Taking R Code from Hours to Seconds

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# Taking R Code from Hours to Seconds
### Jared P. Lander

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.center2[.largest[The Ask]]

???

- What are we trying to solve?

---
class: middle, center

.large[
Out of Millions of Points, Which are Similar to Each Other?
]

???

- For millions of points
- Which points are near each other?

---
class: middle, center

.large[
Which Points are Within a Certain Distance of Each Other?
]

???

- Essentially

- Range searching problem

---
class: center, middle

.largest[The Problem]

???

- What's the big deal?

---
class: middle, center

.large[This is Slow]

???

- So slow

---
class: middle, center

.large[How Slow?]

???

- Quantify this

- How bad is it?
- In terms of calculations

---
class: center, middle

`$n(n-1)/2$` Calculations

???

- Quadratic Relationship

For 500,000 rows this is 124,999,750,000

???

- 125 billion calculations
- 125 billion slots in memory

For 1,000,000 rows this is 499,999,500,000

???

- A milllion rows: 500 billion calculations
- Double rows, quadruple calculations

---
class: middle, center

???

- Calculations are `$O(n^{2})$`
- A million rows isn't that much data

---
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.largest[The Data]

???

- Our particular data

---
class: center, middle

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<div id="qzscpgtqtc" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;"><table class="gt_table">
  
  <thead class="gt_col_headings">
    <tr>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Var1</th>
      <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Var2</th>
    </tr>
  </thead>
  <tbody class="gt_table_body">
    <tr>
      <td class="gt_row gt_right">-1.829996</td>
      <td class="gt_row gt_right">51.04901</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-1.038547</td>
      <td class="gt_row gt_right">50.87115</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">31.130743</td>
      <td class="gt_row gt_right">33.69047</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-0.733131</td>
      <td class="gt_row gt_right">52.09273</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-4.916367</td>
      <td class="gt_row gt_right">38.70388</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-75.365101</td>
      <td class="gt_row gt_right">40.40710</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-4.015215</td>
      <td class="gt_row gt_right">39.99676</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">2.951305</td>
      <td class="gt_row gt_right">41.62434</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">-6.039258</td>
      <td class="gt_row gt_right">41.07505</td>
    </tr>
    <tr>
      <td class="gt_row gt_right">13.596565</td>
      <td class="gt_row gt_right">42.80572</td>
    </tr>
  </tbody>
  
  
</table></div>

???

- Just a sampling of about 500 thousand points
- Simulated data
- Actual data had millions

- Each row has two dimensions

- Want to calculate how similar each row is to every other
- Then find those that are most similar (by some definition)

---
class: center, middle

???

- Like a Rorschach test
- More density in certain areas

---
class: center, middle

.large[First Attempt]

???

- Start with obvious function

---
class: middle

```r
dist(all_points)
```

???

- Built into Base R
- Returns distance between every pair of rows

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/ComputerFire.jpg")
background-size: cover
class: hide_logo

???

- Did not go well

- Who knows when this will finish

---
class: center, middle

???

- Look at data again
- Noticed something about the data

---
class: middle

```r
all_points %>% 
  summarize(range(Var1), range(Var2))
```

```
## # A tibble: 2 x 2
##   `range(Var1)` `range(Var2)`
##           <dbl>         <dbl>
## 1         -102.          4.40
## 2          107.         68.1
```

???

- Look at ranges
- First: -100 to 100
- Second: 5 to 68

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/globe-lat-long.jpg")
background-size: contain
class: hide_logo

???

- Looks like lat/long

---
class: center, middle

.large[Let's use `{sf}`]

???

- Figure `{sf}` has functions for this

---
class: middle

```r
library(sf)
sf_points <- all_points %>% 
  # Var1: Longitude, Var2: latitude
  st_as_sf(coords=c('Var1', 'Var2')) %>% 
  # Use lat/long projection
  st_set_crs(4326)
sf_points
```

```
## Simple feature collection with 500000 features and 0 fields
## geometry type:  POINT
## dimension:      XY
## bbox:           xmin: -102.1256 ymin: 4.397471 xmax: 106.855 ymax: 68.06752
## CRS:            EPSG:4326
## # A tibble: 500,000 x 1
##                geometry
##  *          <POINT [°]>
##  1 (-1.829996 51.04901)
##  2 (-1.038547 50.87115)
##  3  (31.13074 33.69047)
##  4 (-0.733131 52.09273)
##  5 (-4.916367 38.70388)
##  6   (-75.3651 40.4071)
##  7 (-4.015215 39.99676)
##  8  (2.951305 41.62434)
##  9 (-6.039258 41.07505)
## 10  (13.59657 42.80572)
## # … with 499,990 more rows
```

