Trying to plot a spectrum, ie, velocity versus intensity, with lower x axis = velocity, on the upper twin axis = frequency
The relationship between them (doppler formula) is
f = (1-v/c)*f_0
where f is the resulting frequency, v the velocity, c the speed of light, and f_0 the frequency at v=0, ie. the v_lsr.
I have tried to solve it by looking at http://matplotlib.sourceforge.net/examples/axes_grid/parasite_simple2.html , where it is solved by
pm_to_kms = 1./206265.*2300*3.085e18/3.15e7/1.e5
aux_trans = matplotlib.transforms.Affine2D().scale(pm_to_kms, 1.)
ax_pm = ax_kms.twin(aux_trans)
ax_pm.set_viewlim_mode("transform")
my problem is, how do I replace the pm_to_kms with my function for frequency?
Anyone know how to solve this?
The solution I ended up using was:
ax_hz = ax_kms.twiny()
x_1, x_2 = ax_kms.get_xlim()
# i want the frequency in GHz so, divide by 1e9
ax_hz.set_xlim(calc_frequency(x_1,data.restfreq/1e9),calc_frequency(x_2,data.restfreq/1e9))
This works perfect, and much less complicated solution.
EDIT : Found a very fancy answer.
EDIT2 : Changed the transform call according to the comment by #u55
This basically involves defining our own conversion/transform. Because of the excellent AstroPy Units equivalencies, it becomes even easier to understand and more illustrative.
from matplotlib import transforms as mtransforms
import astropy.constants as co
import astropy.units as un
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('ggplot')
from mpl_toolkits.axes_grid.parasite_axes import SubplotHost
class Freq2WavelengthTransform(mtransforms.Transform):
input_dims = 1
output_dims = 1
is_separable = False
has_inverse = True
def __init__(self):
mtransforms.Transform.__init__(self)
def transform_non_affine(self, fr):
return (fr*un.GHz).to(un.mm, equivalencies=un.spectral()).value
def inverted(self):
return Wavelength2FreqTransform()
class Wavelength2FreqTransform(Freq2WavelengthTransform):
input_dims = 1
output_dims = 1
is_separable = False
has_inverse = True
def __init__(self):
mtransforms.Transform.__init__(self)
def transform_non_affine(self, wl):
return (wl*un.mm).to(un.GHz, equivalencies=un.spectral()).value
def inverted(self):
return Freq2WavelengthTransform()
aux_trans = mtransforms.BlendedGenericTransform(Wavelength2FreqTransform(), mtransforms.IdentityTransform())
fig = plt.figure(2)
ax_GHz = SubplotHost(fig, 1,1,1)
fig.add_subplot(ax_GHz)
ax_GHz.set_xlabel("Frequency (GHz)")
xvals = np.arange(199.9, 999.9, 0.1)
# data, noise + Gaussian (spectral) lines
data = np.random.randn(len(xvals))*0.01 + np.exp(-(xvals-300.)**2/100.)*0.5 + np.exp(-(xvals-600.)**2/400.)*0.5
ax_mm = ax_GHz.twin(aux_trans)
ax_mm.set_xlabel('Wavelength (mm)')
ax_mm.set_viewlim_mode("transform")
ax_mm.axis["right"].toggle(ticklabels=False)
ax_GHz.plot(xvals, data)
ax_GHz.set_xlim(200, 1000)
plt.draw()
plt.show()
This now produces the desired results:
Your "linear function" is a "simple scaling law" (with an offset). Just replace the pm_to_kms definition with your function.
Related
I've been trying to create a 2D map of blobs of matter (Gaussian random field) using a variance I have calculated. This variance is a 2D array. I have tried using numpy.random.normal since it allows for a 2D input of the variance, but it doesn't really create a map with the trend I expect from the input parameters. One of the important input constants lambda_c should manifest itself as the physical size (diameter) of the blobs. However, when I change my lambda_c, the size of the blobs does not change if at all. For example, if I set lambda_c = 40 parsecs, the map needs blobs that are 40 parsecs in diameter. A MWE to produce the map using my variance:
import numpy as np
import random
import matplotlib.pyplot as plt
from matplotlib.pyplot import show, plot
import scipy.integrate as integrate
from scipy.interpolate import RectBivariateSpline
n = 300
c = 3e8
G = 6.67e-11
M_sun = 1.989e30
pc = 3.086e16 # parsec
Dds = 1097.07889283e6*pc
Ds = 1726.62069147e6*pc
Dd = 1259e6*pc
FOV_arcsec_original = 5.
