[2] | 1 | ;+ |
---|
| 2 | ; NAME: |
---|
| 3 | ; CMAPPLY |
---|
| 4 | ; |
---|
| 5 | ; AUTHOR: |
---|
| 6 | ; Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770 |
---|
| 7 | ; craigm@lheamail.gsfc.nasa.gov |
---|
| 8 | ; |
---|
| 9 | ; PURPOSE: |
---|
| 10 | ; Applies a function to specified dimensions of an array |
---|
| 11 | ; |
---|
| 12 | ; MAJOR TOPICS: |
---|
| 13 | ; Arrays |
---|
| 14 | ; |
---|
| 15 | ; CALLING SEQUENCE: |
---|
| 16 | ; XX = CMAPPLY(OP, ARRAY, DIMS, [/DOUBLE], [TYPE=TYPE]) |
---|
| 17 | ; |
---|
| 18 | ; DESCRIPTION: |
---|
| 19 | ; CMAPPLY will apply one of a few select functions to specified |
---|
| 20 | ; dimensions of an array. Unlike some IDL functions, you *do* have |
---|
| 21 | ; a choice of which dimensions that are to be "collapsed" by this |
---|
| 22 | ; function. Iterative loops are avoided where possible, for |
---|
| 23 | ; performance reasons. |
---|
| 24 | ; |
---|
| 25 | ; The possible functions are: (and number of loop iterations:) |
---|
| 26 | ; + - Performs a sum (as in TOTAL) number of collapsed dimensions |
---|
| 27 | ; AND - Finds LOGICAL "AND" (not bitwise) same |
---|
| 28 | ; OR - Finds LOGICAL "OR" (not bitwise) same |
---|
[31] | 29 | ; * - Performs a product LOG_2[no. of collapsed elts.] |
---|
[2] | 30 | ; |
---|
[31] | 31 | ; MIN - Finds the minimum value smaller of no. of collapsed |
---|
| 32 | ; MAX - Finds the maximum value or output elements |
---|
[2] | 33 | ; |
---|
[31] | 34 | ; USER - Applies user-defined function no. of output elements |
---|
| 35 | ; |
---|
| 36 | ; |
---|
| 37 | ; It is possible to perform user-defined operations arrays using |
---|
| 38 | ; CMAPPLY. The OP parameter is set to 'USER:FUNCTNAME', where |
---|
| 39 | ; FUNCTNAME is the name of a user-defined function. The user |
---|
| 40 | ; defined function should be defined such that it accepts a single |
---|
| 41 | ; parameter, a vector, and returns a single scalar value. Here is a |
---|
| 42 | ; prototype for the function definition: |
---|
| 43 | ; |
---|
| 44 | ; FUNCTION FUNCTNAME, x, KEYWORD1=key1, ... |
---|
| 45 | ; scalar = ... function of x or keywords ... |
---|
| 46 | ; RETURN, scalar |
---|
| 47 | ; END |
---|
| 48 | ; |
---|
| 49 | ; The function may accept keywords. Keyword values are passed in to |
---|
| 50 | ; CMAPPLY through the FUNCTARGS keywords parameter, and passed to |
---|
| 51 | ; the user function via the _EXTRA mechanism. Thus, while the |
---|
| 52 | ; definition of the user function is highly constrained in the |
---|
| 53 | ; number of positional parameters, there is absolute freedom in |
---|
| 54 | ; passing keyword parameters. |
---|
| 55 | ; |
---|
| 56 | ; It's worth noting however, that the implementation of user-defined |
---|
| 57 | ; functions is not particularly optimized for speed. Users are |
---|
| 58 | ; encouraged to implement their own array if the number of output |
---|
| 59 | ; elements is large. |
---|
| 60 | ; |
---|
| 61 | ; |
---|
[2] | 62 | ; INPUTS: |
---|
| 63 | ; |
---|
| 64 | ; OP - The operation to perform, as a string. May be upper or lower |
---|
| 65 | ; case. |
---|
| 66 | ; |
---|
[31] | 67 | ; If a user-defined operation is to be passed, then OP is of |
---|
| 68 | ; the form, 'USER:FUNCTNAME', where FUNCTNAME is the name of |
---|
| 69 | ; the user-defined function. |
---|
| 70 | ; |
---|
[2] | 71 | ; ARRAY - An array of values to be operated on. Must not be of type |
---|
