nlcpy.block
- nlcpy.block(arrays)[ソース]
Assembles an nd-array from nested lists of blocks.
Blocks in the innermost lists are concatenated (see
concatenate()
) along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached.Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make
block.ndim
the same for all blocks. This is primarily useful for working with scalars, and means that code likevp.block([v, 1])
is valid, wherev.ndim == 1
.When the nested list is two levels deep, this allows block matrices to be constructed from their components.
- Parameters
- arraysnested list of array_like or scalars (but not tuples)
If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied). Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match.
- Returns
- block_arrayndarray
The array assembled from the given blocks. The dimensionality of the output is equal to the greatest of: - the dimensionality of all the inputs - the depth to which the input list is nested
参考
vsplit
Splits an array into multiple sub-arrays vertically (row-wise).
concatenate
Joins a sequence of arrays along an existing axis.
stack
Joins a sequence of arrays along a new axis.
hstack
Stacks arrays in sequence horizontally (column wise).
vstack
Stacks arrays in sequence vertically (row wise).
注釈
When called with only scalars,
vp.block
is equivalent to an ndarray call. Sovp.block([[1, 2], [3, 4]])
is equivalent tovp.array([[1, 2], [3, 4]])
.This function does not enforce that the blocks lie on a fixed grid.
vp.block([[a, b], [c, d]])
is not restricted to arrays of the form:AAAbb AAAbb cccDD
But is also allowed to produce, for some
a, b, c, d
:AAAbb AAAbb cDDDD
Since concatenation happens along the last axis first, block is not capable of producing the following directly:
AAAbb cccbb cccDD
Matlab's "square bracket stacking",
[A, B, ...; p, q, ...]
, is equivalent tovp.block([[A, B, ...], [p, q, ...]])
.Examples
The most common use of this function is to build a block matrix
>>> import nlcpy as vp >>> A = vp.eye(2) * 2 >>> B = vp.eye(3) * 3 >>> vp.block([ ... [A, vp.zeros((2, 3))], ... [vp.ones((3, 2)), B ] ... ]) array([[2., 0., 0., 0., 0.], [0., 2., 0., 0., 0.], [1., 1., 3., 0., 0.], [1., 1., 0., 3., 0.], [1., 1., 0., 0., 3.]])
With a list of depth 1, block can be used as
hstack()
>>> vp.block([1, 2, 3]) # hstack([1, 2, 3]) array([1, 2, 3])
>>> a = vp.array([1, 2, 3]) >>> b = vp.array([2, 3, 4]) >>> vp.block([a, b, 10]) # hstack([a, b, 10]) array([ 1, 2, 3, 2, 3, 4, 10])
>>> A = vp.ones((2, 2), int) >>> B = 2 * A >>> vp.block([A, B]) # hstack([A, B]) array([[1, 1, 2, 2], [1, 1, 2, 2]])
With a list of depth 2, block can be used in place of
vstack()
:>>> a = vp.array([1, 2, 3]) >>> b = vp.array([2, 3, 4]) >>> vp.block([[a], [b]]) # vstack([a, b]) array([[1, 2, 3], [2, 3, 4]])
>>> A = vp.ones((2, 2), int) >>> B = 2 * A >>> vp.block([[A], [B]]) # vstack([A, B]) array([[1, 1], [1, 1], [2, 2], [2, 2]])
It can also be used in places of
atleast_1d()
andatleast_2d()
>>> a = vp.array(0) >>> b = vp.array([1]) >>> vp.block([a]) # atleast_1d(a) array([0]) >>> vp.block([b]) # atleast_1d(b) array([1])
>>> vp.block([[a]]) # atleast_2d(a) array([[0]]) >>> vp.block([[b]]) # atleast_2d(b) array([[1]])