sas.sascalc.pr package
Subpackages
Submodules
sas.sascalc.pr.distance_explorer module
Module to explore the P(r) inversion results for a range of D_max value. User picks a number of points and a range of distances, then get a series of outputs as a function of D_max over that range.

class
sas.sascalc.pr.distance_explorer.
DistExplorer
(pr_state)[source] Bases:
object
The explorer class

class
sas.sascalc.pr.distance_explorer.
Results
[source] Bases:
object
Class to hold the inversion output parameters as a function of D_max
sas.sascalc.pr.invertor module
Module to perform P(r) inversion. The module contains the Invertor class.
FIXME: The way the Invertor interacts with its C component should be cleaned up

class
sas.sascalc.pr.invertor.
Invertor
[source] Bases:
Cinvertor
Invertor class to perform P(r) inversion
The problem is solved by posing the problem as Ax = b, where x is the set of coefficients we are looking for.
Npts is the number of points.
In the following i refers to the ith base function coefficient. The matrix has its entries j in its first Npts rows set to
A[j][i] = (Fourier transformed base function for point j)
We them choose a number of rpoints, n_r, to evaluate the second derivative of P(r) at. This is used as our regularization term. For a vector r of length n_r, the following n_r rows are set to
A[j+Npts][i] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, evaluated at r[j])
The vector b has its first Npts entries set to
b[j] = (I(q) observed for point j)
The following n_r entries are set to zero.
The result is found by using scipy.linalg.basic.lstsq to invert the matrix and find the coefficients x.
Methods inherited from Cinvertor:
get_peaks(pars)
: returns the number of P(r) peaksoscillations(pars)
: returns the oscillation parameters for the output P(r)get_positive(pars)
: returns the fraction of P(r) that is above zeroget_pos_err(pars)
: returns the fraction of P(r) that is 1sigma above zero

background
= 0

chi2
= 0

clone
()[source] Return a clone of this instance

cov
= None

elapsed
= 0

estimate_alpha
(nfunc)[source] Returns a reasonable guess for the regularization constant alpha
Parameters: nfunc – number of terms to use in the expansion. Returns: alpha, message, elapsed where alpha is the estimate for alpha, message is a message for the user, elapsed is the computation time

estimate_numterms
(isquit_func=None)[source] Returns a reasonable guess for the number of terms
Parameters: isquit_func – reference to thread function to call to check whether the computation needs to be stopped. Returns: number of terms, alpha, message

from_file
(path)[source] Load the state of the Invertor from a file, to be able to generate P(r) from a set of parameters.
Parameters: path – path of the file to load

info
= {}

invert
(nfunc=10, nr=20)[source] Perform inversion to P(r)
The problem is solved by posing the problem as Ax = b, where x is the set of coefficients we are looking for.
Npts is the number of points.
In the following i refers to the ith base function coefficient. The matrix has its entries j in its first Npts rows set to
A[i][j] = (Fourier transformed base function for point j)
We them choose a number of rpoints, n_r, to evaluate the second derivative of P(r) at. This is used as our regularization term. For a vector r of length n_r, the following n_r rows are set to
A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, evaluated at r[j])
The vector b has its first Npts entries set to
b[j] = (I(q) observed for point j)
The following n_r entries are set to zero.
The result is found by using scipy.linalg.basic.lstsq to invert the matrix and find the coefficients x.
Parameters:  nfunc – number of base functions to use.
 nr – number of r points to evaluate the 2nd derivative at for the reg. term.
Returns: c_out, c_cov  the coefficients with covariance matrix

invert_optimize
(nfunc=10, nr=20)[source] Slower version of the P(r) inversion that uses scipy.optimize.leastsq.
This probably produce more reliable results, but is much slower. The minimization function is set to sum_i[ (I_obs(q_i)  I_theo(q_i))/err**2 ] + alpha * reg_term, where the reg_term is given by Svergun: it is the integral of the square of the first derivative of P(r), d(P(r))/dr, integrated over the full range of r.
Parameters:  nfunc – number of base functions to use.
 nr – number of r points to evaluate the 2nd derivative at for the reg. term.
Returns: c_out, c_cov  the coefficients with covariance matrix

iq
(out, q)[source] Function to call to evaluate the scattering intensity
Parameters: args – cparameters, and q Returns: I(q)

lstsq
(nfunc=5, nr=20)[source] The problem is solved by posing the problem as Ax = b, where x is the set of coefficients we are looking for.
Npts is the number of points.
In the following i refers to the ith base function coefficient. The matrix has its entries j in its first Npts rows set to
A[i][j] = (Fourier transformed base function for point j)
We them choose a number of rpoints, n_r, to evaluate the second derivative of P(r) at. This is used as our regularization term. For a vector r of length n_r, the following n_r rows are set to
A[i+Npts][j] = (2nd derivative of P(r), d**2(P(r))/d(r)**2, evaluated at r[j])
The vector b has its first Npts entries set to
b[j] = (I(q) observed for point j)
The following n_r entries are set to zero.
The result is found by using scipy.linalg.basic.lstsq to invert the matrix and find the coefficients x.
Parameters:  nfunc – number of base functions to use.
 nr – number of r points to evaluate the 2nd derivative at for the reg. term.
If the result does not allow us to compute the covariance matrix, a matrix filled with zeros will be returned.

nfunc
= 10

out
= None

pr_err
(c, c_cov, r)[source] Returns the value of P(r) for a given r, and base function coefficients, with error.
Parameters:  c – base function coefficients
 c_cov – covariance matrice of the base function coefficients
 r – rvalue to evaluate P(r) at
Returns: P(r)

pr_fit
(nfunc=5)[source] This is a direct fit to a given P(r). It assumes that the y data is set to some P(r) distribution that we are trying to reproduce with a set of base functions.
This method is provided as a test.

suggested_alpha
= 0

to_file
(path, npts=100)[source] Save the state to a file that will be readable by SliceView.
Parameters:  path – path of the file to write
 npts – number of P(r) points to be written

sas.sascalc.pr.invertor.
help
()[source] Provide general online help text Future work: extend this function to allow topic selection
sas.sascalc.pr.num_term module

class
sas.sascalc.pr.num_term.
NTermEstimator
(invertor)[source] Bases:
object

compare_err
()[source]

get0_out
()[source]

is_odd
(n)[source]

ls_osc
()[source]

median_osc
()[source]

num_terms
(isquit_func=None)[source]

sort_osc
()[source]


sas.sascalc.pr.num_term.
load
(path)[source]
Module contents
P(r) inversion for SAS