shgpy.core.data_handler module¶

class shgpy.core.data_handler.DataContainer(iterable, input_angle_units, normal_to_oblique=False)¶

Bases: object

Contains SHG data in phi-space.

Parameters:

iterabledict or array_like: dict which defines the data. Should be in form {‘PP’:array([xdata, ydata]), ‘PS’:…}. Also accepts array_like of form ((‘PP’:array([xdata, ydata])), (‘PS’, …), …).
input_angle_units{‘radians’, ‘degrees’}: Units of xdata.
normal_to_obliquebool, optional: Defaults to False. If True, iterable should have only two elements: one with key ‘PP’ or ‘SS’, and one with key ‘PS’ or ‘SP’. Then, upon initialization, compute the “missing” polarization components by rotating by 90 degrees. The final object has dat.get_keys() = ['PP', 'PS', 'SP', 'SS'].

Notes

The function of the DataContainer class is to hold data which could just as well be contained in a dictionary defined like data = {'PP':array([xdata, ydata]), 'PS':array([xdata, ydata]), ...}. Many of the associated methods involve getting and setting this data like you would in a dictionary. However, putting this data in a predefined objects allows one to keep track of whatever manipulations (scaling, offsetting) have been applied to the data, as well as other attributes like the units with which the data was defined.

as_pandas(requested_angle_units, index='multi')¶

Get data as a pandas DataFrame.

Parameters:

requested_angle_units{‘radians’, ‘degrees’}: Units requested for xdata
index{‘multi’, ‘none’}, optional: If ‘multi’, the returned pandas.DataFrame object has a MultiIndex structure. If ‘none’, no index is supplied to pandas.DataFrame. Default is ‘multi’

copy()¶: Return a copy of the DataContainer.

filter(filter, *args, **kwargs)¶

Apply a filter to the y-axis data.

Parameters:

filterfunction: The function to apply to the y-axis data. Must have the signature filter(ydata, *args, **kwargs).
argslist-like: Arguments to pass to filter.
kwargsdict: Keywork arguments to pass to filter.

get_items(requested_angle_units)¶

Get a list of (pc, data) pairs.

Equivalent to dict.items().

Parameters:

requested_angle_units{‘radians’, ‘degrees’}: Units requested for xdata.

Returns:

datalist of (pc, ndarray) tuple: List of data for each polarization combination, each in the form (pc, array([xdata, ydata]))

get_keys()¶

Get the polarization combinations for this data.

Equivalent to dict.keys().

Returns:

pcslist of str

get_maxval()¶

Get the maximum value of the data.

Returns:

mac_pcstr: The polarization combination for which the maximum occurred
maximum_valuefloat: The maximum value attained.

get_minval()¶

Get the minimum value of the data.

Returns:

min_pcstr: The polarization combination for which the minimum occurred.
minimum_valuefloat: The minimum value attained.

get_offset()¶: Returns the degree to which the data has been offset

get_pc(pc, requested_angle_units)¶

Get data for single polarization combination.

Parameters:

pcstr: Polarization combination of interest.
requested_angle_units{‘radians’, ‘degrees’}: Units requested for xdata.

Returns:

datandarray: Data for polarization combination pc in the form array([xdata, ydata]).

get_pc_maxval(pc)¶

Get the maximum value of a particular polarization combination.

Parameters:

pcstr: The polarization combination of interest.

Returns:

maximum_valuefloat

get_pc_minval(pc)¶

Get the minimum value of a particular polarization combination.

Parameters:

pcstr: The polarization combination of interest.

Returns:

minimum_valuefloat

get_phase_shift(requested_angle_units)¶

Get the extent to which this data has been phase shifted from the original.

Parameters:

requested_angle_units{‘radians’, ‘degrees’}

Returns:

phase_shiftfloat

get_scale()¶: Get the extent to which this data has been scaled from the original.

get_values(requested_angle_units)¶

Get a list of data (without polarization combination reference)

Equivalent to dict.values().

Parameters:

requested_angle_units{‘radians’, ‘degrees’}: Units requested for xdata.

Returns:

datalist of ndarray: Data for each polarization combination in the form array([xdata, ydata])

normalize_data(desired_maximum=1)¶: Normalize the data to a desired maximum.

phase_shift_data(angle, angle_units)¶

Phase shift the data by a constant amount.

