bandltsol ============================================== Purpose ---------------- Solves the system of equations :math:`Ax = b` for *x*, where *A* is a lower triangular banded matrix. Format ---------------- .. function:: x = bandltsol(b, A) :param b: :type b: KxM matrix :param A: :type A: KxN compact form matrix :return x: KxM matrix. :rtype x: matrix Examples ---------------- :: // Create matrix 'A' and right-hand side 'b' A = { 1 2 0 0, 2 8 1 0, 0 1 5 2, 0 0 2 3 }; b = { 1.3, 2.1, 0.7, 1.8 }; /* ** Create a matrix containing the lower triangular part ** of 'A' */ Alower = lowmat(A); // Create banded matrix from of 'Alower' Abandlow = band(Alower, 1); // Solve the system of equations x = bandltsol(b, Abandlow); After the code above: :: 1 0 0 0 0 1 1.300 1.3 1.3 Alower = 2 8 0 0 Aband = 2 8 x = -0.063 b = 2.1 Alower*x = 2.1 0 1 5 0 1 5 0.153 0.7 0.7 0 0 2 3 2 3 0.498 1.8 1.8 Remarks ------- *A* is a lower triangular banded matrix in compact form. See :func:`band` for a description of the format of *A*. *b* can have more than one column. If so, :math:`Ax = b` is solved for each column. That is, .. math:: A*x[.,i] = b[.,i]; .. seealso:: Functions :func:`band`, :func:`bandchol`, :func:`bandcholsol`, :func:`bandrv`, :func:`bandsolpd`