a
    <bY9                     @   s   d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 ddl
mZ ddlmZmZ dd	lmZ dd
lmZmZmZmZ ddlmZmZ G dd deZG dd deeZeZdS )    )Callable)Dict)sympy_deprecation_warningis_sequence)as_int   )
MatrixBase)MutableRepMatrix	RepMatrix)_iszero)_liupc _row_structure_symbolic_cholesky_cholesky_sparse_LDLdecomposition_sparse)_lower_triangular_solve_sparse_upper_triangular_solve_sparsec                       s  e Zd ZdZe fddZedd Zdd Zdd	 Z	d
d Z
dd Zdd Zdd Zdd Zdd Zd*ddZd+ddZeedddZeedddZdd Zdd  Zd,d"d#Zd-d$d%Zd&d' Zd(d) Zeje_eje_eje_eje_eje_eje_  ZS ).SparseRepMatrixa  
    A sparse matrix (a matrix with a large number of zero elements).

    Examples
    ========

    >>> from sympy import SparseMatrix, ones
    >>> SparseMatrix(2, 2, range(4))
    Matrix([
    [0, 1],
    [2, 3]])
    >>> SparseMatrix(2, 2, {(1, 1): 2})
    Matrix([
    [0, 0],
    [0, 2]])

    A SparseMatrix can be instantiated from a ragged list of lists:

    >>> SparseMatrix([[1, 2, 3], [1, 2], [1]])
    Matrix([
    [1, 2, 3],
    [1, 2, 0],
    [1, 0, 0]])

    For safety, one may include the expected size and then an error
    will be raised if the indices of any element are out of range or
    (for a flat list) if the total number of elements does not match
    the expected shape:

    >>> SparseMatrix(2, 2, [1, 2])
    Traceback (most recent call last):
    ...
    ValueError: List length (2) != rows*columns (4)

    Here, an error is not raised because the list is not flat and no
    element is out of range:

    >>> SparseMatrix(2, 2, [[1, 2]])
    Matrix([
    [1, 2],
    [0, 0]])

    But adding another element to the first (and only) row will cause
    an error to be raised:

    >>> SparseMatrix(2, 2, [[1, 2, 3]])
    Traceback (most recent call last):
    ...
    ValueError: The location (0, 2) is out of designated range: (1, 1)

    To autosize the matrix, pass None for rows:

    >>> SparseMatrix(None, [[1, 2, 3]])
    Matrix([[1, 2, 3]])
    >>> SparseMatrix(None, {(1, 1): 1, (3, 3): 3})
    Matrix([
    [0, 0, 0, 0],
    [0, 1, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 0, 3]])

    Values that are themselves a Matrix are automatically expanded:

    >>> SparseMatrix(4, 4, {(1, 1): ones(2)})
    Matrix([
    [0, 0, 0, 0],
    [0, 1, 1, 0],
    [0, 1, 1, 0],
    [0, 0, 0, 0]])

    A ValueError is raised if the expanding matrix tries to overwrite
    a different element already present:

    >>> SparseMatrix(3, 3, {(0, 0): ones(2), (1, 1): 2})
    Traceback (most recent call last):
    ...
    ValueError: collision at (1, 1)

    See Also
    ========
    DenseMatrix
    MutableSparseMatrix
    ImmutableSparseMatrix
    c              
      s  t |dkrDt|d trD|d j}|d j}|d  ||fS i t |dkrn|d d u rnd d |d g}t |dkr|d d \}}||  u rd u rn n
d  }}n0d ||fv rtdnt|d t|d  }}t|d tr|d }d ||fv rtd	|| fddt
|D } fd	dt
|D }	|D ]:}
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|}| jkrL||
|f< qLqD||fS t|d ttfrxfd
d}|d  D ]\\}}}t|tr |  D ]"\\}
}}|||
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}|||
 || |
|f  q,n |}||| | qnt|d rDtdd |d D  }|s j|d fi |\}}n|d }t ||| krtd	t |||t
|D ]H}
t
|D ]8}||
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|f< qq|d u r }|rrtdd |D d nd}|rtdd |D d nd}nV D ]L\}
}|
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|ks|r||krtd	|
|fd|d d|d q||fS t |dkrt|d ttfr|d }d}t|D ]`\}
}t|ttfsL|g}t|D ](\}}| jkrT ||
|f< qTt|t |}q.|rt |nd}|}||fS t j| \}}}t
|D ]>}
t
|D ].}|||
 |  }| jkr||
|f< q֐q||fS d S )Nr   r         z*Pass rows=None and no cols for autosizing.z2{} and {} must be integers for this specification.c                    s   g | ]}  |qS  _sympify.0iclsr   e/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/matrices/sparse.py
<listcomp>       z;SparseRepMatrix._handle_creation_inputs.<locals>.<listcomp>c                    s   g | ]}  |qS r   r   )r   jr   r   r   r      r    c                    sN   |rJ| |f v r>| | |f kr>t d| |f| | |f | | |f< d S )Nz)There is a collision at {} for {} and {}.)
ValueErrorformat)r   r!   v)smatr   r   update   s    z7SparseRepMatrix._handle_creation_inputs.<locals>.updatec                 s   s   | ]}t |V  qd S Nr   r   r   r   r   	<genexpr>   r    z:SparseRepMatrix._handle_creation_inputs.<locals>.<genexpr>zMThe length of the flat list ({}) does not match the specified size ({} * {}).c                 S   s   g | ]\}}|qS r   r   )r   r_r   r   r   r      r    c                 S   s   g | ]\}}|qS r   r   )r   r*   cr   r   r   r      r    z?The location {} is out of the designated range[{}, {}]x[{}, {}])len
isinstancer	   rowscolstodokr"   r   r   r#   ranger   Zzerodictr   itemslisttuple_handle_creation_inputsr   anykeysmax	enumeratesuper)r   argskwargsr.   r/   r)   r+   opZrow_indicesZcol_indicesr   r!   valuer&   r$   vvr*   ZflatZ	flat_listr8   rowmat	__class__)r   r%   r   r6   k   s    




