symforce.geo.matrix module#

class Matrix(*args, **kwargs)[source]#

Bases: Storage

Matrix type that wraps the SymPy Matrix class. Care has been taken to allow this class to create fixed-size child classes like Matrix31. Anytime __new__() is called, the appropriate fixed size class is returned rather than the type of the arguments. The API is meant to parallel the way Eigen’s C++ matrix classes work with dynamic and fixed sizes, as well as internal use cases within SymPy and SymEngine.

Examples:

1) Matrix32()  # Zero constructed Matrix32
2) Matrix(sm.Matrix([[1, 2], [3, 4]]))  # Matrix22 with [1, 2, 3, 4] data
3A) Matrix([[1, 2], [3, 4]])  # Matrix22 with [1, 2, 3, 4] data
3B) Matrix22([1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (must matched fixed shape)
3C) Matrix([1, 2, 3, 4])  # Matrix41 with [1, 2, 3, 4] data - column vector assumed
4) Matrix(4, 3)  # Zero constructed Matrix43
5) Matrix(2, 2, [1, 2, 3, 4])  # Matrix22 with [1, 2, 3, 4] data (first two are shape)
6) Matrix(2, 2, lambda row, col: row + col)  # Matrix22 with [0, 1, 1, 2] data
7) Matrix22(1, 2, 3, 4)  # Matrix22 with [1, 2, 3, 4] data (must match fixed length)

References

https://docs.sympy.org/latest/tutorial/matrices.html https://eigen.tuxfamily.org/dox/group__TutorialMatrixClass.html https://en.wikipedia.org/wiki/Vector_space

Matrix does not implement the group or lie group concepts using instance/class methods directly, because we want it to represent the group R^{NxM}, not GL(n), which leads to the identity and inverse methods being confusingly named. For the group ops and lie group ops, use symforce.ops.group_ops.GroupOps and symforce.ops.lie_group_ops.LieGroupOps respectively, which use the implementation in symforce.ops.impl.vector_class_lie_group_ops of the R^{NxM} group under matrix addition. For the identity matrix and inverse matrix, see Matrix.eye() and Matrix.inv() respectively.

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

MatrixT = ~MatrixT#
SHAPE = (-1, -1)#
static __new__(cls, *args, **kwargs)[source]#

Beast of a method for creating a Matrix. Handles a variety of construction use cases and always returns a fixed size child class of Matrix rather than Matrix itself. The available construction options depend on whether cls is a fixed size type or not. See the Matrix docstring for a summary of the construction options.

Parameters:

  • args (Any) –

  • kwargs (Any) –

Return type:

Matrix

property rows: int#
property cols: int#
property shape: Tuple[int, int]#
property is_Matrix: bool#
classmethod storage_dim()[source]#

Dimension of underlying storage

Return type:

int

classmethod from_storage(vec)[source]#

Construct from a flat list representation. Opposite of to_storage().

Parameters:

vec (_T.Union[_T.Sequence[_T.Scalar], Matrix]) –

Return type:

MatrixT

to_storage()[source]#

Flat list representation of the underlying storage, length of storage_dim(). This is used purely for plumbing, it is NOT like a tangent space.

Return type:

List[float]

classmethod tangent_dim()[source]#
Return type:

int

classmethod from_tangent(vec, epsilon=0.0)[source]#
Parameters:

  • vec (_T.Sequence[_T.Scalar]) –

  • epsilon (_T.Scalar) –

Return type:

MatrixT

to_tangent(epsilon=0.0)[source]#
Parameters:

epsilon (float) –

Return type:

List[float]

storage_D_tangent()[source]#
Return type:

Matrix

tangent_D_storage()[source]#
Return type:

Matrix

classmethod zero()[source]#

Matrix of zeros.

Return type:

MatrixT

classmethod zeros(rows, cols)[source]#

Matrix of zeros.

Parameters:

  • rows (int) –

  • cols (int) –

Return type:

MatrixT

classmethod one()[source]#

Matrix of ones.

Return type:

MatrixT

classmethod ones(rows, cols)[source]#

Matrix of ones.

Parameters:

  • rows (int) –

  • cols (int) –

Return type:

MatrixT

classmethod diag(diagonal)[source]#

Construct a square matrix from the diagonal.