???
- Convert with `st_as_sf()`

- Specify lat/long columns
- Like points on map

- Data weren't points on map, but no reason we couldn't use those methods

---
class: middle

```r
countries <- rnaturalearth::ne_countries(returnclass='sf')
ggplot() + geom_sf(data=countries) + geom_sf(data=sf_points)
```

???

- Weird shape, not point
- Simulated data

- Let's us use `{sf}` functions

---
class: middle

```r
st_distance(sf_points)
```

???

- needs `{lwgeom}`
- Measures distance between every point and every other point

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/ComputerFire.jpg")
background-size: cover
class: hide_logo

???

- Dumpster fire
- Or computer fire
- Doesn't finish

---
class: middle

```r
st_is_within_distance(sf_points %>% st_transform(3857), dist=11000)
```

???

- Exactly what we want!
- Need to convert our numbers to meters
    - .1 degree roughly 11,000 meters

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/ComputerFire.jpg")
background-size: cover
class: hide_logo

???

- But doesn't finish
- Need a new idea

---
class: center, middle

???

- No point comparing points that are far apart

---
class: center, middle

.large[Split the Data]

???

- Break into grid

---
class: middle

```r
sf_grid <- sf_points %>% 
  # project to meters
  st_transform(3857) %>% 
  # build the grid
  # use hexagons since they fit better
  st_make_grid(cellsize=1500000, square=FALSE) %>% 
  # back to original scale
  st_transform(4326)
```

???

- Convert to meters for calculations
- Use hexagons for better spacing

- Buckets should be small enough so we don't compare too many points

- But not so small it is hard to create grid

- 1.5 million meters

---
class: middle

```r
ggplot() + geom_sf(data=countries) + 
  geom_sf(data=sf_grid, color='blue') + geom_sf(data=sf_points)
```

???

- Only compare points within a grid cell
- Points in different cells don't need to be compared

- Let's see how this affects computation time

---
class: middle, center

.large[
`$g*\frac{n}{g}(\frac{n}{g}-1)/2$` Calculations
]

???

- Assuming the points are evenly distributed
- Perform fewer calculations `$g$` times

For 500,000 rows and 600 groups this is 208,083,333 calculations

???

- For 500,000 rows and 600 groups, 208 million calculations

124,791,666,667 fewer calculations

???

- 125 billion fewer
- Assuming points evenly distributed
- They're not

---
class: middle, center

???

- The difference is stark
- Millions versus billions

---
class: center, middle

.large[What About Points near the Edges of Hexagons?]

???

- Points near edges could be near each other

---
class: middle

```r
sf_buffer <- sf_grid %>%
  st_transform(3857) %>% 
  st_buffer(11000*2) %>% 
  st_transform(4326)
```

???

- Make each grid cell overlap
- Points can pair to neighboring cell
- Some points counted twice, deal with later

---
class: middle

```r
ggplot() + 
  geom_sf(data=countries) + 
  geom_sf(data=sf_buffer, color='blue') + geom_sf(data=sf_points)
```

???

- Can't see difference in plot since buffer is so small

---
class: middle

```r
sf_points_grid <- sf_points %>% 
  st_join(
    sf_buffer %>% st_as_sf() %>% tibble::rowid_to_column('Cell'),
    join=st_intersects, left=FALSE)
sf_points_grid
```

```
## Simple feature collection with 540525 features and 1 field
## geometry type:  POINT
## dimension:      XY
## bbox:           xmin: -102.1256 ymin: 4.397471 xmax: 106.855 ymax: 68.06752
## CRS:            EPSG:4326
## # A tibble: 540,525 x 2
##                geometry  Cell
##  *          <POINT [°]> <int>
##  1 (-1.829996 51.04901)    27
##  2 (-1.038547 50.87115)    27
##  3  (31.13074 33.69047)    37
##  4 (-0.733131 52.09273)    27
##  5 (-4.916367 38.70388)    26
##  6   (-75.3651 40.4071)     9
##  7 (-4.015215 39.99676)    26
##  8  (2.951305 41.62434)    28
##  9 (-6.039258 41.07505)    25
## 10  (13.59657 42.80572)    33
## # … with 540,515 more rows
```

???

