.. currentmodule:: jax.numpy
.. automodule:: jax.numpy
Implements the NumPy API, using the primitives in :mod:`jax.lax`.
While JAX tries to follow the NumPy API as closely as possible, sometimes JAX cannot follow NumPy exactly.
- Notably, since JAX arrays are immutable, NumPy APIs that mutate arrays
in-place cannot be implemented in JAX. However, often JAX is able to provide
an alternative API that is purely functional. For example, instead of in-place
array updates (
x[i] = y), JAX provides an alternative pure indexed update functionx.at[i].set(y)(see :attr:`ndarray.at`). - Relatedly, some NumPy functions often return views of arrays when possible (examples are :func:`transpose` and :func:`reshape`). JAX versions of such functions will return copies instead, although such are often optimized away by XLA when sequences of operations are compiled using :func:`jax.jit`.
- NumPy is very aggressive at promoting values to
float64type. JAX sometimes is less aggressive about type promotion (See :ref:`type-promotion`). - Some NumPy routines have data-dependent output shapes (examples include
:func:`unique` and :func:`nonzero`). Because the XLA compiler requires array
shapes to be known at compile time, such operations are not compatible with
JIT. For this reason, JAX adds an optional
sizeargument to such functions which may be specified statically in order to use them with JIT.
Nearly all applicable NumPy functions are implemented in the jax.numpy
namespace; they are listed below.
.. autosummary::
:toctree: _autosummary
ndarray.at
abs
absolute
acos
acosh
add
all
allclose
amax
amin
angle
any
append
apply_along_axis
apply_over_axes
arange
arccos
arccosh
arcsin
arcsinh
arctan
arctan2
arctanh
argmax
argmin
argpartition
argsort
argwhere
around
array
array_equal
array_equiv
array_repr
array_split
array_str
asarray
asin
asinh
astype
atan
atanh
atan2
atleast_1d
atleast_2d
atleast_3d
average
bartlett
bincount
bitwise_and
bitwise_count
bitwise_invert
bitwise_left_shift
bitwise_not
bitwise_or
bitwise_right_shift
bitwise_xor
blackman
block
bool_
broadcast_arrays
broadcast_shapes
broadcast_to
c_
can_cast
cbrt
cdouble
ceil
character
choose
clip
column_stack
complex_
complex128
complex64
complexfloating
ComplexWarning
compress
concat
concatenate
conj
conjugate
convolve
copy
copysign
corrcoef
correlate
cos
cosh
count_nonzero
cov
cross
csingle
cumprod
cumsum
cumulative_sum
deg2rad
degrees
delete
diag
diag_indices
diag_indices_from
diagflat
diagonal
diff
digitize
divide
divmod
dot
double
dsplit
dstack
dtype
ediff1d
einsum
einsum_path
empty
empty_like
equal
exp
exp2
expand_dims
expm1
extract
eye
fabs
fill_diagonal
finfo
fix
flatnonzero
flexible
flip
fliplr
flipud
float_
float_power
float16
float32
float64
floating
floor
floor_divide
fmax
fmin
fmod
frexp
frombuffer
fromfile
fromfunction
fromiter
frompyfunc
fromstring
from_dlpack
full
full_like
gcd
generic
geomspace
get_printoptions
gradient
greater
greater_equal
hamming
hanning
heaviside
histogram
histogram_bin_edges
histogram2d
histogramdd
hsplit
hstack
hypot
i0
identity
iinfo
imag
index_exp
indices
inexact
inner
insert
int_
int16
int32
int64
int8
integer
interp
intersect1d
invert
isclose
iscomplex
iscomplexobj
isdtype
isfinite
isin
isinf
isnan
isneginf
isposinf
isreal
isrealobj
isscalar
issubdtype
iterable
ix_
kaiser
kron
lcm
ldexp
left_shift
less
less_equal
lexsort
linspace
load
log
log10
log1p
log2
logaddexp
logaddexp2
logical_and