Parameters:

diagonal (_T.Sequence[_T.Scalar]) –

Return type:

MatrixT

classmethod eye(rows=None, cols=None)[source]#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

det()[source]#

Determinant of the matrix.

Return type:

float

inv(method='LU')[source]#

Inverse of the matrix.

Parameters:

  • self (MatrixT) –

  • method (str) –

Return type:

MatrixT

classmethod symbolic(name, **kwargs)[source]#

Create with symbols.

Parameters:

  • name (str) – Name prefix of the symbols

  • **kwargs (dict) – Forwarded to sf.Symbol

Return type:

MatrixT

row_join(right)[source]#

Concatenates self with another matrix on the right

Parameters:

right (Matrix) –

Return type:

Matrix

col_join(bottom)[source]#

Concatenates self with another matrix below

Parameters:

bottom (Matrix) –

Return type:

Matrix

classmethod block_matrix(array)[source]#

Constructs a matrix from block elements.

For example:

[[Matrix22(...), Matrix23(...)], [Matrix11(...), Matrix14(...)]]

constructs a Matrix35 with elements equal to given blocks

Parameters:

array (Sequence[Sequence[Matrix]]) –

Return type:

Matrix

simplify(*args, **kwargs)[source]#

Simplify this expression.

This overrides the sympy implementation because that clobbers the class type.

Parameters:

  • args (Any) –

  • kwargs (Any) –

Return type:

Matrix

limit(*args, **kwargs)[source]#

Take the limit at z = z0

This overrides the sympy implementation because that clobbers the class type.

Parameters:

  • args (Any) –

  • kwargs (Any) –

Return type:

Matrix

jacobian(X, tangent_space=True)[source]#

Compute the jacobian with respect to the tangent space of X if tangent_space = True, otherwise returns the jacobian wih respect to the storage elements of X.

Parameters:

  • X (Any) –

  • tangent_space (bool) –

Return type:

Matrix

diff(*args)[source]#

Differentiate w.r.t. a scalar.

Parameters:

args (float) –

Return type:

Matrix

property T: Matrix#

Matrix Transpose

transpose()[source]#

Matrix Transpose

Return type:

Matrix

lower_triangle()[source]#

Returns the lower triangle (including diagonal) of self

self must be square

Parameters:

self (MatrixT) –

Return type:

MatrixT

class Triangle(value)[source]#

Bases: Enum

An enumeration.

LOWER = 'lower'#
UPPER = 'upper'#
symmetric_copy(upper_or_lower)[source]#

Returns a symmetric copy of self by copying the lower or upper triangle to the opposite triangle.

Parameters:

  • upper_or_lower (Triangle) – The triangle to copy to the opposite triangle

  • self (MatrixT) –

Return type:

MatrixT

reshape(rows, cols)[source]#
Parameters:

  • rows (int) –

  • cols (int) –

Return type:

Matrix

dot(other)[source]#

Dot product, also known as inner product.

Only supports mapping 1 x n or n x 1 Matrices to scalars. Note that both matrices must have the same shape.

Parameters:

other (Matrix) –

Return type:

float

cross(other)[source]#

Cross product.

Parameters:

  • self (MatrixT) –

  • other (MatrixT) –

Return type:

Vector3

squared_norm()[source]#

Squared norm of a vector, equivalent to the dot product with itself.

Return type:

float

norm(epsilon=0.0)[source]#

Norm of a vector (square root of magnitude).

Parameters:

epsilon (float) –

Return type:

float

normalized(epsilon=0.0)[source]#

Returns a unit vector in this direction (divide by norm).

Parameters:

  • self (MatrixT) –

  • epsilon (_T.Scalar) –

Return type:

MatrixT

clamp_norm(max_norm, epsilon=0.0)[source]#

Clamp a vector to the given norm in a safe/differentiable way.

Is NOT safe if max_norm can be negative, or if derivatives are needed w.r.t. max_norm and max_norm can be 0 or small enough that max_squared_norm / squared_norm is truncated to 0 in the particular floating point type being used (e.g. all of these are true if max_norm is optimized).

