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Ticks and Labels on Twin Axes

How can I set the labels on the extra axes?
The ticks and labels should be the same on all 4 axes. I'm doing something wrong... Thanks!
import matplotlib.pyplot as plt
plt.rcParams['text.usetex'] = True
plt.figure(figsize=(5,5))
f, ax1 = plt.subplots()
ax2 = ax1.twinx()
ax3 = ax1.twiny()
plt.show()
# create reusable ticks and labels
ticks = [0,1/2,3.14159/4,3.14159/2,1]
labels = [r"$0$", r"$\displaystyle\frac{1}{2}$", r"$\displaystyle\frac{\pi}{4}$", r"$\displaystyle\frac{\pi}{2}$", r"$1$"]
# Version 1: twinx() + xaxis.set_ticks()
plt.figure(figsize=(5,5))
f, ax1 = plt.subplots()
ax2 = ax1.twinx()
ax3 = ax1.twiny()
ax1.xaxis.set_ticks(ticks, labels=labels)
ax1.yaxis.set_ticks(ticks, labels=labels)
ax2.xaxis.set_ticks(ticks, labels=labels)
ax3.yaxis.set_ticks(ticks, labels=labels)
plt.show()
# Version 2: twinx() + set_xticklabels)()
plt.figure(figsize=(5,5))
f, ax1 = plt.subplots()
ax2 = ax1.twinx()
ax3 = ax1.twiny()
ax1.set_xticks(ticks)
ax1.set_xticklabels(labels)
ax1.set_yticks(ticks)
ax1.set_yticklabels(labels)
ax2.set_xticks(ticks)
ax2.set_xticklabels(labels)
ax3.set_yticks(ticks)
ax3.set_yticklabels(labels)
plt.show()
Confused: How come ax1 has both xaxis and yaxis, while ax2, ax3 do not appear to?

A unintuitive solution based on matplotlib.axes.Axes.twinx:
Create a new Axes with an invisible x-axis and an independent y-axis
positioned opposite to the original one (i.e. at right).
This means unintuitively (at least for me) you have to switch x/y at the .twin call.
unintuitively not concerning the general matplotlib twinx functionality, but concerning such a manual ticks and label assignment
To highlight that a bit more I used ax2_x and ax3_y in the code.
Disclaimer: Not sure if that will break your plot intention when data is added.
Probably at least you have to take special care with the data assignment to those twin axes - keeping that "axis switch" in mind.
Also keep that axis switch" in mind when assigning different ticks and labels to the x/y axis.
But for now I think that's the plot you were looking for:
Code:
import matplotlib.pyplot as plt
plt.rcParams['text.usetex'] = True
# create reusable ticks and labels
ticks = [0,1/2,3.14159/4,3.14159/2,1]
labels = [r"$0$", r"$\displaystyle\frac{1}{2}$", r"$\displaystyle\frac{\pi}{4}$", r"$\displaystyle\frac{\pi}{2}$", r"$1$"]
plt.figure(figsize=(5,5))
f, ax1 = plt.subplots()
ax1.xaxis.set_ticks(ticks, labels=labels)
ax1.yaxis.set_ticks(ticks, labels=labels)
ax2_x = ax1.twiny() # switch
ax3_y = ax1.twinx() # switch
ax2_x.xaxis.set_ticks(ticks, labels=labels)
ax3_y.yaxis.set_ticks(ticks, labels=labels)
plt.show()
Or switch the x/yaxis.set_ticks - with the same effect:
On second thought, I assume that's the preferred way to do it, especially when data comes into play.
ax2_x = ax1.twinx()
ax3_y = ax1.twiny()
ax2_x.yaxis.set_ticks(ticks, labels=labels) # switch
ax3_y.xaxis.set_ticks(ticks, labels=labels) # switch
In case you don't intend to use the twin axis functionality (that means having different data with different scaling assigned to those axis) but 'only' want the ticks and labels on all 4 axis for better plot readability:
Solution based on answer of ImportanceOfBeingErnest with the same plot result:
import matplotlib.pyplot as plt
plt.rcParams['text.usetex'] = True
# create reusable ticks and labels
ticks = [0,1/2,3.14159/4,3.14159/2,1]
labels = [r"$0$", r"$\displaystyle\frac{1}{2}$", r"$\displaystyle\frac{\pi}{4}$", r"$\displaystyle\frac{\pi}{2}$", r"$1$"]
plt.figure(figsize=(5,5))
f, ax1 = plt.subplots()
ax1.xaxis.set_ticks(ticks, labels=labels)
ax1.yaxis.set_ticks(ticks, labels=labels)
ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True, labeltop=True)
ax1.tick_params(axis="y", left=True, right=True, labelleft=True, labelright=True)
plt.show()

