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Two container types are provided. :cpp:type:`xt::xarray` :cpp:type:`xt::xtensor`
Lazy helper functions return tensor expressions. Return types don't hold any value and are
evaluated upon access or assignment. They can be assigned to a container or directly used in
expressions.
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.linspace(1.0, 10.0, 100) <numpy.linspace>` :cpp:func:`xt::linspace\<double\>(1.0, 10.0, 100) <xt::linspace>` :any:`np.logspace(2.0, 3.0, 4) <numpy.logspace>` :cpp:func:`xt::logspace\<double\>(2.0, 3.0, 4) <xt::logspace>` :any:`np.arange(3, 7) <numpy.arange>` :cpp:func:`xt::arange(3, 7) <xt::arange>` :any:`np.eye(4) <numpy.eye>` :cpp:func:`xt::eye(4) <xt::eye>` :any:`np.zeros([3, 4]) <numpy.zeros>` :cpp:func:`xt::zeros\<double\>({3, 4}) <xt::zeros>` :any:`np.ones([3, 4]) <numpy.ones>` :cpp:func:`xt::ones\<double\>({3, 4}) <xt::ones>` :any:`np.empty([3, 4]) <numpy.empty>` :cpp:func:`xt::empty\<double\>({3, 4}) <xt::empty>` :any:`np.meshgrid(x0, x1, x2, indexing='ij') <numpy.meshgrid>` :cpp:func:`xt::meshgrid(x0, x1, x2) <xt::meshgrid>`
xtensor's :cpp:func:`meshgrid <xt::meshgrid>` 'ij' indexing order.
See :any:`numpy indexing <numpy:arrays.indexing>`
Python 3 - NumPy
C++ 14 - xtensor
a[3, 2]:cpp:func:`a(3, 2) <xt::xcontainer::operator()>` :any:`a.flat[4] <numpy.ndarray.flat>` :cpp:func:`a.flat(4) <xt::xcontainer::flat>` a[3]
a[:, 2]
a[:5, 1:]:cpp:func:`xt::view(a, xt::range(_, 5), xt::range(1, _)) <xt::range>` a[5:1:-1, :]:cpp:func:`xt::view(a, xt::range(5, 1, -1), xt::all()) <xt::all>` a[..., 3]:cpp:func:`xt::strided_view(a, {xt::ellipsis(), 3}) <xt::ellipsis>` :any:`a[:, np.newaxis] <numpy.newaxis>` :cpp:func:`xt::view(a, xt::all(), xt::newaxis()) <xt::newaxis>`
xtensor offers lazy numpy-style broadcasting, and universal functions. Unlike numpy, no copy
or temporary variables are created.
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.broadcast(a, [4, 5, 7]) <numpy.broadcast>` :cpp:func:`xt::broadcast(a, {4, 5, 7}) <xt::broadcast>` :any:`np.vectorize(f) <numpy.vectorize>` :cpp:func:`xt::vectorize(f) <xt::vectorize>` a[a > 5]:cpp:func:`xt::filter(a, a > 5) <xt::filter>` a[[0, 1], [0, 0]]:cpp:func:`xt::index_view(a, {{0, 0}, {1, 0}}) <xt::index_view>`
The random module provides simple ways to create random tensor expressions, lazily.
See :any:`numpy.random` :ref:`xtensor random <random>`
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.random.seed(0) <numpy.random.seed>` :cpp:func:`xt::random::seed(0) <xt::random::seed>` :any:`np.random.randn(10, 10) <numpy.random.randn>` :cpp:func:`xt::random::randn\<double\>({10, 10}) <xt::random::randn>` :any:`np.random.randint(10, 10) <numpy.random.randint>` :cpp:func:`xt::random::randint\<int\>({10, 10}) <xt::random::randint>` :any:`np.random.rand(3, 4) <numpy.random.rand>` :cpp:func:`xt::random::rand\<double\>({3, 4}) <xt::random::rand>` :any:`np.random.choice(arr, 5[, replace][, p]) <numpy.random.choice>` :cpp:func:`xt::random::choice(arr, 5[, weights][, replace]) <xt::random::choice>` :any:`np.random.shuffle(arr) <numpy.random.shuffle>` :cpp:func:`xt::random::shuffle(arr) <xt::random::shuffle>` :any:`np.random.permutation(30) <numpy.random.permutation>` :cpp:func:`xt::random::permutation(30) <xt::random::permutation>`
Concatenation, splitting, squeezing Concatenating expressions does not allocate memory, it returns a tensor or view expression holding
closures on the specified arguments.
