Doing mathematics with R: Control structures
Conditional repetition
Often in an algorithm, a series of commands must be repeated: this can be a predetermined number of times ( restricted repetition) or depend on a condition (conditional repetition). We will encounting both forms of repetition, but we will begin with the second.
The general form of a conditional repetition (while instruction) is shown below. Read the explanation for detailed information:
Conditional repetition
while (condition) {
indented instructions if the condition is met
}
The second line in the while statement is indented (starting with two spaces in this case). This means that exactly those lines are under the control of the while; we call this the while part. As soon as the indentation ends, the end of the loop has been reached. We have written italicized indented instruction... here to indicate that there may be one or more instructions spread over multiple lines.
As long as the condition is true, the series of statements in the while part is executed until the condition is no longer true.
The flowchart below shows the possible execution of the conditional repetition. We have emphasised in this diagram that there are often initial instructions (for example, assigning initial values to variables) before the while instruction, and there are often preparatory instructions at the end of the iteration loop that prepare the next step in the while loop (for example, adjusting variable values ).
> x <- 1.0 > y <- x/2 + 1/x > n <- 0 > while (abs(y-x)>0) { + x <- y + y <- x/2 + 1/x + n <- n + 1 + } > io <- sprintf("y = %.15f after %d steps\n", y, n) > cat(io) y = 1.414213562373095 after 5 steps
In the form of a conditional repetition shown, the evaluation of the condition takes place at the beginning of the iteration loop: this is called a pre-checked loop. An alternative is to first execute a series of instructions and then check a condition. This is called a post-checked loop. It works like "perform operations until a condition is met". You can simulate a post-checked loop with a while instruction. The example above could then look as follows (note that now the counting variable n ends at 6, instead of 5 in the above code):
> x <- 1.0 > n <- 0 > not_ready <- TRUE > while (not_ready) { + y <- x/2 + 1/x + n <- n + 1 + if (abs(x-y) == 0) { + not_ready <- FALSE + } else { + x <- y + } + } > io <- sprintf("y = %.15f after %d steps\n", y, n) > cat(io) y = 1.414213562373095 after 6 steps
The break instruction also allows you to jump right out of the while loop and continue with the instructions that follow. In the example below, we have modified the stop condition so that it is computationally safer, i.e., cannot result in an infinite repetition.
> x <- 1.0 > n <- 0 > epsilon <- 10^(-10) > while (TRUE) { + y <- x/2 + 1/x + n <- n + 1 + if (abs(x-y) < epsilon) { + break + } else { + x <- y + } + } > io <- sprintf("y = %.10f after %d steps\n", y, n) > cat(io) y = 1.4142135624 after 5 steps
