1 | % 'check_peaklocking': estimte peaklocking error in a civ field series TODO: UPDATE |
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2 | %------------------------------------------------------------------------ |
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3 | % function ParamOut=check_peaklocking(Param) |
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4 | % |
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5 | %%%%%%%%%%% GENERAL TO ALL SERIES ACTION FCTS %%%%%%%%%%%%%%%%%%%%%%%%%%% |
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6 | % |
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7 | % This function is used in four modes by the GUI series: |
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8 | % 1) config GUI: with no input argument, the function determine the suitable GUI configuration |
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9 | % 2) interactive input: the function is used to interactively introduce input parameters, and then stops |
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10 | % 3) RUN: the function itself runs, when an appropriate input structure Param has been introduced. |
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11 | % 4) BATCH: the function itself proceeds in BATCH mode, using an xml file 'Param' as input. |
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12 | % |
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13 | % This function is used in four modes by the GUI series: |
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14 | % 1) config GUI: with no input argument, the function determine the suitable GUI configuration |
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15 | % 2) interactive input: the function is used to interactively introduce input parameters, and then stops |
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16 | % 3) RUN: the function itself runs, when an appropriate input structure Param has been introduced. |
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17 | % 4) BATCH: the function itself proceeds in BATCH mode, using an xml file 'Param' as input. |
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18 | % |
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19 | %OUTPUT |
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20 | % GUI_input=list of options in the GUI series.fig needed for the function |
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21 | % |
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22 | %INPUT: |
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23 | % In run mode, the input parameters are given as a Matlab structure Param copied from the GUI series. |
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24 | % In batch mode, Param is the name of the corresponding xml file containing the same information |
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25 | % In the absence of input (as activated when the current Action is selected |
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26 | % in series), the function ouput GUI_input set the activation of the needed GUI elements |
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27 | % |
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28 | % Param contains the elements:(use the menu bar command 'export/GUI config' in series to see the current structure Param) |
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29 | % .InputTable: cell of input file names, (several lines for multiple input) |
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30 | % each line decomposed as {RootPath,SubDir,Rootfile,NomType,Extension} |
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31 | % .OutputSubDir: name of the subdirectory for data outputs |
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32 | % .OutputDirExt: directory extension for data outputs |
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33 | % .Action: .ActionName: name of the current activated function |
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34 | % .ActionPath: path of the current activated function |
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35 | % .IndexRange: set the file or frame indices on which the action must be performed |
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36 | % .FieldTransform: .TransformName: name of the selected transform function |
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37 | % .TransformPath: path of the selected transform function |
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38 | % .TransformHandle: corresponding function handle |
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39 | % .InputFields: sub structure describing the input fields withfields |
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40 | % .FieldName: name of the field |
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41 | % .VelType: velocity type |
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42 | % .FieldName_1: name of the second field in case of two input series |
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43 | % .VelType_1: velocity type of the second field in case of two input series |
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44 | % .ProjObject: %sub structure describing a projection object (read from ancillary GUI set_object) |
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45 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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46 | function ParamOut=check_peaklocking(Param) |
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47 | |
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48 | %% set the input elements needed on the GUI series when the action is selected in the menu ActionName |
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49 | if ~exist('Param','var') % case with no input parameter |
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50 | ParamOut={'AllowInputSort';'off';...% allow alphabetic sorting of the list of input files (options 'off'/'on', 'off' by default) |
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51 | 'WholeIndexRange';'off';...% prescribes the file index ranges from min to max (options 'off'/'on', 'off' by default) |
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52 | 'NbSlice';'on'; ...%nbre of slices ('off' by default) |
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53 | 'VelType';'two';...% menu for selecting the velocity type (options 'off'/'one'/'two', 'off' by default) |
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54 | 'FieldName';'off';...% menu for selecting the field (s) in the input file(options 'off'/'one'/'two', 'off' by default) |
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55 | 'FieldTransform'; 'off';...%can use a transform function |
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56 | 'ProjObject';'on';...%can use projection object(option 'off'/'on', |
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57 | 'Mask';'off';...%can use mask option (option 'off'/'on', 'off' by default) |
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58 | 'OutputDirExt';'.pklock';...%set the output dir extension |
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59 | ''}; |
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60 | return |
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61 | end |
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62 | |
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63 | %%%%%%%%%%%% STANDARD PART %%%%%%%%%%%% |
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64 | %% select different modes, RUN, parameter input, BATCH |
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65 | % BATCH case: read the xml file for batch case |
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66 | if ischar(Param) |
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67 | Param=xml2struct(Param); |
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68 | checkrun=0; |