ax2 = ax1.twinx() shares the x-axis with ax1.
ax3 = ax1.twiny() shares the y-axis with ax1.
As a result, the two lines where you set ax2.xaxis and ax3.yaxis's ticks and ticklabels are redundant with the changes you already applied on ax1.
import matplotlib.pyplot as plt
plt.rcParams['text.usetex'] = False # My computer doesn't have LaTeX, don't mind me.
# Create reusable ticks and labels.
ticks = [0, 1/2, 3.14159/4, 3.14159/2, 1]
labels = [r"$0$", r"$\frac{1}{2}$", r"$\frac{\pi}{4}$", r"$\frac{\pi}{2}$", r"$1$"]
# Set the ticks and ticklabels for each axis.
fig = plt.figure(figsize=(5,5))
ax1 = fig.add_subplot()
ax2 = ax1.twinx()
ax3 = ax1.twiny()
for axis in (ax1.xaxis,
ax1.yaxis,
ax2.yaxis,
ax3.xaxis):
axis.set_ticks(ticks)
axis.set_ticklabels(labels)
fig.show()
Notice that if I comment out the work on ax2 and ax3, we get exactly what you have in your question:
for axis in (ax1.xaxis, ax1.yaxis,
# ax2.yaxis,
# ax3.xaxis,
):
axis.set_ticks(ticks)
axis.set_ticklabels(labels)
Now let's ruin ax1 via modifications on ax2, just to show that the bound between twins works well:
ax2.xaxis.set_ticks(range(10))
ax2.xaxis.set_ticklabels(tuple("abcdefghij"))

How do I align gridlines for two y-axis scales using Matplotlib?

I'm plotting two datasets with different units on the y-axis. Is there a way to make the ticks and gridlines aligned on both y-axes?
The first image shows what I get, and the second image shows what I would like to get.
This is the code I'm using to plot:
import seaborn as sns
import numpy as np
import pandas as pd
np.random.seed(0)
fig = plt.figure()
ax1 = fig.add_subplot(111)
ax1.plot(pd.Series(np.random.uniform(0, 1, size=10)))
ax2 = ax1.twinx()
ax2.plot(pd.Series(np.random.uniform(10, 20, size=10)), color='r')

I am not sure if this is the prettiest way to do it, but it does fix it with one line:
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import pandas as pd
np.random.seed(0)
fig = plt.figure()
ax1 = fig.add_subplot(111)
ax1.plot(pd.Series(np.random.uniform(0, 1, size=10)))
ax2 = ax1.twinx()
ax2.plot(pd.Series(np.random.uniform(10, 20, size=10)), color='r')
# ADD THIS LINE
ax2.set_yticks(np.linspace(ax2.get_yticks()[0], ax2.get_yticks()[-1], len(ax1.get_yticks())))
plt.show()

I could solve it by deactivating ax.grid(None) in one of the grid`s axes:
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import pandas as pd
fig = plt.figure()
ax1 = fig.add_subplot(111)
ax1.plot(pd.Series(np.random.uniform(0, 1, size=10)))
ax2 = ax1.twinx()
ax2.plot(pd.Series(np.random.uniform(10, 20, size=10)), color='r')
ax2.grid(None)
plt.show()