Currently only L2 norm is supported

Parameters:

  • self (MatrixT) –

  • max_norm (_T.Scalar) –

  • epsilon (_T.Scalar) –

Return type:

MatrixT

multiply_elementwise(rhs)[source]#

Do the elementwise multiplication between self and rhs, and return the result as a new Matrix

Parameters:

  • self (MatrixT) –

  • rhs (MatrixT) –

Return type:

MatrixT

applyfunc(func)[source]#

Apply a unary operation to every scalar.

Parameters:

  • self (MatrixT) –

  • func (_T.Callable) –

Return type:

MatrixT

__getitem__(item)[source]#

Get a scalar value or submatrix slice.

Unlike sympy, for 1D matrices the submatrix slice is returned as a 1D matrix instead of as a list.

Parameters:

item (Any) –

Return type:

Any

row(r)[source]#

Extract a row of the matrix

Parameters:

r (int) –

Return type:

Matrix

col(c)[source]#

Extract a column of the matrix

Parameters:

c (int) –

Return type:

Matrix

__neg__()[source]#

Negate matrix.

Parameters:

self (MatrixT) –

Return type:

MatrixT

__add__(right)[source]#

Add a scalar or matrix to this matrix.

Parameters:

  • self (MatrixT) –

  • right (_T.Union[_T.Scalar, MatrixT]) –

Return type:

MatrixT

__sub__(right)[source]#

Subtract a scalar or matrix from this matrix.

Parameters:

  • self (MatrixT) –

  • right (_T.Union[_T.Scalar, MatrixT]) –

Return type:

MatrixT

__mul__(right)[source]#

Multiply a matrix by a scalar or matrix

Parameters:

right (_T.Union[MatrixT, _T.Scalar, Matrix, sf.sympy.MutableDenseMatrix]) –

Return type:

_T.Union[MatrixT, Matrix]

__rmul__(left)[source]#

Left multiply a matrix by a scalar or matrix

Parameters:

left (_T.Union[MatrixT, _T.Scalar, Matrix, sf.sympy.MutableDenseMatrix]) –

Return type:

_T.Union[MatrixT, Matrix]

__div__(right)[source]#

Divide a matrix by a scalar or a matrix (which takes the inverse).

Parameters:

right (_T.Union[MatrixT, _T.Scalar, Matrix, sf.sympy.MutableDenseMatrix]) –

Return type:

_T.Union[MatrixT, Matrix]

compute_AtA(lower_only=False)[source]#

Compute a symmetric product A.transpose() * A

Parameters:

lower_only (bool) – If given, only fill the lower half and set upper to zero

Returns:

(Matrix (N, N)) – Symmetric matrix AtA = self.transpose() * self

Return type:

Matrix

LU()[source]#

LU matrix decomposition

Return type:

Tuple[Matrix, Matrix] | Tuple[Matrix, Matrix, List[Tuple[int, int]]]

LDL()[source]#

LDL matrix decomposition (stable cholesky)

Return type:

Tuple[Matrix, Matrix]

FFLU()[source]#

Fraction-free LU matrix decomposition

Return type:

Tuple[Matrix, Matrix]

FFLDU()[source]#

Fraction-free LDU matrix decomposition

Return type:

Tuple[Matrix, Matrix, Matrix] | Tuple[Matrix, Matrix, Matrix, Matrix]

solve(b, method='LU')[source]#

Solve a linear system using the given method.

Parameters:
Return type:

Matrix

__truediv__(right)#

Divide a matrix by a scalar or a matrix (which takes the inverse).

Parameters:

right (_T.Union[MatrixT, _T.Scalar, Matrix, sf.sympy.MutableDenseMatrix]) –

Return type:

_T.Union[MatrixT, Matrix]

static are_parallel(a, b, tolerance)[source]#

Returns 1 if a and b are parallel within tolerance, and 0 otherwise.

Parameters:
Return type:

float

static skew_symmetric(a)[source]#

Compute a skew-symmetric matrix of given a 3-vector.

Parameters:

a (Matrix31) –

Return type:

Matrix33

evalf()[source]#

Perform numerical evaluation of each element in the matrix.

Return type:

Matrix

to_list()[source]#

Convert to a nested list

Return type:

List[List[float]]

to_flat_list()[source]#

Convert to a flattened list

Return type:

List[float]

classmethod from_flat_list(vec)[source]#
Parameters:

vec (Sequence[float]) –

Return type:

Matrix

to_numpy(scalar_type=<class 'numpy.float64'>)[source]#

Convert to a numpy array.

