From 0585b800092ffc46e01f7b1aefaa8c2d3d4c6ad0 Mon Sep 17 00:00:00 2001 From: rnhmjoj Date: Tue, 2 Jun 2020 00:22:27 +0200 Subject: [PATCH] notes: use native div syntax --- notes/sections/3.md | 4 ++-- notes/sections/6.md | 16 ++++++++-------- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/notes/sections/3.md b/notes/sections/3.md index ba5a456..dae1426 100644 --- a/notes/sections/3.md +++ b/notes/sections/3.md @@ -43,7 +43,7 @@ The proper distribution of $\theta$ is obtained by applying a transform to a variable $x$ with uniform distribution in $[0, 1)$, easily generated by the GSL function `gsl_rng_uniform()`. -
+::: { id=fig:compare } ![Uniformly distributed points with $\theta$ evenly distributed between 0 and $\pi$.](images/3-histo-i-u.pdf){width=50%} ![Points uniformly distributed on a spherical @@ -56,7 +56,7 @@ easily generated by the GSL function `gsl_rng_uniform()`. Examples of samples. On the left, points with $\theta$ evenly distributed between 0 and $\pi$; on the right, points with $\theta$ properly distributed. -
+::: The transformation can be found by imposing the angular PDF to be a constant: \begin{align*} diff --git a/notes/sections/6.md b/notes/sections/6.md index 54d0eed..de01c77 100644 --- a/notes/sections/6.md +++ b/notes/sections/6.md @@ -594,7 +594,7 @@ amplitude changes: it always gives the same outcome, which would be exactly the original signal, if the floating point precision would not affect the result. In fact, the FFT is the analytical result of the deconvolution. -
+::: {id=fig:rounds-noiseless} ![](images/6-nonoise-rounds-0.1.pdf){#fig:rless-0.1} ![](images/6-nonoise-rounds-0.5.pdf){#fig:rless-0.5} @@ -604,9 +604,9 @@ fact, the FFT is the analytical result of the deconvolution. EMD as a function of RL rounds for different kernel $\sigma$ values. The average is shown in red and the standard deviation in grey. Noiseless results shown. -
+::: -
+::: {id="fig:emd-noiseless"} ![$\sigma = 0.1 \, \Delta \theta$](images/6-nonoise-emd-0.1.pdf){#fig:eless-0.1} ![$\sigma = 0.5 \, \Delta \theta$](images/6-nonoise-emd-0.5.pdf){#fig:eless-0.5} @@ -617,7 +617,7 @@ EMD distributions for different kernel $\sigma$ 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. Noiseless results. -
+::: For this reason, the EMD obtained with the FFT can be used as a reference point against which to compare the EMDs measured with RL. @@ -706,7 +706,7 @@ However, in real world applications the measures are affected by (possibly unknown) noise and the signal can only be partially reconstructed by either method. -
+::: {id=fig:rounds-noise} ![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005} ![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01} @@ -716,9 +716,9 @@ method. 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. -
+::: -
+::: {id=fig:emd-noisy} ![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005} ![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01} @@ -729,4 +729,4 @@ 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. -
+:::