Parameters:

anglefloat
angle_units{‘radians’, ‘degrees’}: Units of argument angle.

scale_data(scale_factor)¶: Scale the data by a constant factor.

subtract_min()¶: Subtract the minimum from the data.

class shgpy.core.data_handler.FormContainer(iterable)¶

Bases: object

Contains an SHG formula in phi-space.

Parameters:

iterabledict or array_like: dict which defines the formula. Should be in form {‘PP’:sympy.Expr, ‘PS’:…, …}. Also accepts array_like of form ((‘PP’:sympy.Expr), (‘PS’, …), …).

Notes

While fitting RA-SHG in Fourier space is usually faster, for simple problems it is acceptable to fit in real space. An instance of the FormContainer class provides a convenient means of storing and manipulating such a formula. It basically acts as a dictionary of {pc:formula} pairs, where pc labels the polarization combination and formula is an instance of the sympy.Expr class.

apply_arbitrary_scale(scale_var)¶

apply_phase_shift(phase_shift, var_to_shift)¶

Phase shift the formula.

Parameters:

phase_shiftsympy.Expr: Amount to shift by
var_to_shiftsympy.Symbol: Variable to shift

Notes

This method is equivalent to subs([var_to_shift, var_to_shift+phase_shift])

as_pandas(index='multi')¶

Get data as a pandas DataFrame.

Parameters:

index{‘multi’, ‘none’}, optional: If ‘multi’, the returned pandas.DataFrame object has a MultiIndex structure. If ‘none’, no index is supplied to pandas.DataFrame. Default is ‘multi’

copy()¶: Return a copy of the FormContainer.

expand()¶: Apply the sympy.expand method to every polarization combination.

get_free_symbols()¶: Return a sorted list of the free symbols in the Fourier formula.

get_items()¶

Get a list of (pc, formula) pairs.

Equivalent to dict.items().

Returns:

itemslist of (str, sympy.Expr) tuple: List of data for each polarization combination, each in the form (pc, formula)

get_keys()¶

Get the polarization combinations for this formula.

Equivalent to dict.keys().

Returns:

pcslist of str

get_pc(pc)¶

Get the formula for single polarization combination.

Parameters:

pcstr: Polarization combination of interest.

Returns:

formulasympy.Expr: Formula expression for polarization combination pc.

get_values()¶

Get a list of the formulas (without polarization combination reference)

Equivalent to dict.values().

Returns:

valueslist of sympy.Expr

simplify()¶: Apply the sympy.simplify method to every polarization combination.

subs(subs_array)¶

Substitute for some variables in the Fourier formula.

Parameters:

subs_arrayarray_like of array_like of sympy.Expr: An array of pairs of values. For example, to substitute the expression 2*psi for the variable phi, use subs_array = ((phi, 2*psi)).

shgpy.core.data_handler.dat_add(dat1, dat2)¶

Add two DataContainer instances.

Parameters:

dat1DataContainer: Instance of DataContainer
dat2DataContainer: Instance of DataContainer

Returns:

dat_resultDataContainer: Instance of DataContainer containing the contents of dat1+dat2.

shgpy.core.data_handler.dat_subtract(dat1, dat2)¶

Subtract two DataContainer instances.

Parameters:

dat1DataContainer: Instance of DataContainer
dat2DataContainer: Instance of DataContainer

Returns:

dat_resultDataContainer: Instance of DataContainer containing the contents of dat1-dat2.

shgpy.core.data_handler.dat_to_fdat(dat, interp_kind='cubic', M=16)¶

Convert instance of DataContainer to instance of fDataContainer

Parameters:

datDataContainer: Instance of DataContainer
interp_kindstr or int, optional: Specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, ‘next’, where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order; ‘previous’ and ‘next’ simply return the previous or next value of the point) or as an integer specifying the order of the spline interpolator to use. Default is ‘cubic’.
Mint, optional: Number of Fourier frequencies, defaults to 16.

Returns:

fdatfDataContainer: Instance of fDataContainer

Notes

This function works by taking a DataContainer instance and performing an interpolation so that the points are equally spaced along phi. Then it performs a Fourier transform and returns an fDataContainer instance. The interpolation is necessary because a large portion of the codebase requires equally spaced points in order for the Fourier transform to be well-defined.

class shgpy.core.data_handler.fDataContainer(iterable, M=16)¶

Bases: object

Contains SHG data in Fourier space.

Parameters:

iterabledict or array_like: dict which defines the data. Should be in form {‘PP’:ndarray(…), ‘PS’:…, …}. Also accepts array_like of form ((‘PP’:ndarray(…)), (‘PS’, …), …).

