Finding root of an equation by using value of three different matrices-CodePudding

I have three matrices named a_b , pop and event

df<- data_frame(a=c(-5.8221,-6.4678,-6.1213,-5.4518,-5.3527,-5.3517,-5.3169),
                b= c(.0234,.0199,.0162,.0151,.0148,.0138,.0123))

a_b<-as.matrix(df[1:7, 1:2])

df1<- data_frame("2000" =c(716209.27,642504.69,644640.11,632239.35,552437.34,554395.34,539358.87),
                "2005" = c(653040.76,637752.95,651635.40,647572.55,641183.99,570938.83,554092.75),
                "2010" =c(5643.6,876123,665412.5,98643,89012,776321,8863))
               

pop<-as.matrix(df1[1:7, 1:3])

df2<- data_frame("2000"=c(9968.50418,2605.16992,2937.01261,4286.23376,5718.80904,4843.19769,5077.52440),
                 "2005"= c(6037.16994,2336.72681,2391.55031,4085.62207,5000.77218,4425.02331,5097.25052),
                 "2010" =c(19123.45,87765.54,102345.44,98000,12396,90076,10133))
              

event <-as.matrix(df2[1:7, 1:3])

Using following function, I want to apply uniroot to find root of each row of event and pop. a and b in a_b are constant for each column of event and pop .

fun<-function(x) (event - (exp(a b* x )* pop))
u1 <- uniroot(fun, c(-10000,10000),extendInt="yes", trace=1)$root

My problem is how should I apply my function to the corresponding value in a, b , event and pop. Because I have three years, my expected output would be like this:

2000    2005    2010
66.1349 48.6493 300.9612
48.2373 43.1457 209.395
45.0617 31.7133 262.299
30.3271 25.5657 360.6132
52.8459 33.7145 228.4664
44.3041 35.6299 231.7237
52.9546 51.0787 443.1554

CodePudding user response：

This is probably not the most efficient implementation, but it only took my computer about 0.03 seconds for the seven rows. I loop through all the different parameter options and use uniroot() each time. The output matches your example output reasonably well.

df<- data.frame(a=c(-5.8221,-6.4678,-6.1213,-5.4518,-5.3527,-5.3517,-5.3169),
                b= c(.0234,.0199,.0162,.0151,.0148,.0138,.0123))

a_b<-as.matrix(df[1:7, 1:2])

df1<- data.frame("2000" =c(716209.27,642504.69,644640.11,632239.35,552437.34,554395.34,539358.87),
                 "2005" = c(653040.76,637752.95,651635.40,647572.55,641183.99,570938.83,554092.75),
                 "2010" =c(5643.6,876123,665412.5,98643,89012,776321,8863))


pop<-as.matrix(df1[1:7, 1:3])

df2<- data.frame("2000"=c(9968.50418,2605.16992,2937.01261,4286.23376,5718.80904,4843.19769,5077.52440),
                 "2005"= c(6037.16994,2336.72681,2391.55031,4085.62207,5000.77218,4425.02331,5097.25052),
                 "2010" =c(19123.45,87765.54,102345.44,98000,12396,90076,10133))


event <-as.matrix(df2[1:7, 1:3])

fun<-function(x) (event_t - (exp(a_t b_t* x )* pop_t))

output <- data.frame(matrix(ncol=3,nrow=0, dimnames=list(NULL, c("2000", "2005", "2010"))))
start_time <- Sys.time()
for(i in 1:nrow(pop)){
  row_vals = rep(NA,3)
  for(j in 1:ncol(pop)){
    a_t=a_b[i,1]
    b_t=a_b[i,2]
    event_t=event[i,j]
    pop_t=pop[i,j]
    u1 <- uniroot(fun,interval=c(-10000,10000),extendInt="yes", trace=1)$root
    row_vals[j] <- u1
  }
  output <- rbind(output, row_vals)
}
end_time <- Sys.time()

print(end_time - start_time)

names(output) <- c("2000", "2005", "2010")
output

The output is:

      2000     2005     2010
1 66.13496 48.64939 300.9612
2 48.23738 43.14574 209.3951
3 45.06177 31.71337 262.2992
4 30.32718 25.56577 360.6133
5 52.84598 33.71459 228.4664
6 44.30414 35.62997 231.7237
7 52.95467 51.07877 443.1555