jax.numpy package

Implements the NumPy API, using the primitives in 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 a alternative API that is purely functional. For example, instead of in-place array updates (x[i] = y), JAX provides an alternative pure indexed update function jax.ops.index_update().

• NumPy is very aggressive at promoting values to float64 type. JAX sometimes is less aggressive about type promotion.

A small number of NumPy operations that have data-dependent output shapes are incompatible with jax.jit() compilation. The XLA compiler requires that shapes of arrays be known at compile time. While it would be possible to provide a JAX implementation of an API such as numpy.nonzero(), we would be unable to JIT-compile it because the shape of its output depends on the contents of the input data.

Not every function in NumPy is implemented; contributions are welcome!

abs(x)	Calculate the absolute value element-wise.
absolute(x)	Calculate the absolute value element-wise.
add(x1, x2)	Add arguments element-wise.
all(a[, axis, out, keepdims])	Test whether all array elements along a given axis evaluate to True.
allclose(a, b[, rtol, atol, equal_nan])	Returns True if two arrays are element-wise equal within a tolerance.
alltrue(a[, axis, out, keepdims])	Test whether all array elements along a given axis evaluate to True.
amax(a[, axis, out, keepdims, initial, where])	Return the maximum of an array or maximum along an axis.
amin(a[, axis, out, keepdims, initial, where])	Return the minimum of an array or minimum along an axis.
angle(z)	Return the angle of the complex argument.
any(a[, axis, out, keepdims])	Test whether any array element along a given axis evaluates to True.
append(arr, values[, axis])	Append values to the end of an array.
apply_along_axis(func1d, axis, arr, *args, …)	Apply a function to 1-D slices along the given axis.
apply_over_axes(func, a, axes)	Apply a function repeatedly over multiple axes.
arange(start[, stop, step, dtype])	Return evenly spaced values within a given interval.
arccos(x)	Trigonometric inverse cosine, element-wise.
arccosh(x)	Inverse hyperbolic cosine, element-wise.
arcsin(x)	Inverse sine, element-wise.
arcsinh(x)	Inverse hyperbolic sine element-wise.
arctan(x)	Trigonometric inverse tangent, element-wise.
arctan2(x1, x2)	Element-wise arc tangent of x1/x2 choosing the quadrant correctly.
arctanh(x)	Inverse hyperbolic tangent element-wise.
argmax(a[, axis, out])	Returns the indices of the maximum values along an axis.
argmin(a[, axis, out])	Returns the indices of the minimum values along an axis.
argsort(a[, axis, kind, order])	Returns the indices that would sort an array.
argwhere(a)	Find the indices of array elements that are non-zero, grouped by element.
around(a[, decimals, out])	Round an array to the given number of decimals.
array(object[, dtype, copy, order, ndmin])	Create an array.
array_equal(a1, a2[, equal_nan])	True if two arrays have the same shape and elements, False otherwise.
array_equiv(a1, a2)	Returns True if input arrays are shape consistent and all elements equal.
array_repr(arr[, max_line_width, precision, …])	Return the string representation of an array.
array_split(ary, indices_or_sections[, axis])	Split an array into multiple sub-arrays.
array_str(a[, max_line_width, precision, …])	Return a string representation of the data in an array.
asarray(a[, dtype, order])	Convert the input to an array.
atleast_1d(*arys)	Convert inputs to arrays with at least one dimension.
atleast_2d(*arys)	View inputs as arrays with at least two dimensions.
atleast_3d(*arys)	View inputs as arrays with at least three dimensions.
average(a[, axis, weights, returned])	Compute the weighted average along the specified axis.
bartlett(*args, **kwargs)	Return the Bartlett window.
bincount(x[, weights, minlength, length])	Count number of occurrences of each value in array of non-negative ints.
bitwise_and(x1, x2)	Compute the bit-wise AND of two arrays element-wise.
bitwise_not(x)	Compute bit-wise inversion, or bit-wise NOT, element-wise.
bitwise_or(x1, x2)	Compute the bit-wise OR of two arrays element-wise.
bitwise_xor(x1, x2)	Compute the bit-wise XOR of two arrays element-wise.