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69 | % RUN case: parameters introduced as the input structure Param |
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70 | else |
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71 | hseries=guidata(Param.hseries);%handles of the GUI series |
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72 | if isfield(Param,'Specific')&& strcmp(Param.Specific,'?') |
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73 | checkrun=1;% will only search interactive input parameters (preparation of BATCH mode) |
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74 | else |
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75 | checkrun=2; % indicate the RUN option is used |
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76 | end |
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77 | end |
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78 | ParamOut=Param; %default output |
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79 | OutputDir=[Param.OutputSubDir Param.OutputDirExt]; |
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80 | |
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81 | %% root input file(s) and type |
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82 | RootPath=Param.InputTable(:,1); |
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83 | RootFile=Param.InputTable(:,3); |
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84 | SubDir=Param.InputTable(:,2); |
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85 | NomType=Param.InputTable(:,4); |
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86 | FileExt=Param.InputTable(:,5); |
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87 | [filecell,i1_series,i2_series,j1_series,j2_series]=get_file_series(Param); |
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88 | %%%%%%%%%%%% |
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89 | % The cell array filecell is the list of input file names, while |
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90 | % filecell{iview,fileindex}: |
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91 | % iview: line in the table corresponding to a given file series |
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92 | % fileindex: file index within the file series, |
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93 | % i1_series(iview,ref_j,ref_i)... are the corresponding arrays of indices i1,i2,j1,j2, depending on the input line iview and the two reference indices ref_i,ref_j |
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94 | % i1_series(iview,fileindex) expresses the same indices as a 1D array in file indices |
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95 | %%%%%%%%%%%% |
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96 | NbSlice=1;%default |
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97 | if isfield(Param.IndexRange,'NbSlice')&&~isempty(Param.IndexRange.NbSlice) |
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98 | NbSlice=Param.IndexRange.NbSlice; |
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99 | end |
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100 | nbview=1;%number of input file series (lines in InputTable) |
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101 | nbfield_j=size(i1_series{1},1); %nb of fields for the j index (bursts or volume slices) |
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102 | nbfield_i=size(i1_series{1},2); %nb of fields for the i index |
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103 | nbfield=nbfield_j*nbfield_i; %total number of fields |
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104 | nbfield_i=floor(nbfield/NbSlice);%total number of indexes in a slice (adjusted to an integer number of slices) |
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105 | nbfield=nbfield_i*NbSlice; %total number of fields after adjustement |
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106 | |
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107 | %determine the file type on each line from the first input file |
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108 | ImageTypeOptions={'image','multimage','mmreader','video'}; |
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109 | NcTypeOptions={'netcdf','civx','civdata'}; |
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110 | for iview=1:nbview |
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111 | if ~exist(filecell{iview,1}','file') |
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112 | displ_uvmat('ERROR',['the first input file ' filecell{iview,1} ' does not exist'],checkrun) |
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113 | return |
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114 | end |
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115 | [FileType{iview},FileInfo{iview},MovieObject{iview}]=get_file_type(filecell{iview,1}); |
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116 | CheckImage{iview}=~isempty(find(strcmp(FileType{iview},ImageTypeOptions)));% =1 for images |
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117 | CheckNc{iview}=~isempty(find(strcmp(FileType{iview},NcTypeOptions)));% =1 for netcdf files |
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118 | if ~isempty(j1_series{iview}) |
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119 | frame_index{iview}=j1_series{iview}; |
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120 | else |
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121 | frame_index{iview}=i1_series{iview}; |
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122 | end |
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123 | end |
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124 | |
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125 | %% calibration data and timing: read the ImaDoc files |
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126 | %none |
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127 | |
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128 | %% coordinate transform or other user defined transform |
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129 | % none |
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130 | |
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131 | %%%%%%%%%%%% END STANDARD PART %%%%%%%%%%%% |
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132 | % EDIT FROM HERE |
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133 | |
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134 | %% check the validity of ctinput file types |
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135 | %none |
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136 | |
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137 | %% Set field names and velocity types |
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138 | InputFields{1}=[];%default (case of images) |
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139 | if isfield(Param,'InputFields') |
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140 | InputFields{1}=Param.InputFields; |
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141 | end |
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142 | % only one input fieldseries |
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143 | |
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144 | %% Initiate output fields |
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145 | %initiate the output structure as a copy of the first input one (reproduce fields) |
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146 | [DataOut,tild,errormsg] = read_field(filecell{1,1},FileType{1},InputFields{1},1); |
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147 | if ~isempty(errormsg) |
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148 | displ_uvmat('ERROR',['error reading ' filecell{1,1} ': ' errormsg],checkrun) |
