BSW_Action

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MaplePrimes Activity


These are questions asked by BSW_Action

Hi,
I don't understand how contourplot chooses it's view range. I would like a contour plot to go from r=0..10 and display axes from [-10..10, -10..10].


plots:-contourplot(r*sin(phi), r = 0 .. 10, phi = 0 .. Pi, coords = spherical, grid = [80, 80]);

doesn't produce a plot with range [-10..10]. Adding view doesnt compute anything differeently, just makes the axes bigger.plots:-

contourplot(r*sin(phi), r = 0 .. 10, phi = 0 .. Pi, coords = spherical, grid = [80, 80], view=[-10..10,-10..10]);

I want more contour lines near the endpoints of the range. why is it focused in the middle?

any help is appreciated, 

Thanks!

 


 

Hi All,

I have a fucntion f(x,y,z) = exp(-x^2 -y^2 - z^4) and would like to plot the probabity density in real space. One method would be to randomly sample points in a grid based on f(x,y,z). The function f(x,y,z) is clearly peaked around x=y=z=0, so you would expect many points to lie around there. So the plot would look like a clump near (0,0,0) which gets less dense away from (0,0,0).

In the worksheet below, I sampled points from the Uniform distribution to file in the 3d-plot. I would like these points to be sampled from f instead, but am not sure how to do this.

Any help is appreciated,

restart;

with(Statistics):

R := 10; # x-axis size
N := 100; # Number f points to sample

10

 

100

(1)

# Unnormalized Probability distrubution

f := (x,y,z) -> exp(-x^2 -y^2 - z^2);

proc (x, y, z) options operator, arrow; exp(-x^2-y^2-z^2) end proc

(2)

# Clearly f is peaked at (0,0,0) and decays. Therefore I want a plot a lot of points near (0,0,0), and fewer points away from (0,0,0)

plot3d(f(x,y,0), x = -1..1, y = -1..1);

 

X := Sample(Uniform(-R, R), N):

Y := Sample(Uniform(-R, R), N):
Z := Sample(Uniform(-R, R), N):
XYZ := Matrix([[X], [Y], [Z]])^%T;