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.stack([a, b, c], axis=1) <numpy.stack>` :cpp:func:`xt::stack(xtuple(a, b, c), 1) <xt::stack>` :any:`np.hstack([a, b, c]) <numpy.hstack>` :cpp:func:`xt::hstack(xtuple(a, b, c)) <xt::hstack>` :any:`np.vstack([a, b, c]) <numpy.vstack>` :cpp:func:`xt::vstack(xtuple(a, b, c)) <xt::vstack>` :any:`np.concatenate([a, b, c], axis=1) <numpy.concatenate>` :cpp:func:`xt::concatenate(xtuple(a, b, c), 1) <xt::concatenate>` :any:`np.tile(a, reps) <numpy.tile>` :cpp:func:`xt::tile(a, reps) <xt::tile>` :any:`np.squeeze(a) <numpy.squeeze>` :cpp:func:`xt::squeeze(a) <xt::squeeze>` :any:`np.expand_dims(a, 1) <numpy.expand_dims>` :cpp:func:`xt::expand_dims(a ,1) <xt::expand_dims>` :any:`np.atleast_3d(a) <numpy.atleast_3d>` :cpp:func:`xt::atleast_3d(a) <xt::atleast_3d>` :any:`np.split(a, 4, axis=0) <numpy.split>` :cpp:func:`xt::split(a, 4, 0) <xt::split>` :any:`np.hsplit(a, 4) <numpy.hsplit>` :cpp:func:`xt::hsplit(a, 4) <xt::hsplit>` :any:`np.vsplit(a, 4) <numpy.vsplit>` :cpp:func:`xt::vsplit(a, 4) <xt::vsplit>` :any:`np.trim_zeros(a, trim='fb') <numpy.trim_zeros>` :cpp:func:`xt::trim_zeros(a, "fb") <xt::trim_zeros>` :any:`np.pad(a, pad_width, mode='constant', constant_values=0) <numpy.pad>` :cpp:func:`xt::pad(a, pad_width[, xt::pad_mode::constant][, 0]) <xt::pad>`
In the same spirit as concatenation, the following operations do not allocate any memory and do
not modify the underlying xexpression.
Python3 - NumPy
C++14 - xtensor
:any:`np.nan_to_num(a) <numpy.nan_to_num>` :cpp:func:`xt::nan_to_num(a) <xt::nan_to_num>` :any:`np.diag(a) <numpy.diag>` :cpp:func:`xt::diag(a) <xt::diag>` :any:`np.diagonal(a) <numpy.diagonal>` :cpp:func:`xt::diagonal(a) <xt::diagonal>` :any:`np.triu(a) <numpy.triu>` :cpp:func:`xt::triu(a) <xt::triu>` :any:`np.tril(a, k=1) <numpy.tril>` :cpp:func:`xt::tril(a, 1) <xt::tril>` :any:`np.flip(a, axis=3) <numpy.flip>` :cpp:func:`xt::flip(a, 3) <xt::flip>` :any:`np.flipud(a) <numpy.flipud>` :cpp:func:`xt::flip(a, 0) <xt::flip>` :any:`np.fliplr(a) <numpy.fliplr>` :cpp:func:`xt::flip(a, 1) <xt::flip>` :any:`np.transpose(a, (1, 0, 2)) <numpy.transpose>` :cpp:func:`xt::transpose(a, {1, 0, 2}) <xt::transpose>` :any:`np.swapaxes(a, 0, -1) <numpy.swapaxes>` :cpp:func:`xt::swapaxes(a, 0, -1) <xt::swapaxes>` :any:`np.moveaxis(a, 0, -1) <numpy.moveaxis>` :cpp:func:`xt::moveaxis(a, 0, -1) <xt::moveaxis>` :any:`np.ravel(a, order='F') <numpy.ravel>` :cpp:func:`xt::ravel\<xt::layout_type::column_major\>(a) <xt::ravel>` :any:`np.rot90(a) <numpy.rot90>` :cpp:func:`xt::rot90(a) <xt::rot90>` :any:`np.rot90(a, 2, (1, 2)) <numpy.rot90>` :cpp:func:`xt::rot90\<2\>(a, {1, 2}) <xt::rot90>` :any:`np.roll(a, 2, axis=1) <numpy.roll>` :cpp:func:`xt::roll(a, 2, 1) <xt::roll>`
xtensor follows the idioms of the C++ STL providing iterator pairs to iterate on arrays in
different fashions.
