# 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 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.

## Random distributions¶

• `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.

## 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.