solve_op

→TensorImplPtr

int solve_op(const int & a, const int & b)

source edit

Python wrappers

pylucid.linalg.solvefunction

Solve the linear system $AX = B$ for $X$ .

Shape

a: (..., N, N).
b: (..., N) or (..., N, K).
Output: same shape as b.

References

Giles, "Collected Matrix Derivative Results" (Oxford, 2008), §2.4. LAPACK sgesv/dgesv; LAPACK Users' Guide §2.5.

See Also

[[lu_factor_op]] : Standalone LU factorisation (no autograd). [[lu_solve_op]] : Apply pre-computed LU factors (no autograd). [[matmul_op]] : Used in the backward outer product $-dB\, X^\top$ .

Parameters

aconst TensorImplPtr&

Square float tensor of shape (..., N, N). Must share dtype and device with b.

bconst TensorImplPtr&

Right-hand side of shape (..., N) or (..., N, K).

Returns

TensorImplPtr

Solution tensor $X = A^{-1} B$ with the same shape as b. When grad mode is active, the result has [[SolveBackward]] wired into the autograd graph with $A$ saved as input and $X$ saved as output.

Raises

LinAlgError

When a is not square, not float-typed, when dtypes/devices mismatch between a and b, or when

A

is singular (zero pivot detected by LU).

Examples

Single RHS solve:

    auto x = solve_op(a, b);  // a: (n, n), b: (n,) → x: (n,)

Batched multi-RHS solve:

    auto x = solve_op(a, b);  // a: (B, n, n), b: (B, n, k)