# scipy.interpolate.KroghInterpolator.__init__¶

KroghInterpolator.__init__(xi, yi)

Construct an interpolator passing through the specified points

The polynomial passes through all the pairs (xi,yi). One may additionally specify a number of derivatives at each point xi; this is done by repeating the value xi and specifying the derivatives as successive yi values.

Parameters : xi : array-like, length N known x-coordinates yi : array-like, N by R known y-coordinates, interpreted as vectors of length R, or scalars if R=1. When an xi occurs two or more times in a row, the corresponding yi’s represent derivative values.

Examples

To produce a polynomial that is zero at 0 and 1 and has derivative 2 at 0, call

```>>> KroghInterpolator([0,0,1],[0,2,0])
```

This constructs the quadratic 2*X**2-2*X. The derivative condition is indicated by the repeated zero in the xi array; the corresponding yi values are 0, the function value, and 2, the derivative value.

For another example, given xi, yi, and a derivative ypi for each point, appropriate arrays can be constructed as:

```>>> xi_k, yi_k = np.repeat(xi, 2), np.ravel(np.dstack((yi,ypi)))
>>> KroghInterpolator(xi_k, yi_k)
```

To produce a vector-valued polynomial, supply a higher-dimensional array for yi:

```>>> KroghInterpolator([0,1],[[2,3],[4,5]])
```

This constructs a linear polynomial giving (2,3) at 0 and (4,5) at 1.