ex-6: wrote something about ex-6 in the readme file and put in order ex.6/plots
ex-6/plots/emd-round.py renamed into ex-6/plots/emd.py and made interactive.
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39
README.md
39
README.md
@ -162,19 +162,42 @@ To plot the results do:
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`ex-6/bin/main` simulates a Fraunhöfer diffraction experiment. The program
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prints to `stdout` the bin counts of the intensity as a function of the
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diffraction angle. To plot a histogram simply pipe the output to the
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program `ex-6/plot.py`.
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diffraction angle. To plot a histogram do:
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$ ex-6/bin/main | ex-6/plot.py
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The program convolves the original signal with a Gaussian kernel (`-s` to
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change the σ), optionally adds a Poisson noise (`-m` to change the mean μ) and
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performs either a naive deconvolution by a FFT (`-m fft` mode) or applying the
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Richard-Lucy deconvolution algorithm (`-m rl` mode), which is expected to
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perform optimally in this case.
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change the kernel σ), optionally adds a Gaussian noise (`-n` to change the
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noise σ) and performs either a naive deconvolution by a FFT (`-m fft` mode)
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or applying the Richardson-Lucy deconvolution algorithm (`-m rl` mode).
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The `-c` and `-d` options control whether the convolved or deconvolved
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histogram counts should be printed to `stdout`. For more options
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The `-o`, `-c` and `-d` options control whether the original, convolved or
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deconvolved histogram counts should be printed to `stdout`. For more options
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run the program with `-h` to see the usage screen.
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`ex-6/bin/test` simulates a customizable number of experiments and prints
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to `stdout` the histograms of the distribution of the EMD of the convolved
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signal together with the deconvolved signal EMD histograms with both FFT and
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Richardson-Lucy procedures. It also prints to `stderr` the average, standard
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deviation and skewness of the histograms. To plot the results, do:
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$ ex-6/bin/test | ex-6/dist-plot.py
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The program accepts some parameters to control the histogram and number of
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events, run it with `-h` to see their usage.
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`ex-6/plots/emd.py` plots the content of the files `ex-6/plots/emd-noisy.txt`
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and `ex-6/plots/emd-noiseless.txt` depending on the argument passed to it from
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stdin. Do:
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$ ex-6/plots/emd.py 'noisy'
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to plot the content of the first file and do:
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$ ex-6/plots/emd.py 'noiseless'
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to plot the content of the second file.
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### Exercise 7
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@ -30,6 +30,4 @@ hist(a[2*n:], insert(b[2*n:], 0, a[2*n]), weights=f[2*n:],
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ticklabel_format(style='sci', axis='x', scilimits=(0, 0), useMathText=True)
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tight_layout()
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name = (sys.argv[1] if len(sys.argv) > 1 else "prova")
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savefig('notes/images/' + name + '.pdf' )
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show()
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@ -14,5 +14,4 @@ xlabel(r'$\theta$ (radians)')
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ylabel(r'$I(\theta)$ (a.u.)')
