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== Bioinformatics == === Web app: protein browser === by Marshall Hampton (tested by William Stein) {{{ import urllib2 as U @interact def protein_browser(GenBank_ID = input_box('165940577', type = str), file_type = selector([(1,'fasta'),(2,'GenPept')])): if file_type == 2: gen_str = 'http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?db=protein&sendto=t&id=' else: gen_str = 'http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?db=protein&sendto=t&dopt=fasta&id=' f = U.urlopen(gen_str + GenBank_ID) g = f.read() f.close() html(g) }}} attachment:biobrowse.png === Coalescent simulator === by Marshall Hampton {{{ def next_gen(x, selection=1.0): '''Creates the next generation from the previous; also returns parent-child indexing list''' next_x = [] for ind in range(len(x)): if random() < (1 + selection)/len(x): rind = 0 else: rind = int(round(random()*(len(x)-1)+1/2)) next_x.append((x[rind],rind)) next_x.sort() return [[x[0] for x in next_x],[x[1] for x in next_x]] def coal_plot(some_data): '''Creates a graphics object from coalescent data''' gens = some_data[0] inds = some_data[1] gen_lines = line([[0,0]]) pts = Graphics() ngens = len(gens) gen_size = len(gens[0]) for x in range(gen_size): pts += point((x,ngens-1), hue = gens[0][x]/float(gen_size*1.1)) p_frame = line([[-.5,-.5],[-.5,ngens-.5], [gen_size-.5,ngens-.5], [gen_size-.5,-.5], [-.5,-.5]]) for g in range(1,ngens): for x in range(gen_size): old_x = inds[g-1][x] gen_lines += line([[x,ngens-g-1],[old_x,ngens-g]], hue = gens[g-1][old_x]/float(gen_size*1.1)) pts += point((x,ngens-g-1), hue = gens[g][x]/float(gen_size*1.1)) return pts+gen_lines+p_frame d_field = RealField(10) @interact def coalescents(pop_size = slider(2,100,1,15,'Population size'), selection = slider(-1,1,.1,0, 'Selection for first taxon'), s = selector(['Again!'], label='Refresh', buttons=True)): print 'Population size: ' + str(pop_size) print 'Selection coefficient for first taxon: ' + str(d_field(selection)) start = [i for i in range(pop_size)] gens = [start] inds = [] while gens[-1][0] != gens[-1][-1]: g_index = len(gens) - 1 n_gen = next_gen(gens[g_index], selection = selection) gens.append(n_gen[0]) inds.append(n_gen[1]) coal_data1 = [gens,inds] print 'Generations until coalescence: ' + str(len(gens)) show(coal_plot(coal_data1), axes = False, figsize = [8,4.0*len(gens)/pop_size], ymax = len(gens)-1) }}} attachment:coalescent.png == Miscellaneous Graphics == === Catalog of 3D Parametric Plots === {{{ var('u,v') plots = ['Two Interlinked Tori', 'Star of David', 'Double Heart', 'Heart', 'Green bowtie', "Boy's Surface", "Maeder's Owl", 'Cross cap'] plots.sort() @interact def _(example=selector(plots, buttons=True, nrows=2), tachyon=("Raytrace", False), frame = ('Frame', False), opacity=(1,(0.1,1))): url = '' if example == 'Two Interlinked Tori': f1 = (4+(3+cos(v))*sin(u), 4+(3+cos(v))*cos(u), 4+sin(v)) f2 = (8+(3+cos(v))*cos(u), 3+sin(v), 4+(3+cos(v))*sin(u)) p1 = parametric_plot3d(f1, (u,0,2*pi), (v,0,2*pi), color="red", opacity=opacity) p2 = parametric_plot3d(f2, (u,0,2*pi), (v,0,2*pi), color="blue",opacity=opacity) P = p1 + p2 elif example == 'Star of David': f_x = cos(u)*cos(v)*(abs(cos(3*v/4))^500 + abs(sin(3*v/4))^500)^(-1/260)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200) f_y = cos(u)*sin(v)*(abs(cos(3*v/4))^500 + abs(sin(3*v/4))^500)^(-1/260)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200) f_z = sin(u)*(abs(cos(4*u/4))^200 + abs(sin(4*u/4))^200)^(-1/200) P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, 0, 2*pi),opacity=opacity) elif example == 'Double Heart': f_x = ( abs(v) - abs(u) - abs(tanh((1/sqrt(2))*u)/(1/sqrt(2))) + abs(tanh((1/sqrt(2))*v)/(1/sqrt(2))) )*sin(v) f_y = ( abs(v) - abs(u) - abs(tanh((1/sqrt(2))*u)/(1/sqrt(2))) - abs(tanh((1/sqrt(2))*v)/(1/sqrt(2))) )*cos(v) f_z = sin(u)*(abs(cos(4*u/4))^1 + abs(sin(4*u/4))^1)^(-1/1) P = parametric_plot3d([f_x, f_y, f_z], (u, 0, pi), (v, -pi, pi),opacity=opacity) elif example == 'Heart': f_x = cos(u)*(4*sqrt(1-v^2)*sin(abs(u))^abs(u)) f_y = sin(u) *(4*sqrt(1-v^2)*sin(abs(u))^abs(u)) f_z = v P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, -1, 1), frame=False, color="red",opacity=opacity) elif example == 'Green bowtie': f_x = sin(u) / (sqrt(2) + sin(v)) f_y = sin(u) / (sqrt(2) + cos(v)) f_z = cos(u) / (1 + sqrt(2)) P = parametric_plot3d([f_x, f_y, f_z], (u, -pi, pi), (v, -pi, pi), frame=False, color="green",opacity=opacity) elif example == "Boy's Surface": url = "http://en.wikipedia.org/wiki/Boy's_surface" fx = 2/3* (cos(u)* cos(2*v) + sqrt(2)* sin(u)* cos(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v)) fy = 2/3* (cos(u)* sin(2*v) - sqrt(2)* sin(u)* sin(v))* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v)) fz = sqrt(2)* cos(u)* cos(u) / (sqrt(2) - sin(2*u)* sin(3*v)) P = parametric_plot3d([fx, fy, fz], (u, -2*pi, 2*pi), (v, 0, pi), plot_points = [90,90], frame=False, color="orange",opacity=opacity) elif example == "Maeder's Owl": fx = v *cos(u) - 0.5* v^2 * cos(2* u) fy = -v *sin(u) - 0.5* v^2 * sin(2* u) fz = 4 *v^1.5 * cos(3 *u / 2) / 3 P = parametric_plot3d([fx, fy, fz], (u, -2*pi, 2*pi), (v, 0, 1),plot_points = [90,90], frame=False, color="purple",opacity=opacity) elif example =='Cross cap': url = 'http://en.wikipedia.org/wiki/Cross-cap' fx = (1+cos(v))*cos(u) fy = (1+cos(v))*sin(u) fz = -tanh((2/3)*(u-pi))*sin(v) P = parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0, 2*pi), frame=False, color="red",opacity=opacity) else: print "Bug selecting plot?" return html('<h2>%s</h2>'%example) if url: html('<h3><a target="_new" href="%s">%s</a></h3>'%(url,url)) show(P, viewer='tachyon' if tachyon else 'jmol', frame=frame) }}} attachment:parametricplot3d.png === Interactive rotatable raytracing with Tachyon3d === {{{ C = cube(color=['red', 'green', 'blue'], aspect_ratio=[1,1,1], viewer='tachyon') + sphere((1,0,0),0.2) @interact def example(theta=(0,2*pi), phi=(0,2*pi), zoom=(1,(1,4))): show(C.rotate((0,0,1), theta).rotate((0,1,0),phi), zoom=zoom) }}} attachment:tachyonrotate.png === Interactive 3d plotting === {{{ var('x,y') @interact def example(clr=Color('orange'), f=4*x*exp(-x^2-y^2), xrange='(-2, 2)', yrange='(-2,2)', zrot=(0,pi), xrot=(0,pi), zoom=(1,(1/2,3)), square_aspect=('Square Frame', False), tachyon=('Ray Tracer', True)): xmin, xmax = sage_eval(xrange); ymin, ymax = sage_eval(yrange) P = plot3d(f, (x, xmin, xmax), (y, ymin, ymax), color=clr) html('<h1>Plot of $f(x,y) = %s$</h1>'%latex(f)) aspect_ratio = [1,1,1] if square_aspect else [1,1,1/2] show(P.rotate((0,0,1), -zrot).rotate((1,0,0),xrot), viewer='tachyon' if tachyon else 'jmol', figsize=6, zoom=zoom, frame=False, frame_aspect_ratio=aspect_ratio) }}} attachment:tachyonplot3d.png [[Anchor(eggpaint)]] === Somewhat Silly Egg Painter === by Marshall Hampton (refereed by William Stein) {{{ var('s,t') g(s) = ((0.57496*sqrt(121 - 16.0*s^2))/sqrt(10.