schrodinger.application.matsci.gsas.GSASIImath module¶

# Third-party code. No Schrodinger Copyright.

GSASIImath: computation module¶

Routines for least-squares minimization and other stuff

schrodinger.application.matsci.gsas.GSASIImath.sind(x)¶

schrodinger.application.matsci.gsas.GSASIImath.cosd(x)¶

schrodinger.application.matsci.gsas.GSASIImath.tand(x)¶

schrodinger.application.matsci.gsas.GSASIImath.asind(x)¶

schrodinger.application.matsci.gsas.GSASIImath.acosd(x)¶

schrodinger.application.matsci.gsas.GSASIImath.atand(x)¶

schrodinger.application.matsci.gsas.GSASIImath.atan2d(y, x)¶

schrodinger.application.matsci.gsas.GSASIImath.pinv(a, rcond=1e-15)¶

Compute the (Moore-Penrose) pseudo-inverse of a matrix. Modified from numpy.linalg.pinv; assumes a is Hessian & returns no. zeros found Calculate the generalized inverse of a matrix using its singular-value decomposition (SVD) and including all large singular values.

Parameters

a (array) – (M, M) array_like - here assumed to be LS Hessian Matrix to be pseudo-inverted.
rcond (float) – Cutoff for small singular values. Singular values smaller (in modulus) than rcond * largest_singular_value (again, in modulus) are set to zero.

Returns

B : (M, M) ndarray The pseudo-inverse of a

Raises: LinAlgError: If the SVD computation does not converge.
Notes:: The pseudo-inverse of a matrix A, denoted A^+, is defined as: “the matrix that ‘solves’ [the least-squares problem] Ax = b,” i.e., if \bar{x} is said solution, then A^+ is that matrix such that \bar{x} = A^+b.

It can be shown that if Q_1 \Sigma Q_2^T = A is the singular value decomposition of A, then A^+ = Q_2 \Sigma^+ Q_1^T, where Q_{1,2} are orthogonal matrices, \Sigma is a diagonal matrix consisting of A’s so-called singular values, (followed, typically, by zeros), and then \Sigma^+ is simply the diagonal matrix consisting of the reciprocals of A’s singular values (again, followed by zeros). [1]

References: .. [1] G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL, Academic Press, Inc., 1980, pp. 139-142.

schrodinger.application.matsci.gsas.GSASIImath.HessianLSQ(func, x0, Hess, args=(), ftol=1.49012e-08, xtol=1e-06, maxcyc=0, lamda=- 3, Print=False, refPlotUpdate=None)¶

Minimize the sum of squares of a function (f) evaluated on a series of values (y): sum_{y=0}^{N_{obs}} f(y,{args}) where x = arg min(sum_{y=0}^{N_{obs}} (func(y)^2,axis=0))

Parameters

func (function) – callable method or function should take at least one (possibly length N vector) argument and returns M floating point numbers.
x0 (np.ndarray) – The starting estimate for the minimization of length N
Hess (function) – callable method or function A required function or method to compute the weighted vector and Hessian for func. It must be a symmetric NxN array
args (tuple) – Any extra arguments to func are placed in this tuple.
ftol (float) – Relative error desired in the sum of squares.
xtol (float) – Relative tolerance of zeros in the SVD solution in nl.pinv.
maxcyc (int) – The maximum number of cycles of refinement to execute, if -1 refine until other limits are met (ftol, xtol)
lamda (int) – initial Marquardt lambda=10**lamda
Print (bool) – True for printing results (residuals & times) by cycle

Returns

(x,cov_x,infodict) where

x : ndarray The solution (or the result of the last iteration for an unsuccessful call).
cov_x : ndarray Uses the fjac and ipvt optional outputs to construct an estimate of the jacobian around the solution. None if a singular matrix encountered (indicates very flat curvature in some direction). This matrix must be multiplied by the residual standard deviation to get the covariance of the parameter estimates – see curve_fit.
infodict : dict a dictionary of optional outputs with the keys:
- ’fvec’ : the function evaluated at the output
- ’num cyc’:
- ’nfev’:
- ’lamMax’:
- ’psing’:
- ’SVD0’:

schrodinger.application.matsci.gsas.GSASIImath.HessianSVD(func, x0, Hess, args=(), ftol=1.49012e-08, xtol=1e-06, maxcyc=0, lamda=- 3, Print=False, refPlotUpdate=None)¶

Minimize the sum of squares of a function (f) evaluated on a series of values (y): sum_{y=0}^{N_{obs}} f(y,{args}) where x = arg min(sum_{y=0}^{N_{obs}} (func(y)^2,axis=0))

