# 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 $$A$$.

Functions chol()