Silas work PC
eye diagram working for all signals again... A problem: I found that the Tx eyes look weird (i.e. PAM-8) vibecoded ML_MLSE_GPU ... a bit faster :-)
This commit is contained in:
Silas Oettinghaus
@@ -927,7 +927,7 @@ classdef Signal
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options.displayname = "";
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options.displayname = "";
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end
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end
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mode = 2;
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mode = 1;
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histpoints = 2048; %% verticale resolution
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histpoints = 2048; %% verticale resolution
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histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven
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histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven
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@@ -978,8 +978,8 @@ classdef Signal
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maxA = max(sig(100:end-100))*1.3;
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maxA = max(sig(100:end-100))*1.3;
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minA = min(sig(100:end-100))*1.3;
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minA = min(sig(100:end-100))*1.3;
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maxA = 0.12;
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% maxA = 0.12;
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minA = -0.08;
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% minA = -0.08;
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difference= maxA-minA;
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difference= maxA-minA;
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525
Classes/04_DSP/Equalizer/ML_MLSE_GPU.m
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525
Classes/04_DSP/Equalizer/ML_MLSE_GPU.m
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@@ -0,0 +1,525 @@
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classdef ML_MLSE_GPU < handle
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% ---------------------------------------------------------------------
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% W. Lanneer and Y. Lefevre,
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% “Machine Learning-Based Pre-Equalizers for Maximum Likelihood
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% Sequence Estimation in High-Speed PONs,” EUSIPCO 2023
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% ---------------------------------------------------------------------
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% This implementation reproduces the closed-loop ML-based
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% pre-equalizer training for MLSE, supporting both training and
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% detection (decision-directed) modes.
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% ---------------------------------------------------------------------
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properties
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sps
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order
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e
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e_tr
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error
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len_tr
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mu_tr
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epochs_tr
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dd_mode
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mu_dd
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epochs_dd
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adaptive_mu
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constellation
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L
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alpha
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DIR
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DIR_flip
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trellis_states
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traceback_depth
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delta
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% --- New: GPU Support ---
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use_gpu
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% Internal variables
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S
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Nf
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nStates
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nFeasible
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combs
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first_sym
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last_sym
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valid
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valid_to_idx
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valid_from_idx
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w
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% Fast lookup
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nSym
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key_table
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trans_index
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true_to_state_idx
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% Debug metrics
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ber = []
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ce = ones(1,1)
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end
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methods
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function obj = ML_MLSE_GPU(options)
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arguments(Input)
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options.sps = 2;
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options.order = 15;
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options.len_tr = 4096;
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options.mu_tr = 0.001;
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options.epochs_tr = 5;
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options.dd_mode = 1;
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options.mu_dd = 1e-5;
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options.epochs_dd = 5;
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options.adaptive_mu = 1;
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options.delta = 0;
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options.traceback_depth = 1024;
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options.L = 1;
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options.use_gpu = 0; % Default: CPU
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end
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fn = fieldnames(options);
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for n = 1:numel(fn)
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obj.(fn{n}) = options.(fn{n});
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end
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% Check GPU availability
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if obj.use_gpu
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if gpuDeviceCount() > 0
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% GPU is available, keeping use_gpu = 1
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else
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warning('GPU requested but not available. Falling back to CPU.');
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obj.use_gpu = 0;
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end
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end
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obj.e = zeros(obj.order,1);
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obj.error = 0;
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end
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% ==============================================================
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% PROCESS
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% ==============================================================
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function [X,X_viterbi] = process(obj, X, D)
