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

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.