-pyerrors.npr
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-import warnings -import numpy as np -from .linalg import inv, matmul -from .dirac import gamma - - -L = None -T = None - - -class Npr_matrix(np.ndarray): - - def __new__(cls, input_array, mom_in=None, mom_out=None): - obj = np.asarray(input_array).view(cls) - obj.mom_in = mom_in - obj.mom_out = mom_out - return obj - - @property - def g5H(self): - """Gamma_5 hermitean conjugate - - Uses the fact that the propagator is gamma5 hermitean, so just the - in and out momenta of the propagator are exchanged. - """ - return Npr_matrix(self, - mom_in=self.mom_out, - mom_out=self.mom_in) - - def _propagate_mom(self, other, name): - s_mom = getattr(self, name, None) - o_mom = getattr(other, name, None) - if s_mom is not None and o_mom is not None: - if not np.allclose(s_mom, o_mom): - raise Exception(name + ' does not match.') - return o_mom if o_mom is not None else s_mom - - def __matmul__(self, other): - return self.__new__(Npr_matrix, - super().__matmul__(other), - self._propagate_mom(other, 'mom_in'), - self._propagate_mom(other, 'mom_out')) - - def __array_finalize__(self, obj): - if obj is None: - return - self.mom_in = getattr(obj, 'mom_in', None) - self.mom_out = getattr(obj, 'mom_out', None) - - -def _check_geometry(): - if L is None: - raise Exception("Spatial extent 'L' not set.") - else: - if not isinstance(L, int): - raise Exception("Spatial extent 'L' must be an integer.") - if T is None: - raise Exception("Temporal extent 'T' not set.") - if not isinstance(T, int): - raise Exception("Temporal extent 'T' must be an integer.") - - -def inv_propagator(prop): - """ Inverts a 12x12 quark propagator""" - if prop.shape != (12, 12): - raise Exception("Only 12x12 propagators can be inverted.") - return Npr_matrix(inv(prop), prop.mom_in) - - -def Zq(inv_prop, fermion='Wilson'): - """ Calculates the quark field renormalization constant Zq - - Parameters - ---------- - inv_prop : array - Inverted 12x12 quark propagator - fermion : str - Fermion type for which the tree-level propagator is used - in the calculation of Zq. Default Wilson. - """ - _check_geometry() - mom = np.copy(inv_prop.mom_in) - mom[3] /= T / L - sin_mom = np.sin(2 * np.pi / L * mom) - - if fermion == 'Wilson': - p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3]) / np.sum(sin_mom ** 2) - elif fermion == 'Continuum': - p_mom = 2 * np.pi / L * mom - p_slash = -1j * (p_mom[0] * gamma[0] + p_mom[1] * gamma[1] + p_mom[2] * gamma[2] + p_mom[3] * gamma[3]) / np.sum(p_mom ** 2) - elif fermion == 'DWF': - W = np.sum(1 - np.cos(2 * np.pi / L * mom)) - s2 = np.sum(sin_mom ** 2) - p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3]) - p_slash /= 2 * (W - 1 + np.sqrt((1 - W) ** 2 + s2)) - else: - raise Exception("Fermion type '" + fermion + "' not implemented") - - res = 1 / 12. * np.trace(matmul(inv_prop, np.kron(np.eye(3, dtype=int), p_slash))) - res.gamma_method() - - if not res.imag.is_zero_within_error(5): - warnings.warn("Imaginary part of Zq is not zero within 5 sigma") - return res - - res.real.tag = "Zq '" + fermion + "', p=" + str(inv_prop.mom_in) - - return res.real -
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-class Npr_matrix(np.ndarray): - - def __new__(cls, input_array, mom_in=None, mom_out=None): - obj = np.asarray(input_array).view(cls) - obj.mom_in = mom_in - obj.mom_out = mom_out - return obj - - @property - def g5H(self): - """Gamma_5 hermitean conjugate - - Uses the fact that the propagator is gamma5 hermitean, so just the - in and out momenta of the propagator are exchanged. - """ - return Npr_matrix(self, - mom_in=self.mom_out, - mom_out=self.mom_in) - - def _propagate_mom(self, other, name): - s_mom = getattr(self, name, None) - o_mom = getattr(other, name, None) - if s_mom is not None and o_mom is not None: - if not np.allclose(s_mom, o_mom): - raise Exception(name + ' does not match.') - return o_mom if o_mom is not None else s_mom - - def __matmul__(self, other): - return self.__new__(Npr_matrix, - super().__matmul__(other), - self._propagate_mom(other, 'mom_in'), - self._propagate_mom(other, 'mom_out')) - - def __array_finalize__(self, obj): - if obj is None: - return - self.mom_in = getattr(obj, 'mom_in', None) - self.mom_out = getattr(obj, 'mom_out', None) -
ndarray(shape, dtype=float, buffer=None, offset=0, - strides=None, order=None)
- -An array object represents a multidimensional, homogeneous array -of fixed-size items. An associated data-type object describes the -format of each element in the array (its byte-order, how many bytes it -occupies in memory, whether it is an integer, a floating point number, -or something else, etc.)