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% Normalize input RMS
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X = X.normalize("mode","rms");
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obj.constellation = sort(unique(D.signal),'ascend');
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obj.nSym = numel(obj.constellation);
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if length(X)/length(D) ~= obj.sps
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warning('Signal length does not fit to reference!');
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end
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% --- Parameters
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obj.S = obj.nSym;
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obj.Nf = obj.order * obj.sps;
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obj.nStates = obj.S^obj.L;
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obj.nFeasible = obj.nStates * obj.S;
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% --- Trellis mapping
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obj.trellis_states = reshape(obj.constellation,1,[]);
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pre_comb_mat = repmat(obj.trellis_states, obj.L, 1);
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pre_comb_cell = mat2cell(pre_comb_mat, ones(1,obj.L), size(pre_comb_mat,2));
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obj.combs = fliplr(combvec(pre_comb_cell{:}).');
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obj.first_sym = obj.combs(:,1);
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obj.last_sym = obj.combs(:,end);
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obj.nStates = size(obj.combs,1);
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% --- Valid transitions
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obj.valid = false(obj.nStates);
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for from = 1:obj.nStates
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for to = 1:obj.nStates
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if all(obj.combs(to,2:end) == obj.combs(from,1:end-1))
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obj.valid(to,from) = true;
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end
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end
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end
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[obj.valid_to_idx,obj.valid_from_idx] = find(obj.valid);
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% --- Initialize weights
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if isempty(obj.w) || any(size(obj.w) ~= [obj.Nf+1,obj.nFeasible])
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obj.w = randn(obj.Nf+1,obj.nFeasible);
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obj.w = zeros(obj.Nf+1,obj.nFeasible);
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end
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% --- Fast lookup tables
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[~, sym_idx_mat] = ismember(obj.combs, obj.constellation);
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key_vals = 1 + sum((sym_idx_mat - 1) .* (obj.nSym .^ (0:obj.L-1)), 2);
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max_key = obj.nSym^obj.L;
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obj.key_table = zeros(max_key,1,'uint32');
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obj.key_table(key_vals) = 1:obj.nStates;
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obj.trans_index = sparse(obj.nStates,obj.nStates);
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for i = 1:length(obj.valid_from_idx)
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f = obj.valid_from_idx(i);
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t = obj.valid_to_idx(i);
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obj.trans_index(t,f) = i;
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end
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% ==============================================================
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% TRAINING
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% ==============================================================
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fprintf('\n--- Training mode ---\n');
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% Always run training on CPU to avoid loop latency on GPU
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obj.equalize(X.signal, D.signal, obj.mu_tr, obj.epochs_tr, obj.len_tr, true);
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obj.e_tr = obj.e;
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% ==============================================================
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% DECISION-DIRECTED / TESTING
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% ==============================================================
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fprintf('--- Decision-directed / detection mode ---\n');
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x_sig = X.signal;
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d_sig = D.signal;
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% Move to GPU only for inference if requested
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if obj.use_gpu
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try
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x_sig = gpuArray(single(x_sig));
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if isa(obj.w, 'double')
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obj.w = gpuArray(single(obj.w));
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end
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catch
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warning('Failed to move data to GPU. Falling back to CPU.');
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obj.use_gpu = 0;
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end
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end
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[y, y_vit] = obj.equalize(x_sig, d_sig, obj.mu_dd, obj.epochs_dd, X.length, false);
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% Gather results back to CPU
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if obj.use_gpu
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y = gather(y);
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y_vit = gather(y_vit);
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obj.w = gather(obj.w);
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end
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X_viterbi = X;
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X.signal = y;
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X_viterbi.signal = y_vit;
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end
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% ==============================================================
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% EQUALIZE
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% ==============================================================
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function [y,y_ref] = equalize(obj,x,d,mu,epochs,N,training)
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debug = 1;
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showPlots = 1;
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% Ensure basic types
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if obj.use_gpu && ~isa(x, 'gpuArray') && training % Only force gpu for training if desired, but here we focus on inference
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% For training, we keep existing flow for now.
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end
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y = zeros(N,1);
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% On GPU, y should be gpuArray if we build it there, but we return it at the end.
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if obj.use_gpu && ~training
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y = gpuArray.zeros(N,1);
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end
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nSymbols = ceil(N/obj.sps);
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for epoch = 1:epochs
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pm = zeros(obj.nStates,1);
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pred = zeros(nSymbols,obj.nStates,'uint32');
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% pred is large uint32, GPU support for uint32 exists but sometimes limited.
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% We'll keep pred on CPU for Viterbi path storage or gather per chunk if needed.
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pm_sto = nan(obj.nStates,nSymbols,'like',pm);
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CE_accum = 0;
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start_sample = 1;
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end_sample = N;
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start_symbol = 1 + floor((start_sample - 1)/obj.sps);
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% --- initialize true state
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if numel(d) >= obj.L && start_symbol >= obj.L
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init_seq = d(start_symbol-obj.L+1:start_symbol);
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key_init = obj.seq2key(init_seq);
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true_to_state_idx = obj.key_table(key_init);
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if true_to_state_idx==0, true_to_state_idx=1; end
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else
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true_to_state_idx = uint32(1);
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end
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% =========================================================
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% INFERENCE OPTIMIZATION (Vectorized Branch Metrics)
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% =========================================================
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run_vectorized = ~training && obj.use_gpu;
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% --- Pre-calculate symbol indices for fast key generation (Training Only)
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% This avoids slow ismember() calls inside the loop
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d_indices = [];
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if training
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% Map d to 0..M-1 indices once
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[~, d_indices] = ismember(d, obj.constellation);
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d_indices = d_indices - 1; % 0-based
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end
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if run_vectorized
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% 1. Construct Sliding Window Input Matrix
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% Windows corresponding to symbol centers: start_sample:sps:end_sample
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% Each window is [x(sample-Nf+1+delta : sample+delta); 1]
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% Create index matrix
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num_syms = numel(start_sample:obj.sps:end_sample);
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samples_idx = start_sample + (0:num_syms-1)*obj.sps; % [1 x nSymbols]
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% Indices for window: relative -Nf+1+delta to +delta
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rel_idx = (-obj.Nf + 1 + obj.delta : obj.delta)'; % [Nf x 1]
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% Full index matrix (implicit expansion)
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idx_mat = rel_idx + samples_idx; % [Nf x nSymbols]
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% Handle boundary padding (clamping indices)
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% Since x is gpuArray, indexing with clamp is efficient if rewritten
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% But MATLAB indexing x(idx_mat) with OOB indices is tricky vectorized.
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% Faster approach: Clamp indices to [1, length(x)] and mask zero-pads.
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mask_valid = (idx_mat >= 1) & (idx_mat <= length(x));
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idx_clamped = max(1, min(length(x), idx_mat));
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X_windows = x(idx_clamped); % [Nf x nSymbols]
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X_windows = X_windows .* mask_valid; % Zero pad out-of-bounds
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% Add bias row
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X_windows = [X_windows; ones(1, num_syms, 'like', x)]; % [(Nf+1) x nSymbols]
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% 2. Bulk Compute Branch Metrics
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% C_all: [nFeasible x nSymbols] = ( [(Nf+1) x nFeasible] )' * [(Nf+1) x nSymbols]
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% obj.w usually (Nf+1)xFeasible
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C_all = obj.w' * X_windows;
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% 3. Bring Metrics to CPU for Viterbi
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% Processing Viterbi on CPU is often faster than serial kernel launches on GPU
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C_all_cpu = gather(C_all);
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% Pre-computation done. Now loop for Viterbi (Add-Compare-Select)
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% Prepare CPU variables
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pm = gather(pm);