- Which points belong to which grid cell?

---

```r
ggplot() + 
  geom_sf(data=countries) + 
  geom_sf(data=sf_buffer, color='blue') + 
  geom_sf(data=sf_points_grid, aes(color=factor(Cell))) + 
  theme(legend.position='none')
```

???

- Search within grid cells independently

---
class: center, middle

.large[
`st_make_grid()` and `st_join()` Can be Slow
]

???

- But `st_make_grid()` and `st_join()` are Slow

---
class: middle, center

.large[
`hexbin::hexbin()`
]

???

- `hexbin()` is much faster than `st_make_grid()`

---
class: middle, center

.large[
Does Not Deal with Border Issues
]

???

- Draw polygons and create buffer
- Not much faster overall

---
class: center, middle

.large[
Back to our Grid
]

???

- False Start
- Back to grid

---
class: middle

```r
group_counts <- sf_points_grid %>% 
  st_drop_geometry() %>% 
  count(Cell) %>% 
  filter(n > 1) %>% 
  mutate(Calculations=n*(n-1)/2)
group_counts
```

```
## # A tibble: 56 x 3
##     Cell     n Calculations
##    <int> <int>        <dbl>
##  1     1     7           21
##  2     2     4            6
##  3     3   335        55945
##  4     4 18395    169178815
##  5     5  3127      4887501
##  6     6   196        19110
##  7     7 27539    379184491
##  8     8 35760    639370920
##  9     9 37565    705545830
## 10    10     4            6
## # … with 46 more rows
```

```r
summary(group_counts$n)
```

```
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##       2      10     201    9652    7450  100170
```

```r
summary(group_counts$Calculations)
```

```
##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 1.000e+00 4.500e+01 2.011e+04 2.454e+08 2.858e+07 5.017e+09
```

???

- 56 groups
    - Could have made more groups, but that takes more time
- 2 to 100,000 points in each

- Average of 9600; Median 201
- Average calculations: 245 Million; Median 20,000
- Still 5 billion for just one group

- `count()` is much faster after dropping geometry
    - because `count()` aggregates the geometries

---
class: middle, center

.large[
13,742,167,792 vs 124,999,750,000
]

???

- All groups combined: 14 billion
- 14 billion vs 125 billion
- Order of magnitude fewer

---
class: middle, center

.large[
`group_nest()` + `mutate()` + `map()`
]

???

- Split data into separate `data.frame`s in a `list`-column, essentially
- Apply work to each individually
- Easier to reason about this way

---
class: middle

```r
library(purrr)
distance_nested <- sf_points_grid %>% 
  st_transform(3857) %>% 
  group_nest(Cell, keep=TRUE) %>% 
  mutate(GroupDist=map(
    data, 
    ~st_is_within_distance(.x, dist=11000))
  )
```

???

- .1 is the metric we want, convert to meters
- Computes if points fall within threshold
- For each group

---
class: middle, center

.large[
Went from Impossible to Hours...
]

???

- Doable

.large[
...if Each Group was Small Enough for `st_is_within_distance()`
]

???

- Only if `st_is_within_distance()` could finish

---
class: middle, center

.large[
Two Issues
]

???
- Two issues

.large[
`group_nest()` Can be Slow
]

???

- `group_nest()` slow
- Especially for wider data

.large[
`st_is_within_distance()` is Slow and Might Not Finish
]

???

- `st_is_within_distance()` is slow
- and might not finish

---
class: middle

.large[
First: Deal with `group_nest()`

Then: Deal with `st_is_within_distance()`
]

???

- One thing at a time
- `group_nest()`
- Then `st_is_within_distance()`

---
class: center, middle

.large[
`group_by() + group_map()`
]

???

- `group_by()`
- Instead of `group_nest()`
- `group_map()` gives a `list` of results
    - like `dlply()` from `{plyr}`

---
class: middle

```r
distance_grouped <- sf_points_grid %>% 
  st_transform(3857) %>% 
  group_by(Cell) %>% 
  group_map(~st_is_within_distance(.x, threshold=11000))
```

???

- Pass `.x` to `st_is_within_distance()`
- So it will work with grouped `tibble`

---
class: middle, center

.large[
Went from Hours to Minutes...
]

???