FOV_arcmin = FOV_arcsec_original/60.
pix2rad = ((FOV_arcmin/60.)/float(n))*np.pi/180.
rad2pix = 1./pix2rad
x_pix = np.linspace(-FOV_arcsec_original/2/pix2rad/180.*np.pi/3600.,FOV_arcsec_original/2/pix2rad/180.*np.pi/3600.,n)
y_pix = np.linspace(-FOV_arcsec_original/2/pix2rad/180.*np.pi/3600.,FOV_arcsec_original/2/pix2rad/180.*np.pi/3600.,n)
X_pix,Y_pix = np.meshgrid(x_pix,y_pix)
conc = 10.
M = 1e13*M_sun
r_s = 18*1e3*pc
lambda_c = 40*pc ### The important parameter that doesn't seem to manifest itself in the map when changed
rho_s = M/((4*np.pi*r_s**3)*(np.log(1+conc) - (conc/(1+conc))))
sigma_crit = (c**2*Ds)/(4*np.pi*G*Dd*Dds)
k_s = rho_s*r_s/sigma_crit
theta_s = r_s/Dd
Renorm = (4*G/c**2)*(Dds/(Dd*Ds))
#### Here I just interpolate and zoom into my field of view to get better resolutions
A = np.sqrt(X_pix**2 + Y_pix**2)*pix2rad/theta_s
A_1 = A[100:200,0:100]
n_x = n_y = 100
FOV_arcsec_x = FOV_arcsec_original*(100./300)
FOV_arcmin_x = FOV_arcsec_x/60.
pix2rad_x = ((FOV_arcmin_x/60.)/float(n_x))*np.pi/180.
rad2pix_x = 1./pix2rad_x
FOV_arcsec_y = FOV_arcsec_original*(100./300)
FOV_arcmin_y = FOV_arcsec_y/60.
pix2rad_y = ((FOV_arcmin_y/60.)/float(n_y))*np.pi/180.
rad2pix_y = 1./pix2rad_y
x1 = np.linspace(-FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,n_x)
y1 = np.linspace(-FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,n_y)
X1,Y1 = np.meshgrid(x1,y1)
n_x_2 = 500
n_y_2 = 500
x2 = np.linspace(-FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,n_x_2)
y2 = np.linspace(-FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,n_y_2)
X2,Y2 = np.meshgrid(x2,y2)
interp_spline = RectBivariateSpline(y1,x1,A_1)
A_2 = interp_spline(y2,x2)
A_3 = A_2[50:450,0:400]
n_x_3 = n_y_3 = 400
FOV_arcsec_x = FOV_arcsec_original*(100./300)*400./500.
FOV_arcmin_x = FOV_arcsec_x/60.
pix2rad_x = ((FOV_arcmin_x/60.)/float(n_x_3))*np.pi/180.
rad2pix_x = 1./pix2rad_x
FOV_arcsec_y = FOV_arcsec_original*(100./300)*400./500.
FOV_arcmin_y = FOV_arcsec_y/60.
pix2rad_y = ((FOV_arcmin_y/60.)/float(n_y_3))*np.pi/180.
rad2pix_y = 1./pix2rad_y
x3 = np.linspace(-FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,n_x_3)
y3 = np.linspace(-FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,n_y_3)
X3,Y3 = np.meshgrid(x3,y3)
n_x_4 = 1000
n_y_4 = 1000
x4 = np.linspace(-FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,FOV_arcsec_x/2/pix2rad_x/180.*np.pi/3600.,n_x_4)
y4 = np.linspace(-FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,FOV_arcsec_y/2/pix2rad_y/180.*np.pi/3600.,n_y_4)
X4,Y4 = np.meshgrid(x4,y4)
interp_spline = RectBivariateSpline(y3,x3,A_3)
A_4 = interp_spline(y4,x4)
############### Function to calculate variance
variance = np.zeros((len(A_4),len(A_4)))
def variance_fluctuations(x):
for i in xrange(len(x)):
for j in xrange(len(x)):
if x[j][i] < 1.:
variance[j][i] = (k_s**2)*(lambda_c/r_s)*((np.pi/x[j][i]) - (1./(x[j][i]**2 -1)**3.)*(((6.*x[j][i]**4. - 17.*x[j][i]**2. + 26)/3.)+ (((2.*x[j][i]**6. - 7.*x[j][i]**4. + 8.*x[j][i]**2. - 8)*np.arccosh(1./x[j][i]))/(np.sqrt(1-x[j][i]**2.)))))
