Eqn_helpers: Helpers to Compose Equations with Eqn

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

Helpers to Compose Equations with Eqn

Description

These functions extend Eqn to facilitate composing LaTeX equations with desirable features and pleasant typography.

• Eqn_overset and Eqn_underset typesets a label over or under a LaTeX expression or a "latexMatrix" object

• Eqn_overbrace and Eqn_underbrace typesets a brace, with an optional label over or under an object

• Eqn_newline, Eqn_hspace and Eqn_vspace facilitate spacing of parts of an equation.

• Eqn_size changes size of LaTeX text; Eqn_text includes a literal string in equations.

Each of these (except Eqn_text) have aliases without the Eqn_ prefix for brevity.

For example, given the matrix A = matrix(1:4), 2, 2), the call Eqn(overset(A, "A")) generates:

\overset{\mathbf{A}} 
 { \begin{pmatrix} 
  1 & 3 \ 
  2 & 4 \ 
  \end{pmatrix}
 }

When rendered in LaTeX, this produces:

\overset{\mathbf{A}} { \begin{pmatrix} 1 & 3 \\ 2 & 4 \\ \end{pmatrix} }

You can also use these for straight LaTeX expressions, such this equation showing and labeling the Hat matrix in regression. See the examples for the call to underbrace for this.

\mathbf{\hat{y}} = \underbrace{\mathbf{X}(\mathbf{X}^{\top}\mathbf{X})^{-1} \mathbf{X}^{\top}}_{\mathbf{\mathbf{H}}}\mathbf{y}

Eqn_newline() emits a newline (\) in an equation, with an optional increase to the padding following the newline.

Eqn_text() inserts a literal string to be rendered in a text font in an equation.

Eqn_hspace() is used to create (symmetric) equation spaces, most typically around = signs Input to lhs, rhs can be a numeric to increase the size of the space or a character vector to be passed to the LaTeX macro \hspace{}.

Eqn_vspace() inserts vertical space between lines in an equation. Typically used for aligned, multiline equations.

Eqn_size() is used to increase or decrease the size of LaTeX text and equations. Can be applied to a specific string or applied to all subsequent text until overwritten.

Usage

overset(
  x,
  label,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

underset(
  x,
  label,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

overbrace(
  x,
  label = NULL,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

underbrace(
  x,
  label = NULL,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

Eqn_overset(
  x,
  label,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

Eqn_underset(
  x,
  label,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

Eqn_overbrace(
  x,
  label = NULL,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

Eqn_underbrace(
  x,
  label = NULL,
  label.style = c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " ")
)

Eqn_newline(space = 0)

newline(space = 0)

Eqn_text(text)

Eqn_hspace(lhs = 5, mid = "", rhs = NULL, times = 1)

hspace(lhs = 5, mid = "", rhs = NULL, times = 1)

Eqn_vspace(space)

vspace(space)

Eqn_size(string, size = 0)

size(string, size = 0)

Arguments

x	a numeric or character matrix, or a character string LaTeX expression or a "latexMatrix" object
label	a character string used as the label above or below the object x. If missing, and a "matrix" object was passed, it's name is used as the label. In LaTeX, these are rendered in a size appropriate for superscripts and subscripts, but you can use a size modifier to change this, for example '\Large{"A"}'.
label.style	The name of a math font used to to typeset the label. One of c("mathbf", "mathrm", "mathit", "mathsf", "mathcal", "mathtt", " "). The default, "mathbf" wraps the label inside "\mathbf{ }" commonly used for the name of a matrix.
space	includes extra vertical space. Metric of the vertical space must be 'ex', 'pt', 'mm', 'cm', 'em', 'bp', 'dd', 'pc', or 'in'
text	argument to be used within \text{}
lhs	spacing size. Can be a number between -1 and 6. -1 provides negative spaces and 0 gives no spacing. Input can also be a character vector, which will be passed to \hspace{} (e.g., '1cm'; see space argument for supported metrics). Default is 5, resulting in a \quad space.
mid	character vector to place in the middle of the space specification. Most commonly this will be operators like '='
rhs	see lhs for details. If left as NULL and mid is specified the this will be set to rhs to create symmetric spaces around mid
times	number of times to repeat the spacings
string	a string that should have its text size modified. If missing the size modifier is returned, which applies the size modifier to the remainder of the text until reset with Eqn_size()
size	numeric size of LaTeX text modifier, ranging from -3 (\tiny) to 5 (\HUGE), with 0 defining the normal test size (\normalsize; default)

Value

Returns a character vector containing the LaTeX expressions for the given operation. You can pass this to cat to display the result on the console, or include it inside a call to Eqn to typeset it.

Author(s)

Michael Friendly, Phil Chalmers

Examples

library(matlib)
A <- matrix(1:4, 2, 2)
B <- matrix(4:1, 2, 2)
AB <- A + B
Eqn(overset(A, "A"))
  #  missing label: uses the name of the object
Eqn(overset(A))

# test just a character LaTeX expression
Eqn('a', overset('=', '?'), 'b')

# a labelled latexMatrix equation
Eqn(overset(A, "A"), "+",
    overset(B, "B"), "=",
    underset(AB, "A+B"))
    
 # using a LaTeX expression as the label  
 Lambda <- latexMatrix("\\lambda", nrow=2, ncol=2,
                       diag=TRUE)
 Eqn(overset(Lambda, "\\Lambda"))

 # generate LaTeX expression for the Hat matrix, label as "H"
H <- "\\mathbf{X} (\\mathbf{X}^{\\top}\\mathbf{X})^{-1} \\mathbf{X}^{\\top}"
Eqn("\\mathbf{\\hat{y}} =", underbrace(H, "\\mathbf{H}"), "\\mathbf{y}")

# Combine this with overbrace
Eqn(overbrace(underbrace(H, "\\mathbf{H}"), "\\LARGE\\mathbf{\\hat{y}}"))


Eqn_newline()
Eqn_newline('10ex')

# more complete example  
Eqn(underset("\\mathbf{X}", "(4 \\times 3)"), "& = \\mathbf{U} \\mathbf{\\Lambda} \\mathbf{V}^\\top",
    Eqn_newline('1ex'),
    ' & =',
    latexMatrix("u", 4, 3),
    latexMatrix("\\lambda", 3, 3, diag=TRUE),
    latexMatrix("v", 3, 3, transpose = TRUE),
    align=TRUE)



Eqn_hspace()
Eqn_hspace(3) # smaller
Eqn_hspace(3, times=2)
Eqn_hspace('1cm')

# symmetric spacing around mid
Eqn_hspace(mid='=')
Eqn_hspace(mid='=', times=2)


Eqn_vspace('1.5ex')
Eqn_vspace('1cm')



# set size globally
Eqn_size(size=3)
Eqn_size() # reset

# locally for defined string
string <- 'e = mc^2'
Eqn_size(string, size=1)

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