| 72 | ; STRING (7) or STRUCTURE (8). |
---|
| 73 | ; |
---|
| 74 | ; OPTIONAL INPUTS: |
---|
| 75 | ; |
---|
| 76 | ; DIMS - An array of dimensions that are to be "collapsed", where |
---|
| 77 | ; the the first dimension starts with 1 (ie, same convention |
---|
| 78 | ; as IDL function TOTAL). Whereas TOTAL only allows one |
---|
| 79 | ; dimension to be added, you can specify multiple dimensions |
---|
| 80 | ; to CMAPPLY. Order does not matter, since all operations |
---|
| 81 | ; are associative and transitive. NOTE: the dimensions refer |
---|
| 82 | ; to the *input* array, not the output array. IDL allows a |
---|
| 83 | ; maximum of 8 dimensions. |
---|
| 84 | ; DEFAULT: 1 (ie, first dimension) |
---|
| 85 | ; |
---|
| 86 | ; KEYWORDS: |
---|
| 87 | ; |
---|
| 88 | ; DOUBLE - Set this if you wish the internal computations to be done |
---|
| 89 | ; in double precision if necessary. If ARRAY is double |
---|
| 90 | ; precision (real or complex) then DOUBLE=1 is implied. |
---|
| 91 | ; DEFAULT: not set |
---|
| 92 | ; |
---|
| 93 | ; TYPE - Set this to the IDL code of the desired output type (refer |
---|
| 94 | ; to documentation of SIZE()). Internal results will be |
---|
| 95 | ; rounded to the nearest integer if the output type is an |
---|
| 96 | ; integer type. |
---|
| 97 | ; DEFAULT: same is input type |
---|
| 98 | ; |
---|
[31] | 99 | ; FUNCTARGS - If OP is 'USER:...', then the contents of this keyword |
---|
| 100 | ; are passed to the user function using the _EXTRA |
---|
| 101 | ; mechanism. This way you can pass additional data to |
---|
| 102 | ; your user-supplied function, via keywords, without |
---|
| 103 | ; using common blocks. |
---|
| 104 | ; DEFAULT: undefined (i.e., no keywords passed by _EXTRA) |
---|
| 105 | ; |
---|
[2] | 106 | ; RETURN VALUE: |
---|
| 107 | ; |
---|
| 108 | ; An array of the required TYPE, whose elements are the result of |
---|
| 109 | ; the requested operation. Depending on the operation and number of |
---|
| 110 | ; elements in the input array, the result may be vulnerable to |
---|
| 111 | ; overflow or underflow. |
---|
| 112 | ; |
---|
| 113 | ; EXAMPLES: |
---|
| 114 | ; Shows how CMAPPLY can be used to total the second dimension of the |
---|
| 115 | ; array called IN. This is equivalent to OUT = TOTAL(IN, 2) |
---|
| 116 | ; |
---|
| 117 | ; IDL> IN = INDGEN(5,5) |
---|
| 118 | ; IDL> OUT = CMAPPLY('+', IN, [2]) |
---|
| 119 | ; IDL> HELP, OUT |
---|
| 120 | ; OUT INT = Array[5] |
---|
| 121 | ; |
---|
| 122 | ; Second example. Input is assumed to be an 5x100 array of 1's and |
---|
| 123 | ; 0's indicating the status of 5 detectors at 100 points in time. |
---|
| 124 | ; The desired output is an array of 100 values, indicating whether |
---|
| 125 | ; all 5 detectors are on (=1) at one time. Use the logical AND |
---|
| 126 | ; operation. |
---|
| 127 | ; |
---|
| 128 | ; IDL> IN = detector_status ; 5x100 array |
---|
| 129 | ; IDL> OUT = CMAPPLY('AND', IN, [1]) ; collapses 1st dimension |
---|
| 130 | ; IDL> HELP, OUT |
---|
| 131 | ; OUT BYTE = Array[100] |
---|
| 132 | ; |
---|
| 133 | ; (note that MIN could also have been used in this particular case, |
---|
| 134 | ; although there would have been more loop iterations). |
---|
| 135 | ; |
---|
| 136 | ; Third example. Shows sum over first and third dimensions in an |
---|
| 137 | ; array with dimensions 4x4x4: |
---|
| 138 | ; |
---|
| 139 | ; IDL> IN = INDGEN(4,4,4) |
---|
