src/xmaxima_def.lisp

   1 ;; xmaxima.lisp: routines for Maxima's interface to xmaxima
   2 ;; Copyright (C) 2007-2021 J. Villate
   3 ;;
   4 ;; This program is free software; you can redistribute it and/or
   5 ;; modify it under the terms of the GNU General Public License
   6 ;; as published by the Free Software Foundation; either version 2
   7 ;; of the License, or (at your option) any later version.
   8 ;;
   9 ;; This program is distributed in the hope that it will be useful,
  10 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
  11 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12 ;; GNU General Public License for more details.
  13 ;;
  14 ;; You should have received a copy of the GNU General Public License
  15 ;; along with this program; if not, write to the Free Software
  16 ;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
  17 ;; MA  02110-1301, USA
  18
  19 (in-package :maxima)
  20
  21 ;; Given a list of valid colors (see rgb-color function) and an object c
  22 ;; that can be a real number or a string, produces an rgb color
  23 ;; specification for c; when c is real, its nearest integer is assigned
  24 ;; to one of the numbers in the list, using modulo length of the list.
  25 (defun xmaxima-color (colors c)
  26   (unless (listp colors) (setq colors (list colors)))
  27   (when (realp c)
  28     (unless (integerp c) (setq c (round c)))
  29     (setq c (nth (mod (1- c) (length colors)) colors)))
  30   (rgb-color c))
  31
  32 ;; style is a list starting with a symbol from the list: points, lines,
  33 ;; linespoints or dots,
  34 ;; The meaning of the numbers that follow the symbol are:
  35 ;;
  36 ;;   lines, linewidth, color
  37 ;;   points, radius, color
  38 ;;   linespoints, linewidth, radius, color
  39 ;;   dots, color
  40 ;;
  41 ;; linewidth and radius are measured in the same units and can be
  42 ;; floating-point numbers.
  43 ;;
  44 ;; type must be an integer
  45 ;; color can be an integer, used as index to get one of the colors defined
  46 ;; by the color option, or a 6-digit hexadecimal number #rrggbb
  47
  48 (defun xmaxima-curve-style (style colors i)
  49   (unless (listp style) (setq style (list style)))
  50   (unless (listp colors) (setq colors (list colors)))
  51   (with-output-to-string
  52     (st)
  53     (case (first style)
  54       ($dots
  55        (format st "\{ nolines 1 \} \{ plotpoints 1 \} \{ pointsize 0.7 \}")
  56        (if (second style)
  57          (format st " \{ color ~a \}" (xmaxima-color colors (second style)))
  58          (format st " \{ color ~a \}" (xmaxima-color colors i))))
  59       ($lines
  60        (format st "\{ nolines 0 \} \{ plotpoints 0 \}")
  61        (if (realp (second style))
  62          (format st " \{ linewidth ~,2f \}" (second style)))
  63        (if (third style)
  64          (format st " \{ color ~a \}" (xmaxima-color colors (third style)))
  65          (format st " \{ color ~a \}" (xmaxima-color colors i))))
  66       ($points
  67        (format st "\{ nolines 1 \} \{ plotpoints 1 \}")
  68        (if (realp (second style))
  69          (format st " \{ pointsize ~,2f \}" (second style))
  70          (format st " \{ pointsize 3 \}"))
  71        (if (third style)
  72          (format st " \{ color ~a \}" (xmaxima-color colors (third style)))
  73          (format st " \{ color ~a \}" (xmaxima-color colors i))))
  74       ($linespoints
  75        (format st "\{ nolines 0 \} \{ plotpoints 1 \}")
  76        (if (realp (second style))
  77          (format st " \{ linewidth ~,2f \}" (second style)))
  78        (if (realp (third style))
  79          (format st " \{ pointsize ~,2f \}" (third style))
  80          (format st " \{ pointsize 3 \}"))
  81        (if (fourth style)
  82          (format st " \{ color ~a \}" (xmaxima-color colors (fourth style)))
  83          (format st " \{ color ~a \}" (xmaxima-color colors i))))
  84       (t
  85        (format st "\{ nolines 0 \} \{ plotpoints 0 \} \{ color ~a \}"
  86                (xmaxima-color colors i))))))
  87
  88 (defun xmaxima-palette (palette)
  89 ;; palette should be a list starting with one of the symbols: hue,
  90 ;; saturation, value, gray or gradient.
  91 ;;
  92 ;; If the symbol is gray, it should be followed by two floating point
  93 ;; numbers that indicate the initial gray level and the interval of
  94 ;; gray values.
  95 ;;
  96 ;; If the symbol is one of hue, saturation or value, it must be followed
  97 ;; by three numbers that specify the hue, saturation and value for the
  98 ;; initial color, and a fourth number that gives the range of values for
  99 ;; the increment of hue, saturation or value.