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149 | return |
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150 | end |
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151 | time_1=[]; |
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152 | if isfield(DataOut,'Time') |
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153 | time_1=DataOut.Time(1); |
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154 | end |
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155 | if CheckNc{iview} |
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156 | if isempty(strcmp('Conventions',DataOut.ListGlobalAttribute)) |
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157 | DataOut.ListGlobalAttribute=['Conventions' DataOut.ListGlobalAttribute]; |
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158 | end |
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159 | DataOut.Conventions='uvmat'; |
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160 | DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {Param.Action}]; |
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161 | ActionKey='Action'; |
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162 | while isfield(DataOut,ActionKey) |
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163 | ActionKey=[ActionKey '_1']; |
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164 | end |
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165 | DataOut.(ActionKey)=Param.Action; |
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166 | DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {ActionKey}]; |
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167 | if isfield(DataOut,'Time') |
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168 | DataOut.ListGlobalAttribute=[DataOut.ListGlobalAttribute {'Time','Time_end'}]; |
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169 | end |
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170 | end |
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171 | |
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172 | %%%%%%%%%%%%%%%% loop on field indices %%%%%%%%%%%%%%%% |
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173 | index_slice=1:nbfield;% select the file indices |
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174 | for index=index_slice |
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175 | if checkrun |
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176 | update_waitbar(hseries.Waitbar,index/(nbfield)) |
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177 | stopstate=get(hseries.RUN,'BusyAction'); |
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178 | else |
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179 | stopstate='queue'; |
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180 | end |
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181 | if isequal(stopstate,'queue')% enable STOP command |
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182 | Data=cell(1,nbview);%initiate the set Data; |
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183 | nbtime=0; |
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184 | dt=[]; |
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185 | %%%%%%%%%%%%%%%% loop on views (input lines) %%%%%%%%%%%%%%%% |
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186 | for iview=1:nbview |
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187 | % reading input file(s) |
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188 | [Data{iview},tild,errormsg] = read_field(filecell{iview,index},FileType{iview},InputFields{iview},frame_index{iview}(index)); |
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189 | if ~isempty(errormsg) |
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190 | errormsg=['time_series / read_field / ' errormsg]; |
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191 | display(errormsg) |
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192 | break |
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193 | end |
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194 | if ~isempty(NbSlice_calib) |
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195 | Data{iview}.ZIndex=mod(i1_series{iview}(index)-1,NbSlice_calib{iview})+1;%Zindex for phys transform |
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196 | end |
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197 | end |
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198 | if isempty(errormsg) |
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199 | Field=Data{1}; % default input field structure |
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200 | % coordinate transform (or other user defined transform) |
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201 | % none |
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202 | |
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203 | %field projection on an object |
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204 | if Param.CheckObject |
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205 | [Field,errormsg]=proj_field(Field,Param.ProjObject); |
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206 | if ~isempty(errormsg) |
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207 | msgbox_uvmat('ERROR',['time_series / proj_field / ' errormsg]) |
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208 | return |
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209 | end |
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210 | end |
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211 | nbfile=nbfile+1; |
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212 | |
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213 | % initiate the time series at the first iteration |
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214 | if nbfile==1 |
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215 | % stop program if the first field reading is in error |
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216 | if ~isempty(errormsg) |
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217 | displ_uvmat('ERROR',['time_series / sub_field / ' errormsg],checkrun) |
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218 | return |
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219 | end |
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220 | DataOut=Field;%default |
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221 | DataOut.NbDim=Field.NbDim+1; %add the time dimension for plots |
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222 | nbvar=length(Field.ListVarName); |
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223 | if nbvar==0 |
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224 | displ_uvmat('ERROR','no input variable selected',checkrun) |
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225 | return |
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226 | end |
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227 | testsum=2*ones(1,nbvar);%initiate flag for action on each variable |
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228 | if isfield(Field,'VarAttribute') % look for coordinate and flag variables |
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229 | for ivar=1:nbvar |
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230 | if length(Field.VarAttribute)>=ivar && isfield(Field.VarAttribute{ivar},'Role') |
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231 | var_role=Field.VarAttribute{ivar}.Role;%'role' of the variable |
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232 | if isequal(var_role,'errorflag') |
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233 | displ_uvmat('ERROR','do not handle error flags in time series',checkrun) |
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234 | return |
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235 | end |
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236 | if isequal(var_role,'warnflag') |
