# cctbx.miller package¶

cctbx.miller is one of the most important modules in CCTBX; it encompasses nearly every operation performed directly on experimental data. The core classes in cctbx.miller are the set and the array. The set (not to be confused with the built-in Python type) contains the crystal symmetry, an array (type cctbx.array_family.flex.miller_index) of Miller indices (h,k,l), and a boolean flag indicating anomalous pairs. It does not contain actual data, although many of its methods will return an array. The array subclasses the Miller set and adds a flex array containing data (and, optionally, a flex array of experimental sigmas) and many extensions for supporting a variety of data types. The underlying “data” is often X-ray amplitudes or intensities, but many other array types are also supported.

One important distinction needs to be made for developers used to working with specific file formats or more archaic programming languages: the Miller arrays that you will work with do not necessarily correspond to a single column of data in a reflection file. There are several major differences:

• Friedel mates will be stored separate if present. This means that a pair of columns F(+) and F(-) from an MTZ file will become a single array with both (h,k,l) and (-h,-k,-l) present as distinct items. The same also applies to any other data type. (Note that one consequence of this behavior is that the number of reflections will appear to double-count acentric reflections for which both Friedel mates are present.)

• For experimental data (amplitudes or intensities), the array will also store the corresponding experimental sigmas; array.data() returns the experimental data, while array.sigmas() returns sigmas. In combination with the treatment of anomalous data, this means that a single Miller array can represent the combination of columns I(+),SIGI(+),I(-),SIGI(-) from a file.

• Weighted map coefficients such as FWT,DELFWT or 2FOFCWT,PH2FOFCWT will be treated as a single array with data type scitbx.array_family.flex.complex_double.

• Hendrickson-Lattman phase probability coefficients are also grouped together, and have their own data type cctbx.array_family.flex.hendrickson_lattman.

These conventions greatly simplify keeping track of and manipulating related data items. Output to various file formats will still follow the appropriate conventions.

## Getting started¶

Miller sets (and arrays) can be created in three ways: programatically, by reading from a file, or from a cctbx.xray.structure object. (In practice, the latter two options almost always return an array object rather than a set.) Programmatic creation can be done directly, or through the convenience method cctbx.miller.build_set():

>>> from cctbx import miller
>>> from cctbx import crystal
>>> ms = miller.build_set(
...   crystal_symmetry=crystal.symmetry(
...     space_group_symbol="P212121",
...     unit_cell=(6,6,6,90,90,90)),
...   anomalous_flag=False,
...   d_min=3.0)
>>> print ms.size()
7
>>> print list(ms.indices())
[(0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1), (2, 0, 0)]
>>> print ms.d_max_min()
(4.242640687119285, 3.0)


The same set, instantiated directly:

>>> from cctbx import miller
>>> from cctbx import crystal
>>> from cctbx.array_family import flex
>>> ms = miller.set(
...   crystal_symmetry=crystal.symmetry(
...     space_group_symbol="P212121",
...     unit_cell=(6,6,6,90,90,90)),
...   anomalous_flag=False,
...   indices=flex.miller_index(
...     [(0,0,2),(0,1,1),(0,2,0),(1,0,1),(1,1,0),(1,1,1),(2,0,0)]))


From here we can retrieve a variety of information, even before we have experimental data. For instance, exploring systematic absences (starting from the above example):

>>> from cctbx import sgtbx
>>> point_group = ms.space_group().build_derived_point_group()
>>> ms_base = ms.customized_copy(space_group=point_group)
>>> ms_all = ms_base.complete_set()
>>> print ms_all.size()
10
>>> sys_abs = ms_all.lone_set(other=ms_base)
>>> print type(sys_abs)
<class 'cctbx.miller.set'>
>>> print list(sys_abs.indices())
[(0, 0, 1), (0, 1, 0), (1, 0, 0)]
>>> ms_all_p212121 = ms_all.customized_copy(
...   space_group_info=ms.space_group_info())
>>> sys_abs_flags = ms_all_p212121.sys_absent_flags()
>>> print type(sys_abs_flags)
<class 'cctbx.miller.array'>
>>> print list(sys_abs_flags.indices())
[(0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 1), (0, 2, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1), (2, 0, 0)]
>>> print list(sys_abs_flags.data())
[True, False, True, False, False, True, False, False, False, False]
>>> sys_abs = ms_all_p212121.select(sys_abs_flags.data())
>>> print list(sys_abs.indices())
[(0, 0, 1), (0, 1, 0), (1, 0, 0)]
>>> not_sys_abs = ms_all_p212121.select(~sys_abs_flags.data())
>>> print list(not_sys_abs.indices())
[(0, 0, 2), (0, 1, 1), (0, 2, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1), (2, 0, 0)]


This block of code performed the following actions:

• change the symmetry to the point group (P 2 2 2) corresponding to the original space group (P 21 21 21)

• generate the complete list of reflections for the new set in P 2 2 2

• obtain the “lone set” of reflections missing from the original set relative to the new complete set; these correspond to reflections that are systematically absent in P 21 21 21 (but not P 2 2 2)

• change the symmetry for the complete set in P 2 2 2 back to the original space group P 21 21 21

• call the method sys_absent_flags() to obtain a Miller array whose data are a flex.bool array indicating those reflections that are systematically absent

• call the method select() using the resulting boolean array and its inverse, first to extract the set of systematic absences for P 21 21 21, and then extract the non-absent set we started with

There are two more important details that are not immediately obvious from the code example:

1) customized_copy() will create a new set object, but it will not copy any underlying flex arrays (the same applies to the array class). This means that modifications to these arrays via the new copy will be propagated back to the original object. If you want to avoid this behavior, use the deep_copy() method:

>>> ms_base = ms.customized_copy(space_group=point_group).deep_copy()


2) The comparison of sets in lone_set(), and in general most other methods that involve an other argument, will fail if the crystal symmetry is not identical. For instance, in the above example, if we instead tried to call lone_set() using the original P 21 21 21 set as other:

>>> sys_abs = ms_all.lone_set(other=ms)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/nat/src/cctbx_project/cctbx/miller/__init__.py", line 1047, in lone_set
assert_is_similar_symmetry=assert_is_similar_symmetry).singles(1))
File "/Users/nat/src/cctbx_project/cctbx/miller/__init__.py", line 1007, in match_indices
assert self.is_similar_symmetry(other)
AssertionError


We can prevent this if we want:

>>> sys_abs = ms_all.lone_set(other=ms, assert_is_similar_symmetry=False)


However, you should use caution when disabling the symmetry check, as this will also mean that comparisons between radically different crystal symmetries (e.g. P 63 2 2 versus I 41) will be performed silently.

## File I/O¶

Of course, if you are interested in working with actual experimental data, additional APIs are required. Methods for reading input files are covered in more detail in the documentation for iotbx.reflection_file_reader and iotbx.file_reader, but in the simplest case we can obtain experimental data in just a couple of lines of code:

>>> from iotbx.reflection_file_reader import any_reflection_file
>>> hkl_in = any_reflection_file(file_name="data.sca")
>>> miller_arrays = hkl_in.as_miller_arrays()
>>> i_obs = miller_arrays[0]


This of course assumes that the file format includes crystal symmetry, which is not the case for some popular formats; in these cases you will need to obtain the symmetry information separately and pass it to as_miller_arrays().

Some of the file metadata will be preserved in the embedded array_info object; other attributes are properties of the array itself:

>>> print i_obs.info()
data.sca:I(+),SIGI(+),I(-),SIGI(-)
>>> print i_obs.observation_type()
xray.intensity
>>> i_obs.show_summary()
Miller array info: data.sca:I(+),SIGI(+),I(-),SIGI(-)
Observation type: xray.intensity
Type of data: double, size=7
Type of sigmas: double, size=7
Number of Miller indices: 7
Anomalous flag: False
Unit cell: (6.000, 6.000, 6.000, 90, 90, 90)
Space group: P 21 21 21 (No. 19)
<cctbx.miller.array object at 0x1071a6690>


(The final line is simply printing the Python representation of the array itself - this is because the show_summary() method returns a reference to self, which allows chaining of successive methods.) Note that the array_info object returned by array.info() contains the file name and original column labels; elsewhere, these attributes are used to select specific arrays from multi-purpose formats such as MTZ.

