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:

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:

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(epsilon=0.0)[source]¶

Parameters:: epsilon (float) –
Return type:: Matrix

tangent_D_storage(epsilon=0.0)[source]¶

Parameters:: epsilon (float) –
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:

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:

jacobian(X, tangent_space=True, epsilon=0.0)[source]¶

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

Note that the jacobian is always 2D, even if self or X are matrices - it will be M x N, where M is the size of self and N is the size of X

Parameters:

X (Any) –
tangent_space (bool) –
epsilon (float) –

Return type:

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:

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]

__truediv__(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:

b (Matrix) –
method (str) –

Return type:

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

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

Parameters:

a (Matrix31) –
b (Matrix31) –
tolerance (float) –

Return type:

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:

SHAPE = (1, 1)¶

class Matrix21(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

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:

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:

SHAPE = (4, 1)¶

class Matrix51(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 1)¶

class Matrix61(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 1)¶

class Matrix71(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 1)¶

class Matrix81(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 1)¶

class Matrix91(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 1)¶

class Matrix12(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 2)¶

class Matrix22(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 2)¶

class Matrix32(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 2)¶

class Matrix42(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 2)¶

class Matrix52(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 2)¶

class Matrix62(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 2)¶

class Matrix72(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 2)¶

class Matrix82(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 2)¶

class Matrix92(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 2)¶

class Matrix13(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 3)¶

class Matrix23(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 3)¶

class Matrix33(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 3)¶

class Matrix43(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 3)¶

class Matrix53(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 3)¶

class Matrix63(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 3)¶

class Matrix73(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 3)¶

class Matrix83(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 3)¶

class Matrix93(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 3)¶

class Matrix14(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 4)¶

class Matrix24(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 4)¶

class Matrix34(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 4)¶

class Matrix44(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 4)¶

class Matrix54(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 4)¶

class Matrix64(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 4)¶

class Matrix74(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 4)¶

class Matrix84(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 4)¶

class Matrix94(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 4)¶

class Matrix15(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 5)¶

class Matrix25(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 5)¶

class Matrix35(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 5)¶

class Matrix45(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 5)¶

class Matrix55(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 5)¶

class Matrix65(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 5)¶

class Matrix75(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 5)¶

class Matrix85(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 5)¶

class Matrix95(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 5)¶

class Matrix16(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 6)¶

class Matrix26(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 6)¶

class Matrix36(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 6)¶

class Matrix46(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 6)¶

class Matrix56(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 6)¶

class Matrix66(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 6)¶

class Matrix76(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 6)¶

class Matrix86(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 6)¶

class Matrix96(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 6)¶

class Matrix17(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 7)¶

class Matrix27(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 7)¶

class Matrix37(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 7)¶

class Matrix47(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 7)¶

class Matrix57(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 7)¶

class Matrix67(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 7)¶

class Matrix77(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 7)¶

class Matrix87(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 7)¶

class Matrix97(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 7)¶

class Matrix18(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 8)¶

class Matrix28(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 8)¶

class Matrix38(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 8)¶

class Matrix48(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 8)¶

class Matrix58(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 8)¶

class Matrix68(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 8)¶

class Matrix78(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 8)¶

class Matrix88(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 8)¶

class Matrix98(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (9, 8)¶

class Matrix19(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (1, 9)¶

class Matrix29(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (2, 9)¶

class Matrix39(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (3, 9)¶

class Matrix49(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (4, 9)¶

class Matrix59(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (5, 9)¶

class Matrix69(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (6, 9)¶

class Matrix79(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (7, 9)¶

class Matrix89(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

SHAPE = (8, 9)¶

class Matrix99(*args, **kwargs)[source]¶

Bases: Matrix

Parameters:

args (_T.Any) –
kwargs (_T.Any) –

Return type:

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