numpy.core.multiarray

Examples

>>> np.bincount(np.arange(5))
array([1, 1, 1, 1, 1])
>>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))
array([1, 3, 1, 1, 0, 0, 0, 1])

>>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])
>>> np.bincount(x).size == np.amax(x)+1
True

The input array needs to be of integer dtype, otherwise a TypeError is raised:

>>> np.bincount(np.arange(5, dtype=float))
Traceback (most recent call last):
  ...
TypeError: Cannot cast array data from dtype('float64') to dtype('int64')
according to the rule 'safe'

A possible use of bincount is to perform sums over variable-size chunks of an array, using the weights keyword.

>>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights
>>> x = np.array([0, 1, 1, 2, 2, 2])
>>> np.bincount(x,  weights=w)
array([ 0.3,  0.7,  1.1])

Examples

>>> # Number of weekdays in January 2011
... np.busday_count('2011-01', '2011-02')
21
>>> # Number of weekdays in 2011
>>> np.busday_count('2011', '2012')
260
>>> # Number of Saturdays in 2011
... np.busday_count('2011', '2012', weekmask='Sat')
53

Examples

>>> # First business day in October 2011 (not accounting for holidays)
... np.busday_offset('2011-10', 0, roll='forward')
numpy.datetime64('2011-10-03')
>>> # Last business day in February 2012 (not accounting for holidays)
... np.busday_offset('2012-03', -1, roll='forward')
numpy.datetime64('2012-02-29')
>>> # Third Wednesday in January 2011
... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')
numpy.datetime64('2011-01-19')
>>> # 2012 Mother's Day in Canada and the U.S.
... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')
numpy.datetime64('2012-05-13')

>>> # First business day on or after a date
... np.busday_offset('2011-03-20', 0, roll='forward')
numpy.datetime64('2011-03-21')
>>> np.busday_offset('2011-03-22', 0, roll='forward')
numpy.datetime64('2011-03-22')
>>> # First business day after a date
... np.busday_offset('2011-03-20', 1, roll='backward')
numpy.datetime64('2011-03-21')
>>> np.busday_offset('2011-03-22', 1, roll='backward')
numpy.datetime64('2011-03-23')

Examples

Basic examples

>>> np.can_cast(np.int32, np.int64)
True
>>> np.can_cast(np.float64, complex)
True
>>> np.can_cast(complex, float)
False

>>> np.can_cast('i8', 'f8')
True
>>> np.can_cast('i8', 'f4')
False
>>> np.can_cast('i4', 'S4')
False

Casting scalars

>>> np.can_cast(100, 'i1')
True
>>> np.can_cast(150, 'i1')
False
>>> np.can_cast(150, 'u1')
True

>>> np.can_cast(3.5e100, np.float32)
False
>>> np.can_cast(1000.0, np.float32)
True

Array scalar checks the value, array does not

>>> np.can_cast(np.array(1000.0), np.float32)
True
>>> np.can_cast(np.array([1000.0]), np.float32)
False

Using the casting rules

>>> np.can_cast('i8', 'i8', 'no')
True
>>> np.can_cast('<i8', '>i8', 'no')
False

>>> np.can_cast('<i8', '>i8', 'equiv')
True
>>> np.can_cast('<i4', '>i8', 'equiv')
False

>>> np.can_cast('<i4', '>i8', 'safe')
True
>>> np.can_cast('<i8', '>i4', 'safe')
False

>>> np.can_cast('<i8', '>i4', 'same_kind')
True
>>> np.can_cast('<i8', '>u4', 'same_kind')
False

>>> np.can_cast('<i8', '>u4', 'unsafe')
True

Examples

>>> a = np.array([[1, 2], [3, 4]])
>>> b = np.array([[5, 6]])
>>> np.concatenate((a, b), axis=0)
array([[1, 2],
       [3, 4],
       [5, 6]])
>>> np.concatenate((a, b.T), axis=1)
array([[1, 2, 5],
       [3, 4, 6]])
>>> np.concatenate((a, b), axis=None)
array([1, 2, 3, 4, 5, 6])

This function will not preserve masking of MaskedArray inputs.

>>> a = np.ma.arange(3)
>>> a[1] = np.ma.masked
>>> b = np.arange(2, 5)
>>> a
masked_array(data=[0, --, 2],
             mask=[False,  True, False],
       fill_value=999999)
>>> b
array([2, 3, 4])
>>> np.concatenate([a, b])
masked_array(data=[0, 1, 2, 2, 3, 4],
             mask=False,
       fill_value=999999)
>>> np.ma.concatenate([a, b])
masked_array(data=[0, --, 2, 2, 3, 4],
             mask=[False,  True, False, False, False, False],
       fill_value=999999)

Examples

>>> A = np.array([4, 5, 6])
>>> B = [1, 2, 3]
>>> np.copyto(A, B)
>>> A
array([1, 2, 3])

