flesh out dev/under-over.R tests

dev/Eqn_test_quarto.qmd

@@ -1,5 +1,5 @@
 ---
-title: "Eqn() and ref() test with Quarto"
+title: "Using Eqn() and ref() test with Quarto"
 engine: knitr
 ---
 
@@ -8,13 +8,13 @@ engine: knitr
 library(matlib)
 ```
 
-Standard equation and reference
+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}
 
-See @eq-binom, and [-@eq-binom]
+This can be referenced as: See @eq-binom, and [-@eq-binom]
 
 Syntax generated with `Eqn()`. Raw output:
 
@@ -23,7 +23,7 @@ Eqn("f\\left(k\\right) = \\binom{n}{k} p^k\\left(1-p\\right)^{n-k}",
     quarto=TRUE)
 ```
 
-Rendered.
+Rendered:
 
 ```{r}
 #| results: 'asis'
@@ -51,7 +51,7 @@ Will also work within an equation, not that this is particularly useful.
 "@eq-binom"
 ```
 
-# Auto use `quarto=TRUE` if .qmd file used
+## 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).
 
@@ -63,3 +63,15 @@ Eqn("f\\left(k\\right) = \\binom{n}{k} p^k\\left(1-p\\right)^{n-k}", label = 'eq
 
 
 See `{r} ref("eq-auto", quarto=TRUE)` for auto-detected quarto label. Of course, the @ notation still works too; e.g., see @eq-auto for details
+
+## A more complex example
+
+Here, we illustrate the decomposition of sums of squares and product (SSP) matrices in a simple one-way MANOVA design.
+```{r}
+data(dogfood, package = "heplots")
+str(dogfood)
+
+#fit the model
+dogfood.mod <- lm(cbind(start, amount) ~ formula, data=dogfood) 
+```
+

dev/under-over.R

@@ -24,51 +24,76 @@ underbrace <- function(x, label=NULL){
 }
 
 if (FALSE) {
-  X <- latexMatrix("x", 2,2)
-  SSP_E <- latexMatrix("y", 2,2)
-
-
-  Eqn(X + SSP_E)
-
-  # do overbrace directly  
-  Eqn("\\overset{\\mathbf{X}}{", X, "}")
-
-  # show X + SSP_E = (X+SSP_E)
-
-  Eqn("\\overset{\\mathbf{X}}{", X, "}", 
-      "+",
-      "\\overset{\\mathbf{SSP_E}}{", SSP_E, "}",
-      "=",
-      "\\overset{\\mathbf{X + SSP_E}}{", X+SSP_E, "}",
-  )
-
-  # but these don't work
-  Eqn(overset(X, "\\mathbf{X}"))
-  Eqn(overset(SSP_E, "\\mathbf{SSP_E}"))
 
-
   data(dogfood, package = "heplots")
   dogfood.mod <- lm(cbind(start, amount) ~ formula, data=dogfood) 
   dogfood.aov <- car::Anova(dogfood.mod) 
-  SSP_H <- dogfood.aov$SSP 
-  SSP_E <- dogfood.aov$SSPE 
-  SSP_T <- SSP_H$formula + SSP_E
-  # make row/colnames disappear
-  rownames(SSP_T) <- rownames(SSP_H) <- rownames(SSP_E) <- NULL
-  colnames(SSP_T) <- colnames(SSP_H) <- colnames(SSP_E) <- NULL
-
+  SSP_H <- dogfood.aov$SSP[["formula"]]   |> round(digits = 2)
+  SSP_E <- dogfood.aov$SSPE               |> round(digits = 2)
+  SSP_T <- SSP_H + SSP_E
+
+    # make row/colnames disappear
+  options(print.latexMatrix = list(display.labels=FALSE))  
+  # do overbrace directly: WORKS
   Eqn("\\overset{\\mathbf{SSP}_T}{", SSP_T, "}")
 
+  # but these don't work:
+  Eqn(overset(SSP_H, "\\mathbf{SSP_H}"))
+  Eqn(overset(SSP_E, "\\mathbf{SSP_E}"))
+
+  # use latexMatrix()
+  H <- latexMatrix(SSP_H)
+  Eqn(overset(H, "\\mathbf{SSP_H}"))
+
   # show SSP_H + SSP_E = (SSP_H+SSP_E)
+  # What I want to get here:
+  eqn <- "
+\begin{equation*}
+\overset{\mathbf{SSP}_T}
+  {\begin{pmatrix} 
+   35.4 & -59.2 \\ 
+  -59.2 & 975.9 \\ 
+  \end{pmatrix}}
+=
+\overset{\mathbf{SSP}_H}
+  {\begin{pmatrix} 
+    9.69 & -70.94 \\ 
+  -70.94 & 585.69 \\ 
+  \end{pmatrix}}
++
+\overset{\mathbf{SSP}_E}
+  {\begin{pmatrix} 
+   25.8 &  11.8 \\ 
+   11.8 & 390.3 \\ 
+  \end{pmatrix}}
+\end{equation*} 
+ "
 
-  Eqn("\\overset{\\mathbf{SSP_H}}{", SSP_H, "}", 
+  # this generates an error:
+  # argument is missing, with no default
+  Eqn("\\overset{\\mathbf{SSP_T}}{", SSP_T, "}", 
       "+",
-      "\\overset{\\mathbf{SSP_E}}{", SSP_E, "}",
+      "\\overset{\\mathbf{SSP_H}}{", SSP_H, "}",
       "=",
-      "\\overset{\\mathbf{SSP_T}}{", SSP_T, "}",
+      "\\overset{\\mathbf{SSP_E}}{", SSP_E, "}",
   )
 
+ ## -------Underbrace: 
+  # I want to generate the equation \hat{y} = X (X'X)^{-1} X' y with a brace underneath showing the H matrix
+  # This manual LaTeX works:
+  eqn <- "
+  \mathbf{\hat{y}} 
+   = \underbrace{\mathbf{X}(\mathbf{X}^{\top}\mathbf{X})^{-1}\mathbf{X}^{\top}}_\mathbf{H}\mathbf{y}   
+  "
 
+  # generate this with underbrace()
+  H <- "\\mathbf{X}(\\mathbf{X}^{\\top}\\mathbf{X})^{-1}\\mathbf{X}^{\\top}"
+  underbrace(H, "\\mathbf{H}")
 
+  # Do this with Eqn() - WORKS, at least when all the elements are just symbols, not matrices
+  Eqn("\\mathbf{\\hat{y}} =", underbrace(H, "\\mathbf{H}"), "\\mathbf{y}")
+
+  # We can even combine this with overbrace 
+  Eqn(overbrace(underbrace(H, "\\mathbf{H}"), "\\mathbf{\\hat{y}}"))
 
 }