cholsol#

Purpose#

Solves a system of linear equations given the Cholesky factorization of the system.

Format#

x = cholsol(b, C)#

Parameters:

b (NxK matrix) – The system is solved for each column in b, i.e., \(A*x[., i] = b[., i]\).
C (NxN matrix) – The Cholesky factorization of a linear system of equations \(A\).

Returns:

x (NxK matrix) – the solution for \(Ax = b\).

Examples#

/*
** Assign the right-hand side 'b' and the Cholesky
** factorization 'C'
*/
b = { 0.03177513, 0.41823100, 1.70129375 };
C = { 1.73351215 1.53201723 1.78102499,
               0 1.09926365 0.63230050,
               0          0 0.67015361 };

// Solve the system of equations
x = cholsol(b, C);

// Note: C'C is equivalent to C'*C
A = C'C;

// Solve the system of equations
x2 = b/A;

After the above code, R will equal:

    -1.9440       -1.9440
x = -1.5269  x2 = -1.5269
     3.2158        3.2158

Remarks#

Since \(A^{-1} = I/A\) and eye(N) creates an identity matrix of size \(N\):

cholsol(eye(N), C);

is equivalent to:

invpd(A);

Thus, if you have the Cholesky factorization of \(A\), cholsol is the most efficient way to obtain the inverse of \(A\).