From here we can quickly convert to amplitudes:

>>> f_obs = i_obs.f_sq_as_f()
>>> print f_obs.observation_type()
xray.amplitude


(Note that for macromolecular data, the more sophisticated French-Wilson treatment is recommended for dealing sensibly with weak or negative intensities; this can be performed by calling array.french_wilson(). For many purposes, however, the simpler and faster f_sq_as_f() will be sufficient.)

The Miller array can also be easily output to CIF, MTZ, Scalepack (unmerged format only), SHELX, or CNS formats, although some restrictions apply. Some of these methods (where the format is limited to certain data types) can directly write to a file:

>>> i_obs.export_as_scalepack_unmerged(file_name="data2.sca")
>>> f = open("data.hkl", "w")
>>> i_obs.export_as_shelx_hklf(file_object=f)
>>> f.close()


Others require multiple steps, but this has the advantage of allowing multiple arrays to be combined (provided that they have identical crystal symmetry):

>>> mtz_dataset = i_obs.as_mtz_dataset(column_root_label="I")
...   column_root_label="FreeR_flag")
>>> mtz_dataset.mtz_object().write("data.mtz")


In addition to conventional formats, since all of the internal types can be serialized as Python pickles, the same applies to set and array objects.

### Processing input data - practical aspects¶

In practice, preparing input arrays for the various other algorithms in CCTBX is often significantly more complicated than implied in the previous section. Suppose for example we have an MTZ file with these columns (output excerpted from phenix.mtz.dump data.mtz):

label      #valid  %valid    min     max type
H           75612 100.00% -40.00   38.00 H: index h,k,l
K           75612 100.00%   0.00   25.00 H: index h,k,l
L           75612 100.00%   0.00   70.00 H: index h,k,l
I(+)        74981  99.17% -11.10 2777.70 K: I(+) or I(-)
SIGI(+)     74981  99.17%   0.10   89.50 M: standard deviation
I(-)        69529  91.95% -14.00 2808.50 K: I(+) or I(-)
SIGI(-)     69529  91.95%   0.10   64.90 M: standard deviation
FreeR_flag  75773 100.00%   0.00    1.00 I: integer


We would eventually like to be able to use these data for calculation of R-factors (versus some hypothetical set of structure factors derived from a model or map). This requires several steps to ensure that any subsequent actions will behave sensibly: we must make sure that the input data are of the correct type, symmetry-unique, using conventional indices, and consistent with the R-free flags; we also want to use the R-free flags to separate out “working” and “test” arrays. To begin with, we read in the data:

>>> from iotbx.reflection_file_reader import any_reflection_file
>>> hkl_in = any_reflection_file(file_name="data.mtz")
>>> miller_arrays = hkl_in.as_miller_arrays()
>>> i_obs = miller_arrays[0]
>>> flags = miller_arrays[1]
>>> f_obs = i_obs.f_sq_as_f().map_to_asu()
>>> flags = flags.customized_copy(data=flags.data()==1).map_to_asu()
>>> f_obs = f_obs.merge_equivalents().array()
>>> flags = flags.merge_equivalents().array()
>>> flags_plus_minus = flags.generate_bijvoet_mates()
>>> f_obs, flags_plus_minus = f_obs.common_sets(other=flags_plus_minus)
>>> f_obs_work = f_obs.select(~flags_plus_minus.data())
>>> f_obs_free = f_obs.select(flags_plus_minus.data())


By the end of this block of code, we have ensured that the experimental amplitudes and R-free flags have identically sized and ordered arrays, and are suitable for comparison with any other (similarly prepared) set of data. A number of consistency checks built in to the various set and array methods may raise exceptions if these steps are skipped - for instance, the separate storage of (h,k,l) and (-h,-k,-l) requires us to expand the R-free flags to be “anomalous”, and if we skip that step:

>>> f_obs, flags = f_obs.common_sets(other=flags)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/nat/src/cctbx_project/cctbx/miller/__init__.py", line 1032, in common_sets
assert_is_similar_symmetry=assert_is_similar_symmetry)
File "/home/nat/src/cctbx_project/cctbx/miller/__init__.py", line 1008, in match_indices
assert self.anomalous_flag() == other.anomalous_flag()
AssertionError


Or if we omit the call to common_sets():

>>> f_obs_work = f_obs.select(~flags_plus_minus.data())
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/nat/src/cctbx_project/cctbx/miller/__init__.py", line 3232, in select
i = self.indices().select(selection)
RuntimeError: scitbx Internal Error: /home/nat/src/cctbx_project/scitbx/array_family/selections.h(44): SCITBX_ASSERT(flags.size() == self.size()) failure.


(In practice, our use of common_sets() here is less than ideal; programs in Phenix instead check that every reflection for which we have data also has a corresponding R-free flag - after expansion to anomalous if necessary - and exit with an error if this is not the case.)

Note that in the above example we are making many assumptions about the contents and order of the input file, whereas in practice MTZ and CIF formats may be arbitrarily complex and contain multiple arrays of each type. (Additionally, the conventions for specifying R-free flags differ between various software suites, and 1 will not necessarily be the appropriate test flag value; fortunately, it is usually possible to guess the convention being used.) For actual applications (as opposed to quick scripts and development code), the utilities available in iotbx.reflection_file_utils enable standardized retrieval of different array types based on a combination of automatic behavior and user input (i.e. label strings), and the general-purpose input wrapper in mmtbx.command_line encapsulates nearly all of these steps.

## Comparing arrays¶

Here is a slightly more complex example of comparing data output by a refinement program. The input arrays are assumed to already be merged and in the same ASU, but normally this would be taken care of by previous routines.

def compute_r_factors (fobs, fmodel, flags) :
fmodel, fobs = fmodel.common_sets(other=fobs)
fmodel, flags = fmodel.common_sets(other=flags)
fc_work = fmodel.select(~(flags.data()))
fo_work = fobs.select(~(flags.data()))
fc_test = fmodel.select(flags.data())
fo_test = fobs.select(flags.data())
r_work = fo_work.r1_factor(fc_work)
r_free = fo_test.r1_factor(fc_test)
print "r_work = %.4f" % r_work
print "r_free = %.4f" % r_free
print ""
flags.setup_binner(n_bins=20)
fo_work.use_binning_of(flags)
fc_work.use_binner_of(fo_work)
fo_test.use_binning_of(fo_work)
fc_test.use_binning_of(fo_work)
for i_bin in fo_work.binner().range_all() :
sel_work = fo_work.binner().selection(i_bin)
sel_test = fo_test.binner().selection(i_bin)
fo_work_bin = fo_work.select(sel_work)
fc_work_bin = fc_work.select(sel_work)
fo_test_bin = fo_test.select(sel_test)
fc_test_bin = fc_test.select(sel_test)
if fc_test_bin.size() == 0 : continue
r_work_bin = fo_work_bin.r1_factor(other=fc_work_bin,
assume_index_matching=True)
r_free_bin = fo_test_bin.r1_factor(other=fc_test_bin,
assume_index_matching=True)
cc_work_bin = fo_work_bin.correlation(fc_work_bin).coefficient()
cc_free_bin = fo_test_bin.correlation(fc_test_bin).coefficient()
legend = flags.binner().bin_legend(i_bin, show_counts=False)
print "%s  %8d %8d  %.4f %.4f  %.3f %.3f" % (legend, fo_work_bin.size(),
fo_test_bin.size(), r_work_bin, r_free_bin, cc_work_bin, cc_free_bin)


(The full source code is available in iotbx/examples/recalculate_phenix_refine_r_factors.py.)

