R語言模擬疫情傳播圖RVirusBroadcast展示疫情數(shù)據(jù)
更新時間：2022年02月18日 14:01:55 作者：hxj7
本文用RVirusBroadcast展示模擬的疫情數(shù)據(jù)，讓R語言模擬疫情傳播圖來告訴你為什么還不到出門的時候，有需要的朋友可以借鑒參考下，希望能夠有所幫助
前言
前幾天微博的一個熱搜主題是**“計算機仿真程序告訴你為什么現(xiàn)在還沒到出門的時候?。。?rdquo;**，該視頻用模擬的疫情數(shù)據(jù)告訴大家“不要隨便出門（宅在家）”對戰(zhàn)勝疫情很重要，生動形象，廣受好評。
所用的程序叫VirusBroadcast，源碼已經(jīng)公開，是用Java寫的。鑒于畫圖是R語言的優(yōu)勢，所以筆者在讀過源碼后，寫了一個VirusBroadcast程序的R語言版本，暫且叫做RVirusBroadcast。與VirusBroadcast相比，RVirusBroadcast所用的模型和邏輯大體不變，只是在少許細節(jié)上做了修改。
（為了防止上面的超鏈接被過濾掉而打不開，文末也放上了明文鏈接）
效果展示
下面兩段視頻是RVirusBroadcast用模擬的數(shù)據(jù)展示的效果，由于筆者的電腦性能實在一般，所以暫時只模擬了30天的數(shù)據(jù)。請再次注意下面兩段視頻的數(shù)據(jù)是模擬生成的，純屬虛構(gòu)，不具有現(xiàn)實意義，僅供電腦模擬實驗所用。
其他條件不變，當人們隨意移動時，病毒傳播迅速，疫情很難控制
其他條件不變，當人們控制自己的移動時，病毒傳播緩慢，疫情逐漸得到控制
小結(jié)
誠如VirusBroadcast的作者所說，現(xiàn)在的模型是一個很簡單的模型，所用的數(shù)據(jù)也是模擬生成的，還需優(yōu)化改進。朋友們?nèi)绻信d趣，可以自行查閱復(fù)制下文中的R代碼，自由修改。
參考
[1] “計算機仿真程序告訴你為什么現(xiàn)在還沒到出門的時候” 原視頻地址：
https://www.bilibili.com/video/av86478875?spm_id_from=333.788.b_765f64657363.1
附錄：RVirusBroadcast代碼
###name:RVirusBroadcast
###author:hxj7(hxj5hxj5@126.com)
###version:202002010
###note:本程序是"VirusBroadcast (in Java)"的R版本
### VirusBroadcast (in Java) 項目鏈接：
### https://github.com/KikiLetGo/VirusBroadcast/tree/master/src
library(tibble)
library(dplyr)
########## 模擬參數(shù) ##########
ORIGINAL_COUNT <- 50 # 初始感染數(shù)量
BROAD_RATE <- 0.8 # 傳播率
SHADOW_TIME <- 140 # 潛伏時間，14天為140
HOSPITAL_RECEIVE_TIME <- 10 # 醫(yī)院收治響應(yīng)時間
BED_COUNT <- 1000 # 醫(yī)院床位
MOVE_WISH_MU <- -0.99 # 流動意向平均值，建議調(diào)整范圍：[-0.99,0.99];
# -0.99 人群流動最慢速率，甚至完全控制疫情傳播;
# 0.99為人群流動最快速率, 可導致全城感染
CITY_PERSON_SIZE <- 5000 # 城市總?cè)丝跀?shù)量
FATALITY_RATE <- 0.02 # 病死率，根據(jù)2月6日數(shù)據(jù)估算（病死數(shù)/確診數(shù)）為0.02
SHADOW_TIME_SIGMA <- 25 # 潛伏時間方差
CURED_TIME <- 50 # 治愈時間均值，從入院開始計時
CURED_SIGMA <- 10 # 治愈時間標準差
DIE_TIME <- 300 # 死亡時間均值，30天，從發(fā)?。ù_診）時開始計時
DIE_SIGMA <- 50 # 死亡時間標準差
CITY_WIDTH <- 700 # 城市大小即窗口邊界，限制不允許出城
CITY_HEIGHT <- 800
MAX_TRY <- 300 # 最大模擬次數(shù)，300代表30天
########## 生成人群點，用不同顏色代表不同健康狀態(tài)。 ##########
# 用正態(tài)分布刻畫人群點的分布
CITY_CENTERX <- 400 # x軸的mu值
CITY_CENTERY <- 400
PERSON_DIST_X_SIGMA <- 100 # x軸的sigma值
PERSON_DIST_Y_SIGMA <- 100
# 市民狀態(tài)應(yīng)該需要細分，雖然有的狀態(tài)暫未納入模擬，但是細分狀態(tài)應(yīng)該保留
STATE_NORMAL <- 0 # 正常人，未感染的健康人
STATE_SUSPECTED <- STATE_NORMAL + 1 # 有暴露感染風險
STATE_SHADOW <- STATE_SUSPECTED + 1 # 潛伏期
STATE_CONFIRMED <- STATE_SHADOW + 1 # 發(fā)病且已確診為感染病人
STATE_FREEZE <- STATE_CONFIRMED + 1 # 隔離治療，禁止位移
STATE_DEATH <- STATE_FREEZE + 1 # 病死者
