def unravel_index(x,dims):
"""Convert a flat index into an index tuple for an array of given shape.
e.g. for a 2x2 array, unravel_index(2,(2,2)) returns (1,0).
Example usage:
p = x.argmax()
idx = unravel_index(p,x.shape)
x[idx] == x.max()
Note: x.flat[p] == x.max()
Thus, it may be easier to use flattened indexing than to re-map
the index to a tuple.
"""
if x > _nx.prod(dims)-1 or x < 0:
raise ValueError("Invalid index, must be 0 <= x <= number of elements.")
idx = _nx.empty_like(dims)
# Take dimensions
# [a,b,c,d]
# Reverse and drop first element
# [d,c,b]
# Prepend [1]
# [1,d,c,b]
# Calculate cumulative product
# [1,d,dc,dcb]
# Reverse
# [dcb,dc,d,1]
dim_prod = _nx.cumprod([1] + list(dims)[:0:-1])[::-1]
# Indeces become [x/dcb % a, x/dc % b, x/d % c, x/1 % d]
return tuple(x/dim_prod % dims)
def unravel_index(x,dims):
"""Convert a flat index into an index tuple for an array of given shape.
e.g. for a 2x2 array, unravel_index(2,(2,2)) returns (1,0).
Example usage:
p = x.argmax()
idx = unravel_index(p,x.shape)
x[idx] == x.max()
Note: x.flat[p] == x.max()
Thus, it may be easier to use flattened indexing than to re-map
the index to a tuple.
"""
if x > _nx.prod(dims)-1 or x < 0:
raise ValueError("Invalid index, must be 0 <= x <= number of elements.")
idx = _nx.empty_like(dims)
# Take dimensions
# [a,b,c,d]
# Reverse and drop first element
# [d,c,b]
# Prepend [1]
# [1,d,c,b]
# Calculate cumulative product
# [1,d,dc,dcb]
# Reverse
# [dcb,dc,d,1]
dim_prod = _nx.cumprod([1] + list(dims)[:0:-1])[::-1]
# Indices become [x/dcb % a, x/dc % b, x/d % c, x/1 % d]
return tuple(x/dim_prod % dims)
def unravel_index(x, dims):
"""
Convert a flat index to an index tuple for an array of given shape.
Parameters
----------
x : int
Flattened index.
dims : tuple of ints
Input shape, the shape of an array into which indexing is
required.
Returns
-------
idx : tuple of ints
Tuple of the same shape as `dims`, containing the unraveled index.
Notes
-----
In the Examples section, since ``arr.flat[x] == arr.max()`` it may be
easier to use flattened indexing than to re-map the index to a tuple.
Examples
--------
>>> arr = np.arange(20).reshape(5, 4)
>>> arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
>>> x = arr.argmax()
>>> x
19
>>> dims = arr.shape
>>> idx = np.unravel_index(x, dims)
>>> idx
(4, 3)
>>> arr[idx] == arr.max()
True
"""
if x > _nx.prod(dims) - 1 or x < 0:
raise ValueError("Invalid index, must be 0 <= x <= number of elements.")
idx = _nx.empty_like(dims)
# Take dimensions
# [a,b,c,d]
# Reverse and drop first element
# [d,c,b]
# Prepend [1]
# [1,d,c,b]
# Calculate cumulative product
# [1,d,dc,dcb]
# Reverse
# [dcb,dc,d,1]
dim_prod = _nx.cumprod([1] + list(dims)[:0:-1])[::-1]
# Indices become [x/dcb % a, x/dc % b, x/d % c, x/1 % d]
return tuple(x / dim_prod % dims)
def unravel_index(x, dims):
"""
Convert a flat index into an index tuple for an array of given shape.
Parameters
----------
x : int
Flattened index.
dims : shape tuple
Input shape.
Notes
-----
In the Examples section, since ``arr.flat[x] == arr.max()`` it may be
easier to use flattened indexing than to re-map the index to a tuple.
Examples
--------
>>> arr = np.ones((5,4))
>>> arr
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
>>> x = arr.argmax()
>>> x
19
>>> dims = arr.shape
>>> idx = np.unravel_index(x, dims)
>>> idx
(4, 3)
>>> arr[idx] == arr.max()
True
"""
if x > _nx.prod(dims) - 1 or x < 0:
raise ValueError(
"Invalid index, must be 0 <= x <= number of elements.")
idx = _nx.empty_like(dims)
# Take dimensions
# [a,b,c,d]
# Reverse and drop first element
# [d,c,b]
# Prepend [1]
# [1,d,c,b]
# Calculate cumulative product
# [1,d,dc,dcb]
# Reverse
# [dcb,dc,d,1]
dim_prod = _nx.cumprod([1] + list(dims)[:0:-1])[::-1]
# Indices become [x/dcb % a, x/dc % b, x/d % c, x/1 % d]
return tuple(x / dim_prod % dims)
def fill_diagonal(a, val, wrap=False):
"""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.
