dev/Eqn_test_quarto.knit.md

In friendly/matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

title: "Using Eqn() and ref() test with Quarto" engine: knitr

::: {.cell}

```{.r .cell-code} library(matlib) library(car)

::: {.cell-output .cell-output-stderr}

Loading required package: carData

:::
:::



Quarto has it's own syntax for creating displayed equations with equation numbers and a way to refer to them in text.
We illustrate these here.

## Simple equations
A standard equation and reference, as a displayed equation in Quarto:

$$
f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k}
$$ {#eq-binom}

This can be referenced as: See @eq-binom, and [-@eq-binom]

Syntax generated with `Eqn()`. Raw output:



::: {.cell}

```{.r .cell-code}
Eqn("f\\left(k\\right) = \\binom{n}{k} p^k\\left(1-p\\right)^{n-k}",
    quarto=TRUE)

::: {.cell-output .cell-output-stdout}

$$
f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k}
$$ 

::: :::

Using results: 'asis' in the chunk renders this as:

```{.r .cell-code} Eqn("f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k}", quarto=TRUE)

$$
f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k}
$$ 



Add an equation label and number:




```{.r .cell-code}
Eqn("f\\left(k\\right) = \\binom{n}{k} p^k\\left(1-p\\right)^{n-k}",
    quarto=TRUE, label='eq-binom2')

$$ f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k} $$ {#eq-binom2}

Inline equation referencing.

• Manually with Quarto syntax (works): @eq-binom and @eq-binom2
• With matlib using ref(., quarto=TRUE): ([-@eq-binom]) and ([-@eq-binom2])

Will also work within an equation, not that this is particularly useful.

```{.r .cell-code} "@eq-binom"

[1] "@eq-binom"



## Auto use `quarto=TRUE` if .qmd file used

Internally, set global to TRUE if .qmd file detected. Error raised if files have the same name but different extension (`Eqn.qmd` and `Eqn.Rmd` will raise error if in same dir).





```{.r .cell-code}
Eqn("f\\left(k\\right) = \\binom{n}{k} p^k\\left(1-p\\right)^{n-k}", label = 'eq-auto')

$$ f\left(k\right) = \binom{n}{k} p^k\left(1-p\right)^{n-k} $$ {#eq-auto}

See ([-@eq-auto]) for auto-detected quarto label. Of course, the @ notation still works too; e.g., see @eq-auto for details

Testing latexMatrix()

Even this simple test doesn't work:

::: {.cell}

```{.r .cell-code} Eqn("\mathbf{X}=", latexMatrix(), quarto=TRUE)

::: {.cell-output .cell-output-stdout}

$$ \mathbf{X}=\begin{pmatrix} x_{11} & x_{12} & \cdots & x_{1m} \ x_{21} & x_{22} & \cdots & x_{2m} \ \vdots & \vdots & & \vdots \ x_{n1} & x_{n2} & \cdots & x_{nm} \ \end{pmatrix}

$$

:::
:::



Rendered:




```{.r .cell-code}
Eqn("\\mathbf{X}=", latexMatrix(), quarto=TRUE)

$$ \mathbf{X}=\begin{pmatrix} x_{11} & x_{12} & \cdots & x_{1m} \ x_{21} & x_{22} & \cdots & x_{2m} \ \vdots & \vdots & & \vdots \ x_{n1} & x_{n2} & \cdots & x_{nm} \ \end{pmatrix}

$$

A more complex example

Here, we illustrate the decomposition of sums of squares and product (SSP) matrices in a simple one-way MANOVA design.

::: {.cell}

```{.r .cell-code} data(dogfood, package = "heplots") str(dogfood)

::: {.cell-output .cell-output-stdout}

'data.frame': 16 obs. of 3 variables: $ formula: Factor w/ 4 levels "Old","New","Major",..: 1 1 1 1 2 2 2 2 3 3 ... $ start : int 0 1 1 0 0 1 2 3 1 5 ... $ amount : int 100 97 88 92 95 85 82 89 77 84 ...

:::

```{.r .cell-code}
#fit the model
dogfood.mod <- lm(cbind(start, amount) ~ formula, data=dogfood)

:::

Do the MANOVA tests and extract the SSP_H and SSP_E:

::: {.cell}

```{.r .cell-code} dogfood.aov <- Anova(dogfood.mod) SSP_H <- dogfood.aov$SSP[["formula"]] |> print()

::: {.cell-output .cell-output-stdout}

      start   amount

start 9.6875 -70.9375 amount -70.9375 585.6875

:::

```{.r .cell-code}
SSP_E <- dogfood.aov$SSPE              |> print()

::: {.cell-output .cell-output-stdout}

       start amount
start  25.75  11.75
amount 11.75 390.25

:::

```{.r .cell-code} SSP_T <- SSP_H + SSP_E

:::



Now, show that `SSP_T = SSP_H + SSP_E` numerically. As generated, each of these matrices have `rownames()` and `colnames()`. 



::: {.cell}

```{.r .cell-code}
options(print.latexMatrix = list(display.labels=FALSE))
options(digits = 4)
Eqn(latexMatrix(SSP_T), "=", latexMatrix(SSP_H), "+", latexMatrix(SSP_E),
    quarto = TRUE)

::: {.cell-output .cell-output-stdout}

$$
\begin{pmatrix} 
 35 & -59 \\ 
-59 & 976 \\ 
\end{pmatrix}
=\begin{pmatrix} 
  9.7 & -70.9 \\ 
-70.9 & 585.7 \\ 
\end{pmatrix}
+\begin{pmatrix} 
 26 &  12 \\ 
 12 & 390 \\ 
\end{pmatrix}

$$ 

::: :::

Rendered by Quarto:

{.r .cell-code} Eqn(latexMatrix(SSP_T), "=", latexMatrix(SSP_H), "+", latexMatrix(SSP_E), quarto = TRUE)

$$ \begin{pmatrix} 35 & -59 \ -59 & 976 \ \end{pmatrix} =\begin{pmatrix} 9.7 & -70.9 \ -70.9 & 585.7 \ \end{pmatrix} +\begin{pmatrix} 26 & 12 \ 12 & 390 \ \end{pmatrix}

$$

friendly/matlib documentation built on Dec. 6, 2024, 9:25 a.m.