iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddB_derivs

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iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddB_derivs#

iqm.benchmarks.compressive_gst.mgst.low_level_jit.ddB_derivs(X: ndarray, A: ndarray, B: ndarray, J: ndarray, y: ndarray, r: int, pdim: int, mle: bool = False) → tuple[ndarray, ndarray, ndarray, ndarray]#

Calculate all nonzero terms of the second derivative with respect to the state tensor B.

Parameters:

  • X (ndarray) – The input matrix X, of shape (pdim, pdim).

  • A (ndarray) – A 3D array of shape (n_povm, pdim, pdim) representing the POVM elements.

  • B (ndarray) – A 2D array of shape (pdim, pdim) representing the isometry matrix.

  • J (ndarray) – A 2D array representing the indices for which the derivatives will be computed.

  • y (ndarray) – A 2D array of shape (n_povm, len(J)) containing the target values.

  • r (int) – The rank of the problem.

  • pdim (int) – The dimension of the input matrices A and B.

  • mle (bool) – If True, the log-likelihood objective function is used instead of the least squares objective function

Returns:

  • dB: The derivative w.r.t. B, of shape (pdim, pdim).

  • dMdM: The product of the derivatives dM and dM, of shape (r, r).

  • dMconjdM: The product of the conjugate of dM and dM, of shape (r, r).

  • dconjdB: The mixed second derivative of by dB and dB*, of shape (r, r).

Return type:

A tuple containing the computed derivatives

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