invariant

sans.invariant.invariant

This module implements invariant and its related computations.

author:Gervaise B. Alina/UTK author:Mathieu Doucet/UTK author:Jae Cho/UTK

class sans.invariant.invariant.Extrapolator(data, model=None)

Extrapolate I(q) distribution using a given model

fit(power=None, qmin=None, qmax=None)

Fit data for y = ax + b return a and b

Parameters:

• power – a fixed, otherwise None
• qmin – Minimum Q-value
• qmax – Maximum Q-value

class sans.invariant.invariant.Guinier(scale=1, radius=60)

Bases: sans.invariant.invariant.Transform

class of type Transform that performs operations related to guinier function

evaluate_model(x)

return F(x)= scale* e-((radius*x)**2/3)

evaluate_model_errors(x)

Returns the error on I(q) for the given array of q-values

Parameters:

• x – array of q-values

extract_model_parameters(constant, slope, dconstant=0, dslope=0)

assign new value to the scale and the radius

get_allowed_bins(data)

Goes through the data points and returns a list of boolean values to indicate whether each points is allowed by the model or not.

Parameters:

• data – Data1D object

linearize_data(data)

Linearize data so that a linear fit can be performed. Filter out the data that can’t be transformed.

Parameters:

• data – LoadData1D instance

linearize_q_value(value)

Transform the input q-value for linearization

Parameters:

• value – q-value

Returns:

q*q

class sans.invariant.invariant.InvariantCalculator(data, background=0, scale=1)

Bases: object

Compute invariant if data is given. Can provide volume fraction and surface area if the user provides Porod constant and contrast values.

Precondition :the user must send a data of type DataLoader.Data1D the user provide background and scale values. Note :Some computations depends on each others.

get_data()

Returns:self._data

get_extra_data_high(npts_in=None, q_end=10, npts=20)

Returns the extrapolated data used for the high-Q invariant calculation. By default, the distribution will cover the data points used for the extrapolation. The number of overlap points is a parameter (npts_in). By default, the maximum q-value of the distribution will be Q_MAXIMUM, the maximum q-value used when extrapolating for the purpose of the invariant calculation.

Parameters:

• npts_in – number of data points for which the extrapolated data overlap
• q_end – is the maximum value to uses for extrapolated data
• npts – the number of points in the extrapolated distribution

get_extra_data_low(npts_in=None, q_start=None, npts=20)

Returns the extrapolated data used for the loew-Q invariant calculation. By default, the distribution will cover the data points used for the extrapolation. The number of overlap points is a parameter (npts_in). By default, the maximum q-value of the distribution will be the minimum q-value used when extrapolating for the purpose of the invariant calculation.

Parameters:

• npts_in – number of data points for which the extrapolated data overlap
• q_start – is the minimum value to uses for extrapolated data
• npts – the number of points in the extrapolated distribution

get_extrapolation_power(range='high')

Returns:the fitted power for power law function for a given extrapolation range

get_qstar(extrapolation=None)

Compute the invariant of the local copy of data.

Parameters:

• extrapolation – string to apply optional extrapolation

Return q_star:

invariant of the data within data’s q range

Warning :

When using setting data to Data1D , the user is responsible of checking that the scale and the background are properly apply to the data

get_qstar_high()

Compute the invariant for extrapolated data at high q range.

Implementation:

data = self._get_extra_data_high() return self._get_qstar()

Return q_star:the invariant for data extrapolated at high q.

get_qstar_low()

Compute the invariant for extrapolated data at low q range.

Implementation:

data = self._get_extra_data_low() return self._get_qstar()

Return q_star:the invariant for data extrapolated at low q.

get_qstar_with_error(extrapolation=None)

Compute the invariant uncertainty. This uncertainty computation depends on whether or not the data is smeared.

Parameters:

• extrapolation – string to apply optional extrapolation

Returns:

invariant, the invariant uncertainty

get_surface(contrast, porod_const, extrapolation=None)

Compute the specific surface from the data.