Parameters:

scalar_type (type) –

Return type:

ndarray

classmethod column_stack(*columns)[source]#

Take a sequence of 1-D vectors and stack them as columns to make a single 2-D Matrix.

Parameters:

columns (Matrix) – 1-D vectors

Return type:

Matrix

is_vector()[source]#
Return type:

bool

static init_printing()[source]#

Initialize SymPy pretty printing

_ipython_display_ is sufficient in Jupyter, but this covers other locations

Return type:

None

class Matrix11(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 1)#
class Matrix21(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 1)#
static unit_x()[source]#

The unit vector [1, 0]

Return type:

Matrix21

static unit_y()[source]#

The unit vector [0, 1]

Return type:

Matrix21

property x: float#

The entry self[0, 0]

property y: float#

The entry self[1, 0]

class Matrix31(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 1)#
static unit_x()[source]#

The unit vector [1, 0, 0]

Return type:

Matrix31

static unit_y()[source]#

The unit vector [0, 1, 0]

Return type:

Matrix31

static unit_z()[source]#

The unit vector [0, 0, 1]

Return type:

Matrix31

property x: float#

The entry self[0, 0]

property y: float#

The entry self[1, 0]

property z: float#

The entry self[2, 0]

class Matrix41(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 1)#
class Matrix51(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 1)#
class Matrix61(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 1)#
class Matrix71(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 1)#
class Matrix81(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 1)#
class Matrix91(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 1)#
class Matrix12(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 2)#
class Matrix22(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 2)#
class Matrix32(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 2)#
class Matrix42(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 2)#
class Matrix52(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 2)#
class Matrix62(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 2)#
class Matrix72(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 2)#
class Matrix82(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 2)#
class Matrix92(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 2)#
class Matrix13(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 3)#
class Matrix23(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 3)#
class Matrix33(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 3)#
class Matrix43(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 3)#
class Matrix53(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 3)#
class Matrix63(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 3)#
class Matrix73(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 3)#
class Matrix83(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 3)#
class Matrix93(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 3)#
class Matrix14(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 4)#
class Matrix24(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 4)#
class Matrix34(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 4)#
class Matrix44(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 4)#
class Matrix54(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 4)#
class Matrix64(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 4)#
class Matrix74(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 4)#
class Matrix84(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 4)#
class Matrix94(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 4)#
class Matrix15(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 5)#
class Matrix25(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 5)#
class Matrix35(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 5)#
class Matrix45(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 5)#
class Matrix55(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 5)#
class Matrix65(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 5)#
class Matrix75(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 5)#
class Matrix85(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 5)#
class Matrix95(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 5)#
class Matrix16(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 6)#
class Matrix26(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 6)#
class Matrix36(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 6)#
class Matrix46(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 6)#
class Matrix56(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 6)#
class Matrix66(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 6)#
class Matrix76(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 6)#
class Matrix86(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 6)#
class Matrix96(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 6)#
class Matrix17(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 7)#
class Matrix27(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 7)#
class Matrix37(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 7)#
class Matrix47(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 7)#
class Matrix57(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 7)#
class Matrix67(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 7)#
class Matrix77(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 7)#
class Matrix87(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 7)#
class Matrix97(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 7)#
class Matrix18(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 8)#
class Matrix28(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 8)#
class Matrix38(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 8)#
class Matrix48(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 8)#
class Matrix58(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 8)#
class Matrix68(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 8)#
class Matrix78(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 8)#
class Matrix88(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 8)#
class Matrix98(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 8)#
class Matrix19(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (1, 9)#
class Matrix29(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (2, 9)#
class Matrix39(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (3, 9)#
class Matrix49(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (4, 9)#
class Matrix59(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (5, 9)#
class Matrix69(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (6, 9)#
class Matrix79(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (7, 9)#
class Matrix89(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (8, 9)#
class Matrix99(*args, **kwargs)[source]#

Bases: Matrix

Parameters:

  • args (_T.Any) –

  • kwargs (_T.Any) –

Return type:

Matrix

SHAPE = (9, 9)#
m#

alias of Matrix99

matrix_type_from_shape(shape)[source]#

Return a fixed size matrix type (like Matrix32) given a shape

Either uses the statically defined ones or dynamically creates a new one if not available.

