numpy.lib.index

module documentation

(source)

Undocumented

Class	`AxisConcatenator`	Translates slice objects to concatenation along an axis.
Class	`CClass`	Translates slice objects to concatenation along the second axis.
Class	`IndexExpression`	A nicer way to build up index tuples for arrays.
Class	`MGridClass`	`nd_grid` instance which returns a dense multi-dimensional "meshgrid".
Class	`nd_grid`	Construct a multi-dimensional "meshgrid".
Class	`ndenumerate`	Multidimensional index iterator.
Class	`ndindex`	An N-dimensional iterator object to index arrays.
Class	`OGridClass`	`nd_grid` instance which returns an open multi-dimensional "meshgrid".
Class	`RClass`	Translates slice objects to concatenation along the first axis.
Function	`diag_indices`	Return the indices to access the main diagonal of an array.
Function	`diag_indices_from`	Return the indices to access the main diagonal of an n-dimensional array.
Function	`fill_diagonal`	Fill the main diagonal of the given array of any dimensionality.
Function	`ix_`	Construct an open mesh from multiple sequences.
Variable	`array_function_dispatch`	Undocumented
Variable	`c_`	Undocumented
Variable	`index_exp`	Undocumented
Variable	`mgrid`	Undocumented
Variable	`ogrid`	Undocumented
Variable	`r_`	Undocumented
Variable	`s_`	Undocumented
Function	`_diag_indices_from`	Undocumented
Function	`_fill_diagonal_dispatcher`	Undocumented
Function	`_ix__dispatcher`	Undocumented

@set_module('numpy')
def diag_indices(n, ndim=2): (source) ¶

Return the indices to access the main diagonal of an array.

This returns a tuple of indices that can be used to access the main diagonal of an array a with a.ndim >= 2 dimensions and shape (n, n, ..., n). For a.ndim = 2 this is the usual diagonal, for a.ndim > 2 this is the set of indices to access a[i, i, ..., i] for i = [0..n-1].

See Also

diag_indices_from

Notes

New in version 1.4.0.

Examples

Create a set of indices to access the diagonal of a (4, 4) array:

>>> di = np.diag_indices(4)
>>> di
(array([0, 1, 2, 3]), array([0, 1, 2, 3]))
>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])
>>> a[di] = 100
>>> a
array([[100,   1,   2,   3],
       [  4, 100,   6,   7],
       [  8,   9, 100,  11],
       [ 12,  13,  14, 100]])

Now, we create indices to manipulate a 3-D array:

>>> d3 = np.diag_indices(2, 3)
>>> d3
(array([0, 1]), array([0, 1]), array([0, 1]))

And use it to set the diagonal of an array of zeros to 1:

>>> a = np.zeros((2, 2, 2), dtype=int)
>>> a[d3] = 1
>>> a
array([[[1, 0],
        [0, 0]],
       [[0, 0],
        [0, 1]]])

Parameters
n:`int`	The size, along each dimension, of the arrays for which the returned indices can be used.
ndim:`int`, optional	The number of dimensions.

@array_function_dispatch(_diag_indices_from)
def diag_indices_from(arr): (source) ¶

Return the indices to access the main diagonal of an n-dimensional array.

See diag_indices for full details.

See Also

diag_indices

Notes

New in version 1.4.0.

Parameters
arr:`array`, at least 2-D

@array_function_dispatch(_fill_diagonal_dispatcher)
def fill_diagonal(a, val, wrap=False): (source) ¶

Fill the main diagonal of the given array of any dimensionality.

For an array a with a.ndim >= 2, the diagonal is the list of locations with indices a[i, ..., i] all identical. This function modifies the input array in-place, it does not return a value.

See Also

diag_indices, diag_indices_from

Notes

New in version 1.4.0.

This functionality can be obtained via diag_indices, but internally this version uses a much faster implementation that never constructs the indices and uses simple slicing.