Implementation:

V =  self.get_volume_fraction(contrast, extrapolation)

Compute the surface given by:
  surface = (2*pi *V(1- V)*porod_const)/ q_star

Parameters:

• contrast – contrast value to compute the volume
• porod_const – Porod constant to compute the surface
• extrapolation – string to apply optional extrapolation

Returns:

specific surface

get_surface_with_error(contrast, porod_const, extrapolation=None)

Compute uncertainty of the surface value as well as the surface value. The uncertainty is given as follow:

dS = porod_const *2*pi[( dV -2*V*dV)/q_star
     + dq_star(v-v**2)
     
q_star: the invariant value
dq_star: the invariant uncertainty
V: the volume fraction value
dV: the volume uncertainty

Parameters:

• contrast – contrast value
• porod_const – porod constant value
• extrapolation – string to apply optional extrapolation

Return S, dS:

the surface, with its uncertainty

get_volume_fraction(contrast, extrapolation=None)

Compute volume fraction is deduced as follow:

q_star = 2*(pi*contrast)**2* volume( 1- volume)
for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2)
we get 2 values of volume:
     with   1 - 4 * k >= 0
     volume1 = (1- sqrt(1- 4*k))/2
     volume2 = (1+ sqrt(1- 4*k))/2

q_star: the invariant value included extrapolation is applied
             unit  1/A^(3)*1/cm
        q_star = self.get_qstar()
        
the result returned will be 0 <= volume <= 1

Parameters:

• contrast – contrast value provides by the user of type float. contrast unit is 1/A^(2)= 10^(16)cm^(2)
• extrapolation – string to apply optional extrapolation

Returns:

volume fraction

Note :

volume fraction must have no unit

get_volume_fraction_with_error(contrast, extrapolation=None)

Compute uncertainty on volume value as well as the volume fraction This uncertainty is given by the following equation:

dV = 0.5 * (4*k* dq_star) /(2* math.sqrt(1-k* q_star))
                     
for k = 10^(-8)*q_star/(2*(pi*|contrast|)**2)

q_star: the invariant value including extrapolated value if existing
dq_star: the invariant uncertainty
dV: the volume uncertainty

The uncertainty will be set to -1 if it can’t be computed.

Parameters:

• contrast – contrast value
• extrapolation – string to apply optional extrapolation

Returns:

V, dV = volume fraction, error on volume fraction

set_extrapolation(range, npts=4, function=None, power=None)

Set the extrapolation parameters for the high or low Q-range. Note that this does not turn extrapolation on or off.

Parameters:

• range – a keyword set the type of extrapolation . type string
• npts – the numbers of q points of data to consider for extrapolation
• function – a keyword to select the function to use for extrapolation. of type string.
• power – an power to apply power_low function

class sans.invariant.invariant.PowerLaw(scale=1, power=4)

Bases: sans.invariant.invariant.Transform

class of type transform that perform operation related to power_law function

evaluate_model(x)

given a scale and a radius transform x, y using a power_law function

evaluate_model_errors(x)

Returns the error on I(q) for the given array of q-values :param x: array of q-values

extract_model_parameters(constant, slope, dconstant=0, dslope=0)

Assign new value to the scale and the power

get_allowed_bins(data)

Goes through the data points and returns a list of boolean values to indicate whether each points is allowed by the model or not.

Parameters:

• data – Data1D object

linearize_data(data)

Linearize data so that a linear fit can be performed. Filter out the data that can’t be transformed.

Parameters:

• data – LoadData1D instance

linearize_q_value(value)

Transform the input q-value for linearization

Parameters:

• value – q-value

Returns:

log(q)

class sans.invariant.invariant.Transform

Bases: object

Define interface that need to compute a function or an inverse function given some x, y

evaluate_model(x)

Returns an array f(x) values where f is the Transform function.

evaluate_model_errors(x)

Returns an array of I(q) errors

extract_model_parameters(constant, slope, dconstant=0, dslope=0)

set private member

get_allowed_bins(data)

Goes through the data points and returns a list of boolean values to indicate whether each points is allowed by the model or not.

Parameters:

• data – Data1D object

linearize_data(data)

Linearize data so that a linear fit can be performed. Filter out the data that can’t be transformed.

Parameters:

• data – LoadData1D instance

linearize_q_value(value)

Transform the input q-value for linearization