pchip extrapolation?

Hi All Trying to use pchip to process sensor data from raw digital values. Seems to work fine when the raw values are within the range of calibration values used us inputs to pchip. However, when raw values are smaller than those values used to calibrate the sensor the output is unexpected. Using the example for pchip from Mlab help:

x = -3:3; y = [-1 -1 -1 0 1 1 1]; t = -3:.01:3; p = pchip(x,y,t);

pchip (x,y,-4); ans = -1 (as expected)

However, if change y to:

y = [-1 -0.98 -0.94 0 0.94 0.98 1];

pchip (x,y,-4); ans = -0.9933

Why do answers for x values <-3 increase? I would expect them to linearly decrease i.e. pchip (x,y,-4); ans = -1.02

Thanks in advance

Answer 1

[Robert Cumming]

your extrapolating quite far (compared to the source data), plot the data and you will see why the numbers are not what "you expect" - extrapolation must always be treated with care.

x = -3:3; 
y = [-1 -1 -1 0 1 1 1]; 
t = -3:.01:3; 
plot ( [-5:0.01:5], pchip(x,y,[-5:0.01:5]), 'r' );
hold on; 
y = [-1 -0.98 -0.94 0 0.94 0.98 1]; 
plot ( [-5:0.01:5], pchip(x,y,[-5:0.01:5]), 'k' );
grid on

[Walter Roberson]

"Prediction is very difficult, especially if it's about the future."

(Nils Bohr)

[Robert Cumming]

Indeed...

maybe I should have put "extreme" care...

Answer 2

[Andrew Newell]

Why would you expect the output to be linear when the input isn't? Look at the end points:

y = [-1 -0.98 -0.94 0 0.94 0.98 1];
diff(y)

ans =

    0.0200    0.0400    0.9400    0.9400    0.0400    0.0200

If you change y to

y = [-1.02 -0.98 -0.94 0 0.94 0.98 1.02];

then you do get linear extrapolation: pchip(x,y,-4) is equal to -1.06.

EDIT: moreover, the extrapolation remains linear for larger absolute values.