Parameters:

shape (Tuple[int, int]) –

Return type:

Type[Matrix]

M#

alias of Matrix

Vector1#

alias of Matrix11

Vector2#

alias of Matrix21

Vector3#

alias of Matrix31

Vector4#

alias of Matrix41

Vector5#

alias of Matrix51

Vector6#

alias of Matrix61

Vector7#

alias of Matrix71

Vector8#

alias of Matrix81

Vector9#

alias of Matrix91

V1#

alias of Matrix11

V2#

alias of Matrix21

V3#

alias of Matrix31

V4#

alias of Matrix41

V5#

alias of Matrix51

V6#

alias of Matrix61

V7#

alias of Matrix71

V8#

alias of Matrix81

V9#

alias of Matrix91

M11#

alias of Matrix11

M21#

alias of Matrix21

M31#

alias of Matrix31

M41#

alias of Matrix41

M51#

alias of Matrix51

M61#

alias of Matrix61

M71#

alias of Matrix71

M81#

alias of Matrix81

M91#

alias of Matrix91

M12#

alias of Matrix12

M22#

alias of Matrix22

M32#

alias of Matrix32

M42#

alias of Matrix42

M52#

alias of Matrix52

M62#

alias of Matrix62

M72#

alias of Matrix72

M82#

alias of Matrix82

M92#

alias of Matrix92

M13#

alias of Matrix13

M23#

alias of Matrix23

M33#

alias of Matrix33

M43#

alias of Matrix43

M53#

alias of Matrix53

M63#

alias of Matrix63

M73#

alias of Matrix73

M83#

alias of Matrix83

M93#

alias of Matrix93

M14#

alias of Matrix14

M24#

alias of Matrix24

M34#

alias of Matrix34

M44#

alias of Matrix44

M54#

alias of Matrix54

M64#

alias of Matrix64

M74#

alias of Matrix74

M84#

alias of Matrix84

M94#

alias of Matrix94

M15#

alias of Matrix15

M25#

alias of Matrix25

M35#

alias of Matrix35

M45#

alias of Matrix45

M55#

alias of Matrix55

M65#

alias of Matrix65

M75#

alias of Matrix75

M85#

alias of Matrix85

M95#

alias of Matrix95

M16#

alias of Matrix16

M26#

alias of Matrix26

M36#

alias of Matrix36

M46#

alias of Matrix46

M56#

alias of Matrix56

M66#

alias of Matrix66

M76#

alias of Matrix76

M86#

alias of Matrix86

M96#

alias of Matrix96

M17#

alias of Matrix17

M27#

alias of Matrix27

M37#

alias of Matrix37

M47#

alias of Matrix47

M57#

alias of Matrix57

M67#

alias of Matrix67

M77#

alias of Matrix77

M87#

alias of Matrix87

M97#

alias of Matrix97

M18#

alias of Matrix18

M28#

alias of Matrix28

M38#

alias of Matrix38

M48#

alias of Matrix48

M58#

alias of Matrix58

M68#

alias of Matrix68

M78#

alias of Matrix78

M88#

alias of Matrix88

M98#

alias of Matrix98

M19#

alias of Matrix19

M29#

alias of Matrix29

M39#

alias of Matrix39

M49#

alias of Matrix49

M59#

alias of Matrix59

M69#

alias of Matrix69

M79#

alias of Matrix79

M89#

alias of Matrix89

M99#

alias of Matrix99

I1(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I11(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I2(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I22(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I3(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I33(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I4(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I44(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I5(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I55(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I6(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I66(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I7(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I77(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I8(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I88(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I9(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT

I99(rows=None, cols=None)#

Construct an identity matrix

If neither rows nor cols is provided, this must be called as a class method on a fixed-size class.

If rows is provided, returns a square identity matrix of shape (rows x rows).

If rows and cols are provided, returns a (rows x cols) matrix, with ones on the diagonal.

Parameters:

  • rows (_T.Optional[int]) –

  • cols (_T.Optional[int]) –

Return type:

MatrixT