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tight_layout()
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name = sys.argv[2] if len(sys.argv) > 2 else "prova"
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savefig('notes/images/' + name + '.pdf' )
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show()
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75
ex-6/plots/emd-noiseless.txt
Normal file
75
ex-6/plots/emd-noiseless.txt
Normal file
@ -0,0 +1,75 @@
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#rounds mean stddev
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#σ = 1
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1 1.88e-04 1.4e-05
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2 3.17e-04 1.4e-05
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3 1.80e-04 1.4e-05
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4 2.02e-04 1.5e-05
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5 1.70e-04 1.4e-05
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6 1.64e-04 1.4e-05
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7 1.75e-04 1.4e-05
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8 1.67e-04 1.4e-05
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9 1.61e-04 1.4e-05
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10 1.57e-04 1.4e-05
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11 1.59e-04 1.4e-05
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12 1.56e-04 1.4e-05
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13 1.54e-04 1.4e-05
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14 1.53e-04 1.4e-05
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15 1.51e-04 1.4e-05
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16 1.50e-04 1.3e-05
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17 1.49e-04 1.3e-05
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18 1.48e-04 1.3e-05
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19 1.46e-04 1.3e-05
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20 1.47e-04 1.3e-05
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40 1.35e-04 1.3e-05
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60 1.28e-04 1.3e-05
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80 1.24e-04 1.3e-05
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100 1.21e-04 1.3e-05
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400 1.02e-04 1.2e-05
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800 9.37e-05 1.1e-05
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1600 8.61e-05 1.0e-05
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3800 7.98e-05 9.2e-06
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7600 7.97e-05 9.2e-06
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10000 8.06e-05 9.2e-06
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15000 8.16e-05 9.2e-06
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#σ = 0.5
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1 1.17e-04 8.0e-06
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2 2.47e-05 3.0e-06
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3 3.65e-05 3.8e-06
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4 5.85e-05 5.4e-06
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5 1.48e-05 3.3e-06
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6 1.82e-05 3.0e-06
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7 1.22e-05 3.8e-06
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8 1.31e-05 3.6e-06
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9 1.19e-05 3.9e-06
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10 1.17e-05 3.9e-06
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11 1.16e-05 4.0e-06
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12 1.16e-05 4.0e-06
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13 1.16e-05 4.0e-06
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14 1.16e-05 4.0e-06
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15 1.16e-05 4.0e-06
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16 1.16e-05 4.0e-06
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17 1.16e-05 4.0e-06
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18 1.16e-05 4.0e-06
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19 1.16e-05 4.0e-06
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20 1.16e-05 4.0e-06
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#σ = 0.1
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1 4.23e-16 3.1e-16
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2 4.23e-16 3.2e-16
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3 4.24e-16 3.1e-16
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4 4.24e-16 3.1e-16
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5 4.25e-16 3.2e-16
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6 4.25e-16 3.2e-16
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7 4.24e-16 3.1e-16
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8 4.24e-16 3.1e-16
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9 4.24e-16 3.1e-16
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10 4.25e-16 3.2e-16
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11 4.25e-16 3.2e-16
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12 4.24e-16 3.1e-16
