Module sqrmat_method
Expand source code
import numpy as np
# TODO install package into enviroment
# import PyTPSA # * Must be in the same folder as PyTPSA or in the path
# TODO install these as packages
# ! Import sys and run ' sys.path.insert(1, '../Square-Matrix/Custom_Libraries/') ' and ' sys.path.insert(1, '../Library/CodeLib/') '
# from sqrmat import jordan_chain_structure, tpsvar
# from commonfuncs import numpify
class square_matrix:
# TODO Add tracking
def __init__(self, dim, order):
self.dim = dim
self.order = order
self._hp = tpsvar(dim, order=order)
# self.variables = self._hp.get_variables()
self.variables = self._hp.vars
self.degenerate_list = [None for i in range(dim)]
self.left_vector = [None for i in range(dim)]
self.jordan_norm_form_matrix = [None for i in range(dim)]
self.jordan_chain_structure = [None for i in range(dim)]
self.square_matrix = None
self.__fztow = [None for i in range(dim)]
self.__wftoz = [None for i in range(dim)]
self.__fzmap = [None for i in range(dim)]
def construct_square_matrix(self, periodic_map):
self.__fzmap = [numpify(f) for f in periodic_map]
self._hp.construct_sqr_matrix(periodic_map=periodic_map)
self.square_matrix = self._hp.sqr_mat
def get_transformation(self, target=None, res=None, chain=0, dim=None, epsilon=1e-15):
# Check if contruct sqrmat was run
if self.square_matrix is None:
raise Exception("The square matrix has not been constructed. Run \"construct_square_matrix\" first.")
# First get the degenerate list
if target is None:
target = [i for i in range(1, self.dim+1)]
# TODO Does this do what I want it to do?
if dim is None:
dim_iter = self.dim
else:
dim_iter = dim
for di in range(dim_iter):
self.degenerate_list[di] = self._hp.get_degenerate_list(di+1, resonance=res)
self._hp.sqrmat_reduction()
self._hp.jordan_form()
self.jordan_norm_form_matrix[di] = self._hp.jnf_mat
self.left_vector[di] = self._hp.left_vector[chain]
self.jordan_chain_structure[di] = jordan_chain_structure(self.jordan_norm_form_matrix[di], epsilon=epsilon)
wx0z = PyTPSA.tpsa(input_map=self.left_vector[0], dtype=complex)
wx0cz = wx0z.conjugate(mode='CP')
wy0z = PyTPSA.tpsa(input_map=self.left_vector[1], dtype=complex)
wy0cz = wy0z.conjugate(mode='CP')
w0list = [wx0z, wx0cz, wy0z, wy0cz]
invw0z = PyTPSA.inverse_map(w0list)
self.__fztow = [numpify(f) for f in w0list]
self.__wftoz = [numpify(f) for f in invw0z]
# Build Jacobian function
self.__fjacobian = [numpify(wtemp.derivative(i+1)) for wtemp in w0list for i in range(2*self.dim)]
def w(self, z):
"""Transforms normalized complex coordinates into the transformed phase space.
Inputs:
z: Array-like; [zx, zx*, zy, zy*]
Returns:
w; Numpy Array; [wx, wx*, wy, wy*]
"""
if self.__fztow[0] is None:
raise Exception("The transformation has not been found. Run \"get_transformation\" first.")
return np.array([self.__fztow[0](z), self.__fztow[1](z), self.__fztow[2](z), self.__fztow[3](z)])
def z(self, w):
"""Tranformes transformed coordinates into the normalized complex coordinate phase space.
Inputs:
w: Array-like; [wx, wx*, wy, wy*]
Returns:
z; Numpy Array; [zx, zx*, zy, zy*]
"""
if self.__wftoz[0] is None:
raise Exception("The transformation has not been found. Run \"get_transformation\" first.")
return np.array([self.__wftoz[0](w), self.__wftoz[1](w), self.__wftoz[2](w), self.__wftoz[3](w)])
def jacobian(self, z):
"""Returns the value of the jacobian matrix at z.