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237 | testsum(ivar)=0; % not recorded variable |
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238 | eval(['DataOut=rmfield(DataOut,''' Field.ListVarName{ivar} ''');']);%remove variable |
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239 | end |
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240 | if isequal(var_role,'coord_x')| isequal(var_role,'coord_y')|... |
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241 | isequal(var_role,'coord_z')|isequal(var_role,'coord') |
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242 | testsum(ivar)=1; %constant coordinates, record without time evolution |
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243 | end |
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244 | end |
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245 | % check whether the variable ivar is a dimension variable |
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246 | DimCell=Field.VarDimName{ivar}; |
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247 | if ischar(DimCell) |
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248 | DimCell={DimCell}; |
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249 | end |
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250 | if numel(DimCell)==1 && isequal(Field.ListVarName{ivar},DimCell{1})%detect dimension variables |
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251 | testsum(ivar)=1; |
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252 | end |
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253 | end |
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254 | end |
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255 | for ivar=1:nbvar |
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256 | if testsum(ivar)==2 |
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257 | eval(['DataOut.' Field.ListVarName{ivar} '=[];']) |
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258 | end |
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259 | end |
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260 | DataOut.ListVarName=[{'Time'} DataOut.ListVarName]; |
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261 | end |
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262 | |
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263 | % add data to the current field |
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264 | for ivar=1:length(Field.ListVarName) |
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265 | VarName=Field.ListVarName{ivar}; |
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266 | VarVal=Field.(VarName); |
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267 | if testsum(ivar)==2% test for recorded variable |
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268 | if isempty(errormsg) |
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269 | if isequal(Param.ProjObject.ProjMode,'inside')% take the average in the domain for 'inside' mode |
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270 | if isempty(VarVal) |
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271 | displ_uvmat('ERROR',['empty result at frame index ' num2str(i1_series{iview}(index))],checkrun) |
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272 | return |
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273 | end |
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274 | VarVal=mean(VarVal,1); |
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275 | end |
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276 | VarVal=shiftdim(VarVal,-1); %shift dimension |
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277 | DataOut.(VarName)=cat(1,DataOut.(VarName),VarVal);%concanete the current field to the time series |
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278 | else |
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279 | DataOut.(VarName)=cat(1,DataOut.(VarName),0);% put each variable to 0 in case of input reading error |
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280 | end |
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281 | elseif testsum(ivar)==1% variable representing fixed coordinates |
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282 | VarInit=DataOut.(VarName); |
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283 | if isempty(errormsg) && ~isequal(VarVal,VarInit) |
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284 | displ_uvmat('ERROR',['time series requires constant coordinates ' VarName],checkrun) |
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285 | return |
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286 | end |
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287 | end |
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288 | end |
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289 | |
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290 | % record the time: |
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291 | if isempty(time)% time not set by xml filer(s) |
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292 | if isfield(Data{1},'Time') |
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293 | DataOut.Time(nbfile,1)=Field.Time; |
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294 | else |
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295 | DataOut.Time(nbfile,1)=index;%default |
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296 | end |
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297 | else % time from ImaDoc prevails TODO: correct |
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298 | DataOut.Time(nbfile,1)=time(index);% |
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299 | end |
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300 | |
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301 | % record the number of missing input fields |
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302 | if ~isempty(errormsg) |
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303 | nbmissing=nbmissing+1; |
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304 | display(['index=' num2str(index) ':' errormsg]) |
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305 | end |
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306 | end |
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307 | end |
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308 | end |
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309 | %%%%%%% END OF LOOP WITHIN A SLICE |
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310 | |
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311 | %remove time for global attributes if exists |
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312 | Time_index=find(strcmp('Time',DataOut.ListGlobalAttribute)); |
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313 | if ~isempty(Time_index) |
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314 | DataOut.ListGlobalAttribute(Time_index)=[]; |
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315 | end |
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316 | DataOut.Conventions='uvmat'; |
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317 | for ivar=1:numel(DataOut.ListVarName) |
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318 | VarName=DataOut.ListVarName{ivar}; |
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319 | eval(['DataOut.' VarName '=squeeze(DataOut.' VarName ');']) %remove singletons |
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320 | end |
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321 | |
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322 | % add time dimension |
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323 | for ivar=1:length(Field.ListVarName) |
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324 | DimCell=Field.VarDimName(ivar); |
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325 | if testsum(ivar)==2%variable used as time series |
