# mono - Freeform - Monotonic Spline¶

 monospline Monotonic cubic hermite interpolation. hermite Computes the cubic hermite polynomial $$p(x_t)$$. count_inflections Count the number of inflection points in a curve. plot_inflections Plot inflection points in a curve.

Monotonic spline modeling.

bumps.mono.monospline(x, y, xt)[source]

Monotonic cubic hermite interpolation.

Returns $$p(x_t)$$ where $$p(x_i)= y_i$$ and $$p(x) \leq p(x_i)$$ if $$y_i \leq y_{i+1}$$ for all $$y_i$$. Also works for decreasing values $$y$$, resulting in decreasing $$p(x)$$. If $$y$$ is not monotonic, then $$p(x)$$ may peak higher than any $$y$$, so this function is not suitable for a strict constraint on the interpolated function when $$y$$ values are unconstrained.

http://en.wikipedia.org/wiki/Monotone_cubic_interpolation

bumps.mono.hermite(x, y, m, xt)[source]

Computes the cubic hermite polynomial $$p(x_t)$$.

The polynomial goes through all points $$(x_i,y_i)$$ with slope $$m_i$$ at the point.

bumps.mono.count_inflections(x, y)[source]

Count the number of inflection points in a curve.

bumps.mono.plot_inflections(x, y)[source]

Plot inflection points in a curve.