STATE_CURED <- STATE_DEATH + 1 # 治愈數(shù)量用于計算治愈出院后歸還床位數(shù)量，該狀態(tài)是否存續(xù)待定
worldtime <- 0
NTRY_PER_DAY <- 10 # 一天模擬幾次
getday <- function(t) (t - 1) %/% NTRY_PER_DAY + 1
# 生成人群數(shù)據(jù)
format_coord <- function(coord, boundary) {
if (coord < 0) return(runif(1, 0, 10))
else if (coord > boundary) return(runif(1, boundary - 10, boundary))
else return(coord)
}
set.seed(123)
people <- tibble(
id = 1:CITY_PERSON_SIZE,
x = sapply(rnorm(CITY_PERSON_SIZE, CITY_CENTERX, PERSON_DIST_X_SIGMA),
format_coord, boundary = CITY_WIDTH), # (x, y) 為人群點坐標
y = sapply(rnorm(CITY_PERSON_SIZE, CITY_CENTERY, PERSON_DIST_Y_SIGMA),
format_coord, boundary = CITY_HEIGHT),
state = STATE_NORMAL, # 健康狀態(tài)
infected_time = 0, # 感染時刻
confirmed_time = 0, # 確診時刻
freeze_time = 0, # 隔離時刻
cured_moment = 0, # 痊愈時刻，為0代表不確定
die_moment = 0 # 死亡時刻，為0代表未確定，-1代表不會病死
) %>%
mutate(tx = rnorm(CITY_PERSON_SIZE, x, PERSON_DIST_X_SIGMA), # target x
ty = rnorm(CITY_PERSON_SIZE, y, PERSON_DIST_Y_SIGMA),
has_target = T, is_arrived = F)
# 隨機選擇初始感染者
peop_id <- sample(people$id, ORIGINAL_COUNT)
people$state[peop_id] <- STATE_SHADOW
people$infected_time[peop_id] <- worldtime
people$confirmed_time[peop_id] <- worldtime +
max(rnorm(length(peop_id), SHADOW_TIME / 2, SHADOW_TIME_SIGMA), 0)
########## 生成床位點 ##########
HOSPITAL_X <- 720 # 第一張床位的x坐標
HOSPITAL_Y <- 80 # 第一張床位的y坐標
NBED_PER_COLUMN <- 100 # 醫(yī)院每一列有多少張床位
BED_ROW_SPACE <- 6 # 一行中床位的間距
BED_COLUMN_SPACE <- 6 # 一列中床位的間距
bed_ncolumn <- ceiling(BED_COUNT / NBED_PER_COLUMN)
hosp_beds <- tibble(id = 1, x = 0, y = 0, is_empty = T, state = STATE_NORMAL) %>%
slice(-1)
if (BED_COUNT > 0) {
hosp_beds <- tibble(
id = 1:BED_COUNT,
x = HOSPITAL_X + rep(((1:bed_ncolumn) - 1) * BED_ROW_SPACE,
each = NBED_PER_COLUMN)[1:BED_COUNT],
y = HOSPITAL_Y + 10 - BED_COLUMN_SPACE +
rep((1:NBED_PER_COLUMN) * BED_COLUMN_SPACE, bed_ncolumn)[1:BED_COUNT],
is_empty = T,
person_id = 0 # 占用床位的患者的序號，床位為空時為0
)
}
########## 準備畫圖的數(shù)據(jù) ##########
npeople_total <- CITY_PERSON_SIZE
npeople_shadow <- ORIGINAL_COUNT
npeople_confirmed <- npeople_freeze <- npeople_cured <- npeople_death <- 0
nbed_need <- 0
########## 畫出初始數(shù)據(jù) ##########
# 設(shè)置畫圖參數(shù)
person_color <- data.frame( # 不同健康狀態(tài)的顏色不同
label = c("健康", "潛伏", "確診", "隔離", "治愈", "死亡"),
state = c(STATE_NORMAL, STATE_SHADOW, STATE_CONFIRMED, STATE_FREEZE,
STATE_CURED, STATE_DEATH),
color = c(
"lightgreen", # 健康
"#EEEE00", # 潛伏期
"red", # 確診
"#FFC0CB", # 隔離
"green", # 治愈
"black" # 死亡
), stringsAsFactors = F
)