+ s)) def P(color, rng): return parametric_plot3d((cos(t)*g(s), sin(t)*g(s), s), (s,rng[0],rng[1]), (t,0,2*pi), plot_points = [150,150], rgbcolor=color, frame = False, opacity = 1) colorlist = ['red','blue','red','blue'] @interact def _(band_number = selector(range(1,5)), current_color = Color('red')): html('<h1 align=center>Egg Painter</h1>') colorlist[band_number-1] = current_color egg = sum([P(colorlist[i],[-2.75+5.5*(i/4),-2.75+5.5*(i+1)/4]) for i in range(4)]) show(egg) }}} attachment:eggpaint.png |
* [:interact/bio:Bioinformatics] * [:interact/graphics:Drawing Graphics] |
Sage Interactions
Post code that demonstrates the use of the interact command in Sage here. It should be easy to just scroll through and paste examples out of here into their own sage notebooks.If you have suggestions on how to improve interact, add them [:interactSuggestions: here] or email [email protected].
- [:interact/graph_theory:Graph Theory]
- [:interact/calculus:Calculus]
- [:interact/diffeq:Differential Equations]
- [:interact/linear_algebra:Linear Algebra]
- [:interact/algebra:Algebra]
- [:interact/number_theory:Number Theory]
- [:interact/web:Web Applications]
- [:interact/bio:Bioinformatics]
- [:interact/graphics:Drawing Graphics]
Miscellaneous
Profile a snippet of code
html('<h2>Profile the given input</h2>')
import cProfile; import profile
@interact
def _(cmd = ("Statement", '2 + 2'),
do_preparse=("Preparse?", True), cprof =("cProfile?", False)):
if do_preparse: cmd = preparse(cmd)
print "<html>" # trick to avoid word wrap
if cprof:
cProfile.run(cmd)
else:
profile.run(cmd)
print "</html>"attachment:profile.png
Evaluate a bit of code in a given system
by William Stein (there is no way yet to make the text box big):
@interact
def _(system=selector([('sage0', 'Sage'), ('gp', 'PARI'), ('magma', 'Magma')]), code='2+2'):
print globals()[system].eval(code)attachment:evalsys.png
A Random Walk
by William Stein
html('<h1>A Random Walk</h1>')
vv = []; nn = 0
@interact
def foo(pts = checkbox(True, "Show points"),
refresh = checkbox(False, "New random walk every time"),
steps = (50,(10..500))):
# We cache the walk in the global variable vv, so that
# checking or unchecking the points checkbox doesn't change
# the random walk.
html("<h2>%s steps</h2>"%steps)
global vv
if refresh or len(vv) == 0:
s = 0; v = [(0,0)]
for i in range(steps):
s += random() - 0.5
v.append((i, s))
vv = v
elif len(vv) != steps:
# Add or subtract some points
s = vv[-1][1]; j = len(vv)
for i in range(steps - len(vv)):
s += random() - 0.5
vv.append((i+j,s))
v = vv[:steps]
else:
v = vv
L = line(v, rgbcolor='#4a8de2')
if pts: L += points(v, pointsize=10, rgbcolor='red')
show(L, xmin=0, figsize=[8,3])attachment:randomwalk.png
3D Random Walk
@interact
def rwalk3d(n=(50,1000), frame=True):
pnt = [0,0,0]
v = [copy(pnt)]
for i in range(n):
pnt[0] += random()-0.5
pnt[1] += random()-0.5
pnt[2] += random()-0.5
v.append(copy(pnt))
show(line3d(v,color='black'),aspect_ratio=[1,1,1],frame=frame)attachment:randomwalk3d.png