Matrices

  • ti.Matrix is for small matrices (e.g. 3x3) only. If you have 64x64 matrices, you should consider using a 2D tensor of scalars.
  • ti.Vector is the same as ti.Matrix, except that it has only one column.
  • Differentiate element-wise product * and matrix product @.
  • ti.Vector(n, dt=ti.f32) or ti.Matrix(n, m, dt=ti.f32) to create tensors of vectors/matrices.
  • A.transpose()
  • A.inverse()
  • A.trace()
  • A.determinant()
  • A.cast(type) or simply int(A) and float(A)
  • R, S = ti.polar_decompose(A, ti.f32)
  • U, sigma, V = ti.svd(A, ti.f32) (Note that sigma is a 3x3 diagonal matrix)
  • any(A)
  • all(A)
  • Currently, only +, -, @ Matrix operations have experimental support in Python-scope. An exception will be raised if you try to apply other operations in Python-scope, use them in Taichi-scope (@ti.kernel) instead.

TODO: doc here better like Vector. WIP

A matrix in Taichi can have two forms:

  • as a temporary local variable. An n by m matrix consists of n * m scalar values.
  • as a an element of a global tensor. In this case, the tensor is an N-dimensional array of n by m matrices.

Declaration

As global tensors of matrices

ti.Matrix(n, m, dt, shape = None, offset = None)
Parameters:
  • n – (scalar) the number of rows in the matrix
  • m – (scalar) the number of columns in the matrix
  • dt – (DataType) data type of the components
  • shape – (optional, scalar or tuple) shape the tensor of vectors, see Tensors and matrices
  • offset – (optional, scalar or tuple) see Coordinate offsets

For example, this creates a 5x4 tensor of 3x3 matrices:

# Python-scope
a = ti.Matrix(3, 3, dt=ti.f32, shape=(5, 4))

Note

In Python-scope, ti.var declares Tensors of scalars, while ti.Matrix declares tensors of matrices.

As a temporary local variable

ti.Matrix([x, y, ...])
Parameters:
  • x – (scalar) the first component of the vector
  • y – (scalar) the second component of the vector

For example, this creates a 3x1 matrix with components (2, 3, 4):

# Taichi-scope
a = ti.Matrix([2, 3, 4])

Note

this is equivalent to ti.Vector([x, y, …])

ti.Matrix([[x, y, ...][, z, w, ...], ...])
Parameters:
  • x – (scalar) the first component of the first row
  • y – (scalar) the second component of the first row
  • z – (scalar) the first component of the second row
  • w – (scalar) the second component of the second row

For example, this creates a 2x3 matrix with components (2, 3, 4) in the first row and (5, 6, 7) in the second row:

# Taichi-scope
a = ti.Matrix([[2, 3, 4], [5, 6, 7]])
ti.Matrix.rows([v0, v1, v2, ...])
ti.Matrix.cols([v0, v1, v2, ...])
Parameters:
  • v0 – (vector) vector of elements forming first row (or column)
  • v1 – (vector) vector of elements forming second row (or column)
  • v2 – (vector) vector of elements forming third row (or column)

For example, this creates a 3x3 matrix by concactinating vectors into rows (or columns):

# Taichi-scope
v0 = ti.Vector([1.0, 2.0, 3.0])
v1 = ti.Vector([4.0, 5.0, 6.0])
v2 = ti.Vector([7.0, 8.0, 9.0])

# to specify data in rows
a = ti.Matrix.rows([v0, v1, v2])

# to specify data in columns instead
a = ti.Matrix.cols([v0, v1, v2])

# lists can be used instead of vectors
a = ti.Matrix.rows([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]])

Accessing components

As global tensors of vectors

a[p, q, ...][i, j]
Parameters:
  • a – (tensor of matrices) the tensor of matrices
  • p – (scalar) index of the first tensor dimension
  • q – (scalar) index of the second tensor dimension
  • i – (scalar) row index of the matrix
  • j – (scalar) column index of the matrix

This extracts the first element in matrix a[6, 3]:

x = a[6, 3][0, 0]

# or
mat = a[6, 3]
x = mat[0, 0]

Note

Always use two pair of square brackets to access scalar elements from tensors of matrices.

  • The indices in the first pair of brackets locate the matrix inside the tensor of matrices;
  • The indices in the second pair of brackets locate the scalar element inside the matrix.

For 0-D tensors of matrices, indices in the first pair of brackets should be [None].

As a temporary local variable

a[i, j]
Parameters:
  • a – (Matrix) the matrix
  • i – (scalar) row index of the matrix
  • j – (scalar) column index of the matrix

For example, this extracts the element in row 0 column 1 of matrix a:

x = a[0, 1]

This sets the element in row 1 column 3 of a to 4:

a[1, 3] = 4

Methods

TODO: WIP

TODO: add element wise operations docs