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326 | DataOut.VarDimName{ivar}=[{'Time'} DimCell]; |
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327 | elseif testsum(ivar)==1 |
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328 | DataOut.VarDimName{ivar}=DimCell; |
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329 | end |
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330 | end |
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331 | indexremove=find(~testsum); |
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332 | if ~isempty(indexremove) |
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333 | DataOut.ListVarName(1+indexremove)=[]; |
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334 | DataOut.VarDimName(indexremove)=[]; |
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335 | if isfield(DataOut,'Role') && ~isempty(DataOut.Role{1})%generaliser aus autres attributs |
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336 | DataOut.Role(1+indexremove)=[]; |
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337 | end |
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338 | end |
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339 | |
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340 | %shift variable attributes |
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341 | if isfield(DataOut,'VarAttribute') |
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342 | DataOut.VarAttribute=[{[]} DataOut.VarAttribute]; |
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343 | end |
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344 | DataOut.VarDimName=[{'Time'} DataOut.VarDimName]; |
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345 | DataOut.Action=Param.Action;%name of the processing programme |
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346 | test_time=diff(DataOut.Time)>0;% test that the readed time is increasing (not constant) |
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347 | if ~test_time |
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348 | DataOut.Time=1:filecounter; |
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349 | end |
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350 | |
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351 | % display nbmissing |
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352 | if ~isequal(nbmissing,0) |
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353 | displ_uvmat('WARNING',[num2str(nbmissing) ' files skipped: missing files or bad input, see command window display'],checkrun) |
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354 | end |
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355 | |
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356 | %name of result file |
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357 | OutputFile=fullfile_uvmat(RootPath{1},OutputDir,RootFile{1},FileExtOut,NomTypeOut,i1_series{1}(1),i1_series{1}(end),i_slice,[]); |
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358 | errormsg=struct2nc(OutputFile,DataOut); %save result file |
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359 | if isempty(errormsg) |
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360 | display([OutputFile ' written']) |
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361 | else |
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362 | displ_uvmat('ERROR',['error in Series/struct2nc: ' errormsg],checkrun) |
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363 | end |
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364 | |
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365 | return |
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366 | |
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367 | %%%%%%%%%%%%%%%%%% END%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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368 | %evaluation of peacklocking errors |
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369 | %use splinhist: give spline coeff cc for a smooth histo (call spline4) |
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370 | %use histsmooth(x,cc): calculate the smooth histo for any value x |
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371 | %use histder(x,cc): calculate the derivative of the smooth histo |
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372 | global hfig1 hfig2 hfig3 |
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373 | global nbb Uval Vval Uhist Vhist % nbb resolution of the histogram nbb=10: 10 values in unity interval |
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374 | global xval xerror yval yerror |
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375 | |
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376 | set(handles.vector_y,'Value',1)% trigger the option Uhist on the interface |
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377 | set(handles.Vhist_input,'Value',1) |
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378 | set(handles.cm_switch,'Value',0) % put the switch to 'pixel' |
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379 | |
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380 | %adjust the extremal values of the histogram in U with respect to integer |
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381 | %values |
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382 | minimU=round(min(Uval)-0.5)+0.5; %first value of the histogram with integer bins |
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383 | maximU=round(max(Uval)-0.5)+0.5; |
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384 | minim_fin=(minimU-0.5+1/(2*nbb)); % first bin valueat the beginning of an integer interval |
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385 | maxim_fin=(maximU+0.5-1/(2*nbb)); % last integer value |
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386 | nb_bin_min= round(-(minim_fin - min(Uval))*nbb); % nbre of bins added below |
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387 | nb_bin_max=round((maxim_fin -max(Uval))*nbb); %nbre of bins added above |
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388 | Uval=[minim_fin:(1/nbb):maxim_fin]; |
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389 | histu_min=zeros(nb_bin_min,1); |
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390 | histu_max=zeros(nb_bin_max,1); |
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391 | Uhist=[histu_min; Uhist ;histu_max]; % column vector |
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392 | |
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393 | %adjust the extremal values of the histogram in V |
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394 | minimV=round(min(Vval-0.5)+0.5); |
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395 | maximV=round(max(Vval-0.5)+0.5); |
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396 | minim_fin=minimV-0.5+1/(2*nbb); % first bin valueat the beginning of an integer interval |
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397 | maxim_fin=maximV+0.5-1/(2*nbb); % last integer value |
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398 | nb_bin_min=round((min(Vval) - minim_fin)*nbb); % nbre of bins added below |
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399 | nb_bin_max=round((maxim_fin -max(Vval))*nbb); |
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400 | Vval=[minim_fin:(1/nbb):maxim_fin]; |
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401 | histu_min=zeros(nb_bin_min,1); |
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402 | histu_max=zeros(nb_bin_max,1); |
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403 | Vhist=[histu_min; Vhist ;histu_max]; % column vector |
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404 | |
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405 | % RUN_histo_Callback(hObject, eventdata, handles) |
