示例#1
0
 def _eval_expand_basic(self, **hints):
     summand = self.function.expand(**hints)
     if summand.is_Add and summand.is_commutative:
         return Add(*[ self.func(i, *self.limits) for i in summand.args ])
     elif summand.is_Matrix:
         return Matrix._new(summand.rows, summand.cols,
             [self.func(i, *self.limits) for i in summand._mat])
     elif summand != self.function:
         return self.func(summand, *self.limits)
     return self
示例#2
0
 def _eval_expand_basic(self, **hints):
     summand = self.function.expand(**hints)
     if summand.is_Add and summand.is_commutative:
         return Add(*[self.func(i, *self.limits) for i in summand.args])
     elif summand.is_Matrix:
         return Matrix._new(summand.rows, summand.cols,
             [self.func(i, *self.limits) for i in summand._mat])
     elif summand != self.function:
         return self.func(summand, *self.limits)
     return self
示例#3
0
文件: dense.py 项目: gorisaka/sympy
def diag(*values, **kwargs):
    """Create a sparse, diagonal matrix from a list of diagonal values.

    Notes
    =====

    When arguments are matrices they are fitted in resultant matrix.

    The returned matrix is a mutable, dense matrix. To make it a different
    type, send the desired class for keyword ``cls``.

    Examples
    ========

    >>> from sympy.matrices import diag, Matrix, ones
    >>> diag(1, 2, 3)
    Matrix([
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3]])
    >>> diag(*[1, 2, 3])
    Matrix([
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3]])

    The diagonal elements can be matrices; diagonal filling will
    continue on the diagonal from the last element of the matrix:

    >>> from sympy.abc import x, y, z
    >>> a = Matrix([x, y, z])
    >>> b = Matrix([[1, 2], [3, 4]])
    >>> c = Matrix([[5, 6]])
    >>> diag(a, 7, b, c)
    Matrix([
    [x, 0, 0, 0, 0, 0],
    [y, 0, 0, 0, 0, 0],
    [z, 0, 0, 0, 0, 0],
    [0, 7, 0, 0, 0, 0],
    [0, 0, 1, 2, 0, 0],
    [0, 0, 3, 4, 0, 0],
    [0, 0, 0, 0, 5, 6]])

    When diagonal elements are lists, they will be treated as arguments
    to Matrix:

    >>> diag([1, 2, 3], 4)
    Matrix([
    [1, 0],
    [2, 0],
    [3, 0],
    [0, 4]])
    >>> diag([[1, 2, 3]], 4)
    Matrix([
    [1, 2, 3, 0],
    [0, 0, 0, 4]])

    A given band off the diagonal can be made by padding with a
    vertical or horizontal "kerning" vector:

    >>> hpad = ones(0, 2)
    >>> vpad = ones(2, 0)
    >>> diag(vpad, 1, 2, 3, hpad) + diag(hpad, 4, 5, 6, vpad)
    Matrix([
    [0, 0, 4, 0, 0],
    [0, 0, 0, 5, 0],
    [1, 0, 0, 0, 6],
    [0, 2, 0, 0, 0],
    [0, 0, 3, 0, 0]])



    The type is mutable by default but can be made immutable by setting
    the ``mutable`` flag to False:

    >>> type(diag(1))
    <class 'sympy.matrices.dense.MutableDenseMatrix'>
    >>> from sympy.matrices import ImmutableMatrix
    >>> type(diag(1, cls=ImmutableMatrix))
    <class 'sympy.matrices.immutable.ImmutableMatrix'>

    See Also
    ========

    eye
    """
    from .sparse import MutableSparseMatrix

    cls = kwargs.pop('cls', None)
    if cls is None:
        from .dense import Matrix as cls

    if kwargs:
        raise ValueError('unrecognized keyword%s: %s' % (
            's' if len(kwargs) > 1 else '',
            ', '.join(kwargs.keys())))
    rows = 0
    cols = 0
    values = list(values)
    for i in range(len(values)):
        m = values[i]
        if isinstance(m, MatrixBase):
            rows += m.rows
            cols += m.cols
        elif is_sequence(m):
            m = values[i] = Matrix(m)
            rows += m.rows
            cols += m.cols
        else:
            rows += 1
            cols += 1
    res = MutableSparseMatrix.zeros(rows, cols)
    i_row = 0
    i_col = 0
    for m in values:
        if isinstance(m, MatrixBase):
            res[i_row:i_row + m.rows, i_col:i_col + m.cols] = m
            i_row += m.rows
            i_col += m.cols
        else:
            res[i_row, i_col] = m
            i_row += 1
            i_col += 1
    return cls._new(res)
示例#4
0
def diag(*values, **kwargs):
    """Create a sparse, diagonal matrix from a list of diagonal values.

