numpy.core.fromnumeric

Examples

>>> np.all([[True,False],[True,True]])
False

>>> np.all([[True,False],[True,True]], axis=0)
array([ True, False])

>>> np.all([-1, 4, 5])
True

>>> np.all([1.0, np.nan])
True

>>> np.all([[True, True], [False, True]], where=[[True], [False]])
True

>>> o=np.array(False)
>>> z=np.all([-1, 4, 5], out=o)
>>> id(z), id(o), z
(28293632, 28293632, array(True)) # may vary

Examples

>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amax(a)           # Maximum of the flattened array
3
>>> np.amax(a, axis=0)   # Maxima along the first axis
array([2, 3])
>>> np.amax(a, axis=1)   # Maxima along the second axis
array([1, 3])
>>> np.amax(a, where=[False, True], initial=-1, axis=0)
array([-1,  3])
>>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amax(b)
nan
>>> np.amax(b, where=~np.isnan(b), initial=-1)
4.0
>>> np.nanmax(b)
4.0

You can use an initial value to compute the maximum of an empty slice, or to initialize it to a different value:

>>> np.amax([[-50], [10]], axis=-1, initial=0)
array([ 0, 10])

Notice that the initial value is used as one of the elements for which the maximum is determined, unlike for the default argument Python's max function, which is only used for empty iterables.

>>> np.amax([5], initial=6)
6
>>> max([5], default=6)
5

Examples

>>> a = np.arange(4).reshape((2,2))
>>> a
array([[0, 1],
       [2, 3]])
>>> np.amin(a)           # Minimum of the flattened array
0
>>> np.amin(a, axis=0)   # Minima along the first axis
array([0, 1])
>>> np.amin(a, axis=1)   # Minima along the second axis
array([0, 2])
>>> np.amin(a, where=[False, True], initial=10, axis=0)
array([10,  1])

>>> b = np.arange(5, dtype=float)
>>> b[2] = np.NaN
>>> np.amin(b)
nan
>>> np.amin(b, where=~np.isnan(b), initial=10)
0.0
>>> np.nanmin(b)
0.0

>>> np.amin([[-50], [10]], axis=-1, initial=0)
array([-50,   0])

Notice that the initial value is used as one of the elements for which the minimum is determined, unlike for the default argument Python's max function, which is only used for empty iterables.

Notice that this isn't the same as Python's default argument.

>>> np.amin([6], initial=5)
5
>>> min([6], default=5)
6

Examples

>>> np.any([[True, False], [True, True]])
True

>>> np.any([[True, False], [False, False]], axis=0)
array([ True, False])

>>> np.any([-1, 0, 5])
True

>>> np.any(np.nan)
True

>>> np.any([[True, False], [False, False]], where=[[False], [True]])
False

>>> o=np.array(False)
>>> z=np.any([-1, 4, 5], out=o)
>>> z, o
(array(True), array(True))
>>> # Check now that z is a reference to o
>>> z is o
True
>>> id(z), id(o) # identity of z and o              # doctest: +SKIP
(191614240, 191614240)

Examples

>>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10, 11, 12],
       [13, 14, 15]])
>>> np.argmax(a)
5
>>> np.argmax(a, axis=0)
array([1, 1, 1])
>>> np.argmax(a, axis=1)
array([2, 2])

Indexes of the maximal elements of a N-dimensional array:

>>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)
>>> ind
(1, 2)
>>> a[ind]
15

>>> b = np.arange(6)
>>> b[1] = 5
>>> b
array([0, 5, 2, 3, 4, 5])
>>> np.argmax(b)  # Only the first occurrence is returned.
1

>>> x = np.array([[4,2,3], [1,0,3]])
>>> index_array = np.argmax(x, axis=-1)
>>> # Same as np.amax(x, axis=-1, keepdims=True)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
array([[4],
       [3]])
>>> # Same as np.amax(x, axis=-1)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
array([4, 3])

Setting keepdims to True,

>>> x = np.arange(24).reshape((2, 3, 4))
>>> res = np.argmax(x, axis=1, keepdims=True)
>>> res.shape
(2, 1, 4)

Examples

>>> a = np.arange(6).reshape(2,3) + 10
>>> a
array([[10, 11, 12],
       [13, 14, 15]])
>>> np.argmin(a)
0
>>> np.argmin(a, axis=0)
array([0, 0, 0])
>>> np.argmin(a, axis=1)
array([0, 0])

