# Bumps 0.8.1 documentation

## 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.count_inflections(x, y)

  Count the number of inflection points in a curve.

bumps.mono.hermite(x, y, m, xt)

  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.monospline(x, y, xt)

  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.plot_inflections(x, y)

  Plot inflection points in a curve.