`linsolve`

Solves a linear system, optionally telling it about the matrix structure.

Syntax

X = linsolve(A, B)

Solves A*X = B, like A\B.

X = linsolve(A, B, opts)

Uses the structure flags in the struct opts, such as UT, LT, SYM, POSDEF or TRANSA, to pick a faster method.

Description

When you know that A is triangular or symmetric positive definite, passing that fact in opts lets linsolve skip the general factorization. The flags are trusted, not checked: if the claim is false the answer is wrong.

For general use A\B does the same job and detects structure automatically.

Input arguments

A: Coefficient matrix.
B: Right-hand side, a vector or a matrix with size(A,1) rows.
opts: Struct of logical fields describing A. TRANSA = true solves with A'.

Output arguments

X: The solution.

Example

General, upper triangular and transposed solves

A = [2 1; 1 3];
b = [3; 5];
x = linsolve(A, b)
opts.UT = true;
linsolve([2 1; 0 3], b, opts)
opts2.TRANSA = true;
linsolve([2 0; 1 3], b, opts2)

Output

linsolve