I wrote this function that takes Matplotlib axes objects ax1, ax2, and floats minresax1 minresax2:
def align_y_axis(ax1, ax2, minresax1, minresax2):
""" Sets tick marks of twinx axes to line up with 7 total tick marks
ax1 and ax2 are matplotlib axes
Spacing between tick marks will be a factor of minresax1 and minresax2"""
ax1ylims = ax1.get_ybound()
ax2ylims = ax2.get_ybound()
ax1factor = minresax1 * 6
ax2factor = minresax2 * 6
ax1.set_yticks(np.linspace(ax1ylims[0],
ax1ylims[1]+(ax1factor -
(ax1ylims[1]-ax1ylims[0]) % ax1factor) %
ax1factor,
7))
ax2.set_yticks(np.linspace(ax2ylims[0],
ax2ylims[1]+(ax2factor -
(ax2ylims[1]-ax2ylims[0]) % ax2factor) %
ax2factor,
7))
It calculates and sets the ticks such that there are seven ticks. The lowest tick corresponds to the current lowest tick and increases the highest tick such that the separation between each tick is integer multiples of minrexax1 or minrexax2.
To make it general, you can set the total number of ticks you want by changing ever 7 you see to the total number of ticks, and change 6 to the total number of ticks minus 1.
I put a pull request in to incorporate some this into matplotlib.ticker.LinearLocator:
https://github.com/matplotlib/matplotlib/issues/6142
In the future (Matplotlib 2.0 perhaps?), try:
import matplotlib.ticker
nticks = 11
ax1.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))
ax2.yaxis.set_major_locator(matplotlib.ticker.LinearLocator(nticks))
That should just work and choose convenient ticks for both y-axes.

