# Scalar fields

Taichi fields are used to store data.

Field elements could be either a scalar, a vector, or a matrix (see Matrices). In this paragraph, we will only talk about scalar fields, whose elements are simply scalars.

Fields can have up to eight dimensions.

• A 0D scalar field is simply a single scalar.
• A 1D scalar field is a 1D linear array.
• A 2D scalar field can be used to represent a 2D regular grid of values. For example, a gray-scale image.
• A 3D scalar field can be used for volumetric data.

Fields could be either dense or sparse, see Sparse Computation for details on sparse fields. We will only talk about dense fields in this paragraph.

##### note

We once used the term tensor instead of field. Tensor will no longer be used.

## Declaration#

::: {.function} ti.field(dtype, shape = None, offset = None)

parameter dtype

: (DataType) type of the field element

parameter shape

: (optional, scalar or tuple) the shape of field

parameter offset

: (optional, scalar or tuple) see coordinate offset

For example, this creates a dense field with four `int32` as elements: :

``x = ti.field(ti.i32, shape=4)``

This creates a 4x3 dense field with `float32` elements: :

``x = ti.field(ti.f32, shape=(4, 3))``

If shape is `()` (empty tuple), then a 0-D field (scalar) is created: :

``x = ti.field(ti.f32, shape=())``

Then access it by passing `None` as index: :

``x[None] = 2``

If shape is not provided or `None`, the user must manually `place` it afterwards: :

``x = ti.field(ti.f32)ti.root.dense(ti.ij, (4, 3)).place(x)# equivalent to: x = ti.field(ti.f32, shape=(4, 3))``

:::

##### note

Not providing `shape` allows you to place the field in a layout other than the default dense, see Advanced dense layouts for more details.

##### caution

All variables should be created and placed before any kernel invocation or any of them accessed from python-scope. For example:

``x = ti.field(ti.f32)x[None] = 1 # ERROR: x not placed!``
``````x = ti.field(ti.f32, shape=())@ti.kerneldef func():    x[None] = 1
func()y = ti.field(ti.f32, shape=())# ERROR: cannot create fields after kernel invocation!``````
``x = ti.field(ti.f32, shape=())x[None] = 1y = ti.field(ti.f32, shape=())# ERROR: cannot create fields after any field accesses from the Python-scope!``

## Accessing components#

You can access an element of the Taichi field by an index or indices.

::: {.attribute} a[p, q, ...]

parameter a

: (ti.field) the sclar field

parameter p

: (scalar) index of the first field dimension

parameter q

: (scalar) index of the second field dimension

return

: (scalar) the element at `[p, q, ...]`

This extracts the element value at index `[3, 4]` of field `a`: :

``x = a[3, 4]``

This sets the element value at index `2` of 1D field `b` to `5`: :

``b = 5``

:::

##### note

In Python, x[(exp1, exp2, …, expN)] is equivalent to x[exp1, exp2, …, expN]; the latter is just syntactic sugar for the former.

##### note

The returned value can also be `Vector` / `Matrix` if `a` is a vector/matrix field, see [Vectors./vector.md) for more details.

## Meta data#

::: {.attribute} a.shape

parameter a

: (ti.field) the field

return

: (tuple) the shape of field `a`

``<!-- -->``
``````x = ti.field(ti.i32, (6, 5))x.shape  # (6, 5)
y = ti.field(ti.i32, 6)y.shape  # (6,)
z = ti.field(ti.i32, ())z.shape  # ()``````

:::

::: {.attribute} a.dtype

parameter a

: (ti.field) the field

return

: (DataType) the data type of `a`

``<!-- -->``
``x = ti.field(ti.i32, (2, 3))x.dtype  # ti.i32``

:::

::: {.function} a.parent(n = 1)

parameter a

: (ti.field) the field

parameter n

: (optional, scalar) the number of parent steps, i.e. `n=1` for parent, `n=2` grandparent, etc.

return

: (SNode) the parent of `a`'s containing SNode

``<!-- -->``
``````x = ti.field(ti.i32)y = ti.field(ti.i32)blk1 = ti.root.dense(ti.ij, (6, 5))blk2 = blk1.dense(ti.ij, (3, 2))blk1.place(x)blk2.place(y)
x.parent()   # blk1y.parent()   # blk2y.parent(2)  # blk1``````

See Structural nodes (SNodes) for more details. :::