Indices of the minimum elements of a N-dimensional array:

>>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)
>>> ind
(0, 0)
>>> a[ind]
10

>>> b = np.arange(6) + 10
>>> b[4] = 10
>>> b
array([10, 11, 12, 13, 10, 15])
>>> np.argmin(b)  # Only the first occurrence is returned.
0

>>> x = np.array([[4,2,3], [1,0,3]])
>>> index_array = np.argmin(x, axis=-1)
>>> # Same as np.amin(x, axis=-1, keepdims=True)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)
array([[2],
       [0]])
>>> # Same as np.amax(x, axis=-1)
>>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)
array([2, 0])

Setting keepdims to True,

>>> x = np.arange(24).reshape((2, 3, 4))
>>> res = np.argmin(x, axis=1, keepdims=True)
>>> res.shape
(2, 1, 4)

Examples

One dimensional array:

>>> x = np.array([3, 4, 2, 1])
>>> x[np.argpartition(x, 3)]
array([2, 1, 3, 4])
>>> x[np.argpartition(x, (1, 3))]
array([1, 2, 3, 4])

>>> x = [3, 4, 2, 1]
>>> np.array(x)[np.argpartition(x, 3)]
array([2, 1, 3, 4])

Multi-dimensional array:

>>> x = np.array([[3, 4, 2], [1, 3, 1]])
>>> index_array = np.argpartition(x, kth=1, axis=-1)
>>> np.take_along_axis(x, index_array, axis=-1)  # same as np.partition(x, kth=1)
array([[2, 3, 4],
       [1, 1, 3]])

Examples

One dimensional array:

>>> x = np.array([3, 1, 2])
>>> np.argsort(x)
array([1, 2, 0])

Two-dimensional array:

>>> x = np.array([[0, 3], [2, 2]])
>>> x
array([[0, 3],
       [2, 2]])

>>> ind = np.argsort(x, axis=0)  # sorts along first axis (down)
>>> ind
array([[0, 1],
       [1, 0]])
>>> np.take_along_axis(x, ind, axis=0)  # same as np.sort(x, axis=0)
array([[0, 2],
       [2, 3]])

>>> ind = np.argsort(x, axis=1)  # sorts along last axis (across)
>>> ind
array([[0, 1],
       [0, 1]])
>>> np.take_along_axis(x, ind, axis=1)  # same as np.sort(x, axis=1)
array([[0, 3],
       [2, 2]])

Indices of the sorted elements of a N-dimensional array:

>>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)
>>> ind
(array([0, 1, 1, 0]), array([0, 0, 1, 1]))
>>> x[ind]  # same as np.sort(x, axis=None)
array([0, 2, 2, 3])

Sorting with keys:

>>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])
>>> x
array([(1, 0), (0, 1)],
      dtype=[('x', '<i4'), ('y', '<i4')])

>>> np.argsort(x, order=('x','y'))
array([1, 0])

>>> np.argsort(x, order=('y','x'))
array([0, 1])

Examples

>>> np.around([0.37, 1.64])
array([0., 2.])
>>> np.around([0.37, 1.64], decimals=1)
array([0.4, 1.6])
>>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value
array([0., 2., 2., 4., 4.])
>>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned
array([ 1,  2,  3, 11])
>>> np.around([1,2,3,11], decimals=-1)
array([ 0,  0,  0, 10])

Examples

>>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],
...   [20, 21, 22, 23], [30, 31, 32, 33]]
>>> np.choose([2, 3, 1, 0], choices
... # the first element of the result will be the first element of the
... # third (2+1) "array" in choices, namely, 20; the second element
... # will be the second element of the fourth (3+1) choice array, i.e.,
... # 31, etc.
... )
array([20, 31, 12,  3])
>>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)
array([20, 31, 12,  3])
>>> # because there are 4 choice arrays
>>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)
array([20,  1, 12,  3])
>>> # i.e., 0

A couple examples illustrating how choose broadcasts:

>>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]
>>> choices = [-10, 10]
>>> np.choose(a, choices)
array([[ 10, -10,  10],
       [-10,  10, -10],
       [ 10, -10,  10]])

