1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>Maxima 5.47.0 Manual: Functions and Variables for drawdf</title>
<meta name="description" content="Maxima 5.47.0 Manual: Functions and Variables for drawdf">
<meta name="keywords" content="Maxima 5.47.0 Manual: Functions and Variables for drawdf">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link href="maxima_toc.html#Top" rel="start" title="Top">
<link href="maxima_423.html#Function-and-Variable-Index" rel="index" title="Function and Variable Index">
<link href="maxima_toc.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="maxima_253.html#drawdf_002dpkg" rel="up" title="drawdf-pkg">
<link href="maxima_256.html#dynamics_002dpkg" rel="next" title="dynamics-pkg">
<link href="maxima_254.html#Introduction-to-drawdf" rel="previous" title="Introduction to drawdf">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
body {color: black; background: white; margin-left: 8%; margin-right: 13%;
font-family: "FreeSans", sans-serif}
h1 {font-size: 150%; font-family: "FreeSans", sans-serif}
h2 {font-size: 125%; font-family: "FreeSans", sans-serif}
h3 {font-size: 100%; font-family: "FreeSans", sans-serif}
a[href] {color: rgb(0,0,255); text-decoration: none;}
a[href]:hover {background: rgb(220,220,220);}
div.textbox {border: solid; border-width: thin; padding-top: 1em;
padding-bottom: 1em; padding-left: 2em; padding-right: 2em}
div.titlebox {border: none; padding-top: 1em; padding-bottom: 1em;
padding-left: 2em; padding-right: 2em; background: rgb(200,255,255);
font-family: sans-serif}
div.synopsisbox {
border: none; padding-top: 1em; padding-bottom: 1em; padding-left: 2em;
padding-right: 2em; background: rgb(255,220,255);}
pre.example {border: 1px solid rgb(180,180,180); padding-top: 1em;
padding-bottom: 1em; padding-left: 1em; padding-right: 1em;
background-color: rgb(238,238,255)}
div.spacerbox {border: none; padding-top: 2em; padding-bottom: 2em}
div.image {margin: 0; padding: 1em; text-align: center}
div.categorybox {border: 1px solid gray; padding-top: 1em; padding-bottom: 1em;
padding-left: 1em; padding-right: 1em; background: rgb(247,242,220)}
img {max-width:80%; max-height: 80%; display: block; margin-left: auto; margin-right: auto}
-->
</style>
<link rel="icon" href="figures/favicon.ico">
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6>"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Functions-and-Variables-for-drawdf"></a>
<div class="header">
<p>
Previous: <a href="maxima_254.html#Introduction-to-drawdf" accesskey="p" rel="previous">Introduction to drawdf</a>, Up: <a href="maxima_253.html#drawdf_002dpkg" accesskey="u" rel="up">drawdf-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-drawdf-1"></a>
<h3 class="section">54.2 Functions and Variables for drawdf</h3>
<a name="Functions-1"></a>
<h4 class="subsection">54.2.1 Functions</h4>
<a name="drawdf"></a><a name="Item_003a-drawdf_002fdeffn_002fdrawdf"></a><dl>
<dt><a name="index-drawdf"></a>Function: <strong>drawdf</strong> <em><br> <tt>drawdf</tt> (<var>dydx</var>, ...options and objects...) <br> <tt>drawdf</tt> (<var>dvdu</var>, [<var>u</var>,<var>v</var>], ...options and objects...) <br> <tt>drawdf</tt> (<var>dvdu</var>, [<var>u</var>,<var>umin</var>,<var>umax</var>], [<var>v</var>,<var>vmin</var>,<var>vmax</var>], ...options and objects...) <br> <tt>drawdf</tt> ([<var>dxdt</var>,<var>dydt</var>], ...options and objects...) <br> <tt>drawdf</tt> ([<var>dudt</var>,<var>dvdt</var>], [<var>u</var>,<var>v</var>], ...options and objects...) <br> <tt>drawdf</tt> ([<var>dudt</var>,<var>dvdt</var>], [<var>u</var>,<var>umin</var>,<var>umax</var>], [<var>v</var>,<var>vmin</var>,<var>vmax</var>], ...options and objects...)</em></dt>
<dd>
<p>Function <code>drawdf</code> draws a 2D direction field with optional
solution curves and other graphics using the <code>draw</code> package.
</p>
<p>The first argument specifies the derivative(s), and must be either an
expression or a list of two expressions. <var>dydx</var>, <var>dxdt</var> and
<var>dydt</var> are expressions that depend on <var>x</var> and <var>y</var>.
<var>dvdu</var>, <var>dudt</var> and <var>dvdt</var> are expressions that depend on
<var>u</var> and <var>v</var>.
