## A small life counter

… to keep track of magic the gathering games.

Check it out here!

## Permutation Pyramid

OK so here’s an update to the permutation pyramid I made.

I had to make a list of different permutations of models but it became hard to keep track of all the different variables and their combinations. Hence, the permutation pyramid. The goal is to make a list of vector combinations and permutations. I found this super useful when generating formulas for AICc/Model selection.

Enjoy!

The function has a few options:

1. vec
• The vector to draw the combinations/permutations from
2. order.matters = FALSE
• A simple boolean TRUE / FALSE to add in the permutations of each vector combination. This will generate permutations of the combinations and add them to the list. This may only be useful for certain models
3. req
• A vector of elements that should be required in the combinations.
4. interact
• A list of vector combinations that can be found in the original combinations

## Function

```pyramid <- function( vec, order.matters = FALSE, req, interact ){
# pyramid of variable combinations
# this doesn't include different
# arrangements
vrz <- lapply(
1:length( vec ),
function( x ){
combn( vec, x ) %>% as.data.frame()
}
) %>% purrr::flatten() %>% unname()

# If there are interactions
if( !missing( interact ) ){
# possible interaction combos
intx <- seq( from = 1, to = length( interact ), by = 1 ) %>% knp.perm.pyramid()

# extra interactions
vrz.int <- list()

# look through vars
for( v in vrz ){

# make a list of interactions
# and add them to the list
vrz.int <- append(
vrz.int,
lapply( intx, function( ints ){
# count number of matches to compare
# and filter out unaltered var lists
mt <- 0

# for each interaction
# check if its in the array
# then add it if it is
for ( int in ints ) {
if(
length( intersect( v, interact[[ int ]] ) ) == length( interact[[ int ]] ) &
length( interact[[ int ]] ) > 1
){
v <- c( v, paste0( interact[[ int ]], collapse = ":" ) )
mt <- mt + 1
}
}

# if the number of matches equals
# the number of interactions then
# return the altered array
if( mt == length(ints) ){
return( v )
}
return( NULL )

}) %>% plyr::compact()
)
}

# append interactions
vrz <- append( vrz, vrz.int )
}

# order matters so lets rearrange
if( order.matters ){
vrz <- lapply( vrz, function( x ){
combinat::permn( x )
}) %>% purrr::flatten()
}

# if there's any required variables in each combination
if( !missing( req ) ){
vrz <- lapply(vrz, function( x ){
if( length( intersect( x, req ) ) == length( req ) ){
return( x )
}
return( NULL )
}) %>% plyr::compact()
}

# return list of character
# permutations
return( vrz )
}
```

## Examples / Usage

Plain vanilla use

```> a <- c( "A", "B", "C" )
> pyramid( a )
[]
 "A"

[]
 "B"

[]
 "C"

[]
 "A" "B"

[]
 "A" "C"

[]
 "B" "C"

[]
 "A" "B" "C"
```

If the order of the elements matters

```> a <- c( "A", "B", "C" )
> pyramid( a, order.matters = TRUE )
[]
 "A"

[]
 "B"

[]
 "C"

[]
 "A" "B"

[]
 "B" "A"

[]
 "A" "C"

[]
 "C" "A"

[]
 "B" "C"

[]
 "C" "B"

[]
 "A" "B" "C"

[]
 "A" "C" "B"

[]
 "C" "A" "B"

[]
 "C" "B" "A"

[]
 "B" "C" "A"

[]
 "B" "A" "C"
```

Require variables

```> a <- c( "A", "B", "C", "D", "E" )
> b <- c( "B", "D" )
> pyramid( a, req = b )
[]
 "B" "D"

[]
 "A" "B" "D"

[]
 "B" "C" "D"

[]
 "B" "D" "E"

[]
 "A" "B" "C" "D"

[]
 "A" "B" "D" "E"

[]
 "B" "C" "D" "E"

[]
 "A" "B" "C" "D" "E"
```

Include interactions

```> a <- c( "A", "B", "C")
> b <- list( c( "A", "B" ), c( "A", "B", "C" ) )
> pyramid( a, interact = b )
[]
 "A"

[]
 "B"

[]
 "C"

[]
 "A" "B"

[]
 "A" "C"

[]
 "B" "C"

[]
 "A" "B" "C"

[]
 "A"   "B"   "A:B"

[]
 "A"   "B"   "C"   "A:B"

[]
 "A"     "B"     "C"     "A:B:C"

[]
 "A"     "B"     "C"     "A:B"   "A:B:C"
```

## Permutation Pyramid

So I had to make a combination of different values based on elements in a vector. With a few tweaks and what not I made a little function to find all the combinations and permutations of a given vector. Enjoy

The function:

```# creat a list of combinations and
# permutations of elements from
# a single vector. This requires
# a few libraries:
# library( dplyr )
# library( purrr )
# library( combinat )

# "order.matters" is means that
# for every combination of elements
# find every order they can be
# arranged.

permutation.pyramid <- function( v, order.matters = TRUE ){

# get the unique combinations of elements
# and flatten them into a one dimensional list
out <- 1:length(v) %>%
lapply(function( x ){
combn( v, x ) %>% as.data.frame()
}) %>%
purrr::flatten() %>%
unname()

# if order.matters then find all the
# arrangements of each combination
if( order.matters ){
out <- out %>%
lapply(function( x ){
combinat::permn( x )
}) %>%
purrr::flatten()
}

# return list of permutations
return( out )
}

```

Use and examples.

Find all combinations and permutations of a given vector

```> test <- c("A","B","C")
> permutation.pyramid( test )
[]
 "A"

[]
 "B"

[]
 "C"

[]
 "A" "B"

[]
 "B" "A"

[]
 "A" "C"

[]
 "C" "A"

[]
 "B" "C"

[]
 "C" "B"

[]
 "A" "B" "C"

[]
 "A" "C" "B"

[]
 "C" "A" "B"

[]
 "C" "B" "A"

[]
 "B" "C" "A"

[]
 "B" "A" "C"
```

Find all combinations of vector

```> test <- c("A","B","C")
> permutation.pyramid( test, order.matters = FALSE )
[]
 "A"

[]
 "B"

[]
 "C"

[]
 "A" "B"

[]
 "A" "C"

[]
 "B" "C"

[]
 "A" "B" "C"
```

Anyways I hope that’ll be useful for someone!

## Confidence Intervals

A small little function written in R to get the 95% confidence intervals and some quick stats of a vector. I found this useful in error reporting in some stats. I got the concept from this tutorial.

This does require the dplyr library

Function

```library( dplyr )

ci <- function( x ){
cnf <- dplyr::tibble(
mean = mean( x, na.rm = TRUE),
st.dev = sd( x, na.rm = TRUE),
n = length( x ),
error = qnorm( 0.975 ) * st.dev / sqrt( n ),
ci05 = mean - error,
ci95 = mean + error
)

cat( cnf\$mean, "(", cnf\$ci05, "-", cnf\$ci95, ")\n" )
return( cnf )
}
```

Use

```> x <- sample(10)
> ci(x)
5.5 ( 3.623477 - 7.376523 )
# A tibble: 1 x 6
mean st.dev     n error  ci05  ci95
<dbl>  <dbl> <int> <dbl> <dbl> <dbl>
1   5.5   3.03    10  1.88  3.62  7.38
```

## Quick update to Grade Calculator

Just a quick update to make the Grade Calculator more user friendly.

1. Added a very simple notification system for the overall grade. It’ll now tell you if you pass a certain grade threshold for the overall mark. Default is 50% for all the Aussie grading system