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13 4.25e-16 3.2e-16
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14 4.24e-16 3.1e-16
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15 4.25e-16 3.2e-16
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16 4.24e-16 3.1e-16
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17 4.25e-16 3.2e-16
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18 4.24e-16 3.1e-16
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19 4.25e-16 3.2e-16
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20 4.24e-16 3.1e-16
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64
ex-6/plots/emd-noisy.txt
Normal file
64
ex-6/plots/emd-noisy.txt
Normal file
@ -0,0 +1,64 @@
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#rounds mean stddev
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#σ=0.005
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1 2.92e-04 4.7e-05
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2 2.18e-04 4.7e-05
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3 2.28e-04 4.5e-05
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4 2.12e-04 4.8e-05
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5 2.08e-04 4.8e-05
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6 2.02e-04 4.9e-05
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7 2.05e-04 4.9e-05
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8 2.00e-04 4.9e-05
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9 1.98e-04 5.0e-05
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10 1.95e-04 5.0e-05
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11 1.97e-04 5.0e-05
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12 1.94e-04 5.0e-05
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13 1.93e-04 5.0e-05
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14 1.92e-04 5.0e-05
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15 1.91e-04 5.1e-05
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16 1.90e-04 5.1e-05
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17 1.90e-04 5.1e-05
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18 1.89e-04 5.1e-05
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19 1.88e-04 5.1e-05
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20 1.88e-04 5.1e-05
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#σ = 0.01
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1 3.47e-04 1.0e-04
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2 3.96e-04 1.1e-04
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3 3.39e-04 1.1e-04
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4 3.42e-04 1.1e-04
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5 3.34e-04 1.1e-04
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6 3.35e-04 1.1e-04
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7 3.37e-04 1.1e-04
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8 3.33e-04 1.1e-04
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9 3.33e-04 1.1e-04
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10 3.32e-04 1.1e-04
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11 3.32e-04 1.1e-04
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12 3.31e-04 1.1e-04
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13 3.31e-04 1.1e-04
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14 3.31e-04 1.1e-04
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15 3.31e-04 1.1e-04
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16 3.31e-04 1.1e-04
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17 3.31e-04 1.1e-04
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18 3.31e-04 1.1e-04
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19 3.31e-04 1.1e-04
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20 3.31e-04 1.1e-04
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#σ=0.05
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1 1.49e-03 5.7e-04
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2 1.51e-03 5.6e-04
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3 1.50e-03 5.7e-04
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4 1.50e-03 5.6e-04
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5 1.52e-03 5.6e-04
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6 1.53e-03 5.6e-04
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7 1.52e-03 5.6e-04
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8 1.51e-03 5.6e-04
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9 1.54e-03 5.5e-04
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10 1.53e-03 5.5e-04
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11 1.53e-03 5.5e-04
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12 1.54e-03 5.5e-04
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13 1.54e-03 5.5e-04
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14 1.54e-03 5.5e-04
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15 1.55e-03 5.5e-04
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16 1.55e-03 5.5e-04
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17 1.55e-03 5.5e-04
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18 1.56e-03 5.5e-04
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19 1.56e-03 5.4e-04
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20 1.56e-03 5.4e-04
