Cartesian Tensor utils

mrsimulator.utils.cartesian_tensor.to_symmetric_tensor(tensor: ndarray, type: str = 'shielding') → SymmetricTensor

Cartesian 3x3 tensor to mrsimulator SymmetricTensor object. Note that only the traceless symmetric part of the tensor is converted to the SymmetricTensor object.

Parameters:

  • tensor – A 3x3 np.ndarray Cartesian tensor

  • type – String with any one of the allowed listings. ["shielding", "j_coupling", "quadrupolar", "dipolar"]

Returns:

A SymmetricTensor object.

Example

>>> tensor = np.array([
...     [-8.05713333, -1.4523, 35.7252],
...     [-5.5725, 26.38916667, -5.2804],
...     [33.1405, -0.6241, -18.33203333],
... ])
>>> symmetric_tensor = to_symmetric_tensor(tensor, type="shielding")
mrsimulator.utils.cartesian_tensor.dipolar_tensor(site_1: list, site_2: list) → ndarray

Generates a 3x3 symmetric cartesian tensor from isotope site coordinates.

Parameters:

  • site_1 – A list of (isotope_symbol, site_coordiantes) for site 1, where isotope_symbol is a string of any of the mrsimulator allowed isotopes and site_coordiantes is a list or ndarray of (x, y, z) site coordinates in units of Angstrom.

  • site_2 – A list of (isotope_symbol, site_coordiantes) for site 2, where isotope_symbol is a string of any of the mrsimulator allowed isotopes and site_coordiantes is a list or ndarray of (x, y, z) site coordinates in units of Angstrom.

Returns:

A 3x3 ndarray of symmetric dipolar Cartesian tensor in units of Hz.

Example

>>> site1_coords = [2.1, 3.1, 1.3]  # coords for 1H in A
>>> site2_coords = [0, 0, 1.2]  # coords for 13C in A
>>> dipole_tensor = dipolar_tensor(
...     site_1=['1H', site1_coords],
...     site_2=['13C', site2_coords]
... )
mrsimulator.utils.cartesian_tensor.to_mehring_params(tensor: ndarray) → Tuple[ndarray, ndarray]

Cartesian 3x3 tensor to Mehring parameters. Note, for non-symmetric tensors, the conversion is applied by first symmetrizing the tensor using (tensor + tensor.T) / 2.

Parameters:

tensor – A 3x3 np.ndarray Cartesian tensor.

Returns:

A tuple of (euler_angles, eigenvalues) where euler_angles is an ndarray of three Euler angles [alpha, beta, gamma] using the “zyz” convention, and eigenvalues are the corresponding ndarray of three Eigenvalues.

mrsimulator.utils.cartesian_tensor.from_mehring_params(euler_angles: List[float], eigenvalues: List[float]) → ndarray

Mehring parameters to a 3x3 symmetric Cartesian tensor.

Parameters:

  • euler_angles – An ndarray of three Euler angles [alpha, beta, gamma] using the “zyz” convention.

  • eigenvalues – The corresponding ndarray of three Eigenvalues.

Returns:

A 3x3 np.ndarray of symmetric Cartesian tensor.

Return type:

tensor

mrsimulator.utils.cartesian_tensor.to_haeberlen_params(tensor: ndarray) → Tuple[ndarray, float, float, float]

Cartesian 3x3 tensor to Haeberlen parameters. Note, for non-symmetric tensors, the conversion is applied by first symmetrizing the tensor using (tensor + tensor.T) / 2.

Parameters:

tensor – A 3x3 np.ndarray Cartesian tensor.

Returns:

A tuple of (euler_angles, zeta_sigma, eta_sigma, isotropic_component) where euler_angles is an ndarray of three the Euler angles [alpha, beta, gamma] using the “zyz” convention, zeta_sigma, eta_sigma, and isotropic_component are the corresponding Haeberlen anisotropy, asymmetry, and isotropic parameters.

mrsimulator.utils.cartesian_tensor.from_haeberlen_params(euler_angles: List[float], zeta_sigma: float, eta_sigma: float, isotropic_component: float) → ndarray

Haeberlen parameters to a 3x3 symmetric Cartesian tensor.

Parameters:

  • euler_angles – An ndarray of three Euler angles [alpha, beta, gamma] using the “zyz” convention.

  • zeta_sigma – Anisotropy parameter.

  • eta_sigma – Asymmetry parameter

  • isotropic_component – Isotropic parameter

Returns:

A 3x3 np.ndarray of symmetric Cartesian tensor.

Return type:

tensor

mrsimulator.utils.cartesian_tensor.mehring_principal_components_to_maryland(lambdas: List[float]) → Tuple[float, float, float]

Mehring principal components to Maryland.

Parameters:

lambdas – Eigenvalues from Mehring convention.

Returns:

A tuple of (span, skew, isotropic) in Maryland convention where span is the width, skew is the asymmetry, and isotropic is the isotropic components.

mrsimulator.utils.cartesian_tensor.maryland_to_mehring_principal_components(isotropic: float, span: float, skew: float) → ndarray

Maryland components to Mehring principal components.

Parameters:

  • span – Maryland anisotropy component.

  • skew – Maryland asymmetry component.

  • isotropic – Maryland isotropic component.

Returns:

A ndarray of Mehring Eigenvalues.

mrsimulator.utils.cartesian_tensor.maryland_to_haeberlen_params(isotropic: float, span: float, skew: float) → Tuple[float, float, float]
mrsimulator.utils.cartesian_tensor.haeberlen_params_to_maryland(zeta_sigma: float, eta_sigma: float, isotropic_component: float) → Tuple[float, float, float]
mrsimulator.utils.cartesian_tensor.dipolar_coupling_constant(isotope_symbol_1: str, isotope_symbol_2: str, distance: float)

Dipolar coupling constant between two isotopes a distance apart

Parameters:

  • isotope_symbol_1 – A string of any of the mrsimulator allowed isotopes for isotope 1.

  • isotope_symbol_2 – A string of any of the mrsimulator allowed isotopes for isotope 2.

  • distance – Distance between the isotopes in units of Angstrom.

Returns:

Dipolar coupling constant in units of Hz.