Version: v1.3.0

# Fields

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 easy for you to understand fields in Taichi.

Fields in Taichi are the global data containers, which 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.

##### note

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.
• A 1D scalar field is a 1D array of scalars.
• A 2D scalar field is a 2D array of scalars, and so on.

### Declaration

The simplest way to declare a scalar field is to call ti.field(dtype, shape), where dtype is a primitive data type as explained in the Type System and shape is a tuple of integers.

• When declaring a 0D scalar field, you need to set its shape to the empty tuple ():

# Declares a 0D scalar field whose data type is f32
f_0d = ti.field(ti.f32, shape=()) # 0D field

An illustration of f_0d:

┌─────┐
│ │
└─────┘
└─────┘
f_0d.shape=()
• When declaring a 1D scalar field of length n, set its shape to n or (n,):

f_1d = ti.field(ti.i32, shape=9)  # A 1D field of length 9

An illustration of f_1d:

┌───┬───┬───┬───┬───┬───┬───┬───┬───┐
│ │ │ │ │ │ │ │ │ │
└───┴───┴───┴───┴───┴───┴───┴───┴───┘
└───────────────────────────────────┘
f_1d.shape = (9,)

There is little difference between a 0D field and a 1D field of length 1 except for their indexing rules. You must use None as the index to access a 0D field and 0 as the index to access a 1D field of length 1:

# f1 and f2 are basically interchangeable
f1 = ti.field(int, shape=())
f2 = ti.field(int, shape=1)

f1[None] = 1 # Use None to access a 0D field
f2[0] = 1 # Use 0 to access a 1D field of length 1
• When declaring a 2D scalar field, you need to set its two dimensions (numbers of rows and columns) respectively. For example, the following code snippet defines a 2D scalar field in the shape (3, 6) (three rows and six columns):

f_2d = ti.field(int, shape=(3, 6))  # A 2D field in the shape (3, 6)

An illustration of f_2d:

f_2d.shape[1]
(=6)
┌───────────────────────┐

┌ ┌───┬───┬───┬───┬───┬───┐ ┐
│ │ │ │ │ │ │ │ │
│ ├───┼───┼───┼───┼───┼───┤ │
f_2d.shape[0] │ │ │ │ │ │ │ │ │
(=3) │ ├───┼───┼───┼───┼───┼───┤ │
│ │ │ │ │ │ │ │ │
└ └───┴───┴───┴───┴───┴───┘ ┘

Scalar fields of higher dimensions can be similarily defined.

##### WARNING

Taichi only supports fields of dimensions 8.

### Access elements in a scalar field

Once a field is declared, Taichi automatically initializes its elements with the value zero.

To access an element in a scalar field, you need to explicitly specify the element's index.

##### note

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

• To access the element in a 0D field, use the index None even though the field has only one element:

f_0d[None] = 10.0

The layout of f_0d:

┌──────┐
10.0
└──────┘
└──────┘
f_0d.shape=()
• To access an element in a 1D field, use index i, which is an integer in the range [0, f_1d.shape[0]):

for i in range(9):
f_1d[i] = i

The layout of f_1d:

┌───┬───┬───┬───┬───┬───┬───┬───┬───┐
012345678
└───┴───┴───┴───┴───┴───┴───┴───┴───┘
• To access an element in a 2D field, use index (i, j), which is an integer pair.

• i in the range [0, f_2d.shape[0])
• j in the range [0, f_2d.shape[1]):
for i, j in f_2d:
f_2d[i, j] = i

The layout of f_2d:

┌───┬───┬───┬───┬───┬───┐
000000
├───┼───┼───┼───┼───┼───┤
111111
├───┼───┼───┼───┼───┼───┤
222222
└───┴───┴───┴───┴───┴───┘
• To access an element in an n-dimensional field, use index (i, j, k, ...), which is an n-tuple of integers.

You can use a 2D scalar field to represent a 2D grid of values. The following code snippet creates and displays a 640×480 gray scale image of randomly-generated values:

import taichi as ti
ti.init(arch=ti.cpu)

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

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

fill_image()
# Creates a GUI of the size of the gray-scale image
gui = ti.GUI('gray-scale image of random values', (width, height))
while gui.running:
gui.set_image(gray_scale_image)
gui.show()
##### WARNING

Taichi fields do not support slicing. Neither of the following usage is correct:

for x in f_2d[0]:  # Error! You tried to access its first row，but it is not supported
f_2d[0][3:] = [4, 5, 6]  # Error! You tried to access a slice of the first row, but it is not supported

Either way, the system throws an error message 'Slicing is not supported on ti.field'.