Inputs:
z: Array-like; [zx, zx*, zy, zy*]
Returns:
jac: Numpy Array; Jacobian
"""
jac=[]
for f in self.__fjacobian:
jac.append(f(z))
return np.array(jac)
def map(self, z):
"""Runs z through the given one turn map. z' = f(z)
Inputs:
z; Array-like; [zx, zx*, zy, zy*]
Returns:
z'; Numpy Array; [zx', zx'*, zy', zy'*]
"""
if self.__fzmap[0] is None:
raise Exception("The transformation has not been found. Run \"get_transformation\" first.")
return np.array([self.__fzmap[0](z), self.__fzmap[1](z), self.__fzmap[2](z), self.__fzmap[3](z)])
def test_sqrmat(self, atol: float = 1e-8, results: bool = False) -> tuple:
"""Checks that the lower triagular elements of the square matrix are close to zero.
Inputs:
atol: The absolute tolerance to check against.
results: Print results
Returns:
pass: If all the points are close to zero the funtion will return True
"""
dimx, dimy = self.square_matrix.shape
pass_ = False
num_errors = 0
max_error = 0
for i in range(dimx):
for j in range(dimy):
term = np.abs(self.square_matrix[i,j])
if i > j: # On the lower diagonal
if not np.isclose(term, 0, atol=atol): # If the element is not close to zero count it
num_errors += 1
if term > max_error: # Track the largest element
max_error = term*1
if results:
print("Number of Errors:", num_errors)
print("Max Error:", max_error)
if num_errors == 0:
pass_ = True
return pass_, num_errors, max_errorClasses
class square_matrix (dim, order)-
Expand source code
class square_matrix: # TODO Add tracking def __init__(self, dim, order): self.dim = dim self.order = order self._hp = tpsvar(dim, order=order) # self.variables = self._hp.get_variables() self.variables = self._hp.vars self.degenerate_list = [None for i in range(dim)] self.left_vector = [None for i in range(dim)] self.jordan_norm_form_matrix = [None for i in range(dim)] self.jordan_chain_structure = [None for i in range(dim)] self.square_matrix = None self.__fztow = [None for i in range(dim)] self.__wftoz = [None for i in range(dim)] self.__fzmap = [None for i in range(dim)] def construct_square_matrix(self, periodic_map): self.__fzmap = [numpify(f) for f in periodic_map] self._hp.construct_sqr_matrix(periodic_map=periodic_map) self.square_matrix = self._hp.sqr_mat def get_transformation(self, target=None, res=None, chain=0, dim=None, epsilon=1e-15): # Check if contruct sqrmat was run if self.square_matrix is None: raise Exception("The square matrix has not been constructed. Run \"construct_square_matrix\" first.") # First get the degenerate list if target is None: target = [i for i in range(1, self.dim+1)] # TODO Does this do what I want it to do? if dim is None: dim_iter = self.dim else: dim_iter = dim for di in range(dim_iter): self.degenerate_list[di] = self._hp.get_degenerate_list(di+1, resonance=res) self._hp.sqrmat_reduction() self._hp.jordan_form() self.jordan_norm_form_matrix[di] = self._hp.jnf_mat self.left_vector[di] = self._hp.left_vector[chain] self.jordan_chain_structure[di] = jordan_chain_structure(self.jordan_norm_form_matrix[di], epsilon=epsilon) wx0z = PyTPSA.tpsa(input_map=self.left_vector[0], dtype=complex) wx0cz = wx0z.conjugate(mode='CP') wy0z = PyTPSA.tpsa(input_map=self.left_vector[1], dtype=complex) wy0cz = wy0z.conjugate(mode='CP') w0list = [wx0z, wx0cz, wy0z, wy0cz] invw0z = PyTPSA.inverse_map(w0list) self.__fztow = [numpify(f) for f in w0list] self.__wftoz = [numpify(f) for f in invw0z] # Build Jacobian function self.__fjacobian = [numpify(wtemp.derivative(i+1)) for wtemp in w0list for i in range(2*self.dim)] def w(self, z): """Transforms normalized complex coordinates into the transformed phase space. Inputs: z: Array-like; [zx, zx*, zy, zy*] Returns: w; Numpy Array; [wx, wx*, wy, wy*] """ if self.