In [20]:
% matplotlib inline
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
In [21]:
x = np.linspace(0, 10, 512) # evenly spaced grid
In [22]:
x
Out[22]:
array([ 0. , 0.01956947, 0.03913894, 0.05870841,
0.07827789, 0.09784736, 0.11741683, 0.1369863 ,
0.15655577, 0.17612524, 0.19569472, 0.21526419,
0.23483366, 0.25440313, 0.2739726 , 0.29354207,
0.31311155, 0.33268102, 0.35225049, 0.37181996,
0.39138943, 0.4109589 , 0.43052838, 0.45009785,
0.46966732, 0.48923679, 0.50880626, 0.52837573,
0.54794521, 0.56751468, 0.58708415, 0.60665362,
0.62622309, 0.64579256, 0.66536204, 0.68493151,
0.70450098, 0.72407045, 0.74363992, 0.76320939,
0.78277886, 0.80234834, 0.82191781, 0.84148728,
0.86105675, 0.88062622, 0.90019569, 0.91976517,
0.93933464, 0.95890411, 0.97847358, 0.99804305,
1.01761252, 1.037182 , 1.05675147, 1.07632094,
1.09589041, 1.11545988, 1.13502935, 1.15459883,
1.1741683 , 1.19373777, 1.21330724, 1.23287671,
1.25244618, 1.27201566, 1.29158513, 1.3111546 ,
1.33072407, 1.35029354, 1.36986301, 1.38943249,
1.40900196, 1.42857143, 1.4481409 , 1.46771037,
1.48727984, 1.50684932, 1.52641879, 1.54598826,
1.56555773, 1.5851272 , 1.60469667, 1.62426614,
1.64383562, 1.66340509, 1.68297456, 1.70254403,
1.7221135 , 1.74168297, 1.76125245, 1.78082192,
1.80039139, 1.81996086, 1.83953033, 1.8590998 ,
1.87866928, 1.89823875, 1.91780822, 1.93737769,
1.95694716, 1.97651663, 1.99608611, 2.01565558,
2.03522505, 2.05479452, 2.07436399, 2.09393346,
2.11350294, 2.13307241, 2.15264188, 2.17221135,
2.19178082, 2.21135029, 2.23091977, 2.25048924,
2.27005871, 2.28962818, 2.30919765, 2.32876712,
2.34833659, 2.36790607, 2.38747554, 2.40704501,
2.42661448, 2.44618395, 2.46575342, 2.4853229 ,
2.50489237, 2.52446184, 2.54403131, 2.56360078,
2.58317025, 2.60273973, 2.6223092 , 2.64187867,
2.66144814, 2.68101761, 2.70058708, 2.72015656,
2.73972603, 2.7592955 , 2.77886497, 2.79843444,
2.81800391, 2.83757339, 2.85714286, 2.87671233,
2.8962818 , 2.91585127, 2.93542074, 2.95499022,
2.97455969, 2.99412916, 3.01369863, 3.0332681 ,
3.05283757, 3.07240705, 3.09197652, 3.11154599,
3.13111546, 3.15068493, 3.1702544 , 3.18982387,
3.20939335, 3.22896282, 3.24853229, 3.26810176,
3.28767123, 3.3072407 , 3.32681018, 3.34637965,
3.36594912, 3.38551859, 3.40508806, 3.42465753,
3.44422701, 3.46379648, 3.48336595, 3.50293542,
3.52250489, 3.54207436, 3.56164384, 3.58121331,
3.60078278, 3.62035225, 3.63992172, 3.65949119,
3.67906067, 3.69863014, 3.71819961, 3.73776908,
3.75733855, 3.77690802, 3.7964775 , 3.81604697,
3.83561644, 3.85518591, 3.87475538, 3.89432485,
3.91389432, 3.9334638 , 3.95303327, 3.97260274,
3.99217221, 4.01174168, 4.03131115, 4.05088063,
4.0704501 , 4.09001957, 4.10958904, 4.12915851,
4.14872798, 4.16829746, 4.18786693, 4.2074364 ,
4.22700587, 4.24657534, 4.26614481, 4.28571429,
4.30528376, 4.32485323, 4.3444227 , 4.36399217,
