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Version: v1.0.4


The term field is borrowed from mathematics and physics. If you already know scalar field (for example heat field), or vector field (for example gravitational field), then it is straightforward for you to understand fields in Taichi.

Fields in Taichi are the global data containers that can be accessed from both the Python scope and the Taichi scope. Just like an ndarray in NumPy or a tensor in PyTorch, a field in Taichi is defined as a multi-dimensional array of elements, and elements in a field can be a scalar, a vector, a matrix, or a struct.


A 0D (zero-dimensional) field contains only one element.

Scalar fields

Scalar fields refer to the fields that store scalars and are the most basic fields. A 0D scalar field is a single scalar.


import taichi as ti

# Declare a 0D scalar field whose data type is f32
f_0d = ti.field(ti.f32, shape=()) # 0D
# Declare a 1D scalar field whose shape is (128)
f_1d = ti.field(ti.i32, shape=128) # 1D
# Declare a 2D scalar field whose shape is (640, 480)
f_2d = ti.field(ti.u8, shape=(640, 480)) # 2D
# Declare a 3D scalar field whose data type is f32
f_3d = ti.field(ti.f32, shape=(32, 32, 32)) # 3D

Access elements in a scalar field

The initial value of elements in a scalar filed is zero. Always use explicit indexing to access elements in a scalar field.


When accessing a 0D field x, use x[None] = 0, not x = 0.

# For a 0D field, you are required to use the index None even though it has only one element
f_0d[None] = 10.0
f_1d[0] = 1
f_2d[1, 2] = 255
f_3d[3, 3, 3] = 2.0

As mentioned above, you can use a 2D scalar field to represent a 2D grid of values. The following code snippet creates and displays a 640×480 image with randomly-generated gray scales:

import taichi as ti

width, height = 640,480
# Create a 640x480 scalar field, each of its elements representing a pixel value (f32)
gray_scale_image = ti.field(dtype=ti.f32, shape=(width, height))

def fill_image():
# Fill the image with random gray
for i,j in gray_scale_image:
gray_scale_image[i,j] = ti.random()

# Create a GUI of same size as the gray-scale image
gui = ti.GUI('gray-scale image with random values', (width, height))
while gui.running:

With Taichi versions earlier than v0.8.0, you cannot allocate new fields after executing a kernel. Starting from v0.8.0, you can use the FieldsBuilder class to dynamically allocate or destruct fields. See the Field (advanced) for more information.


Taichi does not support slicing on a Taichi field. For example, with the 2D scalar field f_2d, you can do f_2d[1, 2], but not f_2d[1].


Metadata provides the basic information of a scalar field. You can retrieve the data type and shape of a scalar field via its shape and dtype property:

f_1d.shape  # (128)
f_3d.dtype # f32

Vector fields

As the name suggests, vector fields are the fields whose elements are vectors.

  • You can use a vector field to represent an RGB image. Then, each of its elements is an (r, g, b) triple.
  • You can use a vector field to represent a volumetric field. Then, each of its elements can be the velocity of the corresponding particle.


The following code snippet declares a 3D field of 2D vectors:

# Declare a 1x2x3 vector field, whose vector dimension is n=2
f = ti.Vector(ti.f32, n=2).field(shape=(1,2,3))

The following code snippet declares a 300x300x300 vector field volumetric_field, whose vector dimension is 3:

box_size = (300, 300, 300)  # A 300x300x300 grid in a 3D space
# Declare a 300x300x300 vector field, whose vector dimension is n=3
volumetric_field = ti.Vector.field(n=3, dtype=ti.f32, shape=box_size)

Access elements in a vector field

Accessing a vector field is similar to accessing a multi-dimensional array: You use an index operator [] to access an element in the field. The only difference is that, to access a specific component of an element (vector in this case), you need an extra index operator []:

  • To access the velocity vector at a specific position of the volumetric field above:


  • To access the l-th component of the velocity vector:

    volumetric_field[i, j, k][l]

The following code snippet generates and prints a random vector field:

# n: vector dimension; w: width; h: height
n,w,h = 3,128,64
vec_field = ti.Vector.field(n, dtype=ti.f32, shape=(w,h))

def fill_vector():
for i,j in vec_field:
for k in ti.static(range(n)):
#ti.static unrolls the inner loops
vec_field[i,j][k] = ti.random()


To access the p-th component of the 0D vector field x = ti.Vector.field(n=3, dtype=ti.f32, shape=()):

x[None][p] (0 p < n).