I created a method to align the ticks of multiple y- axes (could be more than 2), with possibly different scales in different axes.
Below is an example figure:
There are 3 y- axes, one blue on the left, and a green and a red on the right. The 3 curves are plotted onto the y-axis with the corresponding color. Note that they all have very different order of magnitudes.
Left plot: No alignment.
Mid plot: Aligned at (approximately) the lower bound of each y axis.
Right plot: Aligned at specified values: 0 for blue, 2.2*1e8 for red, and 44 for green. Those are chosen arbitrarily.
What I'm doing is to scale each y array to be within the range of 1-100, then merge all scaled y-values into a single array, from which a new set of ticks is created using MaxNLocator. Then this new set of ticks is scaled back using the corresponding scaling factor to get the new ticks for each axis. If some specific alignment is required, y arrays are shifted before scaling, and shifted back afterwards.
Complete code here (the key function is alignYaxes()):
import matplotlib.pyplot as plt
import numpy as np
def make_patch_spines_invisible(ax):
'''Used for creating a 2nd twin-x axis on the right/left
E.g.
fig, ax=plt.subplots()
ax.plot(x, y)
tax1=ax.twinx()
tax1.plot(x, y1)
tax2=ax.twinx()
tax2.spines['right'].set_position(('axes',1.09))
make_patch_spines_invisible(tax2)
tax2.spines['right'].set_visible(True)
tax2.plot(x, y2)
'''
ax.set_frame_on(True)
ax.patch.set_visible(False)
for sp in ax.spines.values():
sp.set_visible(False)
def alignYaxes(axes, align_values=None):
'''Align the ticks of multiple y axes
Args:
axes (list): list of axes objects whose yaxis ticks are to be aligned.
Keyword Args:
align_values (None or list/tuple): if not None, should be a list/tuple
of floats with same length as <axes>. Values in <align_values>
define where the corresponding axes should be aligned up. E.g.
[0, 100, -22.5] means the 0 in axes[0], 100 in axes[1] and -22.5
in axes[2] would be aligned up. If None, align (approximately)
the lowest ticks in all axes.
Returns:
new_ticks (list): a list of new ticks for each axis in <axes>.
A new sets of ticks are computed for each axis in <axes> but with equal
length.
'''
from matplotlib.pyplot import MaxNLocator
nax=len(axes)
ticks=[aii.get_yticks() for aii in axes]
if align_values is None:
aligns=[ticks[ii][0] for ii in range(nax)]
else:
if len(align_values) != nax:
raise Exception("Length of <axes> doesn't equal that of <align_values>.")
aligns=align_values
bounds=[aii.get_ylim() for aii in axes]
# align at some points
ticks_align=[ticks[ii]-aligns[ii] for ii in range(nax)]
# scale the range to 1-100
ranges=[tii[-1]-tii[0] for tii in ticks]
lgs=[-np.log10(rii)+2. for rii in ranges]
igs=[np.floor(ii) for ii in lgs]
log_ticks=[ticks_align[ii]*(10.**igs[ii]) for ii in range(nax)]
# put all axes ticks into a single array, then compute new ticks for all
comb_ticks=np.concatenate(log_ticks)
comb_ticks.sort()
locator=MaxNLocator(nbins='auto', steps=[1, 2, 2.5, 3, 4, 5, 8, 10])
new_ticks=locator.tick_values(comb_ticks[0], comb_ticks[-1])
new_ticks=[new_ticks/10.**igs[ii] for ii in range(nax)]
new_ticks=[new_ticks[ii]+aligns[ii] for ii in range(nax)]
# find the lower bound
idx_l=0
for i in range(len(new_ticks[0])):
if any([new_ticks[jj][i] > bounds[jj][0] for jj in range(nax)]):
idx_l=i-1
break
# find the upper bound
idx_r=0
for i in range(len(new_ticks[0])):
if all([new_ticks[jj][i] > bounds[jj][1] for jj in range(nax)]):
idx_r=i
break
# trim tick lists by bounds
new_ticks=[tii[idx_l:idx_r+1] for tii in new_ticks]
# set ticks for each axis
for axii, tii in zip(axes, new_ticks):
axii.set_yticks(tii)
return new_ticks
def plotLines(x, y1, y2, y3, ax):
ax.plot(x, y1, 'b-')
ax.tick_params('y',colors='b')
tax1=ax.twinx()
tax1.plot(x, y2, 'r-')
tax1.tick_params('y',colors='r')
tax2=ax.twinx()
tax2.spines['right'].set_position(('axes',1.2))
make_patch_spines_invisible(tax2)
tax2.spines['right'].set_visible(True)
tax2.plot(x, y3, 'g-')
tax2.tick_params('y',colors='g')
ax.grid(True, axis='both')
return ax, tax1, tax2
#-------------Main---------------------------------
if __name__=='__main__':
# craft some data to plot
x=np.arange(20)
y1=np.sin(x)
y2=x/1000+np.exp(x)
y3=x+x**2/3.14
figure=plt.figure(figsize=(12,4),dpi=100)
ax1=figure.add_subplot(1, 3, 1)
axes1=plotLines(x, y1, y2, y3, ax1)
ax1.set_title('No alignment')
ax2=figure.add_subplot(1, 3, 2)
axes2=plotLines(x, y1, y2, y3, ax2)
alignYaxes(axes2)
ax2.set_title('Default alignment')
ax3=figure.add_subplot(1, 3, 3)
axes3=plotLines(x, y1, y2, y3, ax3)
alignYaxes(axes3, [0, 2.2*1e8, 44])
ax3.set_title('Specified alignment')
figure.tight_layout()
figure.show()