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406 | % %adjust the histogram to integer values: |
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407 | |
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408 | %histoU and V |
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409 | [Uhistinter,xval,xerror]=peaklock(nbb,minimU,maximU,Uhist); |
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410 | [Vhistinter,yval,yerror]=peaklock(nbb,minimV,maximV,Vhist); |
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411 | |
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412 | % selection of value ranges such that histo>=10 (enough statistics) |
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413 | Uval_ind=find(Uhist>=10); |
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414 | ind_min=min(Uval_ind); |
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415 | ind_max=max(Uval_ind); |
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416 | U_min=Uval(ind_min);% minimum allowed value |
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417 | U_max=Uval(ind_max);%maximum allowed value |
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418 | |
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419 | % selection of value ranges such that histo>=10 (enough statistics) |
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420 | Vval_ind=find(Vhist>=10); |
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421 | ind_min=min(Vval_ind); |
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422 | ind_max=max(Vval_ind); |
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423 | V_min=Vval(ind_min);% minimum allowed value |
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424 | V_max=Vval(ind_max);%maximum allowed value |
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425 | |
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426 | figure(4)% plot U histogram with smoothed one |
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427 | plot(Uval,Uhist,'b') |
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428 | grid on |
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429 | hold on |
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430 | plot(Uval,Uhistinter,'r'); |
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431 | hold off |
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432 | |
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433 | figure(5)% plot V histogram with smoothed one |
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434 | plot(Vval,Vhist,'b') |
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435 | grid on |
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436 | hold on |
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437 | plot(Vval,Vhistinter,'r'); |
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438 | hold off |
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439 | |
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440 | figure(6)% plot pixel error in two subplots |
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441 | hfig4=subplot(2,1,1); |
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442 | hfig5=subplot(2,1,2); |
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443 | axes(hfig4) |
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444 | plot(xval,xerror) |
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445 | axis([U_min U_max -0.4 0.4]) |
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446 | xlabel('velocity u (pix)') |
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447 | ylabel('peaklocking error (pix)') |
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448 | grid on |
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449 | axes(hfig5) |
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450 | plot(yval,yerror) |
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451 | axis([V_min V_max -0.4 0.4]); |
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452 | xlabel('velocity v (pix)') |
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453 | ylabel('peaklocking error (pix)') |
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454 | grid on |
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455 | |
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456 | |
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457 | |
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458 | |
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459 | |
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460 | |
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461 | |
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462 | |
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463 | |
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464 | %'peaklock': determines peacklocking errors from velocity histograms. |
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465 | %------------------------------------------------------- |
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466 | %first smooth the input histogram 'histu' in such a way that the integral over |
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467 | %n-n+1 is preserved, then deduce the peaklocking 'error' function of the pixcel displacement 'x'. |
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468 | % |
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469 | % [histinter,x,error]=peaklock(nbb,minim,maxim,histu) |
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470 | %OUTPUT: |
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471 | %histinter: smoothed interpolated histogram |
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472 | % x: vector of displacement values. |
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473 | % error: vector of estimated errors corresponding to x |
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474 | %INPUT: |
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475 | %histu=vector representing the values of histogram of measured velocity ; |
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476 | %minim, maxim: extremal values of the measured velocity (absica for histu) |
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477 | %nbb: number of bins inside each integer interval for the histograms |
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478 | %SUBROUTINES INCLUDED: |
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479 | %spline4.m% spline interpolation at 4th order |
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480 | %splinhist.m: give spline coeff cc for a smooth histo (call spline4) |
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481 | %histsmooth.m(x,cc): calculate the smooth histo for any value x |
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482 | %histder.m(x,cc): calculate the derivative of the smooth histo |
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483 | function [histinter,x,error]=peaklock(nbb,minim,maxim,histu) |
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484 | |
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485 | nint=maxim-minim+1 |
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486 | xfin=[minim-0.5+1/(2*nbb):(1/nbb):maxim+0.5-(1/(2*nbb))]; |
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487 | histo=(reshape(histu,nbb,nint));%extract values with x between integer -1/2 integer +1/2 |
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488 | Integ=sum(histo)/nbb; %integral of the pdf on each integer bin |
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489 | [histinter,cc]=splinhist(Integ,minim,nbb); |
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490 | histx=reshape(histinter,nbb,nint); |
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491 | xint=[minim:1:maxim]; |
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492 | x=zeros(nbb,nint); |
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493 | %determination of the displacement x(j,:) |