elif x[j][i] > 1.:
variance[j][i] = (k_s**2)*(lambda_c/r_s)*((np.pi/x[j][i]) - (1./(x[j][i]**2 -1)**3.)*(((6.*x[j][i]**4. - 17.*x[j][i]**2. + 26)/3.)+ (((2.*x[j][i]**6. - 7.*x[j][i]**4. + 8.*x[j][i]**2. - 8)*np.arccos(1./x[j][i]))/(np.sqrt(x[j][i]**2.-1)))))
variance_fluctuations(A_4)
#### Creating the map
mean = 0
delta_kappa = np.random.normal(0,variance,A_4.shape)
xfinal = np.linspace(-FOV_arcsec_x*np.pi/180./3600.*Dd/pc/2,FOV_arcsec_x*np.pi/180./3600.*Dd/pc/2,1000)
yfinal = np.linspace(-FOV_arcsec_x*np.pi/180./3600.*Dd/pc/2,FOV_arcsec_x*np.pi/180./3600.*Dd/pc/2,1000)
Xfinal, Yfinal = np.meshgrid(xfinal,yfinal)
plt.contourf(Xfinal,Yfinal,delta_kappa,100)
plt.show()
The map looks like this, with the density of blobs increasing towards the right. However, the size of the blobs don't change and the map looks virtually the same whether I use lambda_c = 40*pc or lambda_c = 400*pc.
I'm wondering if the np.random.normal function isn't really doing what I expect it to do? I feel like the pixel scale of the map and the way samples are drawn make no link to the size of the blobs. Maybe there is a better way to create the map using the variance, would appreciate any insight.
I expect the map to look something like this , the blob sizes change based on the input parameters for my variance :
This is quite a well visited problem in (surprise surprise) astronomy and cosmology.
You could use lenstool: https://lenstools.readthedocs.io/en/latest/examples/gaussian_random_field.html
You could also try here:
https://andrewwalker.github.io/statefultransitions/post/gaussian-fields
Not to mention:
https://github.com/bsciolla/gaussian-random-fields
I am not reproducing code here because all credit goes to the above authors. However, they did just all come right out a google search :/
Easiest of all is probably a python module FyeldGenerator, apparently designed for this exact purpose:
https://github.com/cphyc/FyeldGenerator
So (adapted from github example):
pip install FyeldGenerator
from FyeldGenerator import generate_field
from matplotlib import use
use('Agg')
import matplotlib.pyplot as plt
import numpy as np
plt.figure()
# Helper that generates power-law power spectrum
def Pkgen(n):
def Pk(k):
return np.power(k, -n)
return Pk
# Draw samples from a normal distribution
def distrib(shape):
a = np.random.normal(loc=0, scale=1, size=shape)
b = np.random.normal(loc=0, scale=1, size=shape)
return a + 1j * b
shape = (512, 512)
field = generate_field(distrib, Pkgen(2), shape)
plt.imshow(field, cmap='jet')
plt.savefig('field.png',dpi=400)
plt.close())
This gives:
Looks pretty straightforward to me :)
PS: FoV implied a telescope observation of the gaussian random field :)
A completely different and much quicker way may be just to blur the delta_kappa array with gaussian filter. Try adjusting sigma parameter to alter the blobs size.
from scipy.ndimage.filters import gaussian_filter
dk_gf = gaussian_filter(delta_kappa, sigma=20)
Xfinal, Yfinal = np.meshgrid(xfinal,yfinal)
plt.contourf(Xfinal,Yfinal,dk_ma,100, cmap='jet')
plt.show();
this is image with sigma=20
this is image with sigma=2.5
ThunderFlash, try this code to draw the map:
# function to produce blobs:
from scipy.stats import multivariate_normal
def blob (positions, mean=(0,0), var=1):
cov = [[var,0],[0,var]]
return multivariate_normal(mean, cov).pdf(positions)
"""
now prepare for blobs generation.
note that I use less dense grid to pick blobs centers (regulated by `step`)
this makes blobs more pronounced and saves calculation time.
use this part instead of your code section below comment #### Creating the map
"""
delta_kappa = np.random.normal(0,variance,A_4.shape) # same
step = 10 #
dk2 = delta_kappa[::step,::step] # taking every 10th element
x2, y2 = xfinal[::step],yfinal[::step]
field = np.dstack((Xfinal,Yfinal))
print (field.shape, dk2.shape, x2.shape, y2.shape)
>> (1000, 1000, 2), (100, 100), (100,), (100,)
result = np.zeros(field.shape[:2])
for x in range (len(x2)):
for y in range (len(y2)):
res2 = blob(field, mean = (x2[x], y2[y]), var=10000)*dk2[x,y]
result += res2
# the cycle above took over 20 minutes on Ryzen 2700X. It could be accelerated by vectorization presumably.
plt.contourf(Xfinal,Yfinal,result,100)
plt.show()
you may want to play with var parameter in blob() to smoothen the image and with step to make it more compressed.
