# Data Objects¶

## What are Data Objects in yt?¶

Data objects (also called *Data Containers*) are used in yt as convenience
structures for grouping data in logical ways that make sense in the context
of the dataset as a whole. Some of the data objects are geometrical groupings
of data (e.g. sphere, box, cylinder, etc.). Others represent
data products derived from your dataset (e.g. slices, streamlines, surfaces).
Still other data objects group multiple objects together or filter them
(e.g. data collection, cut region).

To generate standard plots, objects rarely need to be directly constructed. However, for detailed data inspection as well as hand-crafted derived data, objects can be exceptionally useful and even necessary.

## How to Create and Use an Object¶

To create an object, you usually only need a loaded dataset, the name of
the object type, and the relevant parameters for your object. Here is a common
example for creating a `Region`

object that covers all of your data volume.

```
import yt
ds = yt.load("RedshiftOutput0005")
ad = ds.all_data()
```

Alternatively, we could create a sphere object of radius 1 kpc on location [0.5, 0.5, 0.5]:

```
import yt
ds = yt.load("RedshiftOutput0005")
sp = ds.sphere([0.5, 0.5, 0.5], (1, "kpc"))
```

After an object has been created, it can be used as a data_source to certain
tasks like `ProjectionPlot`

(see
`ProjectionPlot`

), one can compute the
bulk quantities associated with that object (see Processing Objects: Derived Quantities),
or the data can be examined directly. For example, if you want to figure out
the temperature at all indexed locations in the central sphere of your
dataset you could:

```
import yt
ds = yt.load("RedshiftOutput0005")
sp = ds.sphere([0.5, 0.5, 0.5], (1, "kpc"))
# Show all temperature values
print(sp["gas", "temperature"])
# Print things in a more human-friendly manner: one temperature at a time
print("(x, y, z) Temperature")
print("-----------------------")
for i in range(sp["gas", "temperature"].size):
print(
"(%f, %f, %f) %f"
% (
sp["gas", "x"][i],
sp["gas", "y"][i],
sp["gas", "z"][i],
sp["gas", "temperature"][i],
)
)
```

Data objects can also be cloned; for instance:

```
import yt
ds = yt.load("RedshiftOutput0005")
sp = ds.sphere([0.5, 0.5, 0.5], (1, "kpc"))
sp_copy = sp.clone()
```

This can be useful for when manually chunking data or exploring different field parameters.

## Slicing Syntax for Selecting Data¶

yt provides a mechanism for easily selecting data while doing interactive work
on the command line. This allows for region selection based on the full domain
of the object. Selecting in this manner is exposed through a slice-like
syntax. All of these attributes are exposed through the `RegionExpression`

object, which is an attribute of a `DataSet`

object, called `r`

.

### Getting All The Data¶

The `.r`

attribute serves as a persistent means of accessing the full data
from a dataset. You can access this shorthand operation by querying any field
on the `.r`

object, like so:

```
ds = yt.load("RedshiftOutput0005")
rho = ds.r["gas", "density"]
```

This will return a *flattened* array of data. The region expression object
(`r`

) doesn’t have any derived quantities on it. This is completely
equivalent to this set of statements:

```
ds = yt.load("RedshiftOutput0005")
dd = ds.all_data()
rho = dd["gas", "density"]
```

Warning

One thing to keep in mind with accessing data in this way is that it is
*persistent*. It is loaded into memory, and then retained until the dataset
is deleted or garbage collected.

### Selecting Multiresolution Regions¶

To select rectilinear regions, where the data is selected the same way that it is selected in a 3D Objects, you can utilize slice-like syntax, supplying start and stop, but not supplying a step argument. This requires that three components of the slice must be specified. These take a start and a stop, and are for the three axes in simulation order (if your data is ordered z, y, x for instance, this would be in z, y, x order).

The slices can have both position and, optionally, unit values. These define
the value with respect to the `domain_left_edge`

of the dataset. So for
instance, you could specify it like so:

```
ds.r[(100, "kpc"):(200, "kpc"), :, :]
```

This would return a region that included everything between 100 kpc from the left edge of the dataset to 200 kpc from the left edge of the dataset in the first dimension, and which spans the entire dataset in the second and third dimensions. By default, if the units are unspecified, they are in the “native” code units of the dataset.