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@ -1,75 +0,0 @@
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#rounds mean stddev skew
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#σ = 1
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1 1.88e-04 1.4e-05 0.26
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2 3.17e-04 1.4e-05 0.19
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3 1.80e-04 1.4e-05 0.27
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4 2.02e-04 1.5e-05 0.21
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5 1.70e-04 1.4e-05 0.27
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6 1.64e-04 1.4e-05 0.27
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7 1.75e-04 1.4e-05 0.27
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8 1.67e-04 1.4e-05 0.27
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9 1.61e-04 1.4e-05 0.26
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10 1.57e-04 1.4e-05 0.25
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11 1.59e-04 1.4e-05 0.26
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12 1.56e-04 1.4e-05 0.25
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13 1.54e-04 1.4e-05 0.25
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14 1.53e-04 1.4e-05 0.25
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15 1.51e-04 1.4e-05 0.25
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16 1.50e-04 1.3e-05 0.25
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17 1.49e-04 1.3e-05 0.25
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18 1.48e-04 1.3e-05 0.25
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19 1.46e-04 1.3e-05 0.25
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20 1.47e-04 1.3e-05 0.25
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40 1.35e-04 1.3e-05 0.29
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60 1.28e-04 1.3e-05 0.31
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80 1.24e-04 1.3e-05 0.33
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100 1.21e-04 1.3e-05 0.35
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400 1.02e-04 1.2e-05 0.40
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800 9.37e-05 1.1e-05 0.36
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1600 8.61e-05 1.0e-05 0.27
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3800 7.98e-05 9.2e-06 0.26
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7600 7.97e-05 9.2e-06 0.28
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10000 8.06e-05 9.2e-06 0.26
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15000 8.16e-05 9.2e-06 0.25
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#σ = 0.5
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1 1.17e-04 8.0e-06 0.25
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2 2.47e-05 3.0e-06 0.32
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3 3.65e-05 3.8e-06 0.35
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4 5.85e-05 5.4e-06 0.34
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5 1.48e-05 3.3e-06 0.51
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6 1.82e-05 3.0e-06 0.44
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7 1.22e-05 3.8e-06 0.42
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8 1.31e-05 3.6e-06 0.47
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9 1.19e-05 3.9e-06 0.38
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10 1.17e-05 3.9e-06 0.36
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11 1.16e-05 4.0e-06 0.35
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12 1.16e-05 4.0e-06 0.34
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13 1.16e-05 4.0e-06 0.34
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14 1.16e-05 4.0e-06 0.34
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15 1.16e-05 4.0e-06 0.34
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16 1.16e-05 4.0e-06 0.34
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17 1.16e-05 4.0e-06 0.34
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18 1.16e-05 4.0e-06 0.34
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19 1.16e-05 4.0e-06 0.34
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20 1.16e-05 4.0e-06 0.34
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#σ = 0.1
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1 4.23e-16 3.1e-16 0.81
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2 4.23e-16 3.2e-16 0.85
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3 4.24e-16 3.1e-16 0.87
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4 4.24e-16 3.1e-16 0.88
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5 4.25e-16 3.2e-16 0.82
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6 4.25e-16 3.2e-16 0.82
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7 4.24e-16 3.1e-16 0.87
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8 4.24e-16 3.1e-16 0.87
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9 4.24e-16 3.1e-16 0.87
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10 4.25e-16 3.2e-16 0.82
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11 4.25e-16 3.2e-16 0.82
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12 4.24e-16 3.1e-16 0.87
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13 4.25e-16 3.2e-16 0.82
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14 4.24e-16 3.1e-16 0.87