>>> # With thanks to Anne Archibald
>>> a = np.array([0, 1]).reshape((2,1,1))
>>> c1 = np.array([1, 2, 3]).reshape((1,3,1))
>>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))
>>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2
array([[[ 1,  1,  1,  1,  1],
        [ 2,  2,  2,  2,  2],
        [ 3,  3,  3,  3,  3]],
       [[-1, -2, -3, -4, -5],
        [-1, -2, -3, -4, -5],
        [-1, -2, -3, -4, -5]]])

Examples

>>> a = np.arange(10)
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.clip(a, 1, 8)
array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])
>>> np.clip(a, 8, 1)
array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])
>>> np.clip(a, 3, 6, out=a)
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
>>> a
array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])
>>> a = np.arange(10)
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)
array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])

Examples

>>> a = np.array([[1, 2], [3, 4], [5, 6]])
>>> a
array([[1, 2],
       [3, 4],
       [5, 6]])
>>> np.compress([0, 1], a, axis=0)
array([[3, 4]])
>>> np.compress([False, True, True], a, axis=0)
array([[3, 4],
       [5, 6]])
>>> np.compress([False, True], a, axis=1)
array([[2],
       [4],
       [6]])

Working on the flattened array does not return slices along an axis but selects elements.

>>> np.compress([False, True], a)
array([2])

Examples

>>> a = np.array([1,2,3])
>>> np.cumprod(a) # intermediate results 1, 1*2
...               # total product 1*2*3 = 6
array([1, 2, 6])
>>> a = np.array([[1, 2, 3], [4, 5, 6]])
>>> np.cumprod(a, dtype=float) # specify type of output
array([   1.,    2.,    6.,   24.,  120.,  720.])

The cumulative product for each column (i.e., over the rows) of a:

>>> np.cumprod(a, axis=0)
array([[ 1,  2,  3],
       [ 4, 10, 18]])

The cumulative product for each row (i.e. over the columns) of a:

>>> np.cumprod(a,axis=1)
array([[  1,   2,   6],
       [  4,  20, 120]])

Examples

>>> a = np.array([[1,2,3], [4,5,6]])
>>> a
array([[1, 2, 3],
       [4, 5, 6]])
>>> np.cumsum(a)
array([ 1,  3,  6, 10, 15, 21])
>>> np.cumsum(a, dtype=float)     # specifies type of output value(s)
array([  1.,   3.,   6.,  10.,  15.,  21.])

>>> np.cumsum(a,axis=0)      # sum over rows for each of the 3 columns
array([[1, 2, 3],
       [5, 7, 9]])
>>> np.cumsum(a,axis=1)      # sum over columns for each of the 2 rows
array([[ 1,  3,  6],
       [ 4,  9, 15]])

cumsum(b)[-1] may not be equal to sum(b)

>>> b = np.array([1, 2e-9, 3e-9] * 1000000)
>>> b.cumsum()[-1]
1000000.0050045159
>>> b.sum()
1000000.0050000029

Examples

>>> a = np.arange(4).reshape(2,2)
>>> a
array([[0, 1],
       [2, 3]])
>>> a.diagonal()
array([0, 3])
>>> a.diagonal(1)
array([1])

A 3-D example:

>>> a = np.arange(8).reshape(2,2,2); a
array([[[0, 1],
        [2, 3]],
       [[4, 5],
        [6, 7]]])
>>> a.diagonal(0,  # Main diagonals of two arrays created by skipping
...            0,  # across the outer(left)-most axis last and
...            1)  # the "middle" (row) axis first.
array([[0, 6],
       [1, 7]])

The sub-arrays whose main diagonals we just obtained; note that each corresponds to fixing the right-most (column) axis, and that the diagonals are "packed" in rows.