bed_color <- data.frame(
is_empty = c(T, F), color = c("#F8F8FF", "#FFC0CB"), stringsAsFactors = F
)
x11(width = 5, height = 7, xpos = 0, ypos = 0, title = "人群變化模擬")
window_hist <- dev.cur()
x11(width = 7, height = 7, xpos = 460, ypos = 0, title = "疫情傳播模擬")
window_scatter <- dev.cur()
max_plot_x <- ifelse(BED_COUNT > 0, max(hosp_beds$x), CITY_WIDTH) + 10
# 疫情傳播模擬散點圖
dev.set(window_scatter)
plot(x = people$x, y = people$y, cex = .8, pch = 20, xlab = NA, ylab = NA,
xlim = c(5, max_plot_x), xaxt = "n", yaxt = "n", bty = "n", main = "疫情傳播模擬",
sub = paste0("世界時間第 ", getday(worldtime), " 天"),
col = (people %>% left_join(person_color, by = "state") %>%
select(color))$color)
points(x = hosp_beds$x, y = hosp_beds$y, cex = .8, pch = 20,
col = (hosp_beds %>% left_join(bed_color, by = "is_empty") %>%
select(color))$color)
rect(HOSPITAL_X - BED_ROW_SPACE / 2, HOSPITAL_Y + 10 - BED_COLUMN_SPACE,
max(hosp_beds$x) + BED_ROW_SPACE / 2, max(hosp_beds$y + BED_COLUMN_SPACE))
legend(x = 150, y = -30, legend = person_color$label, col = person_color$color,
pch = 20, horiz = T, bty = "n", xpd = T)
# 人群變化模擬條形圖
dev.set(window_hist)
bp_data <- c(npeople_death, npeople_cured, nbed_need, npeople_freeze,
npeople_confirmed, npeople_shadow)
bp_color <- c("black", "green", "#FFE4E1", "#FFC0CB", "red", "#EEEE00")
bp_labels <- c("死亡", "治愈", "不足\n床位", "隔離", "累計\n確診", "潛伏")
bp <- barplot(bp_data, horiz = T, border = NA, col = bp_color,
xlim = c(0, CITY_PERSON_SIZE * 1), main = "人群變化模擬",
sub = paste0("世界時間第 ", getday(worldtime), " 天"))
abline(v = BED_COUNT, col = "gray", lty = 3)
abline(v = CITY_PERSON_SIZE, col = "gray", lty = 1)
text(x = -350, y = bp, labels = bp_labels, xpd = T)
text(x = bp_data + CITY_PERSON_SIZE / 15, y = bp, xpd = T,
labels = ifelse(bp_data > 0, bp_data, ""))
legend(x = 300, y = -.6, legend = c("總床位數(shù)", "城市總?cè)丝?), col = "gray",
lty = c(3, 1), bty = "n", horiz = T, xpd = T)
Sys.sleep(5) # 手動調(diào)整窗口大小
########## 更新人群數(shù)據(jù) ##########
# 市民流動意愿以及移動位置參數(shù)174 MOVE_WISH_SIGMA <- 1
MOVE_DIST_SIGMA <- 50
SAFE_DIST <- 2 # 安全距離
worldtime <- worldtime + 1
get_min_dist <- function(person, peop) { # 一個人和一群人之間的最小距離
min(sqrt((person["x"] - peop$x) ^ 2 + (person["y"] - peop$y) ^ 2))
}
for (i in 1:MAX_TRY) {
# 如果已經(jīng)隔離或者死亡了，就不需要處理了
#
# 處理已經(jīng)確診的感染者（即患者）
peop_id <- people$id[people$state == STATE_CONFIRMED &
people$die_moment == 0]
if ((npeop <- length(peop_id)) > 0) {
people$die_moment[peop_id] <- ifelse(