blackman(*args, **kwargs)	Return the Blackman window.
block(arrays)	Assemble an nd-array from nested lists of blocks.
bool_
broadcast_arrays(*args)	Like Numpy’s broadcast_arrays but doesn’t return views.
broadcast_to(arr, shape)	Broadcast an array to a new shape.
can_cast(from_, to[, casting])	Returns True if cast between data types can occur according to the casting rule.
cbrt(x)	Return the cube-root of an array, element-wise.
cdouble	alias of jax._src.numpy.lax_numpy.complex128
ceil(x)	Return the ceiling of the input, element-wise.
character	Abstract base class of all character string scalar types.
choose(a, choices[, out, mode])	Construct an array from an index array and a set of arrays to choose from.
clip(a[, a_min, a_max, out])	Clip (limit) the values in an array.
column_stack(tup)	Stack 1-D arrays as columns into a 2-D array.
complex_	alias of jax._src.numpy.lax_numpy.complex128
complex128
complex64
complexfloating	Abstract base class of all complex number scalar types that are made up of floating-point numbers.
ComplexWarning	The warning raised when casting a complex dtype to a real dtype.
compress(condition, a[, axis, out])	Return selected slices of an array along given axis.
concatenate(arrays[, axis])	Join a sequence of arrays along an existing axis.
conj(x)	Return the complex conjugate, element-wise.
conjugate(x)	Return the complex conjugate, element-wise.
convolve(a, v[, mode, precision])	Returns the discrete, linear convolution of two one-dimensional sequences.
copysign(x1, x2)	Change the sign of x1 to that of x2, element-wise.
corrcoef(x[, y, rowvar])	Return Pearson product-moment correlation coefficients.
correlate(a, v[, mode, precision])	Cross-correlation of two 1-dimensional sequences.
cos(x)	Cosine element-wise.
cosh(x)	Hyperbolic cosine, element-wise.
count_nonzero(a[, axis, keepdims])	Counts the number of non-zero values in the array a.
cov(m[, y, rowvar, bias, ddof, fweights, …])	Estimate a covariance matrix, given data and weights.
cross(a, b[, axisa, axisb, axisc, axis])	Return the cross product of two (arrays of) vectors.
csingle	alias of jax._src.numpy.lax_numpy.complex64
cumprod(a[, axis, dtype, out])	Return the cumulative product of elements along a given axis.
cumproduct(a[, axis, dtype, out])	Return the cumulative product of elements along a given axis.
cumsum(a[, axis, dtype, out])	Return the cumulative sum of the elements along a given axis.
deg2rad(x)	Convert angles from degrees to radians.
degrees(x)	Convert angles from radians to degrees.
diag(v[, k])	Extract a diagonal or construct a diagonal array.
diagflat(v[, k])	Create a two-dimensional array with the flattened input as a diagonal.
diag_indices(n[, ndim])	Return the indices to access the main diagonal of an array.
diag_indices_from(arr)	Return the indices to access the main diagonal of an n-dimensional array.
diagonal(a[, offset, axis1, axis2])	Return specified diagonals.
diff(a[, n, axis, prepend, append])	Calculate the n-th discrete difference along the given axis.
digitize(x, bins[, right])	Return the indices of the bins to which each value in input array belongs.
divide(x1, x2)	Returns a true division of the inputs, element-wise.
divmod(x1, x2)	Return element-wise quotient and remainder simultaneously.
dot(a, b, *[, precision])	Dot product of two arrays.
double	alias of jax._src.numpy.lax_numpy.float64
dsplit(ary, indices_or_sections)	Split array into multiple sub-arrays along the 3rd axis (depth).
dstack(tup)	Stack arrays in sequence depth wise (along third axis).
dtype(obj[, align, copy])	Create a data type object.
ediff1d(ary[, to_end, to_begin])	The differences between consecutive elements of an array.
einsum(*operands[, out, optimize, precision])	Evaluates the Einstein summation convention on the operands.
einsum_path(subscripts, *operands[, optimize])	Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays.
empty(shape[, dtype])	Return a new array of given shape and type, filled with zeros.
empty_like(a[, dtype, shape])	Return an array of zeros with the same shape and type as a given array.
