Audio waveform matching - python

I am matching two waveform of 400 ms. I am using correlate to check the shift.
cc = correlate(b1,b2,mode="same")
n=len(cc)
cc=2*cc/n
dur=n*dt1/2;
d=linspace( -dur, dur, n )
idx = argmax(cc)
I am getting the shift between 2 waveform. But how to get the actual match position of two waveform?

you probably want mode = "full" and need to do some more math to pick the correlation peak and adjust for the sequence length padding
hopefully this example will help show the issues:
import math
import numpy as np
import matplotlib.pyplot as plt
a = [math.sin(i* math.pi/10) for i in range(300)]
b = [math.cos(i*math.pi/10) for i in range(300)]
plt.plot(a, 'red')
plt.plot(b, 'green')
axb= np.correlate(a,b, mode="full")/100.0
x = range(len(axb))
plt.plot(x, axb)

Related

Python: Plot a histogram given the counts (frequencies) and the bins

To illustrate my problem I prepared an example:
First, I have two arrays 'a'and 'b'and I'm interested in their distribution:
import numpy as np
import matplotlib.pyplot as plt
a = np.array([1,2,2,2,2,4,8,1,9,5,3,1,2,9])
b = np.array([5,9,9,2,3,9,3,6,8,4,2,7,8,8])
n1,bin1,pat1 = plt.hist(a,np.arange(1,10,2),histtype='step')
n2,bin2,pat2 = plt.hist(b,np.arange(1,10,2), histtype='step')
plt.show()
This code gives me a histogram with two 'curves'. Now I want to subtract one 'curve' from the other, and by this I mean that I do this for each bin separately:
n3 = n2-n1
I don't need negative counts so:
for i in range(0,len(n2)):
if n3[i]<0:
n3[i]=0
else:
continue
The new histogram curve should be plotted in the same range as the previous ones and it should have the same number of bins. So I have the number of bins and their position (which will be the same as the ones for the other curves, please refer to the block above) and the frequency or counts (n3) that every bins should have. Do you have any ideas of how I can do this with the data that I have?
You can use a step function to plot n3 = n2 - n1. The only issue is that you need to provide one more value, otherwise the last value is not shown nicely. Also you need to use the where="post" option of the step function.
import numpy as np
import matplotlib.pyplot as plt
a = np.array([1,2,2,2,2,4,8,1,9,5,3,1,2,9])
b = np.array([5,9,9,2,3,9,3,6,8,4,2,7,8,8])
n1,bin1,pat1 = plt.hist(a,np.arange(1,10,2),histtype='step')
n2,bin2,pat2 = plt.hist(b,np.arange(1,10,2), histtype='step')
n3=n2-n1
n3[n3<0] = 0
plt.step(np.arange(1,10,2),np.append(n3,[n3[-1]]), where='post', lw=3 )
plt.show()

Is there any solution for better fit beta prime distribution to data than using Scipy?

I was trying to fit beta prime distribution to my data using python. As there's scipy.stats.betaprime.fit, I tried this:
import numpy as np
import math
import scipy.stats as sts
import matplotlib.pyplot as plt
N = 5000
nb_bin = 100
a = 12; b = 106; scale = 36; loc = -a/(b-1)*scale
y = sts.betaprime.rvs(a,b,loc,scale,N)
a_hat,b_hat,loc_hat,scale_hat = sts.betaprime.fit(y)
print('Estimated parameters: \n a=%.2f, b=%.2f, loc=%.2f, scale=%.2f'%(a_hat,b_hat,loc_hat,scale_hat))
plt.figure()
count, bins, ignored = plt.hist(y, nb_bin, normed=True)
pdf_ini = sts.betaprime.pdf(bins,a,b,loc,scale)
pdf_est = sts.betaprime.pdf(bins,a_hat,b_hat,loc_hat,scale_hat)
plt.plot(bins,pdf_ini,'g',linewidth=2.0,label='ini');plt.grid()
plt.plot(bins,pdf_est,'y',linewidth=2.0,label='est');plt.legend();plt.show()
It shows me the result that:
Estimated parameters:
a=9935.34, b=10846.64, loc=-90.63, scale=98.93
which is quite different from the original one and the figure from the PDF:
If I give the real value of loc and scale as the input of fit function, the estimation result would be better. Has anyone worked on this part already or got a better solution?