TODO

## From arrays to maps¶

TODO

fft_map = map_coeffs.fft_map(resolution_factor=0.25)
fft_map.apply_sigma_scaling()
site_map_values = flex.double()
for site in xray_structure.sites_frac() :
rho = real_map.eight_point_interpolation(site)
site_map_values.append(rho)


As an extreme example of the ease of scripting repetitive actions using cctbx.miller, here is a complete six-line script to convert all sets of map coefficients in an MTZ file to sigma-scaled CCP4-format map files (covering the unit cell):

from iotbx.reflection_file_reader import any_reflection_file
hkl_in = any_reflection_file(file_name="map_coeffs.mtz")
for i_map, array in enumerate(hkl_in.as_miller_arrays()) :
if array.is_complex_array() :
fft_map = array.fft_map(resolution_factor=0.25).apply_sigma_scaling()
fft_map.as_ccp4_map(file_name="map_%d.ccp4" % (i_map+1))


See the documentation for cctbx.maptbx for details of working with map objects.

## The Miller set¶

class cctbx.miller.set(crystal_symmetry, indices, anomalous_flag=None)

Basic class for handling sets of Miller indices (h,k,l), including sorting and matching functions, symmetry handling, generation of R-free flags, and extraction of associated statistics. Does not actually contain data, but this can be added using the array(…) method.

all_selection()
amplitude_normalisations(asu_contents, wilson_plot)

A miller.array whose data N(h) are the normalisations to convert between E’s and F’s: E(h) = F(h) / N(h) The argument wilson_plot shall feature attributes - wilson_intensity_scale_factor - wilson_b

anomalous_flag()

Indicate whether the set or array is anomalous or not.

array(data=None, sigmas=None)

Create an array object, given data and/or sigma arrays of identical dimensions to the indices array.

Parameters
• data – a flex array (any format) or None

• sigmas – a flex array (any format, but almost always double) or None

as_anomalous_set()

Return a copy of the set using the same indices but with the anomalous flag set to true.

as_non_anomalous_set()

Return a copy of the set using the same indices but with the anomalous flag set to false.

at_first_index(ary, miller_index)

Returns the element ary coresponding to the miller_index if miller_index exists, otherwise returns None.

Parameters
• miller_index (tuple) – Miller index as a 3-tuple

• ary (sequence (list, array, etc)) – any array (e.g. self.data(), self.sigmas())

Returns

type of contents of ary, or None

auto_anomalous(min_n_bijvoet_pairs=None, min_fraction_bijvoet_pairs=None)

Set the anomalous flag automatically depending on whether the data contain Bijvoet pairs (optionally given minimum cutoffs).

Returns

a copy of the set with (maybe) a new anomalous flag

binner()

Return a reference to the current resolution binner (or None if undefined).

centric_flags()

Generate a boolean Miller array flagging centric reflections.

change_basis(cb_op)

Get a transformation of the miller set with a new basis specified by cb_op

Parameters

cb_op (string or sgtbx.change_of_basis_operator) – object describing the desired transformation of the basis

Returns

a new miller set with the new basis

Return type

cctbx.miller.set

clear_binner()
common_set(other, assert_is_similar_symmetry=True)

Match the indices in the current set and another set, and return a set (or array) containing only those reflections present in both. Assumes that both sets are already in the asymmetric unit (ASU).

common_sets(other, assert_is_similar_symmetry=True, assert_no_singles=False)

Like common_set(other), but returns a tuple containing matching copies of both sets (or arrays).

complete_set(d_min_tolerance=1e-06, d_min=None, d_max=None, max_index=None)

Generate the complete set of Miller indices expected for the current symmetry, excepting systematic absences.

Parameters
• d_min_tolerance – tolerance factor for d_min (avoid precision errors)

• d_min – High-resolution limit (default = d_min of current set)

• d_max – Low-resolution limit (default = d_max of current set)

completeness(use_binning=False, d_min_tolerance=1e-06, return_fail=None, d_max=None, multiplier=1, as_non_anomalous_array=None)

Calculate the (fractional) completeness of the array relative to the theoretical complete set, either overall or in resolution bins. By default the current low-resolution limit will be used.

Parameters
• d_min_tolerance – tolerance factor for d_min (avoid precision errors)

• d_max – Low-resolution limit (default = d_max of current set)

• multiplier – Factor to multiply the result by (usually 1 or 100)

• as_non_anomalous_array – Report values for non-anomalous array

concatenate(other, assert_is_similar_symmetry=True)

Combine two Miller sets. Both must have the same anomalous flag, and similar symmetry is also assumed.

copy()

Create a copy of the set, keeping references to the same crystal symmetry and indices.

crystal_gridding(resolution_factor=0.3333333333333333, d_min=None, grid_step=None, symmetry_flags=None, mandatory_factors=None, max_prime=5, assert_shannon_sampling=True)

Calculate real-space grid for FFT given array crystal symmetry, d_min, and desired resolution-dependent spacing. The actual grid dimensions will be adjusted to suit the needs of the FFT algorithm.

crystal_symmetry()

Get crystal symmetry of the miller set

Returns

a new crystal.symmetry object

Return type

cctbx.crystal.symmetry

customized_copy(crystal_symmetry=Keep, indices=Keep, anomalous_flag=Keep, unit_cell=Keep, space_group_info=Keep)

Create a copy of the set, optionally changing the symmetry, indices, and/or anomalous flag (default = keep all unmodified).

d_max_min(d_max_is_highest_defined_if_infinite=False)

Low- and high-resolution limits. :returns: Python tuple of floats Modified 2020-10-02 to allow return of maximum defined instead of -1

if F000 present

d_min()

High-resolution limit. :returns: Python float

d_min_along_a_b_c_star()

Returns the effective resolution limits along the reciprocal space axes.

d_spacings()

Generate a double Miller array containing the resolution d of each index.

d_star_cubed()
d_star_sq()
debye_waller_factors(u_iso=None, b_iso=None, u_cart=None, b_cart=None, u_cif=None, u_star=None, exp_arg_limit=50, truncate_exp_arg=False)

Given an isotropic or anisotropic displacement or B-factor, alculate resolution-dependent scale factors corresponding to the indices. (Note that to simply apply one of the input parameters to an existing Miller array, you can call array.apply_debye_waller_factors)

Parameters
• u_iso – Isotropic displacement (in Angstroms)

• b_iso – Isotropic B-factor (8*pi^2*u_iso^2)

• u_cart – Anisotropic displacement tensor

• b_cart – Anisotropic B-factor

• u_star – Anisotropic displacement tensor in fractional space

• u_cif – Anisotropic displacement tensor, dimensionless basis

Returns

cctbx.miller.array object

deep_copy()

Create a copy of the set, also copying the crystal symmetry and indices.

Returns

a set object with all-new attributes.

delete_index(hkl)

Remove all reflections with the specified Miller index.

delete_indices(other)

Delete multiple reflections, as specified by the Miller indices of another set.

epsilons()
expand_to_p1(return_iselection=False)

Get a transformation of the miller set to spacegroup P1

Returns

a new set of parameters (symmetry, miller indices, anomalous_flag) in spacegroup P1

Return type

set(cctbx.crystal.symmetry, cctbx.miller.indices, boolean)

expand_to_p1_iselection(build_iselection=True)
f_obs_minus_xray_structure_f_calc(f_obs_factor, xray_structure, structure_factor_algorithm=None, cos_sin_table=False, quality_factor=None, u_base=None, b_base=None, wing_cutoff=None, exp_table_one_over_step_size=None)
first_index(miller_index)

Returns the first index of the item matching miller_index. If the miller_index is not found in self, then returns None.