Parameters

func (function) – callable method or function should take at least one (possibly length N vector) argument and returns M floating point numbers.
x0 (np.ndarray) – The starting estimate for the minimization of length N
Hess (function) – callable method or function A required function or method to compute the weighted vector and Hessian for func. It must be a symmetric NxN array
args (tuple) – Any extra arguments to func are placed in this tuple.
ftol (float) – Relative error desired in the sum of squares.
xtol (float) – Relative tolerance of zeros in the SVD solution in nl.pinv.
maxcyc (int) – The maximum number of cycles of refinement to execute, if -1 refine until other limits are met (ftol, xtol)
Print (bool) – True for printing results (residuals & times) by cycle

Returns

(x,cov_x,infodict) where

x : ndarray The solution (or the result of the last iteration for an unsuccessful call).
cov_x : ndarray Uses the fjac and ipvt optional outputs to construct an estimate of the jacobian around the solution. None if a singular matrix encountered (indicates very flat curvature in some direction). This matrix must be multiplied by the residual standard deviation to get the covariance of the parameter estimates – see curve_fit.
infodict : dict a dictionary of optional outputs with the keys:
- ’fvec’ : the function evaluated at the output
- ’num cyc’:
- ’nfev’:
- ’lamMax’:0.
- ’psing’:
- ’SVD0’:

schrodinger.application.matsci.gsas.GSASIImath.getVCov(varyNames, varyList, covMatrix)¶

obtain variance-covariance terms for a set of variables. NB: the varyList and covMatrix were saved by the last least squares refinement so they must match.

Parameters

varyNames (list) – variable names to find v-cov matric for
varyList (list) – full list of all variables in v-cov matrix
covMatrix (nparray) – full variance-covariance matrix from the last least squares refinement

Returns

nparray vcov: variance-covariance matrix for the variables given in varyNames

schrodinger.application.matsci.gsas.GSASIImath.FindMolecule(ind, generalData, atomData)¶

schrodinger.application.matsci.gsas.GSASIImath.FindAtomIndexByIDs(atomData, loc, IDs, Draw=True)¶

finds the set of atom array indices for a list of atom IDs. Will search either the Atom table or the drawAtom table.

Parameters

atomData (list) – Atom or drawAtom table containting coordinates, etc.
loc (int) – location of atom id in atomData record
IDs (list) – atom IDs to be found
Draw (bool) – True if drawAtom table to be searched; False if Atom table is searched

Returns

list indx: atom (or drawAtom) indices

schrodinger.application.matsci.gsas.GSASIImath.FillAtomLookUp(atomData, indx)¶

create a dictionary of atom indexes with atom IDs as keys

Parameters: atomData (list) – Atom table to be used
Returns: dict atomLookUp: dictionary of atom indexes with atom IDs as keys

schrodinger.application.matsci.gsas.GSASIImath.GetAtomsById(atomData, atomLookUp, IdList)¶

gets a list of atoms from Atom table that match a set of atom IDs

Parameters

atomData (list) – Atom table to be used
atomLookUp (dict) – dictionary of atom indexes with atom IDs as keys
IdList (list) – atom IDs to be found

Returns

list atoms: list of atoms found

schrodinger.application.matsci.gsas.GSASIImath.GetAtomItemsById(atomData, atomLookUp, IdList, itemLoc, numItems=1)¶

gets atom parameters for atoms using atom IDs

Parameters

atomData (list) – Atom table to be used
atomLookUp (dict) – dictionary of atom indexes with atom IDs as keys
IdList (list) – atom IDs to be found
itemLoc (int) – pointer to desired 1st item in an atom table entry
numItems (int) – number of items to be retrieved

Returns

type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetAtomCoordsByID(pId, parmDict, AtLookup, indx)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetAtomFracByID(pId, parmDict, AtLookup, indx)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.ApplySeqData(data, seqData)¶: Applies result from seq. refinement to drawing atom positions & Uijs

schrodinger.application.matsci.gsas.GSASIImath.FindNeighbors(phase, FrstName, AtNames, notName='')¶

schrodinger.application.matsci.gsas.GSASIImath.FindAllNeighbors(phase, FrstName, AtNames, notName='')¶

schrodinger.application.matsci.gsas.GSASIImath.calcBond(A, Ax, Bx, MTCU)¶

schrodinger.application.matsci.gsas.GSASIImath.AddHydrogens(AtLookUp, General, Atoms, AddHydId)¶

schrodinger.application.matsci.gsas.GSASIImath.TLS2Uij(xyz, g, Amat, rbObj)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.AtomTLS2UIJ(atomData, atPtrs, Amat, rbObj)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetXYZDist(xyz, XYZ, Amat)¶

gets distance from position xyz to all XYZ, xyz & XYZ are np.array: and are in crystal coordinates; Amat is crystal to Cart matrix

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getAtomXYZ(atoms, cx)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRBTransMat(X, Y)¶