"




 " 
"
z'SparseRepMatrix._handle_creation_inputsc                 C   s   t dddd |  S )Nz
            The private _smat attribute of SparseMatrix is deprecated. Use the
            .todok() method instead.
            z1.9z$deprecated-private-matrix-attributes)Zdeprecated_since_versionZactive_deprecations_target)r   r0   selfr   r   r   _smat   s    	zSparseRepMatrix._smatc                 K   s(   | j |dd|dt|dddS )NmethodLDL
iszerofunctry_block_diagF)rH   rJ   rK   )invgetr   )rF   r=   r   r   r   _eval_inverse   s    

zSparseRepMatrix._eval_inversec                 C   sT   t |stdi }|   D ] \}}||}|dkr |||< q | | j| j|S )aX  Apply a function to each element of the matrix.

        Examples
        ========

        >>> from sympy import SparseMatrix
        >>> m = SparseMatrix(2, 2, lambda i, j: i*2+j)
        >>> m
        Matrix([
        [0, 1],
        [2, 3]])
        >>> m.applyfunc(lambda i: 2*i)
        Matrix([
        [0, 2],
        [4, 6]])

        z`f` must be callable.r   )callable	TypeErrorr0   r3   _newr.   r/   )rF   fZdokkr$   Zfvr   r   r   	applyfunc   s    
zSparseRepMatrix.applyfuncc                 C   s   ddl m} || S )z,Returns an Immutable version of this Matrix.r   )ImmutableSparseMatrix)Z	immutablerU   )rF   rU   r   r   r   as_immutable  s    zSparseRepMatrix.as_immutablec                 C   s   t | S )aC  Returns a mutable version of this matrix.

        Examples
        ========

        >>> from sympy import ImmutableMatrix
        >>> X = ImmutableMatrix([[1, 2], [3, 4]])
        >>> Y = X.as_mutable()
        >>> Y[1, 1] = 5 # Can set values in Y
        >>> Y
        Matrix([
        [1, 2],
        [3, 5]])
        )MutableSparseMatrixrE   r   r   r   
as_mutable$  s    zSparseRepMatrix.as_mutablec                    s*    fddt t   dd dD S )a  Returns a column-sorted list of non-zero elements of the matrix.

        Examples
        ========

        >>> from sympy import SparseMatrix
        >>> a=SparseMatrix(((1, 2), (3, 4)))
        >>> a
        Matrix([
        [1, 2],
        [3, 4]])
        >>> a.CL
        [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)]

        See Also
        ========

        sympy.matrices.sparse.SparseMatrix.row_list
        c                    s   g | ]}t | | f qS r   r5   r   rS   rE   r   r   r   I  r    z,SparseRepMatrix.col_list.<locals>.<listcomp>c                 S   s   t t| S r'   )r4   reversed)rS   r   r   r   <lambda>I  r    z*SparseRepMatrix.col_list.<locals>.<lambda>key)sortedr4   r0   r8   rE   r   rE   r   col_list5  s    zSparseRepMatrix.col_listc                 C   s   t |  S )z2Returns the number of non-zero elements in Matrix.)r,   r0   rE   r   r   r   nnzK  s    zSparseRepMatrix.nnzc                    s"    fddt    tdD S )a  Returns a row-sorted list of non-zero elements of the matrix.