</p>
<p>If the independent and dependent variables are not <var>x</var> and
<var>y</var>, then their names must be specified immediately following the
derivative(s), either as a list of two names
<code>[</code><var>u</var>,<var>v</var><code>]</code>, or as two lists of the form
<code>[</code><var>u</var>,<var>umin</var>,<var>umax</var><code>]</code> and
<code>[</code><var>v</var>,<var>vmin</var>,<var>vmax</var><code>]</code>.
</p>
<p>The remaining arguments are <i>graphic options</i>, <i>graphic objects</i>,
or lists containing graphic options and objects, nested to arbitrary
depth. The set of graphic options and objects supported by
<code>drawdf</code> is a superset of those supported by <code>draw2d</code> and
<code>gr2d</code> from the <code>draw</code> package.
</p>
<p>The arguments are interpreted sequentially: <i>graphic options</i> affect
all following <i>graphic objects</i>. Furthermore, <i>graphic objects</i>
are drawn on the canvas in order specified, and may obscure graphics
drawn earlier. Some <i>graphic options</i> affect the global appearance
of the scene.
</p>
<p>The additional <i>graphic objects</i> supported by <code>drawdf</code> include:
<code>solns_at</code>, <code>points_at</code>, <code>saddles_at</code>, <code>soln_at</code>,
<code>point_at</code>, and <code>saddle_at</code>.
</p>
<p>The additional <i>graphic options</i> supported by <code>drawdf</code> include:
<code>field_degree</code>, <code>soln_arrows</code>, <code>field_arrows</code>,
<code>field_grid</code>, <code>field_color</code>, <code>show_field</code>,
<code>tstep</code>, <code>nsteps</code>, <code>duration</code>, <code>direction</code>,
<code>field_tstep</code>, <code>field_nsteps</code>, and <code>field_duration</code>.
</p>
<p>Commonly used <i>graphic objects</i> inherited from the <code>draw</code>
package include: <code>explicit</code>, <code>implicit</code>, <code>parametric</code>,
<code>polygon</code>, <code>points</code>, <code>vector</code>, <code>label</code>, and all
others supported by <code>draw2d</code> and <code>gr2d</code>.
</p>
<p>Commonly used <i>graphic options</i> inherited from the <code>draw</code>
package include:<br>
<code>points_joined</code>, <code>color</code>,
<code>point_type</code>, <code>point_size</code>, <code>line_width</code>,
<code>line_type</code>, <code>key</code>, <code>title</code>, <code>xlabel</code>,
<code>ylabel</code>, <code>user_preamble</code>, <code>terminal</code>,
<code>dimensions</code>, <code>file_name</code>, and all
others supported by <code>draw2d</code> and <code>gr2d</code>.
</p>
<p>See also <code><a href="maxima_250.html#draw2d">draw2d</a></code>, <code><a href="maxima_118.html#rk">rk</a></code>, <code><a href="maxima_111.html#desolve">desolve</a></code> and
<code><a href="maxima_111.html#ode2">ode2</a></code>.
</p>
<p>Users of wxMaxima or Imaxima may optionally use <code>wxdrawdf</code>, which
is identical to <code>drawdf</code> except that the graphics are drawn
within the notebook using <code>wxdraw</code>.
</p>
<p>To make use of this function, write first <code>load("drawdf")</code>.
</p>
<p>Examples:
</p>
<div class="example">
<pre class="example">(%i1) load("drawdf")$
(%i2) drawdf(exp(-x)+y)$ /* default vars: x,y */
(%i3) drawdf(exp(-t)+y, [t,y])$ /* default range: [-10,10] */
(%i4) drawdf([y,-9*sin(x)-y/5], [x,1,5], [y,-2,2])$
</pre></div>
<p>For backward compatibility, <code>drawdf</code> accepts
most of the parameters supported by plotdf.
</p>
<div class="example">
<pre class="example">(%i5) drawdf(2*cos(t)-1+y, [t,y], [t,-5,10], [y,-4,9],
[trajectory_at,0,0])$
</pre></div>
<p><code>soln_at</code> and <code>solns_at</code> draw solution curves
passing through the specified points, using a slightly
enhanced 4th-order Runge Kutta numerical integrator.
</p>
<div class="example">
<pre class="example">(%i6) drawdf(2*cos(t)-1+y, [t,-5,10], [y,-4,9],
solns_at([0,0.1],[0,-0.1]),
color=blue, soln_at(0,0))$
</pre></div>
<p><code>field_degree=2</code> causes the field to be composed of quadratic
splines, based on the first and second derivatives at each grid point.
<code>field_grid=[</code><var>COLS</var>,<var>ROWS</var><code>]</code> specifies the number
of columns and rows in the grid.