__fztow[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__fztow[0](z), self.__fztow[1](z), self.__fztow[2](z), self.__fztow[3](z)]) def z(self, w): """Tranformes transformed coordinates into the normalized complex coordinate phase space. Inputs: w: Array-like; [wx, wx*, wy, wy*] Returns: z; Numpy Array; [zx, zx*, zy, zy*] """ if self.__wftoz[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__wftoz[0](w), self.__wftoz[1](w), self.__wftoz[2](w), self.__wftoz[3](w)]) def jacobian(self, z): """Returns the value of the jacobian matrix at z. Inputs: z: Array-like; [zx, zx*, zy, zy*] Returns: jac: Numpy Array; Jacobian """ jac=[] for f in self.__fjacobian: jac.append(f(z)) return np.array(jac) def map(self, z): """Runs z through the given one turn map. z' = f(z) Inputs: z; Array-like; [zx, zx*, zy, zy*] Returns: z'; Numpy Array; [zx', zx'*, zy', zy'*] """ if self.__fzmap[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__fzmap[0](z), self.__fzmap[1](z), self.__fzmap[2](z), self.__fzmap[3](z)]) def test_sqrmat(self, atol: float = 1e-8, results: bool = False) -> tuple: """Checks that the lower triagular elements of the square matrix are close to zero. Inputs: atol: The absolute tolerance to check against. results: Print results Returns: pass: If all the points are close to zero the funtion will return True """ dimx, dimy = self.square_matrix.shape pass_ = False num_errors = 0 max_error = 0 for i in range(dimx): for j in range(dimy): term = np.abs(self.square_matrix[i,j]) if i > j: # On the lower diagonal if not np.isclose(term, 0, atol=atol): # If the element is not close to zero count it num_errors += 1 if term > max_error: # Track the largest element max_error = term*1 if results: print("Number of Errors:", num_errors) print("Max Error:", max_error) if num_errors == 0: pass_ = True return pass_, num_errors, max_errorMethods
def construct_square_matrix(self, periodic_map)-
Expand source code
def construct_square_matrix(self, periodic_map): self.__fzmap = [numpify(f) for f in periodic_map] self._hp.construct_sqr_matrix(periodic_map=periodic_map) self.square_matrix = self._hp.sqr_mat def get_transformation(self, target=None, res=None, chain=0, dim=None, epsilon=1e-15)-
Expand source code
def get_transformation(self, target=None, res=None, chain=0, dim=None, epsilon=1e-15): # Check if contruct sqrmat was run if self.square_matrix is None: raise Exception("The square matrix has not been constructed. Run \"construct_square_matrix\" first.") # First get the degenerate list if target is None: target = [i for i in range(1, self.dim+1)] # TODO Does this do what I want it to do? if dim is None: dim_iter = self.dim else: dim_iter = dim for di in range(dim_iter): self.degenerate_list[di] = self._hp.get_degenerate_list(di+1, resonance=res) self._hp.sqrmat_reduction() self._hp.jordan_form() self.jordan_norm_form_matrix[di] = self._hp.jnf_mat self.left_vector[di] = self._hp.left_vector[chain] self.jordan_chain_structure[di] = jordan_chain_structure(self.jordan_norm_form_matrix[di], epsilon=epsilon) wx0z = PyTPSA.tpsa(input_map=self.left_vector[0], dtype=complex) wx0cz = wx0z.conjugate(mode='CP') wy0z = PyTPSA.tpsa(input_map=self.left_vector[1], dtype=complex) wy0cz = wy0z.conjugate(mode='CP') w0list = [wx0z, wx0cz, wy0z, wy0cz] invw0z = PyTPSA.inverse_map(w0list) self.__fztow = [numpify(f) for f in w0list] self.__wftoz = [numpify(f) for f in invw0z] # Build Jacobian function self.__fjacobian = [numpify(wtemp.derivative(i+1)) for wtemp in w0list for i in range(2*self.dim)] def jacobian(self, z)-
Returns the value of the jacobian matrix at z.
