Matrices

  • ti.Matrix is for small matrices (e.g. 3x3) only. If you have 64x64 matrices, you should consider using a 2D scalar field.
  • ti.Vector is the same as ti.Matrix, except that it has only one column.
  • Differentiate element-wise product * and matrix product @.
  • ti.Vector.field(n, dtype=ti.f32) or ti.Matrix.field(n, m, dtype=ti.f32) to create vector/matrix fields.
  • A.transpose()
  • 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) (Taichi-scope only)
  • all(A) (Taichi-scope only)

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 field. In this case, the field is an N-dimensional array of n by m matrices.

Declaration

As global matrix fields

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

For example, this creates a 5x4 matrix field with each entry being a 3x3 matrix:

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

Note

In Python-scope, ti.field declares a Scalar fields, while ti.Matrix.field declares a matrix field.

As a temporary local variable

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 matrix fields

a[p, q, ...][i, j]
Parameters:
  • a – (ti.Matrix.field) the matrix field
  • p – (scalar) index of the first field dimension
  • q – (scalar) index of the second field 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 matrix fields.

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

For 0-D matrix fields, 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

a.transpose()
Parameters:a – (ti.Matrix) the matrix
Returns:(ti.Matrix) the transposed matrix of a.

For example:

a = ti.Matrix([[2, 3], [4, 5]])
b = a.transpose()
# Now b = ti.Matrix([[2, 4], [3, 5]])

Note

a.transpose() will not effect the data in a, it just return the result.

a.trace()
Parameters:a – (ti.Matrix) the matrix
Returns:(scalar) the trace of matrix a.

The return value can be computed as a[0, 0] + a[1, 1] + ....

a.determinant()
Parameters:a – (ti.Matrix) the matrix
Returns:(scalar) the determinant of matrix a.

Note

The matrix size of matrix must be 1x1, 2x2, 3x3 or 4x4 for now.

This function only works in Taichi-scope for now.

a.inverse()
Parameters:a – (ti.Matrix) the matrix
Returns:(ti.Matrix) the inverse of matrix a.

Note

The matrix size of matrix must be 1x1, 2x2, 3x3 or 4x4 for now.

This function only works in Taichi-scope for now.