algorithm to round to the next order of magnitude in R

Question

I apologize if the title is not clear, but I couldn't explain it succinctly.

Given a vector of concentrations, I would like to round the maximum value to the next order of magnitude (i.e., 345 to 1000). Also, I would like to round the minimum value to the lower order of magnitude (i.e., 3.2 to 1). These concentrations may also be below 1 so for example 0.034 would need to be rounded to 0.01.

Any ideas?

Answer 1

Here's a simple function that does what you're after:

log10_ceiling <- function(x) {
    10^(ceiling(log10(x)))
}

log10_ceiling(c(345, 3.2, 0.034))
# [1] 1000.0   10.0    0.1

Answer 2

I'm not sure about R, but this is a simple process to describe algorithmically.

Take the base 10 logarithm of the number, and apply a ceiling or floor to the result. Raise 10 to that power. Done.

You need a special case for 0 because you can't take a logarithm of 0.

Answer 3

In case someone is interested, the following is Ostermiller's solution translated to Python:

def roundUpToNearestMagnitude(n):
    if n == 0:
        return 1
    negative = n < 0
    log = np.log10(abs(n))
    if log > 0:
        decimalPlaces = np.ceil(log)
    else:
        decimalPlaces = np.floor(log) + 1
    rounded = np.power(10, decimalPlaces)
    if negative:
        return -rounded
    else:
        return rounded

def test_roundUpToNearestMagnitude():
    assert(100 == roundUpToNearestMagnitude(50))
    assert(10 == roundUpToNearestMagnitude(5))
    assert(1 == roundUpToNearestMagnitude(0.5))
    assert(.1 == roundUpToNearestMagnitude(0.05))
    assert(.01 == roundUpToNearestMagnitude(0.005))
    assert(-100 == roundUpToNearestMagnitude(-50))
    assert(-10 == roundUpToNearestMagnitude(-5))
    assert(-1 == roundUpToNearestMagnitude(-0.5))
    assert(-.1 == roundUpToNearestMagnitude(-0.05))
    assert(-.01 == roundUpToNearestMagnitude(-0.005))
    assert(1 == roundUpToNearestMagnitude(0))