Compute velocity on grid

Usage

compute_velocity_on_grid(
  x_emb,
  v_emb,
  density = 1,
  smooth = 0.5,
  n_neighbors = ceiling(n_obs/50),
  min_mass = 1,
  scale = 1,
  adjust_for_stream = FALSE,
  cutoff_perc = 5
)

Arguments

x_emb: A matrix of dimension n_obs x n_dim specifying the embedding coordinates of the cells.
v_emb: A matrix of dimension n_obs x n_dim specifying the velocity vectors of the cells.
density: A numeric value specifying the density of the grid points along each dimension. Default is 1.
smooth: A numeric value specifying the smoothing factor for the velocity vectors. Default is 0.5.
n_neighbors: A numeric value specifying the number of nearest neighbors for each grid point. Default is ceiling(n_obs / 50).
min_mass: A numeric value specifying the minimum mass required for a grid point to be considered. Default is 1.
scale: A numeric value specifying the scaling factor for the velocity vectors. Default is 1.
adjust_for_stream: Whether to adjust the velocity vectors for streamlines. Default is FALSE.
cutoff_perc: A numeric value specifying the percentile cutoff for removing low-density grid points. Default is 5.

Value

A list with two components: x_grid, the grid coordinates, and v_grid, the smoothed velocity vectors on the grid.

References

https://github.com/theislab/scvelo/blob/master/scvelo/plotting/velocity_embedding_grid.py

Examples

x_emb <- matrix(
  c(
    0, 0,
    1, 0,
    0, 1,
    1, 1
  ),
  ncol = 2,
  byrow = TRUE
)
v_emb <- matrix(
  c(
    1, 0,
    1, 0,
    0, 1,
    0, 1
  ),
  ncol = 2,
  byrow = TRUE
)

velocity_grid <- compute_velocity_on_grid(
  x_emb = x_emb,
  v_emb = v_emb,
  density = 0.1,
  n_neighbors = 2,
  adjust_for_stream = TRUE
)

names(velocity_grid)
#> [1] "x_grid" "v_grid"
dim(velocity_grid$x_grid)
#> [1] 2 5
dim(velocity_grid$v_grid)
#> [1] 2 5 5
head(velocity_grid$x_grid)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0 0.25  0.5 0.75    1
#> [2,]    0 0.25  0.5 0.75    1
head(velocity_grid$v_grid)
#> , , 1
#> 
#>      [,1]         [,2]        [,3]         [,4]         [,5]
#> [1,]    1 4.319277e-01 0.001070642 4.860706e-08 1.266417e-14
#> [2,]    0 4.860706e-08 0.001070642 4.319277e-01 1.000000e+00
#> 
#> , , 2
#> 
#>           [,1]       [,2]         [,3]         [,4]      [,5]
#> [1,] 0.4319278 0.05845507 0.0001448956 6.578251e-09 0.0000000
#> [2,] 0.0000000 0.00000000 0.0001448956 5.845506e-02 0.4319278
#> 
#> , , 3
#> 
#>             [,1]         [,2] [,3]         [,4]        [,5]
#> [1,] 0.002141284 0.0002897912   NA 0.0000000000 0.000000000
#> [2,] 0.000000000 0.0000000000    0 0.0002897912 0.002141284
#> 
#> , , 4
#> 
#>           [,1]       [,2]         [,3]         [,4]      [,5]
#> [1,] 0.4319278 0.05845507 0.0001448956 6.578251e-09 0.0000000
#> [2,] 0.0000000 0.00000000 0.0001448956 5.845506e-02 0.4319278
#> 
#> , , 5
#> 
#>      [,1]         [,2]        [,3]         [,4]         [,5]
#> [1,]    1 4.319277e-01 0.001070642 4.860706e-08 1.266417e-14
#> [2,]    0 4.860706e-08 0.001070642 4.319277e-01 1.000000e+00
#> 

grid_df <- expand.grid(
  x = velocity_grid$x_grid[1, ],
  y = velocity_grid$x_grid[2, ]
)

plot_df <- data.frame(
  x = grid_df$x,
  y = grid_df$y,
  xend = grid_df$x + c(velocity_grid$v_grid[1, , ]) * 0.2,
  yend = grid_df$y + c(velocity_grid$v_grid[2, , ]) * 0.2
)

ggplot2::ggplot(plot_df) +
  ggplot2::geom_segment(
    ggplot2::aes(x = x, y = y, xend = xend, yend = yend),
    arrow = grid::arrow(length = grid::unit(0.12, "inches")),
    na.rm = TRUE
  ) +
  ggplot2::coord_equal()