny - v, maxy - v
    if -miny>maxy or (-miny==maxy and dy > 0):
        nminy = miny
        nmaxy = miny*(maxy+dy)/(miny+dy)
    else:
        nmaxy = maxy
        nminy = maxy*(miny+dy)/(maxy+dy)
    ax.set_ylim(nminy+v, nmaxy+v)

Answer 3

I've cooked up a solution starting from the above that will align any number of axes:

def align_yaxis_np(axes):
    """Align zeros of the two axes, zooming them out by same ratio"""
    axes = np.array(axes)
    extrema = np.array([ax.get_ylim() for ax in axes])

    # reset for divide by zero issues
    for i in range(len(extrema)):
        if np.isclose(extrema[i, 0], 0.0):
            extrema[i, 0] = -1
        if np.isclose(extrema[i, 1], 0.0):
            extrema[i, 1] = 1

    # upper and lower limits
    lowers = extrema[:, 0]
    uppers = extrema[:, 1]

    # if all pos or all neg, don't scale
    all_positive = False
    all_negative = False
    if lowers.min() > 0.0:
        all_positive = True

    if uppers.max() < 0.0:
        all_negative = True

    if all_negative or all_positive:
        # don't scale
        return

    # pick "most centered" axis
    res = abs(uppers+lowers)
    min_index = np.argmin(res)

    # scale positive or negative part
    multiplier1 = abs(uppers[min_index]/lowers[min_index])
    multiplier2 = abs(lowers[min_index]/uppers[min_index])

    for i in range(len(extrema)):
        # scale positive or negative part based on which induces valid
        if i != min_index:
            lower_change = extrema[i, 1] * -1*multiplier2
            upper_change = extrema[i, 0] * -1*multiplier1
            if upper_change < extrema[i, 1]:
                extrema[i, 0] = lower_change
            else:
                extrema[i, 1] = upper_change

        # bump by 10% for a margin
        extrema[i, 0] *= 1.1
        extrema[i, 1] *= 1.1

    # set axes limits
    [axes[i].set_ylim(*extrema[i]) for i in range(len(extrema))]

example:

Answer 4

@drevicko's answer fails for me when plotting the following two sequences of points:

l1 = [0.03, -0.6, 1, 0.05]
l2 = [0.8,  0.9,  1,  1.1]
fig, ax1 = plt.subplots()
ax1.plot(l1)
ax2 = ax1.twinx()
ax2.plot(l2, color='r')
align_yaxis(ax1, 0, ax2, 0)

... so here's my version:

def align_yaxis(ax1, ax2):
    """Align zeros of the two axes, zooming them out by same ratio"""
    axes = (ax1, ax2)
    extrema = [ax.get_ylim() for ax in axes]
    tops = [extr[1] / (extr[1] - extr[0]) for extr in extrema]
    # Ensure that plots (intervals) are ordered bottom to top:
    if tops[0] > tops[1]:
        axes, extrema, tops = [list(reversed(l)) for l in (axes, extrema, tops)]

    # How much would the plot overflow if we kept current zoom levels?
    tot_span = tops[1] + 1 - tops[0]

    b_new_t = extrema[0][0] + tot_span * (extrema[0][1] - extrema[0][0])
    t_new_b = extrema[1][1] - tot_span * (extrema[1][1] - extrema[1][0])
    axes[0].set_ylim(extrema[0][0], b_new_t)
    axes[1].set_ylim(t_new_b, extrema[1][1])

There are in principle infinite different possibilities to align the zeros (or other values, which the other provided solutions accept): wherever you place zero on the y axis, you can zoom each of the two series so that it fits. We just pick the position such that, after the transformation, the two cover a vertical interval of same height. Or in other terms, we minimize them of a same factor compared to the non-aligned plot. (This does not mean that 0 is at half of the plot: this will happen e.g. if one plot is all negative and the other all positive.)

Numpy version:

def align_yaxis_np(ax1, ax2):
    """Align zeros of the two axes, zooming them out by same ratio"""
    axes = np.array([ax1, ax2])
    extrema = np.array([ax.get_ylim() for ax in axes])
    tops = extrema[:,1] / (extrema[:,1] - extrema[:,0])
    # Ensure that plots (intervals) are ordered bottom to top:
    if tops[0] > tops[1]:
        axes, extrema, tops = [a[::-1] for a in (axes, extrema, tops)]

    # How much would the plot overflow if we kept current zoom levels?
    tot_span = tops[1] + 1 - tops[0]

    extrema[0,1] = extrema[0,0] + tot_span * (extrema[0,1] - extrema[0,0])
    extrema[1,0] = extrema[1,1] + tot_span * (extrema[1,0] - extrema[1,1])
    [axes[i].set_ylim(*extrema[i]) for i in range(2)]