def __init__(self, shape, dtype):
"""Initialize a new instance.
Parameters
----------
shape : nonnegative int or sequence of nonnegative ints
Number of entries of type ``dtype`` per axis in this space. A
single integer results in a space with rank 1, i.e., 1 axis.
dtype :
Data type of elements in this space. Can be provided
in any way the `numpy.dtype` constructor understands, e.g.
as built-in type or as a string.
For a data type with a ``dtype.shape``, these extra dimensions
are added *to the left* of ``shape``.
"""
# Handle shape and dtype, taking care also of dtypes with shape
try:
shape, shape_in = tuple(safe_int_conv(s) for s in shape), shape
except TypeError:
shape, shape_in = (safe_int_conv(shape), ), shape
if any(s < 0 for s in shape):
raise ValueError('`shape` must have only nonnegative entries, got '
'{}'.format(shape_in))
dtype = np.dtype(dtype)
# We choose this order in contrast to Numpy, since we usually want
# to represent discretizations of vector- or tensor-valued functions,
# i.e., if dtype.shape == (3,) we expect f[0] to have shape `shape`.
self.__shape = dtype.shape + shape
self.__dtype = dtype.base
if is_real_dtype(self.dtype):
# real includes non-floating-point like integers
field = RealNumbers()
self.__real_dtype = self.dtype
self.__real_space = self
self.__complex_dtype = TYPE_MAP_R2C.get(self.dtype, None)
self.__complex_space = None # Set in first call of astype
elif is_complex_floating_dtype(self.dtype):
field = ComplexNumbers()
self.__real_dtype = TYPE_MAP_C2R[self.dtype]
self.__real_space = None # Set in first call of astype
self.__complex_dtype = self.dtype
self.__complex_space = self
else:
field = None
LinearSpace.__init__(self, field)
def insert(self, index, other):
"""Return a copy with ``other`` inserted before ``index``.
The given grid (``m`` dimensions) is inserted into the current
one (``n`` dimensions) before the given index, resulting in a new
`RectGrid` with ``n + m`` dimensions.
Note that no changes are made in-place.
Parameters
----------
index : int
The index of the dimension before which ``other`` is to
be inserted. Negative indices count backwards from
``self.ndim``.
other : `RectGrid`
The grid to be inserted
Returns
-------
newgrid : `RectGrid`
The enlarged grid
Examples
--------
>>> g1 = RectGrid([0, 1], [-1, 0, 2])
>>> g2 = RectGrid([1], [-6, 15])
>>> g1.insert(1, g2)
RectGrid(
[0.0, 1.0],
[1.0],
[-6.0, 15.0],
[-1.0, 0.0, 2.0]
)
See Also
--------
append
"""
if not isinstance(other, RectGrid):
raise TypeError('`other` must be a `RectGrid` instance, got {}'
''.format(other))
idx = safe_int_conv(index)
# Support backward indexing
if idx < 0:
idx = self.ndim + idx
if not 0 <= idx <= self.ndim:
raise IndexError('index {} outside the valid range 0 ... {}'
''.format(idx, self.ndim))
new_vecs = (self.coord_vectors[:idx] + other.coord_vectors +
self.coord_vectors[idx:])
return RectGrid(*new_vecs)
def insert(self, index, other):
"""Return a copy with ``other`` inserted before ``index``.
The given grid (``m`` dimensions) is inserted into the current
one (``n`` dimensions) before the given index, resulting in a new
`RectGrid` with ``n + m`` dimensions.
Note that no changes are made in-place.
Parameters
----------
index : int
The index of the dimension before which ``other`` is to
be inserted. Negative indices count backwards from
``self.ndim``.
other : `RectGrid`
The grid to be inserted
Returns
-------
newgrid : `RectGrid`
The enlarged grid
Examples
--------
>>> g1 = RectGrid([0, 1], [-1, 0, 2])
>>> g2 = RectGrid([1], [-6, 15])
>>> g1.insert(1, g2)
RectGrid(
[0.0, 1.0],
[1.0],
[-6.0, 15.0],
[-1.0, 0.0, 2.0]
)
See Also
--------
append
"""
if not isinstance(other, RectGrid):
raise TypeError('`other` must be a `RectGrid` instance, got {}'
''.format(other))
idx = safe_int_conv(index)
# Support backward indexing
if idx < 0:
idx = self.ndim + idx
if not 0 <= idx <= self.ndim:
raise IndexError('index {} outside the valid range 0 ... {}'
''.format(idx, self.ndim))
new_vecs = (self.coord_vectors[:idx] + other.coord_vectors +
self.coord_vectors[idx:])
return RectGrid(*new_vecs)
def insert(self, index, *grids):
"""Return a copy with ``grids`` inserted before ``index``.