>>> A = np.array([[1, 2, 3], [4, 5, 6]])
>>> B = [[4, 5, 6], [7, 8, 9]]
>>> np.copyto(A, B)
>>> A
array([[4, 5, 6],
       [7, 8, 9]])

Examples

>>> import pytz
>>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]')
>>> d
array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30',
       '2002-10-27T07:30'], dtype='datetime64[m]')

Setting the timezone to UTC shows the same information, but with a Z suffix

>>> np.datetime_as_string(d, timezone='UTC')
array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z',
       '2002-10-27T07:30Z'], dtype='<U35')

Note that we picked datetimes that cross a DST boundary. Passing in a pytz timezone object will print the appropriate offset

>>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern'))
array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400',
       '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='<U39')

Passing in a unit will change the precision

>>> np.datetime_as_string(d, unit='h')
array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'],
      dtype='<U32')
>>> np.datetime_as_string(d, unit='s')
array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00',
       '2002-10-27T07:30:00'], dtype='<U38')

'casting' can be used to specify whether precision can be changed

>>> np.datetime_as_string(d, unit='h', casting='safe')
Traceback (most recent call last):
    ...
TypeError: Cannot create a datetime string as units 'h' from a NumPy
datetime with units 'm' according to the rule 'safe'

Examples

>>> np.dot(3, 4)
12

Neither argument is complex-conjugated:

>>> np.dot([2j, 3j], [2j, 3j])
(-13+0j)

For 2-D arrays it is the matrix product:

>>> a = [[1, 0], [0, 1]]
>>> b = [[4, 1], [2, 2]]
>>> np.dot(a, b)
array([[4, 1],
       [2, 2]])

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128

Examples

>>> a = ([1,2,3], [4,5,6])                         # a is array-like
>>> np.empty_like(a)
array([[-1073741821, -1073741821,           3],    # uninitialized
       [          0,           0, -1073741821]])
>>> a = np.array([[1., 2., 3.],[4.,5.,6.]])
>>> np.empty_like(a)
array([[ -2.00000715e+000,   1.48219694e-323,  -2.00000572e+000], # uninitialized
       [  4.38791518e-305,  -2.00000715e+000,   4.17269252e-309]])

Examples

Ordinary inner product for vectors:

>>> a = np.array([1,2,3])
>>> b = np.array([0,1,0])
>>> np.inner(a, b)
2

Some multidimensional examples:

>>> a = np.arange(24).reshape((2,3,4))
>>> b = np.arange(4)
>>> c = np.inner(a, b)
>>> c.shape
(2, 3)
>>> c
array([[ 14,  38,  62],
       [ 86, 110, 134]])

>>> a = np.arange(2).reshape((1,1,2))
>>> b = np.arange(6).reshape((3,2))
>>> c = np.inner(a, b)
>>> c.shape
(1, 1, 3)
>>> c
array([[[1, 3, 5]]])

An example where b is a scalar:

>>> np.inner(np.eye(2), 7)
array([[7., 0.],
       [0., 7.]])

Examples

>>> # The weekdays are Friday, Saturday, and Monday
... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],
...                 holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
array([False, False,  True])

Examples

Sort names: first by surname, then by name.

>>> surnames =    ('Hertz',    'Galilei', 'Hertz')
>>> first_names = ('Heinrich', 'Galileo', 'Gustav')
>>> ind = np.lexsort((first_names, surnames))
>>> ind
array([1, 2, 0])

>>> [surnames[i] + ", " + first_names[i] for i in ind]
['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']

Sort two columns of numbers:

>>> a = [1,5,1,4,3,4,4] # First column
>>> b = [9,4,0,4,0,2,1] # Second column
>>> ind = np.lexsort((b,a)) # Sort by a, then by b
>>> ind
array([2, 0, 4, 6, 5, 3, 1])

>>> [(a[i],b[i]) for i in ind]
[(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]

Note that sorting is first according to the elements of a. Secondary sorting is according to the elements of b.

A normal argsort would have yielded:

>>> [(a[i],b[i]) for i in np.argsort(a)]
[(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)]

Structured arrays are sorted lexically by argsort:

>>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)],
...              dtype=np.dtype([('x', int), ('y', int)]))

>>> np.argsort(x) # or np.argsort(x, order=('x', 'y'))
array([2, 0, 4, 6, 5, 3, 1])

Examples

>>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))
False
>>> x = np.zeros([3, 4])
>>> np.may_share_memory(x[:,0], x[:,1])
True

Examples

>>> np.min_scalar_type(10)
dtype('uint8')

>>> np.min_scalar_type(-260)
dtype('int16')

>>> np.min_scalar_type(3.1)
dtype('float16')

>>> np.min_scalar_type(1e50)
dtype('float64')

>>> np.min_scalar_type(np.arange(4,dtype='f8'))
dtype('float64')

Examples

>>> a = np.array([[[1,0,1],
...                [0,1,0]],
...               [[1,1,0],
...                [0,0,1]]])
>>> b = np.packbits(a, axis=-1)
>>> b
array([[[160],
        [ 64]],
       [[192],
        [ 32]]], dtype=uint8)

Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000, and 32 = 0010 0000.