4.38356164, 4.40313112, 4.42270059, 4.44227006,
4.46183953, 4.481409 , 4.50097847, 4.52054795,
4.54011742, 4.55968689, 4.57925636, 4.59882583,
4.6183953 , 4.63796477, 4.65753425, 4.67710372,
4.69667319, 4.71624266, 4.73581213, 4.7553816 ,
4.77495108, 4.79452055, 4.81409002, 4.83365949,
4.85322896, 4.87279843, 4.89236791, 4.91193738,
4.93150685, 4.95107632, 4.97064579, 4.99021526,
5.00978474, 5.02935421, 5.04892368, 5.06849315,
5.08806262, 5.10763209, 5.12720157, 5.14677104,
5.16634051, 5.18590998, 5.20547945, 5.22504892,
5.2446184 , 5.26418787, 5.28375734, 5.30332681,
5.32289628, 5.34246575, 5.36203523, 5.3816047 ,
5.40117417, 5.42074364, 5.44031311, 5.45988258,
5.47945205, 5.49902153, 5.518591 , 5.53816047,
5.55772994, 5.57729941, 5.59686888, 5.61643836,
5.63600783, 5.6555773 , 5.67514677, 5.69471624,
5.71428571, 5.73385519, 5.75342466, 5.77299413,
5.7925636 , 5.81213307, 5.83170254, 5.85127202,
5.87084149, 5.89041096, 5.90998043, 5.9295499 ,
5.94911937, 5.96868885, 5.98825832, 6.00782779,
6.02739726, 6.04696673, 6.0665362 , 6.08610568,
6.10567515, 6.12524462, 6.14481409, 6.16438356,
6.18395303, 6.2035225 , 6.22309198, 6.24266145,
6.26223092, 6.28180039, 6.30136986, 6.32093933,
6.34050881, 6.36007828, 6.37964775, 6.39921722,
6.41878669, 6.43835616, 6.45792564, 6.47749511,
6.49706458, 6.51663405, 6.53620352, 6.55577299,
6.57534247, 6.59491194, 6.61448141, 6.63405088,
6.65362035, 6.67318982, 6.6927593 , 6.71232877,
6.73189824, 6.75146771, 6.77103718, 6.79060665,
6.81017613, 6.8297456 , 6.84931507, 6.86888454,
6.88845401, 6.90802348, 6.92759295, 6.94716243,
6.9667319 , 6.98630137, 7.00587084, 7.02544031,
7.04500978, 7.06457926, 7.08414873, 7.1037182 ,
7.12328767, 7.14285714, 7.16242661, 7.18199609,
7.20156556, 7.22113503, 7.2407045 , 7.26027397,
7.27984344, 7.29941292, 7.31898239, 7.33855186,
7.35812133, 7.3776908 , 7.39726027, 7.41682975,
7.43639922, 7.45596869, 7.47553816, 7.49510763,
7.5146771 , 7.53424658, 7.55381605, 7.57338552,
7.59295499, 7.61252446, 7.63209393, 7.65166341,
7.67123288, 7.69080235, 7.71037182, 7.72994129,
7.74951076, 7.76908023, 7.78864971, 7.80821918,
7.82778865, 7.84735812, 7.86692759, 7.88649706,
7.90606654, 7.92563601, 7.94520548, 7.96477495,
7.98434442, 8.00391389, 8.02348337, 8.04305284,
8.06262231, 8.08219178, 8.10176125, 8.12133072,
8.1409002 , 8.16046967, 8.18003914, 8.19960861,
8.21917808, 8.23874755, 8.25831703, 8.2778865 ,
8.29745597, 8.31702544, 8.33659491, 8.35616438,
8.37573386, 8.39530333, 8.4148728 , 8.43444227,
8.45401174, 8.47358121, 8.49315068, 8.51272016,
8.53228963, 8.5518591 , 8.57142857, 8.59099804,
8.61056751, 8.63013699, 8.64970646, 8.66927593,
8.6888454 , 8.70841487, 8.72798434, 8.74755382,
8.76712329, 8.78669276, 8.80626223, 8.8258317 ,
8.84540117, 8.86497065, 8.88454012, 8.90410959,
8.92367906, 8.94324853, 8.962818 , 8.98238748,