Parameters

miller_index (tuple) – Miller index as a 3-tuple

Returns

int, None – index of first occurrence of miller_index or None

generate_bivoet_mates()

If the array is not already anomalous, expand the miller indices to generate anomalous pairs.

generate_r_free_flags(fraction=0.1, max_free=2000, lattice_symmetry_max_delta=5.0, use_lattice_symmetry=True, use_dataman_shells=False, n_shells=20, format='cns')

Create an array of R-free flags for the current set, keeping anomalous pairs together. Requires that the set already be unique under symmetry, and generally assumes that the set is in the ASU.

Parameters
• fraction – fraction of reflections to flag for the test set

• max_free – limit on size of test set, overrides fraction

• lattice_symmetry_max_delta – limit on lattice symmetry calculation

• use_lattice_symmetry – given the current symmetry, determine the highest possible lattice symmetry and generate flags for that symmetry, then expand to the current (lower) symmetry if necessary. This is almost always a good idea.

• use_dataman_shells – generate flags in thin resolution shells to avoid bias due to non-crystallographic symmetry.

• n_shells – number of resolution shells if use_dataman_shells=True

• format – convention of the resulting flags. ‘cns’ will return a boolean array (True = free), ‘ccp4’ will return an integer array from 0 to X (0 = free, X dependent on fraction), ‘shelx’ will return an integer array with values 1 (work) or -1 (free).

Returns

a boolean or integer Miller array, depending on format.

generate_r_free_flags_basic(fraction=0.1, max_free=2000, use_dataman_shells=False, n_shells=20, format='cns')

Generate R-free flags, without taking lattice symmetry into account (not recommended). Should not normally be called directly - use generate_r_free_flags(…) instead.

generate_r_free_flags_on_lattice_symmetry(fraction=0.1, max_free=2000, max_delta=5.0, return_integer_array=False, n_partitions=None, use_dataman_shells=False, n_shells=20, format='cns')

Generate R-free flags by converting to the highest possible lattice symmetry (regardless of intensity symmetry), creating flags, and expanding back to the original symmetry. This is a safeguard against reflections that are correlated due to twinning being split between the work and test sets.

This method should usually not be called directly, but rather through set.generate_r_free_flags(…).

index_span()
indices()

Return a reference to the internal array of indices.

Returns

a cctbx.array_family.flex.miller_index array

is_in_asu()

Indicate whether the array is entirely contained within the reciprocal space asymmetric unit (ASU). Warning: this calls map_to_asu internally, so it is better to simply call map_to_asu without checking in many cases.

is_unique_set_under_symmetry()

Determine whether the indices in the set are symmetry-unique.

log_binning(n_reflections_in_lowest_resolution_bin=100, eps=0.0001, max_number_of_bins=30, min_reflections_in_bin=50)

Create resolution bins on a logarithmic scale. See Urzhumtsev et al. (2009) Acta Crystallogr D Biol Crystallogr. 65:1283-91.

lone_set(other, assert_is_similar_symmetry=True)

Match the indices in the current set and another set, and return a set (or array) containing reflections which are present only in the current set. Assumes that both sets are already in the asymmetric unit.

lone_sets(other, assert_is_similar_symmetry=True)

Like lone_set(other), but returns a tuple containing the reflections unique to each set (or array).

map_to_asu()

Convert all indices to lie within the canonical asymmetric unit for the current space group (while preserving anomalous flag). Required for many downstream steps.

match_bijvoet_mates(assert_is_unique_set_under_symmetry=True)

Group Bijvoet mates (or Friedel mates) together, returning an object that allows enumeration over matching pairs and/or singletons.

match_indices(other, assert_is_similar_symmetry=True)
miller_indices_as_pdb_file(file_name=None, expand_to_p1=False)

Write out Miller indices as pseudo-waters for visualization. Note that this treats the indices as literal coordinates (times a scale factor), and the distances between points will not correspond to the distances in reciprocal space.

See cctbx/miller/display.py and crys3d/hklview for an alternative (but less lightweight) approach.

min_max_d_star_sq()
min_max_indices()

Return the range of h,k,l indices

minimum_wavelength_based_on_d_min(tolerance=0.01)
multiplicities()

Generate a Miller array (with integer data) indicating the multiplicity of each unique reflection. (If the set or array is already symmetry-unique, the multiplicity will be 1 for every reflection.)

Returns

array object with flex.int data

n_bijvoet_pairs()

Return the number of Bijvoet pairs.

patterson_symmetry()
random_phases_compatible_with_phase_restrictions(deg=False)
reflection_intensity_symmetry()
remove_systematic_absences(negate=False)
resolution_filter(d_max=0, d_min=0, negate=0)

Select a subset within the indicated resolution range. Returns a new miller array (does not change existing array)

Parameters
• d_max – Low-resolution cutoff

• d_min – High-resolution cutoff

• negate – Select outside this range instead

Returns

set or array depending on object type

resolution_filter_selection(d_max=None, d_min=None)

Obtain the selection (flex.bool array) corresponding to the specified resolution range.

resolution_range()

Synonym for d_max_min().

select(selection, negate=False, anomalous_flag=None)

Select a subset of reflections.

Parameters
• selection – flex.bool or flex.size_t selection

• negate – select the inverse of the selection array

• anomalous_flag – anomalous flag for the new set

Returns

a new set with a subset of indices

select_acentric()

Select only acentric reflections.

Returns

A Miller set or array (depending on object type).

select_centric()

Select only centric reflections.

Returns

A Miller set or array (depending on object type).

setup_binner(d_max=0, d_min=0, auto_binning=False, reflections_per_bin=0, n_bins=0)

Create internal resolution binner object; required for many other methods to work.

setup_binner_counting_sorted(d_max=0, d_min=0, reflections_per_bin=None, n_bins=None, d_tolerance=1e-10)
setup_binner_d_star_sq_bin_size(reflections_per_bin=1000, min_bins=6, max_bins=50, d_max=None, d_min=None, d_tolerance=1e-05)

Set up bins of equal width in d_star_sq by target for mean number per bin.

setup_binner_d_star_sq_step(auto_binning=True, d_max=None, d_min=None, d_star_sq_step=None)
show_completeness(reflections_per_bin=500, out=None)

Display the completeness in resolution bins.

show_comprehensive_summary(f=None, prefix='')

Display comprehensive Miller set or array summary

show_summary(f=None, prefix='')

Minimal Miller set summary

sin_theta_over_lambda_sq()
size()

Return the number of reflections in the set or array.

slice(axis=None, axis_index=None, slice_index=None, slice_start=None, slice_end=None)
sort(by_value='resolution', reverse=False)

Reorder reflections by resolution or Miller index.

Parameters

by_value – ‘resolution’ or ‘packed_indices’

sort_permutation(by_value='resolution', reverse=False)

Generate the selection array (flex.size_t object) to reorder the array by resolution or Miller index.

Parameters
• by_value – sort type, must be “resolution” or “packed_indices”

• reverse – invert order

Returns

flex.size_t object

structure_factors_from_asu_map(asu_map_data, n_real)
structure_factors_from_map(map, in_place_fft=False, use_scale=False, anomalous_flag=None, use_sg=False)

Run FFT on a real-space map to calculate structure factors corresponding to the current set of Miller indices.

Parameters
• map – flex.double map with 3D flex.grid accessor

• in_place_fft – perform the FFT in place instead of creating a copy of the map first

• use_scale – perform volume-scaling using current unit cell

• anomalous_flag – determines anomalous_flag for output array

• use_sg – use space-group symmetry

Returns

array with same Miller indices and complex_double data

structure_factors_from_scatterers(xray_structure, algorithm=None, cos_sin_table=False, grid_resolution_factor=0.3333333333333333, quality_factor=None, u_base=None, b_base=None, wing_cutoff=None, exp_table_one_over_step_size=None)

Calculate structure factors for an cctbx.xray.structure object corresponding to the current set of Miller indices. Can use either FFT or direct summation.