Parameters
----------
a : array, at least 2-D.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
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.
See also
--------
diag_indices, diag_indices_from
Notes
-----
.. versionadded:: 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)
>>> 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)
>>> 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)
>>> fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0, 0, 0],
[0, 4, 0, 0, 0],
[0, 0, 4, 0, 0]])
"""
if a.ndim < 2:
raise ValueError("array must be at least 2-d")
end = None
if a.ndim == 2:
# Explicit, fast formula for the common case. For 2-d arrays, we
# accept rectangular ones.
step = a.shape[1] + 1
#This is needed to don't have tall matrix have the diagonal wrap.
if not wrap:
end = a.shape[1] * a.shape[1]
else:
# For more than d=2, the strided formula is only valid for arrays with
# all dimensions equal, so we check first.
if not alltrue(diff(a.shape) == 0):
raise ValueError("All dimensions of input must be of equal length")
step = 1 + (cumprod(a.shape[:-1])).sum()
# Write the value out into the diagonal.
a.flat[:end:step] = val
def fill_diagonal(a, val, wrap=False):
"""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, ..., i]`` all identical. This function
modifies the input array in-place, it does not return a value.
Parameters
----------
a : array, at least 2-D.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
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 affect only tall matrices.
See also
--------
diag_indices, diag_indices_from
Notes
-----
.. versionadded:: 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]])
# tall matrices no wrap
>>> a = np.zeros((5, 3),int)
>>> fill_diagonal(a, 4)
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)
>>> fill_diagonal(a, 4)
array([[4, 0, 0],
[0, 4, 0],
[0, 0, 4],
[0, 0, 0],
[4, 0, 0]])
# wide matrices
>>> a = np.zeros((3, 5),int)
>>> fill_diagonal(a, 4)
array([[4, 0, 0, 0, 0],
[0, 4, 0, 0, 0],
[0, 0, 4, 0, 0]])
"""
if a.ndim < 2:
raise ValueError("array must be at least 2-d")
end = None
if a.ndim == 2:
# Explicit, fast formula for the common case. For 2-d arrays, we
# accept rectangular ones.
step = a.shape[1] + 1
# This is needed to don't have tall matrix have the diagonal wrap.
if not wrap:
end = a.shape[1] * a.shape[1]
else:
# For more than d=2, the strided formula is only valid for arrays with
# all dimensions equal, so we check first.
if not alltrue(diff(a.shape) == 0):
raise ValueError("All dimensions of input must be of equal length")
step = 1 + (cumprod(a.shape[:-1])).sum()
# Write the value out into the diagonal.
a.flat[:end:step] = val
def fill_diagonal(a, val):
"""Fill the main diagonal of the given array of any dimensionality.
For an array with ndim > 2, the diagonal is the list of locations with
indices a[i,i,...,i], all identical.
This function modifies the input array in-place, it does not return a
value.
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.
Parameters
----------
a : array, at least 2-dimensional.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
See also
--------
diag_indices, diag_indices_from
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
>>> a = zeros((3,3),int)
>>> 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 = zeros((3,3,3,3),int)
>>> 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]])
"""
if a.ndim < 2:
raise ValueError("array must be at least 2-d")
if a.ndim == 2:
# Explicit, fast formula for the common case. For 2-d arrays, we
# accept rectangular ones.
step = a.shape[1] + 1
else:
# For more than d=2, the strided formula is only valid for arrays with
# all dimensions equal, so we check first.
if not alltrue(diff(a.shape) == 0):
raise ValueError("All dimensions of input must be of equal length")
step = 1 + (cumprod(a.shape[:-1])).sum()
# Write the value out into the diagonal.
a.flat[::step] = val
def fill_diagonal(a, val):
"""Fill the main diagonal of the given array of any dimensionality.
For an array with ndim > 2, the diagonal is the list of locations with
indices a[i,i,...,i], all identical.
This function modifies the input array in-place, it does not return a
value.
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.
Parameters
----------
a : array, at least 2-dimensional.
Array whose diagonal is to be filled, it gets modified in-place.
val : scalar
Value to be written on the diagonal, its type must be compatible with
that of the array a.
See also
--------
diag_indices, diag_indices_from
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
>>> a = zeros((3,3),int)
>>> 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 = zeros((3,3,3,3),int)
>>> 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]])
"""
if a.ndim < 2:
raise ValueError("array must be at least 2-d")
if a.ndim == 2:
# Explicit, fast formula for the common case. For 2-d arrays, we
# accept rectangular ones.
step = a.shape[1] + 1
else:
# For more than d=2, the strided formula is only valid for arrays with
# all dimensions equal, so we check first.
if not alltrue(diff(a.shape) == 0):
raise ValueError("All dimensions of input must be of equal length")
step = 1 + (cumprod(a.shape[:-1])).sum()
# Write the value out into the diagonal.
a.flat[::step] = val