equal(x1, x2)	Return (x1 == x2) element-wise.
exp(x)	Calculate the exponential of all elements in the input array.
exp2(x)	Calculate 2**p for all p in the input array.
expand_dims(a, axis)	Expand the shape of an array.
expm1(x)	Calculate exp(x) - 1 for all elements in the array.
extract(condition, arr)	Return the elements of an array that satisfy some condition.
eye(N[, M, k, dtype])	Return a 2-D array with ones on the diagonal and zeros elsewhere.
fabs(x)	Compute the absolute values element-wise.
finfo(dtype)	Machine limits for floating point types.
fix(x[, out])	Round to nearest integer towards zero.
flatnonzero(a)	Return indices that are non-zero in the flattened version of a.
flexible	Abstract base class of all scalar types without predefined length.
flip(m[, axis])	Reverse the order of elements in an array along the given axis.
fliplr(m)	Flip array in the left/right direction.
flipud(m)	Flip array in the up/down direction.
float_	alias of jax._src.numpy.lax_numpy.float64
float16
float32
float64
floating	Abstract base class of all floating-point scalar types.
float_power(x1, x2)	First array elements raised to powers from second array, element-wise.
floor(x)	Return the floor of the input, element-wise.
floor_divide(x1, x2)	Return the largest integer smaller or equal to the division of the inputs.
fmax(x1, x2)	Element-wise maximum of array elements.
fmin(x1, x2)	Element-wise minimum of array elements.
fmod(x1, x2)	Return the element-wise remainder of division.
frexp(x)	Decompose the elements of x into mantissa and twos exponent.
full(shape, fill_value[, dtype])	Return a new array of given shape and type, filled with fill_value.
full_like(a, fill_value[, dtype, shape])	Return a full array with the same shape and type as a given array.
gcd(x1, x2)	Returns the greatest common divisor of |x1| and |x2|
geomspace(start, stop[, num, endpoint, …])	Return numbers spaced evenly on a log scale (a geometric progression).
gradient(f, *varargs[, axis, edge_order])	Return the gradient of an N-dimensional array.
greater(x1, x2)	Return the truth value of (x1 > x2) element-wise.
greater_equal(x1, x2)	Return the truth value of (x1 >= x2) element-wise.
hamming(*args, **kwargs)	Return the Hamming window.
hanning(*args, **kwargs)	Return the Hanning window.
heaviside(x1, x2)	Compute the Heaviside step function.
histogram(a[, bins, range, weights, density])	Compute the histogram of a set of data.
histogram_bin_edges(a[, bins, range, weights])	Function to calculate only the edges of the bins used by the histogram function.
histogram2d(x, y[, bins, range, weights, …])	Compute the bi-dimensional histogram of two data samples.
histogramdd(sample[, bins, range, weights, …])	Compute the multidimensional histogram of some data.
hsplit(ary, indices_or_sections)	Split an array into multiple sub-arrays horizontally (column-wise).
hstack(tup)	Stack arrays in sequence horizontally (column wise).
hypot(x1, x2)	Given the “legs” of a right triangle, return its hypotenuse.
i0(x)	Modified Bessel function of the first kind, order 0.
identity(n[, dtype])	Return the identity array.
iinfo(type)	Machine limits for integer types.
imag(val)	Return the imaginary part of the complex argument.
in1d(ar1, ar2[, assume_unique, invert])	Test whether each element of a 1-D array is also present in a second array.
indices(dimensions[, dtype, sparse])	Return an array representing the indices of a grid.
inexact	Abstract base class of all numeric scalar types with a (potentially) inexact representation of the values in its range, such as floating-point numbers.
inner(a, b, *[, precision])	Inner product of two arrays.
int_	alias of jax._src.numpy.lax_numpy.int64
int16
int32
int64
int8
integer	Abstract base class of all integer scalar types.
interp(x, xp, fp[, left, right, period])	One-dimensional linear interpolation.
intersect1d(ar1, ar2[, assume_unique, …])	Find the intersection of two arrays.
invert(x)	Compute bit-wise inversion, or bit-wise NOT, element-wise.