Python 3 - NumPy
C++ 14 - xtensor
:any:`for x in np.nditer(a): <numpy.nditer>` for(auto it=a.begin(); it!=a.end(); ++it)Iterating over a with a prescribed broadcasting shape
a.begin({3, 4})
a.end({3, 4})
Iterating over a in a row-major fashion
a.begin<xt::layout_type::row_major>()
a.begin<xt::layout_type::row_major>()
Iterating over a in a column-major fashion
a.begin<xt::layout_type::column_major>()
a.end<xt::layout_type::column_major>()
Logical universal functions are truly lazy.
:cpp:func:`xt::where(condition, a, b) <xt::where>` a where condition
is falsy, and it does not evaluate b where condition is truthy.
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.where(a > 5, a, b) <numpy.where>` :cpp:func:`xt::where(a > 5, a, b) <xt::where>` :any:`np.where(a > 5) <numpy.where>` :cpp:func:`xt::where(a > 5) <xt::where>` :any:`np.argwhere(a > 5) <numpy.argwhere>` :cpp:func:`xt::argwhere(a > 5) <xt::argwhere>` :any:`np.any(a) <numpy.any>` :cpp:func:`xt::any(a) <xt::any>` :any:`np.all(a) <numpy.all>` :cpp:func:`xt::all(a) <xt::all>` :any:`np.isin(a, b) <numpy.isin>` :cpp:func:`xt::isin(a, b) <xt::isin>` :any:`np.in1d(a, b) <numpy.in1d>` :cpp:func:`xt::in1d(a, b) <xt::in1d>` :any:`np.logical_and(a, b) <numpy.logical_and>` a && b:any:`np.logical_or(a, b) <numpy.logical_or>` a || b:any:`np.isclose(a, b) <numpy.isclose>` :cpp:func:`xt::isclose(a, b) <xt::isclose>` :any:`np.allclose(a, b) <numpy.allclose>` :cpp:func:`xt::allclose(a, b) <xt::allclose>` :any:`a = ~b <numpy.invert>` a = !b
Minimum, Maximum, Sorting
Python3 - NumPy
C++14 - xtensor
:any:`np.amin(a) <numpy.amin>` :cpp:func:`xt::amin(a) <xt::amin>` :any:`np.amax(a) <numpy.amax>` :cpp:func:`xt::amax(a) <xt::amax>` :any:`np.argmin(a) <numpy.argmin>` :cpp:func:`xt::argmin(a) <xt::argmin>` :any:`np.argmax(a, axis=1) <numpy.argmax>` :cpp:func:`xt::argmax(a, 1) <xt::argmax>` :any:`np.sort(a, axis=1) <numpy.sort>` :cpp:func:`xt::sort(a, 1) <xt::sort>` :any:`np.argsort(a, axis=1) <numpy.argsort>` :cpp:func:`xt::argsort(a, 1) <xt::argsort>` :any:`np.unique(a) <numpy.unique>` :cpp:func:`xt::unique(a) <xt::unique>` :any:`np.setdiff1d(ar1, ar2) <numpy.setdiff1d>` :cpp:func:`xt::setdiff1d(ar1, ar2) <xt::setdiff1d>` :any:`np.partition(a, kth) <numpy.partition>` :cpp:func:`xt::partition(a, kth) <xt::partition>` :any:`np.argpartition(a, kth) <numpy.argpartition>` :cpp:func:`xt::argpartition(a, kth) <xt::argpartition>` :any:`np.quantile(a, [.1 .3], method="linear") <numpy.quantile>` :cpp:func:`xt::quantile(a, {.1, .3}, xt::quantile_method::linear) <xt::quantile>` :any:`np.quantile(a, [.1, .3], axis=1 method="linear") <numpy.quantile>` :cpp:func:`xt::quantile(a, {.1, .3}, 1, xt::quantile_method::linear) <xt::quantile>`