XYZ := Matrix(100, 3, {(1, 1) = 9.758694699049908, (1, 2) = 2.6237746853802246, (1, 3) = 5.657441459582465, (2, 1) = -6.591359538862333, (2, 2) = -2.89852696242302, (2, 3) = 3.875752299737945, (3, 1) = -4.844154988559739, (3, 2) = 9.940065432132954, (3, 3) = -9.803954954738758, (4, 1) = -2.0640136273371272, (4, 2) = -5.516570020337457, (4, 3) = 6.864266760210192, (5, 1) = -8.52010460846124, (5, 2) = 3.049021459372298, (5, 3) = 8.446639955925516, (6, 1) = 3.68192133924018, (6, 2) = 2.099812838165187, (6, 3) = 5.41908441347849, (7, 1) = -1.9522333460767616, (7, 2) = -2.2550913703373006, (7, 3) = -9.146802881299026, (8, 1) = 9.65670402787902, (8, 2) = -7.156256814189918, (8, 3) = -2.4362772589956228, (9, 1) = -1.9563202955503058, (9, 2) = -9.497300285795937, (9, 3) = 4.086792489667353, (10, 1) = 2.4134389439915687, (10, 2) = -1.5777549246951743, (10, 3) = 4.590260910092939, (11, 1) = -6.912603890414553, (11, 2) = -6.317994211449776, (11, 3) = -5.514458586709711, (12, 1) = -2.3730959111105605, (12, 2) = 4.515505349389063, (12, 3) = -4.618905364532699, (13, 1) = -6.777320563012783, (13, 2) = -2.592746269696038, (13, 3) = 3.4606233000823785, (14, 1) = 5.162248626548372, (14, 2) = 6.831201749364123, (14, 3) = -.45015604546277466, (15, 1) = 7.422222438307784, (15, 2) = 4.684593823866264, (15, 3) = 2.4743282533488493, (16, 1) = -2.9844651022821473, (16, 2) = 1.4205174564875769, (16, 3) = -5.2711013471817925, (17, 1) = 3.710714174950745, (17, 2) = -6.462898847493945, (17, 3) = -6.457524910033669, (18, 1) = -4.117027324643008, (18, 2) = 9.147680451914468, (18, 3) = 6.592867713951691, (19, 1) = .6125860771377116, (19, 2) = -4.693559276141599, (19, 3) = 5.338433358705297, (20, 1) = 6.648467725703679, (20, 2) = 8.491617904792019, (20, 3) = 8.68956546236539, (21, 1) = 1.9498038374515865, (21, 2) = -5.52459190605918, (21, 3) = -7.842221898312729, (22, 1) = -3.2937733858950775, (22, 2) = -2.5287238471471003, (22, 3) = -6.355449887978885, (23, 1) = -4.015499533337867, (23, 2) = -8.249993008468286, (23, 3) = -8.01809435155083, (24, 1) = -.9481491686135186, (24, 2) = 2.802330964934301, (24, 3) = -.20472396153106232, (25, 1) = -1.5470869355907517, (25, 2) = -6.387662244937832, (25, 3) = -6.13509339062259, (26, 1) = -2.8078736405552878, (26, 2) = -9.098977850528517, (26, 3) = 7.917831475851365, (27, 1) = 1.1663839973859425, (27, 2) = 4.4634695836619045, (27, 3) = -8.01820700636371, (28, 1) = 4.850907314038782, (28, 2) = -3.051247088364198, (28, 3) = -9.116688564746777, (29, 1) = -1.5133043274861873, (29, 2) = 3.2123364900580764, (29, 3) = 1.145903116095237, (30, 1) = -1.4128842284758996, (30, 2) = -2.322627978560572, (30, 3) = 5.449901343752481, (31, 1) = -7.502544825603743, (31, 2) = 2.5469300488693403, (31, 3) = -3.7611988500746225, (32, 1) = -9.511319678992521, (32, 2) = -9.567003707393871, (32, 3) = -6.420350413713298, (33, 1) = -4.196294697385456, (33, 2) = 8.21139977046057, (33, 3) = -3.220886435045635, (34, 1) = -3.6495883420154733, (34, 2) = 6.011173125576221, (34, 3) = -5.7970872591289595, (35, 1) = 3.0738026793295035, (35, 2) = 4.916949686854423, (35, 3) = .20305039530500402, (36, 1) = 9.138718481413683, (36, 2) = 6.262256272215215, (36, 3) = 8.127286465304294, (37, 1) = 8.71461745569761, (37, 2) = -2.3338736274894156, (37, 3) = 2.578478773046358, (38, 1) = -.8422733229126642, (38, 2) = 2.345584646328984, (38, 3) = -7.969322223753757, (39, 1) = -5.190432063358308, (39, 2) = 1.5098971940562773, (39, 3) = -2.1829049454729077, (40, 1) = 5.277958885729566, (40, 2) = .6010340953003119, (40, 3) = -8.907667695526849, (41, 1) = 5.186547662621926, (41, 2) = -4.498604883561299, (41, 3) = 0.25658264064304603e-1, (42, 1) = 4.812961299572285, (42, 2) = -5.027420806760592, (42, 3) = -1.3655765623150558, (43, 1) = 4.87376682974652, (43, 2) = -.9672245909605444, (43, 3) = 9.951206990243783, (44, 1) = -7.881591665344693, (44, 2) = -5.445743479469048, (44, 3) = 6.232051619906457, (45, 1) = 3.631208609406313, (45, 2) = 6.0889916722614, (45, 3) = -.2869666020396462, (46, 1) = -.7347884281256167, (46, 2) = 9.722084837919404, (46, 3) = 7.888955111347865, (47, 1) = -5.756735894901313, (47, 2) = -9.4001609946122, (47, 3) = -7.249068104658704, (48, 1) = -8.029625246237833, (48, 2) = .7132838133447539, (48, 3) = -2.1999017110942916, (49, 1) = 6.471489478556769, (49, 2) = -8.258455601982153, (49, 3) = 8.547124499962496, (50, 1) = -6.499805252358408, (50, 2) = 6.04182881111608, (50, 3) = 8.34987664832234, (51, 1) = -6.728601804300136, (51, 2) = 9.782898194006798, (51, 3) = 4.271480231886315, (52, 