Get transformation for Cartesian axes given 2 vectors X will be parallel to new X-axis; X cross Y will be new Z-axis & (X cross Y) cross Y will be new Y-axis Useful for rigid body axes definintion

Parameters

X (array) – normalized vector
Y (array) – normalized vector

Returns

array M: transformation matrix

use as XYZ’ = np.inner(M,XYZ) where XYZ are Cartesian

schrodinger.application.matsci.gsas.GSASIImath.RotateRBXYZ(Bmat, Cart, oriQ)¶

rotate & transform cartesian coordinates to crystallographic ones no translation applied. To be used for numerical derivatives

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.UpdateRBXYZ(Bmat, RBObj, RBData, RBType)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.UpdateMCSAxyz(Bmat, MCSA)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.SetMolCent(model, RBData)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.UpdateRBUIJ(Bmat, Cart, RBObj)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetSHCoeff(pId, parmDict, SHkeys)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getMass(generalData)¶

Computes mass of unit cell contents

Parameters: generalData (dict) – The General dictionary in Phase
Returns: float mass: Crystal unit cell mass in AMU.

schrodinger.application.matsci.gsas.GSASIImath.getDensity(generalData)¶

calculate crystal structure density

Parameters: generalData (dict) – The General dictionary in Phase
Returns: float density: crystal density in gm/cm^3

schrodinger.application.matsci.gsas.GSASIImath.getWave(Parms)¶

returns wavelength from Instrument parameters dictionary

Parameters: Parms (dict) – Instrument parameters; must contain: Lam: single wavelength or Lam1: Ka1 radiation wavelength
Returns: float wave: wavelength

schrodinger.application.matsci.gsas.GSASIImath.getMeanWave(Parms)¶

returns mean wavelength from Instrument parameters dictionary

Parameters: Parms (dict) – Instrument parameters; must contain: Lam: single wavelength or Lam1,Lam2: Ka1,Ka2 radiation wavelength I(L2)/I(L1): Ka2/Ka1 ratio
Returns: float wave: mean wavelength

schrodinger.application.matsci.gsas.GSASIImath.El2Mass(Elements)¶

compute molecular weight from Elements

Parameters: Elements (dict) – elements in molecular formula; each must contain Num: number of atoms in formula Mass: at. wt.
Returns: float mass: molecular weight.

schrodinger.application.matsci.gsas.GSASIImath.Den2Vol(Elements, density)¶

converts density to molecular volume

Parameters

Elements (dict) – elements in molecular formula; each must contain Num: number of atoms in formula Mass: at. wt.
density (float) – material density in gm/cm^3

Returns

float volume: molecular volume in A^3

schrodinger.application.matsci.gsas.GSASIImath.Vol2Den(Elements, volume)¶

converts volume to density

Parameters

Elements (dict) – elements in molecular formula; each must contain Num: number of atoms in formula Mass: at. wt.
volume (float) – molecular volume in A^3

Returns

float density: material density in gm/cm^3

schrodinger.application.matsci.gsas.GSASIImath.El2EstVol(Elements)¶

Estimate volume from molecular formula; assumes atom volume = 10A^3

Parameters: Elements (dict) – elements in molecular formula; each must contain Num: number of atoms in formula
Returns: float volume: estimate of molecular volume in A^3

schrodinger.application.matsci.gsas.GSASIImath.XScattDen(Elements, vol, wave=0.0)¶

Estimate X-ray scattering density from molecular formula & volume; ignores valence, but includes anomalous effects

Parameters

Elements (dict) – elements in molecular formula; each element must contain Num: number of atoms in formula Z: atomic number
vol (float) – molecular volume in A^3
wave (float) – optional wavelength in A

Returns

float rho: scattering density in 10^10cm^-2; if wave > 0 the includes f’ contribution

Returns

float mu: if wave>0 absorption coeff in cm^-1 ; otherwise 0

Returns

float fpp: if wave>0 f” in 10^10cm^-2; otherwise 0

schrodinger.application.matsci.gsas.GSASIImath.NCScattDen(Elements, vol, wave=0.0)¶

Estimate neutron scattering density from molecular formula & volume; ignores valence, but includes anomalous effects

Parameters

Elements (dict) – elements in molecular formula; each element must contain Num: number of atoms in formula Z: atomic number
vol (float) – molecular volume in A^3
wave (float) – optional wavelength in A

Returns

float rho: scattering density in 10^10cm^-2; if wave > 0 the includes f’ contribution