isclose(a, b[, rtol, atol, equal_nan])	Returns a boolean array where two arrays are element-wise equal within a tolerance.
iscomplex(x)	Returns a bool array, where True if input element is complex.
iscomplexobj(x)	Check for a complex type or an array of complex numbers.
isfinite(x)	Test element-wise for finiteness (not infinity or not Not a Number).
isin(element, test_elements[, …])	Calculates element in test_elements, broadcasting over element only.
isinf(x)	Test element-wise for positive or negative infinity.
isnan(x)	Test element-wise for NaN and return result as a boolean array.
isneginf(x[, out])	Test element-wise for negative infinity, return result as bool array.
isposinf(x[, out])	Test element-wise for positive infinity, return result as bool array.
isreal(x)	Returns a bool array, where True if input element is real.
isrealobj(x)	Return True if x is a not complex type or an array of complex numbers.
isscalar(element)	Returns True if the type of element is a scalar type.
issubdtype(arg1, arg2)	Returns True if first argument is a typecode lower/equal in type hierarchy.
issubsctype(arg1, arg2)	Determine if the first argument is a subclass of the second argument.
iterable(y)	Check whether or not an object can be iterated over.
ix_(*args)	Construct an open mesh from multiple sequences.
kaiser(*args, **kwargs)	Return the Kaiser window.
kron(a, b)	Kronecker product of two arrays.
lcm(x1, x2)	Returns the lowest common multiple of |x1| and |x2|
ldexp(x1, x2)	Returns x1 * 2**x2, element-wise.
left_shift(x1, x2)	Shift the bits of an integer to the left.
less(x1, x2)	Return the truth value of (x1 < x2) element-wise.
less_equal(x1, x2)	Return the truth value of (x1 =< x2) element-wise.
lexsort(keys[, axis])	Perform an indirect stable sort using a sequence of keys.
linspace(start, stop[, num, endpoint, …])	Return evenly spaced numbers over a specified interval.
load(file[, mmap_mode, allow_pickle, …])	Load arrays or pickled objects from .npy, .npz or pickled files.
log(x)	Natural logarithm, element-wise.
log10(x)	Return the base 10 logarithm of the input array, element-wise.
log1p(x)	Return the natural logarithm of one plus the input array, element-wise.
log2(x)	Base-2 logarithm of x.
logaddexp	Logarithm of the sum of exponentiations of the inputs.
logaddexp2	Logarithm of the sum of exponentiations of the inputs in base-2.
logical_and(*args)	Compute the truth value of x1 AND x2 element-wise.
logical_not(*args)	Compute the truth value of NOT x element-wise.
logical_or(*args)	Compute the truth value of x1 OR x2 element-wise.
logical_xor(*args)	Compute the truth value of x1 XOR x2, element-wise.
logspace(start, stop[, num, endpoint, base, …])	Return numbers spaced evenly on a log scale.
mask_indices(*args, **kwargs)	Return the indices to access (n, n) arrays, given a masking function.
matmul(a, b, *[, precision])	Matrix product of two arrays.
max(a[, axis, out, keepdims, initial, where])	Return the maximum of an array or maximum along an axis.
maximum(x1, x2)	Element-wise maximum of array elements.
mean(a[, axis, dtype, out, keepdims])	Compute the arithmetic mean along the specified axis.
median(a[, axis, out, overwrite_input, keepdims])	Compute the median along the specified axis.
meshgrid(*args, **kwargs)	Return coordinate matrices from coordinate vectors.
min(a[, axis, out, keepdims, initial, where])	Return the minimum of an array or minimum along an axis.
minimum(x1, x2)	Element-wise minimum of array elements.
mod(x1, x2)	Return element-wise remainder of division.
modf(x[, out])	Return the fractional and integral parts of an array, element-wise.
moveaxis(a, source, destination)	Move axes of an array to new positions.
msort(a)	Return a copy of an array sorted along the first axis.
multiply(x1, x2)	Multiply arguments element-wise.
nanargmax(a[, axis])	Return the indices of the maximum values in the specified axis ignoring NaNs.
nanargmin(a[, axis])	Return the indices of the minimum values in the specified axis ignoring NaNs.
nancumprod(a[, axis, dtype, out])	Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one.
