Modified linear interpolation with missing data

Question

Imagine a set of data with given x-values (as a column vector) and several y-values combined in a matrix (row vector of column vectors). Some of the values in the matrix are not available:

%% Create the test data
N = 1e2; % Number of x-values

x = 2*sort(rand(N, 1))-1;
Y = [x.^2, x.^3, x.^4, x.^5, x.^6]; % Example values
Y(50:80, 4) = NaN(31, 1); % Some values are not avaiable

Now i have a column vector of new x-values for interpolation.

K = 1e2; % Number of interplolation values
x_i = rand(K, 1);

My goal is to find a fast way to interpolate all y-values for the given x_i values. If there are NaN values in the y-values, I want to use the y-value which is before the missing data. In the example case this would be the data in Y(49, :).

If I use interp1, I get NaN-values and the execution is slow for large x and x_i:

starttime = cputime;
Y_i1 = interp1(x, Y, x_i);
executiontime1 = cputime - starttime

An alternative is interp1q, which is about two times faster.

What is a very fast way which allows my modifications?

Possible ideas:

1. Do postprocessing of Y_i1 to eliminate NaN-values.
2. Use a combination of a loop and the find-command to always use the neighbour without interpolation.

Answer 1

Using interp1 with spline interpolation (spline) ignores NaN's.