interp_lagrange Subroutine

From a space of DIM_NUM dimensions, we are given a sequence of
DATA_NUM points, which are presumed to be successive samples
from a curve of points P.

We are also given a parameterization of this data, that is,
an associated sequence of DATA_NUM values of a variable T.

Thus, we have a sequence of values P(T), where T is a scalar,
and each value of P is of dimension DIM_NUM.

We are then given INTERP_NUM values of T, for which values P
are to be produced, by linear interpolation of the data we are given.

Note that the user may request extrapolation.  This occurs whenever
a T_INTERP value is less than the minimum T_DATA or greater than the
maximum T_DATA.  In that case, extrapolation is used.

Note that, for each spatial component, a polynomial of degree
( DATA_NUM - 1 ) is generated for the interpolation.  In most cases,
such a polynomial interpolant begins to oscillate as DATA_NUM
increases, even if the original data seems well behaved.  Typically,
values of DATA_NUM should be no greater than 10!

This code is distributed under the GNU LGPL license.

03 December 2007

John Burkardt

Input, integer ( kind = 4 ) DIM_NUM, the spatial dimension.

Input, integer ( kind = 4 ) DATA_NUM, the number of data points.

Input, real ( kind = 8 ) T_DATA(DATA_NUM), the value of the
independent variable at the sample points.

Input, real ( kind = 8 ) P_DATA(DIM_NUM,DATA_NUM), the value of the
dependent variables at the sample points.

Input, integer ( kind = 4 ) INTERP_NUM, the number of points
at which interpolation is to be done.

Input, real ( kind = 8 ) T_INTERP(INTERP_NUM), the value of the
independent variable at the interpolation points.

Output, real ( kind = 8 ) P_INTERP(DIM_NUM,DATA_NUM), the interpolated
values of the dependent variables at the interpolation points.