 100 ;; The values for the initial hue, saturation, value and grayness should
 101 ;; be within 0 and 1, while the range can be higher or even negative.
 102 ;;
 103 ;; If the symbol is gradient, it must be followed by either a list of valid
 104 ;; colors or by a list of lists with two elements, a number and a valid color.
 105
 106   (unless (listp palette) (setq palette (list palette)))
 107   (let (hue sat val gray range fun)
 108     (case (first palette)
 109       ($gray
 110        (case (length (rest palette))
 111          (2 (setq gray (second palette)) (setq range (third palette)))
 112          (t (merror
 113              (intl:gettext
 114               "palette: gray must be followed by two numbers."))))
 115        (when (or (< gray 0) (> gray 1))
 116          (setq gray (- gray (floor gray))))
 117        (setq fun (format nil "{value ~,8f} {colorrange ~,8f}" gray range)))
 118       (($hue $saturation $value)
 119        (case (length (rest palette))
 120          (4 (setq hue (second palette))
 121             (setq sat (third palette))
 122             (setq val (fourth palette))
 123             (setq range (fifth palette)))
 124          (t (merror
 125              (intl:gettext
 126               "palette: ~M must be followed by four numbers.")
 127               (first palette))))
 128        (when (or (< hue 0) (> hue 1)) (setq hue (- hue (floor hue))))
 129        (when (or (< sat 0) (> sat 1)) (setq sat (- sat (floor sat))))
 130        (when (or (< val 0) (> val 1)) (setq val (- val (floor val))))
 131        (setq fun
 132              (format nil " {hue ~,8f} {saturation ~,8f} {value ~,8f} {colorrange ~,8f}"
 133                      hue sat val range))))
 134     (with-output-to-string (st)
 135       (case (first palette)
 136         ($hue (format st "~&~a {colorscheme hue}" fun))
 137         ($saturation (format st "~&~a {colorscheme saturation}" fun))
 138         ($value (format st "~&~a {colorscheme value}" fun))
 139         ($gray (format st "~&~a {colorscheme gray}" fun))
 140         ($gradient
 141          (let* ((colors (rest palette)) (n (length colors)) (map nil))
 142            ;; map is constructed as (n1 c1 n2 c2 ... nj cj) where ni is a
 143            ;; decreasing sequence of numbers (n1=1, nj=0) and ci are colors
 144            (cond
 145              ;; Maxima list of numbers and colors (((mlist) ni ci) ...)
 146              ((listp (first colors))
 147               (setq colors (sort colors #'< :key #'cadr))
 148               (dotimes (i n)
 149                 (setq map (cons (rgb-color (third (nth i colors))) ;; color
 150                                 (cons
 151                                  (/ (- (second (nth i colors))   ;; ni minus
 152                                        (second (first colors)))  ;; smallest ni
 153                                     (- (second (nth (- n 1) colors));; biggest
 154                                        (second (first colors)))) ;; - smallest
 155                                  map)))))
 156              ;; list of only colors
 157              (t (dotimes (i n)
 158                   (setq map (cons (rgb-color (nth i colors))  ;; color i
 159                                   (cons (/ i (1- n)) map))))))    ;; number i
 160
 161            ;; prints map with the format:  nj, "cj", ...,n1, "c1"
 162            (setq fun (format nil "~{{ ~,8f ~s}~^ ~}" (reverse map)))
 163            (format st "~&{colorscheme gradient} ")
 164            ;; writes: {gradlist {{nj "cj"} ...{n1 "c1"}}}
 165            (format st "{gradlist {~a}}" fun)))
 166         (t
 167          (merror
 168           (intl:gettext
 169            "palette: wrong keyword ~M. Must be hue, saturation, value, gray or gradient.")