Returns

float mu: if wave>0 absorption coeff in cm^-1 ; otherwise 0

Returns

float fpp: if wave>0 f” in 10^10cm^-2; otherwise 0

schrodinger.application.matsci.gsas.GSASIImath.wavekE(wavekE)¶

Convert wavelength to energy & vise versa

:param float waveKe:wavelength in A or energy in kE

:returns float waveKe:the other one

schrodinger.application.matsci.gsas.GSASIImath.XAnomAbs(Elements, wave)¶

schrodinger.application.matsci.gsas.GSASIImath.makeWaves(waveTypes, FSSdata, XSSdata, USSdata, MSSdata, Mast)¶

waveTypes: array nAtoms: ‘Fourier’,’ZigZag’ or ‘Block’ FSSdata: array 2 x atoms x waves (sin,cos terms) XSSdata: array 2x3 x atoms X waves (sin,cos terms) USSdata: array 2x6 x atoms X waves (sin,cos terms) MSSdata: array 2x3 x atoms X waves (sin,cos terms)

Mast: array orthogonalization matrix for Uij

schrodinger.application.matsci.gsas.GSASIImath.MagMod(glTau, XYZ, modQ, MSSdata, SGData, SSGData)¶: this needs to make magnetic moment modulations & magnitudes as fxn of gTau points

schrodinger.application.matsci.gsas.GSASIImath.Modulation(H, HP, nWaves, Fmod, Xmod, Umod, glTau, glWt)¶: H: array nRefBlk x ops X hklt HP: array nRefBlk x ops X hklt proj to hkl nWaves: list number of waves for frac, pos, uij & mag Fmod: array 2 x atoms x waves (sin,cos terms) Xmod: array atoms X 3 X ngl Umod: array atoms x 3x3 x ngl glTau,glWt: arrays Gauss-Lorentzian pos & wts

schrodinger.application.matsci.gsas.GSASIImath.ModulationTw(H, HP, nWaves, Fmod, Xmod, Umod, glTau, glWt)¶: H: array nRefBlk x tw x ops X hklt HP: array nRefBlk x tw x ops X hklt proj to hkl Fmod: array 2 x atoms x waves (sin,cos terms) Xmod: array atoms X ngl X 3 Umod: array atoms x ngl x 3x3 glTau,glWt: arrays Gauss-Lorentzian pos & wts

schrodinger.application.matsci.gsas.GSASIImath.makeWavesDerv(ngl, waveTypes, FSSdata, XSSdata, USSdata, Mast)¶: Only for Fourier waves for fraction, position & adp (probably not used for magnetism) FSSdata: array 2 x atoms x waves (sin,cos terms) XSSdata: array 2x3 x atoms X waves (sin,cos terms) USSdata: array 2x6 x atoms X waves (sin,cos terms) Mast: array orthogonalization matrix for Uij

schrodinger.application.matsci.gsas.GSASIImath.ModulationDerv(H, HP, Hij, nWaves, waveShapes, Fmod, Xmod, UmodAB, SCtauF, SCtauX, SCtauU, glTau, glWt)¶: Compute Fourier modulation derivatives H: array ops X hklt proj to hkl HP: array ops X hklt proj to hkl Hij: array 2pi^2[a*^2h^2 b*^2k^2 c*^2l^2 a*b*hk a*c*hl b*c*kl] of projected hklm to hkl space

schrodinger.application.matsci.gsas.GSASIImath.posFourier(tau, psin, pcos)¶

schrodinger.application.matsci.gsas.GSASIImath.posZigZag(T, Tmm, Xmax)¶

schrodinger.application.matsci.gsas.GSASIImath.posBlock(T, Tmm, Xmax)¶

schrodinger.application.matsci.gsas.GSASIImath.fracCrenel(tau, Toff, Twid)¶

schrodinger.application.matsci.gsas.GSASIImath.fracFourier(tau, fsin, fcos)¶

schrodinger.application.matsci.gsas.GSASIImath.ApplyModulation(data, tau)¶: Applies modulation to drawing atom positions & Uijs for given tau

schrodinger.application.matsci.gsas.GSASIImath.gaulegf(a, b, n)¶

schrodinger.application.matsci.gsas.GSASIImath.BessJn(nmax, x)¶

compute Bessel function J(n,x) from scipy routine & recurrance relation returns sequence of J(n,x) for n in range [-nmax…0…nmax]

Parameters

nmax (integer) – maximul order for Jn(x)
x (float) – argument for Jn(x)

Returns numpy array

[J(-nmax,x)…J(0,x)…J(nmax,x)]

schrodinger.application.matsci.gsas.GSASIImath.BessIn(nmax, x)¶

compute modified Bessel function I(n,x) from scipy routines & recurrance relation returns sequence of I(n,x) for n in range [-nmax…0…nmax]

Parameters

nmax (integer) – maximul order for In(x)
x (float) – argument for In(x)

