From numpy to xtensor¶
Containers¶
Two container types are provided. xarray
(dynamic number of dimensions) and xtensor
(static number of dimensions).
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.array([[3, 4], [5, 6]]) |
xt::xarray<double>({{3, 4}, {5, 6}}) xt::xtensor<double, 2>({{3, 4}, {5, 6}}) |
arr.reshape([3, 4]) |
arr.reshape{{3, 4}) |
Initializers¶
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 |
---|---|
np.linspace(1.0, 10.0, 100) |
xt::linspace<double>(1.0, 10.0, 100) |
np.logspace(2.0, 3.0, 4) |
xt::logspace<double>(2.0, 3.0, 4) |
np.arange(3, 7) |
xt::arange(3, 7) |
np.eye(4) |
xt::eye(4) |
np.zeros([3, 4]) |
xt::zeros<double>({3, 4}) |
np.ones([3, 4]) |
xt::ones<double>({3, 4}) |
np.meshgrid(x0, x1, x2, indexing='ij') |
xt::meshgrid(x0, x1, x2) |
xtensor’s meshgrid
implementation corresponds to numpy’s 'ij'
indexing order.
Broadcasting¶
xtensor offers lazy numpy-style broadcasting, and universal functions. Unlike numpy, no copy or temporary variables are created.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
a[:, np.newaxis] a[:5, 1:] a[5:1:-1, :] |
xt::view(a, xt::all(), xt::newaxis()) xt::view(a, xt::range(_, 5), xt::range(1, _)) xt::view(a, xt::range(5, 1, -1), xt::all()) |
np.broadcast(a, [4, 5, 7]) |
xt::broadcast(a, {4, 5, 7}) |
np.vectorize(f) |
xt::vectorize(f) |
a[a > 5] |
xt::filter(a, a > 5) |
a[[0, 1], [0, 0]] |
xt::index_view(a, {{0, 0}, {1, 0}}) |
Random¶
The random module provides simple ways to create random tensor expressions, lazily.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.random.seed(0) |
xt::random::seed(0) |
np.random.randn(10, 10) |
xt::random::randn<double>({10, 10}) |
np.random.randint(10, 10) |
xt::random::randint<int>({10, 10}) |
np.random.rand(3, 4) |
xt::random::rand<double>({3, 4}) |
Concatenation¶
Concatenating expressions does not allocate memory, it returns a tensor expression holding closures on the specified arguments.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.stack([a, b, c], axis=1) |
xt::stack(xtuple(a, b, c), 1) |
np.concatenate([a, b, c], axis=1) |
xt::concatenate(xtuple(a, b, c), 1) |
Diagonal, triangular and flip¶
In the same spirit as concatenation, the following operations do not allocate any memory and do not modify the underlying xexpression.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.diag(a) |
xt::diag(a) |
np.diagonal(a) |
xt::diagonal(a) |
np.triu(a) |
xt::triu(a) |
np.tril(a, k=1) |
xt::tril(a, 1) |
np.flip(a, axis=3) |
xt::flip(a, 3) |
np.flipud(a) |
xt::flip(a, 0) |
np.fliplr(a) |
xt::flip(a, 1) |
Iteration¶
xtensor follows the idioms of the C++ STL providing iterator pairs to iterate on arrays in different fashions.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
for x in np.nditer(a): |
for(auto it=a.xbegin(); it!=a.xend(); ++it) |
Iterating over a with a prescribed broadcasting shape |
a.xbegin({3, 4}) a.xend({3, 4}) |
Iterating over a in a row-major fashion |
a.xbegin<layout_type::row_major>() a.xbegin<layout_type::row_major>() |
Iterating over a in a column-major fashion |
a.begin<layout_type::column_major>() a.xend<layout_type::column_major>() |
Logical¶
Logical universal functions are truly lazy. xt::where(condition, a, b)
does not evaluate a
where condition
is falsy, and it does not evaluate b
where condition
is truthy.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.where(a > 5, a, b) |
xt::where(a > 5, a, b) |
np.where(a > 5) |
xt::where(a > 5) |
np.any(a) |
xt::any(a) |
np.all(a) |
xt::all(a) |
np.logical_and(a, b) |
a && b |
np.logical_or(a, b) |
a || b |
np.isclose(a, b) |
xt::isclose(a, b) |
np.allclose(a, b) |
xt::allclose(a, b) |
Comparisons¶
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.equal(a, b) |
xt::equal(a, b) |
np.not_equal(a) |
xt::not_equal(a) |
np.nonzero(a) |
xt::nonzero(a) |
Complex numbers¶
Functions xt::real
and xt::imag
respectively return views on the real and imaginary part
of a complex expression. The returned value is an expression holding a closure on the passed
argument.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.real(a) |
xt::real(a) |
np.imag(a) |
xt::imag(a) |
- The constness and value category (rvalue / lvalue) of
real(a)
is the same as that ofa
. Hence, ifa
is a non-const lvalue,real(a)
is an non-const lvalue reference, to which one can assign a real expression. - If
a
has complex values, the same holds forimag(a)
. The constness and value category ofimag(a)
is the same as that ofa
. - If
a
has real values,imag(a)
returnszeros(a.shape())
.
