问题描述
我正在寻找一个简单的代码,可以模拟网格中的二维随机游走(使用 R
),然后使用 ggplot
绘制数据。
特别是,我对从 2D 网格中的几个位置(5 个点)到方形网格中心的随机游走很感兴趣。仅用于可视化目的。
然后我的想法是用 ggplot
在离散网格(模拟的网格)上绘制结果,可能使用函数 geom_tile
。
对于我可以轻松操作的预先存在的代码,您有什么建议吗?
解决方法
这是一个带有 for
循环的小例子。从这里,您可以简单地调整 X_t
和 Y_t
的定义方式:
Xt = 0; Yt = 0
for (i in 2:1000)
{
Xt[i] = Xt[i-1] + rnorm(1,1)
Yt[i] = Yt[i-1] + rnorm(1,1)
}
df <- data.frame(x = Xt,y = Yt)
ggplot(df,aes(x=x,y=y)) + geom_path() + theme_classic() + coord_fixed(1)
,
编辑----
在与 OP 交谈后,我修改了代码以包含步进概率。这可能导致步行更频繁地静止。在更高的维度中,您需要将 prob
因子调整得更低以补偿更多选项。
最后,我的函数不考虑绝对距离,它只考虑网格上所有维度都在某个步长内的点。例如,假设在位置 c(0,0)
,您可以使用此函数转到 c(1,1)
。但我想这与电网的连通性有关。
如果 OP 只想考虑当前位置 1(距离)内的节点,则使用以下版本的 move_step()
move_step <- function(cur_pos,grid,prob = 0.04,size = 1){
opts <- grid %>%
rowwise() %>%
mutate(across(.fns = ~(.x-.env$cur_pos[[cur_column()]])^2,.names = '{.col}_square_diff')) %>%
filter(sqrt(sum(c_across(ends_with("_square_diff"))))<=.env$size) %>%
select(-ends_with("_square_diff")) %>%
left_join(y = mutate(cur_pos,current = TRUE),by = names(grid))
new_pos <- opts %>%
mutate(weight = case_when(current ~ 1-(prob*(n()-1)),#calculate chance to move,TRUE ~ prob),#in higher dimensions,we may have more places to move
weight = if_else(weight<0,weight)) %>% #thus depending on prob,we may always move.
sample_n(size = 1,weight = weight) %>%
select(-weight,-current)
new_pos
}
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter,lag
#> The following objects are masked from 'package:base':
#>
#> intersect,setdiff,setequal,union
library(ggplot2)
library(gganimate)
move_step <- function(cur_pos,size = 1){
opts <- grid %>%
filter(across(.fns = ~ between(.x,.env$cur_pos[[cur_column()]]-.env$size,.env$cur_pos[[cur_column()]]+.env$size))) %>%
left_join(y = mutate(cur_pos,-current)
new_pos
}
sim_walk <- function(cur_pos,grid_prob = 0.04,steps = 50,size = 1){
iterations <- cur_pos
for(i in seq_len(steps)){
cur_pos <- move_step(cur_pos,prob = grid_prob,size = size)
iterations <- bind_rows(iterations,cur_pos)
}
iterations$i <- 1:nrow(iterations)
iterations
}
origin <- data.frame(x = 0,y =0)
small_grid <- expand.grid(x = -1:1,y = -1:1)
small_walk <- sim_walk(cur_pos = origin,grid = small_grid)
ggplot(small_walk,aes(x,y)) +
geom_path() +
geom_point(color = "red") +
transition_reveal(i) +
labs(title = "Step {frame_along}") +
coord_fixed()
large_grid <- expand.grid(x = -10:10,y = -10:10)
large_walk <- sim_walk(cur_pos = origin,grid = large_grid,steps = 100)
ggplot(large_walk,y)) +
geom_path() +
geom_point(color = "red") +
transition_reveal(i) +
labs(title = "Step {frame_along}") +
xlim(c(-10,10)) + ylim(c(-10,10))+
coord_fixed()
large_walk %>%
count(x,y) %>%
right_join(y = expand.grid(x = -10:10,y = -10:10),by = c("x","y")) %>%
mutate(n = if_else(is.na(n),0L,n)) %>%
ggplot(aes(x,y)) +
geom_tile(aes(fill = n)) +
coord_fixed()
multi_dim_walk <- sim_walk(cur_pos = data.frame(x = 0,y = 0,z = 0),grid = expand.grid(x = -20:20,y = -20:20,z = -20:20),steps = 100,size = 2)
library(cowplot)
plot_grid(
ggplot(multi_dim_walk,y)) + geom_path(),ggplot(multi_dim_walk,z)) + geom_path(),aes(y,z)) + geom_path())
由 reprex package (v1.0.0) 于 2021 年 5 月 6 日创建
,这是使用 Reduce
+ replicate
+ plot
进行 2D 随机游走过程的基本 R 选项
set.seed(0)
plot(
setNames(
data.frame(replicate(
2,Reduce(`+`,rnorm(99),init = 0,accumulate = TRUE)
)),c("X","Y")
),type = "o"
)