The given grids are inserted (as a block) into ``self``, yielding
a new grid whose number of dimensions is the sum of the numbers of
dimensions of all involved grids.
Note that no changes are made in-place.
Parameters
----------
index : int
The index of the dimension before which ``grids`` are to
be inserted. Negative indices count backwards from
``self.ndim``.
grid1, ..., gridN : `RectGrid`
The grids to be inserted into ``self``.
Returns
-------
newgrid : `RectGrid`
The enlarged grid.
Examples
--------
>>> g1 = RectGrid([0, 1], [-1, 0, 2])
>>> g2 = RectGrid([1], [-6, 15])
>>> g1.insert(1, g2)
RectGrid(
[ 0., 1.],
[ 1.],
[ -6., 15.],
[-1., 0., 2.]
)
>>> g1.insert(1, g2, g2)
RectGrid(
[ 0., 1.],
[ 1.],
[ -6., 15.],
[ 1.],
[ -6., 15.],
[-1., 0., 2.]
)
See Also
--------
append
"""
index, index_in = safe_int_conv(index), index
if not -self.ndim <= index <= self.ndim:
raise IndexError('index {0} outside the valid range -{1} ... {1}'
''.format(index_in, self.ndim))
if index < 0:
index += self.ndim
if len(grids) == 0:
# Copy of `self`
return RectGrid(*self.coord_vectors)
elif len(grids) == 1:
# Insert single grid
grid = grids[0]
if not isinstance(grid, RectGrid):
raise TypeError('{!r} is not a `RectGrid` instance'
''.format(grid))
new_vecs = (self.coord_vectors[:index] + grid.coord_vectors +
self.coord_vectors[index:])
return RectGrid(*new_vecs)
else:
# Recursively insert first grid and the remaining into the result
return self.insert(index, grids[0]).insert(
index + grids[0].ndim, *(grids[1:]))
def insert(self, index, *intvs):
"""Return a copy with ``intvs`` inserted before ``index``.
The given interval products are inserted (as a block) into ``self``,
yielding a new interval product whose number of dimensions is the
sum of the numbers of dimensions of all involved interval products.
Note that no changes are made in-place.
Parameters
----------
index : int
Index of the dimension before which ``other`` is to
be inserted. Must fulfill ``-ndim <= index <= ndim``.
Negative indices count backwards from ``self.ndim``.
intv1, ..., intvN : `IntervalProd`
Interval products to be inserted into ``self``.
Returns
-------
newintvp : `IntervalProd`
The enlarged interval product.
Examples
--------
>>> intv = IntervalProd([-1, 2], [-0.5, 3])
>>> intv2 = IntervalProd(0, 1)
>>> intv.insert(0, intv2)
IntervalProd([0.0, -1.0, 2.0], [1.0, -0.5, 3.0])
>>> intv.insert(-1, intv2)
IntervalProd([-1.0, 0.0, 2.0], [-0.5, 1.0, 3.0])
>>> intv.insert(1, intv2, intv2)
IntervalProd([-1.0, 0.0, 0.0, 2.0], [-0.5, 1.0, 1.0, 3.0])
"""
index, index_in = safe_int_conv(index), index
if not -self.ndim <= index <= self.ndim:
raise IndexError('index {0} outside the valid range -{1} ... {1}'
''.format(index_in, self.ndim))
if index < 0:
index += self.ndim
if len(intvs) > 1:
return self.insert(index, intvs[0]).insert(index + intvs[0].ndim,
*(intvs[1:]))
else:
intv = intvs[0]
if not isinstance(intv, IntervalProd):
raise TypeError('{!r} is not a `IntervalProd` instance'
''.format(intv))
new_min_pt = np.empty(self.ndim + intv.ndim)
new_max_pt = np.empty(self.ndim + intv.ndim)
new_min_pt[:index] = self.min_pt[:index]
new_max_pt[:index] = self.max_pt[:index]
new_min_pt[index:index + intv.ndim] = intv.min_pt
new_max_pt[index:index + intv.ndim] = intv.max_pt
if index < self.ndim: # Avoid IndexError
new_min_pt[index + intv.ndim:] = self.min_pt[index:]
new_max_pt[index + intv.ndim:] = self.max_pt[index:]
return IntervalProd(new_min_pt, new_max_pt)