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15 4.25e-16 3.2e-16 0.82
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16 4.24e-16 3.1e-16 0.87
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17 4.25e-16 3.2e-16 0.82
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18 4.24e-16 3.1e-16 0.87
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19 4.25e-16 3.2e-16 0.82
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20 4.24e-16 3.1e-16 0.87
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@ -1,92 +0,0 @@
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#rounds mean stddev skew
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#σ = 0
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1 2.43e-4 1.3e-5 0.22
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2 1.67e-4 1.3e-5 0.27
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3 1.52e-4 1.3e-5 0.29
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4 1.43e-4 1.3e-5 0.29
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5 1.36e-4 1.2e-5 0.28
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6 1.31e-4 1.2e-5 0.29
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7 1.26e-4 1.2e-5 0.29
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8 1.22e-4 1.2e-5 0.30
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9 1.19e-4 1.2e-5 0.31
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10 1.16e-4 1.2e-5 0.33
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11 1.13e-4 1.2e-5 0.34
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12 1.11e-4 1.2e-5 0.34
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13 1.09e-4 1.2e-5 0.36
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14 1.07e-4 1.1e-5 0.36
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15 1.05e-4 1.1e-5 0.36
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16 1.03e-4 1.1e-5 0.37
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17 1.01e-4 1.1e-5 0.37
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18 9.97e-5 1.1e-5 0.37
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19 9.82e-5 1.1e-5 0.37
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20 9.68e-5 1.1e-5 0.37
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40 7.74e-5 1.0e-5 0.35
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60 6.57e-5 9.4e-6 0.32
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80 5.78e-5 9.1e-6 0.30
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100 5.20e-5 9.0e-6 0.30
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400 3.61e-5 1.0e-5 0.33
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800 3.60e-5 1.0e-5 0.33
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1600 3.60e-5 1.0e-5 0.33
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#σ=0.005
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1 2.92e-04 4.7e-05 1.43
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2 2.18e-04 4.7e-05 1.72
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3 2.28e-04 4.5e-05 1.73
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4 2.12e-04 4.8e-05 1.72
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5 2.08e-04 4.8e-05 1.71
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6 2.02e-04 4.9e-05 1.69
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7 2.05e-04 4.9e-05 1.70
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8 2.00e-04 4.9e-05 1.69
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9 1.98e-04 5.0e-05 1.68
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10 1.95e-04 5.0e-05 1.67
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11 1.97e-04 5.0e-05 1.68
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12 1.94e-04 5.0e-05 1.67
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13 1.93e-04 5.0e-05 1.67
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14 1.92e-04 5.0e-05 1.67
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15 1.91e-04 5.1e-05 1.66
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16 1.90e-04 5.1e-05 1.66
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17 1.90e-04 5.1e-05 1.66
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18 1.89e-04 5.1e-05 1.66
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19 1.88e-04 5.1e-05 1.66
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20 1.88e-04 5.1e-05 1.66
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#σ = 0.01
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1 3.47e-04 1.0e-04 1.58
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2 3.96e-04 1.1e-04 1.53
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3 3.39e-04 1.1e-04 1.56
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4 3.42e-04 1.1e-04 1.57
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5 3.34e-04 1.1e-04 1.55
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6 3.35e-04 1.1e-04 1.55
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7 3.37e-04 1.1e-04 1.55
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8 3.33e-04 1.1e-04 1.55
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9 3.33e-04 1.1e-04 1.55
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10 3.32e-04 1.1e-04 1.55
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11 3.32e-04 1.1e-04 1.54
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12 3.31e-04 1.1e-04 1.54