Parameters
Returns

array with same Miller indices and complex_double data

sys_absent_flags(integral_only=False)

Generate a boolean Miller array flagging those reflections which are systematically absent under the current symmetry.

two_theta(wavelength, deg=False)

Generate a double Miller array containing the scattering angle of each index.

unique_under_symmetry()
unique_under_symmetry_selection()
use_binner_of(other)

Use the exact binner of another set, which must have identical indices.

use_binning(binning)

Use the resolution binning of the specified binner object (does not need to be from an identically sized set).

use_binning_of(other)

Use the resolution binning of the specified set (does not need to be an identical set of indices).

cctbx.miller.build_set(crystal_symmetry, anomalous_flag, d_min=None, d_max=None, max_index=None)

Given crystal symmetry, anomalous flag, and resolution limits, create a complete set object.

Parameters
• crystal_symmetry – cctbx.crystal.symmetry object

• anomalous_flag – Boolean, indicates whether to generate anomalous indices

• d_min – High-resolution limit (optional if max_index is specified)

• d_max – Low-resolution limit (optional)

• max_index – highest-resolution Miller index

Returns

a set object

## The Miller array¶

class cctbx.miller.array(miller_set, data=None, sigmas=None)

Extension of the set class with addition of data and (optional) sigmas flex arrays, plus an optional array_info object and an optional flag for the observation type (amplitude, intensity, or reconstructed amplitude).

amplitude_normalisations(asu_contents, wilson_plot=None)

Overriden version of set.amplitude_normalisation which computes the Wilson parameters from the array data if wilson_plot is None.

amplitude_quasi_normalisations(d_star_power=1)

A miller.array whose data N(h) are the normalisations to convert between locally normalised E’s and F’s: E(h) = F(h) / N(h)

self features the F’s, which are then binned with the current binner and N(h) is the average of F’s in the bin h belongs to.

amplitudes()

For a complex array, return array of absolute values.

analyze_intensity_statistics(d_min=2.5, completeness_as_non_anomalous=None, log=None)

Detect translational pseudosymmetry and twinning, using methods in Xtriage. Returns a mmtbx.scaling.twin_analyses.twin_law_interpretation object. (Requires mmtbx to be configured to be functional.)

anomalous_completeness(use_binning=False, d_min_tolerance=1e-06, d_max=None, d_min=None, relative_to_complete_set=True)

Return the percent of acentric reflections with both h,k,l and -h,-k,-l observed (only meaningful for amplitude and intensity arrays). By default this is calculated relative to the complete set.

anomalous_differences(enforce_positive_sigmas=False)

Returns an array object with DANO (i.e. F(+) - F(-)) as data, and optionally SIGDANO as sigmas.

anomalous_probability_plot(expected_delta=None)
anomalous_signal(use_binning=False)

Get the anomalous signal according to this formula:

$\sqrt{\dfrac{<||F(+)|-|F(-)||^2>}{\frac{1}{2} (<|F(+)|>^2 + <|F(-)|>^2)}}$
Parameters

use_binning (boolean) – If ‘True’ the anomalous signal will be calculated for each bin of the data set individually

Returns

the anomalous signal

Return type

float or cctbx.miller.binned_data

apply_change_of_basis(change_of_basis, eliminate_invalid_indices=True, out=None)

Encapsulates a variety of reindexing operations, including handling for a variety of corner cases.

Parameters
• change_of_basis – Python str for change-of-basis operator

• eliminate_invalid_indices – remove reflections with non-integral indices

Returns

new Miller array

apply_debye_waller_factors(u_iso=None, b_iso=None, u_cart=None, b_cart=None, u_cif=None, u_star=None, apply_to_sigmas=True, exp_arg_limit=50, truncate_exp_arg=False)

Given an isotropic or anisotropic displacement or B-factor, apply resolution-dependent scale factors to the data (and optionally sigmas).

Parameters
• u_iso – Isotropic displacement (in Angstroms)

• b_iso – Isotropic B-factor (8*pi^2*u_iso^2)

• u_cart – Anisotropic displacement tensor

• b_cart – Anisotropic B-factor

• u_star – Anisotropic displacement tensor in fractional space

• u_cif – Anisotropic displacement tensor, dimensionless basis

• apply_to_sigmas – Also scale sigma values (if present)

Returns

cctbx.miller.array object with scaled data

apply_scaling(target_max=None, factor=None)

Apply a scale factor to the data (and optionally sigmas).

Parameters
• target_max – target maximum value for the scaled data - the scale factor will be determined automatically

• factor – explicit scale factor

Returns

custumozed copy with scaled data and sigmas

apply_shelxl_extinction_correction(x, wavelength)
arg(deg=False)
as_amplitude_array(algorithm='xtal_3_7')

Convert the array to simple amplitudes if not already in that format. Only valid for complex (i.e. F,PHI), intensity, or amplitude arrays.

as_anomalous_array()

Return a copy of the array with identical contents (keeping original flex arrays) but with the anomalous flag set to true.

as_cif_block(array_type)
as_cif_simple(array_type, out=None, data_name='global')
as_double()

Create a copy of the array with the data converted to a flex.double type. Will fail for incompatible arrays.

as_intensity_array(algorithm='simple')

Convert the array to intensities if not already in that format. Only valid for complex (F,PHI), amplitude, or intensity arrays.

as_map_manager(resolution_factor=0.25, crystal_gridding=None, grid_step=None, d_min=None, d_max=None, apply_sigma_scaling=True, apply_volume_scaling=False, wrapping=True)
as_mtz_dataset(column_root_label, column_types=None, label_decorator=None, title=None, crystal_name='crystal', project_name='project', dataset_name='dataset', wavelength=None)

Generate an iotbx.mtz.dataset object for the array, which can be extended with additional arrays and eventually written to an MTZ file.

as_non_anomalous_array()

Return a copy of the array with identical contents (keeping original flex arrays) but with the anomalous flag set to false.

as_phases_phs(out, scale_amplitudes=True, phases=None, phases_deg=None, figures_of_merit=None)

Write phases to .phs file.

as_xray_observations(scale_indices=None, twin_fractions=None, twin_components=None)
average_bijvoet_mates()

Given an anomalous array, merge the anomalous pairs and return the non-anomalous average.

average_neighbors(layers=1, include_origin=False, offset_list=None, average_with_cc=None)
bijvoet_ratios(obs_type='intensity', measurable_only=True, cutoff=3.0)
cc_anom(*args, **kwds)

Alias for array.half_dataset_anomalous_correlation()

cc_one_half(use_binning=False, n_trials=1, anomalous_flag=False, return_n_refl=False)

Calculate the correlation between two randomly assigned pools of unmerged data (“CC 1/2”). If desired the mean over multiple trials can be taken. See Karplus PA & Diederichs K (2012) Science 336:1030-3 for motivation. This method assumes that the reflections still have the original indices and maps them to the ASU first; the underlying compute_cc_one_half function skips this method.

cc_one_half_sigma_tau(use_binning=False, return_n_refl=False)

Calculation of CC1/2 by the ‘sigma-tau’ method, avoiding the random assignment into half-datasets of the above method. See Assmann et al., J. Appl. Cryst. (2016). 49, 1021–1028.

var_y is the variange of the average intensities across the unique reflections of a resolution shell. var_e is the average variance of the observations contributing to the merged intensities

change_basis(cb_op, deg=None)

Get a transformation of the miller set with a new basis specified by cb_op

Parameters

cb_op (string or sgtbx.change_of_basis_operator) – object describing the desired transformation of the basis

Returns

a new miller set with the new basis

Return type

cctbx.miller.set

change_symmetry(space_group_symbol=None, space_group_info=None, volume_warning_threshold=0.001, expand_to_p1_if_necessary=True, remove_systematic_absences=True, merge_non_unique=True, log=None)

Encapsulates all operations required to convert the original data to a different symmetry (e.g. as suggested by Xtriage). This includes reindexing and adjusting the unit cell parameters if necessary, and expansion to P1 (for moving to lower symmetry) or merging equivalents.