 170           (first palette)))))))
 171
 172 (defun xmaxima-palettes (palette n)
 173   (unless (integerp n) (setq n (round n)))
 174   (if (find 'mlist palette :key #'car) (setq palette (list palette)))
 175   (xmaxima-palette (rest (nth (mod (- n 1) (length palette)) palette))))
 176
 177 (defmethod plot-preamble ((plot xmaxima-plot) plot-options)
 178   (let (outfile)
 179     (setf
 180      (slot-value plot 'data)
 181      (concatenate
 182       'string
 183       (slot-value plot 'data)
 184       (with-output-to-string (dest)
 185         (cond ($show_openplot
 186                (format dest "~a -data {~%" (getf plot-options :type)))
 187               (t (format dest "{~a " (getf plot-options :type))))
 188         (when (string= (getf plot-options :type) "plot3d")
 189           (let ((palette (getf plot-options :palette))
 190                 (meshcolor (if (member :mesh_lines_color plot-options)
 191                                (getf plot-options :mesh_lines_color)
 192                                '$black))
 193                 (elev (getf plot-options :elevation))
 194                 (azim (getf plot-options :azimuth)))
 195             (if (find 'mlist palette :key #'car) (setq palette (list palette)))
 196             (if palette
 197                 (progn
 198                   (if meshcolor
 199                       (format dest " {mesh_lines ~a}" (rgb-color meshcolor))
 200                       (format dest " {mesh_lines 0}")))
 201                 (format dest " {colorscheme 0}~%"))
 202             (when elev (format dest " {el ~d}" elev))
 203             (when azim (format dest " {az ~d}" azim))
 204             (format dest "~%")))
 205         (when (getf plot-options :ps_file)
 206           (setq outfile (plot-file-path (getf plot-options :ps_file) t))
 207           (format dest " {psfile ~s}" outfile))
 208         (when (member :legend plot-options)
 209           (unless (getf plot-options :legend)
 210             (format dest " {nolegend 1}")))
 211         (when (member :box plot-options)
 212           (unless (getf plot-options :box)
 213             (format dest " {nobox 1}")))
 214         (if (getf plot-options :axes)
 215             (case (getf plot-options :axes)
 216               ($x (format dest " {axes {x} }"))
 217               ($y (format dest " {axes {y} }"))
 218               (t (format dest " {axes {xy} }")))
 219             (format dest " {axes 0}"))
 220         (when (getf plot-options :x)
 221           (format dest " {xrange ~{~g~^ ~}}" (getf plot-options :x)))
 222         (when (getf plot-options :y)
 223           (format dest " {yrange ~{~g~^ ~}}" (getf plot-options :y)))
 224         (when (getf plot-options :xlabel)
 225           (format dest " {xaxislabel ~s}" (getf plot-options :xlabel)))
 226         (when (getf plot-options :ylabel)
 227           (format dest " {yaxislabel ~s}" (getf plot-options :ylabel)))
 228         (when (getf plot-options :z)
 229           (format $pstream " {zcenter ~g }"
 230                   (/ (apply #'+ (getf plot-options :z)) 2))
 231           (format $pstream " {zradius ~g }~%"
 232                   (/ (apply #'- (getf plot-options :z)) -2)))
 233         (format dest "~%"))))
 234     ;;returns a list with the name of the file to be created, or nil
 235     (if (null outfile) nil (list outfile))))
 236
 237 (defmethod plot2d-command ((plot xmaxima-plot) fun options range)
 238   (let (points-lists)
 239     (setq points-lists
 240           (mapcar #'(lambda (f) (cdr (draw2d f range options))) (cdr fun)))
 241     (when (= (count-if #'(lambda (x) x) points-lists) 0)
 242       (merror (intl:gettext "plot2d: nothing to plot.~%")))
 243     (setf
 244      (slot-value plot 'data)
 245      (concatenate
 246       'string
 247       (slot-value plot 'data)
 248       (with-output-to-string (st)
 249         (let ((legend (getf options :legend))
 250               (colors (getf options :color))
 251               (styles (getf options :style)) (i 0) style plot-name)
 252           (unless (listp legend) (setq legend (list legend)))
 253           (unless (listp colors) (setq colors (list colors)))
 254           (unless (listp styles) (setq styles (list styles)))
 255           (loop for v in (cdr fun) for points-list in points-lists do
 256                (when points-list
 257                  (if styles
 258                      (setq style (nth (mod i (length styles)) styles))
 259                      (setq style nil))
 260                  (when ($listp style) (setq style (cdr style)))
 261                  (incf i)
 262                  ;; label the expression according to the legend,
 263                  ;; unless it is "false" or there is only one expression
 264                  (if (member :legend options)
 265                      (setq plot-name
 266                            (if (first legend)
 267                                (ensure-string
 268                                 (nth (mod (- i 1) (length legend)) legend)) nil))
 269                      (if (= 2 (length fun))
 270                          (setq plot-name nil)
 271                          (progn
 272                            (setq
 273                             plot-name
 274                             (with-output-to-string (pn)
 275                               (cond ((atom v) (format pn "~a" ($sconcat v)))
 276                                     ((eq (second v) '$parametric)
 277                                      (format pn "~a, ~a"
 278                                              ($sconcat (third v))
 279                                              ($sconcat (fourth v))))
