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Package sympycore :: Package matrices :: Module algebra :: Class MatrixRing

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Class MatrixRing

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Base class to matrix rings that hold matrix element information pairs (<indices>: <element>) stored in Python dictionary.

Represents rectangular matrix.

Nested Classes

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__metaclass__
Metaclass for Basic classes.

ring
Represents an element of a symbolic algebra.

Instance Methods

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__add__(self, other)

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__array__(self)

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__div__(self, other)

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__eq__(self, other)

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__getitem__(self, key)

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__mul__(self, other)

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__neg__(self)

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__setitem__(self, key, value)

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__str__(self)
str(x)

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__sub__(self, other)

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column_indices(self, row=None)

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copy(self)

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crop(self)
Remove elements that are out of dimensions.

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inv(self)
Return inverse of a square matrix.

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inv_l(self)
Return inverse of lower triangular matrix L.

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lu(self)
Perform LU factorization of a m x n matrix A.

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row_indices(self, column=None)

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swap_columns(self, i, j)
Swap i-th and j-th columns inplace.

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swap_rows(self, i, j)
Swap i-th and j-th rows inplace.

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Inherited from basealgebra.ring.CommutativeRing: __pos__, __pow__, __radd__, __rdiv__, __rmul__, __rpow__, __rsub__, __rtruediv__, __truediv__, as_Add_args, as_Factors_args, as_Log_args, as_Mul_args, as_Pow_args, as_Terms_args

Inherited from basealgebra.ring.CommutativeRing (private): _matches

Inherited from basealgebra.algebra.BasicAlgebra: __repr__, as_algebra, as_primitve, as_tree, has, match, matches, subs

Inherited from basealgebra.algebra.BasicAlgebra (private): _subs

Inherited from object: __delattr__, __getattribute__, __hash__, __init__, __reduce__, __reduce_ex__, __setattr__

Class Methods

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Number(cls, obj)
Construct algebra number directly from obj.

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random(cls, interval=(-10, 10)) source code
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Inherited from basealgebra.ring.CommutativeRing: Add, Div, Factors, Log, Mul, Pow, Sub, Terms

Inherited from basealgebra.algebra.BasicAlgebra: Symbol, convert, convert_coefficient, convert_exponent, get_predefined_symbols

Inherited from basealgebra.algebra.BasicAlgebra (private): _matches_seq

Static Methods

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__new__(cls, data={})
Returns: a new object with type S, a subtype of T source code
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Class Variables

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is_square = None

one = MatrixRing('[((), 1)]')

shape = None

zero = MatrixRing('[((), 0)]')

Inherited from basealgebra.ring.CommutativeRing (private): _symbols

Inherited from basealgebra.algebra.BasicAlgebra (private): _str_value

Properties

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T
Return a transposed copy of the matrix.

data

Inherited from basealgebra.algebra.BasicAlgebra: args, func, symbols

Inherited from object: __class__

Method Details

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Number(cls, obj)
Class Method

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Construct algebra number directly from obj.

Overrides: basealgebra.algebra.BasicAlgebra.Number: (inherited documentation)

Returns:

a new object with type S, a subtype of T

Overrides: object.__new__

(inherited documentation)

str(self)
(Informal representation operator)

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str(x)

Overrides: basealgebra.algebra.BasicAlgebra.__str__

sub(self, other)
(Subtraction operator)

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Overrides: basealgebra.ring.CommutativeRing.__sub__

lu(self)

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Perform LU factorization of a m x n matrix A.

Outputs:

P, L, U - LU decomposition matrices of A.

Definitions:

P - m x m permuation matrix
L - m x k lower triangular or trapezoidal matrix with unit-diagonal
U - k x n upper triangular or trapezoidal matrix
k = min(m,n)

A = P * L * U

Property Details

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T

Return a transposed copy of the matrix.

Get Method:: unreachable.T(self) - Return a transposed copy of the matrix.

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Class MatrixRing

Number(cls, obj) Class Method

__add__(self, other) (Addition operator)

__div__(self, other)

__mul__(self, other)

__neg__(self)

__new__(cls, data={}) Static Method

__str__(self) (Informal representation operator)

__sub__(self, other) (Subtraction operator)

lu(self)

T

Number(cls, obj)
Class Method

add(self, other)
(Addition operator)

div(self, other)

mul(self, other)

neg(self)

new(cls, data=`{}`)
Static Method

str(self)
(Informal representation operator)

sub(self, other)
(Subtraction operator)