logical_not
logical_or
logical_xor
logspace
mask_indices
matmul
matrix_transpose
max
maximum
mean
median
meshgrid
mgrid
min
minimum
mod
modf
moveaxis
multiply
nan_to_num
nanargmax
nanargmin
nancumprod
nancumsum
nanmax
nanmean
nanmedian
nanmin
nanpercentile
nanprod
nanquantile
nanstd
nansum
nanvar
ndarray
ndim
negative
nextafter
nonzero
not_equal
number
object_
ogrid
ones
ones_like
outer
packbits
pad
partition
percentile
permute_dims
piecewise
place
poly
polyadd
polyder
polydiv
polyfit
polyint
polymul
polysub
polyval
positive
pow
power
printoptions
prod
promote_types
ptp
put
quantile
r_
rad2deg
radians
ravel
ravel_multi_index
real
reciprocal
remainder
repeat
reshape
resize
result_type
right_shift
rint
roll
rollaxis
roots
rot90
round
round_
s_
save
savez
searchsorted
select
set_printoptions
setdiff1d
setxor1d
shape
sign
signbit
signedinteger
sin
sinc
single
sinh
size
sort
sort_complex
split
sqrt
square
squeeze
stack
std
subtract
sum
swapaxes
take
take_along_axis
tan
tanh
tensordot
tile
trace
trapezoid
transpose
tri
tril
tril_indices
tril_indices_from
trim_zeros
triu
triu_indices
triu_indices_from
true_divide
trunc
ufunc
uint
uint16
uint32
uint64
uint8
union1d
unique
unique_all
unique_counts
unique_inverse
unique_values
unpackbits
unravel_index
unstack
unsignedinteger
unwrap
vander
var
vdot
vecdot
vectorize
vsplit
vstack
where
zeros
zeros_like
.. automodule:: jax.numpy.fft
.. autosummary:: :toctree: _autosummary fft fft2 fftfreq fftn fftshift hfft ifft ifft2 ifftn ifftshift ihfft irfft irfft2 irfftn rfft rfft2 rfftfreq rfftn
.. automodule:: jax.numpy.linalg
.. autosummary:: :toctree: _autosummary cholesky cond cross det diagonal eig eigh eigvals eigvalsh inv lstsq matmul matrix_norm matrix_power matrix_rank matrix_transpose multi_dot norm outer pinv qr slogdet solve svd svdvals tensordot tensorinv tensorsolve trace vector_norm vecdot
The JAX :class:`~jax.Array` (along with its alias, :class:`jax.numpy.ndarray`) is the core array object in JAX: you can think of it as JAX's equivalent of a :class:`numpy.ndarray`. Like :class:`numpy.ndarray`, most users will not need to instantiate :class:`~jax.Array` objects manually, but rather will create them via :mod:`jax.numpy` functions like :func:`~jax.numpy.array`, :func:`~jax.numpy.arange`, :func:`~jax.numpy.linspace`, and others listed above.
JAX :class:`~jax.Array` objects are designed to work seamlessly with Python standard library tools where appropriate.
With the built-in :mod:`copy` module, when :func:`copy.copy` or :func:`copy.deepcopy` encounder an :class:`~jax.Array`, it is equivalent to calling the :meth:`~jax.Array.copy` method, which will create a copy of the buffer on the same device as the original array. This will work correctly within traced/JIT-compiled code, though copy operations may be elided by the compiler in this context.
When the built-in :mod:`pickle` module encounters an :class:`~jax.Array`, it will be serialized via a compact bit representation in a similar manner to pickled :class:`numpy.ndarray` objects. When unpickled, the result will be a new :class:`~jax.Array` object on the default device. This is because in general, pickling and unpickling may take place in different runtime environments, and there is no general way to map the device IDs of one runtime to the device IDs of another. If :mod:`pickle` is used in traced/JIT-compiled code, it will result in a :class:`~jax.errors.ConcretizationTypeError`.