nancumsum(a[, axis, dtype, out])	Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
nanmax(a[, axis, out, keepdims])	Return the maximum of an array or maximum along an axis, ignoring any NaNs.
nanmean(a[, axis, dtype, out, keepdims])	Compute the arithmetic mean along the specified axis, ignoring NaNs.
nanmedian(a[, axis, out, overwrite_input, …])	Compute the median along the specified axis, while ignoring NaNs.
nanmin(a[, axis, out, keepdims])	Return minimum of an array or minimum along an axis, ignoring any NaNs.
nanpercentile(a, q[, axis, out, …])	Compute the qth percentile of the data along the specified axis, while ignoring nan values.
nanprod(a[, axis, dtype, out, keepdims])	Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones.
nanquantile(a, q[, axis, out, …])	Compute the qth quantile of the data along the specified axis, while ignoring nan values.
nanstd(a[, axis, dtype, out, ddof, keepdims])	Compute the standard deviation along the specified axis, while ignoring NaNs.
nansum(a[, axis, dtype, out, keepdims])	Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
nan_to_num(x[, copy, nan, posinf, neginf])	Replace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the nan, posinf and/or neginf keywords.
nanvar(a[, axis, dtype, out, ddof, keepdims])	Compute the variance along the specified axis, while ignoring NaNs.
ndarray([dtype, buffer, offset, strides, order])
ndim(a)	Return the number of dimensions of an array.
negative(x)	Numerical negative, element-wise.
nextafter(x1, x2)	Return the next floating-point value after x1 towards x2, element-wise.
nonzero(a)	Return the indices of the elements that are non-zero.
not_equal(x1, x2)	Return (x1 != x2) element-wise.
number	Abstract base class of all numeric scalar types.
object_	Any Python object.
ones(shape[, dtype])	Return a new array of given shape and type, filled with ones.
ones_like(a[, dtype, shape])	Return an array of ones with the same shape and type as a given array.
outer(a, b[, out])	Compute the outer product of two vectors.
packbits(a[, axis, bitorder])	Packs the elements of a binary-valued array into bits in a uint8 array.
pad(array, pad_width[, mode])	Pad an array.
percentile(a, q[, axis, out, …])	Compute the q-th percentile of the data along the specified axis.
piecewise(x, condlist, funclist, *args, **kw)	Evaluate a piecewise-defined function.
polyadd(a1, a2)	Find the sum of two polynomials.
polyder(p[, m])	Return the derivative of the specified order of a polynomial.
polymul(a1, a2, *[, trim_leading_zeros])	Find the product of two polynomials.
polysub(a1, a2)	Difference (subtraction) of two polynomials.
polyval(p, x)	Evaluate a polynomial at specific values.
positive(x)	Numerical positive, element-wise.
power(x1, x2)	First array elements raised to powers from second array, element-wise.
prod(a[, axis, dtype, out, keepdims, …])	Return the product of array elements over a given axis.
product(a[, axis, dtype, out, keepdims, …])	Return the product of array elements over a given axis.
promote_types(a, b)	Returns the type to which a binary operation should cast its arguments.
ptp(a[, axis, out, keepdims])	Range of values (maximum - minimum) along an axis.
quantile(a, q[, axis, out, overwrite_input, …])	Compute the q-th quantile of the data along the specified axis.
rad2deg(x)	Convert angles from radians to degrees.
radians(x)	Convert angles from degrees to radians.
ravel(a[, order])	Return a contiguous flattened array.
ravel_multi_index(multi_index, dims[, mode, …])	Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index.
real(val)	Return the real part of the complex argument.
reciprocal(x)	Return the reciprocal of the argument, element-wise.
remainder(x1, x2)	Return element-wise remainder of division.
repeat(a, repeats[, axis, total_repeat_length])	Repeat elements of an array.
reshape(a, newshape[, order])	Gives a new shape to an array without changing its data.
result_type(*args)	Returns the type that results from applying the NumPy type promotion rules to the arguments.
right_shift(x1, x2)	Shift the bits of an integer to the right.
rint(x)	Round elements of the array to the nearest integer.
roll(a, shift[, axis])	Roll array elements along a given axis.