:cpp:func:`xt::quantile(a, {.1, .3}, 1, 1.0, 1.0) <xt::quantile>` :any:`np.median(a, axis=1) <numpy.median>` :cpp:func:`xt::median(a, 1) <xt::median>`
Functions :cpp:func:`xt::real` :cpp:func:`xt::imag`
Reducers accumulate values of tensor expressions along specified axes. When no axis is specified,
values are accumulated along all axes. Reducers are lazy, meaning that returned expressions don't
hold any values and are computed upon access or assignment.
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.sum(a, axis=(0, 1)) <numpy.sum>` :cpp:func:`xt::sum(a, {0, 1}) <xt::sum>` :any:`np.sum(a, axis=1) <numpy.sum>` :cpp:func:`xt::sum(a, 1) <xt::sum>` :any:`np.sum(a) <numpy.sum>` :cpp:func:`xt::sum(a) <xt::sum>` :any:`np.prod(a, axis=(0, 1)) <numpy.prod>` :cpp:func:`xt::prod(a, {0, 1}) <xt::prod>` :any:`np.prod(a, axis=1) <numpy.prod>` :cpp:func:`xt::prod(a, 1) <xt::prod>` :any:`np.prod(a) <numpy.prod>` :cpp:func:`xt::prod(a) <xt::prod>` :any:`np.mean(a, axis=(0, 1)) <numpy.mean>` :cpp:func:`xt::mean(a, {0, 1}) <xt::mean>` :any:`np.mean(a, axis=1) <numpy.mean>` :cpp:func:`xt::mean(a, 1) <xt::mean>` :any:`np.mean(a) <numpy.mean>` :cpp:func:`xt::mean(a) <xt::mean>` :any:`np.std(a, [axis]) <numpy.std>` :cpp:func:`xt::stddev(a, [axis]) <xt::stddev>` :any:`np.var(a, [axis]) <numpy.var>` :cpp:func:`xt::variance(a, [axis]) <xt::variance>` :any:`np.diff(a[, n, axis]) <numpy.diff>` :cpp:func:`xt::diff(a[, n, axis]) <xt::diff>` :any:`np.trapz(a, dx=2.0, axis=-1) <numpy.trapz>` :cpp:func:`xt::trapz(a, 2.0, -1) <xt::trapz>` :any:`np.trapz(a, x=b, axis=-1) <numpy.trapz>` :cpp:func:`xt::trapz(a, b, -1) <xt::trapz>` :any:`np.count_nonzero(a, axis=(0, 1)) <numpy.count_nonzero>` :cpp:func:`xt::count_nonzero(a, {0, 1}) <xt::count_nonzero>` :any:`np.count_nonzero(a, axis=1) <numpy.count_nonzero>` :cpp:func:`xt::count_nonzero(a, 1) <xt::count_nonzero>` :any:`np.count_nonzero(a) <numpy.count_nonzero>` :cpp:func:`xt::count_nonzero(a) <xt::count_nonzero>`
More generally, one can use the :cpp:func:`xt::reduce(function, input, axes) <xt::reduce>`
NaN functions allow disregarding NaNs during computation, changing the effective number of elements
considered in reductions.