9.00195695, 9.02152642, 9.04109589, 9.06066536,
9.08023483, 9.09980431, 9.11937378, 9.13894325,
9.15851272, 9.17808219, 9.19765166, 9.21722114,
9.23679061, 9.25636008, 9.27592955, 9.29549902,
9.31506849, 9.33463796, 9.35420744, 9.37377691,
9.39334638, 9.41291585, 9.43248532, 9.45205479,
9.47162427, 9.49119374, 9.51076321, 9.53033268,
9.54990215, 9.56947162, 9.5890411 , 9.60861057,
9.62818004, 9.64774951, 9.66731898, 9.68688845,
9.70645793, 9.7260274 , 9.74559687, 9.76516634,
9.78473581, 9.80430528, 9.82387476, 9.84344423,
9.8630137 , 9.88258317, 9.90215264, 9.92172211,
9.94129159, 9.96086106, 9.98043053, 10. ])
In [23]:
(xx, yy) = np.meshgrid(x, x)
In [24]:
xx
Out[24]:
array([[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ],
[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ],
[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ],
...,
[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ],
[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ],
[ 0. , 0.01956947, 0.03913894, ..., 9.96086106,
9.98043053, 10. ]])
In [25]:
xx[0]
Out[25]:
array([ 0. , 0.01956947, 0.03913894, 0.05870841,
0.07827789, 0.09784736, 0.11741683, 0.1369863 ,
0.15655577, 0.17612524, 0.19569472, 0.21526419,
0.23483366, 0.25440313, 0.2739726 , 0.29354207,
0.31311155, 0.33268102, 0.35225049, 0.37181996,
0.39138943, 0.4109589 , 0.43052838, 0.45009785,
0.46966732, 0.48923679, 0.50880626, 0.52837573,
0.54794521, 0.56751468, 0.58708415, 0.60665362,
0.62622309, 0.64579256, 0.66536204, 0.68493151,
0.70450098, 0.72407045, 0.74363992, 0.76320939,
0.78277886, 0.80234834, 0.82191781, 0.84148728,
0.86105675, 0.88062622, 0.90019569, 0.91976517,
0.93933464, 0.95890411, 0.97847358, 0.99804305,
1.01761252, 1.037182 , 1.05675147, 1.07632094,
1.09589041, 1.11545988, 1.13502935, 1.15459883,
1.1741683 , 1.19373777, 1.21330724, 1.23287671,
1.25244618, 1.27201566, 1.29158513, 1.3111546 ,
1.33072407, 1.35029354, 1.36986301, 1.38943249,
1.40900196, 1.42857143, 1.4481409 , 1.46771037,
1.48727984, 1.50684932, 1.52641879, 1.54598826,
1.56555773, 1.5851272 , 1.60469667, 1.62426614,
1.64383562, 1.66340509, 1.68297456, 1.70254403,
1.7221135 , 1.74168297, 1.76125245, 1.78082192,
1.80039139, 1.81996086, 1.83953033, 1.8590998 ,
1.87866928, 1.89823875, 1.91780822, 1.93737769,
1.95694716, 1.97651663, 1.99608611, 2.01565558,
2.03522505, 2.05479452, 2.07436399, 2.09393346,
2.11350294, 2.13307241, 2.15264188, 2.17221135,
2.19178082, 2.21135029, 2.23091977, 2.25048924,
2.27005871, 2.28962818, 2.30919765, 2.32876712,
2.34833659, 2.36790607, 2.38747554, 2.40704501,
2.42661448, 2.44618395, 2.46575342, 2.4853229 ,
2.50489237, 2.52446184, 2.54403131, 2.56360078,
2.58317025, 2.60273973, 2.6223092 , 2.64187867,
2.66144814, 2.68101761, 2.70058708, 2.72015656,
2.73972603, 2.7592955 , 2.77886497, 2.79843444,
2.81800391, 2.83757339, 2.85714286, 2.87671233,
