sas.sascalc.pr package
Submodules
sas.sascalc.pr.calc module
Converted invertor.c’s methods. Implements low level inversion functionality, with conditional Numba njit compilation.
- sas.sascalc.pr.calc.dprdr(pars, d_max, r)[source]
dP(r)/dr calculated from the expansion.
- Parameters
pars – c-parameters.
d_max – d_max.
r – r-value.
- Returns
dP(r)/dr.
- sas.sascalc.pr.calc.dprdr_calc(i, d_max, r)[source]
- sas.sascalc.pr.calc.int_pr(pars, d_max, nslice)[source]
Integral of P(r).
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
Integral of P(r).
- sas.sascalc.pr.calc.int_pr_square(pars, d_max, nslice)[source]
Regularization term calculated from the expansion.
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
Regularization term calculated from the expansion.
- sas.sascalc.pr.calc.iq(pars, d_max, q)[source]
Scattering intensity calculated from the expansion.
- Parameters
pars – c-parameters.
d_max – d_max.
q – q (vector).
- Returns
Scattering intensity from the expansion across all q.
- sas.sascalc.pr.calc.iq_smeared(p, q, d_max, height, width, npts)[source]
Scattering intensity calculated from the expansion, slit-smeared.
- Parameters
p – c-parameters.
q – q (vector).
height – slit_height.
width – slit_width.
npts – npts.
- Returns
Scattering intensity from the expansion slit-smeared across all q.
- sas.sascalc.pr.calc.njit(*args, **kw)
- sas.sascalc.pr.calc.npeaks(pars, d_max, nslice)[source]
Get the number of P(r) peaks.
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
Number of P(r) peaks.
- sas.sascalc.pr.calc.ortho(d_max, n, r)[source]
Orthogonal Functions: B(r) = 2r sin(pi*nr/d)
- Parameters
d_max – d_max.
n –
- Returns
B(r).
- sas.sascalc.pr.calc.ortho_derived(d_max, n, r)[source]
First derivative in of the orthogonal function dB(r)/dr.
- Parameters
d_max – d_max.
n –
- Returns
First derivative in dB(r)/dr.
- sas.sascalc.pr.calc.ortho_transformed(q, d_max, n)[source]
Fourier transform of the nth orthogonal function.
- Parameters
q – q (vector).
d_max – d_max.
n –
- Returns
Fourier transform of nth orthogonal function across all q.
- sas.sascalc.pr.calc.ortho_transformed_smeared(q, d_max, n, height, width, npts)[source]
Slit-smeared Fourier transform of the nth orthogonal function. Smearing follows Lake, Acta Cryst. (1967) 23, 191.
- Parameters
q – q (vector).
d_max – d_max.
n –
height – slit_height.
width – slit_width.
npts – npts.
- Returns
Slit-smeared Fourier transform of nth orthogonal function across all q.
- sas.sascalc.pr.calc.positive_errors(pars, err, d_max, nslice)[source]
Get the fraction of the integral of P(r) over the whole range of r that is at least one sigma above 0.
- Parameters
pars – c-parameters.
err – error terms.
d_max – d_max.
nslice – nslice.
- Returns
The fraction of the integral of P(r) over the whole range of r that is at least one sigma above 0.
- sas.sascalc.pr.calc.positive_integral(pars, d_max, nslice)[source]
Get the fraction of the integral of P(r) over the whole range of r that is above 0. A valid P(r) is defined as being positive for all r.
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
The fraction of the integral of P(r) over the whole range of r that is above 0.
- sas.sascalc.pr.calc.pr(pars, d_max, r)[source]
P(r) calculated from the expansion
- Parameters
pars – c-parameters.
d_max – d_max.
r – r-value to evaluate P(r).
- Returns
P(r).
- sas.sascalc.pr.calc.pr_err(pars, err, d_max, r)[source]
P(r) calculated from the expansion, with errors.
- Parameters
pars – c-parameters.
err – err.
r – r-value.
- Returns
[P(r), dP(r)].
- sas.sascalc.pr.calc.reg_term(pars, d_max, nslice)[source]
Regularization term calculated from the expansion.
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
Regularization term calculated from the expansion.
- sas.sascalc.pr.calc.rg(pars, d_max, nslice)[source]
R_g radius of gyration calculation
R_g**2 = integral[r**2 * p(r) dr] / (2.0 * integral[p(r) dr])
- Parameters
pars – c-parameters.
d_max – d_max.
nslice – nslice.
- Returns
R_g radius of gyration.
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:
sas.sascalc.pr.p_invertor.Pinvertor
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 then choose a number of r-points, 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 1-sigma 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 then choose a number of r-points, 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 – c-parameters, 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 then choose a number of r-points, 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 – r-value 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]
sas.sascalc.pr.p_invertor module
Python implementation of the P(r) inversion Pinvertor is the base class for the Invertor class and provides the underlying computations.
- class sas.sascalc.pr.p_invertor.Pinvertor[source]
Bases:
object
- accept_q(q)[source]
Check whether a q-value is within acceptable limits.
- Returns
1 if accepted, 0 if rejected.
- basefunc_ft(d_max, n, q)[source]
Returns the value of the nth Fourier transformed base function.
- Parameters
d_max – d_max.
n –
q – q, scalar or vector.
- Returns
nth Fourier transformed base function, evaluated at q.