Python3 - NumPy
C++14 - xtensor
:any:`np.nan_to_num(a) <numpy.nan_to_num>` :cpp:func:`xt::nan_to_num(a) <xt::nan_to_num>` :any:`np.nanmin(a) <numpy.nanmin>` :cpp:func:`xt::nanmin(a) <xt::nanmin>` :any:`np.nanmin(a, axis=(0, 1)) <numpy.nanmin>` :cpp:func:`xt::nanmin(a, {0, 1}) <xt::nanmin>` :any:`np.nanmax(a) <numpy.nanmax>` :cpp:func:`xt::nanmax(a) <xt::nanmax>` :any:`np.nanmax(a, axis=(0, 1)) <numpy.nanmax>` :cpp:func:`xt::nanmax(a, {0, 1}) <xt::nanmax>` :any:`np.nansum(a) <numpy.nansum>` :cpp:func:`xt::nansum(a) <xt::nansum>` :any:`np.nansum(a, axis=0) <numpy.nansum>` :cpp:func:`xt::nansum(a, 0) <xt::nansum>` :any:`np.nansum(a, axis=(0, 1)) <numpy.nansum>` :cpp:func:`xt::nansum(a, {0, 1}) <xt::nansum>` :any:`np.nanprod(a) <numpy.nanprod>` :cpp:func:`xt::nanprod(a) <xt::nanprod>` :any:`np.nanprod(a, axis=0) <numpy.nanprod>` :cpp:func:`xt::nanprod(a, 0) <xt::nanprod>` :any:`np.nanprod(a, axis=(0, 1)) <numpy.nanprod>` :cpp:func:`xt::nanprod(a, {0, 1}) <xt::nanprod>` :any:`np.nancumsum(a) <numpy.nancumsum>` :cpp:func:`xt::nancumsum(a) <xt::nancumsum>` :any:`np.nancumsum(a, axis=0) <numpy.nancumsum>` :cpp:func:`xt::nancumsum(a, 0) <xt::nancumsum>` :any:`np.nancumprod(a) <numpy.nancumsum>` :cpp:func:`xt::nancumsum(a) <xt::nancumsum>` :any:`np.nancumprod(a, axis=0) <numpy.nancumsum>` :cpp:func:`xt::nancumsum(a, 0) <xt::nancumsum>` :any:`np.nanmean(a) <numpy.nanmean>` :cpp:func:`xt::nanmean(a) <xt::nanmean>` :any:`np.nanmean(a, axis=(0, 1)) <numpy.nanmean>` :cpp:func:`xt::nanmean(a, {0, 1}) <xt::nanmean>` :any:`np.nanvar(a) <numpy.nanvar>` :cpp:func:`xt::nanvar(a) <xt::nanvar>` :any:`np.nanvar(a, axis=(0, 1)) <numpy.nanvar>` :cpp:func:`xt::nanvar(a, {0, 1}) <xt::nanvar>` :any:`np.nanstd(a) <numpy.nanstd>` :cpp:func:`xt::nanstd(a) <xt::nanstd>` :any:`np.nanstd(a, axis=(0, 1)) <numpy.nanstd>` :cpp:func:`xt::nanstd(a, {0, 1}) <xt::nanstd>`
Print options
These options determine the way floating point numbers, tensors and other xtensor expressions are displayed.
Reading npy, csv file formats
Functions :cpp:func:`xt::load_csv` :cpp:func:`xt::dump_csv`
xtensor universal functions are provided for a large set number of mathematical functions.
