R-在可变间隔上计算滚动统计信息的更快方法

Question

我很好奇，是否有人可以提出一种(更快的)方法来在可变的时间间隔(窗口)内计算滚动统计数据(滚动平均值，中位数，百分位数等)。

也就是说，假设给定一个随机计时的观测值(即，不是每日或每周的数据，观测值只有一个时间戳，如滴答数据)，并且假设您希望查看中心统计数据和离散统计数据扩大并收紧计算这些统计信息的时间间隔。

我做了一个简单的for循环来做到这一点。但是它显然运行非常慢(事实上，我认为我的循环仍然在为测试其速度而设置的一小部分数据上运行)。我一直在尝试类似ddply的方法来执行此操作-似乎无法获得每日统计数据-但我似乎无法摆脱困境。

例子:

样本设置:

df <- data.frame(Date = runif(1000,0,30))
df$Price <- I((df$Date)^0.5 * (rnorm(1000,30,4)))
df$Date <- as.Date(df$Date, origin = "1970-01-01")

示例函数(运行很慢，有很多观察结果)

SummaryStats <- function(dataframe, interval){
  # Returns daily simple summary stats, 
  # at varying intervals
  # dataframe is the data frame in question, with Date and Price obs
  # interval is the width of time to be treated as a day

  firstDay <- min(dataframe$Date)
  lastDay  <- max(dataframe$Date)
  result <- data.frame(Date = NULL,
                       Average = NULL,  Median = NULL,
                       Count = NULL,
                       Percentile25 = NULL, Percentile75 = NULL)

  for (Day in firstDay:lastDay){

    dataframe.sub = subset(dataframe,
                Date > (Day - (interval/2))
                & Date < (Day + (interval/2)))

    nu = data.frame(Date = Day, 
                    Average = mean(dataframe.sub$Price),
                    Median = median(dataframe.sub$Price),
                    Count = length(dataframe.sub$Price),
                    P25 = quantile(dataframe.sub$Price, 0.25),
                    P75 = quantile(dataframe.sub$Price, 0.75))

    result = rbind(result,nu)

  }

  return(result)

}

您的建议将受到欢迎!

Answer 1

如果您最关心速度，Rcpp是一个不错的方法。我将使用滚动均值统计数据来举例说明。

基准测试:Rcpp与R

x = sort(runif(25000,0,4*pi))
y = sin(x) + rnorm(length(x),0.5,0.5)
system.time( rollmean_r(x,y,xout=x,width=1.1) )   # ~60 seconds
system.time( rollmean_cpp(x,y,xout=x,width=1.1) ) # ~0.0007 seconds

Rcpp和R函数的代码

cppFunction('
  NumericVector rollmean_cpp( NumericVector x, NumericVector y, 
                              NumericVector xout, double width) {
    double total=0;
    unsigned int n=x.size(), nout=xout.size(), i, ledge=0, redge=0;
    NumericVector out(nout);

    for( i=0; i<nout; i++ ) {
      while( x[ redge ] - xout[i] <= width && redge<n ) 
        total += y[redge++];
      while( xout[i] - x[ ledge ] > width && ledge<n ) 
        total -= y[ledge++];
      if( ledge==redge ) { out[i]=NAN; total=0; continue; }
      out[i] = total / (redge-ledge);
    }
    return out;
  }')

rollmean_r = function(x,y,xout,width) {
  out = numeric(length(xout))
  for( i in seq_along(xout) ) {
    window = x >= (xout[i]-width) & x <= (xout[i]+width)
    out[i] = .Internal(mean( y[window] ))
  }
  return(out)
}

现在要移植 rollmean_cpp。 x和 y是数据。 xout是请求滚动统计的点的向量。 width是滚动窗口的宽度* 2。请注意，滑动窗口末端的索引存储在 ledge和 redge中。这些本质上是指向 x和 y中的各个元素的指针。这些索引对于调用其他采用向量并将开始和结束索引作为输入的C++函数(例如，中位数等)可能非常有益。

对于那些想要“详细”版本的rollmean_cpp进行调试(冗长)的用户:

cppFunction('
  NumericVector rollmean_cpp( NumericVector x, NumericVector y, 
                              NumericVector xout, double width) {

    double total=0, oldtotal=0;
    unsigned int n=x.size(), nout=xout.size(), i, ledge=0, redge=0;
    NumericVector out(nout);


    for( i=0; i<nout; i++ ) {
      Rcout << "Finding window "<< i << " for x=" << xout[i] << "..." << std::endl;
      total = 0;

      // numbers to push into window
      while( x[ redge ] - xout[i] <= width && redge<n ) {
        Rcout << "Adding (x,y) = (" << x[redge] << "," << y[redge] << ")" ;
        Rcout << "; edges=[" << ledge << "," << redge << "]" << std::endl;
        total += y[redge++];
      }

      // numbers to pop off window
      while( xout[i] - x[ ledge ] > width && ledge<n ) {
        Rcout << "Removing (x,y) = (" << x[ledge] << "," << y[ledge] << ")";
        Rcout << "; edges=[" << ledge+1 << "," << redge-1 << "]" << std::endl;
        total -= y[ledge++];
      }
      if(ledge==n) Rcout << " OVER ";
      if( ledge==redge ) {
       Rcout<<" NO DATA IN INTERVAL " << std::endl << std::endl;
       oldtotal=total=0; out[i]=NAN; continue;}

      Rcout << "For interval [" << xout[i]-width << "," <<
               xout[i]+width << "], all points in interval [" << x[ledge] <<
               ", " << x[redge-1] << "]" << std::endl ;
      Rcout << std::endl;

      out[i] = ( oldtotal + total ) / (redge-ledge);
      oldtotal=total+oldtotal;
    }
    return out;
  }')

x = c(1,2,3,6,90,91)
y = c(9,8,7,5.2,2,1)
xout = c(1,2,2,3,6,6.1,13,90,100)
a = rollmean_cpp(x,y,xout=xout,2)
# Finding window 0 for x=1...
# Adding (x,y) = (1,9); edges=[0,0]
# Adding (x,y) = (2,8); edges=[0,1]
# Adding (x,y) = (3,7); edges=[0,2]
# For interval [-1,3], all points in interval [1, 3]
# 
# Finding window 1 for x=2...
# For interval [0,4], all points in interval [1, 3]
# 
# Finding window 2 for x=2...
# For interval [0,4], all points in interval [1, 3]
# 
# Finding window 3 for x=3...
# For interval [1,5], all points in interval [1, 3]
# 
# Finding window 4 for x=6...
# Adding (x,y) = (6,5.2); edges=[0,3]
# Removing (x,y) = (1,9); edges=[1,3]
# Removing (x,y) = (2,8); edges=[2,3]
# Removing (x,y) = (3,7); edges=[3,3]
# For interval [4,8], all points in interval [6, 6]
# 
# Finding window 5 for x=6.1...
# For interval [4.1,8.1], all points in interval [6, 6]
# 
# Finding window 6 for x=13...
# Removing (x,y) = (6,5.2); edges=[4,3]
# NO DATA IN INTERVAL 
# 
# Finding window 7 for x=90...
# Adding (x,y) = (90,2); edges=[4,4]
# Adding (x,y) = (91,1); edges=[4,5]
# For interval [88,92], all points in interval [90, 91]
# 
# Finding window 8 for x=100...
# Removing (x,y) = (90,2); edges=[5,5]
# Removing (x,y) = (91,1); edges=[6,5]
# OVER  NO DATA IN INTERVAL 

print(a)
# [1] 8.0 8.0 8.0 8.0 5.2 5.2 NaN 1.5 NaN