This works in all types of datasets, as well. For instance, if you have a geographic dataset (which is usually ordered latitude, longitude, altitude) you can easily select, for instance, one hemisphere with a region selection:

```
ds.r[:, -180:0, :]
```

If you specify a single slice, it will be repeated along all three dimensions. For instance, this will give all data:

```
ds.r[:]
```

And this will select a box running from 0.4 to 0.6 along all three dimensions:

```
ds.r[0.4:0.6]
```

### Selecting Fixed Resolution Regions¶

yt also provides functionality for selecting regions that have been turned into
voxels. This returns an Arbitrary Grids Objects object. It can be created by
specifying a complex slice “step”, where the start and stop follow the same
rules as above. This is similar to how the numpy `mgrid`

operation works.
For instance, this code block will generate a grid covering the full domain,
but converted to being 21x35x100 dimensions:

```
region = ds.r[::21j, ::35j, ::100j]
```

The left and right edges, as above, can be specified to provide bounds as well. For instance, to select a 10 meter cube, with 24 cells in each dimension, we could supply:

```
region = ds.r[(20, "m"):(30, "m"):24j, (30, "m"):(40, "m"):24j, (7, "m"):(17, "m"):24j]
```

This can select both particles and mesh fields. Mesh fields will be 3D arrays, and generated through volume-weighted overlap calculations.

### Selecting Slices¶

If one dimension is specified as a single value, that will be the dimension along which a slice is made. This provides a simple means of generating a slice from a subset of the data. For instance, to create a slice of a dataset, you can very simply specify the full domain along two axes:

```
sl = ds.r[:, :, 0.25]
```

This can also be very easily plotted:

```
sl = ds.r[:, :, 0.25]
sl.plot()
```

This accepts arguments the same way:

```
sl = ds.r[(20.1, "km"):(31.0, "km"), (504.143, "m"):(1000.0, "m"), (900.1, "m")]
sl.plot()
```

### Making Image Buffers¶

Using the slicing syntax above for choosing a slice, if you also provide an
imaginary step value you can obtain a
`FixedResolutionBuffer`

of the chosen resolution.

For instance, to obtain a 1024 by 1024 buffer covering the entire domain but centered at 0.5 in code units, you can do:

```
frb = ds.r[0.5, ::1024j, ::1024j]
```

This `frb`

object then can be queried like a normal fixed resolution buffer,
and it will return arrays of shape (1024, 1024).

### Making Rays¶

The slicing syntax can also be used select 1D rays of points, whether along an axis or off-axis. To create a ray along an axis:

```
ortho_ray = ds.r[(500.0, "kpc"), (200, "kpc"):(300.0, "kpc"), (-2.0, "Mpc")]
```

To create a ray off-axis, use a single slice between the start and end points of the ray:

```
start = [0.1, 0.2, 0.3] # interpreted in code_length
end = [0.4, 0.5, 0.6] # interpreted in code_length
ray = ds.r[start:end]
```

As for the other slicing options, combinations of unitful quantities with even different units can be used. Here’s a somewhat convoluted (yet working) example:

```
start = ((500.0, "kpc"), (0.2, "Mpc"), (100.0, "kpc"))
end = ((1.0, "Mpc"), (300.0, "kpc"), (0.0, "kpc"))
ray = ds.r[start:end]
```

### Making Fixed-Resolution Rays¶

Rays can also be constructed to have fixed resolution if an imaginary step value is provided, similar to the 2 and 3-dimensional cases described above. This works for rays directed along an axis:

```
ortho_ray = ds.r[0.1:0.6:500j, 0.3, 0.2]
```

or off-axis rays as well:

```
start = [0.1, 0.2, 0.3] # interpreted in code_length
end = [0.4, 0.5, 0.6] # interpreted in code_length
ray = ds.r[start:end:100j]
```

### Selecting Points¶

Finally, you can quickly select a single point within the domain by providing a single coordinate for every axis:

```
pt = ds.r[(10.0, "km"), (200, "m"), (1.0, "km")]
```

Querying this object for fields will give you the value of the field at that point.

