generate.point.in.sphere: Point Generation for a Sphere

In MultiRNG: Multivariate Pseudo-Random Number Generation

Description

This function generates s points on a d-dimensional sphere.

Usage

generate.point.in.sphere(no.row,d)

Arguments

no.row	Number of rows to generate.
d	Number of variables to generate.

Value

A no.row \times d matrix of coordinates of points in sphere.

References

Marsaglia, G. (1972). Choosing a point from the surface of a sphere. Annals of Mathematical Statistics, 43, 645-646.

Examples

generate.point.in.sphere(no.row=1e5,d=3)

Example output

                   [,1]          [,2]          [,3]
     [1,]  8.298172e-01 -4.588340e-01 -3.176079e-01
     [2,] -6.620966e-01 -7.056074e-01 -2.524803e-01
     [3,]  7.004294e-02  4.460368e-02 -9.965463e-01
     [4,] -1.109438e-01  9.827503e-01 -1.479642e-01
     [5,]  5.125178e-02 -9.980875e-01 -3.456248e-02
     [6,] -1.483492e-01  9.748459e-01  1.663369e-01
     [7,]  3.616270e-01 -7.702009e-01  5.253727e-01
     [8,] -8.344797e-02  6.218044e-01 -7.787141e-01
     [9,] -1.837013e-01 -8.017728e-01  5.686953e-01
    [10,] -2.286440e-01 -1.407977e-01  9.632746e-01
    [11,]  1.787884e-01 -9.610012e-01  2.109771e-01
    [12,]  5.976162e-01  6.584457e-01  4.574977e-01
    [13,]  3.641697e-01 -5.303863e-02  9.298211e-01
    [14,] -6.225570e-01  4.745849e-01  6.222475e-01
    [15,] -3.665895e-01 -7.113235e-01 -5.996924e-01
    [16,]  6.674149e-01  1.293085e-01  7.333734e-01
    [17,]  7.016701e-01  4.674211e-01 -5.377515e-01
    [18,] -7.040218e-01 -1.099705e-01 -7.016123e-01
    [19,] -1.318548e-01 -7.082599e-01  6.935289e-01
    [20,] -4.677188e-01 -6.633607e-01 -5.841162e-01
    [21,]  3.559318e-01  2.407492e-01  9.029686e-01
    [22,] -7.325868e-02 -7.542826e-01 -6.524500e-01
    [23,] -9.399054e-01  2.414273e-01  2.414347e-01
    [24,] -6.433898e-03 -2.280070e-02 -9.997193e-01
    [25,]  6.002686e-01  1.719197e-01  7.811026e-01
    [26,] -3.032965e-01  6.744923e-01  6.731057e-01
    [27,]  5.833677e-01  7.782861e-01 -2.322774e-01
    [28,] -9.891138e-01  2.827896e-02  1.444096e-01
    [29,]  5.259933e-01 -7.209390e-01 -4.511962e-01
    [30,] -4.277180e-01 -6.827784e-01 -5.923436e-01
    [31,] -3.102124e-02  2.685989e-01  9.627525e-01
    [32,] -2.666189e-02 -1.284886e-01 -9.913525e-01
    [33,]  8.778790e-01  4.072787e-01  2.518979e-01
    [34,]  2.750479e-01 -9.150271e-01  2.950830e-01
    [35,]  3.473622e-01 -8.724588e-01  3.437371e-01
    [36,] -8.219865e-01 -4.287690e-01 -3.748271e-01
    [37,]  1.145767e-01  7.692796e-01 -6.285548e-01
    [38,]  6.333078e-01  7.225030e-01  2.773276e-01
    [39,] -4.027941e-01 -8.623528e-03  9.152500e-01
    [40,]  2.714626e-01 -7.910332e-01 -5.482468e-01
    [41,] -5.922124e-02 -8.958983e-01 -4.402943e-01
    [42,]  7.574236e-01 -4.368304e-01 -4.852717e-01
    [43,] -1.678893e-01 -8.795027e-01 -4.452956e-01
    [44,] -8.058779e-01  5.459023e-01  2.292409e-01
    [45,] -2.025359e-02  3.392073e-02 -9.992193e-01
    [46,] -6.965218e-01  2.457204e-01 -6.741505e-01
