`decomposition`

Matrix decomposition object for solving linear systems repeatedly.

Syntax

dA = decomposition(A)

Chooses a factorization suited to the structure of A.

dA = decomposition(A, type)

Uses the named factorization, such as 'lu', 'chol', 'qr', 'ldl' or 'diagonal'.

x = dA\b

Solves A*x = b reusing the stored factorization.

Description

Solving A\b factors A each time. When the same matrix is used with many right-hand sides, building a decomposition once and then writing dA\b skips the repeated factorization and gives the same answers.

The object keeps the factorization type it picked, which can be read from dA.Type. It cannot be used as an ordinary matrix: multiplying, indexing and similar operations are not defined for it.

Input arguments

A: Square or rectangular matrix.
type: Name of the factorization to compute.

Output arguments

dA: Object with properties such as Type and MatrixSize, which also works with \, /, isIllConditioned and rcond.

Example

Solving with a stored factorization

A = [4 1; 2 3];
dA = decomposition(A);
x = dA\[1; 2]
dA.Type
disp(dA.MatrixSize)

Output

x = 2×1

    0.1000
    0.6000
ans = 'lu'
     2     2

decomposition