    Notes
    =====

    When arguments are matrices they are fitted in resultant matrix.

    The returned matrix is a mutable, dense matrix. To make it a different
    type, send the desired class for keyword ``cls``.

    Examples
    ========

    >>> from sympy.matrices import diag, Matrix, ones
    >>> diag(1, 2, 3)
    Matrix([
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3]])
    >>> diag(*[1, 2, 3])
    Matrix([
    [1, 0, 0],
    [0, 2, 0],
    [0, 0, 3]])

    The diagonal elements can be matrices; diagonal filling will
    continue on the diagonal from the last element of the matrix:

    >>> from sympy.abc import x, y, z
    >>> a = Matrix([x, y, z])
    >>> b = Matrix([[1, 2], [3, 4]])
    >>> c = Matrix([[5, 6]])
    >>> diag(a, 7, b, c)
    Matrix([
    [x, 0, 0, 0, 0, 0],
    [y, 0, 0, 0, 0, 0],
    [z, 0, 0, 0, 0, 0],
    [0, 7, 0, 0, 0, 0],
    [0, 0, 1, 2, 0, 0],
    [0, 0, 3, 4, 0, 0],
    [0, 0, 0, 0, 5, 6]])

    When diagonal elements are lists, they will be treated as arguments
    to Matrix:

    >>> diag([1, 2, 3], 4)
    Matrix([
    [1, 0],
    [2, 0],
    [3, 0],
    [0, 4]])
    >>> diag([[1, 2, 3]], 4)
    Matrix([
    [1, 2, 3, 0],
    [0, 0, 0, 4]])

    A given band off the diagonal can be made by padding with a
    vertical or horizontal "kerning" vector:

    >>> hpad = ones(0, 2)
    >>> vpad = ones(2, 0)
    >>> diag(vpad, 1, 2, 3, hpad) + diag(hpad, 4, 5, 6, vpad)
    Matrix([
    [0, 0, 4, 0, 0],
    [0, 0, 0, 5, 0],
    [1, 0, 0, 0, 6],
    [0, 2, 0, 0, 0],
    [0, 0, 3, 0, 0]])



    The type is mutable by default but can be made immutable by setting
    the ``mutable`` flag to False:

    >>> type(diag(1))
    <class 'sympy.matrices.dense.MutableDenseMatrix'>
    >>> from sympy.matrices import ImmutableMatrix
    >>> type(diag(1, cls=ImmutableMatrix))
    <class 'sympy.matrices.immutable.ImmutableMatrix'>

    See Also
    ========

    eye
    """
    from .sparse import MutableSparseMatrix

    cls = kwargs.pop('cls', None)
    if cls is None:
        from .dense import Matrix as cls

    if kwargs:
        raise ValueError('unrecognized keyword%s: %s' % (
            's' if len(kwargs) > 1 else '',
            ', '.join(kwargs.keys())))
    rows = 0
    cols = 0
    values = list(values)
    for i in range(len(values)):
        m = values[i]
        if isinstance(m, MatrixBase):
            rows += m.rows
            cols += m.cols
        elif is_sequence(m):
            m = values[i] = Matrix(m)
            rows += m.rows
            cols += m.cols
        else:
            rows += 1
            cols += 1
    res = MutableSparseMatrix.zeros(rows, cols)
    i_row = 0
    i_col = 0
    for m in values:
        if isinstance(m, MatrixBase):
            res[i_row:i_row + m.rows, i_col:i_col + m.cols] = m
            i_row += m.rows
            i_col += m.cols
        else:
            res[i_row, i_col] = m
            i_row += 1
            i_col += 1
    return cls._new(res)