rollaxis(a, axis[, start])	Roll the specified axis backwards, until it lies in a given position.
roots(p, *[, strip_zeros])	Return the roots of a polynomial with coefficients given in p.
rot90(m[, k, axes])	Rotate an array by 90 degrees in the plane specified by axes.
round(a[, decimals, out])	Round an array to the given number of decimals.
row_stack(tup)	Stack arrays in sequence vertically (row wise).
save(file, arr[, allow_pickle, fix_imports])	Save an array to a binary file in NumPy .npy format.
savez(file, *args, **kwds)	Save several arrays into a single file in uncompressed .npz format.
searchsorted(a, v[, side, sorter])	Find indices where elements should be inserted to maintain order.
select(condlist, choicelist[, default])	Return an array drawn from elements in choicelist, depending on conditions.
set_printoptions([precision, threshold, …])	Set printing options.
setdiff1d(ar1, ar2[, assume_unique])	Find the set difference of two arrays.
shape(a)	Return the shape of an array.
sign(x)	Returns an element-wise indication of the sign of a number.
signbit(x)	Returns element-wise True where signbit is set (less than zero).
signedinteger	Abstract base class of all signed integer scalar types.
sin(x)	Trigonometric sine, element-wise.
sinc(x)	Return the sinc function.
single	alias of jax._src.numpy.lax_numpy.float32
sinh(x)	Hyperbolic sine, element-wise.
size(a[, axis])	Return the number of elements along a given axis.
sometrue(a[, axis, out, keepdims])	Test whether any array element along a given axis evaluates to True.
sort(a[, axis, kind, order])	Return a sorted copy of an array.
sort_complex(a)	Sort a complex array using the real part first, then the imaginary part.
split(ary, indices_or_sections[, axis])	Split an array into multiple sub-arrays as views into ary.
sqrt(x)	Return the non-negative square-root of an array, element-wise.
square(x)	Return the element-wise square of the input.
squeeze(a[, axis])	Remove single-dimensional entries from the shape of an array.
stack(arrays[, axis, out])	Join a sequence of arrays along a new axis.
std(a[, axis, dtype, out, ddof, keepdims])	Compute the standard deviation along the specified axis.
subtract(x1, x2)	Subtract arguments, element-wise.
sum(a[, axis, dtype, out, keepdims, …])	Sum of array elements over a given axis.
swapaxes(a, axis1, axis2)	Interchange two axes of an array.
take(a, indices[, axis, out, mode])	Take elements from an array along an axis.
take_along_axis(arr, indices, axis)	Take values from the input array by matching 1d index and data slices.
tan(x)	Compute tangent element-wise.
tanh(x)	Compute hyperbolic tangent element-wise.
tensordot(a, b[, axes, precision])	Compute tensor dot product along specified axes.
tile(A, reps)	Construct an array by repeating A the number of times given by reps.
trace(a[, offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.
transpose(a[, axes])	Reverse or permute the axes of an array; returns the modified array.
trapz(y[, x, dx, axis])	Integrate along the given axis using the composite trapezoidal rule.
tri(N[, M, k, dtype])	An array with ones at and below the given diagonal and zeros elsewhere.
tril(m[, k])	Lower triangle of an array.
tril_indices(*args, **kwargs)	Return the indices for the lower-triangle of an (n, m) array.
tril_indices_from(arr[, k])	Return the indices for the lower-triangle of arr.
trim_zeros(filt[, trim])	Trim the leading and/or trailing zeros from a 1-D array or sequence.
triu(m[, k])	Upper triangle of an array.
triu_indices(*args, **kwargs)	Return the indices for the upper-triangle of an (n, m) array.
triu_indices_from(arr[, k])	Return the indices for the upper-triangle of arr.
true_divide(x1, x2)	Returns a true division of the inputs, element-wise.
trunc(x)	Return the truncated value of the input, element-wise.
uint16
uint32
uint64
uint8
unique(ar[, return_index, return_inverse, …])	Find the unique elements of an array.
unpackbits(a[, axis, count, bitorder])	Unpacks elements of a uint8 array into a binary-valued output array.
