Solve simple equations with unknown value in right side-CodePudding

I want to find the x values in equation y = 2*x 100 when y varies from 200 to 250. I have the F1 function but it does not work. I don't want to change the structure of equation to (y-100)/2 as the main equation is too complex. any help would be appreciated.

F1 <- function(y){
  y = 2*x 100
  return(x)
}

F1(200:250)

CodePudding user response：

By simply rearranging the formula y = 2 * x 100 to solve for x, we have x = (y - 100)/2, so you could do:

 F1 <- function(y) (y - 100)/2 

F1(200:250)
#>  [1] 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0
#> [14] 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5
#> [27] 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0
#> [40] 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0

And check this works by feeding these back in to our original equation, with the above numbers given as the values of x. This should return 200:250

x <- F1(200:250)
 
2 * x   100
#>  [1] 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
#> [17] 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231
#> [33] 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247
#> [49] 248 249 250

For a more general solution, suppose we have your original function:

F0 <- function(x) x * 2   100

We can define a solver that reverses the function to find the x value that gives a particular value of y by using uniroot.

find_x_for_given_y <- function(y, func) {
  
  sapply(y, function(y_i) {
    uniroot(function(x) func(x) - y_i, c(-1e6, 1e6))$root
  })
}

So, to find the values which, when passed to F0 give the values 200:250, we can do:

find_x_for_given_y(200:250, F0)
#>  [1] 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0
#> [14] 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5
#> [27] 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0
#> [40] 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0

Of course, this is the same as above, but is at least generalized to accept any function of one variable.

CodePudding user response：

You could use uniroot() to search for the root of a function.

F1 <- function(x, y) {
  2 * x   100 - y
}

sapply(200:250, \(y) uniroot(F1, c(0, 1), y = y, extendInt = "yes")$root)

#  [1] 50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0
# [18] 58.5 59.0 59.5 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5
# [35] 67.0 67.5 68.0 68.5 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0