Returns numpy array

[I(-nmax,x)…I(0,x)…I(nmax,x)]

schrodinger.application.matsci.gsas.GSASIImath.CalcDist(distance_dict, distance_atoms, parmDict)¶

schrodinger.application.matsci.gsas.GSASIImath.CalcDistDeriv(distance_dict, distance_atoms, parmDict)¶

schrodinger.application.matsci.gsas.GSASIImath.CalcAngle(angle_dict, angle_atoms, parmDict)¶

schrodinger.application.matsci.gsas.GSASIImath.CalcAngleDeriv(angle_dict, angle_atoms, parmDict)¶

schrodinger.application.matsci.gsas.GSASIImath.getSyXYZ(XYZ, ops, SGData)¶

default doc

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestDist(XYZ, Amat)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestDeriv(Func, XYZ, Amat, ops, SGData)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestAngle(XYZ, Amat)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestPlane(XYZ, Amat)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestChiral(XYZ, Amat)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestTorsion(XYZ, Amat)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.calcTorsionEnergy(TOR, Coeff=[])¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getTorsionDeriv(XYZ, Amat, Coeff)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestRama(XYZ, Amat)¶

Computes a pair of torsion angles in a 5 atom string

Parameters

XYZ (nparray) – crystallographic coordinates of 5 atoms
Amat (nparray) – crystal to cartesian transformation matrix

Returns

list (phi,psi) two torsion angles in degrees

schrodinger.application.matsci.gsas.GSASIImath.calcRamaEnergy(phi, psi, Coeff=[])¶

Computes pseudo potential energy from a pair of torsion angles and a numerical description of the potential energy surface. Used to create penalty function in LS refinement: Eval(\phi,\psi) = C[0]*exp(-V/1000)

where V = -C[3] * (\phi-C[1])^2 - C[4]*(\psi-C[2])^2 - 2*(\phi-C[1])*(\psi-C[2])

Parameters

phi (float) – first torsion angle (\phi)
psi (float) – second torsion angle (\psi)
Coeff (list) – pseudo potential coefficients

Returns

list (sum,Eval): pseudo-potential difference from minimum & value; sum is used for penalty function.

schrodinger.application.matsci.gsas.GSASIImath.getRamaDeriv(XYZ, Amat, Coeff)¶

Computes numerical derivatives of torsion angle pair pseudo potential with respect of crystallographic atom coordinates of the 5 atom sequence

Parameters

XYZ (nparray) – crystallographic coordinates of 5 atoms
Amat (nparray) – crystal to cartesian transformation matrix
Coeff (list) – pseudo potential coefficients

Returns

list (deriv) derivatives of pseudopotential with respect to 5 atom crystallographic xyz coordinates.

schrodinger.application.matsci.gsas.GSASIImath.getRestPolefig(ODFln, SamSym, Grid)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRestPolefigDerv(HKL, Grid, SHCoeff)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getDistDerv(Oxyz, Txyz, Amat, Tunit, Top, SGData)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getAngleDerv(Oxyz, Axyz, Bxyz, Amat, Tunit, symNo, SGData)¶

schrodinger.application.matsci.gsas.GSASIImath.getAngSig(VA, VB, Amat, SGData, covData={})¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetDistSig(Oatoms, Atoms, Amat, SGData, covData={})¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetAngleSig(Oatoms, Atoms, Amat, SGData, covData={})¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetTorsionSig(Oatoms, Atoms, Amat, SGData, covData={})¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.GetDATSig(Oatoms, Atoms, Amat, SGData, covData={})¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.ValEsd(value, esd=0, nTZ=False)¶

Format a floating point number with a given level of precision or with in crystallographic format with a “esd”, as value(esd). If esd is negative the number is formatted with the level of significant figures appropriate if abs(esd) were the esd, but the esd is not included. if the esd is zero, approximately 6 significant figures are printed. nTZ=True causes “extra” zeros to be removed after the decimal place. for example:

“1.235(3)” for value=1.2346 & esd=0.003

“1.235(3)e4” for value=12346. & esd=30

“1.235(3)e6” for value=0.12346e7 & esd=3000

“1.235” for value=1.2346 & esd=-0.003

“1.240” for value=1.2395 & esd=-0.003

“1.24” for value=1.2395 & esd=-0.003 with nTZ=True

“1.23460” for value=1.2346 & esd=0.0

Parameters

value (float) – number to be formatted
esd (float) – uncertainty or if esd < 0, specifies level of precision to be shown e.g. esd=-0.01 gives 2 places beyond decimal
nTZ (bool) – True to remove trailing zeros (default is False)

Returns

value(esd) or value as a string

schrodinger.application.matsci.gsas.GSASIImath.validProtein(Phase, old)¶

schrodinger.application.matsci.gsas.GSASIImath.FitTexture(General, Gangls, refData, keyList, pgbar)¶

schrodinger.application.matsci.gsas.GSASIImath.adjHKLmax(SGData, Hmax)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.OmitMap(data, reflDict, pgbar=None)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.FourierMap(data, reflDict)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.Fourier4DMap(data, reflDict)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.printRho(SGLaue, rho, rhoMax)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.findOffset(SGData, A, Fhkl)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.ChargeFlip(data, reflDict, pgbar)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.findSSOffset(SGData, SSGData, A, Fhklm)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.SSChargeFlip(data, reflDict, pgbar)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.getRho(xyz, mapData)¶

get scattering density at a point by 8-point interpolation param xyz: coordinate to be probed param: mapData: dict of map data