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494 | %j=1 |
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495 | delx=histo(1,:)./histsmooth(-0.5*ones(1,nint),cc)/nbb; |
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496 | %del(1,:)=delx; |
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497 | x(1,:)=-0.5+delx-(delx.*delx/2).*histder(-0.5*ones(1,nint),cc); |
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498 | %histx(1,:)=histsmooth(x(j-1,:),cc); |
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499 | for j=2:nbb |
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500 | delx=histo(j,:)./histsmooth(x(j-1,:),cc)/nbb; |
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501 | %delx=delx.*(delx<3*ones(1,nint)/nbb)+3*ones(1,nint)/nbb.*~(delx <3*ones(1,nint)/nbb) |
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502 | x(j,:)=x(j-1,:)+delx-(delx.*delx/2).*histder(x(j-1,:),cc); |
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503 | end |
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504 | %reshape |
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505 | xint=ones(nbb,1)*xint; |
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506 | x=x+xint; |
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507 | x=reshape(x,1,nbb*nint); |
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508 | error=xfin+1/(2*nbb)-x; |
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509 | |
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510 | %------------------------------------------------------- |
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511 | % --- determine the spline coefficients cc for the interpolated histogram. |
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512 | %------------------------------------------------- |
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513 | function [histsmooth,cc]= splinhist(Integ,mini,nbb) |
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514 | % provides a smooth histogramm histmooth, which remains always positive, |
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515 | % and is such that its sum over each integer bin [i-1/2 i+1/2] is equal to |
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516 | % Integ(i). The function determines histmooth as the exponential of a 4th |
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517 | % order spline function and adjust the cefficients by a Newton method to |
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518 | % fit the integral conditions Integ |
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519 | % histmooth is determined at the abscissa |
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520 | % xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))] (maxi=mini+size(aa)-1) |
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521 | %cc(1-5,i) provides the spline coefficients |
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522 | |
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523 | % order 0 |
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524 | siz=size(Integ); |
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525 | nint=siz(2); |
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526 | izero=find(Integ==0); %indices of zero elements |
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527 | inonzero=find(Integ); |
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528 | Integ(izero)=min(Integ(inonzero)); |
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529 | aa=log(Integ);%initial guess for a coeff |
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530 | spli=spline4(aa,mini,nbb); %appel à la fonction spline4 |
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531 | histsmooth=exp(spli); |
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532 | |
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533 | S=(sum(reshape(histsmooth,nbb,nint)))/nbb;% integral of the fit histsmooth on ]i-1/2 i+1/2[ |
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534 | epsilon=max(abs(Integ-S)); |
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535 | iter=0; |
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536 | while epsilon > 0.000001 & iter<10 |
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537 | ident=eye(nint); |
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538 | dSda=ones(nint); |
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539 | for j=1:nint% determination of the jacobian matrix dSda |
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540 | dhistda=spline4(ident(j,:),mini,nbb); |
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541 | expdhistda=dhistda.*histsmooth; |
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542 | dSda(j,:)=(sum(reshape(expdhistda,nbb,nint)))/nbb; |
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543 | end |
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544 | aa=aa+(Integ-S)*inv(dSda);%new estimate of coefficients aa by linear interpolation |
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545 | [spli,bb]=spline4(aa,mini,nbb);% new fit histsmooth |
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546 | histsmooth=exp(spli); |
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547 | S=(sum(reshape(histsmooth,nbb,nint)))/nbb;% integral of the fit histsmooth on ]i-1/2 i+1/2[ |
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548 | epsilon=max(abs(Integ-S)); |
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549 | iter=iter+1; |
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550 | end |
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551 | if iter==10, errordlg('splinhist did not converge after 10 iterations'),end |
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552 | cc(1,:)=aa; |
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553 | cc(2,:)=bb(1,:); |
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554 | cc(3,:)=bb(2,:); |
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555 | cc(4,:)=bb(3,:); |
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556 | cc(5,:)=bb(4,:); |
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557 | |
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558 | %------------------------------------------------------- |
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559 | % --- determine the 4th order spline coefficients from the function values aa. |
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560 | %------------------------------------------------- |
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561 | function [histsmooth,bb]= spline4(aa,mini,n) |
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562 | % spline interpolation at 4th order |
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563 | %aa=vector of values of a function at integer abscissa, starting at mini |
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564 | %n=number of subdivisions for the interpolated function |
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565 | % histmooth =interpolated values at absissa |
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566 | % xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))] (maxi=mini+size(aa)-1) |
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567 | %bb=[b(i);c(i);d(i); e(i)] matrix of spline coeff |
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568 | L1=[1/2 1/4 1/8 1/16;1 1 3/4 1/2;0 2 3 3;0 0 6 12]; |
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569 | L2=[-1/2 1/4 -1/8 1/16;1 -1 3/4 -1/2;0 2 -3 3;0 0 6 -12]; |
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570 | M=inv(L2)*L1; |
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571 | [V,D]=eig(M); |
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572 | F=-inv(V)*inv(L2)*[1 ;0 ;0;0]; |
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573 | a1rev=[1 -1/D(1,1)]; |
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574 | b1rev=[F(1)/D(1,1)]; |
