lu.c file

Functions

static auto vm_mat_at(const vm_mat* m, const int r, const int c) -> vm_float_t*: Column-major element pointer data[r + c * rows].
static auto vm_mat_max_abs(const vm_mat* m) -> vm_float_t: Largest absolute entry of m.
static auto vm_factor_tol(const vm_float_t scale, const int n) -> vm_float_t: Scale-aware cutoff n * eps * scale (at least eps).
auto vm_lu_factor(vm_mat* A, int* pivot, int* sign) -> bool: In-place LU factorization with partial pivoting.
auto vm_lu_solve(const vm_mat* LU, const int* pivot, const vm_float_t* b, vm_float_t* x) -> bool: Solves A x = b from a factored LU.
auto vm_mat_det(const vm_mat* A) -> vm_float_t: Determinant of a square matrix via LU.
auto vm_mat_inverse(vm_mat* out, const vm_mat* A) -> bool: Inverse of a square matrix via LU.

Column-major element pointer data[r + c * rows].

Largest absolute entry of m.

Parameters
m	Matrix.
Returns	Max \|m_ij\|, or 0 if empty.

Scale-aware cutoff n * eps * scale (at least eps).

Parameters
scale	Typical magnitude of the matrix.
n	Matrix order (clamped to at least 1).
Returns	Factorization / rank tolerance.

In-place LU factorization with partial pivoting.

Parameters
A	Square matrix, overwritten with L and U.
pivot	Row permutation; length `A->rows`.
sign	Optional; set to +1 or -1 for the permutation sign.
Returns	True on success.

On success A holds L (unit diagonal, strictly below) and U (on and above the diagonal). pivot[i] is the original row now at position i.

Solves A x = b from a factored LU.

Parameters
LU	Factored matrix from `vm_lu_factor`.
pivot	Row permutation from `vm_lu_factor`.
b	Right-hand side, length `n`.
x	Solution, length `n`.
Returns	True on success.

Determinant of a square matrix via LU.

Parameters
A	Square matrix (not modified).
Returns	det(A), or 0 on failure.

Inverse of a square matrix via LU.

Allocates or resizes out when it is not already n x n.