Reducers¶
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 expressons don’t hold any values and are computed upon access or assigmnent.
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.sum(a, axis=[0, 1]) |
xt::sum(a, {0, 1}) |
np.sum(a) |
xt::sum(a) |
np.prod(a, axis=1) |
xt::prod(a, {1}) |
np.prod(a) |
xt::prod(a) |
np.mean(a, axis=1) |
xt::mean(a, {1}) |
np.mean(a) |
xt::mean(a) |
More generally, one can use the xt::reduce(function, input, axes)
which allows the specification
of an arbitrary binary function for the reduction. The binary function must be cummutative and
associative up to rounding errors.
Mathematical functions¶
xtensor universal functions are provided for a large set number of mathematical functions.
Basic functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.absolute(a) |
xt::abs(a) |
np.sign(a) |
xt::sign(a) |
np.remainder(a, b) |
xt::remainder(a, b) |
np.clip(a, min, max) |
xt::clip(a, min, max) |
xt::fma(a, b, c) |
Exponential functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.exp(a) |
xt::exp(a) |
np.expm1(a) |
xt::expm1(a) |
np.log(a) |
xt::log(a) |
np.log1p(a) |
xt::log1p(a) |
Power functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.power(a, p) |
xt::pow(a, b) |
np.sqrt(a) |
xt::sqrt(a) |
np.cbrt(a) |
xt::cbrt(a) |
Trigonometric functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.sin(a) |
xt::sin(a) |
np.cos(a) |
xt::cos(a) |
np.tan(a) |
xt::tan(a) |
Hyperbolic functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.sinh(a) |
xt::sinh(a) |
np.cosh(a) |
xt::cosh(a) |
np.tang(a) |
xt::tanh(a) |
Error and gamma functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
scipy.special.erf(a) |
xt::erf(a) |
scipy.special.gamma(a) |
xt::tgamma(a) |
scipy.special.gammaln(a) |
xt::lgamma(a) |
Classification functions:
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.isnan(a) |
xt::isnan(a) |
np.isinf(a) |
xt::isinf(a) |
np.isfinite(a) |
xt::isfinite(a) |
Linear algebra¶
Many functions found in the numpy.linalg
module are implemented in xtensor-blas, a seperate 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 dot
.
Matrix and vector products
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.dot(a, b) |
xt::linalg::dot(a, b) |
np.vdot(a, b) |
xt::linalg::vdot(a, b) |
np.outer(a, b) |
xt::linalg::outer(a, b) |
np.matrix_power(a, 123) |
xt::linalg::matrix_power(a, 123) |
np.kron(a, b) |
xt::linalg::kron(a, b) |
Decompositions
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.linalg.cholesky(a) |
xt::linalg::cholesky(a) |
np.linalg.qr(a) |
xt::linalg::qr(a) |
np.linalg.svd(a) |
xt::linalg::svd(a) |
Matrix eigenvalues
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.linalg.eig(a) |
xt::linalg::eig(a) |
np.linalg.eigvals(a) |
xt::linalg::eigvals(a) |
np.linalg.eigh(a) |
xt::linalg::eigh(a) |
np.linalg.eigvalsh(a) |
xt::linalg::eigvalsh(a) |
Norms and other numbers
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.linalg.norm(a, order=2) |
xt::linalg::norm(a, 2) |
np.linalg.cond(a) |
xt::linalg::cond(a) |
np.linalg.det(a) |
xt::linalg::det(a) |
np.linalg.matrix_rank(a) |
xt::linalg::matrix_rank(a) |
np.linalg.slogdet(a) |
xt::linalg::slogdet(a) |
np.trace(a) |
xt::linalg::trace(a) |
Solving equations and inverting matrices
Python 3 - numpy | C++ 14 - xtensor |
---|---|
np.linalg.inv(a) |
xt::linalg::inv(a) |
np.linalg.pinv(a) |
xt::linalg::pinv(a) |
np.linalg.solve(A, b) |
xt::linalg::solve(A, b) |
np.linalg.lstsq(A, b) |
xt::linalg::lstsq(A, b) |