class: center, middle # Some Miscellaneous Topics ## Introductory Computer Programming ### Deepayan Sarkar <h1 onclick="document.documentElement.requestFullscreen();" style="cursor: pointer;"> <svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-arrows-fullscreen" viewBox="0 0 16 16"> <path fill-rule="evenodd" d="M5.828 10.172a.5.5 0 0 0-.707 0l-4.096 4.096V11.5a.5.5 0 0 0-1 0v3.975a.5.5 0 0 0 .5.5H4.5a.5.5 0 0 0 0-1H1.732l4.096-4.096a.5.5 0 0 0 0-.707zm4.344 0a.5.5 0 0 1 .707 0l4.096 4.096V11.5a.5.5 0 1 1 1 0v3.975a.5.5 0 0 1-.5.5H11.5a.5.5 0 0 1 0-1h2.768l-4.096-4.096a.5.5 0 0 1 0-.707zm0-4.344a.5.5 0 0 0 .707 0l4.096-4.096V4.5a.5.5 0 1 0 1 0V.525a.5.5 0 0 0-.5-.5H11.5a.5.5 0 0 0 0 1h2.768l-4.096 4.096a.5.5 0 0 0 0 .707zm-4.344 0a.5.5 0 0 1-.707 0L1.025 1.732V4.5a.5.5 0 0 1-1 0V.525a.5.5 0 0 1 .5-.5H4.5a.5.5 0 0 1 0 1H1.732l4.096 4.096a.5.5 0 0 1 0 .707z"/> </svg> </h1> --- # Some miscellaneous topics * Matrices and arrays: construction and operations * Replacement functions * `do.call()` --- layout: true # Matrix construction --- * `matrix(data, nrow, ncol)` : data + dimension ```r matrix(month.abb, 3, 4) ``` ``` [,1] [,2] [,3] [,4] [1,] "Jan" "Apr" "Jul" "Oct" [2,] "Feb" "May" "Aug" "Nov" [3,] "Mar" "Jun" "Sep" "Dec" ``` ```r matrix(month.abb, 3, 4, byrow = TRUE) ``` ``` [,1] [,2] [,3] [,4] [1,] "Jan" "Feb" "Mar" "Apr" [2,] "May" "Jun" "Jul" "Aug" [3,] "Sep" "Oct" "Nov" "Dec" ``` * `array(data, dim)` similarly allows construction of general arrays --- * `rbind(...)` : construct matrix by combining rows * `cbind(...)` : construct matrix by combining columns .scrollable400[ ```r X <- with(mtcars, cbind(Int = 1, am = am, wt = wt)) # design matrix X ``` ``` Int am wt [1,] 1 1 2.620 [2,] 1 1 2.875 [3,] 1 1 2.320 [4,] 1 0 3.215 [5,] 1 0 3.440 [6,] 1 0 3.460 [7,] 1 0 3.570 [8,] 1 0 3.190 [9,] 1 0 3.150 [10,] 1 0 3.440 [11,] 1 0 3.440 [12,] 1 0 4.070 [13,] 1 0 3.730 [14,] 1 0 3.780 [15,] 1 0 5.250 [16,] 1 0 5.424 [17,] 1 0 5.345 [18,] 1 1 2.200 [19,] 1 1 1.615 [20,] 1 1 1.835 [21,] 1 0 2.465 [22,] 1 0 3.520 [23,] 1 0 3.435 [24,] 1 0 3.840 [25,] 1 0 3.845 [26,] 1 1 1.935 [27,] 1 1 2.140 [28,] 1 1 1.513 [29,] 1 1 3.170 [30,] 1 1 2.770 [31,] 1 1 3.570 [32,] 1 1 2.780 ``` ] --- layout: true # Matrix operations --- * `t(x)` : transpose of matrix * `aperm(x, perm)` : general array permutation * `a * b` : element-wise multiplication * `a %*% b` : matrix multiplication * `crossprod(x)` : More efficient version of `t(x) %*% x` * `crossprod(x, y)` : More efficient version of `t(x) %*% y` * `tcrossprod(x, y)`: Similar version of `x %*% t(y)` --- ```r t(X) %*% X ``` ``` Int am wt Int 32.000 13.000 102.9520 am 13.000 13.000 31.3430 wt 102.952 31.343 360.9011 ``` ```r crossprod(X) ``` ``` Int am wt Int 32.000 13.000 102.9520 am 13.000 13.000 31.3430 wt 102.952 31.343 360.9011 ``` --- * `solve(A, b)` : solve system of linear equations $Ax = b$ ```r y <- mtcars$mpg solve(crossprod(X), crossprod(X, y)) ``` ``` [,1] Int 37.32155131 am -0.02361522 wt -5.35281145 ``` * Compare with ```r coef(lm(mpg ~ 1 + am + wt, data = mtcars)) ``` ``` (Intercept) am wt 37.32155131 -0.02361522 -5.35281145 ``` --- * `lm()` is more numerically efficient (it does not actually compute `crossprod(X)`) * It also handles factor (categorical) variables through its formula interface * The `model.matrix()` function computes just the design matrix without fitting the model --- layout: true # Replacement functions --- * We have seen several examples of the form: ```r x[i] <- value attr(x, "name") <- value colnames(x) <- value ``` * All these calls have a "complex" expression on the LHS of the assignment * These