Here is the image that I got using your code (somehow axes are flipped and more dense areas on the top):
I am trying to animate a plot of two distinct points (blue and green points) moving about the complex unit circle using Python's Matplotlib library. The problem I am having is that the animation does not remove and update the previous data points but rather sequentially smears it on the unit sphere as in the accompanying image. Hence the animation is just a smudging of the various data points as shown in the image. What I am trying to achieve is two distinct points moving about the unit circle as a function of time.
The following is the part of my code where I call 'animation.FuncAnimation' using data in arrays which I call 'A' and 'B'.
##Python Code for Executing Animation##
import matplotlib.animation as animation
import matplotlib.pyplot as plt
import numpy as np
from pylab import *
#Example Data
A = array([0., 0.03435915, 0.06328989, 0.0880305, 0.14199928, 0.2044361, 0.26287941, 0.32484623])
B = array([ 1.75, 1.71564086, 1.69358362, 1.68499179, 1.68255084, 1.67808712, 1.66169597, 1.64407287])
# Total time.
T = 1.0
# Number of steps.
NS = 100
# Time step size
dt = T/NS
t = np.linspace(0.0, NS*dt, NS+1)
# So here are a few utility functions for multiplying scalars and vectors.
# a scalar times a vector returns a vector
def scale_vector(scale, vector):
result = [0]*len(vector)
for i in range(len(result)):
result[i] = scale * vector[i]
return result
# dot product of two vectors = sum(x[0]*y[0] + ... + x[n-1]*y[n-1])
def vector_dot(vector1, vector2):
result = 0
for i in range(len(vector1)):
result += vector1[i] * vector2[i]
return result
# return real part of a vector
def real_vector(vector):
return map(lambda x: x.real, vector)
# return imaginary part of a vector
def imag_vector(vector):
return map(lambda x: x.imag, vector)
## Creating complex unit circle
r = []
im = []
def main():
# Generate numbers around the complex unit circle.
N = 128
theta = scale_vector(2*pi/N, range(N))
exp_theta = map(lambda x: exp(1j * x), theta)
real_part = real_vector(exp_theta)
imag_part = imag_vector(exp_theta)
r.append(real_part)
im.append(imag_part)
# And wait until the user is done with it.
done = raw_input("done? ")
if __name__ == "__main__":
main()
#Form two arrays which have the real and imaginary components of the unit circle
r2 = r[0][:]
im2 = im[0][:]
##Code for Animation##
Aan = np.zeros([len(A),2], float)
for i in range(2):
for j in range(len(A)):
if i == 0:
Aan[j][i] = math.cos(A[j])
elif i == 1:
Aan[j][i] = math.sin(A[j])
Ban = np.zeros([len(B),2], float)
for i in range(2):
for j in range(len(B)):
if i == 0:
Ban[j][i] = math.cos(B[j])
elif i == 1:
Ban[j][i] = math.sin(B[j])
##Plots and animation
fig = figure()
plt.title('Phase Space')
plt.xlabel('Re')
plt.ylabel('Im')
#Plots complex unit circle
plot1 = plt.plot(r2,im2, color = 'g',alpha = 0.4)
#Animation functions
def animate(i):
plot(Aan[i, 0], Aan[i, 1], color='blue', marker= 'o')
plot(Ban[i, 0], Ban[i, 1], color='orange', marker= 'o')
ani = animation.FuncAnimation(fig, animate, interval=101)
show()
Can anyone advise on how this problem could be solved?
Plot creates a new object on the canvas which is not cleared automatically at the next plot.
If you would like to redraw the figure, you can call the cla method and plot the data again.
Or you can update the previously plotted data as it is described in the last example of animation API documentation.
