cirq.diagonalize_real_symmetric_and_sorted_diagonal_matrices

cirq.diagonalize_real_symmetric_and_sorted_diagonal_matrices(symmetric_matrix: numpy.ndarray, diagonal_matrix: numpy.ndarray, tolerance: cirq.linalg.tolerance.Tolerance = Tolerance(rtol=1e-05, atol=1e-08, equal_nan=False)) → numpy.ndarray[source]

Returns an orthogonal matrix that diagonalizes both given matrices.

The given matrices must commute.
Guarantees that the sorted diagonal matrix is not permuted by the
diagonalization (except for nearly-equal values).
Parameters:
  • symmetric_matrix – A real symmetric matrix.
  • diagonal_matrix – A real diagonal matrix with entries along the diagonal sorted into descending order.
  • tolerance – Numeric error thresholds.
Returns:

An orthogonal matrix P such that P.T @ symmetric_matrix @ P is diagonal and P.T @ diagonal_matrix @ P = diagonal_matrix (up to tolerance).

Raises:
  • ValueError – Matrices don’t meet preconditions (e.g. not symmetric).
  • ArithmeticError – Failed to meet specified tolerance.