Returns: density at xyz

schrodinger.application.matsci.gsas.GSASIImath.getRhos(XYZ, rho)¶

get scattering density at an array of point by 8-point interpolation this is faster than gerRho which is only used for single points. However, getRhos is replaced by scipy.ndimage.interpolation.map_coordinates which does a better job & is just as fast. Thus, getRhos is unused in GSAS-II at this time. param xyz: array coordinates to be probed Nx3 param: rho: array copy of map (NB: don’t use original!)

Returns: density at xyz

schrodinger.application.matsci.gsas.GSASIImath.SearchMap(generalData, drawingData, Neg=False)¶

Does a search of a density map for peaks meeting the criterion of peak height is greater than mapData[‘cutOff’]/100 of mapData[‘rhoMax’] where mapData is data[‘General’][‘mapData’]; the map is also in mapData.

Parameters

generalData – the phase data structure; includes the map
drawingData – the drawing data structure
Neg – if True then search for negative peaks (i.e. H-atoms & neutron data)

Returns

(peaks,mags,dzeros) where

peaks : ndarray x,y,z positions of the peaks found in the map
mags : ndarray the magnitudes of the peaks
dzeros : ndarray the distance of the peaks from the unit cell origin
dcent : ndarray the distance of the peaks from the unit cell center

schrodinger.application.matsci.gsas.GSASIImath.sortArray(data, pos, reverse=False)¶: data is a list of items sort by pos in list; reverse if True

schrodinger.application.matsci.gsas.GSASIImath.PeaksEquiv(data, Ind)¶

Find the equivalent map peaks for those selected. Works on the contents of data[‘Map Peaks’].

Parameters

data – the phase data structure
Ind (list) – list of selected peak indices

Returns

augmented list of peaks including those related by symmetry to the ones in Ind

schrodinger.application.matsci.gsas.GSASIImath.PeaksUnique(data, Ind)¶

Finds the symmetry unique set of peaks from those selected. Works on the contents of data[‘Map Peaks’].

Parameters

data – the phase data structure
Ind (list) – list of selected peak indices

Returns

the list of symmetry unique peaks from among those given in Ind

schrodinger.application.matsci.gsas.GSASIImath.getCWsig(ins, pos)¶

get CW peak profile sigma^2

Parameters

ins (dict) – instrument parameters with at least ‘U’, ‘V’, & ‘W’ as values only
pos (float) – 2-theta of peak

Returns

float getCWsig: peak sigma^2

schrodinger.application.matsci.gsas.GSASIImath.getCWsigDeriv(pos)¶

get derivatives of CW peak profile sigma^2 wrt U,V, & W

Parameters: pos (float) – 2-theta of peak
Returns: list getCWsigDeriv: d(sig^2)/dU, d(sig)/dV & d(sig)/dW

schrodinger.application.matsci.gsas.GSASIImath.getCWgam(ins, pos)¶

get CW peak profile gamma

Parameters

ins (dict) – instrument parameters with at least ‘X’, ‘Y’ & ‘Z’ as values only
pos (float) – 2-theta of peak

Returns

float getCWgam: peak gamma

schrodinger.application.matsci.gsas.GSASIImath.getCWgamDeriv(pos)¶

get derivatives of CW peak profile gamma wrt X, Y & Z

Parameters: pos (float) – 2-theta of peak
Returns: list getCWgamDeriv: d(gam)/dX & d(gam)/dY

schrodinger.application.matsci.gsas.GSASIImath.getTOFsig(ins, dsp)¶

get TOF peak profile sigma^2

Parameters

ins (dict) – instrument parameters with at least ‘sig-0’, ‘sig-1’ & ‘sig-q’ as values only
dsp (float) – d-spacing of peak

Returns

float getTOFsig: peak sigma^2

schrodinger.application.matsci.gsas.GSASIImath.getTOFsigDeriv(dsp)¶

get derivatives of TOF peak profile sigma^2 wrt sig-0, sig-1, & sig-q

Parameters: dsp (float) – d-spacing of peak
Returns: list getTOFsigDeriv: d(sig0/d(sig-0), d(sig)/d(sig-1) & d(sig)/d(sig-q)

schrodinger.application.matsci.gsas.GSASIImath.getTOFgamma(ins, dsp)¶

get TOF peak profile gamma

Parameters

ins (dict) – instrument parameters with at least ‘X’, ‘Y’ & ‘Z’ as values only
dsp (float) – d-spacing of peak