This code will ensure that grids from both axes align to each other, without having to hide gridlines from either set. In this example, it allows you to match whichever has the finer grid lines. This builds off of the idea from #Leo. Hope it helps!
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import pandas as pd
fig = plt.figure()
ax1 = fig.add_subplot(111)
ax1.plot(pd.Series(np.random.uniform(0,1,size=10)))
ax2 = ax1.twinx()
ax2.plot(pd.Series(np.random.uniform(10,20,size=10)),color='r')
ax2.grid(None)
# Determine which plot has finer grid. Set pointers accordingly
l1 = len(ax1.get_yticks())
l2 = len(ax2.get_yticks())
if l1 > l2:
a = ax1
b = ax2
l = l1
else:
a = ax2
b = ax1
l = l2
# Respace grid of 'b' axis to match 'a' axis
b_ticks = np.linspace(b.get_yticks()[0],b.get_yticks()[-1],l)
b.set_yticks(b_ticks)
plt.show()

If you're using axis labels, Leo's solution can push them off the side, due to the precision of the numbers in the ticks.
So in addition to something like Leo's solution (repeated here),
ax2.set_yticks(np.linspace(ax2.get_yticks()[0],ax2.get_yticks()[-1],len(ax1.get_yticks())))
you can use the autolayout setting, as mentioned in this answer; e.g., earlier in your script you can update rcParams:
from matplotlib import rcParams
rcParams.update({'figure.autolayout': True})
In a few test cases, this appears to produce the expected result, with both lined-up ticks and labels fully contained in the output.

I had the same issue except this was for a secondary x axis. I solved by setting my secondary x axis equal to the limit of my primary axis.The example below is without setting the limit of the second axis equal to the first:ax2 = ax.twiny()
Once I set the limit of the second axis equal to the first ax2.set_xlim(ax.get_xlim()) here is my result:

fix the limits for both axis (from any number to any number)
divide both axis into same n parts
ax1.set_ylim(a,b)
ax1.set_yticks(np.linspace(a,b, n))
ax2.set_ylim(c,d)
ax2.set_yticks(np.linspace(c,d, n))

Change grid interval and specify tick labels in Matplotlib

I am trying to plot counts in gridded plots, but I haven't been able to figure out how to go about it.
I want:
to have dotted grids at an interval of 5;
to have major tick labels only every 20;
for the ticks to be outside the plot; and
to have "counts" inside those grids.
I have checked for potential duplicates, such as here and here, but have not been able to figure it out.
This is my code:
import matplotlib.pyplot as plt
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
for key, value in sorted(data.items()):
x = value[0][2]
y = value[0][3]
count = value[0][4]
fig = plt.figure()
ax = fig.add_subplot(111)
ax.annotate(count, xy = (x, y), size = 5)
# overwrites and I only get the last data point
plt.close()
# Without this, I get a "fail to allocate bitmap" error.
plt.suptitle('Number of counts', fontsize = 12)
ax.set_xlabel('x')
ax.set_ylabel('y')
plt.axes().set_aspect('equal')
plt.axis([0, 1000, 0, 1000])
# This gives an interval of 200.
majorLocator = MultipleLocator(20)
majorFormatter = FormatStrFormatter('%d')
minorLocator = MultipleLocator(5)
# I want the minor grid to be 5 and the major grid to be 20.
plt.grid()
filename = 'C:\Users\Owl\Desktop\Plot.png'
plt.savefig(filename, dpi = 150)
plt.close()
This is what I get.
I also have a problem with the data points being overwritten.
Could anybody PLEASE help me with this problem?

There are several problems in your code.
First the big ones:
You are creating a new figure and a new axes in every iteration of your loop →
put fig = plt.figure and ax = fig.add_subplot(1,1,1) outside of the loop.
Don't use the Locators. Call the functions ax.set_xticks() and ax.grid() with the correct keywords.
With plt.axes() you are creating a new axes again. Use ax.set_aspect('equal').
The minor things:
You should not mix the MATLAB-like syntax like plt.axis() with the objective syntax.
Use ax.set_xlim(a,b) and ax.set_ylim(a,b)
This should be a working minimal example:
import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
# Major ticks every 20, minor ticks every 5
major_ticks = np.arange(0, 101, 20)
minor_ticks = np.arange(0, 101, 5)
ax.set_xticks(major_ticks)
ax.set_xticks(minor_ticks, minor=True)
ax.set_yticks(major_ticks)
ax.set_yticks(minor_ticks, minor=True)
# And a corresponding grid
ax.grid(which='both')
# Or if you want different settings for the grids:
ax.grid(which='minor', alpha=0.2)
ax.grid(which='major', alpha=0.5)
plt.show()
Output is this:

