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# torch.lu_solve

torch.lu_solve(b, LU_data, LU_pivots, *, out=None) → Tensor

  Returns the LU solve of the linear system A x=b Ax = b A x=b using the partially pivoted LU factorization of A from `lu_factor()`.

  This function supports `float`, `double`, `cfloat` and `cdouble` dtypes for `input`.

  Warning

  `torch.lu_solve()` is deprecated in favor of `torch.linalg.lu_solve()`. `torch.lu_solve()` will be removed in a future PyTorch release. `X = torch.lu_solve(B, LU, pivots)` should be replaced with

      X = linalg.lu_solve(LU, pivots, B)

  Parameters:

    - b (Tensor) – the RHS tensor of size (∗,m,k)(*, m, k)(∗,m,k), where ∗*∗ is zero or more batch dimensions.

    - LU_data (Tensor) – the pivoted LU factorization of A from `lu_factor()` of size (∗,m,m)(*, m, m)(∗,m,m), where ∗*∗ is zero or more batch dimensions.

    - LU_pivots (IntTensor) – the pivots of the LU factorization from `lu_factor()` of size (∗,m)(*, m)(∗,m), where ∗*∗ is zero or more batch dimensions. The batch dimensions of `LU_pivots` must be equal to the batch dimensions of `LU_data`.

  Keyword Arguments:

    out (Tensor, optional) – the output tensor.

  Example:

      >>> A = torch.randn(2, 3, 3)
      >>> b = torch.randn(2, 3, 1)
      >>> LU, pivots = torch.linalg.lu_factor(A)
      >>> x = torch.lu_solve(b, LU, pivots)
      >>> torch.dist(A @ x, b)
      tensor(1.00000e-07 *
             2.8312)

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