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575 | a2rev=[1 -1/D(2,2)]; |
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576 | b2rev=[F(2)/D(2,2)]; |
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577 | a3=[1 -D(3,3)]; |
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578 | b3=[F(3)]; |
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579 | a4=[1 -D(4,4)]; |
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580 | b4=[F(4)]; |
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581 | |
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582 | %data |
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583 | % n=10;% résolution de la pdf: nbre de points par unite de u |
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584 | % mini=-10.0;%general mini=uint16(min(values)-1 CHOOSE maxi-mini+1 EVEN |
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585 | % maxi=9.0; % general maxi=uint16(max(values))+1 |
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586 | %nint=double(maxi-mini+1); % nombre d'intervals entiers EVEN! |
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587 | siz=size(aa); |
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588 | nint=siz(2); |
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589 | maxi=mini+nint-1; |
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590 | npdf=nint*n;% nbre total d'intervals à introduire dans la pdf: hist(u,npdf) |
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591 | %simulation de pdf |
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592 | xfin=[mini-0.5+1/(2*n):(1/n):maxi+0.5-(1/(2*n))];% valeurs d'interpolation: we take n values in each integer interval |
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593 | %histolin=exp(-(xfin-1).*(xfin-1)).*(2+cos(10*(xfin-1)));% simulation d'une pdf |
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594 | %histo=log(histolin); |
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595 | %histo=sin(2*pi*xfin); |
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596 | %histextract=(reshape(histo,n,nint)); |
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597 | %aa=sum(histextract)/n %integral of the pdf on each integer bin |
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598 | IP=[0 diff(aa)]; |
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599 | Irev=zeros(size(aa)); |
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600 | for i=1:nint |
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601 | Irev(i)=aa(end-i+1); |
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602 | end |
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603 | IPrev=[0 diff(Irev)]; |
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604 | |
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605 | %get the spline coelfficients a_d, using filter on the eigen vectors A,B,C |
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606 | Arev=filter(b1rev,a1rev,IPrev); |
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607 | Brev=filter(b2rev,a2rev,IPrev); |
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608 | C=filter(b3,a3,IP); |
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609 | D=filter(b4,a4,IP); |
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610 | A=zeros(size(Arev)); |
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611 | B=zeros(size(Brev)); |
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612 | for i=1:nint |
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613 | A(i)=Arev(end-i+1); |
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614 | B(i)=Brev(end-i+1); |
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615 | end |
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616 | %Matr=V*[A;B;C;D]; |
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617 | bb=V*[A;B;C;D]; |
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618 | %b=Matr(1,:); |
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619 | %c=Matr(2,:); |
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620 | %d=Matr(3,:); |
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621 | %e=Matr(4,:); |
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622 | %a=aa; |
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623 | |
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624 | %calculate the interpolation using the spline coefficients a-d |
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625 | %xextract=(reshape(xfin,n,nint));% |
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626 | chi=xfin+1/(2*n)-min(xfin)-double(int16(xfin+(1/(2*n))-min(xfin)))-0.5;% decimal part |
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627 | chi2=chi.*chi; |
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628 | chi3=chi2.*chi; |
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629 | chi4=chi3.*chi; |
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630 | avec=reshape(ones(n,1)*aa,1,n*nint); |
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631 | bvec=reshape(ones(n,1)*bb(1,:),1,n*nint); |
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632 | cvec=reshape(ones(n,1)*bb(2,:),1,n*nint); |
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633 | dvec=reshape(ones(n,1)*bb(3,:),1,n*nint); |
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634 | evec=reshape(ones(n,1)*bb(4,:),1,n*nint); |
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635 | histsmooth=avec+bvec.*chi+cvec.*chi2+dvec.*chi3+evec.*chi4; |
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636 | |
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637 | %------------------------------------------------------- |
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638 | % --- determine the interpolated histogram at points chi from the spline ceff cc. |
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639 | %------------------------------------------------- |
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640 | function histx= histsmooth(chi,cc) |
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641 | % provides the value of the interpolated histogram at values chi=x-i |
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642 | %(difference with the mnearest integer) |
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643 | % cc(5,size(chi)) is the set of spline coefficients obtained by splinhist |
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644 | chi2=chi.*chi; |
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645 | chi3=chi2.*chi; |
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646 | chi4=chi3.*chi; |
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647 | histx=exp(cc(1,:)+cc(2,:).*chi+cc(3,:).*chi2+cc(4,:).*chi3+cc(5,:).*chi4); |
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648 | |
---|
649 | %------------------------------------------------------- |
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650 | % --- determine the derivative p'/p of the interpolated histogram at points chi from the spline ceff cc. |
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651 | %------------------------------------------------- |
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652 | function histder= histder(chi,cc) |
---|
653 | % provides the logarithmique derivative p'/p of the interpolated histogram |
---|
654 | %at values chi=x-i |
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655 | %(difference with the nearest integer) |
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656 | % cc(5,size(chi)) is the set of spline coefficients obtained by splinhist |
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657 | chi2=chi.*chi; |
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658 | chi3=chi2.*chi; |
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659 | chi4=chi3.*chi; |
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660 | histder=cc(2,:)+2*cc(3,:).*chi+3*cc(4,:).*chi2+4*cc(5,:).*chi3; |
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