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# mir.interpolate.constant

## Constant Interpolation

Authors:
Ilya Yaroshenko
Examples:
```import mir.ndslice;
import mir.math.common: approxEqual;

static immutable x = [0, 1, 2, 3];
static immutable y = [10, 20, 30, 40];

auto interpolant = constant!int(x.rcslice, y.rcslice!(const int));

assert(interpolant(-1) == 10);
assert(interpolant(0) == 10);
assert(interpolant(0.5) == 10);

assert(interpolant(1) == 20);

assert(interpolant(3) == 40);
assert(interpolant(4) == 40);
```
Constant!(F, N, X) `constant`(F, size_t N = 1, X = F)(Repeat!(N, Slice!(RCI!(immutable(X)))) `grid`, Slice!(RCI!(const(F)), N) `values`);
Constructs multivariate constant interpolant with nodes on rectilinear grid.
Parameters:
 Repeat!(N, Slice!(RCI!(immutable(X)))) `grid` x values for interpolant Slice!(RCI!(const(F)), N) `values` f(x) values for interpolant

Constraints `grid`, `values` must have the same length >= 1

Returns:
struct `Constant`(F, size_t N = 1, X = F) if (N && (N <= 6));
Multivariate constant interpolant with nodes on rectilinear grid.
Slice!(RCI!(const(F)), N) `_data`;
Aligned buffer allocated with mir.internal.memory. For internal use.
RCI!(immutable(X))[N] `_grid`;
Grid iterators. For internal use.
@nogc @safe this(Repeat!(N, Slice!(RCI!(immutable(X)))) `grid`, Slice!(RCI!(const(F)), N) `data`);
const @property Constant `lightConst`()();
const @property scope Slice!(RCI!(immutable(X))) `grid`(size_t dimension = 0)() return
if (dimension < N);
const @property scope @trusted immutable(X)[] `gridScopeView`(size_t dimension = 0)() return
if (dimension < N);
const @property scope size_t `intervalCount`(size_t dimension = 0)();
Returns:
intervals count.
const @property scope size_t[N] `gridShape`()();
enum uint `derivativeOrder`;
template `opCall`(uint derivative = 0) if (derivative <= derivativeOrder)
const scope @trusted auto `opCall`(X...)(in X `xs`)
if (X.length == N);
(x) operator.

Complexity O(log(grid.length))