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2025-11-16 14:56:03 +01:00
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---
title: "Untitled"
format: html
editor: visual
---
```{r}
library(tidyverse)
library(plotly)
library(matrixStats)
```
```{r}
log_sum_exp <- function(a,b) {
m <- map2_dbl(a,b,max)
m + log(exp(a-m)+exp(b-m))
}
```
$$
\log(1 - e^b) = \log\left(-e^{(1-b)}\right)
$$
```{r}
log1m_exp <- function(b) {
if (any(b >= 0)) {
stop(glue::glue("b must be negative (b={b})"))
}
return(log(-expm1(b))) # expm1(b) = exp(b) - 1, pour éviter les erreurs d'arrondi
}
```
$$
\log(e^a - e^b) = a + \log(1 - e^{b-a})
$$
```{r}
log_diff_exp <- function(a, b) {
# Vérifier si a > b pour éviter des résultats indéfinis
if (any(a < b)) {
stop(glue::glue("Erreur : a ({a}) doit etre strictement sup<75>rieur <20> b ({b}) pour que e^a - e^b soit positif."))
}
# Calculer log(e^a - e^b) de manière stable
ifelse(a == b, -Inf,a + log1m_exp(b-a))
}
```
$$
P_{error} = 10^{-\frac{Q}{10}}
$$
$$
\begin{aligned}
q_F &= -\frac{Q_F}{10} \cdot \log(10) \\
q_R &= -\frac{Q_R}{10} \cdot \log(10) \\
P(macth | Obs(match)) &= (1-e^{q_F}) (1-e^{q_R}) + (1-e^{q_F})\frac{e^{q_R}}{4}+ (1-e^{q_R})\frac{e^{q_F}}{4} + \frac{e^{q_F+q_R}}{4} \\
&=1 - e^{q_R} - e^{q_F} + e^{q_F+q_R} + \frac{e^{q_R}}{4} - \frac{e^{q_F+q_R}}{4} + \frac{e^{q_F}}{4} - \frac{e^{q_F+q_R}}{4} + \frac{e^{q_F+q_R}}{4} \\
&= \frac{4 - 4e^{q_F} - 4e^{q_R} + 4e^{q_F+q_R} + e^{q_F} + e^{q_R} - e^{q_F+q_R}}{4} \\
&= \frac{4 - 3e^{q_F}- 3e^{q_R} + 3e^{q_F+q_R}}{4}\\
&= \frac{4 - 3(e^{q_F}+e^{q_R}-e^{q_F+q_R})}{4} \\
&= 1 - \frac{3}{4}\left(e^{q_F}+e^{q_R}-e^{q_F+q_R}\right)
\end{aligned}
$$
```{r}
Pm_match_observed <- function(Q_F, Q_R) {
l10 <- log(10)
l3 <- log(3)
l4 <- log(4)
q_F <- -Q_F/10*l10
q_R <- -Q_R/10*l10
term1 <- log_sum_exp(q_F,q_R)
term2 <- log_diff_exp(term1,q_F+q_R) + l3 - l4
log1m_exp(term2)
}
```
$$
\begin{aligned}
P(macth | Obs(mismatch)) &= \frac{(1-e^{q_F})e^{q_R}}{4} + \frac{(1-e^{q_R})e^{q_F}}{4} + \frac{e^{q_F+q_R}}{4} \\
&= \frac{(1-e^{q_F})e^{q_R} + (1-e^{q_R})e^{q_F} + e^{q_F+q_R}}{4} \\
&= \frac{e^{q_R} - e^{q_F+q_R} + e^{q_F} - e^{q_F+q_R} + e^{q_F+q_R}}{4} \\
&= \frac{e^{q_F} + e^{q_R} - e^{q_F+q_R}}{4}
\end{aligned}
$$
```{r}
Pm_mismatch_observed <- function(Q_F, Q_R) {
l10 <- log(10)
l3 <- log(3)
l4 <- log(4)
q_F <- -Q_F/10*l10
q_R <- -Q_R/10*l10
term1 <- log_sum_exp(q_F,q_R)
log_diff_exp(term1,q_F+q_R) - l4
}
```
```{r}
score_match_observed <- function(Q_F, Q_R) {
Pm_match_observed(Q_F,Q_R) - log1m_exp(Pm_match_observed(Q_F,Q_R))
}
score_mismatch_observed <- function(Q_F, Q_R) {
Pm_mismatch_observed(Q_F,Q_R) - log1m_exp(Pm_mismatch_observed(Q_F,Q_R))
}
```
```{r}
scores <- expand_grid(QF=0:40,QR=0:40) %>%
mutate(score_match_observed = round(score_match_observed(QF,QR),2),
score_mismatch_observed = round(score_mismatch_observed(QF,QR),2))
```
```{r}
plot_match <- plot_ly(scores,
x=~QF, y=~QR, z=~score_match_observed,
type="mesh3d") %>%
layout(
plot_bgcolor = "#bababa",
scene = list(
xaxis = list(title = "Q forward read"), # Change x/y/z axis title
yaxis = list(title = "Q reverse read"),
zaxis = list(title = "Score match")))
```
```{r}
plot_mismatch <- plot_ly(scores,
x=~QF, y=~QR, z=~score_mismatch_observed,
type="mesh3d") %>%
layout(
plot_bgcolor = "#bababa",
scene = list(
xaxis = list(title = "Q forward read"), # Change x/y/z axis title
yaxis = list(title = "Q reverse read"),
zaxis = list(title = "Score mismatch")))
```
```{r}
write(plotly_json(plot_match,FALSE),"content/docs/commands/alignments/obipairing/exact-alignment/match.json")
write(plotly_json(plot_mismatch,FALSE),"content/docs/commands/alignments/obipairing/exact-alignment/mismatch.json")
```

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