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.
See also
Functions band(), bandcholsol(), bandltsol(), bandrv(), bandsolpd()