Tensors of scalars


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

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

x = ti.var(ti.i32, shape=4)

This creates a 4x3 dense tensor with float32 elements:

x = ti.var(ti.f32, shape=(4, 3))

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

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


Not providing shape allows you to place the tensor 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.var(ti.f32)
x[None] = 1 # ERROR: x not placed!
x = ti.var(ti.f32, shape=())
def func():
    x[None] = 1

y = ti.var(ti.f32, shape=())
# ERROR: cannot create tensor after kernel invocation!
x = ti.var(ti.f32, shape=())
x[None] = 1
y = ti.var(ti.f32, shape=())
# ERROR: cannot create tensor after any tensor accesses from the Python-scope!

Accessing components

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

a[p, q, ...]
  • a – (Tensor) the tensor of scalars
  • p – (scalar) index of the first tensor dimension
  • q – (scalar) index of the second tensor dimension

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

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

x = a[3, 4]

This sets the element value at index 2 of 1D tensor 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 tensor of vector / matrix, see Vectors for more details.

Meta data

Parameters:a – (Tensor) the tensor
Returns:(scalar) the length of a
x = ti.var(ti.i32, (6, 5))
x.dim()  # 2

y = ti.var(ti.i32, 6)
y.dim()  # 1

z = ti.var(ti.i32, ())
z.dim()  # 0
Parameters:a – (Tensor) the tensor
Returns:(tuple) the shape of tensor a
x = ti.var(ti.i32, (6, 5))
x.shape()  # (6, 5)

y = ti.var(ti.i32, 6)
y.shape()  # (6,)

z = ti.var(ti.i32, ())
z.shape()  # ()
Parameters:a – (Tensor) the tensor
Returns:(DataType) the data type of a
x = ti.var(ti.i32, (2, 3))
x.data_type()  # ti.i32
a.parent(n = 1)
  • a – (Tensor) the tensor
  • 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.var(ti.i32)
y = ti.var(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.