Transformer

This module defines the Transformer class that performs the Fourier transforms

class pystog.transformer.Transformer[source]

Bases: object

The Transformer class is used to Fourier transform between the difference spaces. Either: a reciprocal space function -> real space function or a real space function -> reciprocal space function

Examples:

>>> import numpy
>>> from pystog import Transformer
>>> transformer = Transformer()
>>> q, sq = numpy.loadtxt("my_sofq_file.txt",unpack=True)
>>> r = numpy.linspace(0., 25., 2500)
>>> r, gr, dgr = transformer.S_to_G(q, sq, r)
>>> q = numpy.linspace(0., 25., 2500)
>>> q, sq, dsq = transformer.G_to_S(r, gr, q)

DCS_to_G(q, dcs, r, ddcs=None, **kwargs)[source]

Transforms from reciprocal space $\frac{d \sigma}{d \Omega}(Q)$ to real space $G_{PDFFIT}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
dcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ vector
r (numpy.array or list) – $r$ -space vector
ddcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ uncertainties

Returns:

$r$ , $G_{PDFFIT}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

DCS_to_GK(q, dcs, r, ddcs=None, **kwargs)[source]

Transforms from reciprocal space $\frac{d \sigma}{d \Omega}(Q)$ to real space $G_{Keen Version}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
dcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ vector
r (numpy.array or list) – $r$ -space vector
ddcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ uncertainties

Returns:

$r$ , $G_{Keen Version}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

DCS_to_g(q, dcs, r, ddcs=None, **kwargs)[source]

Transforms from reciprocal space $\frac{d \sigma}{d \Omega}(Q)$ to real space $g(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
dcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ vector
r (numpy.array or list) – $r$ -space vector
ddcs (numpy.array or list) – $\frac{d \sigma}{d \Omega}(Q)$ uncertainties

Returns:

$r$ , $g(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

FK_to_G(q, fq_keen, r, dfq_keen=None, **kwargs)[source]

Transforms from reciprocal space $F(Q)$ to real space $G_{PDFFIT}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq_keen (numpy.array or list) – $F(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dfq_keen (numpy.array or list) – $F(Q)$ vector uncertainties

Returns:

$r$ , $G_{PDFFIT}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

FK_to_GK(q, fq_keen, r, dfq_keen=None, **kwargs)[source]

Transforms from reciprocal space $F(Q)$ to real space $G_{Keen Version}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq_keen (numpy.array or list) – $F(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dfq_keen (numpy.array or list) – $F(Q)$ vector uncertainties

Returns:

$r$ , $G_{Keen Version}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

FK_to_g(q, fq_keen, r, dfq_keen=None, **kwargs)[source]

Transforms from reciprocal space $F(Q)$ to real space $g(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq_keen (numpy.array or list) – $F(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dfq_keen (numpy.array or list) – $F(Q)$ vector uncertainties

Returns:

$r$ , $g(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

F_to_G(q, fq, r, dfq=None, **kwargs)[source]

Transforms from reciprocal space $Q[S(Q)-1]$ to real space $G_{PDFFIT}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq (numpy.array or list) – $Q[S(Q)-1]$ vector
r (numpy.array or list) – $r$ -space vector
dfq (numpy.array or list) – uncertainty on $Q[S(Q)-1]$

Returns:

$r$ , $G_{PDFFIT}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

F_to_GK(q, fq, r, dfq=None, **kwargs)[source]

Transforms from reciprocal space $Q[S(Q)-1]$ to real space $G_{Keen Version}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq (numpy.array or list) – $Q[S(Q)-1]$ vector
r (numpy.array or list) – $r$ -space vector
dfq (numpy.array or list) – uncertainty on $Q[S(Q)-1]$

Returns:

$r$ , $G_{Keen Version}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

F_to_g(q, fq, r, dfq=None, **kwargs)[source]

Transforms from reciprocal space $Q[S(Q)-1]$ to real space $g(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
fq (numpy.array or list) – $Q[S(Q)-1]$ vector
r (numpy.array or list) – $r$ -space vector
dfq (numpy.array or list) – uncertainty on $Q[S(Q)-1]$

Returns:

$r$ , $g(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

GK_to_DCS(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{Keen Version}(r)$ to reciprocal space $\frac{d \sigma}{d \Omega}(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{Keen Version}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{Keen Version}(r)$ uncertainties

Returns:

$Q$ , $\frac{d \sigma}{d \Omega}(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

GK_to_F(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{Keen Version}(r)$ to reciprocal space $Q[S(Q)-1]$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{Keen Version}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{Keen Version}(r)$ uncertainties

Returns:

