linalg/solve

src/linalg/solve.tur

linear system solvers and matrix inverse/determinant

defn

fwd-sub

(fwd-sub [^borrow l : mat ^borrow b : lavec] :)

solve L x = b where L is lower triangular.

defn

(back-sub [^borrow u : mat ^borrow b : lavec] :)

solve U x = b where U is upper triangular.

defn

(chol-solve [^borrow f : cholfac ^borrow b : lavec] :)

solve A x = b given a Cholesky factor (A = L L').

defn

(lu-solve [^borrow f : lufac ^borrow b : lavec] :)

solve A x = b given an LU factor (P A = L U).

defn

(qr-solve [^borrow f : qrfac ^borrow b : lavec] :)

least-squares solve of A x ~= b given a QR factor (A = Q R).

defn

(mat-solve [^borrow a : mat ^borrow b : lavec spd? : int] :)

factorize and solve A x = b. spd? = 1 selects Cholesky.

defn

(mat-inv [^borrow a : mat] :)

inverse of a square matrix via LU column solves.

defn

(mat-det [^borrow a : mat] :)

determinant of a square matrix via LU.

Internal definitions

__fwd-sub-kernel-- forward / backward substitution

__back-sub-kernel-- solve U x = b, U upper triangular (n x n, row stride n).

__qt-b-kernel-- c[i] = sum_j Q[j*m+i] * b[j] for i in 0..n (Q is m x m).

__lu-det-kernel-- determinant from an LU factor: product of U diagonal