Constructing Zipf Distribution with matplotlib, FITTED-LINE

I have a list of paragraphs, where I want to run a zipf distribution on their combination.
My code is below:
from itertools import *
from pylab import *
from collections import Counter
import matplotlib.pyplot as plt
paragraphs = " ".join(targeted_paragraphs)
for paragraph in paragraphs:
frequency = Counter(paragraph.split())
counts = array(frequency.values())
tokens = frequency.keys()
ranks = arange(1, len(counts)+1)
indices = argsort(-counts)
frequencies = counts[indices]
loglog(ranks, frequencies, marker=".")
title("Zipf plot for Combined Article Paragraphs")
xlabel("Frequency Rank of Token")
ylabel("Absolute Frequency of Token")
grid(True)
for n in list(logspace(-0.5, log10(len(counts)-1), 20).astype(int)):
dummy = text(ranks[n], frequencies[n], " " + tokens[indices[n]],
verticalalignment="bottom",
horizontalalignment="left")
PURPOSE I attempt to draw "a fitted line" in this graph, and assign its value to a variable. However I do not know how to add that. Any help would be much appreciated for both of these issues.
I know it's been a while since this question was asked. However, I came across a possible solution for this problem at scipy site.
I thought I would post here in case anyone else required.
I didn't have paragraph info, so here is a whipped up dict called frequency that has paragraph occurrence as its values.
We then get its values and convert to numpy array. Define zipf distribution parameter which has to be >1.
Finally display the histogram of the samples,along with the probability density function
Working Code:
import random
import matplotlib.pyplot as plt
from scipy import special
import numpy as np
#Generate sample dict with random value to simulate paragraph data
frequency = {}
for i,j in enumerate(range(50)):
frequency[i]=random.randint(1,50)
counts = frequency.values()
tokens = frequency.keys()
#Convert counts of values to numpy array
s = np.array(counts)
#define zipf distribution parameter. Has to be >1
a = 2.
# Display the histogram of the samples,
#along with the probability density function
count, bins, ignored = plt.hist(s, 50, normed=True)
plt.title("Zipf plot for Combined Article Paragraphs")
x = np.arange(1., 50.)
plt.xlabel("Frequency Rank of Token")
y = x**(-a) / special.zetac(a)
plt.ylabel("Absolute Frequency of Token")
plt.plot(x, y/max(y), linewidth=2, color='r')
plt.show()
Plot

Python/Matplotlib: Randomly select "sample" scatter points for different marker

Pretty much exactly what the question states, but a little context:
I'm creating a program to plot a large number of points (~10,000, but it will be more later on). This is being done using matplotlib's plt.scatter. This command is part of a loop that saves the figure, so I can later animate it.
What I want to be able to do is randomly select a small portion of these particles (say, maybe 100?) and give them a different marker than the rest, even though they're part of the same data set. This is so I can use them as placeholders to see the motion of individual particles, as well as the bulk material.
Is there a way to use a different marker for a small subset of the same data?
For reference, the particles are uniformly distributed just using the numpy random sampler, but my code for that is:
for i in range(N): # N number of particles
particle_position[i] = np.random.uniform(0, xmax) # Initialize in spatial domain
particle_velocity[i] = np.random.normal(0, 5) # Initialize in velocity space
for i in range(maxtime):
plt.scatter(particle_position, particle_velocity, s=1, c=norm_xvel, cmap=br_disc, lw=0)
The position and velocity change on each iteration of the main loop (there's quite a bit of code), but these are the main initialization and plotting routines.
I had an idea that perhaps I could randomly select a bunch of i values from range(N), and use an ax.scatter() command to plot them on the same axes?
Here is a possible solution to have a subset of your points identified with a different marker:
import matplotlib.pyplot as plt
import numpy as np
SIZE = 100
SAMPLE_SIZE = 10
def select_subset(seq, size):
"""selects a subset of the data using ...
"""
return seq[:size]
points_x = np.random.uniform(-1, 1, size=SIZE)
points_y = np.random.uniform(-1, 1, size=SIZE)
plt.scatter(points_x, points_y, marker=".", color="blue")
plt.scatter(select_subset(points_x, SAMPLE_SIZE),
select_subset(points_y, SAMPLE_SIZE),
marker="o", color="red")
plt.show()
It uses plt.scatter twice; once on the full data set, the other on the sample points.
You will have to decide how you want to select the sample of points - it is isolated in the select_subset function..
You could also extract the sample points from the data set to prevent marking them twice, but numpy is rather inefficient at deleting or resizing.
Maybe a better method is to use a mask? A mask has the advantage of leaving your original data intact and in order.
Here is a way to proceed with masks:
import matplotlib.pyplot as plt
import numpy as np
import random
SIZE = 100
SAMPLE_SIZE = 10
def make_mask(data_size, sample_size):
mask = np.array([True] * sample_size + [False ] * (data_size - sample_size))
np.random.shuffle(mask)
return mask
points_x = np.random.uniform(-1, 1, size=SIZE)
points_y = np.random.uniform(-1, 1, size=SIZE)
mask = make_mask(SIZE, SAMPLE_SIZE)
not_mask = np.invert(mask)
plt.scatter(points_x[not_mask], points_y[not_mask], marker=".", color="blue")
plt.scatter(points_x[mask], points_y[mask], marker="o", color="red")
plt.show()
As you see, scatter is called once on a subset of the data points (the ones not selected in the sample), and a second time on the sampled subset, and draws each subset with its own marker. It is efficient & leaves the original data intact.
The code below does what you want. I have selected a random set v_sub_index of N_sub indices in the correct range (0 to N) and draw those (with _sub suffix) from the larger samples particle_position and particle_velocity. Please note that you don't have to loop to generate random samples. Numpy has great functionality for that without having to use for loops.
import numpy as np
import matplotlib.pyplot as pl
N = 100
xmax = 1.
v_sigma = 2.5 / 2. # 95% of the samples contained within 0, 5
v_mean = 2.5 # mean at 2.5
N_sub = 10
v_sub_index = np.random.randint(0, N, N_sub)
particle_position = np.random.rand (N) * xmax
particle_velocity = np.random.randn(N)
particle_position_sub = np.array(particle_position[v_sub_index])
particle_velocity_sub = np.array(particle_velocity[v_sub_index])
particle_position_nosub = np.delete(particle_position, v_sub_index)
particle_velocity_nosub = np.delete(particle_velocity, v_sub_index)
pl.scatter(particle_position_nosub, particle_velocity_nosub, color='b', marker='o')
pl.scatter(particle_position_sub , particle_velocity_sub , color='r', marker='^')
pl.show()