| 140 | ; IDL> OUT = CMAPPLY('+', IN, [1,3]) |
---|
| 141 | ; IDL> PRINT, OUT |
---|
| 142 | ; 408 472 536 600 |
---|
| 143 | ; |
---|
[31] | 144 | ; Fourth example. A user-function (MEDIAN) is used: |
---|
| 145 | ; |
---|
| 146 | ; IDL> IN = RANDOMN(SEED,10,10,5) |
---|
| 147 | ; IDL> OUT = CMAPPLY('USER:MEDIAN', IN, 3) |
---|
| 148 | ; IDL> HELP, OUT |
---|
| 149 | ; OUT FLOAT = Array[10, 10] |
---|
| 150 | ; |
---|
| 151 | ; (OUT(i,j) is the median value of IN(i,j,*)) |
---|
| 152 | ; |
---|
[2] | 153 | ; MODIFICATION HISTORY: |
---|
| 154 | ; Mar 1998, Written, CM |
---|
[31] | 155 | ; Changed usage message to not bomb, 24 Mar 2000, CM |
---|
| 156 | ; Signficant rewrite for *, MIN and MAX (inspired by Todd Clements |
---|
| 157 | ; <Todd_Clements@alumni.hmc.edu>); FOR loop indices are now type |
---|
| 158 | ; LONG; copying terms are liberalized, CM, 22, Aug 2000 |
---|
| 159 | ; More efficient MAX/MIN (inspired by Alex Schuster), CM, 25 Jan |
---|
| 160 | ; 2002 |
---|
| 161 | ; Make new MAX/MIN actually work with 3d arrays, CM, 08 Feb 2002 |
---|
| 162 | ; Add user-defined functions, ON_ERROR, CM, 09 Feb 2002 |
---|
| 163 | ; Correct bug in MAX/MIN initialization of RESULT, CM, 05 Dec 2002 |
---|
[2] | 164 | ; |
---|
[31] | 165 | ; $Id$ |
---|
| 166 | ; |
---|
[2] | 167 | ;- |
---|
[31] | 168 | ; Copyright (C) 1998, 2000, 2002, Craig Markwardt |
---|
| 169 | ; This software is provided as is without any warranty whatsoever. |
---|
| 170 | ; Permission to use, copy, modify, and distribute modified or |
---|
| 171 | ; unmodified copies is granted, provided this copyright and disclaimer |
---|
| 172 | ; are included unchanged. |
---|
| 173 | ;- |
---|
[2] | 174 | |
---|
[31] | 175 | ;; Utility function, adapted from CMPRODUCT |
---|
| 176 | function cmapply_product, x |
---|
| 177 | sz = size(x) |
---|
| 178 | n = sz(1) |
---|
[2] | 179 | |
---|
[31] | 180 | while n GT 1 do begin |
---|
| 181 | if (n mod 2) EQ 1 then x(0,*) = x(0,*) * x(n-1,*) |
---|
| 182 | n2 = floor(n/2) |
---|
| 183 | x = x(0:n2-1,*) * x(n2:*,*) |
---|
| 184 | n = n2 |
---|
| 185 | endwhile |
---|
| 186 | return, reform(x(0,*), /overwrite) |
---|
| 187 | end |
---|
| 188 | |
---|
| 189 | ;; Utility function, used to collect collaped dimensions |
---|
| 190 | pro cmapply_redim, newarr, dimapply, dimkeep, nkeep, totcol, totkeep |
---|
| 191 | sz = size(newarr) |
---|
| 192 | ;; First task: rearrange dimensions so that the dimensions |
---|
| 193 | ;; that are "kept" (ie, uncollapsed) are at the back |
---|
| 194 | dimkeep = where(histogram(dimapply,min=1,max=sz(0)) ne 1, nkeep) |
---|
| 195 | if nkeep EQ 0 then return |
---|
| 196 | |
---|
| 197 | newarr = transpose(temporary(newarr), [dimapply-1, dimkeep]) |
---|
| 198 | ;; totcol is the total number of collapsed elements |
---|
| 199 | totcol = sz(dimapply(0)) |
---|
| 200 | for i = 1, n_elements(dimapply)-1 do totcol = totcol * sz(dimapply(i)) |
---|
| 201 | totkeep = sz(dimkeep(0)+1) |
---|
| 202 | for i = 1, n_elements(dimkeep)-1 do totkeep = totkeep * sz(dimkeep(i)+1) |
---|
| 203 | |
---|
| 204 | ;; this new array has two dimensions: |
---|
| 205 | ;; * the first, all elements that will be collapsed |
---|
| 206 | ;; * the second, all dimensions that will be preserved |
---|
| 207 | ;; (the ordering is so that all elements to be collapsed are |
---|
| 208 | ;; adjacent in memory) |
---|
| 209 | newarr = reform(newarr, [totcol, totkeep], /overwrite) |
---|
| 210 | end |
