Transformed Values Return NaN in Some Cases but Numbers in Others

Introduction

In R programming language, performing mathematical operations on vectors can sometimes lead to unexpected results. In this article, we’ll delve into a common issue involving transformed values that return NaN (Not a Number) in some cases, while producing the expected numbers in others.

Understanding NaN in R

Before diving deeper, let’s clarify what NaN means in R. NaN represents an invalid or unreliable result due to an arithmetic operation or calculation error. In other words, it signifies that the result is not a valid number.

The Origins of the Issue

This issue stems from the way R evaluates expressions involving unary minus (-) and exponentiation (^). The precedence of these operators can lead to unexpected results when applied to vectors.

Unary Minus Operator Precedence

In R, the unary minus operator has a higher precedence than exponentiation. This means that a ^ b - c is evaluated as (a ^ (b - c)), rather than ((a ^ b) - c).

For example, -0.1^0.1 is parsed as -(0.1^0.1), not (0.1^(-0.1)). This can lead to incorrect results when working with vectors and exponentiation.

The Problem in Action

Let’s look at the provided code snippet:

vals <- c(-0.02964166, -0.01018776, -0.01758487)
vals^(1/10)

As expected, this produces NaN results.

However, if we take each value individually to the power of 1/10 using abs(vals)^(1/10), we get:

abs(vals)^(1/10)

[1] -0.7033804
[2] -0.6321321
[3] -0.6675963

Notice the absence of NaN values.

The Solution: Using Sign and Absolute Values

To avoid losing numbers when applying exponentiation to vectors, we can use the following approach:

sign(vals) * (abs(vals))^(1/10)

This code multiplies each value in the vector by its absolute value raised to the power of 1/10. The sign() function returns a logical vector indicating whether each value is positive or negative.

Using Complex Roots and Polyroots

Alternatively, we can use complex roots to find all possible solutions for the equation x^10 - val = 0. One way to do this is by using the polyroot() function:

polyroot(c(-vals[1], rep(0,9), 1))

This code finds the roots of the polynomial equation corresponding to each value in the vector.

Verifying the Results

To confirm that our solution produces the expected results, we can compare the fifth root of vals[1] with the result obtained using sign(vals) * (abs(vals))^(1/10):

all.equal((0.7033804i)^10, as.complex(vals[1]), tol = 1e-6)

If this code returns TRUE, it confirms that our solution is correct.

Conclusion

Transformed values returning NaN in some cases but numbers in others can be a result of the unary minus operator precedence and exponentiation operations. By using the sign() and abs() functions to manipulate the vector, we can avoid losing numbers when applying exponentiation. Additionally, using complex roots and polyroots provides an alternative approach for finding all possible solutions.

Understanding these concepts is essential for working effectively with vectors in R programming language, ensuring accurate results in mathematical operations and equations.

Last modified on 2023-08-31