(self, B, arbitrary_matrix=None)
return A_pinv * B + (eye(A.cols) - A_pinv*A) * arbitrary_matrix
Solve Ax = B using the Moore-Penrose pseudoinverse.

        There may be zero, one, or infinite solutions.  If one solution
        exists, it will be returned.  If infinite solutions exist, one will
        be returned based on the value of arbitrary_matrix.  If no solutions
        exist, the least-squares solution is returned.

        Parameters
        ==========

        B : Matrix
            The right hand side of the equation to be solved for.  Must have
            the same number of rows as matrix A.
        arbitrary_matrix : Matrix
            If the system is underdetermined (e.g. A has more columns than
            rows), infinite solutions are possible, in terms of an arbitrary
            matrix.  This parameter may be set to a specific matrix to use
            for that purpose; if so, it must be the same shape as x, with as
            many rows as matrix A has columns, and as many columns as matrix
            B.  If left as None, an appropriate matrix containing dummy
            symbols in the form of ``wn_m`` will be used, with n and m being
            row and column position of each symbol.

        Returns
        =======

        x : Matrix
            The matrix that will satisfy Ax = B.  Will have as many rows as
            matrix A has columns, and as many columns as matrix B.

        Examples
        ========

        >>> from sympy import Matrix
        >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
        >>> B = Matrix([7, 8])
        >>> A.pinv_solve(B)
        Matrix([
        [ _w0_0/6 - _w1_0/3 + _w2_0/6 - 55/18],
        [-_w0_0/3 + 2*_w1_0/3 - _w2_0/3 + 1/9],
        [ _w0_0/6 - _w1_0/3 + _w2_0/6 + 59/18]])
        >>> A.pinv_solve(B, arbitrary_matrix=Matrix([0, 0, 0]))
        Matrix([
        [-55/18],
        [   1/9],
        [ 59/18]])

        See Also
        ========

        lower_triangular_solve
        upper_triangular_solve
        cholesky_solve
        diagonal_solve
        LDLsolve
        LUsolve
        QRsolve
        pinv

        Notes
        =====

        This may return either exact solutions or least squares solutions.
        To determine which, check ``A * A.pinv() * B == B``.  It will be
        True if exact solutions exist, and False if only a least-squares
        solution exists.  Be aware that the left hand side of that equation
        may need to be simplified to correctly compare to the right hand
        side.

        References
        ==========

        .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#Obtaining_all_solutions_of_a_linear_system
Solve Ax = B using the Moore-Penrose pseudoinverse.
Solve Ax = B using the Moore - Penrose pseudoinverse .
def pinv_solve(self, B, arbitrary_matrix=None):
        """Solve Ax = B using the Moore-Penrose pseudoinverse.

        There may be zero, one, or infinite solutions.  If one solution
        exists, it will be returned.  If infinite solutions exist, one will
        be returned based on the value of arbitrary_matrix.  If no solutions
        exist, the least-squares solution is returned.

        Parameters
        ==========

        B : Matrix
            The right hand side of the equation to be solved for.  Must have
            the same number of rows as matrix A.
        arbitrary_matrix : Matrix
            If the system is underdetermined (e.g. A has more columns than
            rows), infinite solutions are possible, in terms of an arbitrary
            matrix.  This parameter may be set to a specific matrix to use
            for that purpose; if so, it must be the same shape as x, with as
            many rows as matrix A has columns, and as many columns as matrix
            B.  If left as None, an appropriate matrix containing dummy
            symbols in the form of ``wn_m`` will be used, with n and m being
            row and column position of each symbol.

        Returns
        =======

        x : Matrix
            The matrix that will satisfy Ax = B.  Will have as many rows as
            matrix A has columns, and as many columns as matrix B.

        Examples
        ========

        >>> from sympy import Matrix
        >>> A = Matrix([[1, 2, 3], [4, 5, 6]])
        >>> B = Matrix([7, 8])
        >>> A.pinv_solve(B)
        Matrix([
        [ _w0_0/6 - _w1_0/3 + _w2_0/6 - 55/18],
        [-_w0_0/3 + 2*_w1_0/3 - _w2_0/3 + 1/9],
        [ _w0_0/6 - _w1_0/3 + _w2_0/6 + 59/18]])
        >>> A.pinv_solve(B, arbitrary_matrix=Matrix([0, 0, 0]))
        Matrix([
        [-55/18],
        [   1/9],
        [ 59/18]])

        See Also
        ========

        lower_triangular_solve
        upper_triangular_solve
        cholesky_solve
        diagonal_solve
        LDLsolve
        LUsolve
        QRsolve
        pinv

        Notes
        =====

        This may return either exact solutions or least squares solutions.
        To determine which, check ``A * A.pinv() * B == B``.  It will be
        True if exact solutions exist, and False if only a least-squares
        solution exists.  Be aware that the left hand side of that equation
        may need to be simplified to correctly compare to the right hand
        side.

        References
        ==========

        .. [1] https://en.wikipedia.org/wiki/Moore-Penrose_pseudoinverse#Obtaining_all_solutions_of_a_linear_system

        """
        from sympy.matrices import eye
        A = self
        A_pinv = self.pinv()
        if arbitrary_matrix is None:
            rows, cols = A.cols, B.cols
            w = symbols('w:{0}_:{1}'.format(rows, cols), cls=Dummy)
            arbitrary_matrix = self.__class__(cols, rows, w).T
        return A_pinv * B + (eye(A.cols) - A_pinv*A) * arbitrary_matrix
def pinv_solve ( self , B , arbitrary_matrix = None ) : from sympy . matrices import eye A = self A_pinv = self . pinv ( ) if arbitrary_matrix is None : rows , cols = A . cols , B . cols w = symbols ( 'w:{0}_:{1}' . format ( rows , cols ) , cls = Dummy ) arbitrary_matrix = self . __class__ ( cols , rows , w ) . T return A_pinv * B + ( eye ( A . cols ) - A_pinv * A ) * arbitrary_matrix