m_n_kappa.matrices.Identity#

class m_n_kappa.matrices.Identity(row_column_number, diagonal_value=1.0)#

Bases: Matrix

Identity Matrix

New in version 0.2.0.

Where the diagonal values have a given value and all other values are zero.

Parameters:

row_column_number (int) – number of rows and columns of the matrix
diagonal_value (float) – value along the diagonal (Default: 1.0)

Methods

`add`(matrix)	add this matrix to another matrix
`append`(vector)	Appends the given vector as column-vector to this vector
`column`(number)	give the column with the given number
`column_vector`(column_number)	vector of the given column in the matrix
`diagonal`()	build new matrix inheriting the diagonal from this matrix and put all other places to zero
`entry`(row_number, column_number)	get the of the matrix at the given position
`multiply_by`(multiplicant)	multiplies this matrix with the given multiplicant
`orthonormal_triangular`([algorithm])	Determine orthogonal Matrix \(Q\) and (upper) triangular Matrix \(R\) of this matrix
`replace`(row, column, value)
`row`(number)	give the row with the given number
`row_vector`(row_number)	vector of the given row in the matrix
`subtract`(matrix)	subtracts the given matrix form this matrix
`transpose`()	transposes the matrix and gives a new matrix

Attributes

`column_number`	gives number of columns of the matrix
`matrix`	shows the matrix in `list`-form
`row_number`	gives the number of rows of the matrix

add(matrix)#

add this matrix to another matrix

Parameters:: matrix (Matrix) – the Matrix this matrix is added to
Returns:: new Matrix where each entry is added to the corresponding one in the other matrix
Return type:: Matrix
Raises:: TypeError – if matrix is not of type m_n_kappa.matrices.Matrix

Examples

>>> from m_n_kappa.matrices import Matrix
>>> this_matrix = Matrix([[1, -3, 2], [1, 2, 7]])
>>> other_matrix = Matrix([[0, 3, 5], [2, 1, -1]])
>>> this_matrix.add(other_matrix)
Matrix([[1.0, 0.0, 7.0], [3.0, 3.0, 6.0]])

append(vector)#

Appends the given vector as column-vector to this vector

Parameters:: vector (Vector) – column-vector to append to this matrix
Returns:: this matrix with appended vector as additional column-vector
Return type:: Matrix

column(number)#

give the column with the given number

Parameters:: number (int) – number of the needed column
Returns:: values of the given column in a list from top to bottom
Return type:: list

column_vector(column_number)#

vector of the given column in the matrix

Parameters:: column_number (int) – number of the column
Returns:: vector of the column given by the number
Return type:: Vector

diagonal()#: build new matrix inheriting the diagonal from this matrix and put all other places to zero

entry(row_number, column_number)#

get the of the matrix at the given position

Parameters:

row_number (int) – number of row where the entry is located
column_number (int) – number of the columne where the entry is located

Returns:

value given at the desired position

Return type:

float

Examples

>>> from m_n_kappa.matrices import Matrix
>>> a_matrix = Matrix([[0, 1, 2], [3, 4, 5]])
>>> a_matrix.entry(1, 1)
4.0

multiply_by(multiplicant)#

multiplies this matrix with the given multiplicant

assumes that this matrix is on the left and the multiplicant is on the right of the multiplication-sign

Parameters:: multiplicant (Matrix | Vector | float) – Multiplicant to multiply this matrix with
Returns:: depending on the input the multiplication results in Matrix or a Vector
Return type:: Matrix | Vector
Raises:: ValueError – in case multiplicant is either of type Matrix, nor Matrix nor float

Examples

>>> from m_n_kappa.matrices import Matrix
>>> this_matrix = Matrix([[3, 2, 1], [1, 0, 2]])

Multiply another Matrix:

>>> other_matrix = Matrix([[1, 2], [0, 1], [4, 0]])
>>> this_matrix.multiply_by(other_matrix)
Matrix([[7.0, 8.0], [9.0, 2.0]])

Multiply a vector:

>>> a_vector = Vector([1, 2, 3])
>>> this_matrix.multiply_by(a_vector)
Vector([1.0, 26.0])

Multiply a number (=scalar):

>>> this_matrix.multiply_by(5)
Matrix([[5.0, -15.0, 10.0], [5.0, 10.0, 35.0]])

orthonormal_triangular(algorithm='Givens-rotation')#

Determine orthogonal Matrix \(Q\) and (upper) triangular Matrix \(R\) of this matrix

Parameters:

algorithm (str) –

Algorithm for computation of \(Q\) and \(R\). Currently following algorithms are supported:

'Gram-Schmidt' : Gram-Schmidt
'Modified Gram-Schmidt' : Modified Gram-Schmidt
'Givens-rotation': Givens rotation

Returns:

First entry is the orthogonal matrix of this matrix. Second entry is the (upper) triangluar Matrix of this matrix.

Return type:

tuple[Matrix, Matrix]

row(number)#

give the row with the given number

Parameters:: number (int) – number of the needed row
Returns:: values of the needed row
Return type:: list

row_vector(row_number)#

vector of the given row in the matrix

Parameters:: row_number (int) – number of the row
Returns:: vector of the row given by the number
Return type:: Vector

subtract(matrix)#

subtracts the given matrix form this matrix

Parameters:: matrix (Matrix) – matrix that is subtracted from this one
Returns:: New Matrix where each value of the given matrix is subtracted from this one
Return type:: Matrix

Examples

>>> from m_n_kappa.matrices import Matrix
>>> this_matrix = Matrix([[1, -3, 2], [1, 2, 7]])
>>> other_matrix = Matrix([[0, 3, 5], [2, 1, -1]])
>>> this_matrix.subtract(other_matrix)
Matrix([[1.0, -6.0, -3.0], [-1.0, 1.0, 8.0]])

transpose()#

transposes the matrix and gives a new matrix

Examples

>>> from m_n_kappa.matrices import Matrix
>>> a_matrix = Matrix([[0, 1, 2], [3, 4, 5]])
>>> a_matrix.transpose()
Matrix([[0.0, 3.0], [1.0, 4.0], [2.0, 5.0]])

property column_number: int#: gives number of columns of the matrix

property matrix: list[list]#: shows the matrix in list-form

property row_number: int#: gives the number of rows of the matrix