>>> a[:,:,0]  # main diagonal is [0 6]
array([[0, 2],
       [4, 6]])
>>> a[:,:,1]  # main diagonal is [1 7]
array([[1, 3],
       [5, 7]])

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

>>> a = np.arange(9).reshape(3, 3)
>>> a
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> np.fliplr(a).diagonal()  # Horizontal flip
array([2, 4, 6])
>>> np.flipud(a).diagonal()  # Vertical flip
array([6, 4, 2])

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

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> np.mean(a)
2.5
>>> np.mean(a, axis=0)
array([2., 3.])
>>> np.mean(a, axis=1)
array([1.5, 3.5])

In single precision, mean can be inaccurate:

>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.mean(a)
0.54999924

Computing the mean in float64 is more accurate:

>>> np.mean(a, dtype=np.float64)
0.55000000074505806 # may vary

Specifying a where argument:

>>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]])
>>> np.mean(a)
12.0
>>> np.mean(a, where=[[True], [False], [False]])
9.0

Examples

>>> np.ndim([[1,2,3],[4,5,6]])
2
>>> np.ndim(np.array([[1,2,3],[4,5,6]]))
2
>>> np.ndim(1)
0

Examples

>>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])
>>> x
array([[3, 0, 0],
       [0, 4, 0],
       [5, 6, 0]])
>>> np.nonzero(x)
(array([0, 1, 2, 2]), array([0, 1, 0, 1]))

>>> x[np.nonzero(x)]
array([3, 4, 5, 6])
>>> np.transpose(np.nonzero(x))
array([[0, 0],
       [1, 1],
       [2, 0],
       [2, 1]])

A common use for nonzero is to find the indices of an array, where a condition is True. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the a where the condition is true.

>>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> a > 3
array([[False, False, False],
       [ True,  True,  True],
       [ True,  True,  True]])
>>> np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

Using this result to index a is equivalent to using the mask directly:

>>> a[np.nonzero(a > 3)]
array([4, 5, 6, 7, 8, 9])
>>> a[a > 3]  # prefer this spelling
array([4, 5, 6, 7, 8, 9])

nonzero can also be called as a method of the array.

>>> (a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

Examples

>>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])
>>> p = np.partition(a, 4)
>>> p
array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7])

p[4] is 2; all elements in p[:4] are less than or equal to p[4], and all elements in p[5:] are greater than or equal to p[4]. The partition is:

[0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]

The next example shows the use of multiple values passed to kth.

>>> p2 = np.partition(a, (4, 8))
>>> p2
array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])

p2[4] is 2 and p2[8] is 5. All elements in p2[:4] are less than or equal to p2[4], all elements in p2[5:8] are greater than or equal to p2[4] and less than or equal to p2[8], and all elements in p2[9:] are greater than or equal to p2[8]. The partition is:

[0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]

Examples

By default, calculate the product of all elements:

>>> np.prod([1.,2.])
2.0

Even when the input array is two-dimensional:

>>> a = np.array([[1., 2.], [3., 4.]])
>>> np.prod(a)
24.0

But we can also specify the axis over which to multiply:

>>> np.prod(a, axis=1)
array([  2.,  12.])
>>> np.prod(a, axis=0)
array([3., 8.])

Or select specific elements to include:

>>> np.prod([1., np.nan, 3.], where=[True, False, True])
3.0

If the type of x is unsigned, then the output type is the unsigned platform integer:

>>> x = np.array([1, 2, 3], dtype=np.uint8)
>>> np.prod(x).dtype == np.uint
True

If x is of a signed integer type, then the output type is the default platform integer:

>>> x = np.array([1, 2, 3], dtype=np.int8)
>>> np.prod(x).dtype == int
True

You can also start the product with a value other than one:

>>> np.prod([1, 2], initial=5)
10

Examples

>>> x = np.array([[4, 9, 2, 10],
...               [6, 9, 7, 12]])

>>> np.ptp(x, axis=1)
array([8, 6])

>>> np.ptp(x, axis=0)
array([2, 0, 5, 2])

>>> np.ptp(x)
10

This example shows that a negative value can be returned when the input is an array of signed integers.

>>> y = np.array([[1, 127],
...               [0, 127],
...               [-1, 127],
...               [-2, 127]], dtype=np.int8)
>>> np.ptp(y, axis=1)
array([ 126,  127, -128, -127], dtype=int8)

A work-around is to use the view() method to view the result as unsigned integers with the same bit width:

>>> np.ptp(y, axis=1).view(np.uint8)
array([126, 127, 128, 129], dtype=uint8)

Examples

>>> a = np.arange(5)
>>> np.put(a, [0, 2], [-44, -55])
>>> a
array([-44,   1, -55,   3,   4])

>>> a = np.arange(5)
>>> np.put(a, 22, -5, mode='clip')
>>> a
array([ 0,  1,  2,  3, -5])

Examples

It is equivalent to reshape(-1, order=order).