Notes

A central capability of the shgpy package is to be able to fit RA-SHG data in Fourier space. What that amounts to is fitting the Fourier components of a particular fitting formula to the Fourier components of the data. An instance of the fDataContainer class basically acts as a dictionary holding pairs (pc, fdata), where pc is a str label for the polarization combination and fdata is an ndarray of length 2*M+1. The nth element here denotes the (n-M)th fourier component of the data to be fitted.

as_pandas(index='multi')¶

Get data as a pandas DataFrame.

Parameters:

index{‘multi’, ‘none’}, optional: If ‘multi’, the returned pandas.DataFrame object has a MultiIndex structure. If ‘none’, no index is supplied to pandas.DataFrame. Default is ‘multi’

copy()¶: Return a copy of the fDataContainer.

get_M()¶

Get the number of Fourier frequencies.

Each fdata array has 2*M+1 elements.

get_items()¶

Get a list of (pc, fdata) pairs.

Equivalent to dict.items().

Returns:

fdatalist of (pc, ndarray) tuple: List of data for each polarization combination, each in the form (pc, array(shape=(2*M+1,)))

get_keys()¶

Get the polarization combinations for this data.

Equivalent to dict.keys().

Returns:

pcslist of str

get_maxval()¶

Get the maximum value of the data.

Returns:

mac_pcstr: The polarization combination for which the maximum occurred
maximum_valuefloat: The maximum value attained.

Notes

Since the elements of the fourier transform are in general complex numbers, this method returns the maximum value of the magnitudes of the different elements.

get_pc(pc)¶

Get fdata for single polarization combination.

Parameters:

pcstr: Polarization combination of interest.

Returns:

fdatandarray: Data for polarization combination pc with shape 2*M+1.

get_pc_maxval(pc)¶

Get the maximum value of a particular polarization combination.

Parameters:

pcstr: The polarization combination of interest.

Returns:

maximum_valuefloat: Returns maximum of magnitudes of fourier components (see get_maxval())

get_phase_shift(requested_angle_units)¶

Get the extent to which this data has been phase shifted from the original.

Parameters:

requested_angle_units{‘radians’, ‘degrees’}

Returns:

phase_shiftfloat

get_scale()¶: Get the extent to which this data has been scaled from the original.

get_values()¶

Get a list of data (without polarization combination reference)

Equivalent to dict.values().

Returns:

fdatalist of ndarray: Data for each polarization combination in the form array(shape=(2*M+1,))

normalize_fdata(desired_maximum)¶: Normalize the data to a desired maximum.

phase_shift_fdata(angle, angle_units)¶

Phase shift the data by a constant amount.

Parameters:

anglefloat
angle_units{‘radians’, ‘degrees’}: Units of argument angle.

scale_fdata(scale_factor)¶: Normalize the fdata by a given amount.

class shgpy.core.data_handler.fFormContainer(iterable, M=16)¶

Bases: object

Contains an SHG formula in Fourier space.

Parameters:

iterabledict or array_like: dict which defines the Fourier formula. Should be in form {‘PP’:ndarray(…), ‘PS’:…, …}. Also accepts array_like of form ((‘PP’:ndarray(…)), (‘PS’, …), …).

Notes

In order to fit RA-SHG data in Fourier space, we need to know the different Fourier components of our fitting formula. An instance of the fFormContainer class provides a convenient means of holding and manipulating such a Fourier formula. It basically acts as a dictionary of {pc:fformula} pairs, where pc labels the polarization combination and fformula is an ndarray of length 2*M+1. Here, the nth element of fformula contains a formula for the (n-M)th Fourier coefficient.

apply_arbitrary_scale(scale_var)¶

apply_phase_shift(phase_shift)¶

Phase shift the Fourier formula.

Parameters:

phase_shiftsympy.Expr

Notes

This method works simply by multiplying the mth component of the Fourier formula by sympy.exp(1j * m * phase_shift).

as_pandas(index='multi')¶

Get data as a pandas DataFrame.

Parameters:

index{‘multi’, ‘none’}, optional: If ‘multi’, the returned pandas.DataFrame object has a MultiIndex structure. If ‘none’, no index is supplied to pandas.DataFrame. Default is ‘multi’

copy()¶: Return a copy of the fFormContainer.

get_M()¶

Get the number of Fourier frequencies.

Each Fourier formula array has 2*M+1 elements.

get_free_symbols()¶: Return a sorted list of the free symbols in the Fourier formula.

get_items()¶

Get a list of (pc, fformula) pairs.