A subtle alternative to MaxNoe's answer where you aren't explicitly setting the ticks but instead setting the cadence.
import matplotlib.pyplot as plt
from matplotlib.ticker import (AutoMinorLocator, MultipleLocator)
fig, ax = plt.subplots(figsize=(10, 8))
# Set axis ranges; by default this will put major ticks every 25.
ax.set_xlim(0, 200)
ax.set_ylim(0, 200)
# Change major ticks to show every 20.
ax.xaxis.set_major_locator(MultipleLocator(20))
ax.yaxis.set_major_locator(MultipleLocator(20))
# Change minor ticks to show every 5. (20/4 = 5)
ax.xaxis.set_minor_locator(AutoMinorLocator(4))
ax.yaxis.set_minor_locator(AutoMinorLocator(4))
# Turn grid on for both major and minor ticks and style minor slightly
# differently.
ax.grid(which='major', color='#CCCCCC', linestyle='--')
ax.grid(which='minor', color='#CCCCCC', linestyle=':')

Matplotlib: how to set ticks of twinned axis in log plot

In my plot, a secondary x axis is used to display the value of another variable for some data. Now, the original axis is log scaled. Unfortunaltely, the twinned axis puts the ticks (and the labels) referring to the linear scale of the original axis and not as intended to the log scale. How can this be overcome?
Here the code example that should put the ticks of the twinned axis in the same (absolute axes) position as the ones for the original axis:
def conv(x):
"""some conversion function"""
# ...
return x2
ax = plt.subplot(1,1,1)
ax.set_xscale('log')
# get the location of the ticks of ax
axlocs,axlabels = plt.xticks()
# twin axis and set limits as in ax
ax2 = ax.twiny()
ax2.set_xlim(ax.get_xlim())
#Set the ticks, should be set referring to the log scale of ax, but are set referring to the linear scale
ax2.set_xticks(axlocs)
# put the converted labels
ax2.set_xticklabels(map(conv,axlocs))
An alternative way would be (the ticks are then not set in the same position, but that doesn't matter):
from matplotlib.ticker import FuncFormatter
ax = plt.subplot(1,1,1)
ax.set_xscale('log')
ax2 = ax.twiny()
ax2.set_xlim(ax.get_xlim())
ax2.xaxis.set_major_formatter(FuncFormatter(lambda x,pos:conv(x)))
Both approaches work well as long as no log scale is used.
Perhaps there exists an easy fix. Is there something I missed in the documentation?
As a workaround, I tried to obtain the ax.transAxes coordinates of the ticks of ax and put the ticks at the very same position in ax2. But there does not exist something like
ax2.set_xticks(axlocs,transform=ax2.transAxes)
TypeError: set_xticks() got an unexpected keyword argument 'transform'

This has been asked a while ago, but I stumbled over it with the same question.
I eventually managed to solve the problem by introducing a logscaled (semilogx) transparent (alpha=0) dummy plot.
Example:
import numpy as np
import matplotlib.pyplot as plt
def conversion_func(x): # some arbitrary transformation function
return 2 * x**0.5 # from x to z
x = np.logspace(0, 5, 100)
y = np.sin(np.log(x))
fig = plt.figure()
ax = plt.gca()
ax.semilogx(x, y, 'k')
ax.set_xlim(x[0], x[-1]) # this is important in order that limits of both axes match
ax.set_ylabel("$y$")
ax.set_xlabel("$x$", color='C0')
ax.tick_params(axis='x', which='both', colors='C0')
ax.axvline(100, c='C0', lw=3)
ticks_x = np.logspace(0, 5, 5 + 1) # must span limits of first axis with clever spacing
ticks_z = conversion_func(ticks_x)
ax2 = ax.twiny() # get the twin axis
ax2.semilogx(ticks_z, np.ones_like(ticks_z), alpha=0) # transparent dummy plot
ax2.set_xlim(ticks_z[0], ticks_z[-1])
ax2.set_xlabel("$z \equiv f(x)$", color='C1')
ax2.xaxis.label.set_color('C1')
ax2.tick_params(axis='x', which='both', colors='C1')
ax2.axvline(20, ls='--', c='C1', lw=3) # z=20 indeed matches x=100 as desired
fig.show()
In the above example the vertical lines demonstrate that first and second axis are indeed shifted to one another as wanted. x = 100 gets shifted to z = 2*x**0.5 = 20. The colours are just to clarify which vertical line goes with which axis.

