bandchol

Purpose

Computes the Cholesky decomposition of a positive definite banded matrix.

Format

l = bandchol(a)
Parameters:a (matrix) – KxN compact form matrix
Returns:l (KxN compact form matrix) – lower triangle of the Cholesky decomposition of a.

Examples

// Create a banded matrix in full general matrix form
x = { 1 2 0 0,
      2 8 1 0,
      0 1 5 2,
      0 0 2 3 };

// Convert the matrix to compact (banded) form
bx = band(x, 1);

// Compute the banded form Cholesky decomposition
bl = bandchol(bx);

// Compute standard Cholesky decomposition
l = chol(x);

After the code above:

     0   1        0   1       1   2   0   0
bx = 2   8   bl = 2   2   l = 0   2   1   0
     1   5        1   2       0   0   2   1
     2   3        1   1       0   0   0   1

Remarks

Given a positive definite banded matrix A, there exists a matrix L, the lower triangle of the Cholesky decomposition of A, such that \(A = LL'\). a is the compact form of A; see band() for a description of the format of a.

l is the compact form of L. This is the form of matrix that bandcholsol() expects.