Piecewise linear interpolation
real linear_interpolation(real xout, real[] x, real[] y)
real[] linear_interpolation(real[] xout, real[] x, real[] y)
Torsten also provides function linear_interpolation for piecewise linear interpolation over a
set of x, y pairs. It returns the values of a piecewise linear
function at specified values xout of the first function argument. The
function is specified in terms of a set of x, y
pairs. Specifically, linear_interpolation implements the following function
\begin{align*}
y_{\text{out}} = \left\{\begin{array}{ll}
y_1, & x_{\text{out}} < x_1 \\\
y_i + \frac{y_{i+1} - y_i}{x_{i+1} - x_i}
\left(x_{\text{out}} - x_i\right), & x_{\text{out}} \in [x_i, x_{i+1}) \\\
y_n, & x_{\text{out}} \ge x_n
\end{array}\right.
\end{align*}
- The x values must be in increasing order, i.e. \(x_i < x_{i+1}\).
- All three arguments may be data or parameters.