Returns

float getTOFgamma: peak gamma

schrodinger.application.matsci.gsas.GSASIImath.getTOFgammaDeriv(dsp)¶

get derivatives of TOF peak profile gamma wrt X, Y & Z

Parameters: dsp (float) – d-spacing of peak
Returns: list getTOFgammaDeriv: d(gam)/dX & d(gam)/dY

schrodinger.application.matsci.gsas.GSASIImath.getTOFbeta(ins, dsp)¶

get TOF peak profile beta

Parameters

ins (dict) – instrument parameters with at least ‘beat-0’, ‘beta-1’ & ‘beta-q’ as values only
dsp (float) – d-spacing of peak

Returns

float getTOFbeta: peak beat

schrodinger.application.matsci.gsas.GSASIImath.getTOFbetaDeriv(dsp)¶

get derivatives of TOF peak profile beta wrt beta-0, beta-1, & beat-q

Parameters: dsp (float) – d-spacing of peak
Returns: list getTOFbetaDeriv: d(beta)/d(beat-0), d(beta)/d(beta-1) & d(beta)/d(beta-q)

schrodinger.application.matsci.gsas.GSASIImath.getTOFalpha(ins, dsp)¶

get TOF peak profile alpha

Parameters

ins (dict) – instrument parameters with at least ‘alpha’ as values only
dsp (float) – d-spacing of peak

Returns

flaot getTOFalpha: peak alpha

schrodinger.application.matsci.gsas.GSASIImath.getTOFalphaDeriv(dsp)¶

get derivatives of TOF peak profile beta wrt alpha

Parameters: dsp (float) – d-spacing of peak
Returns: float getTOFalphaDeriv: d(alp)/d(alpha)

schrodinger.application.matsci.gsas.GSASIImath.setPeakparms(Parms, Parms2, pos, mag, ifQ=False, useFit=False)¶

set starting peak parameters for single peak fits from plot selection or auto selection

Parameters

Parms (dict) – instrument parameters dictionary
Parms2 (dict) – table lookup for TOF profile coefficients
pos (float) – peak position in 2-theta, TOF or Q (ifQ=True)
mag (float) – peak top magnitude from pick
ifQ (bool) – True if pos in Q
useFit (bool) – True if use fitted CW Parms values (not defaults)

Returns

list XY: peak list entry: for CW: [pos,0,mag,1,sig,0,gam,0] for TOF: [pos,0,mag,1,alp,0,bet,0,sig,0,gam,0] NB: mag refinement set by default, all others off

class schrodinger.application.matsci.gsas.GSASIImath.base_schedule¶

Bases: object

__init__()¶

init(**options)¶

getstart_temp(best_state)¶

Find a matching starting temperature and starting parameters vector i.e. find x0 such that func(x0) = T0.

Parameters: best_state – _state A _state object to store the function value and x0 found.
Returns: x0 : array The starting parameters vector.

set_range(x0, frac)¶

accept_test(dE)¶

update_guess(x0)¶

update_temp(x0)¶

class schrodinger.application.matsci.gsas.GSASIImath.fast_sa¶

Bases: schrodinger.application.matsci.gsas.GSASIImath.base_schedule

init(**options)¶

update_guess(x0)¶

update_temp()¶

__init__()¶

accept_test(dE)¶

getstart_temp(best_state)¶

Find a matching starting temperature and starting parameters vector i.e. find x0 such that func(x0) = T0.

Parameters: best_state – _state A _state object to store the function value and x0 found.
Returns: x0 : array The starting parameters vector.

set_range(x0, frac)¶

class schrodinger.application.matsci.gsas.GSASIImath.log_sa¶

Bases: schrodinger.application.matsci.gsas.GSASIImath.base_schedule

init(**options)¶

update_guess(x0)¶

update_temp()¶

__init__()¶

accept_test(dE)¶

getstart_temp(best_state)¶

Find a matching starting temperature and starting parameters vector i.e. find x0 such that func(x0) = T0.

Parameters: best_state – _state A _state object to store the function value and x0 found.
Returns: x0 : array The starting parameters vector.

set_range(x0, frac)¶

schrodinger.application.matsci.gsas.GSASIImath.makeTsched(data)¶

schrodinger.application.matsci.gsas.GSASIImath.anneal(func, x0, args=(), schedule='fast', T0=None, Tf=1e-12, maxeval=None, maxaccept=None, maxiter=400, feps=1e-06, quench=1.0, c=1.0, lower=- 100, upper=100, dwell=50, slope=0.9, ranStart=False, ranRange=0.1, autoRan=False, dlg=None)¶

Minimize a function using simulated annealing.