>>> x = np.array([[1, 2, 3], [4, 5, 6]])
>>> np.ravel(x)
array([1, 2, 3, 4, 5, 6])

>>> x.reshape(-1)
array([1, 2, 3, 4, 5, 6])

>>> np.ravel(x, order='F')
array([1, 4, 2, 5, 3, 6])

When order is 'A', it will preserve the array's 'C' or 'F' ordering:

>>> np.ravel(x.T)
array([1, 4, 2, 5, 3, 6])
>>> np.ravel(x.T, order='A')
array([1, 2, 3, 4, 5, 6])

When order is 'K', it will preserve orderings that are neither 'C' nor 'F', but won't reverse axes:

>>> a = np.arange(3)[::-1]; a
array([2, 1, 0])
>>> a.ravel(order='C')
array([2, 1, 0])
>>> a.ravel(order='K')
array([2, 1, 0])

>>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a
array([[[ 0,  2,  4],
        [ 1,  3,  5]],
       [[ 6,  8, 10],
        [ 7,  9, 11]]])
>>> a.ravel(order='C')
array([ 0,  2,  4,  1,  3,  5,  6,  8, 10,  7,  9, 11])
>>> a.ravel(order='K')
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])

Examples

>>> np.repeat(3, 4)
array([3, 3, 3, 3])
>>> x = np.array([[1,2],[3,4]])
>>> np.repeat(x, 2)
array([1, 1, 2, 2, 3, 3, 4, 4])
>>> np.repeat(x, 3, axis=1)
array([[1, 1, 1, 2, 2, 2],
       [3, 3, 3, 4, 4, 4]])
>>> np.repeat(x, [1, 2], axis=0)
array([[1, 2],
       [3, 4],
       [3, 4]])

Examples

>>> a = np.array([[1,2,3], [4,5,6]])
>>> np.reshape(a, 6)
array([1, 2, 3, 4, 5, 6])
>>> np.reshape(a, 6, order='F')
array([1, 4, 2, 5, 3, 6])

>>> np.reshape(a, (3,-1))       # the unspecified value is inferred to be 2
array([[1, 2],
       [3, 4],
       [5, 6]])

Examples

>>> a=np.array([[0,1],[2,3]])
>>> np.resize(a,(2,3))
array([[0, 1, 2],
       [3, 0, 1]])
>>> np.resize(a,(1,4))
array([[0, 1, 2, 3]])
>>> np.resize(a,(2,4))
array([[0, 1, 2, 3],
       [0, 1, 2, 3]])

Examples

>>> np.searchsorted([1,2,3,4,5], 3)
2
>>> np.searchsorted([1,2,3,4,5], 3, side='right')
3
>>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3])
array([0, 5, 1, 2])

Examples

>>> np.shape(np.eye(3))
(3, 3)
>>> np.shape([[1, 3]])
(1, 2)
>>> np.shape([0])
(1,)
>>> np.shape(0)
()

>>> a = np.array([(1, 2), (3, 4), (5, 6)],
...              dtype=[('x', 'i4'), ('y', 'i4')])
>>> np.shape(a)
(3,)
>>> a.shape
(3,)

Examples

>>> a = np.array([[1,2,3],[4,5,6]])
>>> np.size(a)
6
>>> np.size(a,1)
3
>>> np.size(a,0)
2

Examples

>>> a = np.array([[1,4],[3,1]])
>>> np.sort(a)                # sort along the last axis
array([[1, 4],
       [1, 3]])
>>> np.sort(a, axis=None)     # sort the flattened array
array([1, 1, 3, 4])
>>> np.sort(a, axis=0)        # sort along the first axis
array([[1, 1],
       [3, 4]])

Use the order keyword to specify a field to use when sorting a structured array:

>>> dtype = [('name', 'S10'), ('height', float), ('age', int)]
>>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),
...           ('Galahad', 1.7, 38)]
>>> a = np.array(values, dtype=dtype)       # create a structured array
>>> np.sort(a, order='height')                        # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),
       ('Lancelot', 1.8999999999999999, 38)],
      dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])

Sort by age, then height if ages are equal:

>>> np.sort(a, order=['age', 'height'])               # doctest: +SKIP
array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),
       ('Arthur', 1.8, 41)],
      dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])