- Dramatic speed up by avoiding nesting

.large[
...if Each Group was Small Enough for `st_is_within_distance()`
]

???

- Only if `st_is_within_distance()` could finish
- Can't make smaller grid cells

---
class: center, middle

.large[
Better Still
]

???

- We can do even better

---
class: middle, center

.large[
`{data.table}`
]

???

- `{data.table}` excels at grouping

---
class: middle

```r
library(data.table)
distance_dt <- sf_points_grid %>% 
  as.data.table() %>% 
  .[, 
    .(Results=list(st_is_within_distance(.SD[['geometry']], dist=11000))), 
    by=Cell
  ]
```

???

- Pipe into square brackets

- `.SD` allows grouping to work
    - then act on `geometry` column

- Just calling on `geometry` column wouldn't respect grouping

- yes `{data.table}` with pipes

---
class: middle, center

.large[
Now in Fewer Minutes...
]

???

- Cut the time by a third
- Matters when this runs often

.large[
...if Each Group was Small Enough for `st_is_within_distance()`
]

???

- Only if `st_is_within_distance()` could finish

---
class: middle, center

.large[
Need an `st_is_within_distance()` Alternative
]

???

- `st_is_within_distance()` is not cutting it

---
class: middle, center

.large[`{Rfast}`]

???

- Faster functions than base R
- Has a fast distance function

---
class: middle, center

.large[`Dist()`]

???

- Works pretty well

---
class: middle, center

.large[Fast...]

???

- Fast

.large[...Until 46,342 Rows]

???

- Runs out of memory at 46,342 rows

---
class: middle

```cpp
static int proper_size(int nrw, int ncl){
  return ncl*(ncl-1)*0.5;
}
```

???

- Had to dive into C++
- `int` is the problem

---
class: middle, center

.large[R Integers are 32-Bit]

???

- R integers are 32-bits

---
class: middle, center

.large[
`$n(n-1)/2$` Calculations
]

???

- Saw this before

---
class: middle, center

.large[
Have to Compute `$n*(n-1)$`
]

???

- Need to store `$n*(n-1)$` in memory

.large[
`$\text{46,342}*(\text{46,342} - 1) = \text{2,147,534,622}$`
]

???

- 2 billion 147 million 534 thousand 622

---
class: middle, center

.large[
But `$2^{32} - 1 = \text{4,294,967,295} > \text{2,147,534,622}$`
]

???

- 32-bit is bigger than our number

.large[
True, But One Bit is Used for the Sign
]

???

- Need to account for positive or negative

---
class: middle, center

.large[
`$2^{31} - 1 = \text{2,147,483,647} < \text{2,147,534,622}$`
]

???

- So we fail at 46,342 rows

---
class: middle, center

.large[
Need Bigger Integer in C++
]

???

- Need something bigger

.large[
`R_xlen_t`
]

???

- Not 64-bit
- Biggest `int` machine can handle

---
class: middle

```cpp
static int proper_size(int nrw, int ncl){
  return ncl*(ncl-1)*0.5;
}
```

```cpp
static R_xlen_t proper_size(R_xlen_t nrw, R_xlen_t ncl){
  return ncl*(ncl-1)*0.5;
}
```

???

- Change `int` to `R_xlen_t`

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/rfast-pull-request.png")
background-size: contain
class: hide_logo

???

- I made a [pull request](https://github.com/RfastOfficial/Rfast/pull/32/commits/8704c4e5cdb5a72de5dc22b55147718dfb50defa#diff-be4eeb82997d524556d2d9f761b3189160026860e90336e75e60abc4c85e774f)
- Not accepted yet

---
class: middle, center

.large[
`{tcor}`
]

???

- From Bryan Lewis and Michael Kane
- Plus James Baglama and Alex Poliakov
- Built on `{irlba}`
- Meant for threshold correlation matrices
- But can ID points within distance of each other

---
class: middle

```r
library(tcor)
sf_points_grid %>% 
  filter(Cell == 9) %>% 
  st_coordinates() %>% 
  tdist(t=.1, p=2) %>%
  magrittr::extract2('indices') %>% 
  head()
```

```
##          i     j          val
## [1,]  1232 13241 1.047478e-05
## [2,]  5462  1979 6.720093e-05
## [3,] 25128  1284 1.611042e-04
## [4,] 17111  9107 1.790253e-04
## [5,]  5539 19076 1.931850e-04
## [6,] 29849 32388 2.033469e-04
```

???