</p>
<div class="example">
<pre class="example">(%i7) drawdf(2*cos(t)-1+y, [t,-5,10], [y,-4,9],
field_degree=2, field_grid=[20,15],
solns_at([0,0.1],[0,-0.1]),
color=blue, soln_at(0,0))$
</pre></div>
<p><code>soln_arrows=true</code> adds arrows to the solution curves, and (by
default) removes them from the direction field. It also changes the
default colors to emphasize the solution curves.
</p>
<div class="example">
<pre class="example">(%i8) drawdf(2*cos(t)-1+y, [t,-5,10], [y,-4,9],
soln_arrows=true,
solns_at([0,0.1],[0,-0.1],[0,0]))$
</pre></div>
<p><code>duration=40</code> specifies the time duration of numerical
integration (default 10). Integration will also stop automatically if
the solution moves too far away from the plotted region, or if the
derivative becomes complex or infinite. Here we also specify
<code>field_degree=2</code> to plot quadratic splines. The equations below
model a predator-prey system.
</p>
<div class="example">
<pre class="example">(%i9) drawdf([x*(1-x-y), y*(3/4-y-x/2)], [x,0,1.1], [y,0,1],
field_degree=2, duration=40,
soln_arrows=true, point_at(1/2,1/2),
solns_at([0.1,0.2], [0.2,0.1], [1,0.8], [0.8,1],
[0.1,0.1], [0.6,0.05], [0.05,0.4],
[1,0.01], [0.01,0.75]))$
</pre></div>
<p><code>field_degree='solns</code> causes the field to be composed
of many small solution curves computed by 4th-order
Runge Kutta, with better results in this case.
</p>
<div class="example">
<pre class="example">(%i10) drawdf([x*(1-x-y), y*(3/4-y-x/2)], [x,0,1.1], [y,0,1],
field_degree='solns, duration=40,
soln_arrows=true, point_at(1/2,1/2),
solns_at([0.1,0.2], [0.2,0.1], [1,0.8],
[0.8,1], [0.1,0.1], [0.6,0.05],
[0.05,0.4], [1,0.01], [0.01,0.75]))$
</pre></div>
<p><code>saddles_at</code> attempts to automatically linearize the equation at
each saddle, and to plot a numerical solution corresponding to each
eigenvector, including the separatrices. <code>tstep=0.05</code> specifies
the maximum time step for the numerical integrator (the default is
0.1). Note that smaller time steps will sometimes be used in order to
keep the x and y steps small. The equations below model a damped
pendulum.
</p>
<div class="example">
<pre class="example">(%i11) drawdf([y,-9*sin(x)-y/5], tstep=0.05,
soln_arrows=true, point_size=0.5,
points_at([0,0], [2*%pi,0], [-2*%pi,0]),
field_degree='solns,
saddles_at([%pi,0], [-%pi,0]))$
</pre></div>
<p><code>show_field=false</code> suppresses the field entirely.
</p>
<div class="example">
<pre class="example">(%i12) drawdf([y,-9*sin(x)-y/5], tstep=0.05,
show_field=false, soln_arrows=true,
point_size=0.5,
points_at([0,0], [2*%pi,0], [-2*%pi,0]),
saddles_at([3*%pi,0], [-3*%pi,0],
[%pi,0], [-%pi,0]))$
</pre></div>
<p><code>drawdf</code> passes all unrecognized parameters to <code>draw2d</code> or
<code>gr2d</code>, allowing you to combine the full power of the <code>draw</code>
package with <code>drawdf</code>.
</p>
<div class="example">
<pre class="example">(%i13) drawdf(x^2+y^2, [x,-2,2], [y,-2,2], field_color=gray,
key="soln 1", color=black, soln_at(0,0),
key="soln 2", color=red, soln_at(0,1),
key="isocline", color=green, line_width=2,
nticks=100, parametric(cos(t),sin(t),t,0,2*%pi))$
</pre></div>
<p><code>drawdf</code> accepts nested lists of graphic options and objects,
allowing convenient use of makelist and other function calls to
generate graphics.
</p>
<div class="example">
<pre class="example">(%i14) colors : ['red,'blue,'purple,'orange,'green]$
(%i15) drawdf([x-x*y/2, (x*y - 3*y)/4],
[x,2.5,3.5], [y,1.5,2.5],
field_color = gray,
makelist([ key = concat("soln",k),
color = colors[k],
soln_at(3, 2 + k/20) ],
k,1,5))$
</pre></div>
<div class=categorybox>
Categories:<a href="maxima_424.html#Category_003a-Package-drawdf">Package drawdf</a>
·</div>
</dd></dl>
<hr>
<div class="header">
<p>
Previous: <a href="maxima_254.html#Introduction-to-drawdf" accesskey="p" rel="previous">Introduction to drawdf</a>, Up: <a href="maxima_253.html#drawdf_002dpkg" accesskey="u" rel="up">drawdf-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