Inputs
z: Array-like; [zx, zx, zy, zy]
Returns
jac- Numpy Array; Jacobian
Expand source code
def jacobian(self, z): """Returns the value of the jacobian matrix at z. Inputs: z: Array-like; [zx, zx*, zy, zy*] Returns: jac: Numpy Array; Jacobian """ jac=[] for f in self.__fjacobian: jac.append(f(z)) return np.array(jac) def map(self, z)-
Runs z through the given one turn map. z' = f(z)
Inputs
z; Array-like; [zx, zx, zy, zy]
Returns
z'; Numpy Array; [zx', zx', zy', zy']
Expand source code
def map(self, z): """Runs z through the given one turn map. z' = f(z) Inputs: z; Array-like; [zx, zx*, zy, zy*] Returns: z'; Numpy Array; [zx', zx'*, zy', zy'*] """ if self.__fzmap[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__fzmap[0](z), self.__fzmap[1](z), self.__fzmap[2](z), self.__fzmap[3](z)]) def test_sqrmat(self, atol: float = 1e-08, results: bool = False) ‑> tuple-
Checks that the lower triagular elements of the square matrix are close to zero.
Inputs
atol: The absolute tolerance to check against. results: Print results
Returns
pass- If all the points are close to zero the funtion will return True
Expand source code
def test_sqrmat(self, atol: float = 1e-8, results: bool = False) -> tuple: """Checks that the lower triagular elements of the square matrix are close to zero. Inputs: atol: The absolute tolerance to check against. results: Print results Returns: pass: If all the points are close to zero the funtion will return True """ dimx, dimy = self.square_matrix.shape pass_ = False num_errors = 0 max_error = 0 for i in range(dimx): for j in range(dimy): term = np.abs(self.square_matrix[i,j]) if i > j: # On the lower diagonal if not np.isclose(term, 0, atol=atol): # If the element is not close to zero count it num_errors += 1 if term > max_error: # Track the largest element max_error = term*1 if results: print("Number of Errors:", num_errors) print("Max Error:", max_error) if num_errors == 0: pass_ = True return pass_, num_errors, max_error def w(self, z)-
Transforms normalized complex coordinates into the transformed phase space.
Inputs
z: Array-like; [zx, zx, zy, zy]
Returns
w; Numpy Array; [wx, wx, wy, wy]
Expand source code
def w(self, z): """Transforms normalized complex coordinates into the transformed phase space. Inputs: z: Array-like; [zx, zx*, zy, zy*] Returns: w; Numpy Array; [wx, wx*, wy, wy*] """ if self.__fztow[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__fztow[0](z), self.__fztow[1](z), self.__fztow[2](z), self.__fztow[3](z)]) def z(self, w)-
Tranformes transformed coordinates into the normalized complex coordinate phase space.
Inputs
w: Array-like; [wx, wx, wy, wy]
Returns
z; Numpy Array; [zx, zx, zy, zy]
Expand source code
def z(self, w): """Tranformes transformed coordinates into the normalized complex coordinate phase space. Inputs: w: Array-like; [wx, wx*, wy, wy*] Returns: z; Numpy Array; [zx, zx*, zy, zy*] """ if self.__wftoz[0] is None: raise Exception("The transformation has not been found. Run \"get_transformation\" first.") return np.array([self.__wftoz[0](w), self.__wftoz[1](w), self.__wftoz[2](w), self.__wftoz[3](w)])