runif(npeop, 0, 1) < FATALITY_RATE, # 用均勻分布模擬確診患者是否會死亡
people$confirmed_time + max(rnorm(npeop, DIE_TIME, DIE_SIGMA), 0), # 發(fā)病后確定死亡時刻
-1 # 逃過了死神的魔爪
)
}
# 如果患者已經(jīng)確診，且（世界時刻-確診時刻）大于醫(yī)院響應(yīng)時間，
# 即醫(yī)院準備好病床了，可以抬走了
peop_id <- people$id[people$state == STATE_CONFIRMED &
worldtime - people$confirmed_time >= HOSPITAL_RECEIVE_TIME]
if ((npeop <- length(peop_id)) > 0) {
if ((nbed_empty <- sum(hosp_beds$is_empty)) > 0) { # 有空余床位
nbed_use <- min(npeop, nbed_empty)
bed_id <- hosp_beds$id[hosp_beds$is_empty][1:nbed_use]
# 更新患者信息
peop_id2 <- sample(peop_id, nbed_use) # 這里是隨機選擇，理論上應(yīng)該按癥狀輕重
people$x[peop_id2] <- hosp_beds$x[bed_id]
people$y[peop_id2] <- hosp_beds$y[bed_id]
people$state[peop_id2] <- STATE_FREEZE
people$freeze_time[peop_id2] <- worldtime
# 更新床位信息
hosp_beds$is_empty[bed_id] <- F
hosp_beds$person_id[bed_id] <- peop_id2
}
}
# TODO 需要確定一個變量用于治愈時長。
# 為了說明問題，暫時用一個正態(tài)分布模擬治愈時長并且假定治愈的人不會再被感染
peop_id <- people$id[people$state == STATE_FREEZE &
people$cured_moment == 0]
if ((npeop <- length(peop_id)) > 0) { # 正態(tài)分布模擬治愈時間
people$cured_moment[peop_id] <- people$freeze_time[peop_id] +
max(rnorm(npeop, CURED_TIME, CURED_SIGMA), 0)
}
peop_id <- people$id[people$state == STATE_FREEZE & people$cured_moment > 0 &
worldtime >= people$cured_moment]
if ((npeop <- length(peop_id)) > 0) { # 歸還床位
people$state[peop_id] <- STATE_CURED
hosp_beds$is_empty[! hosp_beds$is_empty & hosp_beds$person_id %in% peop_id] <- T
people$x[peop_id] <- sapply(rnorm(npeop, CITY_CENTERX, PERSON_DIST_X_SIGMA),
format_coord, boundary = CITY_WIDTH) # (x, y) 為人群點坐標
people$y[peop_id] <- sapply(rnorm(npeop, CITY_CENTERY, PERSON_DIST_Y_SIGMA),
format_coord, boundary = CITY_HEIGHT)
people$tx[peop_id] <- rnorm(npeop, people$x[peop_id], PERSON_DIST_X_SIGMA)
people$ty[peop_id] <- rnorm(npeop, people$y[peop_id], PERSON_DIST_Y_SIGMA)
people$has_target[peop_id] <- T
people$is_arrived[peop_id] <- F
}
# 處理病死者
peop_id <- people$id[people$state %in% c(STATE_CONFIRMED, STATE_FREEZE) &
worldtime >= people$die_moment & people$die_moment > 0]
if (length(peop_id) > 0) { # 歸還床位
people$state[peop_id] <- STATE_DEATH
hosp_beds$is_empty[! hosp_beds$is_empty & hosp_beds$person_id %in% peop_id] <- T
}
# 處理發(fā)病的潛伏期感染者
peop_id <- people$id[people$state == STATE_SHADOW &
worldtime >= people$confirmed_time]
if ((npeop <- length(peop_id)) > 0) {
people$state[peop_id] <- STATE_CONFIRMED # 潛伏者發(fā)病
}
# 處理未隔離者的移動問題
peop_id <- people$id[
! people$state %in% c(STATE_FREEZE, STATE_DEATH) &