- Returns indices for points within threshold of each other
- `tdist()`  works in parallel

---
class: middle

```r
sf_points_grid %>% 
  bind_cols(st_coordinates(.) %>% as_tibble()) %>% 
  st_drop_geometry() %>% 
  as.data.table() %>% 
  .[, .(
    Results=list(tdist(as.matrix(.SD), t=.1, p=2)$indices)
  ), 
  by=Cell, .SDcols=c('X', 'Y')]
```

???

- Convert to `data.table`for fast grouping
- Compute threshold for each group

- `tdist()` depends on sparsity
- So can be inconsistently slow

---
class: middle, center

.large[
`{torch}`
]

???

- Matrix computations on the GPU
- Pretty new
- No Python, pure R

---
class: middle

```r
library(torch)

torch9 <- sf_points_grid %>% 
  filter(Cell == 9) %>% 
  st_coordinates() %>% 
  torch_tensor(device='cuda')

torchDist <- nnf_pdist(torch9)
```

???

- Unbelievably fast
- 0.003 Seconds for 37,000 rows

- But my GPU only has 11 GB memory
- Easy to blow through it and crash
    - Past 60,000 rows

- Not everyone has GPU

- Takes time to load data onto GPU for each group
- Then extract results
- Then clear GPU memory

---
class: middle, center

.large[
Custom Code
]

???

- Need to build this from scratch
- Help from Michael Beigelmacher, Kaz Sakamoto and Ben Lerner

---
class: middle

Sort data according to one dimension (`X`)  
For row i=1:N
.indent1[For row j=i:N]
.indent2[Compute `X`-distance between points `i` and `j`]
.indent3[If greater than threshold, proceed to next point `i`]
.indent2[Compute squared distance between points `i` and `j`]
.indent3[If greater than threshold-squared, proceed to next point `j`]
.indent2[Compute distance and record indices]

???

- If `X`-dimension is too far, then by triangle inequality, distance must be too far
- Data are sorted, so once one `X` is too far, the remaining are too far for that row

- If that passes check distance

- Don't keep row pairs that are too far apart
- Saves compute time by breaking the loop and skipping not needed points

---
class: middle

```r
within_distance <- function(data, threshold)
{
  keepers <- array(NA, dim=rep(nrow(data), 2))
  keep_dist <- array(NA, dim=rep(nrow(data), 2))
  
  data <- data[order(data[, 1]), ]
  
  for(i in seq(1, nrow(data) - 1, by=1))
  {
    for(j in seq(i + 1, nrow(data), by=1))
    {
      if(abs(data[i, 1] - data[j, 1]) > threshold)
      {
        break
      }
      
      sq_dist <- sum((data[i, ] - data[j, ])^2)
      
      if(sq_dist > threshold^2)
      {
        next
      }
      
      keepers[i, j] <- 1
      keep_dist[i, j] <- sqrt(sq_dist)
    }
  }
  
  list(keepers=keepers, dist=keep_dist)
}
```

???

- Generalizes to multiple dimensions

---
class: middle

```r
sf_points_grid %>% 
  filter(Cell == 9) %>%
  st_coordinates() %>% 
  within_distance(threshold=.1)
```

???

- 1 second for 3,000 rows (Cell 5)
- 21 seconds for 18,000 rows (Cell 4)
- 70 seconds for 37,000 rows if enough memory (Cell 9)

---
class: middle

```r
sf_points_grid %>% 
  group_by(Cell) %>%
  group_map(~within_distance(st_coordinates(.x), threshold=.1))
```

???

- `group_map()` saves a `list` of results

- The individual timings would add up
- Allocating the `array` for large groups could be problematic
    - Inefficient memory use

- Parallel with `{furrr}` might cause memory issues

---
background-image: url("data:image/png;base64,#/home/jared/consulting/talks/images/must-go-faster.gif")
background-size: cover
class: hide_logo

???

- Need more speed

---
class: middle, center

`{Rcpp}`

???