- -Arrays should be constructed using array, zeros or empty (refer
-to the See Also section below). The parameters given here refer to
-a low-level method (ndarray(...)) for instantiating an array.
For more information, refer to the numpy module and examine the
-methods and attributes of an array.
Parameters
- --
-
- (for the __new__ method; see Notes below) -
- shape (tuple of ints): -Shape of created array. -
- dtype (data-type, optional): -Any object that can be interpreted as a numpy data type. -
- buffer (object exposing buffer interface, optional): -Used to fill the array with data. -
- offset (int, optional): -Offset of array data in buffer. -
- strides (tuple of ints, optional): -Strides of data in memory. -
- order ({'C', 'F'}, optional): -Row-major (C-style) or column-major (Fortran-style) order. -
Attributes
- --
-
- T (ndarray): -Transpose of the array. -
- data (buffer): -The array's elements, in memory. -
- dtype (dtype object): -Describes the format of the elements in the array. -
- flags (dict): -Dictionary containing information related to memory use, e.g., -'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. -
- flat (numpy.flatiter object):
-Flattened version of the array as an iterator. The iterator
-allows assignments, e.g.,
x.flat = 3(Seendarray.flatfor -assignment examples; TODO).
- - imag (ndarray): -Imaginary part of the array. -
- real (ndarray): -Real part of the array. -
- size (int): -Number of elements in the array. -
- itemsize (int): -The memory use of each array element in bytes. -
- nbytes (int):
-The total number of bytes required to store the array data,
-i.e.,
itemsize * size.
- - ndim (int): -The array's number of dimensions. -
- shape (tuple of ints): -Shape of the array. -
- strides (tuple of ints):
-The step-size required to move from one element to the next in
-memory. For example, a contiguous
(3, 4)array of type -int16in C-order has strides(8, 2). This implies that -to move from element to element in memory requires jumps of 2 bytes. -To move from row-to-row, one needs to jump 8 bytes at a time -(2 * 4).
- - ctypes (ctypes object): -Class containing properties of the array needed for interaction -with ctypes. -
- base (ndarray):
-If the array is a view into another array, that array is its
base-(unless that array is also a view). Thebasearray is where the -array data is actually stored.
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See Also
- -array: Construct an array.
-zeros: Create an array, each element of which is zero.
-empty: Create an array, but leave its allocated memory unchanged (i.e.,
-it contains "garbage").
-dtype: Create a data-type.
-numpy.typing.NDArray: A :term:generic <generic type> version
-of ndarray.
Notes
- -There are two modes of creating an array using __new__:
-
-
- If
bufferis None, then onlyshape,dtype, andorder-are used.
- - If
bufferis an object exposing the buffer interface, then -all keywords are interpreted.
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No __init__ method is needed because the array is fully initialized
-after the __new__ method.
Examples
- -These examples illustrate the low-level ndarray constructor. Refer
-to the See Also section above for easier ways of constructing an
-ndarray.