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13 3.31e-04 1.1e-04 1.54
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14 3.31e-04 1.1e-04 1.54
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15 3.31e-04 1.1e-04 1.55
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16 3.31e-04 1.1e-04 1.55
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17 3.31e-04 1.1e-04 1.55
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18 3.31e-04 1.1e-04 1.55
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19 3.31e-04 1.1e-04 1.55
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20 3.31e-04 1.1e-04 1.55
|
||||
#σ=0.05
|
||||
1 1.49e-03 5.7e-04 1.38
|
||||
2 1.51e-03 5.6e-04 1.41
|
||||
3 1.50e-03 5.7e-04 1.39
|
||||
4 1.50e-03 5.6e-04 1.40
|
||||
5 1.52e-03 5.6e-04 1.42
|
||||
6 1.53e-03 5.6e-04 1.43
|
||||
7 1.52e-03 5.6e-04 1.43
|
||||
8 1.51e-03 5.6e-04 1.42
|
||||
9 1.54e-03 5.5e-04 1.45
|
||||
10 1.53e-03 5.5e-04 1.44
|
||||
11 1.53e-03 5.5e-04 1.44
|
||||
12 1.54e-03 5.5e-04 1.45
|
||||
13 1.54e-03 5.5e-04 1.45
|
||||
14 1.54e-03 5.5e-04 1.46
|
||||
15 1.55e-03 5.5e-04 1.46
|
||||
16 1.55e-03 5.5e-04 1.46
|
||||
17 1.55e-03 5.5e-04 1.47
|
||||
18 1.56e-03 5.5e-04 1.47
|
||||
19 1.56e-03 5.4e-04 1.47
|
||||
20 1.56e-03 5.4e-04 1.48
|
||||
30
ex-6/plots/emd-round.py → ex-6/plots/emd.py
Normal file → Executable file
30
ex-6/plots/emd-round.py → ex-6/plots/emd.py
Normal file → Executable file
@ -1,5 +1,8 @@
|
||||
#!/usr/bin/env python
|
||||
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
import sys
|
||||
|
||||
|
||||
def plot(table, title='', log=False):
|
||||
@ -24,23 +27,18 @@ def plot(table, title='', log=False):
|
||||
twin.set_ylabel('standard deviation', color='gray')
|
||||
twin.ticklabel_format(style='sci', axis='y',
|
||||
scilimits=(0, 0), useMathText=True)
|
||||
|
||||
# plt.subplot(212)
|
||||
# if log:
|
||||
# plt.xscale('log')
|
||||
# plt.title('skewness', loc='right')
|
||||
# plt.xlabel('RL rounds')
|
||||
# plt.plot(table[0], table[3], color='xkcd:gray')
|
||||
|
||||
plt.tight_layout()
|
||||
|
||||
|
||||
table = np.loadtxt('ex-6/plots/emd-round-noise.txt')
|
||||
file = sys.argv[1] if len(sys.argv) > 1 else 'noiseless'
|
||||
table = np.loadtxt('ex-6/plots/emd-' + file + '.txt')
|
||||
if file == 'noiseless':
|
||||
plot(table[:31].T, title=r'noise at $\sigma_N = 0.005$')
|
||||
plot(table[31:51].T, title=r'noise at $\sigma_N = 0.005$')
|
||||
plot(table[51:].T, title=r'noise at $\sigma_N = 0.01$')
|
||||
else:
|
||||
plot(table[:20].T, title=r'noise at $\sigma_N = 0.005$')
|
||||
plot(table[20:40].T, title=r'noise at $\sigma_N = 0.005$')
|
||||
plot(table[40:].T, title=r'noise at $\sigma_N = 0.01$')
|
||||
plt.show()
|
||||
|
||||
# plot(table[:27].T, title='noiseless', log=True)
|
||||
plot(table[27:47].T, title=r'noise at $\sigma_N = 0.005$')
|
||||
plt.savefig('notes/images/6-rounds-noise-0.005.pdf')
|
||||
plot(table[47:67].T, title=r'noise at $\sigma_N = 0.01$')
|
||||
plt.savefig('notes/images/6-rounds-noise-0.01.pdf')
|
||||
plot(table[67:].T, title=r'noise at $\sigma_N = 0.05$')
|
||||
plt.savefig('notes/images/6-rounds-noise-0.05.pdf')
|
||||
@ -647,31 +647,6 @@ histogram as follow.
|
||||
{#fig:noisy}
|
||||
|
||||
<div id="fig:rounds-noise">
|
||||
{#fig:rnoise-0.005}
|
||||
|
||||
{#fig:rnoise-0.01}
|
||||
|
||||
{#fig:rnoise-0.05}
|
||||
|
||||
EMD as a function of RL rounds for different noise $\sigma_N$ values with the
|
||||
kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the
|
||||
standard deviation in grey. Noisy results.
|
||||
</div>
|
||||
|
||||
<div id="fig:emd-noisy">
|
||||
{#fig:enoise-0.005}
|
||||
|
||||
{#fig:enoise-0.01}
|
||||
|
||||
{#fig:enoise-0.05}
|
||||
|
||||
EMD distributions for different noise $\sigma_N$ values. The plots on the left
|
||||
show the results for the FFT deconvolution, the central column the results for
|
||||
the RL deconvolution and the third one shows the EMD for the convolved signal.
|
||||
Noisy results.
|
||||
</div>
|
||||
|
||||
For each bin, once the convolved histogram was computed, a value $v_N$ was
|
||||
randomly sampled from a Gaussian distribution with standard deviation
|
||||
$\sigma_N$, and the value $v_n \cdot b$ was added to the bin itself, where $b$
|
||||
@ -724,4 +699,28 @@ noise. When the kernel is not known a-priori, either of them turns out to be as
|
||||
good as the FFT in the aforementioned situation: only a poor approximation of
|
||||
the original signal can be derived.
|
||||
|
||||
<div id="fig:rounds-noise">
|
||||
{#fig:rnoise-0.005}
|
||||
|
||||
{#fig:rnoise-0.01}
|
||||
|
||||
{#fig:rnoise-0.05}
|
||||
|
||||
EMD as a function of RL rounds for different noise $\sigma_N$ values with the
|
||||
kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the
|
||||
standard deviation in grey. Noisy results.
|
||||
</div>
|
||||
|
||||
<div id="fig:emd-noisy">
|
||||
{#fig:enoise-0.005}
|
||||
|
||||
{#fig:enoise-0.01}
|
||||
|
||||
{#fig:enoise-0.05}
|
||||
|
||||
EMD distributions for different noise $\sigma_N$ values. The plots on the left
|
||||
show the results for the FFT deconvolution, the central column the results for
|
||||
the RL deconvolution and the third one shows the EMD for the convolved signal.
|
||||
Noisy results.
|
||||
</div>
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user