bandchol ============================================== Purpose ---------------- Computes the Cholesky decomposition of a positive definite banded matrix. Format ---------------- .. function:: l = bandchol(a) :param a: KxN compact form matrix :type a: matrix :return l: lower triangle of the Cholesky decomposition of *a*. :rtype l: KxN compact form matrix 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 :math:`A = LL'`. *a* is the compact form of *A*; see :func:`band` for a description of the format of *a*. *l* is the compact form of *L*. This is the form of matrix that :func:`bandcholsol` expects. .. seealso:: Functions :func:`band`, :func:`bandcholsol`, :func:`bandltsol`, :func:`bandrv`, :func:`bandsolpd`