    [47,]  1.122064e-01 -8.084135e-01 -5.778212e-01
    [48,]  7.876464e-01  6.152649e-01 -3.259325e-02
    [49,]  6.215444e-02 -7.289943e-03 -9.980399e-01
    [50,]  6.716335e-01  2.907257e-01  6.814594e-01
    [51,]  3.770278e-01 -3.050979e-01  8.745086e-01
    [52,]  1.041664e-01  8.753717e-01 -4.720951e-01
    [53,] -9.437685e-01 -2.282756e-01 -2.391469e-01
    [54,]  9.799377e-01  1.014093e-01 -1.715756e-01
    [55,] -3.208768e-02 -9.332710e-01  3.577367e-01
    [56,]  4.160420e-01 -6.233166e-01 -6.621069e-01
    [57,] -6.932877e-01  4.182625e-01 -5.868634e-01
    [58,]  3.592954e-01  6.837726e-01 -6.351077e-01
    [59,] -4.655592e-01 -2.419265e-02  8.846860e-01
    [60,] -5.888467e-01 -7.621680e-01 -2.689972e-01
    [61,] -5.513277e-01  7.303056e-01 -4.033504e-01
    [62,]  6.637654e-02  3.661763e-01  9.281751e-01
    [63,]  3.735912e-01  6.742423e-01  6.370454e-01
    [64,]  2.889056e-01 -7.638065e-01 -5.771769e-01
    [65,] -8.286412e-01  5.591729e-01 -2.606537e-02
    [66,]  2.277049e-01 -3.552829e-01 -9.066006e-01
    [67,]  8.797972e-01  9.095658e-02 -4.665659e-01
    [68,]  4.048446e-02  2.265946e-01 -9.731474e-01
    [69,]  4.281810e-01 -8.745655e-01  2.275878e-01
    [70,]  3.087776e-01 -9.429823e-01 -1.242605e-01
    [71,] -2.780553e-01 -8.421032e-01 -4.621119e-01
    [72,] -8.499098e-01 -5.175885e-01 -9.877037e-02
    [73,]  1.651837e-01  8.857140e-01 -4.338491e-01
    [74,]  9.726186e-01  2.029809e-01  1.131890e-01
    [75,] -4.288589e-01  3.321078e-01  8.401098e-01
    [76,] -3.595309e-01 -7.937381e-01  4.906296e-01
    [77,] -6.149158e-01 -5.032398e-01 -6.071476e-01
    [78,] -7.150614e-01 -2.110968e-01 -6.664273e-01
    [79,] -5.027400e-03  8.344335e-01  5.510857e-01
    [80,]  4.808210e-01  7.349756e-01 -4.781444e-01
    [81,]  5.253616e-01  7.903884e-01 -3.150893e-01
    [82,]  2.783372e-01 -6.289356e-02  9.584220e-01
    [83,] -9.411638e-02  8.562582e-01 -5.079015e-01
    [84,]  8.982860e-01  3.994502e-01  1.830896e-01
    [85,]  8.275123e-01 -6.759112e-02 -5.573642e-01
    [86,] -6.743162e-01 -3.315010e-01  6.598521e-01
    [87,] -6.164395e-01  5.959790e-01 -5.145983e-01
    [88,] -3.681167e-01  1.454138e-01 -9.183381e-01
    [89,]  2.962956e-01 -5.653676e-01 -7.697846e-01
    [90,] -3.305618e-01  5.950826e-01 -7.325337e-01
    [91,]  1.773493e-01 -2.491023e-01 -9.521005e-01
    [92,] -8.803834e-01 -4.670211e-01  8.256156e-02
    [93,] -5.784746e-01 -4.698328e-01 -6.668016e-01
    [94,]  3.512151e-01  2.846586e-01  8.919739e-01
    [95,]  3.950519e-01  2.621789e-01 -8.804523e-01
    [96,] -7.789534e-01  3.827807e-01 -4.966997e-01
    [97,]  4.937717e-01  2.382584e-01 -8.363148e-01
    [98,] -7.102843e-01  6.339905e-01 -3.058633e-01
    [99,]  7.891522e-01 -5.618009e-01 -2.482308e-01
   [100,] -3.459522e-01 -7.417569e-01  5.745552e-01
   [101,]  8.096111e-01  4.657999e-01  3.571559e-01
   [102,]  7.995079e-01  5.030120e-01 -3.282774e-01
   [103,] -5.621200e-01 -5.353890e-01 -6.303806e-01
   [104,] -8.642786e-01  4.930004e-01 -9.986528e-02
