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.
Maybe you are interested:
- pairs() and ggpairs() functions to plot in R
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Hello, my name’s Bruce Warren. You can call me Bruce. I’m interested in programming languages, so I am here to share my knowledge of programming languages with you, especially knowledge of C, C++, Java, JS, PHP.
Name of the university: KMA
Major: ATTT
Programming Languages: C, C++, Java, JS, PHP
