# 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¶

• zeros(shape): generates an expression containing zeros of the specified shape.

• ones(shape): generates an expression containing ones of the specified shape.

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

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

## Numerical ranges¶

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

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

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

## Joining expressions¶

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

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

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

• 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 eval to keep the generated values consistent.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## Meshes¶

• 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.