Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Challenges

Comments on Compute the determinant

Parent

Compute the determinant

+8
−0

Challenge

A simple challenge: Given a two-dimensional matrix (an array of arrays) of real numbers, compute the determinant.

The determinant of a matrix is a mathematical construct used in many applications, such as solving polynomial equations, identifying the invertibility of the matrix, and finding the scaling factor under a matrix transformation. For more information about it, see this Wikipedia entry.

There are a couple of different ways to compute the determinant, and it is up to you how you implement it.

For instance, you may compute it using the Laplace expansion, a recursive algorithm which goes

  1. Pick a row or column.
  2. Start with a sum of zero.
  3. For each entry of the row/column:
    1. Create a new matrix with the row and column of the entry removed. This new matrix is a square matrix of size one less that the original.
    2. Compute the determinant of that smaller matrix.
    3. Multiply that determinant by the entry.
    4. If the row index plus the column index is even[1], add it to the sum, otherwise, subtract it.
  4. The final sum is the determinant.

As an example, here is an ungolfed implementation along the first column.

function laplaceDet(matrix) {
	if (matrix.length === 1) return matrix[0][0];

	let sum = 0;
	for (let rowIndex = 0; rowIndex < matrix.length; ++rowIndex) {
		let minorMatrix = matrix.filter((_, index) => index !== rowIndex)
			          .map(row => row.slice(1));
		sum += ((-1) ** rowIndex) * matrix[rowIndex][0] * laplaceDet(minorMatrix);
	}
	return sum;
}

Try it online!

This is code-golf, so the program with the lowest byte-count wins!

Test cases

$$ \begin{aligned} \det\begin{bmatrix}1&0\\0&1\end{bmatrix}&=1 \\ \det\begin{bmatrix}1.5&2\\-3&4.5\end{bmatrix}&=12.75 \\ \det\begin{bmatrix}3&7\\1&-4\end{bmatrix}&=-19 \\ \det\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}&=1 \\ \det\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}&=0 \end{aligned} $$

In text form,

[[1,0],[0,1]] -> 1
[[1.5,2],[-3,4.5]] -> 12.75
[[3,7],[1,-4]] -> -19
[[1,0,0],[0,1,0],[0,0,1]] -> 1
[[1,2,3],[4,5,6],[7,8,9]] -> 0

  1. Note that it doesn't matter if it is 1-indexed or 0-indexed, as 1+1 and 0+0 are both the same parity. ↩︎

History
Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

1 comment thread

Trivial builtins (1 comment)
Post
+3
−0

Python 3.8 (pre-release), 106 95 bytes

Saved 11 bytes thanks to Peter Taylor!

f=lambda m:sum((-1)**i*x*f([r[:i]+r[i+1:]for r in m[1:]])for i,x in enumerate(m[0]))if m else 1

Try it online!

Here's an attempt at beating Quintec's answer. Only 78 67 more bytes to go!

History
Why does this post require moderator attention?
You might want to add some details to your flag.

1 comment thread

Improvements (2 comments)
Improvements
Peter Taylor‭ wrote over 2 years ago

You can save 9 bytes with base case the 0x0 matrix and 2 bytes with enumerate: it's long, but so is range(len). For 95 bytes: f=lambda m:sum((-1)**i*x*f([r[:i]+r[i+1:]for r in m[1:]])for i,x in enumerate(m[0]))if m else 1

user‭ wrote over 2 years ago

Peter Taylor‭ Thanks!