Examples

>>> a = np.zeros((3, 3), int)
>>> np.fill_diagonal(a, 5)
>>> a
array([[5, 0, 0],
       [0, 5, 0],
       [0, 0, 5]])

The same function can operate on a 4-D array:

>>> a = np.zeros((3, 3, 3, 3), int)
>>> np.fill_diagonal(a, 4)

We only show a few blocks for clarity:

>>> a[0, 0]
array([[4, 0, 0],
       [0, 0, 0],
       [0, 0, 0]])
>>> a[1, 1]
array([[0, 0, 0],
       [0, 4, 0],
       [0, 0, 0]])
>>> a[2, 2]
array([[0, 0, 0],
       [0, 0, 0],
       [0, 0, 4]])

The wrap option affects only tall matrices:

>>> # tall matrices no wrap
>>> a = np.zeros((5, 3), int)
>>> np.fill_diagonal(a, 4)
>>> a
array([[4, 0, 0],
       [0, 4, 0],
       [0, 0, 4],
       [0, 0, 0],
       [0, 0, 0]])

>>> # tall matrices wrap
>>> a = np.zeros((5, 3), int)
>>> np.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0],
       [0, 4, 0],
       [0, 0, 4],
       [0, 0, 0],
       [4, 0, 0]])

>>> # wide matrices
>>> a = np.zeros((3, 5), int)
>>> np.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0, 0, 0],
       [0, 4, 0, 0, 0],
       [0, 0, 4, 0, 0]])

The anti-diagonal can be filled by reversing the order of elements using either numpy.flipud or numpy.fliplr.

>>> a = np.zeros((3, 3), int);
>>> np.fill_diagonal(np.fliplr(a), [1,2,3])  # Horizontal flip
>>> a
array([[0, 0, 1],
       [0, 2, 0],
       [3, 0, 0]])
>>> np.fill_diagonal(np.flipud(a), [1,2,3])  # Vertical flip
>>> a
array([[0, 0, 3],
       [0, 2, 0],
       [1, 0, 0]])

Note that the order in which the diagonal is filled varies depending on the flip function.

Parameters
a:`array`, at least 2-D.	Array whose diagonal is to be filled, it gets modified in-place.
val:`scalar` or `array_like`	Value(s) to write on the diagonal. If `val` is scalar, the value is written along the diagonal. If array-like, the flattened `val` is written along the diagonal, repeating if necessary to fill all diagonal entries.
wrap:`bool`	For tall matrices in NumPy version up to 1.6.2, the diagonal "wrapped" after N columns. You can have this behavior with this option. This affects only tall matrices.

@array_function_dispatch(_ix__dispatcher)
def ix_(*args): (source) ¶

Construct an open mesh from multiple sequences.

This function takes N 1-D sequences and returns N outputs with N dimensions each, such that the shape is 1 in all but one dimension and the dimension with the non-unit shape value cycles through all N dimensions.

Using ix_ one can quickly construct index arrays that will index the cross product. a[np.ix_([1,3],[2,5])] returns the array [[a[1,2] a[1,5]], [a[3,2] a[3,5]]].

See Also

ogrid, mgrid, meshgrid

Examples

>>> a = np.arange(10).reshape(2, 5)
>>> a
array([[0, 1, 2, 3, 4],
       [5, 6, 7, 8, 9]])
>>> ixgrid = np.ix_([0, 1], [2, 4])
>>> ixgrid
(array([[0],
       [1]]), array([[2, 4]]))
>>> ixgrid[0].shape, ixgrid[1].shape
((2, 1), (1, 2))
>>> a[ixgrid]
array([[2, 4],
       [7, 9]])

>>> ixgrid = np.ix_([True, True], [2, 4])
>>> a[ixgrid]
array([[2, 4],
       [7, 9]])
>>> ixgrid = np.ix_([True, True], [False, False, True, False, True])
>>> a[ixgrid]
array([[2, 4],
       [7, 9]])

Parameters
*args:1-D sequences	Each sequence should be of integer or boolean type. Boolean sequences will be interpreted as boolean masks for the corresponding dimension (equivalent to passing in `np.nonzero(boolean_sequence)`).
Returns
`tuple` of `ndarrays`	out - N arrays with N dimensions each, with N the number of input sequences. Together these arrays form an open mesh.