## Available Objects¶

As noted above, there are numerous types of objects. Here we group them into:

*Geometric Objects*Data is selected based on spatial shapes in the dataset*Filtering Objects*Data is selected based on other field criteria*Collection Objects*Multiple objects grouped together*Construction Objects*Objects represent some sort of data product constructed by additional analysis

If you want to create your own custom data object type, see Creating Data Objects.

### Geometric Objects¶

For 0D, 1D, and 2D geometric objects, if the extent of the object
intersects a grid cell, then the cell is included in the object; however,
for 3D objects the *center* of the cell must be within the object in order
for the grid cell to be incorporated.

#### 0D Objects¶

**Point**- Class
`YTPoint`

Usage:`point(coord, ds=None, field_parameters=None, data_source=None)`

A point defined by a single cell at specified coordinates.

#### 1D Objects¶

**Ray (Axis-Aligned)**- Class
`YTOrthoRay`

Usage:`ortho_ray(axis, coord, ds=None, field_parameters=None, data_source=None)`

A line (of data cells) stretching through the full domain aligned with one of the x,y,z axes. Defined by an axis and a point to be intersected. Please see this note about ray data value ordering. **Ray (Arbitrarily-Aligned)**- Class
`YTRay`

Usage:`ray(start_coord, end_coord, ds=None, field_parameters=None, data_source=None)`

A line (of data cells) defined by arbitrary start and end coordinates. Please see this note about ray data value ordering.

#### 2D Objects¶

**Slice (Axis-Aligned)**- Class
`YTSlice`

Usage:`slice(axis, coord, center=None, ds=None, field_parameters=None, data_source=None)`

A plane normal to one of the axes and intersecting a particular coordinate. **Slice (Arbitrarily-Aligned)**- Class
`YTCuttingPlane`

Usage:`cutting(normal, coord, north_vector=None, ds=None, field_parameters=None, data_source=None)`

A plane normal to a specified vector and intersecting a particular coordinate.

#### 3D Objects¶

**All Data**- Function
`all_data()`

Usage:`all_data(find_max=False)`

`all_data()`

is a wrapper on the Box Region class which defaults to creating a Region covering the entire dataset domain. It is effectively`ds.region(ds.domain_center, ds.domain_left_edge, ds.domain_right_edge)`

. **Box Region**- Class
`YTRegion`

Usage:`region(center, left_edge, right_edge, fields=None, ds=None, field_parameters=None, data_source=None)`

Alternatively:`box(left_edge, right_edge, fields=None, ds=None, field_parameters=None, data_source=None)`

A box-like region aligned with the grid axis orientation. It is defined by a left_edge, a right_edge, and a center. The left_edge and right_edge are the minimum and maximum bounds in the three axes respectively. The center is arbitrary and must only be contained within the left_edge and right_edge. By using the`box`

wrapper, the center is assumed to be the midpoint between the left and right edges. **Disk/Cylinder**- Class:
`YTDisk`

Usage:`disk(center, normal, radius, height, fields=None, ds=None, field_parameters=None, data_source=None)`

A cylinder defined by a point at the center of one of the circular bases, a normal vector to it defining the orientation of the length of the cylinder, and radius and height values for the cylinder’s dimensions. Note:`height`

is the distance from midplane to the top or bottom of the cylinder, i.e.,`height`

is half that of the cylinder object that is created. **Ellipsoid**- Class
`YTEllipsoid`

Usage:`ellipsoid(center, semi_major_axis_length, semi_medium_axis_length, semi_minor_axis_length, semi_major_vector, tilt, fields=None, ds=None, field_parameters=None, data_source=None)`

An ellipsoid with axis magnitudes set by`semi_major_axis_length`

,`semi_medium_axis_length`

, and`semi_minor_axis_length`

.`semi_major_vector`

sets the direction of the`semi_major_axis`

.`tilt`

defines the orientation of the semi-medium and semi_minor axes. **Sphere**- Class
`YTSphere`

Usage:`sphere(center, radius, ds=None, field_parameters=None, data_source=None)`

A sphere defined by a central coordinate and a radius. **Minimal Bounding Sphere**- Class
`YTMinimalSphere`

Usage:`minimal_sphere(points, ds=None, field_parameters=None, data_source=None)`

A sphere that contains all the points passed as argument.