unravel_index(indices, shape)	Converts a flat index or array of flat indices into a tuple of coordinate arrays.
unsignedinteger	Abstract base class of all unsigned integer scalar types.
unwrap(p[, discont, axis])	Unwrap by changing deltas between values to 2*pi complement.
vander(x[, N, increasing])	Generate a Vandermonde matrix.
var(a[, axis, dtype, out, ddof, keepdims])	Compute the variance along the specified axis.
vdot(a, b, *[, precision])	Return the dot product of two vectors.
vectorize(pyfunc, *[, excluded, signature])	Define a vectorized function with broadcasting.
vsplit(ary, indices_or_sections)	Split an array into multiple sub-arrays vertically (row-wise).
vstack(tup)	Stack arrays in sequence vertically (row wise).
where(condition[, x, y])	Return elements chosen from x or y depending on condition.
zeros(shape[, dtype])	Return a new array of given shape and type, filled with zeros.
zeros_like(a[, dtype, shape])	Return an array of zeros with the same shape and type as a given array.

jax.numpy.fft

fft(a[, n, axis, norm])	Compute the one-dimensional discrete Fourier Transform.
fft2(a[, s, axes, norm])	Compute the 2-dimensional discrete Fourier Transform
fftfreq(n[, d])	Return the Discrete Fourier Transform sample frequencies.
fftn(a[, s, axes, norm])	Compute the N-dimensional discrete Fourier Transform.
fftshift(x[, axes])	Shift the zero-frequency component to the center of the spectrum.
hfft(a[, n, axis, norm])	Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum.
ifft(a[, n, axis, norm])	Compute the one-dimensional inverse discrete Fourier Transform.
ifft2(a[, s, axes, norm])	Compute the 2-dimensional inverse discrete Fourier Transform.
ifftn(a[, s, axes, norm])	Compute the N-dimensional inverse discrete Fourier Transform.
ifftshift(x[, axes])	The inverse of fftshift.
ihfft(a[, n, axis, norm])	Compute the inverse FFT of a signal that has Hermitian symmetry.
irfft(a[, n, axis, norm])	Compute the inverse of the n-point DFT for real input.
irfft2(a[, s, axes, norm])	Compute the 2-dimensional inverse FFT of a real array.
irfftn(a[, s, axes, norm])	Compute the inverse of the N-dimensional FFT of real input.
rfft(a[, n, axis, norm])	Compute the one-dimensional discrete Fourier Transform for real input.
rfft2(a[, s, axes, norm])	Compute the 2-dimensional FFT of a real array.
rfftfreq(n[, d])	Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft).
rfftn(a[, s, axes, norm])	Compute the N-dimensional discrete Fourier Transform for real input.

jax.numpy.linalg

cholesky(a)	Cholesky decomposition.
cond(x[, p])	Compute the condition number of a matrix.
det	Compute the determinant of an array.
eig(a)	Compute the eigenvalues and right eigenvectors of a square array.
eigh(a[, UPLO, symmetrize_input])	Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.
eigvals(a)	Compute the eigenvalues of a general matrix.
eigvalsh(a[, UPLO])	Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
inv(a)	Compute the (multiplicative) inverse of a matrix.
lstsq(a, b[, rcond, numpy_resid])	Return the least-squares solution to a linear matrix equation.
matrix_power(a, n)	Raise a square matrix to the (integer) power n.
matrix_rank(M[, tol])	Return matrix rank of array using SVD method
multi_dot(arrays, *[, precision])	Compute the dot product of two or more arrays in a single function call, while automatically selecting the fastest evaluation order.
norm(x[, ord, axis, keepdims])	Matrix or vector norm.
pinv	Compute the (Moore-Penrose) pseudo-inverse of a matrix.
qr(a[, mode])	Compute the qr factorization of a matrix.
slogdet	Compute the sign and (natural) logarithm of the determinant of an array.
solve(a, b)	Solve a linear matrix equation, or system of linear scalar equations.
svd(a[, full_matrices, compute_uv])	Singular Value Decomposition.
tensorinv(a[, ind])	Compute the ‘inverse’ of an N-dimensional array.
tensorsolve(a, b[, axes])	Solve the tensor equation a x = b for x.