Parameters
• space_group_symbol – Python str for space group symbol (any format)

• space_group_info – Pre-defined sgtbx.space_group_info object

• volume_warning_threshold – Cutoff for relative change in unit cell volume beyond which a warning is issued.

• expand_to_p1_if_necessary – When moving to lower symmetry, expand the data to P1 first.

• remove_systematic_absences – eliminate reflections that are systematically absent in the new symmetry.

• merge_non_unique – merge reflections that are no longer symmetry- unique under the new symmetry.

• log – filehandle-like object

Returns

Miller array in the new symmetry

combine(other, scale=True, scale_for_lones=1, scale_for_matches=1)
complete_array(d_min_tolerance=1e-06, d_min=None, d_max=None, new_data_value=- 1, new_sigmas_value=- 1)
complete_with(other, scale=False, replace_phases=False)
complete_with_bin_average(reflections_per_bin=100)
concatenate(other, assert_is_similar_symmetry=True)

Combine two Miller sets. Both must have the same anomalous flag, and similar symmetry is also assumed.

conjugate()
convert_to_non_anomalous_if_ratio_pairs_lone_less_than(threshold)

Convert anomalous array into nonanomalous if the number of Bijvoet pairs is too small compared to the number of lone Bijvoet mates.

copy()

Create a new array object using references to internal objects.

correlation(other, use_binning=False, assert_is_similar_symmetry=True)

Calculate correlation coefficient between two arrays (either globally or binned).

Parameters
• other – another array of real numbers

• use_binning – calculate CC in resolution bins (default = calculate a single global value)

• assert_is_similar_symmetry – check that arrays have compatible crystal symmetry

Returns

a Python float (if use_binning=False), or a binned_data object

count_and_fraction_in_bins(data_value_to_count, count_not_equal=False)
crystal_symmetry_is_compatible_with_symmetry_from_file(unit_cell_relative_length_tolerance=0.02, unit_cell_absolute_angle_tolerance=3.0, working_point_group=None)
customized_copy(miller_set=Keep, data=Keep, sigmas=Keep, crystal_symmetry=Keep, indices=Keep, anomalous_flag=Keep, unit_cell=Keep, space_group_info=Keep, observation_type=Keep, info=None)

Create a copy of the set, optionally changing the symmetry, indices, and/or anomalous flag (default = keep all unmodified).

d_min_from_fsc(other=None, fsc_curve=None, bin_width=1000, fsc_cutoff=0.143)

Compute Fourier Shell Correlation (FSC) and derive resolution based on specified cutoff.

data()
data_at_first_index(miller_index)

Returns the value of data of the first index matching miller_index. If the miller_index is not found in self, then returns None.

Parameters

miller_index (tuple) – Miller index as a 3-tuple

Returns

int, float, complex, None – data value or None

deep_copy()

Clone the array, making copies of all internal array objects.

detwin_data(twin_law, alpha)

Detwin data using a known twin fraction, returning an array with the same original data type.

Params twin_law

a valid twin law expressed as h,k,l operations

Params alpha

predicted twin fraction (0 to 0.5)

Returns

a new array with detwinned data

direct_summation_at_point(site_frac, sigma=None)

Calculates the exact map value at the specified fractional coordinate using direct Fourier summation. Relatively slow but avoids interpolation errors.

disagreeable_reflections(f_calc_sq, n_reflections=20)

Create a copy of the array without sigmas.

double_step_filtration(complete_set=None, vol_cutoff_plus_percent=5.0, vol_cutoff_minus_percent=5.0, resolution_factor=0.25, scale_to=None)
eliminate_sys_absent(integral_only=False, log=None, prefix='')

Remove all reflections which should be systematically absent in the current space group.

ellipsoidal_resolutions_and_indices_by_sigma(sigma_cutoff=3)
ellipsoidal_truncation_by_sigma(sigma_cutoff=3)
enforce_positive_amplitudes(i_sig_level=- 4.0)

Takes in an intensity array (including negatives) and spits out amplitudes. The basic assumption is that P(Itrue) propto exp(-(Itrue-Iobs)**2/(2*s)) where Itrue>=0 (positivity constraint on error free amplitudes). For amplitudes, this results in P(Ftrue) propto 2 Ftrue exp( -(Ftrue**2-Iobs)**2/(2s) ) A Gaussian approximation is fitted to the Mode of this distribution. An analytical solution exists and is implemented below. This method does not require any Wilson statistics assumptions.

enforce_positive_sigmas()
expand_to_p1(phase_deg=None, return_iselection=False)

Generate the equivalent P1 dataset.

export_as_cns_hkl(file_object, file_name=None, info=[], array_names=None, r_free_flags=None)

Write reflections to a CNS-format file.

export_as_scalepack_unmerged(file_object=None, file_name=None, batch_numbers=None, spindle_flags=None, scale_intensities_for_scalepack_merge=False)

Write data in unmerged scalepack format.

Parameters
• file_object – filehandle-like object

• file_name – output file to write

• batch_numbers – integer array indicating the batch (image) numbers corresponding to the indices (optional)

• spindle_flags – integer array indicating the position of the reflections on the detector (optional)

export_as_shelx_hklf(file_object=None, normalise_if_format_overflow=False, full_dynamic_range=False, scale_range=None)

Write reflections to a SHELX-format .hkl file.

f_as_f_sq(algorithm='simple')

Convert amplitudes (and associated sigmas, if present) to intensities.

f_obs_f_calc_fan_outlier_selection(f_calc, offset_low=0.05, offset_high=0.1, also_return_x_and_y=False)

Preconditions (not checked explicitly): self is amplitude array, f_calc is complex array or amplitude array.

f_obs_minus_f_calc(f_obs_factor, f_calc)
f_sq_as_f(algorithm='xtal_3_7', tolerance=1e-06)

Given an intensity/F^2 array (or undefined observation type), return the equivalent amplitudes. Note that negative intensities will be discarded; for French-Wilson treatment, call the separate array.french_wilson() method.

fft_map(resolution_factor=0.3333333333333333, d_min=None, grid_step=None, crystal_gridding=None, symmetry_flags=None, mandatory_factors=None, max_prime=5, assert_shannon_sampling=True, f_000=None)

Calculate the FFT for the array, assuming the data are complex doubles.

Parameters
• resolution_factor – when multiplied times the resolution limit, gives the approximate grid spacing of the map.

• d_min – High-resolution cutoff

• crystal_gridding – optional gridding to use (overrides automatic gridding)

• symmetry_flags – specifies how the grid should be constructed to handle symmetry

• f_000 – Optional F(0,0,0) value (scalar added to entire map)

Returns

an fft_map object

french_wilson(**kwds)

Perform French-Wilson treatment of X-ray intensities to estimate the “true” intensities, replacing very weak and/or negative values, and takes the square root to obtain amplitudes.

