更快地找到向量中的第一个TRUE值

Question

在一个函数中,我经常需要使用如下代码:

which(x==1)[1]
which(x>1)[1]
x[x>10][1]

哪里x是数字向量.summaryRprof()表明我花了80%以上的时间在关系运营商身上.我想知道是否有一个函数只进行比较,直到TRUE达到第一个值来加速我的代码.For循环比上面提供的选项慢.

Answer 1

我不知道有一种纯粹的R方法,所以我写了一个C函数来为quantstrat包做.这个函数是出于特定目的而编写的,所以它并不像我想的那样通用.例如,您可能会注意到它仅适用于实数/双/数字数据,因此请务必Data在调用.firstCross函数之前强制执行该数据.

#include <R.h>
#include <Rinternals.h>

SEXP firstCross(SEXP x, SEXP th, SEXP rel, SEXP start)
{
    int i, int_rel, int_start;
    double *real_x=NULL, real_th;

    if(ncols(x) > 1)
        error("only univariate data allowed");

    /* this currently only works for real x and th arguments
     * support for other types may be added later */
    real_th = asReal(th);
    int_rel = asInteger(rel);
    int_start = asInteger(start)-1;

    switch(int_rel) {
        case 1:  /* >  */
            real_x = REAL(x);
            for(i=int_start; i<nrows(x); i++)
                if(real_x[i] >  real_th)
                    return(ScalarInteger(i+1));
            break;
        case 2:  /* <  */
            real_x = REAL(x);
            for(i=int_start; i<nrows(x); i++)
                if(real_x[i] <  real_th)
                    return(ScalarInteger(i+1));
            break;
        case 3:  /* == */
            real_x = REAL(x);
            for(i=int_start; i<nrows(x); i++)
                if(real_x[i] == real_th)
                    return(ScalarInteger(i+1));
            break;
        case 4:  /* >= */
            real_x = REAL(x);
            for(i=int_start; i<nrows(x); i++)
                if(real_x[i] >= real_th)
                    return(ScalarInteger(i+1));
            break;
        case 5:  /* <= */
            real_x = REAL(x);
            for(i=int_start; i<nrows(x); i++)
                if(real_x[i] <= real_th)
                    return(ScalarInteger(i+1));
            break;
        default:
            error("unsupported relationship operator");
  }
  /* return number of observations if relationship is never TRUE */
  return(ScalarInteger(nrows(x)));
}

这是调用它的R函数:

.firstCross <- function(Data, threshold=0, relationship, start=1) {
    rel <- switch(relationship[1],
            '>'    =  ,
            'gt'   = 1,
            '<'    =  ,
            'lt'   = 2,
            '=='   =  ,
            'eq'   = 3,
            '>='   =  ,
            'gte'  =  ,
            'gteq' =  ,
            'ge'   = 4,
            '<='   =  ,
            'lte'  =  ,
            'lteq' =  ,
            'le'   = 5)
    .Call('firstCross', Data, threshold, rel, start)
}

一些基准测试,只是为了好玩.

> library(quantstrat)
> library(microbenchmark)
> firstCross <- quantstrat:::.firstCross
> set.seed(21)
> x <- rnorm(1e6)
> microbenchmark(which(x > 3)[1], firstCross(x,3,">"), times=10)
Unit: microseconds
                  expr      min       lq    median       uq      max neval
       which(x > 3)[1] 9482.081 9578.072 9597.3870 9690.448 9820.176    10
 firstCross(x, 3, ">")   11.370   11.675   31.9135   34.443   38.614    10
> which(x>3)[1]
[1] 919
> firstCross(x,3,">")
[1] 919

注意,firstCross产生更大的相对加速比越大Data(因为R的关系运算符必须完成比较整个向量).

> x <- rnorm(1e7)
> microbenchmark(which(x > 3)[1], firstCross(x,3,">"), times=10)
Unit: microseconds
                  expr      min        lq    median        uq        max neval
       which(x > 3)[1] 94536.21 94851.944 95799.857 96154.756 113962.794    10
 firstCross(x, 3, ">")     5.08     5.507    25.845    32.164     34.183    10
> which(x>3)[1]
[1] 97
> firstCross(x,3,">")
[1] 97

......如果第一个TRUE值接近向量的末尾,它将不会明显更快.

> microbenchmark(which(x==last(x))[1], firstCross(x,last(x),"eq"),times=10)
Unit: milliseconds
                         expr      min       lq   median       uq       max neval
       which(x == last(x))[1] 92.56311 93.85415 94.38338 98.18422 106.35253    10
 firstCross(x, last(x), "eq") 86.55415 86.70980 86.98269 88.32168  92.97403    10
> which(x==last(x))[1]
[1] 10000000
> firstCross(x,last(x),"eq")
[1] 10000000

Answer 2

Base R分别提供Position和Find用于定位谓词返回真值的第一个索引和值.这些高阶函数在第一次命中后立即返回.

f<-function(x) {
  r<-vector("list",3)
  r[[1]]<-which(x==1)[1]
  r[[2]]<-which(x>1)[1]
  r[[3]]<-x[x>10][1]
  return(r)
}

p<-function(f,b) function(a) f(a,b)
g<-function(x) {
  r<-vector("list",3)
  r[[1]]<-Position(p(`==`,1),x)
  r[[2]]<-Position(p(`>`,1),x)
  r[[3]]<-Find(p(`>`,10),x)
  return(r)
}

相对性能在很大程度上取决于相对于谓词的开销与开销的开销相比较早发现命中的概率Position/Find.

library(microbenchmark)
set.seed(1)
x<-sample(1:100,1e5,replace=TRUE)
microbenchmark(f(x),g(x))

Unit: microseconds
 expr      min        lq     mean    median        uq      max neval cld
 f(x) 5034.283 5410.1205 6313.861 5798.4780 6948.5675 26735.52   100   b
 g(x)  587.463  650.4795 1013.183  734.6375  950.9845 20285.33   100  a

y<-rep(0,1e5)
microbenchmark(f(y),g(y))

Unit: milliseconds
 expr        min         lq       mean     median         uq        max neval cld
 f(y)   3.470179   3.604831   3.791592   3.718752   3.866952   4.831073   100  a 
 g(y) 131.250981 133.687454 137.199230 134.846369 136.193307 177.082128   100   b