---|
| 211 | |
---|
| 212 | ;; Main function |
---|
| 213 | function cmapply, op, array, dimapply, double=dbl, type=type, $ |
---|
| 214 | functargs=functargs, nocatch=nocatch |
---|
| 215 | |
---|
[2] | 216 | if n_params() LT 2 then begin |
---|
| 217 | message, "USAGE: XX = CMAPPLY('OP',ARRAY,2)", /info |
---|
[31] | 218 | message, ' where OP is +, *, AND, OR, MIN, MAX', /info |
---|
[2] | 219 | return, -1L |
---|
| 220 | endif |
---|
[31] | 221 | if NOT keyword_set(nocatch) then $ |
---|
| 222 | on_error, 2 $ |
---|
| 223 | else $ |
---|
| 224 | on_error, 0 |
---|
[2] | 225 | |
---|
| 226 | ;; Parameter checking |
---|
| 227 | ;; 1) the dimensions of the array |
---|
| 228 | sz = size(array) |
---|
| 229 | if sz(0) EQ 0 then $ |
---|
| 230 | message, 'ERROR: ARRAY must be an array!' |
---|
| 231 | |
---|
| 232 | ;; 2) The type of the array |
---|
| 233 | if sz(sz(0)+1) EQ 0 OR sz(sz(0)+1) EQ 7 OR sz(sz(0)+1) EQ 8 then $ |
---|
| 234 | message, 'ERROR: Cannot apply to UNDEFINED, STRING, or STRUCTURE' |
---|
| 235 | if n_elements(type) EQ 0 then type = sz(sz(0)+1) |
---|
| 236 | |
---|
| 237 | ;; 3) The type of the operation |
---|
| 238 | szop = size(op) |
---|
| 239 | if szop(szop(0)+1) NE 7 then $ |
---|
| 240 | message, 'ERROR: operation OP was not a string' |
---|
| 241 | |
---|
| 242 | ;; 4) The dimensions to apply (default is to apply to first dim) |
---|
| 243 | if n_params() EQ 2 then dimapply = 1 |
---|
| 244 | dimapply = [ dimapply ] |
---|
| 245 | dimapply = dimapply(sort(dimapply)) ; Sort in ascending order |
---|
| 246 | napply = n_elements(dimapply) |
---|
| 247 | |
---|
| 248 | ;; 5) Use double precision if requested or if needed |
---|
| 249 | if n_elements(dbl) EQ 0 then begin |
---|
| 250 | dbl=0 |
---|
| 251 | if type EQ 5 OR type EQ 9 then dbl=1 |
---|
| 252 | endif |
---|
| 253 | |
---|
| 254 | newop = strupcase(op) |
---|
| 255 | newarr = array |
---|
| 256 | newarr = reform(newarr, sz(1:sz(0)), /overwrite) |
---|
| 257 | case 1 of |
---|
| 258 | |
---|
| 259 | ;; *** Addition |
---|
| 260 | (newop EQ '+'): begin |
---|
[31] | 261 | for i = 0L, napply-1 do begin |
---|
[2] | 262 | newarr = total(temporary(newarr), dimapply(i)-i, double=dbl) |
---|
| 263 | endfor |
---|
| 264 | end |
---|
| 265 | |
---|
| 266 | ;; *** Multiplication |
---|
| 267 | (newop EQ '*'): begin ;; Multiplication (by summation of logarithms) |
---|
[31] | 268 | cmapply_redim, newarr, dimapply, dimkeep, nkeep, totcol, totkeep |
---|
| 269 | if nkeep EQ 0 then begin |
---|
| 270 | newarr = reform(newarr, n_elements(newarr), 1, /overwrite) |
---|
| 271 | return, (cmapply_product(newarr))(0) |
---|
| 272 | endif |
---|
| 273 | |
---|
| 274 | result = cmapply_product(newarr) |
---|
| 275 | result = reform(result, sz(dimkeep+1), /overwrite) |
---|
| 276 | return, result |
---|
[2] | 277 | end |
---|
| 278 | |
---|
| 279 | ;; *** LOGICAL AND or OR |
---|
| 280 | ((newop EQ 'AND') OR (newop EQ 'OR')): begin |
---|
| 281 | newarr = temporary(newarr) NE 0 |
---|
| 282 | totelt = 1L |
---|
[31] | 283 | for i = 0L, napply-1 do begin |
---|
[2] | 284 | newarr = total(temporary(newarr), dimapply(i)-i) |
---|
| 285 | totelt = totelt * sz(dimapply(i)) |
---|
| 286 | endfor |
---|
| 287 | if newop EQ 'AND' then return, (round(newarr) EQ totelt) |
---|
| 288 | if newop EQ 'OR' then return, (round(newarr) NE 0) |
---|
| 289 | end |
---|
| 290 | |
---|
[31] | 291 | ;; Operations requiring a little more attention over how to |