Matrix fields

As the name suggests, matrix fields are the fields whose elements are matrices. In continuum mechanics, at each infinitesimal point in a 3D material exists a strain and stress tensor. The strain and stress tensor is a 3 x 2 matrix. Then, you can use a matrix field to represent such a tensor field.


The following code snippet declares a tensor field:

# Declare a 300x400x500 matrix field, each of its elements being a 3x2 matrix
tensor_field = ti.Matrix.field(n=3, m=2, dtype=ti.f32, shape=(300, 400, 500))

Access elements in a matrix field

Accessing a matrix field is similar to accessing a vector field: You use an index operator [] for field indexing and a second [] for matrix indexing.

  • To retrieve the i, j element of the matrix field tensor_field:

    mat = tensor_field[i, j]

  • To retrieve the member on the first row and second column of the element mat:

    mat[0, 1] or tensor_field[i, j][0, 1]


To access the 0D matrix field x = ti.Matrix.field(n=3, m=4, dtype=ti.f32, shape=()):

x[None][p, q] (0 p < n, 0 q < m)

Considerations: Matrix size

Matrix operations are unrolled during compile time. Take a look at the following example:

import taichi as ti

a = ti.Matrix.field(n=2, m=3, dtype=ti.f32, shape=(2, 2))
def test():
for i in ti.grouped(a):
# a[i] is a 2x3 matrix
a[i] = [[1, 1, 1], [1, 1, 1]]
# The assignment is unrolled to the following during compile time:
# a[i][0, 0] = 1
# a[i][0, 1] = 1
# a[i][0, 2] = 1
# a[i][1, 0] = 1
# a[i][1, 1] = 1
# a[i][1, 2] = 1

Operating on large matrices (for example 32x128) can lead to long compilation time and poor performance. For performance reasons, it is recommended that you keep your matrices small:

  • 2x1, 3x3, and 4x4 matrices work fine.
  • 32x6 is a bit too large.


When declaring the matrix field, leave large dimensions to the fields, rather than to the matrices. If you have a 3x2 field of 64x32 matrices:

  • Not recommended: ti.Matrix.field(64, 32, dtype=ti.f32, shape=(3, 2))
  • Recommended: ti.Matrix.field(3, 2, dtype=ti.f32, shape=(64, 32))

Struct fields

Struct fields are fields that store user-defined structs. Members of a struct element can be:

  • Scalars
  • Vectors
  • Matrices
  • Other struct fields.


The following code snippet declares a 1D field of particle information (position, velocity, acceleration, and mass) using ti.Struct.field(). Note that:

  • Member variables pos, vel, acc, and mass are provided in the dictionary format.
  • Compound types, such as ti.types.vector, ti.types.matrix, and ti.types.struct, can be used to declare vectors, matrices, or structs as struct members.
# Declare a 1D struct field using the ti.Struct.field() method
particle_field = ti.Struct.field({
"pos": ti.types.vector(3, ti.f32),
"vel": ti.types.vector(3, ti.f32),
"acc": ti.types.vector(3, ti.f32),
"mass": ti.f32,
}, shape=(n,))

Alternatively, besides directly using ti.Struct.field(), you can first declare a compound type particle and then create a field of it:

# Declare a compound type vec3f to represent position, velocity, and acceleration.
vec3f = ti.types.vector(3, ti.f32)
# Declare a struct composed of three vectors and one f32 floating-point number
particle = ti.types.struct(
pos=vec3f, vel=vec3f, acc=vec3f, mass=ti.f32,
# Declare a 1D field of the struct particle using field()
particle_field = particle.field(shape=(n,))

Access elements in a struct field

You can access members of elements in a struct field either one by one or universally:

# Set the position of the first particle in the field to origin [0.0, 0.0, 0.0]
particle_field[0].pos = ti.Vector([0.0, 0.0, 0.0]) # pos is a 3D vector

# Set the second particle's pos[0] in the field to 1.0
particle_field[1].pos[0] = 1.0 # pos[0] is the first member of pos

# Universally set the mass of all particles to 1.0