I want to fill a bunch of polygons with line hatch. The lines must have a specific angle with respect to x-axis. I found that matplotlib already suppots some hatch classes and one can define a custom class (like How to fill a polygon with a custom hatch in matplotlib?). I tried to generate a custom hatch but when I append it to the list of hatches the init function doesn't know the angle. I tried with the following class:
class AngularHatch(HatchPatternBase):
def __init__(self, hatch, density, angle):
self.num_lines = int((hatch.count('{'))*density*3)
self.num_vertices = self.num_lines * 2
self.R = np.array([[np.cos(angle), -np.sin(angle)],
[np.sin(angle), np.cos(angle)]])
def set_vertices_and_codes(self, vertices, codes):
steps, stepsize = np.linspace(0.0, 1.0, self.num_lines, False,
retstep=True)
steps += stepsize / 2.
vertices[0::2, 0] = 0
vertices[0::2, 1] = steps
vertices[1::2, 0] = 1
vertices[1::2, 1] = steps
for i, v in enumerate(vertices):
vertices[i] = self.R.dot(v)
codes[0::2] = Path.MOVETO
codes[1::2] = Path.LINETO
Then I add this class to the list of available classes for hatching. However this will not generate the correct lines since the code is modified from the HorizontalHatch source code here and I think this generates lines in the unit square. Moreover I need to generate this patch for a specific angle for each polygon I want to render. ¿Any ideas on how to give the correct angle to this class per polygon?
The following does not solve this issue. It just solves part of the problem and shows at which point the approach fails. I am currently convinced that hatching with arbitrary angles is not possible with matplotlib, because the size of the unit cell is fixed.
To overcome the problem of setting the angle, one may define a custom format from which to take the angle information. E.g. "{angle}{factor}", such that "{45}{2}" would produce a hatching with an angle of 45° and a density factor of 2.
I then do not completely understand the attempt of calculating the vertices. To replicate the behaviour of the hatches which are built-in, one may rotate them directly.
The problem is that this way the line hatches work only for angles of 45°. This is because the lines at the edges of the unit cell do not align well. See the following:
import numpy as np
import matplotlib.hatch
import matplotlib.path
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Rectangle
class AngularHatch(matplotlib.hatch.HatchPatternBase):
def __init__(self, hatch, density):
self.num_lines=0
self.num_vertices=0
if hatch[0] == "{":
h = hatch.strip("{}").split("}{")
angle = np.deg2rad(float(h[0])-45)
d = float(h[1])
self.num_lines = int(density*d)
self.num_vertices = (self.num_lines + 1) * 2
self.R = np.array([[np.cos(angle), -np.sin(angle)],
[np.sin(angle), np.cos(angle)]])
def set_vertices_and_codes(self, vertices, codes):
steps = np.linspace(-0.5, 0.5, self.num_lines + 1, True)
vertices[0::2, 0] = 0.0 + steps
vertices[0::2, 1] = 0.0 - steps
vertices[1::2, 0] = 1.0 + steps
vertices[1::2, 1] = 1.0 - steps
codes[0::2] = matplotlib.path.Path.MOVETO
codes[1::2] = matplotlib.path.Path.LINETO
vertices[:,:] = np.dot((vertices-0.5),self.R)+0.5
matplotlib.hatch._hatch_types.append(AngularHatch)
fig = plt.figure()
ax = fig.add_subplot(111)
ellipse = ax.add_patch(Rectangle((0.1, 0.1), 0.4, 0.8, fill=False))
ellipse.set_hatch('{45}{1}')
ellipse.set_color('red')
ellipse = ax.add_patch(Rectangle((0.55, 0.1), 0.4, 0.8, fill=False))
ellipse.set_hatch('{22}{1}')
ellipse.set_color('blue')
plt.show()
I am trying to animate a bunch of 2D images with chaco, but unfortunately it does not seem to be as fast as my application needs it. At the moment I am building a chaco Plot and using img_plot, e.g.:
pd = ArrayPlotData()
pd.set_data("imagedata", myarray)
plot = Plot(pd)
plot.img_plot("imagedata", interpolation="nearest")
And to update the image, I use the following:
pd.set_data("imagedata", my_new_array)
This works, however is not fast enough. Is there any way to speed it up? Any lower-level function that allows a faster update of the image?
Here's an example of how I do animations in Chaco using a timer. Usually the trick (as J Corson said) is to load your data into an array and then just use an index to take successive slices of the array.
from chaco.api import ArrayPlotData, Plot
from enable.api import ComponentEditor
import numpy as np
from pyface.timer.api import Timer
from traits.api import Array, Bool, Event, HasTraits, Instance, Int
from traitsui.api import ButtonEditor, Item, View
class AnimationDemo(HasTraits):
plot = Instance(Plot)
x = Array
y = Array
run = Bool(False)
go = Event
idx = Int
def _x_default(self):
x = np.linspace(-np.pi, np.pi, 100)
return x
def _y_default(self):
phi = np.linspace(0, 2 * np.pi, 360)
y = np.sin(self.x[:, np.newaxis] + phi[np.newaxis, :]) - \
0.1 * np.sin(13 * self.x[:, np.newaxis] - 7 * phi[np.newaxis, :])
return y
def _plot_default(self):
plot_data = ArrayPlotData(y=self.y[:, 0], x=self.x)
plot = Plot(plot_data)
plot.plot(('x', 'y'))
return plot
def _go_fired(self):
if not self.run:
self.run = True
else:
self.run = False
def _run_changed(self):
if self.run:
self.timer.Start()
else:
self.timer.Stop()
def _run_default(self):
self.timer = Timer(5, self._timer_tick)
return False
def _timer_tick(self):
if not self.run:
raise StopIteration
else:
if self.idx >= 360:
self.idx = 0
self.plot.data.set_data('y', self.y[:, self.idx])
self.idx += 1
traits_view = View(
Item('plot', editor=ComponentEditor(), show_label=False),
Item('go', editor=ButtonEditor(label="Start/Stop"), show_label=False),
)
if __name__ == "__main__":
ad = AnimationDemo()
ad.edit_traits()
I get something like this:
This is just a thought, but would adding every image initially into your ArrayPlotData solve your problem? Then you aren't adding a new image at each step in your animation, and just calling img_plot() on the next series. For example, if your images are stored in a numpy array called images[nt, nx, ny]:
pd = ArrayPlotData()
for index in range(images.shape[0]): #Assuming you want to iterate over nt
pd.set_data('', images[index,:,:], generate_name = True)
plot = Plot(pd)
This automatically names each image 'series1', 'series2', etc.
Then you can call:
plot.img_plot('series1', interpolation = 'nearest') #or 'series2' etc.
for every image in your animation without having to call set_data().
You can get a sorted list of your image names ['series1, 'series2', ...] to iterate over using:
from natsort import natsorted #sort using natural sorting
names = natsorted(pd.list_data())
Would that help with the bottleneck?
I have a function f(x,t) = cos(t)*t + x and i want to display the change of the result over the width x and time t at discretised time steps t_i and discretised width steps x_j.
Now I am a while here on SX and feel really embarrassed to only can post such little code or in other words nothing (since nothing worked I have done...):
Nevertheless if someone has the time to help, I`d appreciate it.
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as pyplot
from astropy.io.ascii.latex import AASTex
def func(xi, ti):
res = np.cos(ti)*ti + xi
return res
timeSpacing = 100
timeStart = 0
timeEnd = 1
time = np.linspace(timeStart, timeEnd, timeSpacing)
widthSpacing = 300
widthStart = 0
widthEnd = 3
width = np.linspace(widthStart, widthEnd, widthSpacing)
resultList = [None]*timeSpacing
resultListInner = [None]*widthSpacing
for i, ithTime in enumerate(time):
for j, jthWidth in enumerate(width):
aas = np.zeros_like(width)
aas.fill(ithTime)
resultListInner[j] = ithTime, jthWidth, func(jthWidth, aas)
resultList[i] = resultListInner
So how do I correctly index the list and array and plot my data using matplotlib?
My plot should look like this:
where in my case the aperature should be the width x, the sky annulus is my time t and the RMS is my func(x,t).
A couple of points:
Numpy provides a very nice function for doing differences of array elements: diff
Matplotlib uses plot_wireframe for creating a plot that you would want (also using Numpy's meshgrid)
Now, combining these into what you may want would look something like this.
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
def func(xi, ti):
res = np.cos(ti)*np.sin(xi)
return res
timeSpacing = 20
timeStart = 0
timeEnd = 1
time = np.linspace(timeStart, timeEnd, timeSpacing)
widthSpacing = 50
widthStart = 0
widthEnd = 3
width = np.linspace(widthStart, widthEnd, widthSpacing)
X,T = np.meshgrid(width,time)
F = func(X,T)
DF = np.diff(np.diff(F,axis=0),axis=1)
fig = plt.figure()
ax = fig.add_subplot(111,projection='3d')
ax.plot_wireframe(X[:-1,:-1],T[:-1,:-1],DF)
plt.show()
Note that diff is applied twice: once in each dimension axis= . I have also changed the toy function you provided to something that actually looks decent in this case.
For your more general use, it seems that you would want to just collect all of your F data into a 2D array, then proceed from the DF = line.