First mode, buffer is None:
>>> np.ndarray(shape=(2,2), dtype=float, order='F')
-array([[0.0e+000, 0.0e+000], # random
- [ nan, 2.5e-323]])
-Second mode:
- ->>> np.ndarray((2,), buffer=np.array([1,2,3]),
-... offset=np.int_().itemsize,
-... dtype=int) # offset = 1*itemsize, i.e. skip first element
-array([2, 3])
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- g5H
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- Gamma_5 hermitean conjugate
- -Uses the fact that the propagator is gamma5 hermitean, so just the -in and out momenta of the propagator are exchanged.
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- Inherited Members
--
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- numpy.ndarray -
- dumps -
- dump -
- all -
- any -
- argmax -
- argmin -
- argpartition -
- argsort -
- astype -
- byteswap -
- choose -
- clip -
- compress -
- conj -
- conjugate -
- copy -
- cumprod -
- cumsum -
- diagonal -
- dot -
- fill -
- flatten -
- getfield -
- item -
- itemset -
- max -
- mean -
- min -
- newbyteorder -
- nonzero -
- partition -
- prod -
- ptp -
- put -
- ravel -
- repeat -
- reshape -
- resize -
- round -
- searchsorted -
- setfield -
- setflags -
- sort -
- squeeze -
- std -
- sum -
- swapaxes -
- take -
- tobytes -
- tofile -
- tolist -
- tostring -
- trace -
- transpose -
- var -
- view -
- ndim -
- flags -
- shape -
- strides -
- data -
- itemsize -
- size -
- nbytes -
- base -
- dtype -
- real -
- imag -
- flat -
- ctypes -
- T - -
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-def inv_propagator(prop): - """ Inverts a 12x12 quark propagator""" - if prop.shape != (12, 12): - raise Exception("Only 12x12 propagators can be inverted.") - return Npr_matrix(inv(prop), prop.mom_in) -
Inverts a 12x12 quark propagator
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-def Zq(inv_prop, fermion='Wilson'): - """ Calculates the quark field renormalization constant Zq - - Parameters - ---------- - inv_prop : array - Inverted 12x12 quark propagator - fermion : str - Fermion type for which the tree-level propagator is used - in the calculation of Zq. Default Wilson. - """ - _check_geometry() - mom = np.copy(inv_prop.mom_in) - mom[3] /= T / L - sin_mom = np.sin(2 * np.pi / L * mom) - - if fermion == 'Wilson': - p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3]) / np.sum(sin_mom ** 2) - elif fermion == 'Continuum': - p_mom = 2 * np.pi / L * mom - p_slash = -1j * (p_mom[0] * gamma[0] + p_mom[1] * gamma[1] + p_mom[2] * gamma[2] + p_mom[3] * gamma[3]) / np.sum(p_mom ** 2) - elif fermion == 'DWF': - W = np.sum(1 - np.cos(2 * np.pi / L * mom)) - s2 = np.sum(sin_mom ** 2) - p_slash = -1j * (sin_mom[0] * gamma[0] + sin_mom[1] * gamma[1] + sin_mom[2] * gamma[2] + sin_mom[3] * gamma[3]) - p_slash /= 2 * (W - 1 + np.sqrt((1 - W) ** 2 + s2)) - else: - raise Exception("Fermion type '" + fermion + "' not implemented") - - res = 1 / 12. * np.trace(matmul(inv_prop, np.kron(np.eye(3, dtype=int), p_slash))) - res.gamma_method() - - if not res.imag.is_zero_within_error(5): - warnings.warn("Imaginary part of Zq is not zero within 5 sigma") - return res - - res.real.tag = "Zq '" + fermion + "', p=" + str(inv_prop.mom_in) - - return res.real -
Calculates the quark field renormalization constant Zq
- -Parameters
- --
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- inv_prop (array): -Inverted 12x12 quark propagator -
- fermion (str): -Fermion type for which the tree-level propagator is used - in the calculation of Zq. Default Wilson. -