---|
| 292 | ;; iterate |
---|
[2] | 293 | ((newop EQ 'MAX') OR (newop EQ 'MIN')): begin |
---|
[31] | 294 | cmapply_redim, newarr, dimapply, dimkeep, nkeep, totcol, totkeep |
---|
| 295 | if nkeep EQ 0 then begin |
---|
| 296 | if newop EQ 'MAX' then return, max(newarr) |
---|
| 297 | if newop EQ 'MIN' then return, min(newarr) |
---|
| 298 | endif |
---|
| 299 | |
---|
| 300 | ;; Next task: create result array |
---|
| 301 | result = make_array(totkeep, type=type) |
---|
| 302 | |
---|
| 303 | ;; Now either iterate over the number of output elements, or |
---|
| 304 | ;; the number of collapsed elements, whichever is smaller. |
---|
| 305 | if totcol LT totkeep then begin |
---|
| 306 | ;; Iterate over the number of collapsed elements |
---|
| 307 | result(0) = reform(newarr(0,*),totkeep,/overwrite) |
---|
| 308 | case newop of |
---|
| 309 | 'MAX': for i = 1L, totcol-1 do $ |
---|
| 310 | result(0) = result > newarr(i,*) |
---|
| 311 | 'MIN': for i = 1L, totcol-1 do $ |
---|
| 312 | result(0) = result < newarr(i,*) |
---|
[2] | 313 | endcase |
---|
[31] | 314 | endif else begin |
---|
| 315 | ;; Iterate over the number of output elements |
---|
| 316 | case newop of |
---|
| 317 | 'MAX': for i = 0L, totkeep-1 do result(i) = max(newarr(*,i)) |
---|
| 318 | 'MIN': for i = 0L, totkeep-1 do result(i) = min(newarr(*,i)) |
---|
| 319 | endcase |
---|
| 320 | endelse |
---|
| 321 | |
---|
| 322 | result = reform(result, sz(dimkeep+1), /overwrite) |
---|
| 323 | return, result |
---|
| 324 | end |
---|
| 325 | |
---|
| 326 | ;; User function |
---|
| 327 | (strmid(newop,0,4) EQ 'USER'): begin |
---|
| 328 | functname = strmid(newop,5) |
---|
| 329 | if functname EQ '' then $ |
---|
| 330 | message, 'ERROR: '+newop+' is not a valid operation' |
---|
| 331 | |
---|
| 332 | cmapply_redim, newarr, dimapply, dimkeep, nkeep, totcol, totkeep |
---|
| 333 | if nkeep EQ 0 then begin |
---|
| 334 | if n_elements(functargs) GT 0 then $ |
---|
| 335 | return, call_function(functname, newarr, _EXTRA=functargs) |
---|
| 336 | return, call_function(functname, newarr) |
---|
[2] | 337 | endif |
---|
| 338 | |
---|
| 339 | ;; Next task: create result array |
---|
[31] | 340 | result = make_array(totkeep, type=type) |
---|
| 341 | |
---|
| 342 | ;; Iterate over the number of output elements |
---|
| 343 | if n_elements(functargs) GT 0 then begin |
---|
| 344 | for i = 0L, totkeep-1 do $ |
---|
| 345 | result(i) = call_function(functname, newarr(*,i), _EXTRA=functargs) |
---|
| 346 | endif else begin |
---|
| 347 | for i = 0L, totkeep-1 do $ |
---|
| 348 | result(i) = call_function(functname, newarr(*,i)) |
---|
| 349 | endelse |
---|
[2] | 350 | |
---|
[31] | 351 | result = reform(result, sz(dimkeep+1), /overwrite) |
---|
[2] | 352 | return, result |
---|
| 353 | end |
---|
[31] | 354 | |
---|
[2] | 355 | |
---|
| 356 | endcase |
---|
| 357 | |
---|
| 358 | newsz = size(newarr) |
---|
| 359 | if type EQ newsz(newsz(0)+1) then return, newarr |
---|
| 360 | |
---|
| 361 | ;; Cast the result into the desired type, if necessary |
---|
| 362 | castfns = ['UNDEF', 'BYTE', 'FIX', 'LONG', 'FLOAT', $ |
---|
| 363 | 'DOUBLE', 'COMPLEX', 'UNDEF', 'UNDEF', 'DCOMPLEX' ] |
---|
| 364 | if type GE 1 AND type LE 3 then $ |
---|
| 365 | return, call_function(castfns(type), round(newarr)) $ |
---|
| 366 | else $ |
---|
| 367 | return, call_function(castfns(type), newarr) |
---|
| 368 | end |
---|
[31] | 369 | |
---|