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mir.interpolate.pchip

Piecewise Cubic Hermite Interpolating Polynomial

See Also:

interp1

License:

Boost License 1.0.

Authors:

Ilya Yaroshenko

template pchip(T, size_t N = 1, FirstGridIterator = immutable(T)*, NextGridIterators = Repeat!(N - 1, FirstGridIterator)) if (isFloatingPoint!T && is(T == Unqual!T) && (N <= 6))

Constructs piecewise cubic hermite interpolating polynomial with nodes on rectilinear grid.

Examples:

import mir.math.common: approxEqual;
import mir.algorithm.iteration: all;
import mir.ndslice.allocation: slice;
import mir.ndslice.slice: sliced;
import mir.ndslice.topology: vmap;

auto x = [1.0, 2, 4, 5, 8, 10, 12, 15, 19, 22].idup.sliced;
auto y = [17.0, 0, 16, 4, 10, 15, 19, 5, 18, 6].idup.sliced;
auto interpolant = pchip!double(x, y);

auto xs = x[0 .. $ - 1] + 0.5;

() @trusted {
    auto ys = xs.vmap(interpolant);

    assert(ys.all!approxEqual([
        5.333333333333334,
        2.500000000000000,
        10.000000000000000,
        4.288971807628524,
        11.202580845771145,
        16.250000000000000,
        17.962962962962962,
        5.558593750000000,
        17.604662698412699,
        ]));
}();

@safe Spline!(T, N, GridIterators) pchip(yIterator, SliceKind ykind)(GridVectors grid, scope Slice!(yIterator, N, ykind) values);

Unbounded piecewise spline hermite interpolating polynomial.

Parameters:

GridVectors `grid`	x `values` for interpolant
Slice!(yIterator, N, ykind) `values`	f(x) `values` for interpolant

Constraints grid and values must have the same length >= 3

Returns:

Spline

@trusted void pchipSlopes(IG, IV, IS, SliceKind gkind, SliceKind vkind, SliceKind skind)(scope Slice!(IG, 1, gkind) points, scope Slice!(IV, 1, vkind) values, scope Slice!(IS, 1, skind) slopes);

Computes slopes for piecewise spline hermite interpolating polynomial.

Parameters:

Slice!(IG, 1, gkind) `points`	x `values` for interpolant
Slice!(IV, 1, vkind) `values`	f(x) `values` for interpolant
Slice!(IS, 1, skind) `slopes`	uninitialized ndslice to write `slopes` into

Constraints points, values, and slopes must have the same length >= 3

Library Reference

mir.interpolate.pchip

Piecewise Cubic Hermite Interpolating Polynomial