传递两个或多个向量来整合函数

Question

我试图整合这个函数，其中 k1 和 m1 是两个输入向量

k_z <- function(z, k1, m1) {
  k_z <- k1 * exp(-z / m1)
}

我改编了this question

的解决方案

integrate(Vectorize(k_z, vectorize.args = "z"), upper = 2, lower = 0, k1 = rnorm(10), m1 = rnorm(10))

但出现以下错误

Error in integrate(Vectorize(k_z, vectorize.args = "z"), upper = 2, lower = 0,  : 
  evaluation of function gave a result of wrong length

我尝试了很多不同的方法都无济于事。我做错了什么？谢谢！

Answer 1

您的函数 k_z 不是标量点“函数”，因为它不会 return 给定一组值的单个值集成函数所需的参数（因为它是一对多的）：让 k_z return 像下面这样的单个值，它将起作用：

k_z <- function(z, k1, m1) {
  sum(k1 * exp(-z / m1)) # return a single value, not a vector of multiple values
}

k_z_vec <- Vectorize(k_z, vectorize.args = "z")
integrate(k_z_vec, upper = 2, lower = 0, k1 = rnorm(10), m1 = rnorm(10))
# -7.338221e+14 with absolute error < 1.4e+07

如果您想计算具有不同值的多个积分向量 k1 和 m1，您可以尝试以下操作：

k_z <- function(z, k1, m1) {
  k1 * exp(-z / m1)
}
k1 <- rnorm(10)
m1 <- rnorm(10)
sapply(1:10, function(x) integrate(k_z, upper = 3, lower = -3, k1=k1[x], m1=m1[x]))

            [,1]         [,2]         [,3]         [,4]         [,5]       [,6]         [,7]         [,8]         [,9]         [,10]       
value        -21.4522     4.330284e+40 19.4474      3.900487e+21 9649111978 2.092415e+57 -34.86148    10103.57     -8.232609    46.35694    
abs.error    2.381672e-13 2.705507e+35 2.159095e-13 1.129735e+17 83251.15   1.180714e+49 3.870402e-13 0.0003484398 9.140032e-14 5.942846e-10
subdivisions 1            4            1            3            2          5            1            1            1            1           
message      "OK"         "OK"         "OK"         "OK"         "OK"       "OK"         "OK"         "OK"         "OK"         "OK"        
call         Expression   Expression   Expression   Expression   Expression Expression   Expression   Expression   Expression   Expression

传递两个或多个向量来整合函数

Pass two or more vectors to integrate function

r

vector

integrate