Equivalent to dict.items().

Returns:

itemslist of (str, ndarray) tuple: List of data for each polarization combination, each in the form (pc, array(shape=(2*M+1,)))

get_keys()¶

Get the polarization combinations for this Fourier formula.

Equivalent to dict.keys().

Returns:

pcslist of str

get_pc(pc)¶

Get the Fourier formula for single polarization combination.

Parameters:

pcstr: Polarization combination of interest.

Returns:

fformulandarray: Fourier formula array for polarization combination pc.

get_values()¶

Get a list of the Fourier formulas (without polarization combination reference)

Equivalent to dict.values().

Returns:

valueslist of ndarray: Data for each polarization combination in the form array([xdata, ydata])

subs(subs_array)¶

Substitute for some variables in the Fourier formula.

Parameters:

subs_arrayarray_like of array_like of sympy.Expr: An array of pairs of values. For example, to substitute the expression 2*xyz for the variable xxx, use subs_array = ((xxx, 2*xyz),).

shgpy.core.data_handler.fdat_to_dat(fdat, num_points)¶

Convert instance of fDataContainer to instance of DataContainer

Parameters:

fdatfDataContainer: Instance of fDataContainer
num_pointsint: Number of different points to put into the DataContainer.

Returns:

datDataContainer: Instance of DataContainer

Notes

This function operates by taking an instance of the fDataContainer class and performing an inverse Fourier transform.

shgpy.core.data_handler.fform_to_dat(fform, subs_dict, num_points)¶

Convert instance of fFormContainer to instance of DataContainer

Parameters:

fformfFormContainer: Instance of fFormContainer
subs_dictdict: Dict of {sympy.Symbol : float} pairs to perform the substitution.
num_pointsint: Number of different points to put into the DataContainer.

Returns:

datDataContainer: Instance of DataContainer

Notes

This function operates by taking an instance of the fFormContainer class and substituting for all the relevant sympy.Symbol`s according to `subs_dict. Then it creates a DataContainer instance with num_points points.

shgpy.core.data_handler.fform_to_fdat(fform, subs_dict)¶

Convert instance of fFormContainer to instance of fDataContainer

Parameters:

fformfFormContainer: Instance of fFormContainer
subs_dictdict: Dict of {sympy.Symbol : float} pairs to perform the substitution.

Returns:

fdatfDataContainer: Instance of fDataContainer

Notes

This function operates by taking an instance of the fFormContainer class and substituting for all the relevant sympy.Symbol`s according to `subs_dict.

shgpy.core.data_handler.fform_to_form(fform)¶

Convert instance of fFormContainer to instance of FormContainer

Parameters:

fformfFormContainer: Instance of fFormContainer

Returns:

formFormContainer: Instance of FormContainer

Notes

This function operates by taking an instance of the fFormContainer class and performing a Fourier transform.

shgpy.core.data_handler.form_to_dat(form, subs_dict, num_points)¶

Convert instance of FormContainer to instance of DataContainer

Parameters:

formFormContainer: Instance of FormContainer
subs_dictdict: Dict of {sympy.Symbol : float} pairs to perform the substitution.
num_pointsint: Number of different points to put into the DataContainer.

Returns:

datDataContainer: Instance of DataContainer

Notes

This function operates by taking an instance of the FormContainer class and substituting for all the relevant sympy.Symbol`s according to `subs_dict. Then it creates a DataContainer instance with num_points points.

shgpy.core.data_handler.form_to_fdat(form, subs_dict, M=16)¶

Convert instance of FormContainer to instance of fDataContainer

Parameters:

fformFormContainer: Instance of FormContainer
subs_dictdict: Dict of {sympy.Symbol : float} pairs to perform the substitution.

Returns:

fdatfDataContainer: Instance of fDataContainer

Notes

This function operates by taking an instance of the FormContainer, doing a Fourier transform to a fFormContainer instance, and then substituting for all the relevant sympy.Symbol`s according to `subs_dict.

shgpy.core.data_handler.form_to_fform(form, M=16)¶

Convert instance of FormContainer to instance of fFormContainer

Parameters:

formFormContainer: Instance of FormContainer
Mint, optional: Number of Fourier frequencies, defaults to 16.

Returns:

fformfFormContainer: Instance of fFormContainer

Notes

This function operates by taking an instance of the FormContainer class and performing a Fourier transform.

shgpy.core.data_handler.load_data(data_filenames_dict, angle_units, normal_to_oblique=False)¶

Load RA-SHG data from a dict of filenames.