Don't need to cover them, just Eliminate the ticks!
d= [7,9,14,17,35,70];
j= [100,80,50,40,20,10];
plt.figure()
plt.xscale('log')
plt.plot(freq, freq*spec) #plot some spectrum
ax1 = plt.gca() #define my first axis
ax1.yaxis.set_ticks_position('both')
ax1.tick_params(axis='y',which='both',direction='in');
ax1.tick_params(axis='x',which='both',direction='in');
ax2 = ax1.twiny() #generates second axis (top)
ax2.set_xlim(ax1.get_xlim()); #same limits
plt.xscale('log') #make it log
ax2.set_xticks(freq[d]); #my own 'major' ticks OVERLAPS!!!
ax2.set_xticklabels(j); #change labels
ax2.tick_params(axis='x',which='major',direction='in');
ax2.tick_params(axis='x',which='minor',top=False); #REMOVE 'MINOR' TICKS
ax2.grid()

I think you can fix your issue by calling ax2.set_xscale('log').
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
ax.semilogx(np.logspace(1.0, 5.0, 20), np.random.random([20]))
new_tick_locations = np.array([10., 100., 1000., 1.0e4])
def tick_function(X):
V = X / 1000.
return ["%.3f" % z for z in V]
ax2 = ax.twiny()
ax2.set_xscale('log')
ax2.set_xlim(ax.get_xlim())
ax2.set_xticks(new_tick_locations)
ax2.set_xticklabels(tick_function(new_tick_locations))
ax2.set_xlabel(r"Modified x-axis: $X/1000$")

Make matplotlib autoscaling ignore some of the plots

I use matplotib's Axes API to plot some figures. One of the lines I plot represents the theoretical expected line. It has no meaning outside of the original y and x limits. What I want, is for matlplotlib to ignore it when autoscaling the limits. What I used to do, is to check what are the current limits, then plot, and reset the limits. The problem is that when I plot a third plot, the limits get recalculated together with the theoretical line, and that really expands the graph.
# Boilerplate
from matplotlib.figure import Figure
from matplotlib.backends.backend_pdf import FigureCanvasPdf
from numpy import sin, linspace
fig = Figure()
ax = fig.add_subplot(1,1,1)
x1 = linspace(-1,1,100)
ax.plot(x1, sin(x1))
ax.plot(x1, 3*sin(x1))
# I wish matplotlib would not consider the second plot when rescaling
ax.plot(x1, sin(x1/2.0))
# But would consider the first and last
canvas_pdf = FigureCanvasPdf(fig)
canvas_pdf.print_figure("test.pdf")