 280                                     ((eq (second v) '$discrete)
 281                                      (format pn "discrete~a" i))
 282                                     (t (format pn "~a" ($sconcat v))))))
 283                            (when (> (length plot-name) 50)
 284                              (setq plot-name (format nil "fun~a" i))))))
 285                  (if plot-name
 286                      (format st " {label ~s} " plot-name)
 287                      (format st " {nolegend 1} "))
 288                  (format st (xmaxima-curve-style style colors i))
 289                  (format st "~%{xversusy~%")
 290                  (let ((lis points-list))
 291                    (loop while lis
 292                       do
 293                         (loop while (and lis (not (eq (car lis) 'moveto)))
 294                            collecting (car lis) into xx
 295                            collecting (cadr lis) into yy
 296                            do (setq lis (cddr lis))
 297                            finally
 298                            ;; only output if at least two points for line
 299                              (when (cdr xx)
 300                                (tcl-output-list st xx)
 301                                (tcl-output-list st yy)))
 302                       ;; remove the moveto
 303                         (setq lis (cddr lis))))
 304                  (format st "}")))
 305           (format st "} ")))))))
 306
 307 (defmethod plot3d-command ((plot xmaxima-plot) functions options titles)
 308   (let ((i 0) fun xrange yrange lvars trans)
 309     (setf
 310      (slot-value plot 'data)
 311      (concatenate
 312       'string
 313       (slot-value plot 'data)
 314       (with-output-to-string ($pstream)
 315         ;; generate the mesh points for each surface in the functions stack
 316         (dolist (f functions)
 317           (setq i (+ 1 i))
 318           (setq fun (first f))
 319           (setq xrange (second f))
 320           (setq yrange (third f))
 321           (if ($listp fun)
 322               (progn
 323                 (setq trans
 324                       ($make_transform `((mlist) ,(second xrange)
 325                                          ,(second yrange) $z)
 326                                        (second fun) (third fun) (fourth fun)))
 327                 (setq fun '$zero_fun))
 328               (let*
 329                   ((x0 (third xrange))
 330                    (x1 (fourth xrange))
 331                    (y0 (third yrange))
 332                    (y1 (fourth yrange))
 333                    (xmid (+ x0 (/ (- x1 x0) 2)))
 334                    (ymid (+ y0 (/ (- y1 y0) 2))))
 335                 (setq lvars `((mlist) ,(second xrange) ,(second yrange)))
 336                 (setq fun (coerce-float-fun fun lvars))
 337                 ;; Evaluate FUN at the middle point of the range.
 338                 ;; Looking at a single point is somewhat unreliable.
 339                 ;; Call FUN with numerical arguments (symbolic arguments may
 340                 ;; fail due to trouble computing real/imaginary parts for
 341                 ;; complicated expressions, or it may be a numerical function)
 342                 (when (cdr ($listofvars (mfuncall fun xmid ymid)))
 343                   (mtell
 344                    (intl:gettext
 345                     "plot3d: expected <expr. of v1 and v2>, [v1,min,max], [v2,min,max]~%"))
 346                   (mtell
 347                    (intl:gettext
 348                     "plot3d: keep going and hope for the best.~%")))))
 349           (let* ((pl
 350                   (draw3d
 351                    fun (third xrange) (fourth xrange) (third yrange)
 352                    (fourth yrange) (first (getf options :grid))
 353                    (second (getf options :grid))))
 354                  (ar (polygon-pts pl))
 355                  (colors (getf options :color))
 356                  (palettes (getf options :palette)))
 357             (declare (type (cl:array t) ar))
 358             (when trans (mfuncall trans ar))
 359             (when (getf options :transform_xy)
 360                 (mfuncall (getf options :transform_xy) ar))
 361             (if palettes
 362                    (format $pstream " ~a~%" (xmaxima-palettes palettes i))
 363                    (format $pstream " {mesh_lines ~a}" (xmaxima-color colors i)))
 364               (output-points-tcl $pstream pl (first (getf options :grid)))))
 365         (format $pstream "}~%"))))))
 366
 367 (defmethod plot-shipout ((plot xmaxima-plot) options &optional output-file)
 368   (let ((file (plot-file-path (format nil "maxout~d.xmaxima" (getpid)))))
 369     (cond ($show_openplot
 370            (with-open-file (fl
 371                             #+sbcl (sb-ext:native-namestring file)
 372                             #-sbcl file
 373                             :direction :output :if-exists :supersede)
 374              (princ (slot-value plot 'data) fl))
 375            ($system (concatenate 'string *maxima-prefix*
 376                                  (if (string= *autoconf-windows* "true")
 377                                      "\\bin\\" "/bin/")
 378                                  $xmaxima_plot_command)
 379                     #-(or (and sbcl win32) (and sbcl win64) (and ccl windows))
 380                     (format nil " ~s &" file)
 381                     #+(or (and sbcl win32) (and sbcl win64) (and ccl windows))
 382                     file))
 383           (t (princ (slot-value plot 'data)) ""))
 384     (cons '(mlist) (cons file output-file))))