   [105,]  6.732425e-01  6.157692e-01 -4.093565e-01
   [106,]  1.297369e-01 -1.927075e-01  9.726418e-01
   [107,]  7.528184e-01  5.536419e-01  3.560128e-01
   [108,]  9.777011e-01 -2.012961e-04  2.100014e-01
   [109,]  3.044569e-01 -7.918204e-01  5.294586e-01
   [110,] -8.562451e-01  1.797831e-01  4.842752e-01
   [111,] -7.161462e-01  4.738717e-01 -5.124259e-01
   [112,]  5.600677e-01  7.940614e-01  2.362004e-01
   [113,] -3.396525e-01 -4.041898e-01 -8.492743e-01
   [114,] -3.996481e-01  1.010256e-01 -9.110847e-01
   [115,]  3.286063e-01 -8.805809e-01  3.414604e-01
   [116,] -4.262213e-01 -1.364916e-01  8.942625e-01
   [117,] -9.540258e-01  7.118547e-02  2.911486e-01
   [118,]  4.683284e-01  7.171833e-01 -5.160587e-01
   [119,] -5.592885e-01 -5.291317e-01  6.381348e-01
   [120,]  7.302658e-01  6.817704e-01  4.360133e-02
   [121,] -9.144254e-01 -3.688510e-01 -1.666587e-01
   [122,] -9.347477e-01  1.363862e-01  3.280938e-01
   [123,]  6.464523e-01  6.827788e-01  3.404594e-01
   [124,]  9.515228e-01  1.098357e-01 -2.872987e-01
   [125,] -7.156575e-01  2.901516e-01  6.353318e-01
   [126,]  6.702387e-01  1.511465e-01 -7.265913e-01
   [127,] -5.779802e-03 -5.456114e-01 -8.380184e-01
   [128,]  5.898445e-01  4.286606e-01  6.843491e-01
   [129,] -1.333052e-01 -8.761447e-01  4.632496e-01
   [130,]  1.163628e-01  4.379987e-01  8.914128e-01
   [131,]  9.863497e-02  7.360422e-01  6.697112e-01
   [132,]  2.474253e-01  9.626476e-01 -1.099562e-01
   [133,] -6.903558e-01  1.538845e-01  7.069147e-01
   [134,] -1.891309e-01  2.037527e-01 -9.605802e-01
   [135,] -3.019872e-01  9.165597e-02  9.488956e-01
   [136,] -4.120299e-01  8.002691e-01  4.356613e-01
   [137,] -2.750163e-01 -6.717732e-01 -6.878131e-01
   [138,] -9.267266e-01  2.841109e-02  3.746607e-01
   [139,] -9.928940e-02 -9.178632e-01  3.842770e-01
   [140,]  5.417890e-01  5.175482e-01 -6.622753e-01
   [141,] -6.893120e-01  3.739839e-01  6.204717e-01
   [142,]  7.748212e-01  2.822486e-01  5.656747e-01
   [143,] -9.557400e-01  1.078120e-01  2.737473e-01
   [144,]  6.301645e-02  9.936814e-01 -9.287757e-02
   [145,]  4.668493e-01 -8.126727e-01 -3.487331e-01
   [146,] -5.882820e-01 -2.545752e-01 -7.675388e-01
   [147,] -2.676694e-01 -8.344378e-01 -4.817330e-01
   [148,] -5.244054e-01  6.727505e-03  8.514421e-01
   [149,] -5.966380e-01 -7.929299e-01  1.236335e-01
   [150,] -5.543131e-01  2.066855e-01  8.062370e-01
   [151,] -4.634273e-01 -6.530118e-01  5.990081e-01
   [152,] -8.741825e-01 -2.005789e-01  4.422364e-01
   [153,] -6.467008e-01 -5.996994e-01 -4.713159e-01
   [154,] -3.081460e-01 -7.590426e-01  5.734984e-01
   [155,]  3.966014e-01 -8.883577e-01  2.313612e-01
   [156,]  8.373008e-02 -7.880237e-01 -6.099245e-01
   [157,] -5.802266e-01 -1.792234e-02  8.142579e-01
   [158,] -6.933147e-01  3.043237e-01 -6.532242e-01
   [159,] -9.729023e-01 -2.296307e-01 -2.703265e-02
   [160,]  3.529153e-01 -4.189232e-01  8.366326e-01
   [161,]  8.239799e-02  1.031743e-01 -9.912445e-01
   [162,] -7.764491e-01 -3.942183e-02 -6.289457e-01