Examples

>>> x = np.array([[[0], [1], [2]]])
>>> x.shape
(1, 3, 1)
>>> np.squeeze(x).shape
(3,)
>>> np.squeeze(x, axis=0).shape
(3, 1)
>>> np.squeeze(x, axis=1).shape
Traceback (most recent call last):
...
ValueError: cannot select an axis to squeeze out which has size not equal to one
>>> np.squeeze(x, axis=2).shape
(1, 3)
>>> x = np.array([[1234]])
>>> x.shape
(1, 1)
>>> np.squeeze(x)
array(1234)  # 0d array
>>> np.squeeze(x).shape
()
>>> np.squeeze(x)[()]
1234

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> np.std(a)
1.1180339887498949 # may vary
>>> np.std(a, axis=0)
array([1.,  1.])
>>> np.std(a, axis=1)
array([0.5,  0.5])

In single precision, std() can be inaccurate:

>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.std(a)
0.45000005

Computing the standard deviation in float64 is more accurate:

>>> np.std(a, dtype=np.float64)
0.44999999925494177 # may vary

Specifying a where argument:

>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
>>> np.std(a)
2.614064523559687 # may vary
>>> np.std(a, where=[[True], [True], [False]])
2.0

Examples

>>> np.sum([0.5, 1.5])
2.0
>>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)
1
>>> np.sum([[0, 1], [0, 5]])
6
>>> np.sum([[0, 1], [0, 5]], axis=0)
array([0, 6])
>>> np.sum([[0, 1], [0, 5]], axis=1)
array([1, 5])
>>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1)
array([1., 5.])

If the accumulator is too small, overflow occurs:

>>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)
-128

You can also start the sum with a value other than zero:

>>> np.sum([10], initial=5)
15

Examples

>>> x = np.array([[1,2,3]])
>>> np.swapaxes(x,0,1)
array([[1],
       [2],
       [3]])

>>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])
>>> x
array([[[0, 1],
        [2, 3]],
       [[4, 5],
        [6, 7]]])

>>> np.swapaxes(x,0,2)
array([[[0, 4],
        [2, 6]],
       [[1, 5],
        [3, 7]]])

Examples

>>> a = [4, 3, 5, 7, 6, 8]
>>> indices = [0, 1, 4]
>>> np.take(a, indices)
array([4, 3, 6])

In this example if a is an ndarray, "fancy" indexing can be used.

>>> a = np.array(a)
>>> a[indices]
array([4, 3, 6])

If indices is not one dimensional, the output also has these dimensions.

>>> np.take(a, [[0, 1], [2, 3]])
array([[4, 3],
       [5, 7]])

Examples

>>> np.trace(np.eye(3))
3.0
>>> a = np.arange(8).reshape((2,2,2))
>>> np.trace(a)
array([6, 8])

>>> a = np.arange(24).reshape((2,2,2,3))
>>> np.trace(a).shape
(2, 3)

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> a
array([[1, 2],
       [3, 4]])
>>> np.transpose(a)
array([[1, 3],
       [2, 4]])

>>> a = np.array([1, 2, 3, 4])
>>> a
array([1, 2, 3, 4])
>>> np.transpose(a)
array([1, 2, 3, 4])

>>> a = np.ones((1, 2, 3))
>>> np.transpose(a, (1, 0, 2)).shape
(2, 1, 3)

>>> a = np.ones((2, 3, 4, 5))
>>> np.transpose(a).shape
(5, 4, 3, 2)

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> np.var(a)
1.25
>>> np.var(a, axis=0)
array([1.,  1.])
>>> np.var(a, axis=1)
array([0.25,  0.25])

In single precision, var() can be inaccurate:

>>> a = np.zeros((2, 512*512), dtype=np.float32)
>>> a[0, :] = 1.0
>>> a[1, :] = 0.1
>>> np.var(a)
0.20250003

Computing the variance in float64 is more accurate:

>>> np.var(a, dtype=np.float64)
0.20249999932944759 # may vary
>>> ((1-0.55)**2 + (0.1-0.55)**2)/2
0.2025

Specifying a where argument:

>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
>>> np.var(a)
6.833333333333333 # may vary
>>> np.var(a, where=[[True], [True], [False]])
4.0