Basic functions:
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.absolute(a) <numpy.absolute>` :cpp:func:`xt::abs(a) <xt::abs>` :any:`np.sign(a) <numpy.sign>` :cpp:func:`xt::sign(a) <xt::sign>` :any:`np.remainder(a, b) <numpy.remainder>` :cpp:func:`xt::remainder(a, b) <xt::remainder>` :any:`np.minimum(a, b) <numpy.minimum>` :cpp:func:`xt::minimum(a, b) <xt::minimum>` :any:`np.maximum(a, b) <numpy.maximum>` :cpp:func:`xt::maximum(a, b) <xt::maximum>` :any:`np.clip(a, min, max) <numpy.clip>` :cpp:func:`xt::clip(a, min, max) <xt::clip>`
:cpp:func:`xt::fma(a, b, c) <xt::fma>` :any:`np.interp(x, xp, fp, [,left, right]) <numpy.interp>` :cpp:func:`xt::interp(x, xp, fp, [,left, right]) <xt::interp>` :any:`np.rad2deg(a) <numpy.rad2deg>` :cpp:func:`xt::rad2deg(a) <xt::rad2deg>` :any:`np.degrees(a) <numpy.degrees>` :cpp:func:`xt::degrees(a) <xt::degrees>` :any:`np.deg2rad(a) <numpy.deg2rad>` :cpp:func:`xt::deg2rad(a) <xt::deg2rad>` :any:`np.radians(a) <numpy.radians>` :cpp:func:`xt::radians(a) <xt::radians>`
Exponential functions:
Power functions:
Trigonometric functions:
Hyperbolic functions:
Error and gamma functions:
Classification functions:
Histogram:
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.histogram(a, bins[, weights][, density]) <numpy.histogram>` :cpp:func:`xt::histogram(a, bins[, weights][, density]) <xt::histogram>` :any:`np.histogram_bin_edges(a, bins[, weights][, left, right][, bins][, mode]) <numpy.histogram_bin_edges>` :cpp:func:`xt::histogram_bin_edges(a, bins[, weights][, left, right][, bins][, mode]) <xt::histogram_bin_edges>` :any:`np.bincount(arr) <numpy.bincount>` :cpp:func:`xt::bincount(arr) <xt::bincount>` :any:`np.digitize(data, bin_edges[, right]) <numpy.digitize>` :cpp:func:`xt::digitize(data, bin_edges[, right][, assume_sorted]) <xt::digitize>`
See :ref:`histogram`
Numerical constants:
Many functions found in the :any:`numpy.linalg` xtensor-blas , a separate package offering BLAS and LAPACK bindings,
as well as a convenient interface replicating the linalg module.
Please note, however, that while we're trying to be as close to NumPy as possible, some features are not
implemented yet. Most prominently that is broadcasting for all functions except for :cpp:func:`xt::linalg::dot`
Matrix, vector and tensor products
Python 3 - NumPy
C++ 14 - xtensor
:any:`np.dot(a, b) <numpy.dot>` :cpp:func:`xt::linalg::dot(a, b) <xt::linalg::dot>` :any:`np.vdot(a, b) <numpy.vdot>` :cpp:func:`xt::linalg::vdot(a, b) <xt::linalg::vdot>` :any:`np.outer(a, b) <numpy.outer>` :cpp:func:`xt::linalg::outer(a, b) <xt::linalg::outer>` :any:`np.linalg.matrix_power(a, 123) <numpy.linalg.matrix_power>` :cpp:func:`xt::linalg::matrix_power(a, 123) <xt::linalg::matrix_power>` :any:`np.kron(a, b) <numpy.kron>` :cpp:func:`xt::linalg::kron(a, b) <xt::linalg::kron>` :any:`np.tensordot(a, b, axes=3) <numpy.tensordot>` :cpp:func:`xt::linalg::tensordot(a, b, 3) <xt::linalg::tensordot>` :any:`np.tensordot(a, b, axes=((0,2),(1,3)) <numpy.tensordot>` :cpp:func:`xt::linalg::tensordot(a, b, {0, 2}, {1, 3}) <xt::linalg::tensordot>`
Decompositions
Matrix eigenvalues
Norms and other numbers
Solving equations and inverting matrices