### Filtering and Collection Objects¶

See also the section on Filtering your Dataset.

**Intersecting Regions**- Most Region objects provide a data_source parameter, which allows you to subselectone region from another (in the coordinate system of the DataSet). Note, this caneasily lead to empty data for non-intersecting regions.Usage:
`slice(axis, coord, ds, data_source=sph)`

**Union Regions**- Usage:
`union()`

**Intersection Regions**- Usage:
`intersection()`

**Filter**- Class
`YTCutRegion`

Usage:`cut_region(base_object, conditionals, ds=None, field_parameters=None)`

A`cut_region`

is a filter which can be applied to any other data object. The filter is defined by the conditionals present, which apply cuts to the data in the object. A`cut_region`

will work for either particle fields or mesh fields, but not on both simultaneously. For more detailed information and examples, see Cut Regions. **Collection of Data Objects**- Class
`YTDataCollection`

Usage:`data_collection(center, obj_list, ds=None, field_parameters=None)`

A`data_collection`

is a list of data objects that can be sampled and processed as a whole in a single data object.

### Construction Objects¶

**Fixed-Resolution Region**- Class
`YTCoveringGrid`

Usage:`covering_grid(level, left_edge, dimensions, fields=None, ds=None, num_ghost_zones=0, use_pbar=True, field_parameters=None)`

A 3D region with all data extracted to a single, specified resolution. See Examining Grid Data in a Fixed Resolution Array. **Fixed-Resolution Region with Smoothing**- Class
`YTSmoothedCoveringGrid`

Usage:`smoothed_covering_grid(level, left_edge, dimensions, fields=None, ds=None, num_ghost_zones=0, use_pbar=True, field_parameters=None)`

A 3D region with all data extracted and interpolated to a single, specified resolution. Identical to covering_grid, except that it interpolates as necessary from coarse regions to fine. See Examining Grid Data in a Fixed Resolution Array. **Fixed-Resolution Region**- Class
`YTArbitraryGrid`

Usage:`arbitrary_grid(left_edge, right_edge, dimensions, ds=None, field_parameters=None)`

When particles are deposited on to mesh fields, they use the existing mesh structure, but this may have too much or too little resolution relative to the particle locations (or it may not exist at all!). An arbitrary_grid provides a means for generating a new independent mesh structure for particle deposition and simple mesh field interpolation. See Arbitrary Grids Objects for more information. **Projection**- Class
`YTQuadTreeProj`

Usage:`proj(field, axis, weight_field=None, center=None, ds=None, data_source=None, method="integrate", field_parameters=None)`

A 2D projection of a 3D volume along one of the axis directions. By default, this is a line integral through the entire simulation volume (although it can be a subset of that volume specified by a data object with the`data_source`

keyword). Alternatively, one can specify a weight_field and different`method`

values to change the nature of the projection outcome. See Types of Projections for more information. **Streamline**- Class
`YTStreamline`

Usage:`streamline(coord_list, length, fields=None, ds=None, field_parameters=None)`

A`streamline`

can be traced out by identifying a starting coordinate (or list of coordinates) and allowing it to trace a vector field, like gas velocity. See Streamlines: Tracking the Trajectories of Tracers in your Data for more information. **Surface**- Class
`YTSurface`

Usage:`surface(data_source, field, field_value)`

The surface defined by all an isocontour in any mesh field. An existing data object must be provided as the source, as well as a mesh field and the value of the field which you desire the isocontour. See 3D Surfaces and Sketchfab.

