plot_derivatives.Rmd

---
title: "first and second derivatives"
author: "Clay Ford"
date: "5/17/2021"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Import data

Just get data for IS481. Not sure this is what you want. 

```{r message=FALSE}
library(readxl)
library(tidyr)
library(dplyr)
d <- read_excel(path = '21.04.29 Probe Concentration Comparison.xlsx', sheet = 2,
                range = 'A1:P44')
# reshape to long format to help with plotting
dL <- pivot_longer(d, cols = -1, names_to = "conc", values_to = "signal")
```

Using the `smooth.spline` and `predict` functions in base R. The `smooth.spline` function fits a cubic smoothing spline to the data. The `predict` function uses the fit to predict a spline at new points and returns the derivative specified.

```{r}
nms <- unique(dL$conc)
mL <- lapply(nms, function(x)smooth.spline(x = dL$`Time (min)`[dL$conc == x], 
                         y = dL$signal[dL$conc == x]))
# first derivative
D1 <- lapply(mL, function(x)predict(x, x = seq(0,19, length.out = 200), 
                                    deriv = 1))
# second derivative
D2 <- lapply(mL, function(x)predict(x, x = seq(0,19, length.out = 200), 
                                    deriv = 2))
# name elements in D2 and D2
names(D1) <- names(D2) <- nms

D1 <- bind_rows(D1,.id = "conc")
D2 <- bind_rows(D2,.id = "conc")

D1$conc <- factor(D1$conc, labels = nms)
D2$conc <- factor(D2$conc, labels = nms)

```

## Create plots

First derivative


```{r}
library(ggplot2)
ggplot(D1) +
  aes(x, y, color = conc) +
  geom_line() +
  labs(title = "IS481 Probe Concentration Comparison\n[First Derivative]", 
       x = "Time (min)", y = "Δ Fluoresence/Δ Time (F.U./min)")
```

Second derivative

```{r}
ggplot(D2) +
  aes(x, y, color = conc) +
  geom_line() +
  coord_cartesian(xlim = c(0,6)) +
  labs(title = "IS481 Probe Concentration Comparison\n[Second Derivative]", 
       x = "Time (min)", y = "Δ Fluoresence/Δ Time (F.U./min)")

```