   [163,]  3.309469e-01 -6.097228e-01  7.202168e-01
   [164,] -1.490956e-01  9.408581e-01 -3.042309e-01
   [165,] -5.601324e-01 -3.063813e-01  7.696637e-01
   [166,]  7.490945e-01 -6.514188e-01 -1.204613e-01
   [167,]  7.530906e-01 -6.637011e-02 -6.545606e-01
   [168,] -2.974347e-01 -8.858979e-01 -3.559741e-01
   [169,]  5.011723e-01 -4.341777e-01 -7.485426e-01
   [170,]  1.127864e-01 -7.492929e-01  6.525637e-01
   [171,]  7.062865e-01 -6.985936e-01  1.145709e-01
   [172,] -6.109826e-01 -1.803742e-01 -7.708213e-01
   [173,] -6.517616e-01  1.478549e-01  7.438721e-01
   [174,]  9.266677e-01 -3.157154e-01  2.039873e-01
   [175,]  5.777050e-01  5.063788e-01  6.401854e-01
   [176,] -6.003432e-01 -6.424666e-01  4.762611e-01
   [177,]  2.980491e-01  9.318946e-01 -2.067348e-01
   [178,]  3.714592e-01 -8.135739e-01 -4.473427e-01
   [179,]  1.906748e-01 -1.496378e-01  9.701813e-01
   [180,]  1.538639e-01 -1.497197e-01  9.766831e-01
   [181,] -5.630422e-01  7.600213e-01 -3.245783e-01
   [182,] -5.345758e-01 -7.041893e-01 -4.672753e-01
   [183,]  4.573776e-02  3.074490e-01  9.504647e-01
   [184,] -7.171091e-01 -3.932084e-01 -5.754491e-01
   [185,]  3.853717e-01 -3.802752e-01 -8.407612e-01
   [186,] -9.992682e-01  2.314851e-02 -3.044937e-02
   [187,]  1.528278e-01  5.524271e-01 -8.194315e-01
   [188,] -5.893474e-01  1.225806e-01 -7.985259e-01
   [189,] -6.111284e-01 -1.201170e-01  7.823643e-01
   [190,] -4.431453e-01 -1.238866e-01 -8.878482e-01
   [191,] -2.228897e-01 -7.365920e-01 -6.385549e-01
   [192,] -5.308992e-01 -8.414398e-01  1.006236e-01
   [193,]  8.466838e-01 -3.229374e-01 -4.228924e-01
   [194,] -5.052901e-01  6.839536e-02 -8.602349e-01
   [195,]  2.051468e-01  6.883992e-01 -6.957164e-01
   [196,]  3.327076e-01  9.429723e-01 -1.043073e-02
   [197,]  1.094594e-01  7.732474e-01  6.245855e-01
   [198,] -8.860684e-02  3.284042e-01 -9.403720e-01
   [199,] -9.701890e-01  2.165751e-01 -1.087589e-01
   [200,]  2.287148e-01 -8.948260e-01 -3.833744e-01
   [201,]  2.078139e-01 -3.545752e-01 -9.116413e-01
   [202,]  9.844157e-01  1.697228e-01  4.604318e-02
   [203,] -9.605146e-02 -8.297569e-01 -5.497978e-01
   [204,]  1.156643e-01 -1.306072e-01 -9.846642e-01
   [205,] -7.210604e-01  6.224659e-01 -3.043159e-01
   [206,]  7.799761e-01  9.893288e-02 -6.179398e-01
   [207,]  6.049647e-01  7.093912e-01 -3.616377e-01
   [208,]  4.741648e-02  3.000896e-01 -9.527318e-01
   [209,]  3.597641e-01  1.220100e-01 -9.250315e-01
   [210,] -6.352430e-01  7.409167e-01  2.179652e-01
   [211,] -6.375650e-01 -1.314605e-01 -7.590975e-01
   [212,]  2.892910e-01 -9.440785e-01  1.581975e-01
   [213,]  9.860957e-01  1.512284e-01  6.888644e-02
   [214,]  8.691549e-02 -9.906055e-01  1.055769e-01
   [215,] -7.238302e-01 -6.093701e-01 -3.236322e-01
   [216,] -2.313098e-01  9.366805e-01 -2.629173e-01
   [217,] -3.755105e-01  3.507524e-01  8.578838e-01
   [218,]  3.283131e-01 -8.968819e-01 -2.963331e-01
   [219,] -5.827122e-01 -7.361805e-01 -3.442161e-01
   [220,]  6.582697e-01 -2.408604e-01  7.132091e-01
   [221,]  9.509256e-01 -2.727150e-01 -1.461747e-01