## Processing Objects: Derived Quantities¶

Derived quantities are a way of calculating some bulk quantities associated
with all of the grid cells contained in a data object.
Derived quantities can be accessed via the `quantities`

interface.
Here is an example of how to get the angular momentum vector calculated from
all the cells contained in a sphere at the center of our dataset.

```
import yt
ds = yt.load("my_data")
sp = ds.sphere("c", (10, "kpc"))
print(sp.quantities.angular_momentum_vector())
```

Some quantities can be calculated for a specific particle type only. For example, to get the center of mass of only the stars within the sphere:

```
import yt
ds = yt.load("my_data")
sp = ds.sphere("c", (10, "kpc"))
print(
sp.quantities.center_of_mass(
use_gas=False, use_particles=True, particle_type="star"
)
)
```

### Quickly Processing Data¶

Most data objects now have multiple numpy-like methods that allow you to quickly process data. More of these methods will be added over time and added to this list. Most, if not all, of these map to other yt operations and are designed as syntactic sugar to slightly simplify otherwise somewhat obtuse pipelines.

These operations are parallelized.

You can compute the extrema of a field by using the `max`

or `min`

functions. This will cache the extrema in between, so calling `min`

right
after `max`

will be considerably faster. Here is an example.

```
import yt
ds = yt.load("IsolatedGalaxy/galaxy0030/galaxy0030")
reg = ds.r[0.3:0.6, 0.2:0.4, 0.9:0.95]
min_rho = reg.min(("gas", "density"))
max_rho = reg.max(("gas", "density"))
```

This is equivalent to:

```
min_rho, max_rho = reg.quantities.extrema(("gas", "density"))
```

The `max`

operation can also compute the maximum intensity projection:

```
proj = reg.max(("gas", "density"), axis="x")
proj.plot()
```

This is equivalent to:

```
proj = ds.proj(("gas", "density"), "x", data_source=reg, method="max")
proj.plot()
```

The same can be done with the `min`

operation, computing a minimum
intensity projection:

```
proj = reg.min(("gas", "density"), axis="x")
proj.plot()
```

This is equivalent to:

```
proj = ds.proj(("gas", "density"), "x", data_source=reg, method="min")
proj.plot()
```

You can also compute the `mean`

value, which accepts a field, axis, and weight
function. If the axis is not specified, it will return the average value of
the specified field, weighted by the weight argument. The weight argument
defaults to `ones`

, which performs an arithmetic average. For instance:

```
mean_rho = reg.mean(("gas", "density"))
rho_by_vol = reg.mean(("gas", "density"), weight=("gas", "cell_volume"))
```

This is equivalent to:

```
mean_rho = reg.quantities.weighted_average(
("gas", "density"), weight_field=("index", "ones")
)
rho_by_vol = reg.quantities.weighted_average(
("gas", "density"), weight_field=("gas", "cell_volume")
)
```

If an axis is provided, it will project along that axis and return it to you:

```
rho_proj = reg.mean(("gas", "temperature"), axis="y", weight=("gas", "density"))
rho_proj.plot()
```

You can also compute the `std`

(standard deviation), which accepts a field,
axis, and weight function. If the axis is not specified, it will
return the standard deviation of the specified field, weighted by the weight
argument. The weight argument defaults to `ones`

. For instance:

```
std_rho = reg.std(("gas", "density"))
std_rho_by_vol = reg.std(("gas", "density"), weight=("gas", "cell_volume"))
```

This is equivalent to:

```
std_rho = reg.quantities.weighted_standard_deviation(
("gas", "density"), weight_field=("index", "ones")
)
std_rho_by_vol = reg.quantities.weighted_standard_deviation(
("gas", "density"), weight_field=("gas", "cell_volume")
)
```

If an axis is provided, it will project along that axis and return it to you:

```
vy_std = reg.std(("gas", "velocity_y"), axis="y", weight=("gas", "density"))
vy_std.plot()
```

The `sum`

function will add all the values in the data object. It accepts a
field and, optionally, an axis. If the axis is left unspecified, it will sum
the values in the object:

```
vol = reg.sum(("gas", "cell_volume"))
```

If the axis is specified, it will compute a projection using the method `sum`

(which does *not* take into account varying path length!) and return that to
you.

```
cell_count = reg.sum(("index", "ones"), axis="z")
cell_count.plot()
```

To compute a projection where the path length *is* taken into account, you can
use the `integrate`

function:

```
proj = reg.integrate(("gas", "density"), "x")
```

All of these projections supply the data object as their base input.