rnorm(CITY_PERSON_SIZE, MOVE_WISH_MU, MOVE_WISH_SIGMA) > 0] # 流動意愿
if ((npeop <- length(peop_id)) > 0) { # 正態(tài)分布模擬要移動到的目標點
pp_id <- peop_id[! people$has_target[peop_id] | people$is_arrived[peop_id]]
if ((npp <- length(pp_id)) > 0) {
people$tx[pp_id] <- rnorm(npp, people$tx[pp_id], PERSON_DIST_X_SIGMA)
people$ty[pp_id] <- rnorm(npp, people$ty[pp_id], PERSON_DIST_Y_SIGMA)
people$has_target[pp_id] <- T
people$is_arrived[pp_id] <- F
}
# 計算運動位移262 dx <- people$tx[peop_id] - people$x[peop_id]
dy <- people$ty[peop_id] - people$y[peop_id]
move_dist <- sqrt(dx ^ 2 + dy ^ 2)
people$is_arrived[peop_id][move_dist < 1] <- T # 判斷是否到達目標點266 pp_id <- peop_id[move_dist >= 1]
if ((npp <- length(pp_id)) > 0) {
udx <- sign(dx[move_dist >= 1]) # x軸運動方向269 udy <- sign(dy[move_dist >= 1])
# 是否到了邊界
pid_x <- (1:npp)[people$x[pp_id] + udx < 0 | people$x[pp_id] + udx > CITY_WIDTH]
pid_y <- (1:npp)[people$y[pp_id] + udy < 0 | people$y[pp_id] + udy > CITY_HEIGHT]
# 更新到了邊界的點的信息
people$x[pp_id[pid_x]] <- people$x[pp_id[pid_x]] - udx[pid_x]
people$y[pp_id[pid_y]] <- people$y[pp_id[pid_y]] - udy[pid_y]
people$has_target[unique(c(pp_id[pid_x], pp_id[pid_y]))] <- F
# 更新沒有到邊界的點的信息278 people$x[pp_id[! pp_id %in% pid_x]] <- people$x[pp_id[! pp_id %in% pid_x]] +
udx[! pp_id %in% pid_x]
people$y[pp_id[! pp_id %in% pid_y]] <- people$y[pp_id[! pp_id %in% pid_y]] +
udy[! pp_id %in% pid_y]
}
}
# 處理健康人被感染的問題
# 通過一個隨機幸運值和安全距離決定感染其他人286 normal_peop_id <- people$id[people$state == STATE_NORMAL]
other_peop_id <- people$id[! people$state %in% c(STATE_NORMAL, STATE_CURED)]
if (length(normal_peop_id) > 0) {
normal_other_dist <- apply(people[normal_peop_id, ], 1, get_min_dist,
peop = people[other_peop_id, ])
normal2other_id <- normal_peop_id[normal_other_dist < SAFE_DIST &
runif(length(normal_peop_id), 0, 1) < BROAD_RATE]
if ((n2other <- length(normal2other_id)) > 0) {
people$state[normal2other_id] <- STATE_SHADOW
people$infected_time[normal2other_id] <- worldtime
people$confirmed_time[normal2other_id] <- worldtime +
max(rnorm(n2other, SHADOW_TIME / 2, SHADOW_TIME_SIGMA), 0)
}
}
# 畫出更新后的數(shù)據(jù)
npeople_confirmed <- sum(people$state >= STATE_CONFIRMED)
npeople_death <- sum(people$state == STATE_DEATH)
npeople_freeze <- sum(people$state == STATE_FREEZE)
npeople_shadow <- sum(people$state == STATE_SHADOW)
npeople_cured <- sum(people$state == STATE_CURED)
nbed_need <- npeople_confirmed - npeople_cured - npeople_death - BED_COUNT
nbed_need <- ifelse(nbed_need > 0, nbed_need, 0) # 不足病床數(shù)