### Fill a scalar field with a given value

To set all elements in a scalar field to a given value, call field.fill():

x = ti.field(int, shape=(5, 5))
x.fill(1) # Sets all elements in x to 1

@ti.kernel
def test():
x.fill(-1) # Sets all elements in x to -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 properties:

f_1d.shape  # (9,)
f_3d.dtype # f32

## Vector fields

As the name suggests, vector fields are the fields whose elements are vectors. What a vector represents depends on the scenario of your program. For example, a vector may stand for the (R, G, B) triple of a pixel, the position of a particle, or the gravitational field in space.

### Declaration

Declaring a vector field where each element is an N-dimensional vector is similar to declaring a scalar field, except that you need to call ti.Vector.field instead of ti.field and specify N as the first positional argument.

For example, the following code snippet declares a 2D field of 2D vectors:

# Declares a 3x3 vector field comprising 2D vectors
f = ti.Vector.field(n=2, dtype=float, shape=(3, 3))

The layout of f:

f.shape[1]
(=3)
┌────────────────────┐

┌ ┌──────┬──────┬──────┐ ┐
│ │[*, *][*, *][*, *]│ │
│ ├──────┼──────┼──────┤ │
f.shape[0] │ │[*, *][*, *][*, *]│ │ [*, *]
(=3) │ ├──────┼──────┼──────┤ │ └─────┘
│ │[*, *][*, *][*, *]│ │ n=2
└ └──────┴──────┴──────┘ ┘

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
# Declares 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:

volumetric_field[i, j, k]

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

volumetric_field[i, j, k][l]

##### note

Alternatively, you can use swizzling with the indices xyzw or rgba to access the components of a vector, provided that the dimension of the vector is no more than four:

volumetric_field[i, j, k].x = 1  # Equivalent to volumetric_field[i, j, k][0] = 1
volumetric_field[i, j, k].y = 2 # Equivalent to volumetric_field[i, j, k][1] = 2
volumetric_field[i, j, k].z = 3 # Equivalent to volumetric_field[i, j, k][2] = 3
volumetric_field[i, j, k].w = 4 # Equivalent to volumetric_field[i, j, k][3] = 4
volumetric_field[i, j, k].xyz = 1, 2, 3 # Assigns 1, 2, 3 to the first three components
volumetric_field[i, j, k].rgb = 1, 2, 3 # Equivalent to the above

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=float, shape=(w,h))

@ti.kernel
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()

fill_vector()
print(vec_field[w-1,h-1][n-1])
##### note

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.

### Declaration

The following code snippet declares a tensor field:

# Declares 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 index operator [] for matrix indexing.

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

mat = tensor_field[i, j]

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

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

##### note

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 at compile time. Take a look at the following example:

import taichi as ti
ti.init()

a = ti.Matrix.field(n=2, m=3, dtype=ti.f32, shape=(2, 2))
@ti.kernel
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 at 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 larger matrices (for example 32x128) can lead to longer compilation time and poorer 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.

Workaround:

When declaring a 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.

### Declaration

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.
• You can use compound types, such as ti.types.vector, ti.types.matrix, and ti.types.struct, to declare vectors, matrices, or structs as struct members.
# Declares a 1D struct field using the ti.Struct.field() method
particle_field = ti.Struct.field({
"pos": ti.math.vec3,
"vel": ti.math.vec3,
"acc": ti.math.vec3,
"mass": float,
}, shape=(n,))

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

# vec3 is a built-in vector type suppied in the `taichi.math` module
vec3 = ti.math.vec3
# Declares a struct comprising three vectors and one floating-point number
particle = ti.types.struct(
pos=vec3, vel=vec3, acc=vec3, mass=float,
)
# Declares a 1D field of the struct particle by calling field()
particle_field = particle.field(shape=(n,))

### Access elements in a struct field

You can access a member of an element in a struct field in either of the following ways: index-first or name-first.

• The index-first approach locates a certain element with its index before specifying the name of the target member:
# Sets the position of the first particle in the field to [0.0, 0.0, 0.0]
particle_field[0].pos = vec3(0) # particle_field is a 1D struct field, pos is a 3D vector
• The name-first approach first creates a sub-field, which gathers all the mass members in the struct field, and then uses the index operator [] to access a specific member:
particle_field.mass[0] = 1.0  # Sets the mass of the first particle in the field to 1.0

Considering that paticle_field.mass is a field consisting of all the mass members of the structs in paticle_field, you can also call fill() to set the members to a specific value all at once:

particle_field.mass.fill(1.0)  # Sets all mass of the particles in the struct field to 1.0