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File: /usr/local/sage2/local/lib/python2.6/site-packages/sagenb-0.7.5.1-py2.6.egg/sagenb/notebook/interact.py
Type: <type ‘function’>
Definition: interact(f)
Docstring:
Use interact as a decorator to create interactive Sage notebook cells with sliders, text boxes, radio buttons, check boxes, and color selectors. Simply put @interact on the line before a function definition in a cell by itself, and choose appropriate defaults for the variable names to determine the types of controls (see tables below).
INPUT:
- f - a Python function
EXAMPLES:
In each example below we use a single underscore for the function name. You can use any name you want; it does not have to be an underscore.
We create an interact control with two inputs, a text input for the variable a and a y slider that runs through the range of integers from 0 to 19.
sage: @interact ... def _(a=5, y=(0..20)): print a + y ... <html>...Draw a plot interacting with the “continuous” variable a. By default continuous variables have exactly 50 possibilities.
sage: @interact ... def _(a=(0,2)): ... show(plot(sin(x*(1+a*x)), (x,0,6)), figsize=4) <html>...Interact a variable in steps of 1 (we also use an unnamed function):
sage: @interact ... def _(n=(10,100,1)): ... show(factor(x^n - 1)) <html>...Interact two variables:
sage: @interact ... def _(a=(1,4), b=(0,10)): ... show(plot(sin(a*x+b), (x,0,6)), figsize=3) <html>...Place a block of text among the controls:
sage: @interact ... def _(t1=text_control("Factors an integer."), n="1"): ... print factor(Integer(n)) <html>...You do not have to use interact as a decorators; you can also simply write interact(f) where f is any Python function that you have defined, though this is frowned upon. E.g., f can also be a library function as long as it is written in Python:
sage: interact(matrix) # put ZZ, 2,2,[1..4] in boxes... <html>...If your the time to evaluate your function takes awhile, you may not want to have it reevaluated every time the inputs change. In order to prevent this, you can add a keyword auto_update=False to your function to prevent it from updating whenever the values are changed. This will cause a button labeled ‘Update’ to appear which you can click on to re-evaluate your function.
sage: @interact ... def _(n=(10,100,1), auto_update=False): ... show(factor(x^n - 1)) <html>...DEFAULTS:
Defaults for the variables of the input function determine interactive controls. The standard controls are input_box, slider, range_slider, checkbox, selector, input_grid, and color_selector. There is also a text control (see the defaults below).
- u = input_box(default=None, label=None, type=None) - input box with given default; use type=str to get input as an arbitrary string
- u = slider(vmin, vmax=None, step_size=1, default=None, label=None) - slider with given list of possible values; vmin can be a list
- u = range_slider(vmin, vmax=None, step_size=1, default=None, label=None) - range slider with given list of possible values; vmin can be a list
- u = checkbox(default=True, label=None) - a checkbox
- u = selector(values, label=None, nrows=None, ncols=None, buttons=False) - a dropdown menu or buttons (get buttons if nrows, ncols, or buttons is set, otherwise a dropdown menu)
- u = input_grid(nrows, ncols, default=None, label=None, to_value=lambda x:x, width=4) - an editable grid of objects (a matrix or array)
- u = color_selector(default=(0,0,1), label=None, widget='farbtastic', hide_box=False) - a color selector with a possibly hidden input box; the widget can also be 'jpicker' or 'colorpicker'
- u = text_control(value='') - a block of text
You can also create a color selector by setting the default value for an input_box to Color(...).
There are also some convenient defaults that allow you to make controls automatically without having to explicitly specify them. E.g., you can make x a continuous slider of values between u and v by just writing x=(u,v) in the argument list of your function. These are all just convenient shortcuts for creating the controls listed above.
- u - blank input_box field
- u = element - input_box with default=element, if element not below.
- u = (umin,umax) - continuous slider (really 100 steps)
- u = (umin,umax,du) - slider with step size du
- u = list - buttons if len(list) at most 5; otherwise, drop down
- u = generator - a slider (up to 10000 steps)
- u = bool - a checkbox
- u = Color('blue') - a color selector; returns Color object
- u = (default, v) - v as above, with given default value
- u = (label, v) - v as above, with given label (a string)
- u = matrix - an input_grid with to_value set to matrix.parent() and default values given by the matrix
Note
Suppose you would like to make an interactive with a default RGB color of (1,0,0), so the function would have signature f(color=(1,0,0)). Unfortunately, the above shortcuts reinterpret the (1,0,0) as a discrete slider with step size 0 between 1 and 0. Instead you should do the following:
sage: @interact ... def _(v = input_box((1,0,0))): ... show(plot(sin,color=v)) <html>...An alternative:
sage: @interact ... def _(c = color_selector((1, 0, 0))): ... show(plot(sin, color = c)) <html>...MORE EXAMPLES:
We give an input box that allows one to enter completely arbitrary strings:
sage: @interact ... def _(a=input_box('sage', label="Enter your name", type=str)): ... print "Hello there %s"%a.capitalize() <html>...The scope of variables that you control via interact() are local to the scope of the function being interacted with. However, by using the global Python keyword, you can still modify global variables as follows:
sage: xyz = 10 sage: @interact ... def _(a=('xyz',5)): ... global xyz ... xyz = a <html>...If you enter the above you obtain an interact() canvas. Entering values in the box changes the global variable xyz. Here’s a example with several controls:
sage: @interact ... def _(title=["A Plot Demo", "Something silly", "something tricky"], a=input_box(sin(x*sin(x*sin(x))), 'function'), ... clr = Color('red'), thickness=[1..30], zoom=(1,0.95,..,0.1), plot_points=(200..2000)): ... html('<h1 align=center>%s</h1>'%title) ... print plot_points ... show(plot(a, -zoom*pi,zoom*pi, color=clr, thickness=thickness, plot_points=plot_points)) <html>...For a more compact color control, use an empty label, a different widget ('colorpicker' or 'jpicker'), and hide the input box:
sage: @interact ... def _(color=color_selector((1,0,1), label='', widget='colorpicker', hide_box=True)): ... show(plot(x/(8/7+sin(x)), (x,-50,50), fill=True, fillcolor=color)) <html>...We give defaults and name the variables:
sage: @interact ... def _(a=('first', (1,4)), b=(0,10)): ... show(plot(sin(a*x+sin(b*x)), (x,0,6)), figsize=3) <html>...Another example involving labels, defaults, and the slider command:
sage: @interact ... def _(a = slider(1, 4, default=2, label='Multiplier'), ... b = slider(0, 10, default=0, label='Phase Variable')): ... show(plot(sin(a*x+b), (x,0,6)), figsize=4) <html>...An example where the range slider control is useful:
sage: @interact ... def _(b = range_slider(-20, 20, 1, default=(-19,3), label='Range')): ... plot(sin(x)/x, b[0], b[1]).show(xmin=b[0],xmax=b[1]) <html>...An example using checkboxes, obtained by making the default values bools:
sage: @interact ... def _(axes=('Show axes', True), square=False): ... show(plot(sin, -5,5), axes=axes, aspect_ratio = (1 if square else None)) <html>...An example generating a random walk that uses a checkbox control to determine whether points are placed at each step:
sage: @interact ... def foo(pts = checkbox(True, "points"), n = (50,(10..100))): ... s = 0; v = [(0,0)] ... for i in range(n): ... s += random() - 0.5 ... v.append((i, s)) ... L = line(v, rgbcolor='#4a8de2') ... if pts: L += points(v, pointsize=20, rgbcolor='black') ... show(L) <html>...You can rotate and zoom into 3-D graphics while interacting with a variable:
sage: @interact ... def _(a=(0,1)): ... x,y = var('x,y') ... show(plot3d(sin(x*cos(y*a)), (x,0,5), (y,0,5)), figsize=4) <html>...A random polygon:
sage: pts = [(random(), random()) for _ in xrange(20)] sage: @interact ... def _(n = (4..len(pts)), c=Color('purple') ): ... G = points(pts[:n],pointsize=60) + polygon(pts[:n], rgbcolor=c) ... show(G, figsize=5, xmin=0, ymin=0) <html>...Two “sinks” displayed simultaneously via a contour plot and a 3-D interactive plot:
sage: @interact ... def _(q1=(-1,(-3,3)), q2=(-2,(-3,3))): ... x,y = var('x,y') ... f = q1/sqrt((x+1)^2 + y^2) + q2/sqrt((x-1)^2+(y+0.5)^2) ... C = contour_plot(f, (-2,2), (-2,2), plot_points=30, contours=15, cmap='cool') ... show(C, figsize=3, aspect_ratio=1) ... show(plot3d(f, (x,-2,2), (y,-2,2)), figsize=4) <html>...This is similar to above, but you can select the color map from a dropdown menu:
sage: @interact ... def _(q1=(-1,(-3,3)), q2=(-2,(-3,3)), ... cmap=['autumn', 'bone', 'cool', 'copper', 'gray', 'hot', 'hsv', ... 'jet', 'pink', 'prism', 'spring', 'summer', 'winter']): ... x,y = var('x,y') ... f = q1/sqrt((x+1)^2 + y^2) + q2/sqrt((x-1)^2+(y+0.5)^2) ... C = contour_plot(f, (x,-2,2), (y,-2,2), plot_points=30, contours=15, cmap=cmap) ... show(C, figsize=3, aspect_ratio=1) <html>...A quadratic roots etch-a-sketch:
sage: v = [] sage: html('<h2>Quadratic Root Etch-a-sketch</h2>') <html>...<h2>Quadratic Root Etch-a-sketch</h2>...</html> sage: @interact ... def _(a=[-10..10], b=[-10..10], c=[-10..10]): ... f = a*x^2 + b*x + c == 0; show(f) ... soln = solve(a*x^2 + b*x + c == 0, x)[0].rhs() ... show(soln) ... P = tuple(CDF(soln)) ... v.append(P) ... show(line(v, rgbcolor='purple') + point(P, pointsize=200)) <html>...In the following example, we only generate data for a given n once, so that as one varies p the data does not randomly change. We do this by simply caching the results for each n in a dictionary.:
sage: data = {} sage: @interact ... def _(n=(500,(100,5000,1)), p=(1,(0.1,10))): ... n = int(n) ... if not data.has_key(n): ... data[n] = [(random(), random()) for _ in xrange(n)] ... show(points([(x^p,y^p) for x,y in data[n]], rgbcolor='black'), xmin=0, ymin=0, axes=False) <html>...A conchoid:
sage: @interact ... def _(k=(1.2,(1.1,2)), k_2=(1.2,(1.1,2)), a=(1.5,(1.1,2))): ... u, v = var('u,v') ... f = (k^u*(1+cos(v))*cos(u), k^u*(1+cos(v))*sin(u), k^u*sin(v)-a*k_2^u) ... show(parametric_plot3d(f, (u,0,6*pi), (v,0,2*pi), plot_points=[40,40], texture=(0,0.5,0))) <html>...An input grid:
sage: @interact ... def _(A=matrix(QQ,3,3,range(9)), v=matrix(QQ,3,1,range(3))): ... try: ... x = A\v ... html('$$%s %s = %s$$'%(latex(A), latex(x), latex(v))) ... except: ... html('There is no solution to $$%s x=%s$$'%(latex(A), latex(v))) <html>...