Plancks Formula for Blackbody spectrum

I am trying to write a simple python code for a plot of intensity vs wavelength for a given temperature, T=200K.
So far I have this...
import scipy as sp
import math
import matplotlib.pyplot as plt
import numpy as np
pi = np.pi
h = 6.626e-34
c = 3.0e+8
k = 1.38e-23
def planck(wav, T):
a = 2.0*h*pi*c**2
b = h*c/(wav*k*T)
intensity = a/ ( (wav**5)*(math.e**b - 1.0) )
return intensity
I don't know how to define wavelength(wav) and thus produce the plot of Plancks Formula. Any help would be appreciated.
Here's a basic plot. To plot using plt.plot(x, y, fmt) you need two arrays x and y of the same size, where x is the x coordinate of each point to plot and y is the y coordinate, and fmt is a string describing how to plot the numbers.
So all you need to do is create an evenly spaced array of wavelengths (an np.array which I named wavelengths). This can be done with arange(start, end, spacing) which will create an array from start to end (not inclusive) spaced at spacing apart.
Then compute the intensity using your function at each of those points in the array (which will be stored in another np.array), and then call plt.plot to plot them. Note numpy let's you do mathematical operations on arrays quickly in a vectorized form which will be computationally efficient.
import matplotlib.pyplot as plt
import numpy as np
h = 6.626e-34
c = 3.0e+8
k = 1.38e-23
def planck(wav, T):
a = 2.0*h*c**2
b = h*c/(wav*k*T)
intensity = a/ ( (wav**5) * (np.exp(b) - 1.0) )
return intensity
# generate x-axis in increments from 1nm to 3 micrometer in 1 nm increments
# starting at 1 nm to avoid wav = 0, which would result in division by zero.
wavelengths = np.arange(1e-9, 3e-6, 1e-9)
# intensity at 4000K, 5000K, 6000K, 7000K
intensity4000 = planck(wavelengths, 4000.)
intensity5000 = planck(wavelengths, 5000.)
intensity6000 = planck(wavelengths, 6000.)
intensity7000 = planck(wavelengths, 7000.)
plt.plot(wavelengths*1e9, intensity4000, 'r-')
# plot intensity4000 versus wavelength in nm as a red line
plt.plot(wavelengths*1e9, intensity5000, 'g-') # 5000K green line
plt.plot(wavelengths*1e9, intensity6000, 'b-') # 6000K blue line
plt.plot(wavelengths*1e9, intensity7000, 'k-') # 7000K black line
# show the plot
plt.show()
And you see:
You probably will want to clean up the axes labels, add a legend, plot the intensity at multiple temperatures on the same plot, among other things. Consult the relevant matplotlib documentation.
You may also want to use the RADIS library, which allows you to plot the Planck function against wavelengths, or against frequency / wavenumber, if needed !
from radis import sPlanck
sPlanck(wavelength_min=135, wavelength_max=3000, T=4000).plot()
sPlanck(wavelength_min=135, wavelength_max=3000, T=5000).plot(nfig='same')
sPlanck(wavelength_min=135, wavelength_max=3000, T=6000).plot(nfig='same')
sPlanck(wavelength_min=135, wavelength_max=3000, T=7000).plot(nfig='same')
Just want to point out that there seems to be an equivalent of what OP wants to do in astropy:
https://docs.astropy.org/en/stable/api/astropy.modeling.physical_models.BlackBody.html
Unfortunately, it is not very clear to me yet how to get wavelength vs frequency based expression.

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