Returns

an array of all-positive X-ray amplitudes

classmethod from_cif(file_object=None, file_path=None, data_block_name=None)

Class method for building an array from a CIF file (or filehandle). Depends on iotbx.cif.

fsc(other, bin_width=1000)

Compute Fourier Shell Correlation (FSC)

generate_bijvoet_mates()

If the array is not already anomalous, expand to generate anomalous pairs (without changing data).

half_dataset_anomalous_correlation(use_binning=False, return_n_pairs=False, return_split_datasets=False)

Calculate the correlation of the anomalous differences of two randomly assigned half-datasets (starting from unmerged data).

has_twinning(d_min=2.5)

Convenience method for identifying twinned data. Note that this is hugely inefficient if any other Xtriage analyses are planned, since it discards the other results. Requires mmtbx.

hemisphere_acentrics(plus_or_minus)
hemispheres_acentrics()
hoppe_gassmann_modification(mean_scale, n_iterations, resolution_factor=0.25, d_min=None)
i_over_sig_i(use_binning=False, return_fail=None)

<I/sigma_I>

info()

Return the associated info object, or None if undefined.

intensities()
intensity_quasi_normalisations(d_star_power=1)

A miller.array whose data N(h) are the normalisations to convert between locally normalised E^2’s and I’s: E^2(h) = I(h) / N(h)

Intensities are binned with the current binner and N(h) is the average of I’s in the bin h belongs to.

is_bool_array()
is_complex_array()
is_hendrickson_lattman_array()
is_integer_array()
is_real_array()
is_string_array()
is_unmerged_intensity_array()

Determine whether the array contains unmerged experimental observations or not. In some files only the centric reflections will appear to be unmerged, so we specifically check the acentrics (if present).

is_xray_amplitude_array()
is_xray_data_array()
is_xray_intensity_array()
is_xray_reconstructed_amplitude_array()
local_overlap_map(other, radius, resolution_factor=0.3333333333333333, d_min=None, grid_step=None, symmetry_flags=None, mandatory_factors=None, max_prime=5, assert_shannon_sampling=True, f_000=None)
local_standard_deviation_map(radius, mean_solvent_density=0, resolution_factor=0.3333333333333333, d_min=None, grid_step=None, symmetry_flags=None, mandatory_factors=None, max_prime=5, assert_shannon_sampling=True, f_000=None)
make_up_hl_coeffs(k_blur, b_blur)
map_correlation(other)
map_to_asu(deg=None)

Convert all indices to lie within the canonical asymmetric unit for the current space group (while preserving anomalous flag). Required for many downstream steps.

matching_set(other, data_substitute, sigmas_substitute=None, assert_is_similar_symmetry=True)
mean(use_binning=False, use_multiplicities=False, squared=False, rms=False)
mean_of_intensity_divided_by_epsilon(use_binning=False, return_fail=None)

<I/epsilon>

mean_of_squared_sigma_divided_by_epsilon(use_binning=False, return_fail=None)

<sigma^2/epsilon>

mean_phase_error(phase_source)
mean_sq(use_binning=False, use_multiplicities=False)
mean_weighted_phase_error(phase_source)
measurability(use_binning=False, cutoff=3.0, return_fail=None)

Fraction of reflections for which ($$\dfrac{|\Delta I|}{\sigma_{dI}}$$ > cutoff and $$min(\dfrac{I_{+}}{\sigma_{+}},\dfrac{I_{-}}{\sigma_{-}})$$ > cutoff

merge_equivalents(algorithm='gaussian', incompatible_flags_replacement=None, use_internal_variance=True)

Given a non-unique array, merge the symmetry-related reflections (keeping anomalous flag).

Returns

a merge_equivalents object, from which the merged array may be extracted by calling the array() method.

min_f_over_sigma(return_none_if_zero_sigmas=False)
multiscale(other, reflections_per_bin=None)
norm()
normalised_amplitudes(asu_contents, wilson_plot=None)
normalize(reflections_per_bin=150, eps_fac=None)

Compute E-values: E = (F/eps**0.5) / rms of (F/eps**0.5) This is ‘Karle’ approach, that is not using overall B from Wilson plot.

observation_type()

Return the (experimental) data type, if defined. See the module cctbx.xray.observation_types for details.

Returns

an object from cctbx.xray.observation_types

patterson_map(resolution_factor=0.3333333333333333, d_min=None, symmetry_flags=None, mandatory_factors=None, max_prime=5, assert_shannon_sampling=True, f_000=None, sharpening=False, origin_peak_removal=False)

Calculate an unphased Patterson map.

patterson_symmetry()
permute_d_range(d_max, d_min)

Randomly shuffle reflections within a given resolution range. Used for control refinements to validate the information content of a dataset.

phase_entropy(exponentiate=False, return_binned_data=False, return_mean=False)

Get phase entropy as measured in terms of an base-360 entropy (base-2 for centrics).

An entropy of 0, indicates that the phase uncertainity is as low as possible An entropy of 1 however, indicates that the uncertainty is maximal: all phases are equally likely!

Parameters
• return_binned_data (boolean) – if ‘True’ you receive a binned object rather then a raw array

• exponentiate (boolean) – whether or not to exponentiate the entropy. This will return a phase uncertainty in degrees (or the ‘alphabet size’)

phase_integrals(n_steps=None, integrator=None)
phase_transfer(phase_source, epsilon=1e-10, deg=False, phase_integrator_n_steps=None)

Combines phases of phase_source with self’s data if real (keeping the sign of self’s data) or with self’s amplitudes if complex.

Centric reflections are forced to be compatible with the phase restrictions.

phase_source can be a miller.array or a plain flex array.

epsilon is only used when phase_source is a complex array. If both the real and the imaginary part of phase_source[i] < epsilon the phase is assumed to be 0.

deg is only used if phase_source is an array of doubles. deg=True indicates that the phases are given in degrees, deg=False indicates phases are given in radians.

phase_integrator_n_steps is only used if phase_source is an array of Hendrickson-Lattman coefficients. The centroid phases are determined on the fly using the given step size.

phased_translation_function_coeff(phase_source, f_calc, fom=None)
phases(deg=False)

For a complex array, return the array of its phases (in radians by default).

quasi_normalize_structure_factors(d_star_power=1)
quasi_normalized_as_normalized()
r1_factor(other, scale_factor=None, assume_index_matching=False, use_binning=False, emulate_sftools=False)

Get the R1 factor according to this formula

$R1 = \dfrac{\sum{||F| - k|F'||}}{\sum{|F|}}$

where F is self.data() and F’ is other.data() and k is the factor to put F’ on the same scale as F

Parameters
• other – array object with the same observation type

• scale_factor – optional scale factor to be applied to ‘other’; if Auto, will be determined automatically

• assume_index_matching – skips calling self.common_sets(other)

• use_binning – divide by resolution shells

• emulate_sftools – copies behavior of SFTOOLS in CCP4: instead of the denominator being sum(self.data()), it will be 0.5*sum(self.data()+ other.data())

Returns

a Python float (if use_binning=False), or a binned_data object

r_anom()

Calculate R_anom, which measures the agreement between Friedel mates. Unlike CC_anom and various other R-factors (such as R_pim, which it is usually compared to), this requires merged data.

$R_{anom} = \dfrac{\sum_{hkl}{|I_{hkl} - I_{-h,-k,-l}|}}{\sum_{hkl}{\left \langle I_{hkl} \right \rangle}}$
r_free_flags_accumulation()
randomize_amplitude_and_phase(amplitude_error, phase_error_deg, selection=None, random_seed=None)

randomize_phases()
regularize()

A series of conversions that are required for many downstream tests, such as refinement, map calculation, etc.

remove_cone(fraction_percent, vertex=(0, 0, 0), axis_point_1=(0, 0, 0), axis_point_2=(0, 0, 1), negate=False)

Remove reflections corresponding to a cone shape in reciprocal space with the apex at the origin. Used to simulate incomplete data due to poor alignment of the crystal with the goniometer axis.

remove_patterson_origin_peak()
rms(use_binning=False, use_multiplicities=False)
rms_filter(cutoff_factor, use_binning=False, use_multiplicities=False, negate=False)
scale(other, resolution_dependent=False)
scale_factor(f_calc, weights=None, cutoff_factor=None, use_binning=False)

The analytical expression for the least squares scale factor.

