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 ref:sparse for details on sparse fields. We will only talk about dense fields in this paragraph.


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


ti.field(dtype, shape = None, offset = None)
  • dtype – (DataType) type of the field element
  • shape – (optional, scalar or tuple) the shape of field
  • offset – (optional, scalar or tuple) see Coordinate offsets

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))


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


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=())
def func():
    x[None] = 1

y = ti.field(ti.f32, shape=())
# ERROR: cannot create fields after kernel invocation!
x = ti.field(ti.f32, shape=())
x[None] = 1
y = 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.

a[p, q, ...]
  • a – (ti.field) the sclar field
  • p – (scalar) index of the first field dimension
  • q – (scalar) index of the second field dimension

(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[2] = 5


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


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

Meta data

Parameters:a – (ti.field) the field
Returns:(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  # ()
Parameters:a – (ti.field) the field
Returns:(DataType) the data type of a
x = ti.field(ti.i32, (2, 3))
x.dtype  # ti.i32
a.parent(n = 1)
  • a – (ti.field) the field
  • n – (optional, scalar) the number of parent steps, i.e. n=1 for parent, n=2 grandparent, etc.

(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))

x.parent()   # blk1
y.parent()   # blk2
y.parent(2)  # blk1

See Structural nodes (SNodes) for more details.