Cosine Similarity

• Write a function cosine_similarity that takes four numbers $a$, $b$, $c$, and $d$ and returns the cosine similarity between two vectors $(a, b)$ and $(c, d)$.

• In a mathematical expression,

$$ \frac{ac + bd}{ \sqrt{a^2+b^2} \sqrt{c^2+d^2} } $$

• Boilerplate source files {go,jl,ml,rs}/similarity.{go,jl,ml,rs} containing the test code is generated and shown below.

• Edit the source files either by opening them in a text editor (e.g., vscode), or editing the cells below and executing them.

1. AI tutor

1-1. Prepare

• Your personal AI tutor is provided for questions and feedback
• Execute the following cell before you use it

import heytutor

1-2. Examples

1-2-1. A general question

%%hey
How to write a function in Go?

1-2-2. A hint on this specific problem

%%hey
Give me a hint on this problem for Rust

1-2-3. NEW: A few builtin variables

• {file:FILENAME} is the content of FILE
• {bash[-1]} is the output of the last %%bash_ cell, {bash[-2]} that of the second last %%bash_ cell, etc.
• {problem} is the content of the file you specified by %%hey problem_file=foo.md
• {answer} is the content of the file you specified by %%hey answer_file=go/foo.go

1-2-4. Help when you struggle

%%hey answer_file=go/foo.go
I get this error when I compile it. What's wrong?"

My program:
{answer}

Error message:
{bash[-1]}

1-2-5. Ask feedback

• You are encouraged to ask a feedback once you think you are done with the problem, to know if there is a better answer. You can do so by something like:

%%hey problem_file=foo.md answer_file=go/foo.md
Give me a feedback to my answer.

Problem:
{problem}

My Answer:
{answer}

2. Go

2-1. Baseline code

import heytutor

%%writefile_ go/similarity.go
package main
import "fmt"
import "math"

/** begin my answer */

func similarity(a, b, c, d float64) float64 {
    return (a*c+b*d) / (math.Sqrt(a*a+b*b)*math.Sqrt(c*c+d*d))
}
/** end my answer */
func main() {
	if !(math.Abs(similarity(1.0, 2.0,  2.0,  4.0) - 1.0) < 1e-5) { panic("wrong") }
	if !(math.Abs(similarity(1.0, 2.0,  3.0,  5.0) - 0.997054) < 1e-5) { panic("wrong") }
	if !(math.Abs(similarity(2.0, 3.0,  3.0, -2.0) - 0.0) < 1e-5) { panic("wrong") }
	if !(math.Abs(similarity(3.0, 4.0, -3.0, -1.0) - -0.82219) < 1e-5) { panic("wrong") }
	fmt.Println("OK")
}

2-2. Compile

%%bash_
export PATH=${PATH}:~/.local/go/bin:~/go/bin
go build -o go/similarity go/similarity.go

• Note: when you run go or other Go commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/go/bin)
• You may consider adding that line in your ~/.bash_profile

2-3. Run

%%bash_
go/similarity

2-4. Ask Questions or Get Feedback

%%hey problem_file=similarity.md answer_file=go/similarity.go

Problem:
{problem}
My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.

3. Julia

3-1. Baseline code

import heytutor

%%writefile_ jl/similarity.jl
### begin my answer

similarity(a,b,c,d) = (a*c + b*d) / (sqrt(a^2+b^2)*sqrt(c^2+d^2))
### end my answer

function main()
    @assert abs(similarity(1.0, 2.0,  2.0,  4.0) - 1.0) < 1e-5
    @assert abs(similarity(1.0, 2.0,  3.0,  5.0) - 0.997054) < 1e-5
    @assert abs(similarity(2.0, 3.0,  3.0, -2.0) - 0.0) < 1e-5
    @assert abs(similarity(3.0, 4.0, -3.0, -1.0) - -0.82219) < 1e-5
    println("OK")
end

main()

3-2. Compile

• Julia code is compiled "just in time" (compiled upon executed), so does not need a specific action for compilation before you run

3-3. Run

%%bash_
export PATH=${PATH}:~/.juliaup/bin
julia jl/similarity.jl

• Note: when you run julia or other Julia commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/.juliaup/bin)
• You may consider adding that line in your ~/.bash_profile

3-4. Interactive execution

• julia command also serves is an interactive command for Julia programs

• You can run a source code and continue interaction

$ julia -i jl/similarity.jl

• For trial and error, you may also consider creating a Julia notebook

3-5. Ask Questions or Get Feedback

%%hey problem_file=similarity.md answer_file=jl/similarity.jl

Problem:
{problem}

My Answer (between ### begin my answer and ### end my answer):
{answer}

Give me a feedback to my answer.

4. OCaml

4-1. Baseline code

import heytutor

%%writefile_ ml/similarity.ml
(** begin my answer *)

let similarity a b c d =
  (a *. c +. b *. d) /.
  (sqrt (a *. a +. b *. b) *. sqrt (c *. c +. d *. d));;
(** end my answer *)

let main () =
  assert (abs_float (similarity 1.0 2.0   2.0    4.0  -. 1.0) < 1e-5);
  assert (abs_float (similarity 1.0 2.0   3.0    5.0  -. 0.997054) < 1e-5);
  assert (abs_float (similarity 2.0 3.0   3.0  (-2.0) -. 0.0) < 1e-5);
  assert (abs_float (similarity 3.0 4.0 (-3.0) (-1.0) -. -0.82219) < 1e-5);
  Printf.printf "OK\n"
;;

main()

4-2. Compile

%%bash_
eval $(opam env)
ocamlc ml/similarity.ml -o ml/similarity

• Note: when you run ocamlc or other OCaml commands (see below) in a terminal (SSH or Jupyter terminal), you need to execute the first line (eval $(opam env))
• You may consider adding that line in your ~/.bash_profile

4-3. Run

%%bash_
ml/similarity

4-4. Interactive execution

• ocaml command is an interactive command for OCaml programs

• In terminal (Jupyter or SSH), you can directly run a source code

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml ml/similarity.ml

• You can run a source code and continue interaction

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml -init ml/similarity.ml

• For trial and error, you may also consider creating an OCaml notebook

4-5. Ask Questions or Get Feedback

%%hey problem_file=similarity.md answer_file=ml/similarity.ml

Problem:
{problem}

My Answer (between (** begin my answer *) and (** end my answer *)):
{answer}

Give me a feedback to my answer.

5. Rust

5-1. Baseline code

import heytutor

%%writefile_ rs/similarity.rs
/** begin my answer */

fn similarity(a: f64, b: f64, c: f64, d: f64) -> f64 {
    (a*c + b*d) / ((a*a+b*b).sqrt() * (c*c+d*d).sqrt())
}
/** end my answer */

fn main() {
    assert!((similarity(1.0, 2.0,  2.0,  4.0) - 1.0).abs() < 1e-5);
    assert!((similarity(1.0, 2.0,  3.0,  5.0) - 0.997054).abs() < 1e-5);
    assert!((similarity(2.0, 3.0,  3.0, -2.0) - 0.0).abs() < 1e-5);
    assert!((similarity(3.0, 4.0, -3.0, -1.0) - -0.82219).abs() < 1e-5);
    println!("OK")
}

5-2. Compile

%%bash_
. ~/.cargo/env
rustc rs/similarity.rs -o rs/similarity

• Note: when you run rustc or other Rust commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (. ~/.cargo/env)
• You may consider adding that line in your ~/.bash_profile

5-3. Run

%%bash_
rs/similarity

5-4. Ask Questions or Get Feedback

%%hey problem_file=similarity.md answer_file=rs/similarity.rs

Problem:
{problem}

My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.