        Examples
        ========

        >>> from sympy import SparseMatrix
        >>> a = SparseMatrix(((1, 2), (3, 4)))
        >>> a
        Matrix([
        [1, 2],
        [3, 4]])
        >>> a.RL
        [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)]

        See Also
        ========

        sympy.matrices.sparse.SparseMatrix.col_list
        c                    s   g | ]}t | | f qS r   rY   rZ   rE   r   r   r   c  r    z,SparseRepMatrix.row_list.<locals>.<listcomp>r]   )r_   r0   r8   r4   rE   r   rE   r   row_listO  s    
zSparseRepMatrix.row_listc                 C   s   ||  S )z"Scalar element-wise multiplicationr   )rF   Zscalarr   r   r   scalar_multiplyf  s    zSparseRepMatrix.scalar_multiplyrI   c                 C   s   | j }||  j|d| | S )a  Return the least-square fit to the data.

        By default the cholesky_solve routine is used (method='CH'); other
        methods of matrix inversion can be used. To find out which are
        available, see the docstring of the .inv() method.

        Examples
        ========

        >>> from sympy import SparseMatrix, Matrix, ones
        >>> A = Matrix([1, 2, 3])
        >>> B = Matrix([2, 3, 4])
        >>> S = SparseMatrix(A.row_join(B))
        >>> S
        Matrix([
        [1, 2],
        [2, 3],
        [3, 4]])

        If each line of S represent coefficients of Ax + By
        and x and y are [2, 3] then S*xy is:

        >>> r = S*Matrix([2, 3]); r
        Matrix([
        [ 8],
        [13],
        [18]])

        But let's add 1 to the middle value and then solve for the
        least-squares value of xy:

        >>> xy = S.solve_least_squares(Matrix([8, 14, 18])); xy
        Matrix([
        [ 5/3],
        [10/3]])

        The error is given by S*xy - r:

        >>> S*xy - r
        Matrix([
        [1/3],
        [1/3],
        [1/3]])
        >>> _.norm().n(2)
        0.58

        If a different xy is used, the norm will be higher:

        >>> xy += ones(2, 1)/10
        >>> (S*xy - r).norm().n(2)
        1.5

        rH   )TrL   )rF   rhsrH   tr   r   r   solve_least_squaresj  s    6z#SparseRepMatrix.solve_least_squaresc                 C   sH   | j s2| j| jk rtdqD| j| jkrDtdn| j|d|S dS )zReturn solution to self*soln = rhs using given inversion method.

        For a list of possible inversion methods, see the .inv() docstring.
        zUnder-determined system.z]For over-determined system, M, having more rows than columns, try M.solve_least_squares(rhs).rd   N)Z	is_squarer.   r/   r"   rL   multiply)rF   rf   rH   r   r   r   solve  s    

zSparseRepMatrix.solveNzAlternate faster representationc                 C   s   t | S r'   )r   rE   r   r   r   liupc  s    zSparseRepMatrix.liupcc                 C   s   t | S r'   )r   rE   r   r   r   row_structure_symbolic_cholesky  s    z/SparseRepMatrix.row_structure_symbolic_choleskyTc                 C   s   t | |dS N)	hermitian)r   rF   rn   r   r   r   cholesky  s    zSparseRepMatrix.choleskyc                 C   s   t | |dS rm   )r   ro   r   r   r   LDLdecomposition  s    z SparseRepMatrix.LDLdecompositionc                 C   s
   t | |S r'   )r   rF   rf   r   r   r   lower_triangular_solve  s    z&SparseRepMatrix.lower_triangular_solvec                 C   s
   t | |S r'   )r   rr   r   r   r   upper_triangular_solve  s    z&SparseRepMatrix.upper_triangular_solve)rI   )rI   )T)T)__name__
__module____qualname____doc__classmethodr6   propertyrG   rN   rT   rV   rX   r`   ra   rb   rc   rh   rj   ZRLZCLrk   rl   rp   rq   rs   rt   r   r   r   r   __classcell__r   r   rC   r   r      s<   U 
 
9

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r   c                   @   s   e Zd Zedd ZdS )rW   c                 O   s.   | j |i |\}}}| |||}| |S r'   )r6   Z_smat_to_DomainMatrixZ_fromrep)r   r<   r=   r.   r/   r%   repr   r   r   rQ     s    zMutableSparseMatrix._newN)ru   rv   rw   ry   rQ   r   r   r   r   rW     s   rW   N)collections.abcr   Zsympy.core.containersr   Zsympy.utilities.exceptionsr   Zsympy.utilities.iterablesr   Zsympy.utilities.miscr   Zmatricesr	   Z	repmatrixr
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