2.8962818 , 2.91585127, 2.93542074, 2.95499022,
2.97455969, 2.99412916, 3.01369863, 3.0332681 ,
3.05283757, 3.07240705, 3.09197652, 3.11154599,
3.13111546, 3.15068493, 3.1702544 , 3.18982387,
3.20939335, 3.22896282, 3.24853229, 3.26810176,
3.28767123, 3.3072407 , 3.32681018, 3.34637965,
3.36594912, 3.38551859, 3.40508806, 3.42465753,
3.44422701, 3.46379648, 3.48336595, 3.50293542,
3.52250489, 3.54207436, 3.56164384, 3.58121331,
3.60078278, 3.62035225, 3.63992172, 3.65949119,
3.67906067, 3.69863014, 3.71819961, 3.73776908,
3.75733855, 3.77690802, 3.7964775 , 3.81604697,
3.83561644, 3.85518591, 3.87475538, 3.89432485,
3.91389432, 3.9334638 , 3.95303327, 3.97260274,
3.99217221, 4.01174168, 4.03131115, 4.05088063,
4.0704501 , 4.09001957, 4.10958904, 4.12915851,
4.14872798, 4.16829746, 4.18786693, 4.2074364 ,
4.22700587, 4.24657534, 4.26614481, 4.28571429,
4.30528376, 4.32485323, 4.3444227 , 4.36399217,
4.38356164, 4.40313112, 4.42270059, 4.44227006,
4.46183953, 4.481409 , 4.50097847, 4.52054795,
4.54011742, 4.55968689, 4.57925636, 4.59882583,
4.6183953 , 4.63796477, 4.65753425, 4.67710372,
4.69667319, 4.71624266, 4.73581213, 4.7553816 ,
4.77495108, 4.79452055, 4.81409002, 4.83365949,
4.85322896, 4.87279843, 4.89236791, 4.91193738,
4.93150685, 4.95107632, 4.97064579, 4.99021526,
5.00978474, 5.02935421, 5.04892368, 5.06849315,
5.08806262, 5.10763209, 5.12720157, 5.14677104,
5.16634051, 5.18590998, 5.20547945, 5.22504892,
5.2446184 , 5.26418787, 5.28375734, 5.30332681,
5.32289628, 5.34246575, 5.36203523, 5.3816047 ,
5.40117417, 5.42074364, 5.44031311, 5.45988258,
5.47945205, 5.49902153, 5.518591 , 5.53816047,
5.55772994, 5.57729941, 5.59686888, 5.61643836,
5.63600783, 5.6555773 , 5.67514677, 5.69471624,
5.71428571, 5.73385519, 5.75342466, 5.77299413,
5.7925636 , 5.81213307, 5.83170254, 5.85127202,
5.87084149, 5.89041096, 5.90998043, 5.9295499 ,
5.94911937, 5.96868885, 5.98825832, 6.00782779,
6.02739726, 6.04696673, 6.0665362 , 6.08610568,
6.10567515, 6.12524462, 6.14481409, 6.16438356,
6.18395303, 6.2035225 , 6.22309198, 6.24266145,
6.26223092, 6.28180039, 6.30136986, 6.32093933,
6.34050881, 6.36007828, 6.37964775, 6.39921722,
6.41878669, 6.43835616, 6.45792564, 6.47749511,
6.49706458, 6.51663405, 6.53620352, 6.55577299,
6.57534247, 6.59491194, 6.61448141, 6.63405088,
6.65362035, 6.67318982, 6.6927593 , 6.71232877,
6.73189824, 6.75146771, 6.77103718, 6.79060665,
6.81017613, 6.8297456 , 6.84931507, 6.86888454,
6.88845401, 6.90802348, 6.92759295, 6.94716243,
6.9667319 , 6.98630137, 7.00587084, 7.02544031,
7.04500978, 7.06457926, 7.08414873, 7.1037182 ,
7.12328767, 7.14285714, 7.16242661, 7.18199609,
7.20156556, 7.22113503, 7.2407045 , 7.26027397,
7.27984344, 7.29941292, 7.31898239, 7.33855186,
7.35812133, 7.3776908 , 7.39726027, 7.41682975,
7.43639922, 7.45596869, 7.47553816, 7.49510763,
