# Expression builders

xtensor provides functions to ease the build of common N-dimensional expressions. The expressions returned by these functions implement the laziness of xtensor, that is, they don’t hold any value. Values are computed upon request.

## Ones and zeros

- `xt::zeros(shape)`: generates an expression containing zeros of the specified shape.

- `xt::ones(shape)`: generates an expression containing ones of the specified shape.

- `xt::eye(shape, k=0)`: generates an expression of the specified shape, with ones on the k-th diagonal.

- `xt::eye(n, k = 0)`: generates an expression of shape `(n, n)` with ones on the k-th diagonal.

## Numerical ranges

- `xt::arange(start=0, stop, step=1)`: generates numbers evenly spaced within given half-open interval.

- `xt::linspace(start, stop, num_samples)`: generates num_samples evenly spaced numbers over given interval.

- `xt::logspace(start, stop, num_samples)`: generates num_samples evenly spaced on a log scale over given interval

## Joining expressions

- `xt::concatenate(tuple, axis=0)`: concatenates a list of expressions along the given axis.

- `xt::stack(tuple, axis=0)`: stacks a list of expressions along the given axis.

- `xt::hstack(tuple)`: stacks expressions in sequence horizontally (i.e. column-wise).

- `xt::vstack(tuple)`: stacks expressions in sequence vertically (i.e. row wise).

## Random distributions

Warning

xtensor uses a lazy generator for random numbers. You need to assign them or use `xt::eval()` to keep the generated values consistent.

- `xt::random::rand(shape, lower, upper)`: generates an expression of the specified shape, containing uniformly distributed random numbers in the half-open interval [lower, upper).

- `xt::random::randint(shape, lower, upper)`: generates an expression of the specified shape, containing uniformly distributed random integers in the half-open interval [lower, upper).

- `xt::random::randn(shape, mean, std_dev)`: generates an expression of the specified shape, containing numbers sampled from the Normal random number distribution.

- `xt::random::binomial(shape, trials, prob)`: generates an expression of the specified shape, containing numbers sampled from the binomial random number distribution.

- `xt::random::geometric(shape, prob)`: generates an expression of the specified shape, containing numbers sampled from the geometric random number distribution.

- `xt::random::negative_binomial(shape, k, prob)`: generates an expression of the specified shape, containing numbers sampled from the negative binomial random number distribution.

- `xt::random::poisson(shape, rate)`: generates an expression of the specified shape, containing numbers sampled from the Poisson random number distribution.

- `xt::random::exponential(shape, rate)`: generates an expression of the specified shape, containing numbers sampled from the exponential random number distribution.

- `xt::random::gamma(shape, alpha, beta)`: generates an expression of the specified shape, containing numbers sampled from the gamma random number distribution.

- `xt::random::weibull(shape, a, b)`: generates an expression of the specified shape, containing numbers sampled from the Weibull random number distribution.

- `xt::random::extreme_value(shape, a, b)`: generates an expression of the specified shape, containing numbers sampled from the extreme value random number distribution.

- `xt::random::lognormal(shape, a, b)`: generates an expression of the specified shape, containing numbers sampled from the Log-Normal random number distribution.

- `xt::random::chi_squared(shape, a, b)`: generates an expression of the specified shape, containing numbers sampled from the chi-squared random number distribution.

- `xt::random::cauchy(shape, a, b)`: generates an expression of the specified shape, containing numbers sampled from the Cauchy random number distribution.

- `xt::random::fisher_f(shape, m, n)`: generates an expression of the specified shape, containing numbers sampled from the Fisher-f random number distribution.

- `xt::random::student_t(shape, n)`: generates an expression of the specified shape, containing numbers sampled from the Student-t random number distribution.

## Meshes

- `xt::meshgrid(x1, x2,...)`: generates N-D coordinate expressions given one-dimensional coordinate arrays `x1`, `x2`… If specified vectors have lengths `Ni = len(xi)`, meshgrid returns `(N1, N2, N3,..., Nn)`-shaped arrays, with the elements of xi repeated to fill the matrix along the first dimension for x1, the second for x2 and so on.