Often, it can be useful to sample a field at the minimum and maximum of a
different field. You can use the `argmax`

and `argmin`

operations to do
this.

```
reg.argmin(("gas", "density"), axis=("gas", "temperature"))
```

This will return the temperature at the minimum density.

If you don’t specify an `axis`

, it will return the spatial position of
the maximum value of the queried field. Here is an example:

```
x, y, z = reg.argmin(("gas", "density"))
```

### Available Derived Quantities¶

**Angular Momentum Vector**- Class
`AngularMomentumVector`

Usage:`angular_momentum_vector(use_gas=True, use_particles=True, particle_type='all')`

The mass-weighted average angular momentum vector of the particles, gas, or both. The quantity can be calculated for all particles or a given particle_type only. **Bulk Velocity**- Class
`BulkVelocity`

Usage:`bulk_velocity(use_gas=True, use_particles=True, particle_type='all')`

The mass-weighted average velocity of the particles, gas, or both. The quantity can be calculated for all particles or a given particle_type only. **Center of Mass**- Class
`CenterOfMass`

Usage:`center_of_mass(use_cells=True, use_particles=False, particle_type='all')`

The location of the center of mass. By default, it computes of the*non-particle*data in the object, but it can be used on particles, gas, or both. The quantity can be calculated for all particles or a given particle_type only. **Extrema****Maximum Location Sampling**- Class
`SampleAtMaxFieldValues`

Usage:`sample_at_max_field_values(fields, sample_fields)`

The value of sample_fields at the maximum value in fields. **Minimum Location Sampling**- Class
`SampleAtMinFieldValues`

Usage:`sample_at_min_field_values(fields, sample_fields)`

The value of sample_fields at the minimum value in fields. **Minimum Location**- Class
`MinLocation`

Usage:`min_location(fields)`

The minimum of a field or list of fields as well as the x,y,z location of that minimum. **Maximum Location**- Class
`MaxLocation`

Usage:`max_location(fields)`

The maximum of a field or list of fields as well as the x,y,z location of that maximum. **Spin Parameter**- Class
`SpinParameter`

Usage:`spin_parameter(use_gas=True, use_particles=True, particle_type='all')`

The spin parameter for the baryons using the particles, gas, or both. The quantity can be calculated for all particles or a given particle_type only. **Total Mass**- Class
`TotalMass`

Usage:`total_mass()`

The total mass of the object as a tuple of (total gas, total particle) mass. **Total of a Field**- Class
`TotalQuantity`

Usage:`total_quantity(fields)`

The sum of a given field (or list of fields) over the entire object. **Weighted Average of a Field**- Class
`WeightedAverageQuantity`

Usage:`weighted_average_quantity(fields, weight)`

The weighted average of a field (or list of fields) over an entire data object. If you want an unweighted average, then set your weight to be the field:`ones`

. **Weighted Standard Deviation of a Field**- Usage:
`weighted_standard_deviation(fields, weight)`

The weighted standard deviation of a field (or list of fields) over an entire data object and the weighted mean. If you want an unweighted standard deviation, then set your weight to be the field:`ones`

.

## Arbitrary Grids Objects¶

The covering grid and smoothed covering grid objects mandate that they be
exactly aligned with the mesh. This is a
holdover from the time when yt was used exclusively for data that came in
regularly structured grid patches, and does not necessarily work as well for
data that is composed of discrete objects like particles. To augment this, the
`YTArbitraryGrid`

object
was created, which enables construction of meshes (onto which particles can be
deposited or smoothed) in arbitrary regions. This eliminates any assumptions
on yt’s part about how the data is organized, and will allow for more
fine-grained control over visualizations.

