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How To Use deriv In R - LearnShareIT

How To Use deriv In R

deriv in r

In programming, you will occasionally need to calculate the derivative of some expressions. The R language provides a function to perform the derivation work, the deriv() function. This article will share about deriv in R and how to use it. Let’s read it now.

What is deriv in R?

There are three functions used to calculate the derivative of expressions in R: the functions D(), deriv(), and deriv3().

Syntax:

D(expr, name)

deriv(expr, name)

# Returns a more complex expression object.

deriv3(expr, name)

Parameters:

  • expr: an expression or call.
  • name: a character vector representing the variable name used to calculate the derivative.

How to compute derivatives using deriv?

We will give specific examples to illustrate how the deriv() function works.

Compute derivatives

In this example, I have a ternary expression like this: x^3 + 2*x + 1. I will use the deriv() function to calculate the derivative of this expression.

Example:

# Create an expression
expr <- expression(x ^ 3 + 2 * x + 1)

# Calculate the derivative of the expression
deriv_expr1 <- deriv(expr, "x")
print(deriv_expr1)

# Returns a more detailed result
deriv_expr2 <- deriv3(expr, "x")
print(deriv_expr2)

# Returns the same result
# deriv_expr1 <- deriv(~ x ^ 3 + 2 * x + 1, "x")
# deriv_expr2 <- deriv3(~ x ^ 3 + 2 * x + 1, "x")

Output:

expression({
    .value <- x^3 + 2 * x + 1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("x")))
    .grad[, "x"] <- 3 * x^2 + 2
    attr(.value, "gradient") <- .grad
    .value
})
expression({
    .expr2 <- 2 * x
    .value <- x^3 + .expr2 + 1
    .grad <- array(0, c(length(.value), 1L), list(NULL, c("x")))
    .hessian <- array(0, c(length(.value), 1L, 1L), list(NULL, 
        c("x"), c("x")))
    .grad[, "x"] <- 3 * x^2 + 2
    .hessian[, "x", "x"] <- 3 * .expr2
    attr(.value, "gradient") <- .grad
    attr(.value, "hessian") <- .hessian
    .value
})

The deriv() and deriv3() functions return an expression object. 

Higher order derivative

The D() function returns a call so you can use the output for the higher-order derivative.

Example:

# Create an expression
expr <- expression(x ^ 3 + 2 * x + 1)

# Calculate the derivative of the expression
cat("Derivative of the 'expr' expression\n")
deriv_expr1 <- D(expr, "x")
print(deriv_expr1)

# Higher order derivative
cat("\nHigher-order derivative\n")
deriv_expr2 <- D(deriv_expr1, "x")
print(deriv_expr2)

Output:

Derivative of the 'expr' expression
3 * x^2 + 2

Higher-order derivative
3 * (2 * x)

Summary

We have shared how to calculate the derivative using deriv in R. If you want to use the result obtained to calculate the higher-order derivative, you can use the D() function. Thank you for reading.

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Posted in R

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