discretize a continuous distribution
Syntax: disD = discretizeDistribution(disC)
The standard method samples 100 points by a uniform distribution in the
unit box with lower corner [0, .., 0] and upper corner [1, .., 1]. The
input disC is generated by obtainDistributionContinuous.
discretizeDistribution(.., 'argument', value) specifies additional
options of the procedure. The method itsef is selected by 'method' and
available values, including additional parameters are:
'uniform', 'box uniform' or 'uniform box' - samples uniformly inside a
rectangular box. The parameters 'regionLower' and 'regionUpper'
specify the lower and upper coordinate of the box.
'normal' - uses importance sampling from a normal distribution. The
parameter 'mean' is the mean value and 'cov' represents the
covariance matrix. 'cov' might be a vector that is transformed to
a diagonal covariance matrix.
The output structure contains all fields from the input distribution,
while 'type' is set to 'disC'. The following fields are added:
parDiscrete - the method and the parameters used for generation
positionMatrix - the coordinates (column index) of each sample
point (column vectors)
valueVector - the assigned value for the sample points from
disC.fhandle
probabilityVector - the probability density for selection of
each sample point.
See also: obtainDistributionContinuous, obtainDistributionDiscrete0001 function disD = discretizeDistribution(disC, varargin) 0002 % discretize a continuous distribution 0003 % 0004 % Syntax: disD = discretizeDistribution(disC) 0005 % 0006 % The standard method samples 100 points by a uniform distribution in the 0007 % unit box with lower corner [0, .., 0] and upper corner [1, .., 1]. The 0008 % input disC is generated by obtainDistributionContinuous. 0009 % 0010 % discretizeDistribution(.., 'argument', value) specifies additional 0011 % options of the procedure. The method itsef is selected by 'method' and 0012 % available values, including additional parameters are: 0013 % 'uniform', 'box uniform' or 'uniform box' - samples uniformly inside a 0014 % rectangular box. The parameters 'regionLower' and 'regionUpper' 0015 % specify the lower and upper coordinate of the box. 0016 % 'normal' - uses importance sampling from a normal distribution. The 0017 % parameter 'mean' is the mean value and 'cov' represents the 0018 % covariance matrix. 'cov' might be a vector that is transformed to 0019 % a diagonal covariance matrix. 0020 % 0021 % The output structure contains all fields from the input distribution, 0022 % while 'type' is set to 'disC'. The following fields are added: 0023 % parDiscrete - the method and the parameters used for generation 0024 % positionMatrix - the coordinates (column index) of each sample 0025 % point (column vectors) 0026 % valueVector - the assigned value for the sample points from 0027 % disC.fhandle 0028 % probabilityVector - the probability density for selection of 0029 % each sample point. 0030 % 0031 % See also: obtainDistributionContinuous, obtainDistributionDiscrete 0032 0033 % The elk-library: convex geometry applied to crystallization modeling. 0034 % Copyright (C) 2013 Alexander Reinhold 0035 % 0036 % This program is free software: you can redistribute it and/or modify it 0037 % under the terms of the GNU General Public License as published by the 0038 % Free Software Foundation, either version 3 of the License, or (at your 0039 % option) any later version. 0040 % 0041 % This program is distributed in the hope that it will be useful, but 0042 % WITHOUT ANY WARRANTY; without even the implied warranty of 0043 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0044 % General Public License for more details. 0045 % 0046 % You should have received a copy of the GNU General Public License along 0047 % with this program. If not, see <http://www.gnu.org/licenses/>. 0048 0049 %% Yet unsupported sampling: 0050 % 'uniform sphere' or 'sphere uniform' - samples uniformly in a ball. The 0051 % parameters 'ballCenter' and 'ballRadius' define the ball. 0052 % 'importance', 'box importance' or 'importance box' - uses importance 0053 % sampling in a rectangular box, where the importance is based on the 0054 % density function. Parameters as for 'uniform'. Note that a lot more 0055 % points are sampled to obtain the total nSample points. 0056 % 'importance sphere' or 'sphere importance' - uses importance sampling 0057 % for a ball 0058 % 'quasi box', 'box quasi' - uses the Sobolov series (a low discrepancy 0059 % series) to sample from a rectangular box. 0060 % 0061 % Importance sampling does not improve performance for Monte Carlo 0062 % integrations as rejection sampling from an original uniform 0063 % distribution is used. 0064 0065 %% input handling 0066 [o.nSample, o.method, o.regionLower, o.regionUpper, o.regionCenter, o.radius, ... 0067 o.mean, o.cov, optionStructIn] = mapOption(varargin, ... 0068 'nSample', 100, ... 0069 'method', 'box uniform', ... 0070 'regionLower', zeros([disC.nDim, 1]), ... 0071 'regionUpper', ones([disC.nDim, 1]), ... 0072 'regionCenter', zeros([disC.nDim, 1]), ... 0073 'regionRadius', 1, ... 0074 'mean', [], ... 0075 'cov', [], ... 0076 'options', struct()); 0077 optionStruct = mergeStruct(optionStructIn, o); 0078 0079 optionStruct.regionCenter = optionStruct.regionCenter(:); 0080 0081 %% initialization 0082 disD = disC; 0083 disD = rmfield(disD, 'fhandle'); 0084 disD.type = 'discrete distribution'; 0085 disD.nSample = optionStruct.nSample; 0086 0087 if strcmpi(optionStruct.method, 'uniform') || ... 0088 strcmpi(optionStruct.method, 'box uniform') || ... 0089 strcmpi(optionStruct.method, 'uniform box') 0090 0091 %% case: uniform box 0092 % parameters 0093 regionLower = optionStruct.regionLower(:); 0094 regionUpper = optionStruct.regionUpper(:); 0095 disD.parDiscrete = struct('regionLower', regionLower, 'regionUpper', ... 0096 regionUpper); 0097 0098 % sample point positions 0099 disD.positionMatrix = bsxfun(@plus, regionLower, ... 0100 diag(regionUpper-regionLower) * ... 0101 rand([disC.nDim, optionStruct.nSample])); 0102 0103 % values at positions 0104 disD.valueVector = disC.fhandle(disD.positionMatrix); 0105 0106 % probability at position 0107 disD.probabilityVector = disD.valueVector * 0 + ... 0108 1/prod(optionStruct.regionUpper - optionStruct.regionLower); 0109 elseif strcmpi(optionStruct.method, 'normal') 0110 0111 %% case: normal distribution 0112 % parameters 0113 [mean, cov] = ensureMeanAndCov(disC.nDim, optionStruct.mean, ... 0114 optionStruct.cov); 0115 0116 disD.parDiscrete = struct('mean', mean, 'cov', cov); 0117 0118 % assign position & probability 0119 [disD.positionMatrix disD.probabilityVector] = sampleNormal(disC.nDim, ... 0120 optionStruct.nSample, mean, cov); 0121 0122 % values at positions 0123 disD.valueVector = disC.fhandle(disD.positionMatrix); 0124 0125 else 0126 %% case: unknown >> error 0127 error('elk:distribution:wrongInput', ... 0128 ['The given method name (' method ') is not supported.']); 0129 end