$Q$ , $Q[S(Q)-1]$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

GK_to_FK(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{Keen Version}(r)$ to reciprocal space $F(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{Keen Version}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{Keen Version}(r)$ uncertainties

Returns:

$Q$ , $F(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

GK_to_S(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{Keen Version}(r)$ to reciprocal space $S(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{Keen Version}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{Keen Version}(r)$ uncertainties

Returns:

$Q$ , $S(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

G_to_DCS(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{PDFFIT}(r)$ to reciprocal space $\frac{d \sigma}{d \Omega}(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{PDFFIT}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{PDFFIT}(r)$ uncertainties

Returns:

$Q$ , $\frac{d \sigma}{d \Omega}(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

G_to_F(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{PDFFIT}(r)$ to reciprocal space $Q[S(Q)-1]$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{PDFFIT}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{PDFFIT}(r)$ uncertainties

Returns:

$Q$ , $Q[S(Q)-1]$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

G_to_FK(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{PDFFIT}(r)$ to reciprocal space $F(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{PDFFIT}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{PDFFIT}(r)$ uncertainties

Returns:

$Q$ , $F(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

G_to_S(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $G_{PDFFIT}(r)$ to reciprocal space $S(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $G_{PDFFIT}(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $G_{PDFFIT}(r)$ uncertainties

Returns:

$Q$ , $S(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

S_to_G(q, sq, r, dsq=None, **kwargs)[source]

Transforms from reciprocal space $S(Q)$ to real space $G_{PDFFIT}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
sq (numpy.array or list) – $S(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dsq (numpy.array or list) – $S(Q)$ uncertainties

Returns:

$r$ , $G_{PDFFIT}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

S_to_GK(q, sq, r, dsq=None, **kwargs)[source]

Transforms from reciprocal space $S(Q)$ to real space $G_{Keen Version}(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
sq (numpy.array or list) – $S(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dsq (numpy.array or list) – $S(Q)$ uncertainties

Returns:

$r$ , $G_{Keen Version}(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

S_to_g(q, sq, r, dsq=None, **kwargs)[source]

Transforms from reciprocal space $S(Q)$ to real space $g(r)$

Parameters:

q (numpy.array or list) – $Q$ -space vector
sq (numpy.array or list) – $S(Q)$ vector
r (numpy.array or list) – $r$ -space vector
dsq (numpy.array or list) – $S(Q)$ uncertainties

Returns:

$r$ , $g(r)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

apply_cropping(x, y, xmin, xmax, dy=None)[source]

Utility to crop x and y based on xmin and xmax along x. Provides the capability to specify the (Qmin,Qmax) or (Rmin,Rmax) in the Fourier transform

Parameters:

x (numpy.array or list) – domain vector
y (numpy.array or list) – range vector
xmin (float) – minimum x-value for crop
xmax (float) – maximum x-value for crop
dy (numpy.array or list) – uncertainty vector

Returns:

vector pair (x,y) with cropping applied

Return type:

(numpy.array, numpy.array, numpy.array)

fourier_transform(xin, yin, xout, xmin=None, xmax=None, dy_in=None, **kwargs)[source]

The Fourier transform function. The kwargs argument allows for different modifications: Lorch dampening, omitted low-x range correction,

Parameters:

xin (numpy.array or list) – domain vector for space to be transformed from
yin (numpy.array or list) – range vector for space to be transformed from
xout (numpy.array or list) – domain vector for space to be transformed to
xmin (float) – minimum x-value for crop
xmax (float) – maximum x-value for crop
dy_in (numpy.array or list) – uncertainty vector for yin

Returns:

vector pair of transformed domain, range vectors, and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

g_to_DCS(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $g(r)$ to reciprocal space $\frac{d \sigma}{d \Omega}(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $g(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $g(r)$ uncertainties

Returns:

$Q$ , $\frac{d \sigma}{d \Omega}(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

g_to_F(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $g(r)$ to reciprocal space $Q[S(Q)-1]$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $g(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $g(r)$ uncertainties

Returns:

$Q$ , $Q[S(Q)-1]$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

g_to_FK(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $g(r)$ to reciprocal space $F(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $g(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $g(r)$ uncertainties

Returns:

$Q$ , $F(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array

g_to_S(r, gr, q, dgr=None, **kwargs)[source]

Transforms from real space $g(r)$ to reciprocal space $S(Q)$

Parameters:

r (numpy.array or list) – $r$ -space vector
gr (numpy.array or list) – $g(r)$ vector
q (numpy.array or list) – $Q$ -space vector
dgr (numpy.array or list) – $g(r)$ uncertainties

Returns:

$Q$ , $S(Q)$ , and uncertainties

Return type:

numpy.array, numpy.array, numpy.array