Linear Interpolation

Linear interpolation• Linear interpolation is using

a straight line connecting two data points to predict any data point in between. Thus:

Therefore:

It is important to note that extrapolation is generally not reliable.

IDL intrinsic functions for linear interpolation

• Linear interpolation y2 = interpol(y, x, x2)

where x and y are the original time series x2 is the desired x coordinate for the new data points y2 is the resultant y coordinate for the new data points

Example x = [0.01, 0.12, 0.23, 0.31, 0.4, 0.52, 0.6, 0.74, 0.8, 0.9, 0.95] y = [0.02, 0.01, 0.04, 0.03, 0.05, 0.06, 0.05, 0.08, 0.12, 0.09, 0.10]

x2=findgen(19)*0.05+0.05 print, x2

y2=interpol(y, x, x2) print, y2

plot, x, y, psym=2, symsize=2.0 oplot, x, y oplot, x2, y2, psym=5, symsize=2.0 end

Graphic devices• Commonly used graphic devices: WIN, MAC, X, PS• Select a graphic device set_plot, device_name (‘X’ or ‘PS’)

• Close a device device, /close device, /close_file

Configure the graphic device• Syntax: device, keywords• Keep windows (for X windows): device, retain=2

• Select color model device, decomposed=0 (for indexed color, recommended) 1 (for decomposed color) IDL has two color models indexed color: 28 colors, used mostly with both 8-bit decomposed color: 224 colors used mostly with 24-bit

Configure the graphic device (cont.)

• Filename and page setup (for PS only):

device, filename=file_name, $ /portrait (or /landscape), $ /inches, xsize=xsiz, xoffset=xoff, ysize=ysiz,

yoffset=yoff

• Select display mode (for PS only) device, bits_per_pixel=8 (or 24) IDL has two display modes PseudoColor (8-bit): each pixel can display one of 28 (256) colors TrueColor (24-bit): each pixel can display one of 224 (16,777,216) colors

Example: Output to a postscript file

set_plot,'ps’device, filename=‘a.ps’, bits_per_pixel=8, /color, /portrait, $ /inches, xsize=6.0, xoffset=1.0, ysize=9.0, yoffset=1.0

Plot, findgen(10)

device,/closeset_plot,'x'

Assignment XI• Read and plot the population history of Columbus, OH

http://www.biggestuscities.com/city/columbus-ohio and the population history of 5 other cities of your interest. Interpolate each of the time series into yearly data.

• Read and plot the maximum temperature data for Boulder, Colorado: http://www.esrl.noaa.gov/psd/boulder/Boulder.mm.maxt.html The data has some missing values. Use linear interpolation to fill the missing values.

• Output some of your previous plots to postscript files