- Integrate R and C++
- R-like C++

---
class: middle

.smallCode[

```cpp
#include <RcppArmadillo.h>
using namespace Rcpp;
// [[Rcpp::plugins(cpp11)]]
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::interfaces(cpp)]]

inline double distance_squared(arma::mat& x){
    return sum(pow(x.row(0) - x.row(1), 2));
}

// [[Rcpp::export]]
DataFrame threshold_distance(arma::mat obj, double threshold)
{
    // precompute squared threshold so we don't compute it each time
    const double threshold_squared = pow(threshold, 2);
    // empty vectors to hold indices below threshold
    std::vector<int> i_keep, j_keep; 
    std::vector<double> distances;
    
    int num_rows = obj.n_rows;
    for(int i = 0; i < num_rows; ++i){
        for(int j = i + 1; j < num_rows; ++j){
            // if the distance is too far even on one dimension, skip the problem
            if(arma::as_scalar(abs(obj.col(0).row(i) - obj.col(0).row(j))) > threshold)
                break;
            
            // compute the distance
            arma::uvec indices; 
            indices << i << j;
            arma::mat mat_ij = obj.rows(indices);
            double the_dist_squared = distance_squared(mat_ij);
            
            // if this distance is too big, skip ahead
            if(the_dist_squared > threshold_squared)
                continue;
            
            // puch_back() doesn't hurt as much in C++
            i_keep.push_back(i);
            j_keep.push_back(j);
            distances.push_back(sqrt(the_dist_squared));
        }
    }
    // need to add 1 back to the indices since C++ starts at 0 while R starts at 1
    transform(i_keep.begin(), i_keep.end(), i_keep.begin(), bind2nd(std::plus<int>(), 1));
    transform(j_keep.begin(), j_keep.end(), j_keep.begin(), bind2nd(std::plus<int>(), 1));
    
    DataFrame results = DataFrame::create(_["i"]=i_keep, _["j"]=j_keep, _["distance"]=distances);
    return results;
}
```
]

???

- R function translated to C++

- Expects a sorted matrix

- Uses Armadillo for matrix computations

- Can grow vectors without slowing down much

- Double for loops are still fast

---
class: middle

```r
sf_points_grid %>% 
  filter(Cell == 9) %>%
  bind_cols(st_coordinates(.) %>% as_tibble()) %>% 
  st_drop_geometry() %>% 
  arrange(X) %>% 
  dplyr::select(X, Y) %>% 
  as.matrix() %>% 
  threshold_distance(threshold=.1)
```

???

- 0.05 seconds for 3,000 rows (Cell 5)
- 0.5 seconds for 18,000 rows (Cell 4)
- 1.3 seconds for 37,000 rows if enough memory (Cell 9)
- Insane speed up
- Not even parallel

---
class: middle, center

???

- Things get worse and worse in pure R

---
class: middle

```r
sf_dt <- sf_points_grid %>% 
  bind_cols(st_coordinates(.) %>% as_tibble()) %>% 
  st_drop_geometry() %>% 
  as.data.table()

# sort the data
setkey(sf_dt, X)

# use data.table for faster grouping
similar_points <- sf_dt[, 
                        threshold_distance(as.matrix(.SD), threshold=.1), 
                        by=Cell, 
                        .SDcols=c('X', 'Y')]

similar_points
```

```
##           Cell   i   j   distance
##        1:    3  27  29 0.06500678
##        2:    3  41  45 0.07625256
##        3:    3  42  44 0.09625963
##        4:    3  50  53 0.05584888
##        5:    3  61  63 0.08657027
##       ---                        
## 25002846:   48 267 274 0.08309678
## 25002847:   48 306 307 0.01747799
## 25002848:   49   9  17 0.08602352
## 25002849:   49  10  14 0.06327113
## 25002850:   49  29  30 0.05506324
```

???

- `.SD` respects the grouping

- 30 seconds for the _WHOLE_ dataset
- Millions of rows: still about 30 seconds

---
class: middle, center

.large[
We Went from Cannot Finish
]

???

- We Went from Cannot Finish

.large[
to Hours, Maybe
]

???

- to Hours, Maybe
- Memory permitting

.large[
to Minutes
]

???

- to Minutes

.large[
to Seconds
]

???

- to Seconds
- Blazing fast
- Matters when running this hourly

---
class: middle

- Splitting the Data into Smaller Pieces
- Using a Smarter Algorithm
- Writing Compiled Code

???

- We did this by
- Splitting the Data into Smaller Pieces
- Using a Smarter Algorithm
- Writing Compiled Code

- Made it solvable

---
class: middle, center

.largest[Thank You]