cosmo synthetic dataset

function ds=cosmo_synthetic_dataset(varargin)
% generate synthetic dataset
%
% ds=cosmo_synthetic_dataset(varargin)
%
% Inputs:
%   'size', s               determines the number of features. One of
%                           'tiny', 'small', 'normal', 'big', or 'huge'
%   'type', t               type of dataset. One of 'fmri', 'meeg',
%                           'timelock', 'timefreq', 'surface', or 'source'.
 %                          'meeg' is equivalent to 'timelock'
%   'sens', c               for meeg datasets ('time{lock}, 'meeg'), this
%                           sets which sensor type is used. Supported are
%                           - neuromag306{all,planar,combined,mag}
%                           - ctf151
%                           - 4d{1,2}48[planar]
%                           - yokogawa{64,160}[planar]
%                           - eeg10{05,10,20}
%   'data_field', f         If the type t is 'source', this can be 'pow' or
%                           'mom'.
%   'sigma', sigma          parameter to influence class distance. The
%                           larger this value, the more discrimable the
%                           classes are.
%
%   'ntargets', nt          number of unique targets (default: 2)
%   'nchunks', nc           number of unique chunks (default: 3)
%
%   'nmodalities', nm       number of unique modalities (default: [])
%   'nsubjects', ns         number of unique subjects (default: [])
%   'nreps', nr             number of sample repeats (default: [])
%   'seed', seed            seed value for pseudo-random number generator
%                           (default: 1). Different seed values give
%                           different random numbers.
%
% Output:
%    ds                     dataset struct according to parameters.
%                           The output has (nt*nc*nm*ns*nr) samples, and
%                           the number of features is determined by s.
%                           If any of the nt, nc, nm, ns, nr values are not
%                           empty, there is a corresponding sample
%                           attribute.
%
% Examples:
%     ds=cosmo_synthetic_dataset();
%     cosmo_disp(ds);
%     %|| .samples
%     %||   [   2.03    -0.892    -0.826      1.16      1.16     -1.29
%     %||      0.584      1.84      1.17    -0.848      3.49    -0.199
%     %||      -1.44    -0.262     -1.92      3.09     -1.37      1.73
%     %||     -0.518      2.34     0.441      1.86     0.479    0.0832
%     %||       1.19    -0.204    -0.209      1.76    -0.955     0.501
%     %||      -1.33      2.72     0.148     0.502      3.41     -0.48 ]
%     %|| .fa
%     %||   .i
%     %||     [ 1         2         3         1         2         3 ]
%     %||   .j
%     %||     [ 1         1         1         2         2         2 ]
%     %||   .k
%     %||     [ 1         1         1         1         1         1 ]
%     %|| .a
%     %||   .fdim
%     %||     .labels
%     %||       { 'i'  'j'  'k' }
%     %||     .values
%     %||       { [ 1         2         3 ]  [ 1         2 ]  [ 1 ] }
%     %||   .vol
%     %||     .mat
%     %||       [ 2         0         0        -3
%     %||         0         2         0        -3
%     %||         0         0         2        -3
%     %||         0         0         0         1 ]
%     %||     .dim
%     %||       [ 3         2         1 ]
%     %||     .xform
%     %||       'scanner_anat'
%     %|| .sa
%     %||   .targets
%     %||     [ 1
%     %||       2
%     %||       1
%     %||       2
%     %||       1
%     %||       2 ]
%     %||   .chunks
%     %||     [ 1
%     %||       1
%     %||       2
%     %||       2
%     %||       3
%     %||       3 ]
%
%     ds=cosmo_synthetic_dataset('sigma',5,...
%                                'nchunks',5,'ntargets',4,...
%                                'nsubjects',10);
%     cosmo_disp(ds)
%     %|| .samples
%     %||   [   3.53      1.65      1.74     0.453      1.22      3.28
%     %||      0.584      3.88     0.856     0.841    -0.899      1.23
%     %||      -3.68      1.38      1.89      -1.4     0.216      0.68
%     %||        :         :         :        :          :         :
%     %||     -0.725      4.41    -0.313     0.111     0.437     -1.03
%     %||      0.297    0.0279       1.8   -0.0303    -0.451     0.346
%     %||       1.64     0.103     -1.22       4.8     0.754      1.03 ]@200x6
%     %|| .fa
%     %||   .i
%     %||     [ 1         2         3         1         2         3 ]
%     %||   .j
%     %||     [ 1         1         1         2         2         2 ]
%     %||   .k
%     %||     [ 1         1         1         1         1         1 ]
%     %|| .a
%     %||   .fdim
%     %||     .labels
%     %||       { 'i'  'j'  'k' }
%     %||     .values
%     %||       { [ 1         2         3 ]  [ 1         2 ]  [ 1 ] }
%     %||   .vol
%     %||     .mat
%     %||       [ 2         0         0        -3
%     %||         0         2         0        -3
%     %||         0         0         2        -3
%     %||         0         0         0         1 ]
%     %||     .dim
%     %||       [ 3         2         1 ]
%     %||     .xform
%     %||       'scanner_anat'
%     %|| .sa
%     %||   .targets
%     %||     [ 1
%     %||       2
%     %||       3
%     %||       :
%     %||       2
%     %||       3
%     %||       4 ]@200x1
%     %||   .chunks
%     %||     [ 1
%     %||       1
%     %||       1
%     %||       :
%     %||       5
%     %||       5
%     %||       5 ]@200x1
%     %||   .subject
%     %||     [  1
%     %||        1
%     %||        1
%     %||        :
%     %||       10
%     %||       10
%     %||       10 ]@200x1
%
%     % example of MEEG dataset with ctf151 layout
%     ds=cosmo_synthetic_dataset('type','meeg',...
%                                   'sens','ctf151','size','huge');
%     % show labels and values for feature dimensions
%     cosmo_disp(ds.a.fdim,'edgeitems',2)
%     %|| .labels
%     %||   { 'chan'
%     %||     'time' }
%     %|| .values
%     %||   { { 'MLC11'  'MLC12' ... 'MZP01'  'MZP02'   }@1x151
%     %||     [ -0.2     -0.15  ...  0.55       0.6 ]@1x17      }
%
%     % example of MEEG dataset with 4d148 layout (3 channels only)
%     ds=cosmo_synthetic_dataset('type','meeg','sens','4d148_planar');
%     cosmo_disp(ds.a.fdim)
%     %|| .labels
%     %||   { 'chan'
%     %||     'time' }
%     %|| .values
%     %||   { { 'A148_dH'  'A147_dH'  'A146_dH' }
%     %||     [ -0.2     -0.15 ]                  }
%
% #   For CoSMoMVPA's copyright information and license terms,   #
% #   see the COPYING file distributed with CoSMoMVPA.           #

    default=struct();
    default.ntargets=2;
    default.nchunks=3;

    default.sigma=3;
    default.size='small';
    default.type='fmri';

    default.nreps=[];
    default.nmodalities=[];
    default.nsubjects=[];
    default.chunks=[];
    default.targets=[];

    default.target1=1;

    % for PRNG
    default.seed=1;

    % for MEEG
    default.sens='neuromag306_all';

    % for MEEG source
    default.data_field='pow'; % 'pow' or 'mom'

    opt=cosmo_structjoin(default,varargin);

    [ds, nfeatures]=get_fdim_fa(opt);

    sa_labels_pl={'ntargets','nchunks','nmodalities','nsubjects','nreps'};
    cp=cosmo_cartprod(cellfun(@(x)1:max([opt.(x) 1]),sa_labels_pl,...
                                            'UniformOutput',false));
    sa_labels_si={'targets','chunks','modality','subject','rep'};
    for k=1:numel(sa_labels_si)
        if ~isempty(opt.(sa_labels_pl{k}))
            ds.sa.(sa_labels_si{k})=cp(:,k);
        end
    end


    nelem=log(nfeatures*max([opt.nreps 1]));
    class_distance=opt.sigma/sqrt(nelem);

    ds.samples=generate_samples(ds, class_distance, opt.seed);
    ds=assign_sa(ds, opt, {'chunks','targets'});

    ds.sa.targets=ds.sa.targets+opt.target1-1;

    cosmo_check_dataset(ds);

function ds=assign_sa(ds, opt, names)
    nsamples=size(ds.samples,1);

    for k=1:numel(names)
        name=names{k};
        v=opt.(name);
        if ~isempty(v)
            if ~isscalar(v)
                error('Value for ''%s'' must be a scalar', name);
            end
            ds.sa.(name)=ones(nsamples,1)*v;
        end
    end


function samples=generate_samples(ds, class_distance, seed)

    targets=ds.sa.targets;
    nsamples=numel(targets);
    nclasses=numel(unique(targets));

    fa_names=fieldnames(ds.fa);
    nfeatures=size(ds.fa.(fa_names{1}),2);

    r=cosmo_rand(nsamples,nfeatures,'seed',seed);
    samples=cosmo_norminv(r);

    add_msk=mod(bsxfun(@minus,1:nclasses+1,targets),nclasses+1)==0;
    add_msk_full=repmat(add_msk,1,ceil(nfeatures/(nclasses+1)));
    add_msk_full=add_msk_full(:,1:nfeatures);
    samples(add_msk_full)=samples(add_msk_full)+class_distance;

function a=dim_labels_values(opt)
    data_type=opt.type;
    sens_type=opt.sens;

    a=struct();

    switch data_type
        case 'fmri'
            a.vol.mat=eye(4);
            a.vol.mat(1:3,1:3)=a.vol.mat(1:3,1:3)*2;

            % ensure negative origin, so that MRIcron displays
            % the matrix correctly
            a.vol.mat(1:3,4)=-3;

            labels={'i';'j';'k'};
            values={1:20;1:20;1:20};

        case {'meeg','timelock','timefreq'}
            % simulate full neuromag 306 system
            chan=get_meeg_channels(sens_type);

            time=(-.2:.05:1.3);

            switch data_type
                case 'timefreq'
                    freq=(2:2:40);
                    values={chan;freq;time};
                    labels={'chan';'freq';'time'};
                    a.meeg.samples_type='freq';
                    a.meeg.samples_field='powspctrm';

                otherwise % meeg and timelock
                    values={chan;time};
                    labels={'chan';'time'};
                    a.meeg.samples_type='timelock';
                    a.meeg.samples_field='trial';
            end

            a.meeg.samples_label='rpt';

        case 'surface'
            labels={'node_indices'};
            values={1:4000};

        case 'source'
            xyz=cosmo_cartprod({-70:10:70,-60:10:60,-110:10:110})';
            [unused,i]=sort(sum(abs(xyz),1));
            switch opt.data_field
                case 'pow'
                    labels={'pos','time'};
                    values={xyz(:,i),-1:.5:14};
                    a.meeg.samples_field='trial.pow';

                case 'mom'
                    labels={'pos','mom','time'};
                    values={xyz(:,i),{'x','y','z'},-1:.5:14};
                    a.meeg.samples_field='trial.mom';
                otherwise
                    error('illegal data_field ''%s''', opt.data_field);
            end


        otherwise
            error('Unsupported type ''%s''', data_type);
    end

    a.fdim.values=values;
    a.fdim.labels=labels;

function labels=get_meeg_channels(sens_type)

    % mapping from name to helper function
    % each name is prefixed with 'T' to allow names that start with a digit
    sens2func=struct();
    sens2func.Tneuromag306=@get_neuromag_chan;
    sens2func.Tctf151=@get_CTF151_chan;
    sens2func.T4d148=@get_4d148_chan;
    sens2func.T4d248=@get_4d248_chan;
    sens2func.Teeg1020=@get_eeg1020_chan;
    sens2func.Teeg1010=@get_eeg1010_chan;
    sens2func.Teeg1005=@get_eeg1005_chan;
    sens2func.Tyokogawa64=@get_yokogawa64_chan;
    sens2func.Tyokogawa160=@get_yokogawa160_chan;

    sp=cosmo_strsplit(['T' sens_type],'_');
    key=sp{1};
    if ~isfield(sens2func,key)
        supported_sens=fieldnames(sens2func);
        supported_labels=cellfun(@(x)[x(2:end) '*'],supported_sens,...
                        'UniformOutput',false);
        error('Unsupported sens_type %s, supported are: %s ',...
                    key(2:end),cosmo_strjoin(supported_labels, ', '));
    end

    func=sens2func.(key);
    chan_type=[cosmo_strjoin(sp(2:end),'_') '']; % ensure string
    labels=func(chan_type);
    labels=labels(:)';


function labels=get_eeg1020_chan(chan_type)
    labels=get_eeg10XX_chan_helper(chan_type,'1020');

function labels=get_eeg1010_chan(chan_type)
    labels=get_eeg10XX_chan_helper(chan_type,'1010');

function labels=get_eeg1005_chan(chan_type)
    labels=get_eeg10XX_chan_helper(chan_type,'1005');


function labels=get_eeg10XX_chan_helper(chan_type,sens_type)
    assert(isempty(chan_type));

    % build mapping from prefix to postfixes
    ch=struct();
    switch sens_type
        case '1020'
            ch.Fp={ '1' '2' 'z' };
            ch.F={ '3' '4' '7' '8' 'z' };
            ch.T={ '3' '4' '5' '6' '7' '8' };
            ch.C={ '3' '4' 'z' };
            ch.P={ '3' '4' '7' '8' 'z' };
            ch.O={ '1' '2' 'z' };
            ch.A={ '1' '2' };
            ch.M={ '1' '2' };

        case '1010'
            ch.TP={ '10' '7' '8' '9' };
            ch.CP={ '1' '2' '3' '4' '5' '6' 'z' };
            ch.Fp={ '1' '2' 'z' };
            ch.AF={ '1' '10' '2' '3' '4' '5' '6' '7' '8' '9' 'z' };
            ch.F={ '1' '10' '2' '3' '4' '5' '6' '7' '8' '9' 'z' };
            ch.FT={ '10' '7' '8' '9' };
            ch.FC={ '1' '2' '3' '4' '5' '6' 'z' };
            ch.T={ '10' '3' '4' '5' '6' '7' '8' '9' };
            ch.C={ '1' '2' '3' '4' '5' '6' 'z' };
            ch.P={ '1' '10' '2' '3' '4' '5' '6' '7' '8' '9' 'z' };
            ch.PO={ '1' '10' '2' '3' '4' '5' '6' '7' '8' '9' 'z' };
            ch.O={ '1' '2' 'z' };
            ch.I={ '1' '2' 'z' };
            ch.A={ '1' '2' };
            ch.M={ '1' '2' };

        case '1005'
            ch.FCC={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h' '6'...
                    '6h' 'z' };
            ch.F={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h'...
                    '5' '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' ...
                    'p1' 'p1h' 'p2' 'p2h' 'pz' 'z' };
            ch.AF={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h'...
                    '5' '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' ...
                    'p1' 'p10' 'p10h' 'p1h' 'p2' 'p2h' 'p3' 'p3h' ...
                    'p4' 'p4h' 'p5' 'p5h' 'p6' 'p6h' 'p7' 'p7h' ...
                    'p8' 'p8h' 'p9' 'p9h' 'pz' 'z' };
            ch.FT={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.FC={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h'...
                    '6' '6h' 'z' };
            ch.T={ '10' '10h' '3' '4' '5' '6' '7' '7h' '8' '8h'...
                    '9' '9h' };
            ch.C={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h'...
                    '6' '6h' 'z' };
            ch.TP={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.CP={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h'...
                    '6' '6h' 'z' };
            ch.P={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h'...
                    '5' '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' 'z' };
            ch.PO={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h'...
                    '5' '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' 'z' };
            ch.O={ '1' '1h' '2' '2h' 'z' };
            ch.I={ '1' '1h' '2' '2h' 'z' };
            ch.AFF={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h'...
                    '5' '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' 'z' };
            ch.FFT={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.FFC={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h' '6'...
                    '6h' 'z' };
            ch.FTT={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.TTP={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.CCP={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h' '6'...
                    '6h' 'z' };
            ch.TPP={ '10' '10h' '7' '7h' '8' '8h' '9' '9h' };
            ch.CPP={ '1' '1h' '2' '2h' '3' '3h' '4' '4h' '5' '5h' '6'...
                    '6h' 'z' };
            ch.PPO={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h' '5'...
                    '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' 'z' };
            ch.POO={ '1' '10' '10h' '1h' '2' '2h' '3' '3h' '4' '4h' '5'...
                    '5h' '6' '6h' '7' '7h' '8' '8h' '9' '9h' 'z' };
            ch.OI={ '1' '1h' '2' '2h' 'z' };
            ch.A={ '1' '2' };
            ch.M={ '1' '2' };

        otherwise
            error('illegal senstype %s',sens_type);
    end

    prefixes=fieldnames(ch);
    nprefix=numel(prefixes);
    label_cell=cell(nprefix,1);
    for k=1:nprefix
        prefix=prefixes{k};
        postfixes=ch.(prefix);
        npostfix=numel(postfixes);
        prefix_labels=cell(npostfix,1);
        for j=1:npostfix
            postfix=postfixes{j};
            prefix_labels{j}=[prefix postfix];
        end
        label_cell{k}=prefix_labels;
    end
    labels=cat(1,label_cell{:});




function labels=get_4d248_chan(chan_type)
    labels=get_4dX48_chan_helper(chan_type,248);

function labels=get_4d148_chan(chan_type)
    labels=get_4dX48_chan_helper(chan_type,148);

function labels=get_yokogawa64_chan(chan_type)
    labels=get_yokogawaX_chan_helper(chan_type,64);

function labels=get_yokogawa160_chan(chan_type)
    labels=get_yokogawaX_chan_helper(chan_type,160);

function labels=get_yokogawaX_chan_helper(chan_type,nchan)
    labels=get_general_chan_helper(chan_type,nchan,...
                        'AG%03d','AG%03d_dH','AG%03d_dV');

function labels=get_4dX48_chan_helper(chan_type,nchan)
    labels=get_general_chan_helper(chan_type,nchan,...
                        'A%d','A%d_dH','A%d_dV');

function labels=get_general_chan_helper(chan_type,chan_vals,...
                        pat_combined, pat_planar1, pat_planar2)

    % if chan_vals is a scalar, it indicates the number of channels
    if isnumeric(chan_vals) && numel(chan_vals)==1
        % take the last channels
        chan_vals=num2cell(chan_vals:-1:1);
    end

    generate=@(pat) cellfun(@(x)sprintf(pat,x),chan_vals,...
                        'UniformOutput',false);
    switch chan_type
        case {'','planar_combined'}
            labels=generate(pat_combined)';
        case 'planar'
            labels=[generate(pat_planar1) generate(pat_planar2)]';
        otherwise
            error('illegal chan type %s', chan_type);
    end

function labels=get_CTF151_chan(chan_type)
    chan_vals=get_CTF151_chan_prefixes();
    labels=get_general_chan_helper(chan_type,chan_vals,...
                        '%s','%s_dH','%s_dV');

function labels=get_CTF151_chan_prefixes()
    % get channels for CTF151
    lats='LRZ';   % lateralities
    locs='CFOPT'; % brain part
    counts=[repmat({{[0,5,4,3,3],[0,2,3,4,5,2],[0,2,2,3,3],...
                            [0,3,2,4],[0,6,6,5,4]}},2,1);...
                    {{2,3,2,2}}];

    labels=cell(1,151);
    pos=0;
    for i=1:numel(lats)
        lat=lats(i);
        count=counts{i};
        for k=1:numel(count)
            loc=locs(k);
            cs=count{k};
            for j=1:numel(cs)
                for m=1:cs(j)
                    label=sprintf('M%s%s%d%d',lat,loc,j-1,m);
                    pos=pos+1;
                    labels{pos}=label;
                end
            end
        end
    end




function labels=get_neuromag_chan(chan_type)
    % get channels for neuromag system
    all_chan_idxs=[repmat((1:26)',4,1) kron((1:4)',ones(26,1))];
    remove_msk=cosmo_match(all_chan_idxs(:,1), 8) & ...
                        cosmo_match(all_chan_idxs(:,2),[3 4]);
    chan_idxs=all_chan_idxs(~remove_msk,:);
    nloc=size(chan_idxs,1);
    assert(nloc==102);

    infix=reshape(sprintf('%02d%d',chan_idxs'),3,[])';
    as_column=@(x) repmat(x,nloc,1);

    meg=as_column('MEG');
    one=as_column('1');
    two=as_column('2');
    three=as_column('3');
    plus_=as_column('+');

    labels=cell(nloc,4);
    labels(:,1)=cellstr([meg infix one]);
    labels(:,2)=cellstr([meg infix two]);
    labels(:,3)=cellstr([meg infix three]);
    labels(:,4)=cellstr([meg infix two plus_ infix three]);

    keep_col=false(1,4);
    types=cosmo_strsplit(chan_type,'+');
    for k=1:numel(types)
        tp=types{k};
        switch tp
            case {'all',''}
                keep_col([1 2 3])=true;
            case 'planar_combined'
                keep_col(4)=true;
            case 'planar'
                keep_col([2 3])=true;
            case 'axial'
                keep_col(1)=true;
            otherwise
                error('Unsupported channel type %s', tp);
        end
    end

    if any(keep_col(2:3)) && keep_col(4)
        error('planar and cmb/combined are mutually exclusive');
    end

    labels=labels(:,keep_col)';
    labels=labels(:);


function dim_size=get_dim_size(size_label,opt)
    % get dimension size. NaN means use input size
    size2dim=struct();
    size2dim.tiny=[2 1 1];
    size2dim.small=[3 2 1];
    size2dim.normal=[3 2 5];
    size2dim.big=[NaN 7 5];
    size2dim.huge=[NaN 17 19];

    if ~isfield(size2dim, size_label)
        error('Unsupported size %s. Supported are: %s',...
                    size_label, cosmo_strjoin(fieldnames(size2dim),', '));
    end

    dim_size=size2dim.(size_label);

    if strcmp(opt.type,'source')
        dim_size(1)=4;
        if strcmp(opt.data_field,'mom')
            dim_size(2)=3;
        end
    end


function [ds, nfeatures]=get_fdim_fa(opt)
    data_type=opt.type;
    size_label=opt.size;

    % get dimension labels
    a=dim_labels_values(opt);
    labels=a.fdim.labels;
    values=a.fdim.values;
    a=rmfield(a,'fdim');

    % get dimension values
    dim_sizes=get_dim_size(size_label,opt);
    nlabel=numel(labels);
    if nlabel==1
        % surface case
        dim_sizes=prod(dim_sizes);
    else
        % everything else
        dim_sizes=dim_sizes(1:nlabel);
    end

    for k=1:numel(dim_sizes)
        if isnan(dim_sizes(k))
            dim_sizes(k)=size(values{k},2);
        end

        if isvector(values{k})
            values{k}=values{k}(1:dim_sizes(k));
        else
            values{k}=values{k}(:,1:dim_sizes(k));
        end
    end

    % get ds with proper size
    ds=cosmo_flatten(zeros([1 dim_sizes]),labels,values,2,...
                                            'matrix_labels',{'pos'});
    ds.a=cosmo_structjoin(ds.a,a);
    switch data_type
        case 'fmri'
            ds.a.vol.dim=dim_sizes;
            ds.a.vol.xform='scanner_anat';
    end

    nfeatures=prod(dim_sizes);