An example of creating an arbitrary grid would be to construct one, then query the deposited particle density, like so:

```
import yt
ds = yt.load("snapshot_010.hdf5")
obj = ds.arbitrary_grid([0.0, 0.0, 0.0], [0.99, 0.99, 0.99], dims=[128, 128, 128])
print(obj["deposit", "all_density"])
```

While these cannot yet be used as input to projections or slices, slices and projections can be taken of the data in them and visualized by hand.

These objects, as of yt 3.3, are now also able to “voxelize” mesh fields. This means that you can query the “density” field and it will return the density field as deposited, identically to how it would be deposited in a fixed resolution buffer. Note that this means that contributions from misaligned or partially-overlapping cells are added in a volume-weighted way, which makes it inappropriate for some types of analysis.

## Combining Objects: Boolean Data Objects¶

A special type of data object is the *boolean* data object, which works with
data selection objects of any dimension. It is built by relating already existing
data objects with the bitwise operators for AND, OR and XOR, as well as the
subtraction operator. These are created by using the operators `&`

for an
intersection (“AND”), `|`

for a union (“OR”), `^`

for an exclusive or
(“XOR”), and `+`

and `-`

for addition (“OR”) and subtraction (“NEG”).
Here are some examples:

```
import yt
ds = yt.load("snapshot_010.hdf5")
sp1 = ds.sphere("c", (0.1, "unitary"))
sp2 = ds.sphere(sp1.center + 2.0 * sp1.radius, (0.2, "unitary"))
sp3 = ds.sphere("c", (0.05, "unitary"))
new_obj = sp1 + sp2
cutout = sp1 - sp3
sp4 = sp1 ^ sp2
sp5 = sp1 & sp2
```

Note that the `+`

operation and the `|`

operation are identical. For when
multiple objects are to be combined in an intersection or a union, there are
the data objects `intersection`

and `union`

which can be called, and which
will yield slightly higher performance than a sequence of calls to `+`

or
`&`

. For instance:

```
import yt
ds = yt.load("Enzo_64/DD0043/data0043")
sp1 = ds.sphere((0.1, 0.2, 0.3), (0.05, "unitary"))
sp2 = ds.sphere((0.2, 0.2, 0.3), (0.10, "unitary"))
sp3 = ds.sphere((0.3, 0.2, 0.3), (0.15, "unitary"))
isp = ds.intersection([sp1, sp2, sp3])
usp = ds.union([sp1, sp2, sp3])
```

The `isp`

and `usp`

objects will act the same as a set of chained `&`

and
`|`

operations (respectively) but are somewhat easier to construct.

## Connected Sets and Clump Finding¶

The underlying machinery used in Clump Finding is accessible from any data object. This includes the ability to obtain and examine topologically connected sets. These sets are identified by examining cells between two threshold values and connecting them. What is returned to the user is a list of the intervals of values found, and extracted regions that contain only those cells that are connected.

To use this, call
`extract_connected_sets()`

on
any 3D data object. This requests a field, the number of levels of levels sets to
extract, the min and the max value between which sets will be identified, and
whether or not to conduct it in log space.

```
sp = ds.sphere("max", (1.0, "pc"))
contour_values, connected_sets = sp.extract_connected_sets(
("gas", "density"), 3, 1e-30, 1e-20
)
```

The first item, `contour_values`

, will be an array of the min value for each
set of level sets. The second (`connected_sets`

) will be a dict of dicts.
The key for the first (outer) dict is the level of the contour, corresponding
to `contour_values`

. The inner dict returned is keyed by the contour ID. It
contains `YTCutRegion`

objects. These can be queried just as any other data object. The clump finder
(Clump Finding) differs from the above method in that the contour
identification is performed recursively within each individual structure, and
structures can be kept or remerged later based on additional criteria, such as
gravitational boundedness.

## Storing and Loading Objects¶

Often, when operating interactively or via the scripting interface, it is convenient to save an object to disk and then restart the calculation later or transfer the data from a container to another filesystem. This can be particularly useful when working with extremely large datasets. Field data can be saved to disk in a format that allows for it to be reloaded just like a regular dataset. For information on how to do this, see Geometric Data Containers.