- check_for_zero(x)[source]
- err = array([], dtype=float64)
- get_alpha()[source]
Gets the alpha parameter.
- Returns
alpha.
- get_dmax()[source]
Gets the maximum distance.
- Returns
d_max.
- get_err(data)[source]
Function to get the err data.
- Parameters
data – Array of doubles to place err into.
- Returns
npoints - number of entries found
- get_est_bck()[source]
Gets background flag.
- Returns
est_bck.
- get_iq_smeared(pars, q)[source]
Function to call to evaluate the scattering intensity. The scattering intensity is slit-smeared.
- Parameters
pars – c-parameters
q – q, scalar or vector.
- Returns
I(q), either scalar or vector depending on q.
- get_nerr()[source]
Gets the number of error points.
- Returns
nerr.
- get_nx()[source]
Gets the number of x points.
- Returns
npoints.
- get_ny()[source]
Gets the number of y points.
- Returns
ny.
- get_peaks(pars)[source]
Returns the number of peaks in the output P(r) distribution for the given set of coefficients.
- Parameters
pars – c-parameters.
- Returns
number of P(r) peaks.
- get_pos_err(pars, pars_err)[source]
Returns the fraction of P(r) that is 1 standard deviation above zero over the full range of r for the given set of coefficients.
- Parameters
pars – c-parameters.
pars_err – pars_err.
- Returns
fraction of P(r) that is positive.
- get_positive(pars)[source]
Returns the fraction of P(r) that is positive over the full range of r for the given set of coefficients.
- Parameters
pars – c-parameters.
- Returns
fraction of P(r) that is positive.
- get_pr_err(pars, pars_err, r)[source]
Function to call to evaluate P(r) with errors.
- Parameters
pars – c-parameters.
pars_err – pars_err.
r – r-value.
- Returns
(P(r), dP(r))
- get_qmax()[source]
Gets the maximum q.
- Returns
q_max.
- get_qmin()[source]
Gets the minimum q.
- Returns
q_min.
- get_slit_height()[source]
Gets the slit height.
- Returns
slit_height.
- get_slit_width()[source]
Gets the slit width.
- Returns
slit_width.
- get_x(data)[source]
Function to get the x data.
- Parameters
data – Array to place x into
- Returns
npoints - Number of entries found.
- get_y(data)[source]
Function to get the y data.
- Parameters
data – Array of doubles to place y into.
- Returns
npoints - Number of entries found.
- iq(pars, q)[source]
Function to call to evaluate the scattering intensity.
- Parameters
pars – c-parameters
q – q, scalar or vector.
- Returns
I(q)
- iq0(pars)[source]
Returns the value of I(q=0).
- Parameters
pars – c-parameters.
- Returns
I(q=0)
- is_valid()[source]
Check the validity of the stored data.
- Returns
Returns the number of points if it’s all good, -1 otherwise.
- nerr = 0
- npoints = 0
- ny = 0
- oscillations(pars)[source]
Returns the value of the oscillation figure of merit for the given set of coefficients. For a sphere, the oscillation figure of merit is 1.1.
- Parameters
pars – c-parameters.
- Returns
oscillation figure of merit.
- pr(pars, r)[source]
Function to call to evaluate P(r).
- Parameters
pars – c-parameters.
r – r-value to evaluate P(r) at.
- Returns
P(r)
- pr_residuals(pars)[source]
Function to call to evaluate the residuals for P(r) minimization (for testing purposes).
- Parameters
pars – input parameters.
- Returns
residuals - list of residuals.
- residuals(pars)[source]
Function to call to evaluate the residuals for P(r) inversion.
- Parameters
pars – input parameters.
- Returns
residuals - list of residuals.
- rg(pars)[source]
Returns the value of the radius of gyration Rg.
- Parameters
pars – c-parameters.
- Returns
Rg.
- set_alpha(alpha)[source]
Sets the alpha parameter.
- Parameters
alpha – float to set alpha to.
- Returns
alpha.
- set_dmax(d_max)[source]
Sets the maximum distance.
- Parameters
d_max – float to set d_max to.
- Returns
d_max
- set_err(data)[source]
Function to set the err data.
- Parameters
data – Array of doubles to set err to.
- Returns
nerr - Number of entries found.
- set_est_bck(est_bck)[source]
Sets background flag.
- Parameters
est_bck – int to set est_bck to.
- Returns
est_bck.
- set_qmax(max_q)[source]
Sets the maximum q.
- Parameters
max_q – float to set q_max to.
- Returns
q_max.
- set_qmin(min_q)[source]
Sets the minimum q.
- Parameters
min_q – float to set q_min to.
- Returns
q_min.
- set_slit_height(slit_height)[source]
Sets the slit height in units of q [A-1].
- Parameters
slit_height – float to set slit-height to.
- Returns
slit_height.
- set_slit_width(slit_width)[source]
Sets the slit width in units of q [A-1].
- Parameters
slit_width – float to set slit_width to.
- Returns
slit_width.
- set_x(data)[source]
Function to set the x data.
- Parameters
data – Array of doubles to set x to.
- Returns
npoints - Number of entries found, the size of x.
- set_y(data)[source]
Function to set the y data.
- Parameters
data – Array of doubles to set y to.
- Returns
ny - Number of entries found.
- slit_height = 0.0
- slit_width = 0.0
- x = array([], dtype=float64)
- y = array([], dtype=float64)
Module contents
P(r) inversion for SAS