# 疫情傳播模擬散點圖
dev.set(window_scatter)
plot(x = people$x, y = people$y, cex = .8, pch = 20, xlab = NA, ylab = NA,
xlim = c(5, max_plot_x), xaxt = "n", yaxt = "n", bty = "n", main = "疫情傳播模擬",
sub = paste0("世界時間第 ", getday(worldtime), " 天"),
col = (people %>% left_join(person_color, by = "state") %>%
select(color))$color)
points(x = hosp_beds$x, y = hosp_beds$y, cex = .8, pch = 20,
col = (hosp_beds %>% left_join(bed_color, by = "is_empty") %>%
select(color))$color)
rect(HOSPITAL_X - BED_ROW_SPACE / 2, HOSPITAL_Y + 10 - BED_COLUMN_SPACE,
max(hosp_beds$x) + BED_ROW_SPACE / 2, max(hosp_beds$y + BED_COLUMN_SPACE))
legend(x = 150, y = -30, legend = person_color$label, col = person_color$color,
pch = 20, horiz = T, bty = "n", xpd = T)
# 人群變化模擬條形圖
dev.set(window_hist)
bp_data <- c(npeople_death, npeople_cured, nbed_need, npeople_freeze,
npeople_confirmed, npeople_shadow)
bp <- barplot(bp_data, horiz = T, border = NA, col = bp_color,
xlim = c(0, CITY_PERSON_SIZE * 1), main = "人群變化模擬",
sub = paste0("世界時間第 ", getday(worldtime), " 天"))
abline(v = BED_COUNT, col = "gray", lty = 3)
abline(v = CITY_PERSON_SIZE, col = "gray", lty = 1)
text(x = -350, y = bp, labels = bp_labels, xpd = T)
text(x = bp_data + CITY_PERSON_SIZE / 15, y = bp, xpd = T,
labels = ifelse(bp_data > 0, bp_data, ""))
legend(x = 300, y = -.6, legend = c("總床位數(shù)", "城市總?cè)丝?), col = "gray",
lty = c(3, 1), bty = "n", horiz = T, xpd = T)
# 更新世界時間
worldtime <- worldtime + 1
}
以上就是R語言模擬疫情傳播圖告訴你為什么還沒到出門的時候的詳細內(nèi)容，更多關(guān)于R語言模擬疫情傳播圖的資料請關(guān)注腳本之家其它相關(guān)文章！
相關(guān)文章
這篇文章主要介紹了R語言strsplit函數(shù)用法深入詳解，代碼實例講解的很清晰，有感興趣的同學可以研究下2021-03-03
這篇文章主要介紹了R語言時間序列TAR閾值自回歸模型,本文通過實例代碼給大家介紹的非常詳細，對大家的學習或工作具有一定的參考借鑒價值，需要的朋友可以參考下2021-03-03
在本篇文章里小編給大家整理的是一篇關(guān)于R語言操作XML文件實例分析，有興趣的朋友們可以跟著學習下。2021-05-05
R語言 實現(xiàn)data.frame 分組計數(shù)、求和等
這篇文章主要介紹了R語言 實現(xiàn)data.frame 分組計數(shù)、求和等操作，具有很好的參考價值，希望對大家有所幫助。一起跟隨小編過來看看吧2021-03-03
主成分分析（Principal?Component?Analysis，PCA）是一種無監(jiān)督的數(shù)據(jù)降維方法，通過主成分分析可以盡可能保留下具備區(qū)分性的低維數(shù)據(jù)特征。本文將用R語言實現(xiàn)PCA主成分分析圖，需要的可以參考一下2022-04-04
這篇文章主要介紹了R語言 數(shù)據(jù)集行列互換的技巧分享，具有很好的參考價值，希望對大家有所幫助。一起跟隨小編過來看看吧2021-03-03
本文主要介紹了R語言非線性模型的實現(xiàn)，文中通過示例代碼介紹的非常詳細，具有一定的參考價值，感興趣的小伙伴們可以參考一下2021-08-08
R語言-進行數(shù)據(jù)的重新編碼(recode)操作
這篇文章主要介紹了R語言-進行數(shù)據(jù)的重新編碼(recode)操作，具有很好的參考價值，希望對大家有所幫助。一起跟隨小編過來看看吧2021-04-04
在本篇文章里小編給大家整理的是一篇關(guān)于R語言中時間序列分析淺析內(nèi)容，有需要的朋友們跟著學習下。2021-05-05
在本篇文章里小編給大家整理的是一篇關(guān)于R語言向量知識點及實例講解內(nèi)容，有興趣的朋友們可以學習下。2021-03-03