1) = 3.319744328222212, (52, 2) = -8.661074832044998, (52, 3) = 2.3667476724388, (53, 1) = 7.887787507084855, (53, 2) = 8.787967237690697, (53, 3) = -3.1342421951730914, (54, 1) = .33116416702540796, (54, 2) = -9.636449327266085, (54, 3) = 8.720546533795396, (55, 1) = 4.054046139009506, (55, 2) = 3.6767722749271066, (55, 3) = -7.504519186790148, (56, 1) = -6.9281924676119955, (56, 2) = 5.674729601664373, (56, 3) = 4.611707230114142, (57, 1) = 9.069141397724955, (57, 2) = .6827513576545652, (57, 3) = 2.929548648516276, (58, 1) = .8176816248295289, (58, 2) = 7.7071890186228345, (58, 3) = 6.663039713385899, (59, 1) = 3.594677964209339, (59, 2) = 7.980097978122803, (59, 3) = -2.034355435624491, (60, 1) = -9.268739639030944, (60, 2) = 2.518752521609917, (60, 3) = 4.9964441872127185, (61, 1) = 6.184077025875865, (61, 2) = -7.242620151748835, (61, 3) = 6.70441020956261, (62, 1) = 4.972377435523942, (62, 2) = -5.6439681257575085, (62, 3) = -3.5507920527548116, (63, 1) = -7.596259640258387, (63, 2) = -6.357178482191326, (63, 3) = 1.0452323371671, (64, 1) = .5009032952521757, (64, 2) = -9.163602720540913, (64, 3) = 9.582582648677842, (65, 1) = -3.483327424735016, (65, 2) = -7.86116682899586, (65, 3) = .9861706603660547, (66, 1) = .9289887980613702, (66, 2) = 2.328869701713703, (66, 3) = -3.391527807867945, (67, 1) = -2.0223849523360204, (67, 2) = 8.793220203221335, (67, 3) = 2.389431103555598, (68, 1) = -1.6981322677390676, (68, 2) = -2.910885380653423, (68, 3) = -2.7872685799559456, (69, 1) = -6.3852447949041125, (69, 2) = -1.7874181988097213, (69, 3) = 5.130190870038886, (70, 1) = -4.892265190238985, (70, 2) = 9.68698833968903, (70, 3) = -1.7219850261962062, (71, 1) = -9.589284506836309, (71, 2) = 8.911583780705254, (71, 3) = -.15309791230124503, (72, 1) = 8.473512252408145, (72, 2) = 3.532893568670783, (72, 3) = 3.8948646626522017, (73, 1) = 3.073997780165058, (73, 2) = 9.766045246265726, (73, 3) = 9.454677701595681, (74, 1) = 8.652271440971283, (74, 2) = 5.336627744331885, (74, 3) = -3.4449007901318645, (75, 1) = -6.729752629449488, (75, 2) = -3.2660147121704775, (75, 3) = 6.756063661571513, (76, 1) = 8.42194511784395, (76, 2) = 3.2476372079896247, (76, 3) = 4.781444545470562, (77, 1) = 5.893157707775064, (77, 2) = -5.116694264194415, (77, 3) = 9.083489127590862, (78, 1) = 1.5478839341329742, (78, 2) = -4.089854983368064, (78, 3) = -9.361547409920432, (79, 1) = -1.1992880847949277, (79, 2) = 3.6035674246100413, (79, 3) = -2.8626202763491593, (80, 1) = -4.8477252657512455, (80, 2) = .5569366083759579, (80, 3) = 3.25307668574429, (81, 1) = 5.038927877349, (81, 2) = -1.7681297318493083, (81, 3) = -4.369968817030188, (82, 1) = -5.426610357889972, (82, 2) = 2.0527643607279433, (82, 3) = -5.392338653650725, (83, 1) = -8.716258252162028, (83, 2) = 5.010401118474713, (83, 3) = 4.222571023606502, (84, 1) = 5.346590215531489, (84, 2) = 1.6706634852391726, (84, 3) = 2.4914583398661705, (85, 1) = 3.4240437071307106, (85, 2) = 1.0358502987193496, (85, 3) = 1.8121730583927196, (86, 1) = 4.304250295716802, (86, 2) = 1.6714123751542882, (86, 3) = 3.2087593262520375, (87, 1) = 2.8412165686770443, (87, 2) = .236398399169504, (87, 3) = -9.04890653772268, (88, 1) = -1.6190341275023385, (88, 2) = -8.348145460026013, (88, 3) = -3.0243038297988223, (89, 1) = -2.184758355916509, (89, 2) = 4.391402697189795, (89, 3) = -.9731883928851364, (90, 1) = 6.322802057506454, (90, 2) = 9.923122225937387, (90, 3) = -5.181900057597786, (91, 1) = -3.6514427268830074, (91, 2) = -2.909313900861563, (91, 3) = 4.300900265923531, (92, 1) = 6.290795458013026, (92, 2) = 9.425176303668113, (92, 3) = 7.123645840125757, (93, 1) = 5.7814702987791655, (93, 2) = -3.071024773992807, (93, 3) = -4.369846097628933, (94, 1) = 7.045277806876914, (94, 2) = 7.730877235206126, (94, 3) = 4.621016594474829, (95, 1) = .11273235143512395, (95, 2) = -.9061027001618438, (95, 3) = -7.244742149609673, (96, 1) = 2.7132277772275373, (96, 2) = -1.7314542195836946, (96, 3) = 6.734455634994351, (97, 1) = 9.017888307562703, (97, 2) = -5.645358632853991, (97, 3) = -7.2279656851528, (98, 1) = -1.1207168996237922, (98, 2) = -7.486908252747475, (98, 3) = 1.7641877077898727, (99, 1) = -8.799623604410481, (99, 2) = -3.821708128663694, (99, 3) = -2.6768639909012437, (100, 1) = 7.334997939986373, (100, 2) = 4.522088633296637, (100, 3) = 6.135190893222113}, datatype = float[8])

(3)

ScatterPlot3D(XYZ, color = blue, symbolsize = 20);

 

 

 

 

 


 

Download Sample_Test.m

 

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