Examples

>>> x = np.arange(6).reshape(2, 3)
>>> np.putmask(x, x>2, x**2)
>>> x
array([[ 0,  1,  2],
       [ 9, 16, 25]])

If values is smaller than a it is repeated:

>>> x = np.arange(5)
>>> np.putmask(x, x>1, [-33, -44])
>>> x
array([  0,   1, -33, -44, -33])

Examples

>>> arr = np.array([[3,6,6],[4,5,1]])
>>> np.ravel_multi_index(arr, (7,6))
array([22, 41, 37])
>>> np.ravel_multi_index(arr, (7,6), order='F')
array([31, 41, 13])
>>> np.ravel_multi_index(arr, (4,6), mode='clip')
array([22, 23, 19])
>>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))
array([12, 13, 13])

>>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))
1621

Examples

>>> np.result_type(3, np.arange(7, dtype='i1'))
dtype('int8')

>>> np.result_type('i4', 'c8')
dtype('complex128')

>>> np.result_type(3.0, -2)
dtype('float64')

Examples

>>> x = np.array([1, 2, 3, 4])
>>> np.shares_memory(x, np.array([5, 6, 7]))
False
>>> np.shares_memory(x[::2], x)
True
>>> np.shares_memory(x[::2], x[1::2])
False

Checking whether two arrays share memory is NP-complete, and runtime may increase exponentially in the number of dimensions. Hence, max_work should generally be set to a finite number, as it is possible to construct examples that take extremely long to run:

>>> from numpy.lib.stride_tricks import as_strided
>>> x = np.zeros([192163377], dtype=np.int8)
>>> x1 = as_strided(x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049))
>>> x2 = as_strided(x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1))
>>> np.shares_memory(x1, x2, max_work=1000)
Traceback (most recent call last):
...
numpy.TooHardError: Exceeded max_work

Running np.shares_memory(x1, x2) without max_work set takes around 1 minute for this case. It is possible to find problems that take still significantly longer.

Examples

>>> a = np.array([[2], [7], [23]], dtype=np.uint8)
>>> a
array([[ 2],
       [ 7],
       [23]], dtype=uint8)
>>> b = np.unpackbits(a, axis=1)
>>> b
array([[0, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 1, 1, 1],
       [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)
>>> c = np.unpackbits(a, axis=1, count=-3)
>>> c
array([[0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0],
       [0, 0, 0, 1, 0]], dtype=uint8)

>>> p = np.packbits(b, axis=0)
>>> np.unpackbits(p, axis=0)
array([[0, 0, 0, 0, 0, 0, 1, 0],
       [0, 0, 0, 0, 0, 1, 1, 1],
       [0, 0, 0, 1, 0, 1, 1, 1],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)
>>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0]))
True

Examples

>>> np.unravel_index([22, 41, 37], (7,6))
(array([3, 6, 6]), array([4, 5, 1]))
>>> np.unravel_index([31, 41, 13], (7,6), order='F')
(array([3, 6, 6]), array([4, 5, 1]))

>>> np.unravel_index(1621, (6,7,8,9))
(3, 1, 4, 1)

Examples

>>> a = np.array([1+2j,3+4j])
>>> b = np.array([5+6j,7+8j])
>>> np.vdot(a, b)
(70-8j)
>>> np.vdot(b, a)
(70+8j)

Note that higher-dimensional arrays are flattened!

>>> a = np.array([[1, 4], [5, 6]])
>>> b = np.array([[4, 1], [2, 2]])
>>> np.vdot(a, b)
30
>>> np.vdot(b, a)
30
>>> 1*4 + 4*1 + 5*2 + 6*2
30

Examples

>>> a = np.arange(10)
>>> a
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> np.where(a < 5, a, 10*a)
array([ 0,  1,  2,  3,  4, 50, 60, 70, 80, 90])

This can be used on multidimensional arrays too:

>>> np.where([[True, False], [True, True]],
...          [[1, 2], [3, 4]],
...          [[9, 8], [7, 6]])
array([[1, 8],
       [3, 4]])

The shapes of x, y, and the condition are broadcast together:

>>> x, y = np.ogrid[:3, :4]
>>> np.where(x < y, x, 10 + y)  # both x and 10+y are broadcast
array([[10,  0,  0,  0],
       [10, 11,  1,  1],
       [10, 11, 12,  2]])

>>> a = np.array([[0, 1, 2],
...               [0, 2, 4],
...               [0, 3, 6]])
>>> np.where(a < 4, a, -1)  # -1 is broadcast
array([[ 0,  1,  2],
       [ 0,  2, -1],
       [ 0,  3, -1]])