1. Arrays

2. Review of last lecture Overview of IDL Strength of IDL: (1) Interactive/compiled modes; (2) Array-oriented; (3) Variables easily redefined; (4) Many built-in subroutines Open and run IDL Variables and data types Operators Line plots: basics and cosmetics

3. General structure of an IDL program Define variables and arrays Read input data Process data Output results and/or make plots End Note: 1.Use semicolon ; to add comments after it 2.Use $ to break a long line into multiple lines 3.Can use read, x to pause the program for example between different plots

4. Introduction to Arrays Two most compelling reasons to use arrays in IDL 1. Array operations are much faster than loops 2. Array syntax is more compact than a corresponding loop construct One of the secrets to becoming an effective IDL programmer is learning how to use arrays effectively

5. Creating arrays Functions for creating arrays (1-8 dimensions) zeroed arrays: intarr( ), fltarr( ), strarr( ) index arrays: indgen( ), findgen( ), sindgen( ) Note in IDL, index starts from 0 instead of 1 Use index array to create a evenly-spaced array n=10 x0=5 dx=10 arr=x0+findgen(n)*dx print, arr Please try to create all the arrays at the beginning of your program

6. Creating arrays (cont.) For multi-dimensional arrays, zeroed arrays and index arrays can be created using similar functions as those used for 1-D arrays arr = intarr(3, 4) arr = findgen(3, 4) Multi-dimensional arrays in IDL are stored in column-major format (same as Fortran), which means that consecutive array elements are stored sequentially in memory, with the first array dimension (the column) varying the fastest. a[0,0], a[1,0], a[2,0], a[0,1], a[1,1], a[2,1]

7. Extract a sub-array using index 1-D Scalar index: print, arr[6] Index range: print, arr[0:3] All indices: print, arr[*] All indices from a specific index to the last index: print, arr[5:*] Indices given by a variable expression: I=3 print, arr[I-1:I+1] Indices specified by an array: index=indgen(3)*2 print, index print, arr[index]

8. Extract a sub-array using index (cont.) Multi-dimensional One element: print, arr(i, j) All elements in a row: print, arr[*,0] All elements in a column: print, arr[0,*] Index range over two dimensions: print, arr[0:3,1:2]

9. Extract a sub-array with values meeting a certain criteria Use the function “where” arr = indgen(10)*2 print, arr index = where(arr gt 5) print, index print, arr[index] index = where(arr ne 8) print, index print, arr[index]

10. Initialize an array or sub-array with certain values All elements: Arr[*] = -9999.0 One element: Arr[0] = 3.0 Subset range: Arr[5:*] = 2.0 Subset specified by an array index=indgen(3)*2 print, index arr[index] = 4.0

11. Array properties moment(arr) returns an array, with the first element being the mean, second being the variance, third being the skew, … another useful function: median

12. Array reordering Changing array dimensions (reform) automatically remove dimensions with a size of 1 arr=findgen(3,5) arr2=arr(0,*) help, arr2 arr2=reform(arr2) help, arr2 Shifting array elements (shift) Syntax: shift(array, shift_value) arr=indgen(5) print, arr print, shift(arr, 1) print, shift(arr, -2)

13. Array resizing (useful for remapping) Resizing by an integer factor (rebin) lon=findgen(144)*2.5 print, lon print, rebin(lon, 36) Resizing to arbitrary size with customized interpolation syntax: result=interpol(array, old_ordinate, new_ordinate) x=findgen(11) y=x^2.0 x2=findgen(20)/2 y2=interpol(y, x, x2) plot, x, y oplot, x2, y2, psym=4

14. Plot: Omitting default axes Plot, x, y, xstyle=4 (or 8), ystyle=4 (or 8)

15. Creating customized axes The axis procedure may be used to create customized axes on existing plots. Often used when one or more variables with different units are plotted with respect to the same ordinates axis, [x or y]axis=[0 or 1], [xy]range= …, [xy]title=… (where xaxis=0 bottom, xaxis=1 top, yaxis=0 left, yaxis=1 right) Example: t=findgen(11) g=9.8 v=g*t x=0.5*g*t^2.0 plot, t, v, /nodata, ystyle=4, xtitle=“Time” axis, yaxis=0, yrange=[0,100], /save, ytitle=“Velocity” oplot, t, v axis, yaxis=1, yrange=[0, 500], /save, ytitle=“Distance” oplot, t, x, linestyle=2

16. Multiple panels and plot positioning Global system variables Multiple panels !p.multi=[0, n_columns, n_rows, 0, 0] To disable multiple panels: !p.multi=0 Plot positioning !p.position=[x1, y1, x2, y2]

17. Summary Creating arrays Extract a sub-array using index Initialize an array Array properties: n_elements, size, max, min, moment, total Array reordering: reform, reverse, rotate, transpose, shift, sort, unique Array resizing: rebin, congrid, interpolate

18. In-class assignment II Create a 3x3 snake array. Calculate and print (1) mean, variance, and total of the array; (2) rotate the array by 90 and 180 degrees; (3) transpose the array; and (4) shift the first index of the array by 2. Assume time t=findgen(12)+1 is the 12 months of a year, the GDP index is GDP1=2sin(  t/2.0)+5 for country A and GDP2=3cos(  t/3.0)+5 for country B, while the stock index is STOCK1=5sin(  t/2.5)+7 for country A and STOCK2=4cos(  t/3.5)+8 for country B. Please make a 5-panel plot with each time series in one separate panel, and all four time series in the last panel. Please adjust the titles and axes to make the plots look good. The ticknames for x axis should be “Jan”, “Feb”, …, “Dec”.