Parameters:

data_filenames_dictdict of (strstr or file object): dict of form (polarization combination : filename).
data_angle_units{‘radians’, ‘degrees’}: Units of xdata
normal_to_obliquebool, optional: Defaults to False. See DataContainer.

Returns:

datDataContainer

shgpy.core.data_handler.load_data_and_dark_subtract(data_filenames_dict, data_angle_units, dark_filenames_dict, dark_angle_units, normal_to_oblique=False)¶

Load RA-SHG data from a dict of filenames and dark subtract.

Parameters:

data_filenames_dictdict of (strstr or file object): dict of form (polarization combination : filename).
data_angle_units{‘radians’, ‘degrees’}: Units of xdata
dark_filenames_dictdict of (strstr or file object): dict of form (polarization combination : filename).
dark_angle_units{‘radians’, ‘degrees’}: Units of xdata for the dark.
normal_to_obliquebool, optional: Defaults to False. See DataContainer.

Returns:

datDataContainer

shgpy.core.data_handler.load_data_and_fourier_transform(data_filenames_dict, data_angle_units, dark_filenames_dict=None, dark_angle_units=None, interp_kind='cubic', M=16, min_subtract=False, scale=1, normal_to_oblique=False)¶

Load RA-SHG data from a dict of filenames and Fourier transform

Parameters:

data_filenames_dictdict of (strstr or file object): dict of form (polarization combination : filename).
data_angle_units{‘radians’, ‘degrees’}: Units of xdata
dark_filenames_dictdict of (strstr or file object): dict of form (polarization combination : filename).
dark_angle_units{‘radians’, ‘degrees’}: Units of xdata for the dark.
interp_kindstr or int, optional: Specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, ‘next’, where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order; ‘previous’ and ‘next’ simply return the previous or next value of the point) or as an integer specifying the order of the spline interpolator to use. Default is ‘cubic’ Dict of {sympy.Symbol : float} pairs to perform the substitution.
Mint, optional: Number of Fourier frequencies, defaults to 16.
min_subtractbool: Whether to subtract the minimum before Fourier transforming. Default is False.
normal_to_obliquebool, optional: Defaults to False. See DataContainer.

Returns:

datDataContainer
fdatfDataContainer

shgpy.core.data_handler.load_fform(fform_filename)¶

Creat instance of fFormContainer from a fform_filename.

fform_filename s are generated using the utilities provided in the fformgen module. Those utilities output a pickled fFormContainer-like object which can be loaded into a true fFormContainer instance using this function.

Parameters:

fform_filenamestr or file object

shgpy.core.data_handler.merge_containers(containers, mapping)¶

Merge two contains with new keys according to mapping.

Parameters:

containerslist of Container_like: List of Containers (DataContainer, fDataContainer, FormContainer, or fFormContainer). Must be the same type.
mappingfunction(key, index): Function which maps key of Container and index of a Container in containers to str.

Returns:

containerContainer_like: Container object of type type(containers[0]) with items ((k1, v1), (k2, v2), …), where ki are the mapped keys of the containers and vi are the corresponding values.

Examples

>>> xdata = np.linspace(0, 2*np.pi, 1000)
>>> ydata = np.sin(xdata)**2
>>> iterable = {k:np.array([xdata, ydata]) for k in ['PP', 'PS']}
>>> dat1 = DataContainer(iterable)
>>> dat2 = DataContainer(iterable)
>>> def mapping(key, index):
>>>     return key+str(index)
>>> dat3 = merge_containers([dat1, dat2], mapping)
>>> dat3.get_keys():
['PP0', 'PS0', 'PP1', 'PS2']
>>> dat3.get_values():
[array([xdata, ydata]), array([xdata, ydata]), ...]

shgpy.core.data_handler.n2i(n, M=16)¶

Convert between Fourier index and array index

Returns the index (0-2*M+1) in a Fourier array corresponding to the nth Fourier component

shgpy.core.data_handler.read_csv(filename, delimiter=',')¶

Read a csv file.

Parameters:

filenamestr or file object
delimiterstr: Defaults to ','.

Returns:

datandarray: Data from csv file of the form array([xdata, ydata]).

shgpy.core.data_handler.save_fform(fform, fform_filename)¶

Save an instance of fFormContainer to fform_filename.

Parameters:

fformfFormContainer: Instance of fFormContainer
fform_filenamestr or file object

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shgpy.core.data_handler module¶