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# torch.cholesky_solve

torch.cholesky_solve(input, input2, upper=False, *, out=None) → Tensor

  Solves a linear system of equations with a positive semidefinite matrix to be inverted given its Cholesky factor matrix u u u.

  If `upper` is `False`, u u u is and lower triangular and c is returned such that:

  c=(u u T)−1 b c = (u u^T)^{{-1}} b c=(u u T)−1 b

  If `upper` is `True` or not provided, u u u is upper triangular and c is returned such that:

  c=(u T u)−1 b c = (u^T u)^{{-1}} b c=(u T u)−1 b

  torch.cholesky_solve(b, u) can take in 2D inputs b, u or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs c

  Supports real-valued and complex-valued inputs. For the complex-valued inputs the transpose operator above is the conjugate transpose.

  Parameters:

    - input (Tensor) – input matrix b b b of size (∗,m,k)(*, m, k)(∗,m,k), where ∗*∗ is zero or more batch dimensions

    - input2 (Tensor) – input matrix u u u of size (∗,m,m)(*, m, m)(∗,m,m), where ∗*∗ is zero of more batch dimensions composed of upper or lower triangular Cholesky factor

    - upper (bool, optional) – whether to consider the Cholesky factor as a lower or upper triangular matrix. Default: `False`.

  Keyword Arguments:

    out (Tensor, optional) – the output tensor for c

  Example:

      >>> a = torch.randn(3, 3)
      >>> a = torch.mm(a, a.t()) # make symmetric positive definite
      >>> u = torch.linalg.cholesky(a)
      >>> a
      tensor([[ 0.7747, -1.9549,  1.3086],
              [-1.9549,  6.7546, -5.4114],
              [ 1.3086, -5.4114,  4.8733]])
      >>> b = torch.randn(3, 2)
      >>> b
      tensor([[-0.6355,  0.9891],
              [ 0.1974,  1.4706],
              [-0.4115, -0.6225]])
      >>> torch.cholesky_solve(b, u)
      tensor([[ -8.1625,  19.6097],
              [ -5.8398,  14.2387],
              [ -4.3771,  10.4173]])
      >>> torch.mm(a.inverse(), b)
      tensor([[ -8.1626,  19.6097],
              [ -5.8398,  14.2387],
              [ -4.3771,  10.4173]])

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