Schedule is a schedule class implementing the annealing schedule. Available ones are ‘fast’, ‘cauchy’, ‘boltzmann’

Parameters

func (callable) – f(x, *args) Function to be optimized.
x0 (ndarray) – Initial guess.
args (tuple) – Extra parameters to func.
schedule (base_schedule) – Annealing schedule to use (a class).
T0 (float) – Initial Temperature (estimated as 1.2 times the largest cost-function deviation over random points in the range).
Tf (float) – Final goal temperature.
maxeval (int) – Maximum function evaluations.
maxaccept (int) – Maximum changes to accept.
maxiter (int) – Maximum cooling iterations.
feps (float) – Stopping relative error tolerance for the function value in last four coolings.
quench,c (float) – Parameters to alter fast_sa schedule.
lower,upper (float/ndarray) – Lower and upper bounds on x.
dwell (int) – The number of times to search the space at each temperature.
slope (float) – Parameter for log schedule
ranStart=False (bool) – True for set 10% of ranges about x

Returns

(xmin, Jmin, T, feval, iters, accept, retval) where

xmin (ndarray): Point giving smallest value found.
Jmin (float): Minimum value of function found.
T (float): Final temperature.
feval (int): Number of function evaluations.
iters (int): Number of cooling iterations.
accept (int): Number of tests accepted.
retval (int): Flag indicating stopping condition:
- 0: Points no longer changing
- 1: Cooled to final temperature
- 2: Maximum function evaluations
- 3: Maximum cooling iterations reached
- 4: Maximum accepted query locations reached
- 5: Final point not the minimum amongst encountered points

Notes: Simulated annealing is a random algorithm which uses no derivative information from the function being optimized. In practice it has been more useful in discrete optimization than continuous optimization, as there are usually better algorithms for continuous optimization problems.

Some experimentation by trying the difference temperature schedules and altering their parameters is likely required to obtain good performance.

The randomness in the algorithm comes from random sampling in numpy. To obtain the same results you can call numpy.random.seed with the same seed immediately before calling scipy.optimize.anneal.

We give a brief description of how the three temperature schedules generate new points and vary their temperature. Temperatures are only updated with iterations in the outer loop. The inner loop is over range(dwell), and new points are generated for every iteration in the inner loop. (Though whether the proposed new points are accepted is probabilistic.)

For readability, let d denote the dimension of the inputs to func. Also, let x_old denote the previous state, and k denote the iteration number of the outer loop. All other variables not defined below are input variables to scipy.optimize.anneal itself.

In the ‘fast’ schedule the updates are

u ~ Uniform(0, 1, size=d)
y = sgn(u - 0.5) * T * ((1+ 1/T)**abs(2u-1) -1.0)
xc = y * (upper - lower)
x_new = x_old + xc

T_new = T0 * exp(-c * k**quench)

schrodinger.application.matsci.gsas.GSASIImath.worker(iCyc, data, RBdata, reflType, reflData, covData, out_q, out_t, out_n, nprocess=- 1)¶

schrodinger.application.matsci.gsas.GSASIImath.MPmcsaSearch(nCyc, data, RBdata, reflType, reflData, covData, nprocs)¶

schrodinger.application.matsci.gsas.GSASIImath.mcsaSearch(data, RBdata, reflType, reflData, covData, pgbar, start=True)¶

default doc string

Parameters: name (type) – description
Returns: type name: description

schrodinger.application.matsci.gsas.GSASIImath.prodQQ(QA, QB)¶: Grassman quaternion product QA,QB quaternions; q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.normQ(QA)¶: get length of quaternion & normalize it q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.invQ(Q)¶: get inverse of quaternion q=r+ai+bj+ck; q* = r-ai-bj-ck

schrodinger.application.matsci.gsas.GSASIImath.prodQVQ(Q, V)¶: compute the quaternion vector rotation qvq-1 = v’ q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.Q2Mat(Q)¶: make rotation matrix from quaternion q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.AV2Q(A, V)¶: convert angle (radians) & vector to quaternion q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.AVdeg2Q(A, V)¶: convert angle (degrees) & vector to quaternion q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.Q2AVdeg(Q)¶: convert quaternion to angle (degrees 0-360) & normalized vector q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.Q2AV(Q)¶: convert quaternion to angle (radians 0-2pi) & normalized vector q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.randomQ(r0, r1, r2, r3)¶: create random quaternion from 4 random numbers in range (-1,1)

schrodinger.application.matsci.gsas.GSASIImath.randomAVdeg(r0, r1, r2, r3)¶: create random angle (deg),vector from 4 random number in range (-1,1)

schrodinger.application.matsci.gsas.GSASIImath.makeQuat(A, B, C)¶

Make quaternion from rotation of A vector to B vector about C axis

Parameters: A,B,C (np.array) – Cartesian 3-vectors
Returns: quaternion & rotation angle in radians q=r+ai+bj+ck

schrodinger.application.matsci.gsas.GSASIImath.annealtests()¶