Computer Algorithm for Solving Determinants

Question

I wanted a computer algorithm which could solve an n x n Determinant and return a value. Most recommendably in C++ language, where input is a 2D Array, and N, and output is the value.

There is an exhaustive method in Mathematics to solve Determinants whose size is more than 3 x 3. If somebody could just find a code snippet which solves the determinant, that'll be helpful.

The main aim was to solve 'n' variables, given the coefficients of a system of 'n' Linear Equations. Once 'n' exceeds 4, this matter gets messy on paper. There is one 'Determinant' way of solving such equations. Although once 'n' exceeds 3, it gets messy on paper too, but its doable if i can just find how the computer can solve it instead. Thanks!

This has been asked dozens of times before *(just check the related bar on the side of the page)* — BlueRaja - Danny Pflughoeft, Apr 09 '12 at 17:41
*solve 'n' variables* Have fun with your personal projects, folks, but please don't use Cramer's rule in production unless n is small. — oldboy, Apr 09 '12 at 23:05

score 3 · Answer 1 · answered Apr 09 '12 at 16:58

3

As described in Numerical Recipes, the determinant is simply the product of the diagonal elements after an LU decomposition. (This book is available online, and has code for computing the LU decomposition).

answered Apr 09 '12 at 16:58

Oliver Charlesworth

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score 1 · Answer 2 · answered Apr 09 '12 at 16:57

Lots of languages have this functionality built in.

For instance, if you create a C# program, you can use the Matrix.Determinant property to get this instantly:

private Double determinantExample()
{
    Matrix myMatrix = new Matrix(5, 10, 15, 20, 25, 30);

    // Get the determinant, which is equal to -50.
    Double determinant = myMatrix.Determinant;

    return determinant;

}

If this is an educational exercise, wikipedia shows you how to solve the determinant at the top of the article: http://en.wikipedia.org/wiki/Determinant

Thanks, ill try to see what i can get for C++. – User3.14159265 Apr 09 '12 at 17:14 — User3.14159265, Apr 09 '12 at 17:14

score 1 · Answer 3 · answered Apr 09 '12 at 16:58

1

Wikipedia has a list of algorithms. LAPACK and its cousins are the standard tools, and it looks like there's a C++ version.

answered Apr 09 '12 at 16:58

Xodarap

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score 1 · Answer 4 · answered Apr 09 '12 at 17:18

Simpler approch is using a recursive metho by applying the laplae formula (http://en.wikipedia.org/wiki/Determinant#Laplace.27s_formula_and_the_adjugate_matrix)

Here you have a class Matrix which implements a det() function take a look. http://www.dreamincode.net/forums/topic/55772-determinant-of-matrix-in-c/

Two solutions are given here: http://cboard.cprogramming.com/cplusplus-programming/30001-determinant-calculation.html

The first one is not recursive, the second one is basically the same solution of first link. The non recursive method basically transform your matrix in a triangular matrix. The determinant of triangular matrix is the multiplication of diagonal elements. See here : http://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant (rule 6)

Computer Algorithm for Solving Determinants

4 Answers4