The obvious way is to just manually set the limits to what you want. (e.g. ax.axis([xmin, xmax, ymin, ymax]))
If you don't want to bother with finding out the limits manually, you have a couple of options...
As several people (tillsten, Yann, and Vorticity) have mentioned, if you can plot the function you want to ignore last, then you can disable autoscaling before plotting it or pass the scaley=False kwarg to plot
import numpy as np
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
ax.plot(x1, np.sin(x1))
ax.plot(x1, np.sin(x1 / 2.0))
ax.autoscale(False) #You could skip this line and use scalex=False on
ax.plot(x1, 3 * np.sin(x1)) #the "theoretical" plot. It has to be last either way
fig.savefig('test.pdf')
Note that you can adjust the zorder of the last plot so that it's drawn in the "middle", if you want control over that.
If you don't want to depend on the order, and you do want to just specify a list of lines to autoscale based on, then you could do something like this: (Note: This is a simplified version assuming you're dealing with Line2D objects, rather than matplotlib artists in general.)
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.transforms as mtransforms
def main():
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
line1, = ax.plot(x1, np.sin(x1))
line2, = ax.plot(x1, 3 * np.sin(x1))
line3, = ax.plot(x1, np.sin(x1 / 2.0))
autoscale_based_on(ax, [line1, line3])
plt.show()
def autoscale_based_on(ax, lines):
ax.dataLim = mtransforms.Bbox.unit()
for line in lines:
xy = np.vstack(line.get_data()).T
ax.dataLim.update_from_data_xy(xy, ignore=False)
ax.autoscale_view()
if __name__ == '__main__':
main()

Use the scalex/scaley kw arg:
plot(x1, 3*sin(x1), scaley=False)

LineCollection objects can be ignored by using the autolim=False argument:
from matplotlib.collections import LineCollection
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
# Will update limits
ax.plot(x1, np.sin(x1))
# Will not update limits
col = LineCollection([np.column_stack((x1, 3 * np.sin(x1)))], colors='g')
ax.add_collection(col, autolim=False)
# Will still update limits
ax.plot(x1, np.sin(x1 / 2.0))

This can be done regardless of plotting order by creating another axes to work on.
In this version, we create a twin axes and disable the autoscaling on that twin axes. In this way, the plot is scaled based on anything plotted in the original axes, but is not scaled by anything put into the twin axes.
import numpy as np
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
twin_ax = ax.twinx() # Create a twin axes.
twin_ax.autoscale(False) # Turn off autoscaling on the twin axes.
twin_ax.set_yticks([]) # Remove the extra tick numbers from the twin axis.
ax.plot(x1, np.sin(x1))
twin_ax.plot(x1, 3 * np.sin(x1), c='green') # Plotting the thing we don't want to scale on in the twin axes.
ax.plot(x1, np.sin(x1 / 2.0))
twin_ax.set_ylim(ax.get_ylim()) # Make sure the y limits of the twin matches the autoscaled of the original.
fig.savefig('test.pdf')
Note, the above only prevents the un-twined axis from auto scaling (y in the above case). To get it to work for both x and y, we can do the twinning process for both x and y (or create the new axes from scratch):
import numpy as np
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
x2 = np.linspace(-2,2,100) # Would extend the x limits if auto scaled
twin_ax = ax.twinx().twiny() # Create a twin axes.
twin_ax.autoscale(False) # Turn off autoscaling on the twin axes.
twin_ax.set_yticks([]) # Remove the extra tick numbers from the twin axis.
twin_ax.set_xticks([]) # Remove the extra tick numbers from the twin axis.
ax.plot(x1, np.sin(x1))
twin_ax.plot(x2, 3 * np.sin(x2), c='green') # Plotting the thing we don't want to scale on in the twin axes.
ax.plot(x1, np.sin(x1 / 2.0))
twin_ax.set_ylim(ax.get_ylim()) # Make sure the y limits of the twin matches the autoscaled of the original.
twin_ax.set_xlim(ax.get_xlim()) # Make sure the x limits of the twin matches the autoscaled of the original.
fig.savefig('test.png')

As a generalisation of jam's answer, a collection object can be obtained from any of matplotlib's plotting functions and then re-added with autolim=False. For example,
fig, ax = plt.subplots()
x1 = np.linspace(-1,1,100)
# Get hold of collection
collection = ax.plot(x1, np.sin(x1))
# Remove collection from the plot
collection.remove()
# Rescale
ax.relim()
# Add the collection without autoscaling
ax.add_collection(collection, autolim=False)