are known as _replacement functions_ -- * These are very natural once you get used to them * However, they are somewhat unusual, and we should be aware of why they are needed * The main reason is that R functions are not allowed to _modify_ their arguments --- * Example: setting names ```r d <- data.frame(1, mtcars$wt, mtcars$am) names(d) ``` ``` [1] "X1" "mtcars.wt" "mtcars.am" ``` * Suppose we want to change the names to `"Int", "wt", "am"` * In other languages, we would have something like ```r setNames(d, c("Int", "wt", "am")) ``` --- * Unfortunately, such a function _cannot_ modify `d` * The best it can do is to return a modified version of `d`: ```r d <- setNames(d, c("Int", "wt", "am")) ``` * This is similar to how `transform()`, `dplyr::mutate()`, etc., work --- * Replacement functions provide a more "natural" alternative ```r str(d) ``` ``` 'data.frame': 32 obs. of 3 variables: $ X1 : num 1 1 1 1 1 1 1 1 1 1 ... $ mtcars.wt: num 2.62 2.88 2.32 3.21 3.44 ... $ mtcars.am: num 1 1 1 0 0 0 0 0 0 0 ... ``` ```r names(d) <- c("Int", "wt", "am") str(d) ``` ``` 'data.frame': 32 obs. of 3 variables: $ Int: num 1 1 1 1 1 1 1 1 1 1 ... $ wt : num 2.62 2.88 2.32 3.21 3.44 ... $ am : num 1 1 1 0 0 0 0 0 0 0 ... ``` * It is easy to write your own replacement functions * For now, those details are not important --- layout: true # The `do.call()` function to call a function --- * It is easy to manipulate the language itself in R (e.g., `quote()`) * Such manipulation is usually only needed for advanced programming, not routine use * But one particular tool is very useful in practice: `do.call()` --- * Example ```r am.summary <- with(mtcars, tapply(mpg, am, FUN = summary)) am.summary ``` ``` $`0` Min. 1st Qu. Median Mean 3rd Qu. Max. 10.40 14.95 17.30 17.15 19.20 24.40 $`1` Min. 1st Qu. Median Mean 3rd Qu. Max. 15.00 21.00 22.80 24.39 30.40 33.90 ``` * Suppose we want to combine these into a matrix: ```r cbind(am.summary[[1]], am.summary[[2]]) ``` ``` [,1] [,2] Min. 10.40000 15.00000 1st Qu. 14.95000 21.00000 Median 17.30000 22.80000 Mean 17.14737 24.39231 3rd Qu. 19.20000 30.40000 Max. 24.40000 33.90000 ``` --- ```r gear.summary <- with(mtcars, tapply(mpg, gear, FUN = summary)) # different variable gear.summary ``` ``` $`3` Min. 1st Qu. Median Mean 3rd Qu. Max. 10.40 14.50 15.50 16.11 18.40 21.50 $`4` Min. 1st Qu. Median Mean 3rd Qu. Max. 17.80 21.00 22.80 24.53 28.07 33.90 $`5` Min. 1st Qu. Median Mean 3rd Qu. Max. 15.00 15.80 19.70 21.38 26.00 30.40 ``` ```r cbind(gear.summary[[1]], gear.summary[[2]], gear.summary[[3]]) # three arguments instead of two ``` ``` [,1] [,2] [,3] Min. 10.40000 17.80000 15.00 1st Qu. 14.50000 21.00000 15.80 Median 15.50000 22.80000 19.70 Mean 16.10667 24.53333 21.38 3rd Qu. 18.40000 28.07500 26.00 Max. 21.50000 33.90000 30.40 ``` --- * Alternative: `do.call(what, args)` - `what` is a function - `args` is a _list_ of arguments - Calls the function `what` with arguments given in `args` * The following are equivalent: ```r FUN(val1, val2, arg3 = val3) ``` * and ```r do.call(FUN, args = list(val1, val2, arg3 = val3)) ``` --- * So we can rewrite the previous `cbind()` calls as ```r do.call(cbind, am.summary) ``` ``` 0 1 Min. 10.40000 15.00000 1st Qu. 14.95000 21.00000 Median 17.30000 22.80000 Mean 17.14737 24.39231 3rd Qu. 19.20000 30.40000 Max. 24.40000 33.90000 ``` ```r do.call(cbind, gear.summary) ``` ``` 3 4 5 Min. 10.40000 17.80000 15.00 1st Qu. 14.50000 21.00000 15.80 Median 15.50000 22.80000 19.70 Mean 16.10667 24.53333 21.38 3rd Qu. 18.40000 28.07500 26.00 Max. 21.50000 33.90000 30.40 ``` --- layout: false class: middle, center # Questions?