K = sum(w * yo * yc) / sum(w * yc^2)

If the optional cutoff_factor argument is provided, only the reflections whose magnitudes are greater than cutoff_factor * max(yo) will be included in the calculation.

second_moment(use_binning=False)

<data^2>/(<data>)^2

second_moment_of_intensities(use_binning=False)

<I^2>/(<I>)^2 (2.0 for untwinned, 1.5 for twinned data)

second_moments_centric_acentric(reflections_per_bin=150, eps_fac=None)

Compute <E**4>/<E**2>**2 for centric and acentric reflections.

select(selection, negate=False, anomalous_flag=None)

Select a sub-array.

Parameters
• selection – flex.bool or flex.size_t selection

• negate – select the inverse of the selection array

• anomalous_flag – anomalous flag for the new set

Returns

a new array with a subset of indices and data/sigmas

select_indices(indices, map_indices_to_asu=False, negate=False)
select_sys_absent(integral_only=False)
set(crystal_symmetry=Keep, indices=Keep, anomalous_flag=Keep, unit_cell=Keep, space_group_info=Keep)

Return the basic cctbx.miller.set object for the array.

set_info(info)
set_observation_type(observation_type)
set_observation_type_xray_amplitude()

Flag the array as X-ray amplitudes (F).

set_observation_type_xray_intensity()

Flag the array as X-ray intensities (I).

set_sigmas(sigmas)
shelxl_extinction_correction(x, wavelength)
Extinction parameter x, where Fc is multiplied by:

k[1 + 0.001 x Fc^2 wavelength^3 / sin(2theta)]^(-1/4)

Note: The scale factor, k, is not applied nor calculated by

this function. The scale factor should be calculated and applied *AFTER* the application of the extinction corrections.

show_all_possible_systematic_absences(out=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>, prefix='')

For each possible space group sharing the same basic intensity symmetry, show a list of possible systematically absent reflections and corresponding I/sigmaI. Note that if the data have already been processed in a specific space group rather than the basic point group, for example P212121 instead of P222, all systematically absent reflections are likely to have been removed already.

Returns

a systematic_absences_info object

show_array(f=None, prefix='', deg=None)

Listing of Miller indices and data

show_comprehensive_summary(f=None, prefix='')

Display comprehensive Miller set or array summary

show_disagreeable_reflections(f_calc_sq, n_reflections=20, out=None)
show_mean_data_over_sigma_along_a_b_c_star()
show_r_free_flags_info(n_bins=10, binner_range='used', out=None, prefix='')
show_summary(f=None, prefix='')

Minimal Miller set summary

sigma_at_first_index(miller_index)

Returns the value of sigmas of the first index matching miller_index. If the miller_index is not found in self, then returns None`.

Parameters

miller_index (tuple) – Miller index as a 3-tuple

Returns

int, float, complex, None – sigmas value or None

sigma_filter(cutoff_factor, negate=False)

Return a copy of the array filtered to remove reflections whose value is less than cutoff_factor*sigma (or the reverse, if negate=True).

sigmas()
sigmas_are_sensible(critical_ratio=0.75, epsilon=1e-06)
size()

Return the number of reflections in the set or array.

sort_permutation(by_value='resolution', reverse=False)

Generate the selection array (flex.size_t object) to reorder the array by resolution, Miller index, data values, or absolute data values.

Parameters
• by_value – sort type, must be “resolution”, “packed_indices”, “data”, or “abs”

• reverse – invert order

Returns

flex.size_t object

statistical_mean(use_binning=0)
sum(use_binning=False, use_multiplicities=False, squared=False)
sum_sq(use_binning=False, use_multiplicities=False)
symmetry_agreement_factor(op, assert_is_similar_symmetry=True)

The factor phi_{sym} quantifying whether complex structure factors are invariant under the given symmetry operator, as used in Superflip. Ref: J. Appl. Cryst. (2008). 41, 975-984

translational_shift(shift_frac, deg=None)
Adjust a complex array (map coefficients) or phase array

corresponding to a shift of all coordinates by new_xyz_frac = old_xyz_frac + shift_frac.

If a phase array, must specify whether it is in degrees. Only makes sense in P1

F’=exp( i 2 pi h.(x+shift_frac)) -> F’ = F exp ( i 2 pi h.shift_frac) phase_shift = 2 * pi * h . shift_frac

twin_data(twin_law, alpha)

Apply a twin law to the data, returning an array of the same original type.

Params twin_law

a valid twin law expressed as h,k,l operations

Params alpha

predicted twin fraction (0 to 0.5)

Returns

a new array with synthetically twinned data

value_at_index(hkl)

Extract the value of the array for the specified reflection h,k,l

wilson_plot(use_binning=False)

<F^2>

wilson_ratio(use_binning=False)

(<F>)^2/<F^2> (0.785 for untwinned, 0.885 for twinned data)

write_mtz(file_name=None, column_root_label=None, column_types=None, label_decorator=None, title=None, crystal_name='crystal', project_name='project', dataset_name='dataset', wavelength=None)

Simple version of write_mtz for a single array, typically map coefficients

## Utility classes¶

class cctbx.miller.merge_equivalents(miller_array, algorithm='gaussian', incompatible_flags_replacement=None, use_internal_variance=True)

Wrapper for merging redundant observations to obtain a symmetry-unique array. This also calculates some useful statistics resulting from the merging operation. Normally this would not be instantiated directly, but instead obtained by calling array.merge_equivalents(…).

array()

Return the merged Miller array.

r_linear()

R-linear = sum(abs(data - mean(data))) / sum(abs(data))

r_meas()

Alternate metric of dataset internal consistency. Explained in detail in Diederichs K & Karplus PA (1997) Nature Structural Biology 4:269-275.

$R_{meas} = \dfrac{\sum_{hkl}{ {\left \{ N(hkl) / [N(hkl) - 1] \right \} }^{1/2} \times \sum_{i}{|I_{i}(hkl) - \left \langle I_{i}(hkl) \right \rangle|}}}{\sum_{hkl}{\sum_{i}{I_{i}(hkl)}}}$
r_merge()

Standard (but flawed) metric of dataset internal consistency.

$R_{merge} = \dfrac{\sum_{hkl}{\sum_{i}{|I_{i}(hkl) - \left \langle I_{i}(hkl) \right \rangle|}}}{\sum_{hkl}{\sum_{i}{I_{i}(hkl)}}}$
r_pim()

Alternate metric of dataset internal consistency or quality. Explained in detail in Weiss MS (2001) J Appl Cryst 34:130-135.

$R_{meas} = \dfrac{\sum_{hkl}{ {\left \{ 1 / [N(hkl) - 1] \right \} }^{1/2} \times \sum_{i}{|I_{i}(hkl) - \left \langle I_{i}(hkl) \right \rangle|}}}{\sum_{hkl}{\sum_{i}{I_{i}(hkl)}}}$
r_square()

R-square = sum((data - mean(data))**2) / sum(data**2)

redundancies()

Return an array representing the redundancy or multiplicity of each reflection in the merged array.

class cctbx.miller.fft_map(crystal_gridding, fourier_coefficients, f_000=None)

Container for an FFT from reciprocal space (complex double) into real space. Normally this is obtained by calling array.fft_map(…), not instantiated directly outside this module. If the input array is anomalous, the resulting map will be a flex.complex_double (with grid accessor), otherwise it will be a flex.double.

class cctbx.miller.array_info(source=None, source_type=None, history=None, labels=None, merged=False, systematic_absences_eliminated=False, crystal_symmetry_from_file=None, type_hints_from_file=None, wavelength=None)

Container for metadata associated with a Miller array, including labels read from a data file.

class cctbx.miller.normalised_amplitudes(miller_array, asu_contents, wilson_plot=None)

E-values and related statistics

class cctbx.miller.crystal_symmetry_is_compatible_with_symmetry_from_file(miller_array, unit_cell_relative_length_tolerance=0.02, unit_cell_absolute_angle_tolerance=3.0, working_point_group=None)
class cctbx.miller.binner(binning, miller_set)