7.5146771 , 7.53424658, 7.55381605, 7.57338552,
7.59295499, 7.61252446, 7.63209393, 7.65166341,
7.67123288, 7.69080235, 7.71037182, 7.72994129,
7.74951076, 7.76908023, 7.78864971, 7.80821918,
7.82778865, 7.84735812, 7.86692759, 7.88649706,
7.90606654, 7.92563601, 7.94520548, 7.96477495,
7.98434442, 8.00391389, 8.02348337, 8.04305284,
8.06262231, 8.08219178, 8.10176125, 8.12133072,
8.1409002 , 8.16046967, 8.18003914, 8.19960861,
8.21917808, 8.23874755, 8.25831703, 8.2778865 ,
8.29745597, 8.31702544, 8.33659491, 8.35616438,
8.37573386, 8.39530333, 8.4148728 , 8.43444227,
8.45401174, 8.47358121, 8.49315068, 8.51272016,
8.53228963, 8.5518591 , 8.57142857, 8.59099804,
8.61056751, 8.63013699, 8.64970646, 8.66927593,
8.6888454 , 8.70841487, 8.72798434, 8.74755382,
8.76712329, 8.78669276, 8.80626223, 8.8258317 ,
8.84540117, 8.86497065, 8.88454012, 8.90410959,
8.92367906, 8.94324853, 8.962818 , 8.98238748,
9.00195695, 9.02152642, 9.04109589, 9.06066536,
9.08023483, 9.09980431, 9.11937378, 9.13894325,
9.15851272, 9.17808219, 9.19765166, 9.21722114,
9.23679061, 9.25636008, 9.27592955, 9.29549902,
9.31506849, 9.33463796, 9.35420744, 9.37377691,
9.39334638, 9.41291585, 9.43248532, 9.45205479,
9.47162427, 9.49119374, 9.51076321, 9.53033268,
9.54990215, 9.56947162, 9.5890411 , 9.60861057,
9.62818004, 9.64774951, 9.66731898, 9.68688845,
9.70645793, 9.7260274 , 9.74559687, 9.76516634,
9.78473581, 9.80430528, 9.82387476, 9.84344423,
9.8630137 , 9.88258317, 9.90215264, 9.92172211,
9.94129159, 9.96086106, 9.98043053, 10. ])
In [26]:
xx[0:5, 0:5]
Out[26]:
array([[ 0. , 0.01956947, 0.03913894, 0.05870841, 0.07827789],
[ 0. , 0.01956947, 0.03913894, 0.05870841, 0.07827789],
[ 0. , 0.01956947, 0.03913894, 0.05870841, 0.07827789],
[ 0. , 0.01956947, 0.03913894, 0.05870841, 0.07827789],
[ 0. , 0.01956947, 0.03913894, 0.05870841, 0.07827789]])
In [27]:
yy[0:5, 0:5]
Out[27]:
array([[ 0. , 0. , 0. , 0. , 0. ],
[ 0.01956947, 0.01956947, 0.01956947, 0.01956947, 0.01956947],
[ 0.03913894, 0.03913894, 0.03913894, 0.03913894, 0.03913894],
[ 0.05870841, 0.05870841, 0.05870841, 0.05870841, 0.05870841],
[ 0.07827789, 0.07827789, 0.07827789, 0.07827789, 0.07827789]])
In [33]:
zz = np.exp( (-(xx-5)**2 - (yy-5)**2)/(10) )
In [34]:
zz[0:5, 0:5]
Out[34]:
array([[ 0.00673795, 0.00687084, 0.00700582, 0.0071429 , 0.00728211],
[ 0.00687084, 0.00700636, 0.007144 , 0.00728378, 0.00742573],
[ 0.00700582, 0.007144 , 0.00728434, 0.00742687, 0.00757161],
[ 0.0071429 , 0.00728378, 0.00742687, 0.00757219, 0.00771977],
[ 0.00728211, 0.00742573, 0.00757161, 0.00771977, 0.00787022]])
In [35]:
plt.imshow(zz)
Out[35]:
<matplotlib.image.AxesImage at 0x11832f320>
In [36]:
plt.figure()
axis = plt.subplot(111, projection='3d')
axis.plot_surface(xx, yy, zz)
Out[36]:
<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x118cca780>
In [ ]: