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VMPS_TreeMPS.m
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VMPS_TreeMPS.m
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function filename = VMPS_TreeMPS(varargin)
%% function filename = VMPS_TreeMPS(varargin)
%
% Initialises the model and starts the TDVP computation with treeMPS.
% Supports flexible calling syntax via input parser. Input can be Struct with appropriate field names
%
% Created by FS 26/02/2016
%
%% Define Input Parser
p = inputParser; % parses for para
p.CaseSensitive = true;
p.KeepUnmatched = true;
p.FunctionName = 'VMPS_TreeMPS';
pt = inputParser; % parses for para.tdvp
pt.CaseSensitive = false;
pt.KeepUnmatched = true;
pt.FunctionName = 'VMPS_TreeMPS';
pSBM = inputParser; % parses for para.SpinBoson
pSBM.CaseSensitive = false;
pSBM.KeepUnmatched = true;
pSBM.FunctionName = 'VMPS_TreeMPS';
pDPMES = inputParser; % parses for para.SpinBoson
pDPMES.CaseSensitive = false;
pDPMES.KeepUnmatched = true;
pDPMES.FunctionName = 'VMPS_TreeMPS';
%% Define local parameters
SBMInitialStates = {'sz', '-sz', 'sx', '-sx', 'sy', '-sy', 'none'};
DPMESInitialStates = {'TT','LE+', 'LE-', 'CT+', 'CT-'}; % Position of Name = number of InitialState
%% Define validation functions for string expressions
% para input parser
p.addParameter('model' ,'SpinBoson',@(x) any(validatestring(x,...
{'SpinBoson','SpinBoson2C', 'DPMES5-7C', 'DPMESclust7-1', 'DPMES-Tree1','DPMES-Tree2',...
'DPMES-Tree3','DPMES-Tree4','DPMES-Tree6','testTree'}))); % possible model inputs
p.addParameter('s' ,1 ,@isnumeric);
p.addParameter('L' ,50 ,@isnumeric); % longest L between root and all leaves
p.addParameter('alpha' ,0.1,@isnumeric);
p.addParameter('delta' ,0 ,@isnumeric); % in sx
p.addParameter('epsilon' ,0.1,@isnumeric); % in sz
p.addParameter('wc' ,1 ,@isnumeric);
p.addParameter('dk_start' ,5 ,@isnumeric);
p.addParameter('D_start' ,5 ,@isnumeric);
p.addParameter('d_opt_start' ,5 ,@isnumeric);
p.addParameter('M' ,2 ,@isnumeric);
p.addParameter('useDkExpand' ,0 ,@isnumeric);
p.addParameter('dkmax' ,1e3,@isnumeric);
p.addParameter('Dmin' ,2 ,@isnumeric);
p.addParameter('svmaxtol' ,1e-6 ,@isnumeric);
p.addParameter('svmintol' ,10^-8,@isnumeric);
p.addParameter('logging' ,0 ,@isnumeric);
p.addParameter('rescaling' ,0 ,@isnumeric);
p.addParameter('complex' ,0 ,@isnumeric);
p.addParameter('tdvp' ,1 ,@isnumeric); % do time-evolution?
p.addParameter('spinposition' ,1 ,@isnumeric);
p.addParameter('resume' ,0 ,@isnumeric);
p.addParameter('precision' ,5e-15 ,@isnumeric);
p.addParameter('parity' ,'n',@isstr);
p.addParameter('eigs_tol' ,1e-8 ,@isnumeric);
p.addParameter('foldedChain' ,0 ,@isnumeric);
p.addParameter('d_opt_min' ,2 ,@isnumeric);
p.addParameter('spinbase' ,'Z',@isstr);
p.addParameter('useshift' ,0 ,@isnumeric);
p.addParameter('useTreeMPS' ,1 ,@isnumeric);
p.addParameter('useStarMPS' ,0 ,@isnumeric);
p.addParameter('useVmat' ,1 ,@isnumeric);
p.addParameter('useVtens' ,0 ,@isnumeric);
p.addParameter('initChainState' ,'vac',@(x) any(validatestring(x,...
{'rand','vac'}))); % possible initial chain states
p.addParameter('comment' ,'',@isstr);
% para.tdvp input parser
% pt.addParameter('model' ,'SpinBoson',@(x) any(validatestring(x,...
% {'SpinBoson','SpinBoson2C', 'DPMES5-7C','testTree'}))); % possible model inputs
pt.addParameter('imagT' ,0 ,@isnumeric);
pt.addParameter('tmax' ,20 ,@isnumeric);
pt.addParameter('deltaT' ,1 ,@isnumeric);
pt.addParameter('resume' ,0 ,@isnumeric);
pt.addParameter('saveInterval' ,10 ,@isnumeric);
pt.addParameter('serialize' ,1 ,@isnumeric);
pt.addParameter('logSV' ,0 ,@isnumeric);
pt.addParameter('Observables' ,'.dm.n.' ,@isstr);
pt.addParameter('extractObsInterval',1 ,@isnumeric);
pt.addParameter('extractStarInterval',1 ,@isnumeric);
pt.addParameter('storeMPS' ,0 ,@isnumeric);
pt.addParameter('evolveSysTrotter' ,1 ,@isnumeric);
pt.addParameter('HEffSplitIsometry' ,1 ,@isnumeric);
pt.addParameter('maxExpMDim' ,120,@isnumeric); % E5: 160, P40: 120
pt.addParameter('maxExpVDim' ,200,@isnumeric); % E5: 270, P40: 256
pt.addParameter('expvCustom' ,1 ,@isnumeric);
pt.addParameter('useDkExpand' ,0 ,@isnumeric);
pt.addParameter('expandOBB' ,1 ,@isnumeric);
pt.addParameter('truncateExpandBonds',1 ,@isnumeric);
pt.addParameter('maxOBBDim' ,20 ,@isnumeric);
pt.addParameter('maxBondDim' ,5 ,@isnumeric);
pt.addParameter('zAveraging' ,0 ,@isnumeric);
pt.addParameter('logError' ,0 ,@isnumeric);
pt.addParameter('logTruncError' ,0 ,@isnumeric);
pt.addParameter('rescaling' ,0 ,@isnumeric);
% pt.addParameter('storeMPS' ,0 ,@isnumeric);
pSBM.addParameter('GroundStateMode' ,'artificial',@(x) any(validatestring(x,...
{'decoupled','coupled', 'artificial','artTTM'}))); % GroundState preparations
pSBM.addParameter('InitialState' ,'sx',@(x) any(validatestring(x,SBMInitialStates))); % Initial States
pDPMES.addParameter('InitialState' ,'LE+',@(x) any(validatestring(x,DPMESInitialStates))); % Initial States
pDPMES.addParameter('CTShift' ,0 ,@isnumeric);
pDPMES.addParameter('BroadenChain' ,zeros(1,7),@isnumeric); % logic, indicate which chains shall be broadened
pDPMES.addParameter('PeakWidth' ,cmToeV(20),@isnumeric); % width of 20 cm^-1 as standard?
%%
p.parse(varargin{:});
para = p.Results;
if para.tdvp == 1
pt.parse(varargin{:});
para.tdvp = pt.Results;
para.complex = 1;
end
%% Defaults to the models
%% Settings for SBM
if strfind(para.model,'SpinBoson')
pSBM.parse(varargin{:});
para.SpinBoson = pSBM.Results;
%% Setting Hamiltonian for single-spin models
% H0 = -para.hx./2.*sigmaX -para.hz./2.*sigmaZ
para.hx = -para.delta; % Splitting with sigma_X
para.hz = -para.epsilon; % Splitting with sigma_Z
%% Setting Chain for SBM
if strcmp(para.model,'SpinBoson')
para.nChains = 1;
else
out = regexp(para.model,'SpinBoson(?<nChains>\d)C','names');
para.nChains = str2double(out.nChains);
end
% para.wc = [1,5]; % only for testing purposes
for mc = 1:para.nChains
para.chain{mc}.mapping = 'OrthogonalPolynomials';
para.chain{mc}.spectralDensity = 'Leggett_Hard';
para.chain{mc}.discretization = 'None';
% para.chain{1}.discrMethod = 'Numeric';
para.chain{mc}.s = para.s(min(mc,length(para.s))); % SBM spectral function power law behaviour
para.chain{mc}.alpha = para.alpha(min(mc,length(para.alpha))); % SBM spectral function magnitude; see Bulla 2003 - 10.1103/PhysRevLett.91.170601
para.chain{mc}.L = para.L(min(mc,length(para.L)));
para.chain{mc}.w_cutoff = para.wc(min(mc,length(para.wc)));
para.chain{mc}.initState = para.initChainState; % choose: 'rand', 'vac',
end
%% Setting TreeMPS for SBM
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.nNodes = 1;
para.treeMPS.maxDegree = para.nChains;
para.treeMPS.leafIdx = num2cell((1:para.nChains)'+1); % maps from chain number to leaf index in para
para.treeMPS.nodeIdx = {0+1}; % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% para.SpinBoson.GroundStateMode = 'artificial'; % input arg
% choose: 'decoupled', 'coupled', 'artificial', 'artTTM'
% -artificial & artTTM does no optimization! this only sets up an artificial
% ground state with <n> = 0 on chain and InitialState 'sz'
% - 'artificial' for SBM2CT sets up maximally entangled state between odd and even chains in the Bath
% odd: thermal bath, even: ancilla
% para.SpinBoson.InitialState = 'sz'; % input arg
% choose: 'sz', '-sz', 'sx', '-sx', 'sy', '-sy', 'none'
% works with all options
if strcmp(para.SpinBoson.GroundStateMode, 'decoupled')
para.SpinBoson.t1 = para.t(1);
para.t(1) = 0; % switches off interaction with bath
end
if strcmp(para.SpinBoson.InitialState, 'sx') && ~strcmp(para.SpinBoson.GroundStateMode, 'artificial')
para.SpinBoson.hx = para.hx;
para.SpinBoson.hz = para.hz;
para.hz = 0;
para.hx = 10; % some value to do a sx splitting
elseif strcmp(para.SpinBoson.InitialState, 'sz') && ~strcmp(para.SpinBoson.GroundStateMode, 'artificial')
para.SpinBoson.hx = para.hx;
para.SpinBoson.hz = para.hz;
para.hz = 10; % some value to get sz+ eigenstate
para.hx = 0;
end
if isempty(strfind(para.model,'TTM'))
assert(length(para.spinposition) == 1, 'Only one spin is allowed in SBM');
end
end
%% Settings for DPMES
if strfind(para.model,'DPMES5-7C')
pDPMES.parse(varargin{:});
%% Setting Chain for SBM
para.nChains = 7;
para.systemStates = load('DPMESdata_20160129/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.chain{1}.mapping = 'LanczosTriDiag';
para.chain{1}.spectralDensity = 'CoupDiscr';
para.chain{1}.Lambda = 1;
para.chain{1}.initState = para.initChainState;
para.chain{1}.dataPoints = cmToeV(load('DPMESdata_20160129/W44-A1-7-01.dat'));
para.chain{1}.L = min(length(para.chain{1}.dataPoints),para.L-1);
%% chain 2 & more:
para.chain{2} = para.chain{1}; % simple copy
para.chain{2}.dataPoints = cmToeV(load('DPMESdata_20160129/W44-A1-10-x1.dat'));
para.chain{2}.L = min(length(para.chain{2}.dataPoints),para.L-1);
para.chain{3} = para.chain{2};
para.chain{3}.dataPoints = cmToeV(load('DPMESdata_20160129/W14-A2-10-highv2.dat'));
para.chain{3}.L = min(length(para.chain{3}.dataPoints),para.L-1);
para.chain{4} = para.chain{2};
para.chain{4}.dataPoints = cmToeV(load('DPMESdata_20160129/W24-B1-17-highv2.dat'));
para.chain{4}.L = min(length(para.chain{4}.dataPoints),para.L-1);
para.chain{5} = para.chain{2};
para.chain{5}.dataPoints = cmToeV(load('DPMESdata_20160129/W23-B2-8-10.dat'));
para.chain{5}.L = min(length(para.chain{5}.dataPoints),para.L-1);
para.chain{6} = para.chain{2};
para.chain{6}.dataPoints = cmToeV(load('DPMESdata_20160129/W45-B2-9-1x.dat'));
para.chain{6}.L = min(length(para.chain{6}.dataPoints),para.L-1);
para.chain{7} = para.chain{2};
para.chain{7}.dataPoints = cmToeV(load('DPMESdata_20160129/W45-B2-9-1-x.dat'));
para.chain{7}.L = min(length(para.chain{7}.dataPoints),para.L-1);
%% Setting TreeMPS for SBM
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.nNodes = 1;
para.treeMPS.maxDegree = para.nChains;
para.treeMPS.leafIdx = num2cell((1:para.nChains)'+1); % maps from chain number to leaf index in para
para.treeMPS.nodeIdx = {0+1}; % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
if strfind(para.model,'DPMESclust7-1')
% This is star-model obtained using fkmeans from 08/04/2017
% clusters under weighting by coupling strength only!
% Works only for TreeMPS now!
pDPMES.parse(varargin{:});
%% Setting Chain for SBM
para.nChains = 7;
para.systemStates = load('DPMESdata_20170408/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.BroadenChain = pDPMES.Results.BroadenChain; % save for reference
% Chains: 1 2 3 4 5 6 7
ChainFiles = { 'B11', 'B12', 'A11', 'A12', 'B22', 'B23', 'A2'}; % order similar to Tree2 since this is more likely to be optimal
for ii = 1:length(ChainFiles)
para.chain{ii}.mapping = 'LanczosTriDiag';
para.chain{ii}.spectralDensity = 'CoupDiscr';
para.chain{ii}.Lambda = 1;
para.chain{ii}.initState = para.initChainState;
para.chain{ii}.dataPoints = cmToeV(load(sprintf('DPMESdata_20170408/Modes-%s.dat',ChainFiles{ii})));
para.chain{ii}.H1 = load(sprintf('DPMESdata_20170408/H1-%s.dat',ChainFiles{ii}));
para.chain{ii}.L = min(length(para.chain{ii}.dataPoints),para.L-1);
if pDPMES.Results.BroadenChain(ii)
% allows individual broadening of each chain
para.chain{ii}.spectralDensity = 'CoupBroad';
para.chain{ii}.discrMethod = 'Direct';
para.chain{ii}.discretization = 'Linear';
para.chain{ii}.mapping = 'Stieltjes';
para.chain{ii}.L = max(length(para.chain{ii}.dataPoints),para.L-1);
para.chain{ii}.peakWidth = pDPMES.Results.PeakWidth;
para.chain{ii}.w_cutoff = max(para.chain{ii}.dataPoints(:,1))+pDPMES.Results.PeakWidth*10; % 10*width above highest mode to be safe?
end
end
%% Setting TreeMPS for SBM
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.nNodes = 1;
para.treeMPS.maxDegree = para.nChains;
para.treeMPS.leafIdx = num2cell((1:para.nChains)'+1); % maps from chain number to leaf index in para
para.treeMPS.nodeIdx = {0+1}; % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
%% Settings for DPMES-TreeN
if strfind(para.model,'DPMES-Tree1')
pDPMES.parse(varargin{:});
%% Setting Chain 1
para.nChains = 7;
para.systemStates = load('DPMESdata_20160129/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.chain{1}.mapping = 'LanczosTriDiag';
para.chain{1}.spectralDensity = 'CoupDiscr';
para.chain{1}.Lambda = 1;
para.chain{1}.initState = para.initChainState;
para.chain{1}.dataPoints = cmToeV(load('DPMESdata_20160129/W24-B1-17-highv2.dat'));
para.chain{1}.L = min(length(para.chain{1}.dataPoints),para.L-1);
%% chain 2 & more:
para.chain{2} = para.chain{1}; % simple copy
para.chain{2}.dataPoints = cmToeV(load('DPMESdata_20160129/W44-A1-7-01.dat'));
para.chain{2}.L = min(length(para.chain{2}.dataPoints),para.L-1);
para.chain{3} = para.chain{2};
para.chain{3}.dataPoints = cmToeV(load('DPMESdata_20160129/W44-A1-10-x1.dat'));
para.chain{3}.L = min(length(para.chain{3}.dataPoints),para.L-1);
para.chain{4} = para.chain{2};
para.chain{4}.dataPoints = cmToeV(load('DPMESdata_20160129/W23-B2-8-10.dat'));
para.chain{4}.L = min(length(para.chain{4}.dataPoints),para.L-1);
para.chain{5} = para.chain{2};
para.chain{5}.dataPoints = cmToeV(load('DPMESdata_20160129/W45-B2-9-1x.dat'));
para.chain{5}.L = min(length(para.chain{5}.dataPoints),para.L-1);
para.chain{6} = para.chain{2};
para.chain{6}.dataPoints = cmToeV(load('DPMESdata_20160129/W45-B2-9-1-x.dat'));
para.chain{6}.L = min(length(para.chain{6}.dataPoints),para.L-1);
para.chain{7} = para.chain{2};
para.chain{7}.dataPoints = cmToeV(load('DPMESdata_20160129/W14-A2-10-highv2.dat'));
para.chain{7}.L = min(length(para.chain{7}.dataPoints),para.L-1);
%% Setting TreeMPS structure
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.maxDegree = para.nChains;
leafTreeIdx = [1,1,1,0; % the treeIdx for each leaf; Order 1-7 as defined in genh1h2term_onesite
1,1,2,0;
1,2,0,0;
2,1,1,1;
2,1,1,2;
2,1,2,0;
2,2,0,0];
para.treeMPS.leafIdx = num2cell(leafTreeIdx+1); % maps from chain number to leaf index in para
nodeTreeIdx = [0,0,0,0; % the treeIdx of each node; order as defined by occurrence sweep
1,0,0,0;
1,1,0,0;
2,0,0,0;
2,1,0,0;
2,1,1,0];
para.treeMPS.nNodes = size(nodeTreeIdx,1);
para.treeMPS.nodeIdx = num2cell(nodeTreeIdx+1); % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
if strfind(para.model,'DPMES-Tree2')
pDPMES.parse(varargin{:});
%% Setting Chain 1
para.nChains = 7;
para.systemStates = load('DPMESdata_20160129/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states
para.BroadenChain = pDPMES.Results.BroadenChain; % save for reference
% Chains: 1 2 3 4 5 6 7
ChainFiles = {'W24-B1-17-highv2','W44-A1-7-01','W44-A1-10-x1','W23-B2-8-10','W45-B2-9-1x','W45-B2-9-1-x','W14-A2-10-highv2'}
% B1 A11 A12 B21 B22 B23 A2
for ii = 1:length(ChainFiles)
para.chain{ii}.mapping = 'LanczosTriDiag';
para.chain{ii}.spectralDensity = 'CoupDiscr';
para.chain{ii}.Lambda = 1;
para.chain{ii}.initState = para.initChainState;
para.chain{ii}.dataPoints = cmToeV(load(sprintf('DPMESdata_20160129/%s.dat',ChainFiles{ii})));
para.chain{ii}.L = min(length(para.chain{ii}.dataPoints),para.L-1);
if pDPMES.Results.BroadenChain(ii)
% allows individual broadening of each chain
para.chain{ii}.spectralDensity = 'CoupBroad';
para.chain{ii}.discrMethod = 'Direct';
para.chain{ii}.discretization = 'Linear';
para.chain{ii}.mapping = 'Stieltjes';
para.chain{ii}.L = max(length(para.chain{ii}.dataPoints),para.L-1);
para.chain{ii}.peakWidth = pDPMES.Results.PeakWidth;
para.chain{ii}.w_cutoff = max(para.chain{ii}.dataPoints(:,1))+pDPMES.Results.PeakWidth*10; % 10*width above highest mode to be safe?
end
end
%% Setting TreeMPS structure
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.maxDegree = para.nChains;
leafTreeIdx = [1,0,0,0; % the treeIdx for each leaf; Order 1-7 as defined in genh1h2term_onesite
2,1,1,0;
2,1,2,0;
2,2,1,1;
2,2,1,2;
2,2,2,1;
2,2,2,2];
para.treeMPS.leafIdx = num2cell(leafTreeIdx+1); % maps from chain number to leaf index in para
nodeTreeIdx = [0,0,0,0; % the treeIdx of each node; order as defined by occurrence sweep
2,0,0,0;
2,1,0,0;
2,2,0,0;
2,2,1,0;
2,2,2,0];
para.treeMPS.nNodes = size(nodeTreeIdx,1);
para.treeMPS.nodeIdx = num2cell(nodeTreeIdx+1); % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
if strfind(para.model,'DPMES-Tree3')
% This is star-model obtained using fkmeans from 08/04/2017
% clusters under weighting by coupling strength only!
pDPMES.parse(varargin{:});
%% Setting Chain for SBM
para.nChains = 7;
para.systemStates = load('DPMESdata_20170408/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.BroadenChain = pDPMES.Results.BroadenChain; % save for reference
% Chains: 1 2 3 4 5 6 7
ChainFiles = { 'A2', 'A11', 'A12', 'B11', 'B12', 'B22', 'B23' }; % order similar to Tree2 since this is more likely to be optimal
for ii = 1:length(ChainFiles)
para.chain{ii}.mapping = 'LanczosTriDiag';
para.chain{ii}.spectralDensity = 'CoupDiscr';
para.chain{ii}.Lambda = 1;
para.chain{ii}.initState = para.initChainState;
para.chain{ii}.dataPoints = cmToeV(load(sprintf('DPMESdata_20170408/Modes-%s.dat',ChainFiles{ii})));
para.chain{ii}.H1 = load(sprintf('DPMESdata_20170408/H1-%s.dat',ChainFiles{ii}));
para.chain{ii}.L = min(length(para.chain{ii}.dataPoints),para.L-1);
if pDPMES.Results.BroadenChain(ii)
% allows individual broadening of each chain
para.chain{ii}.spectralDensity = 'CoupBroad';
para.chain{ii}.discrMethod = 'Direct';
para.chain{ii}.discretization = 'Linear';
para.chain{ii}.mapping = 'Stieltjes';
para.chain{ii}.L = max(length(para.chain{ii}.dataPoints),para.L-1);
para.chain{ii}.peakWidth = pDPMES.Results.PeakWidth;
para.chain{ii}.w_cutoff = max(para.chain{ii}.dataPoints(:,1))+pDPMES.Results.PeakWidth*10; % 10*width above highest mode to be safe?
end
end
%% Setting TreeMPS structure
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.maxDegree = para.nChains;
leafTreeIdx = [1,0,0,0; % the treeIdx for each leaf; Order 1-7 as defined in genh1h2term_onesite
2,1,1,0;
2,1,2,0;
2,2,1,1;
2,2,1,2;
2,2,2,1;
2,2,2,2];
para.treeMPS.leafIdx = num2cell(leafTreeIdx+1); % maps from chain number to leaf index in para
nodeTreeIdx = [0,0,0,0; % the treeIdx of each node; order as defined by occurrence sweep
2,0,0,0;
2,1,0,0;
2,2,0,0;
2,2,1,0;
2,2,2,0];
para.treeMPS.nNodes = size(nodeTreeIdx,1);
para.treeMPS.nodeIdx = num2cell(nodeTreeIdx+1); % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
if strfind(para.model,'DPMES-Tree4')
% This is star-model obtained using fkmeans from 08/04/2017
% clusters under weighting by coupling strength only!
pDPMES.parse(varargin{:});
%% Setting Chain for SBM
% Set Folders: 20170408: 252 modes; 20170626: 75 Modes
para.nChains = 7;
para.systemStates = load('DPMESdata_20170408/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.BroadenChain = pDPMES.Results.BroadenChain; % save for reference
% Chains: 1 2 3 4 5 6 7
ChainFiles = { 'B11', 'B12', 'A11', 'A12', 'A2', 'B22', 'B23' };
for ii = 1:length(ChainFiles)
para.chain{ii}.mapping = 'LanczosTriDiag';
para.chain{ii}.spectralDensity = 'CoupDiscr';
para.chain{ii}.Lambda = 1;
para.chain{ii}.initState = para.initChainState;
para.chain{ii}.dataPoints = cmToeV(load(sprintf('DPMESdata_20170408/Modes-%s.dat',ChainFiles{ii})));
para.chain{ii}.H1 = load(sprintf('DPMESdata_20170408/H1-%s.dat',ChainFiles{ii}));
para.chain{ii}.L = min(length(para.chain{ii}.dataPoints),para.L-1);
if pDPMES.Results.BroadenChain(ii)
% allows individual broadening of each chain
para.chain{ii}.spectralDensity = 'CoupBroad';
para.chain{ii}.discrMethod = 'Direct';
para.chain{ii}.discretization = 'Linear';
para.chain{ii}.mapping = 'Stieltjes';
para.chain{ii}.L = max(length(para.chain{ii}.dataPoints),para.L-1);
para.chain{ii}.peakWidth = pDPMES.Results.PeakWidth;
para.chain{ii}.w_cutoff = max(para.chain{ii}.dataPoints(:,1))+pDPMES.Results.PeakWidth*10; % 10*width above highest mode to be safe?
end
end
%% Setting TreeMPS structure
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.maxDegree = para.nChains;
leafTreeIdx = [1,0,0,0,0; % the treeIdx for each leaf; Order 1-7 as defined in genh1h2term_onesite
2,1,0,0,0;
2,2,1,1,1;
2,2,1,1,2;
2,2,1,2,0;
2,2,2,1,0;
2,2,2,2,0];
para.treeMPS.leafIdx = num2cell(leafTreeIdx+1); % maps from chain number to leaf index in para
nodeTreeIdx = [0,0,0,0,0; % the treeIdx of each node; order as defined by occurrence sweep
2,0,0,0,0;
2,2,0,0,0;
2,2,1,0,0;
2,2,1,1,0;
2,2,2,0,0];
para.treeMPS.nNodes = size(nodeTreeIdx,1);
para.treeMPS.nodeIdx = num2cell(nodeTreeIdx+1); % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
if strfind(para.model,'DPMES-Tree6')
% This is star-model obtained using fkmeans from 08/04/2017
% clusters under weighting by coupling strength only!
pDPMES.parse(varargin{:});
%% Setting Chain for SBM
% Set Folders: DPMESdata_20170720
para.nChains = 9;
para.systemStates = load('DPMESdata_20170720/states.dat'); % [#state, E(eV)]
para.systemStates([4,5],2) = para.systemStates([4,5],2)*(1+pDPMES.Results.CTShift); % use delta as percentual shift of CT states!
para.BroadenChain = pDPMES.Results.BroadenChain; % save for reference
% Chains: 1 2 3 4 5 6 7 8 9
ChainFiles = { 'B21', 'B22', 'B11', 'B12', 'B13', 'B14', 'A2', 'A11', 'A12' };
for ii = 1:length(ChainFiles)
para.chain{ii}.mapping = 'LanczosTriDiag';
para.chain{ii}.spectralDensity = 'CoupDiscr';
para.chain{ii}.Lambda = 1;
para.chain{ii}.initState = para.initChainState;
para.chain{ii}.dataPoints = cmToeV(load(sprintf('DPMESdata_20170720/Modes-%s.dat',ChainFiles{ii})));
para.chain{ii}.H1 = load(sprintf('DPMESdata_20170720/H1-%s.dat',ChainFiles{ii}));
para.chain{ii}.L = min(length(para.chain{ii}.dataPoints),para.L-1);
if pDPMES.Results.BroadenChain(ii)
% allows individual broadening of each chain
para.chain{ii}.spectralDensity = 'CoupBroad';
para.chain{ii}.discrMethod = 'Direct';
para.chain{ii}.discretization = 'Linear';
para.chain{ii}.mapping = 'Stieltjes';
para.chain{ii}.L = max(length(para.chain{ii}.dataPoints),para.L-1);
para.chain{ii}.peakWidth = pDPMES.Results.PeakWidth;
para.chain{ii}.w_cutoff = max(para.chain{ii}.dataPoints(:,1))+pDPMES.Results.PeakWidth*10; % 10*width above highest mode to be safe?
end
end
%% Setting TreeMPS structure
para.treeMPS.height = 1; % star structure, since only tree node + leaves
para.treeMPS.maxDegree = para.nChains;
leafTreeIdx = [1,0,0,0,0; % the treeIdx for each leaf; Order 1-7 as defined in genh1h2term_onesite
2,1,0,0,0;
2,2,1,1,1;
2,2,1,1,2;
2,2,1,2,1;
2,2,1,2,2;
2,2,2,1,0;
2,2,2,2,1;
2,2,2,2,2];
para.treeMPS.leafIdx = num2cell(leafTreeIdx+1); % maps from chain number to leaf index in para
nodeTreeIdx = [0,0,0,0,0; % the treeIdx of each node; order as defined by occurrence sweep
2,0,0,0,0;
2,2,0,0,0;
2,2,1,0,0;
2,2,1,1,0;
2,2,1,2,0;
2,2,2,0,0;
2,2,2,2,0];
para.treeMPS.nNodes = size(nodeTreeIdx,1);
para.treeMPS.nodeIdx = num2cell(nodeTreeIdx+1); % maps from node number to nodeIdx
%% Set-up parameters for specific ground state preparation!
% Initial States: TT LE+ LE- CT+ CT-
% para.IntialState: 1 2 3 4 5
para.InitialState = find(~cellfun('isempty', strfind(DPMESInitialStates,pDPMES.Results.InitialState)));
end
%% Defaults to para
para.loopmax = 50; % (minimizeE)
para.increasedk = 0; % Tells by how much dk should have been increased to achieve good sv in MPS. start with 0.
para.adjust = 0; % (minimizeE) Initialize as 0, no need the edit. To adjust D. Is set = 1 in minimizeE.m
para.dimlock = 0; % (minimizeE) set to 0 will change D and d_dop adaptively
para.minDimChange = 0.01; % (minimizeE) sets dimlock = 1 if relative dimension change < minDimChange. (larger makes less loops)
para.timeslice = 0;
para.sitej = 0;
%%%% dk Expansion related %%%%
% only works together with OBB! (para.useVmat = 1)
% para.useDkExpand = 1; % input arg. Enable dk expansion, own algorithm. General switch
para.expandprecision = 1e-5; % unused in dk expand?
para.hasexpanded = 0; % for dk Expand
% Method 1:
para.useDkExpand1 = 0; % Expand dk if largest SV of site is smaller than this thershold. EMPIRICAL. Below this value, Vmat seems to need higher dk
para.expandBelowSV = 0.995;
% Method 2:
para.useDkExpand2 = 1; % Expand if wavefunction on site occupies the high energy dimensions
para.dkEx2_tail = 0.4; % tail length [0 1] of occupation in Vmat to analyse
para.dkEx2_maxDev = 1.5; % if std(log10(tail)) < maxDev --> no increase; Measures orders of magnitude in fluctuations of tail.
para.dkEx2_minExp = 13; % if tail below this order than do not expand.
%%%% Boson shift related %%%%
% para.useshift=0; % input arg
% only choose one of the following Methods
para.useFloShift = 0; % shift all sites if trustsite > 0
para.useFloShift2 = 1; para.FloShift2minSV = 0.995; % shift everything if maximum Vmat SV fall below this value
para.useFloShift3 = 0; para.FloShift3minMaxSV = 1; % shift every 3rd loop. Shifts only sites where max SV worse than half of the worst SV
para.FloShift3loops = 5; % FloShift3 needs logging of results.Vmat_sv!
para.useChengShift=0; % shifts sites < trustsite
para.useEveryShift=0; % shift in every loop
% para.shift = zeros(para.nChains,para.L); % separate shift for each chain!
para.shift = {}; % separate shift for each chain!
para.relativeshift=zeros(para.nChains,para.L);
para.relativeshiftprecision=0.01; % When the relative shift is below this value then stop shifting
% para = maxshift(para); % TODO!
para.version = 'v79';
if isstruct(para.tdvp)
%% Defaults to para for tdvp
para.trustsite = para.L+1; % add system manually here
%% Defaults to para.tdvp
para.tdvp.t = 0:para.tdvp.deltaT:para.tdvp.tmax;
para.tdvp.expvCustomTestAccuracy = 0; % do expvCustom alongside expv for testing.
para.tdvp.expvCustomTestAccuracyRMS = 0; % display RMS of expvCustom from expv(); set only if para.tdvp.expvCustomTestAccuracy = 1;
para.tdvp.expvTol = 1e-15; % error tolerance of expv(); default: 1e-7
para.tdvp.expvM = 50; % dim of Krylov subspace in expv(); default: 30
para.tdvp.version = para.version;
end
%% Folder and File name definition
[~, name] = system('hostname');
para.hostname = strtrim(name); % save hostname for later reference
Descr = para.version;
if ~strcmp(computer,'PCWIN64')
Descr = sprintf('%sTCM%s',Descr,para.hostname(3:end));
end
if para.useTreeMPS
MPStype = 'Tree-';
elseif para.useStarMPS
MPStype = 'Star-';
elseif para.useVtens
MPStype = 'VT-';
else
MPStype = '';
end
Descr = [MPStype,Descr];
if isfield(para.chain{1},'s') && para.chain{1}.s ~= 1 && isfield(para,'SpinBoson')
Descr = sprintf('%s-s%g',Descr,para.chain{1}.s);
end
if any(strfind(para.model,'DPMES'))
para.folder = sprintf('%s-%s-%s%s-L%dCT%g%s',datestr(now,'yyyymmdd-HHMM-SS'), para.model, Descr, para.comment, para.L,pDPMES.Results.CTShift,pDPMES.Results.InitialState);
else
para.folder = sprintf('%s-%s-%s-L%d',datestr(now,'yyyymmdd-HHMM-SS'), para.model, Descr, para.L);
end
para.filename = [para.folder,'/results.mat'];
para.tdvp.filename = sprintf([para.filename(1:end-4),'-Till%dStep%.2g%s'],para.tdvp.tmax,para.tdvp.deltaT,para.tdvp.version);
% para.tdvp.filename = sprintf('%s-alpha%g',para.tdvp.filename,alpha);
if para.tdvp.expandOBB
para.tdvp.filename = sprintf('%s-OBBmax%d',para.tdvp.filename, para.tdvp.maxOBBDim);
end
if para.tdvp.truncateExpandBonds
if length(para.tdvp.maxBondDim) > 1
para.tdvp.filename = sprintf('%s-Dmax(%d-%d)',para.tdvp.filename,para.tdvp.maxBondDim(1),para.tdvp.maxBondDim(2));
else
para.tdvp.filename = sprintf('%s-Dmax%d',para.tdvp.filename,para.tdvp.maxBondDim);
end
end
if para.tdvp.expvCustom
para.tdvp.filename = sprintf('%s-expvCustom%d',para.tdvp.filename,para.tdvp.maxExpVDim);
end
% finish Filenames
para.tdvp.filename = sprintf('%s-%dcore.mat',para.tdvp.filename,maxNumCompThreads);
para.tdvp.filenameSmall = sprintf('%s-small.mat',para.tdvp.filename(1:end-4)); % only for para, tresults
% Set MPS filename if needed
if para.tdvp.storeMPS == 1
para.tdvp.filenameMPS = [para.tdvp.filename,'-MPS.mat']; % only for tmps, tVmat
end
if ~exist(para.tdvp.filename,'file')
mkdir(para.folder);
para.savedexist=0;
else
para.savedexist=1;
end
for k = 1:para.nChains
if ~strcmp(para.chain{k}.mapping,'')
[para.chain{k}]=SBM_genpara(para.chain{k}); % only need alpha, s, Lambda. Returns epsilon and t of Wilson chain. Auto choose L if L == 0
end
end
[treeMPS, para] = initState(para);
results = initresults(para);
%% Do one prepare sweep to bring MPS onto right-canonical form
[treeMPS,~,para] = prepare(treeMPS,[],para);
%% Calculate effective Hamiltonians
treeMPS = initstorage(treeMPS,[],[],para); % new call pattern for treeMPS
filename = para.tdvp.filename;
save(para.tdvp.filename,'para','results','treeMPS','-v7.3');
if strcmp(computer,'PCWIN64')
% Only calculate if this is not the cluster. Otherwise needs moving to scratch
tdvp_1site_tree(treeMPS,para,results,[]);
end
end
function [treeMPS, para] = initState(para)
%% function treeMPS = initState(treeMPS)
%
% initialisation of the treeMPS.
%
% Created by FS 29/02/2016
temp = allocateTreeStruct();
chains = repmat(temp,para.nChains,1); % will contain all chains
nodes = repmat(temp,para.treeMPS.nNodes,1); % will contain all nodes
dk = para.dk_start;
d_opt = para.d_opt_start;
D = para.D_start;
%%
for mc = 1:para.nChains
%% initialise each chain
L = para.chain{mc}.L;
chains(mc).mps = cell(1,L);
chains(mc).Vmat = cell(1,L);
chains(mc).L = L;
chains(mc).treeIdx = [para.treeMPS.leafIdx{mc,:}]-1;
chains(mc).chainIdx = mc;
chains(mc).level = nnz(chains(mc).treeIdx)+1;
chains(mc).D = [ones(1,L)*D,1];
chains(mc).d_opt = ones(1,L)*d_opt;
chains(mc).dk = ones(1,L)*dk;
chains(mc).shift = zeros(1,L);
%% Fill the MPS of each chain
% default: vacuum in the chains
for ii = 1:L
switch para.chain{mc}.initState
case 'rand'
chains(mc).mps{ii} = randn([chains(mc).D(ii:ii+1),d_opt]); % end-of-chain -> Dr = 1
case 'vac'
chains(mc).mps{ii} = zeros([chains(mc).D(ii:ii+1),d_opt]); % end-of-chain -> Dr = 1
chains(mc).mps{ii}(1,1,1) = 1;
end
chains(mc).Vmat{ii} = sparse(1:d_opt,1:d_opt,1,dk,d_opt);
end
%% Set in para
pIdx = para.treeMPS.leafIdx(mc,:);
para.dk{pIdx{:}} = chains(mc).dk;
para.D{pIdx{:}} = chains(mc).D;
para.d_opt{pIdx{:}} = chains(mc).d_opt;
para.shift{pIdx{:}} = chains(mc).shift;
para.treeMPS.L(pIdx{:}) = chains(mc).L;
para.treeMPS.chainIdx{para.treeMPS.leafIdx{mc,:}} = mc;
%% generate Hamiltonian terms:
chains(mc).op.h1term = cell(1,L);
chains(mc).op.h2term = cell(para.M,2,L);
for ii = 1:L
temp = genh1h2term_onesite(para,chains(mc).treeIdx,ii);
chains(mc).op.h1term(ii) = temp.h1term;
chains(mc).op.h2term(:,:,ii) = temp.h2term;
end
end
leafIndices = cell2mat(para.treeMPS.leafIdx)-1; % nLeaves x nLevels
nodeIndices = cell2mat(para.treeMPS.nodeIdx)-1; % nNodes x nLevels
para.L = max([chains.level]+[chains.L]-1);
%%
for mc = para.treeMPS.nNodes:-1:1
L = 1; % for now: only single nodes
pIdx = para.treeMPS.nodeIdx(mc,:);
nodes(mc).mps = cell(1,L);
nodes(mc).Vmat = cell(1,L);
nodes(mc).L = L;
nodes(mc).treeIdx = [para.treeMPS.nodeIdx{mc,:}]-1;
% nodes(mc).chainIdx = mc; % dummy value?
nodes(mc).level = nnz(nodes(mc).treeIdx)+1;
% nodes(mc).D = [ones(1,L)*D,1]; % assign after children
% nodes(mc).d_opt = ones(1,L)*d_opt; % assign after genh1h2term_onesite, derive from H
% nodes(mc).dk = ones(1,L)*dk;
nodes(mc).shift = zeros(1,L);
if nodes(mc).level == 1
nodes(mc).isRoot = 1;
end
nodes(mc).useStarMPS = 0;
nodes(mc).useTreeMPS = 1;
nodes(mc).spinposition = 1;
%% Attach children
currentChild = 0;
hasChild = 1;
while hasChild
currentChild = currentChild + 1; % each node has at least 1 child
% construct index of child to look for
idx = nodes(mc).treeIdx;
idx(nodes(mc).level) = currentChild; % look for [ 4 3 3 i 0 0 0] if at current node is at level 4 of 8
leafPos = find(all(bsxfun(@eq,leafIndices,idx),2));
nodePos = find(all(bsxfun(@eq,nodeIndices,idx),2));
if ~isempty(leafPos) && leafPos
if isempty(nodes(mc).child)
nodes(mc).child = chains(leafPos);
else
nodes(mc).child(currentChild,1) = chains(leafPos);
end
elseif ~isempty(nodePos) && nodePos
if isempty(nodes(mc).child)
nodes(mc).child = nodes(nodePos);
else
nodes(mc).child(currentChild,1) = nodes(nodePos);
end
else
hasChild = 0;
end
end
%% Set parameters
nodes(mc).op = genh1h2term_onesite(para,nodes(mc).treeIdx,1);
nodes(mc).degree = currentChild-1;
nodes(mc).chainIdx = [nodes(mc).child.chainIdx]; % min(chainIdx) is chainIdx of current node
nodes(mc).nChains = length(nodes(mc).chainIdx);
nodes(mc).height = max([nodes(mc).child.height])+1;
nodes(mc).L = getTreeLength(nodes(mc));
nodes(mc).D = ones(nodes(mc).degree+1,1)*D;
if nodes(mc).isRoot
nodes(mc).D(1) = 1;
end
if isempty(nodes(mc).op.h1term{1})
nodes(mc).hasSite = 0;
nodes(mc).dk = 1; % leads to singleton
nodes(mc).d_opt = 1;
else
nodes(mc).hasSite = 1;
nodes(mc).chainIdx = min(nodes(mc).chainIdx); % collapse chain index to indicate, that node has only one coupling to right
nodes(mc).dk = size(nodes(mc).op.h1term{1},1);
nodes(mc).d_opt = nodes(mc).dk; % assume non-boson
end
para.treeMPS.L(pIdx{:}) = 1;
para.shift{pIdx{:}} = 0;
%% Fill the MPS
dk = nodes(mc).dk;
d_opt = nodes(mc).d_opt;
NC = nodes(mc).degree;
nodes(mc).mps{1} = zeros([nodes(mc).D',d_opt]);
if ~nodes(mc).isRoot
idx = num2cell(ones(length(nodes(mc).D),1)); % indexes all left and child bonds;
nodes(mc).mps{1}(idx{:},1) = 1; % initially connect as product states
elseif any(strfind(para.model,'DPMES'))
idx = num2cell([ones(1,NC+1),para.InitialState]); % start in second excited state!
nodes(mc).mps{1}(idx{:}) = 1;
elseif isfield(para,'SpinBoson') && strcmp(para.SpinBoson.GroundStateMode, 'artificial')
d_opt = 2;
if strcmp(para.SpinBoson.InitialState, 'sz')
%% prepare +Sz eigenstate
idx = num2cell(ones(1,NC+1)); % select state coupling to all first chain states
nodes(mc).mps{1}(idx{:},1) = 1;
elseif strcmp(para.SpinBoson.InitialState, '-sz')
idx = num2cell(ones(1,NC+1));
nodes(mc).mps{1}(idx{:},2) = 1;
elseif strcmp(para.SpinBoson.InitialState, 'sx')
idx = num2cell(ones(1,NC+1)); % select state coupling to all first chain states
nodes(mc).mps{1}(idx{:},1) = 1/sqrt(2);
nodes(mc).mps{1}(idx{:},2) = 1/sqrt(2);
elseif strcmp(para.SpinBoson.InitialState, '-sx')
idx = num2cell(ones(1,NC+1)); % select state coupling to all first chain states
nodes(mc).mps{1}(idx{:},1) = -1/sqrt(2);
nodes(mc).mps{1}(idx{:},2) = 1/sqrt(2);
end
else
error('VMPS:VMPS_TreeMPS:WrongParameters','');
end
nodes(mc).Vmat{1} = sparse(1:d_opt,1:d_opt,1,dk,d_opt);
end
treeMPS = nodes(1);
function treeMPS = allocateTreeStruct()
%% function treeMPS = allocateTreeStruct()
%
% initialises an empty struct template and defines all used fields
% Already fill in defaults for leaves
treeMPS = struct;
treeMPS.mps = {};
treeMPS.Vmat = {};
treeMPS.treeIdx = [];
treeMPS.chainIdx = 0; % = [# chains connected to]
treeMPS.height = 0; % this struct is a leaf
treeMPS.degree = 0; % = n(children)
treeMPS.level = 1; % = site number of first chain site if counted from the root node
treeMPS.child = []; % contains all children nodes
treeMPS.currentChild = []; % leaf: [], node: currentChain;
treeMPS.currentChain = []; % leaf: [], node: currentChain;
treeMPS.L = []; % StarMPS can have array L
treeMPS.D = 0; % first is Dl of chain, last is Dr of chain, here horizontal!
treeMPS.d_opt = 0;
treeMPS.dk = 0;
treeMPS.M = para.M;
treeMPS.shift = 0;
treeMPS.useVmat = para.useVmat;
treeMPS.useVtens = 0;
treeMPS.useStarMPS = 0;
treeMPS.useTreeMPS = 0;
treeMPS.nChains = 1; % n(chains connected through node) = length(chainIdx) >= degree
treeMPS.sweepto = 'l'; % 'l' for initial preparation
treeMPS.spinposition = []; % pure Boson Chain
treeMPS.sitej = 1; % currently focused site
treeMPS.isRoot = 0;
treeMPS.BondCenter = [];
treeMPS.tdvp = [];
treeMPS.op.h1term = {};
treeMPS.op.h2term = {};
treeMPS.hasSite = 1; % whether node has real site; no Site nodes need: op.h1term{1} = []
treeMPS.Amat_sv = {}; % Singular values for each bond within node/leaf
end
function L = getTreeLength(treeMPS)
%% function L = getTreeLength(treeMPS)
% extracts the length of the treeMPS, based on the length of its children
%
if isfield(treeMPS,'L') && ~isempty(treeMPS.L)
L = treeMPS.L;
return
elseif treeMPS.height == 0
if isfield(treeMPS,'mps')
L = length(treeMPS.mps);
else
L = 0; % is leaf without MPS
end
return
end
% first determine size(L)
h = treeMPS.height; % ndims of L > 0
d = zeros(1,h); % this will be size(L)
d(1) = treeMPS.degree+1;
if h == 1 % this is StarMPS with leaves only
Lchild = arrayfun(@getTreeLength, treeMPS.child);
L = [1;reshape(Lchild,d(1)-1,1)];
return
end
% else height >= 2
if h == 2
d(3) = 1; % need singleton to allow comparisons later
end
Lchild = arrayfun(@getTreeLength, treeMPS.child,'UniformOutput',false);
% find out maximum dimensions per level to zero-pad Lchild
Idx = find([treeMPS.child.height] == h-1); % only pick the ones with maximum height
for jj = Idx
d(2:end) = max(d(2:end),size(Lchild{jj}));
end
% now d contains the maximum dimensions of L -> initialise
L = zeros(d);
L(1) = 1; % length of nodes = 1 always for now!
for jj = 1:treeMPS.degree
Idx = arrayfun(@(x) 1:x,size(Lchild{jj}),'UniformOutput',false); % create cell array containing index ranges of Lchild{ii}
L(jj+1,Idx{:}) = Lchild{jj};
end
end
end
function dummy()