   [222,]  6.618591e-02 -9.976916e-01 -1.519550e-02
   [223,]  6.139684e-01  3.018395e-01  7.293392e-01
   [224,] -7.987180e-01 -2.320702e-01 -5.551514e-01
   [225,]  3.318400e-02 -7.785282e-01 -6.267317e-01
   [226,] -9.442553e-01  1.529923e-01 -2.915051e-01
   [227,]  7.781686e-01  3.151376e-01 -5.432697e-01
   [228,]  6.067725e-01  7.910405e-01 -7.798711e-02
   [229,]  4.110231e-01  9.106442e-01 -4.227458e-02
   [230,] -1.484933e-01  4.589527e-01 -8.759636e-01
   [231,] -8.778109e-01  3.009079e-01  3.726962e-01
   [232,] -3.881283e-01 -8.168557e-01  4.267356e-01
   [233,]  5.850340e-01  7.950288e-01 -1.602014e-01
   [234,] -2.497989e-02 -9.733906e-02 -9.949377e-01
   [235,]  9.304346e-01 -2.857164e-01  2.294726e-01
   [236,]  7.052459e-01  1.569862e-01 -6.913636e-01
   [237,] -7.305254e-01  6.093938e-01  3.081751e-01
   [238,]  3.025727e-01 -9.528942e-01 -2.103511e-02
   [239,] -4.816993e-01 -3.367481e-01 -8.090528e-01
   [240,]  2.799079e-01  8.934060e-01  3.513934e-01
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  [1937,] -3.247674e-01  8.669929e-01  3.779543e-01
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  [1939,]  7.616042e-01  3.949168e-01  5.138091e-01
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 [19198,]  2.044951e-01  9.016712e-01 -3.810128e-01
 [19199,] -5.566384e-01  8.276095e-01 -7.222368e-02
 [19200,]  4.995366e-01 -2.255358e-01 -8.364190e-01
 [19201,]  5.469727e-01 -7.842062e-01  2.929872e-01
 [19202,]  5.220962e-01  7.405571e-01 -4.230729e-01
 [19203,] -8.464674e-01  1.043930e-01 -5.221063e-01
 [19204,] -2.051071e-01  2.732129e-01 -9.398329e-01
 [19205,] -7.451399e-01  6.137291e-01 -2.609658e-01
 [19206,]  4.584900e-01 -9.906296e-02  8.831610e-01
 [19207,]  2.597979e-01 -4.903705e-01 -8.318905e-01
 [19208,]  3.183812e-01  7.137522e-01 -6.238520e-01
 [19209,] -9.366741e-01  2.399709e-01  2.550598e-01
 [19210,]  9.185121e-01 -8.825561e-02  3.854172e-01
 [19211,] -7.858295e-01  2.865890e-01  5.480318e-01
 [19212,]  9.817428e-01  1.831712e-01 -5.127724e-02
 [19213,] -8.578152e-01 -4.611252e-01 -2.269725e-01
 [19214,] -7.016015e-01 -3.561499e-01 -6.171812e-01
 [19215,] -4.650384e-01 -7.403328e-01  4.854345e-01
 [19216,]  2.148540e-01 -3.980891e-01  8.918312e-01
 [19217,]  4.875139e-01  8.315634e-01 -2.661436e-01
 [19218,]  7.006048e-01  4.437915e-01 -5.587504e-01
 [19219,]  7.349970e-01  1.011868e-01  6.704779e-01
 [19220,] -5.209796e-01 -6.051874e-02  8.514210e-01
 [19221,]  4.674329e-01  4.180943e-01 -7.789118e-01
 [19222,]  6.147999e-01 -7.830549e-01  9.405363e-02
 [19223,] -8.034918e-01  3.980749e-01  4.426481e-01
 [19224,]  6.560810e-01  3.615915e-01  6.624268e-01
 [19225,] -9.158098e-01  1.627167e-01  3.671726e-01
 [19226,] -3.295825e-01 -9.311444e-01 -1.560306e-01
 [19227,] -3.284037e-01 -4.504958e-03  9.445267e-01
 [19228,] -3.595410e-01  2.594567e-01 -8.963328e-01
 [19229,]  4.165514e-01 -8.708898e-01  2.608370e-01
 [19230,] -6.636100e-01 -1.363203e-01  7

MultiRNG documentation built on March 6, 2021, 1:06 a.m.