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pm_sto = gather(pm_sto);
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pred = gather(pred);
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v_tilde_mat = inf(obj.nStates, obj.nStates);
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% Loop over symbols (pure CPU Viterbi)
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for sym_i = 1:num_syms
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% Current branch metrics for all edges
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c_hat_curr = C_all_cpu(:, sym_i); % [nFeasible x 1]
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% ACS Update
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pm = pm - min(pm);
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v_tilde = pm(obj.valid_from_idx) + c_hat_curr;
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v_tilde_mat(obj.valid) = v_tilde;
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[pm_next, pred(sym_i,:)] = min(v_tilde_mat, [], 2);
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pm_next = pm_next - min(pm_next);
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pm = pm_next;
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pm_sto(:,sym_i) = pm;
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end
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symbol = num_syms; % Update for traceback
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else
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% =========================================================
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% STANDARD SEQUENTIAL LOOP (Training / CPU Inference)
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% =========================================================
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pow_vec = (obj.nSym .^ (0:obj.L-1)).'; % Pre-calc powers for keygen
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for sample = start_sample:obj.sps:end_sample
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symbol = (sample - start_sample)/obj.sps + 1;
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sym_idx = start_symbol + (symbol - 1);
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% --- Observation window (with delta)
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i1 = sample - obj.Nf + 1 + obj.delta;
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i2 = sample + obj.delta;
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buf = x(max(1,i1):min(length(x),i2));
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padL = max(0,1 - i1);
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padR = max(0,i2 - length(x));
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yk = [zeros(padL,1); buf(:); zeros(padR,1)];
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yk = [yk;1];
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% --- Branch metrics
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c_hat = (yk.' * obj.w).';
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pm = pm - min(pm);
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v_tilde = pm(obj.valid_from_idx) + c_hat;
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% --- allocate once
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if epoch==1 && symbol==1
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obj.true_to_state_idx = ones(ceil(N/obj.sps),1,'uint32');
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end
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% --- previous "to" becomes "from"
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if symbol>1
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true_from_state_idx = obj.true_to_state_idx(symbol-1);
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else
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||||||
|
true_from_state_idx = 1;
|
||||||
|
end
|
||||||
|
|
||||||
|
% --- compute or reuse "to" state
|
||||||
|
if epoch==1
|
||||||
|
if sym_idx>=obj.L
|
||||||
|
% OPTIMIZED KEY GENERATION: Use pre-calculated indices
|
||||||
|
% key_to = obj.seq2key(d(sym_idx-obj.L+1:sym_idx));
|
||||||
|
|
||||||
|
% Extract subsequence of indices (flip needed as per seq2key logic?)
|
||||||
|
% seq2key does: ismember(flip(seq)...).
|
||||||
|
% d_indices is 0-based index of d.
|
||||||
|
% We want indices of d(sym_idx-obj.L+1 : sym_idx)
|
||||||
|
|
||||||
|
d_sub = d_indices(sym_idx-obj.L+1 : sym_idx);
|
||||||
|
% seq2key flips the sequence.
|
||||||
|
% So we need to efficiently calculate scalar key from d_sub.
|
||||||
|
% key = 1 + sum( flip(d_sub) .* pow );
|
||||||
|
% Let's do it manually to be fast
|
||||||
|
|
||||||
|
key_to = 1 + sum(flip(d_sub) .* pow_vec);
|
||||||
|
|
||||||
|
state_idx = obj.key_table(key_to);
|
||||||
|
if state_idx==0
|
||||||
|
state_idx = true_from_state_idx;
|
||||||
|
end
|
||||||
|
obj.true_to_state_idx(symbol) = state_idx;
|
||||||
|
else
|
||||||
|
obj.true_to_state_idx(symbol) = true_from_state_idx;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
true_to_state_idx = obj.true_to_state_idx(symbol);
|
||||||
|
|
||||||
|
% --- fast Dirac creation
|
||||||
|
dirac = zeros(obj.nFeasible,1,'like',x); % inherit type (gpu or cpu)
|
||||||
|
trans_idx = obj.trans_index(true_to_state_idx,true_from_state_idx);
|
||||||
|
if trans_idx~=0
|
||||||
|
dirac(trans_idx)=1;
|
||||||
|
end
|
||||||
|
|
||||||
|
% --- ensure valid (from,to)
|
||||||
|
if ~any(dirac)
|
||||||
|
mask = obj.valid_from_idx==true_from_state_idx & ...
|
||||||
|
obj.valid_to_idx ==true_to_state_idx;
|
||||||
|
if any(mask)
|
||||||
|
dirac(mask) = 1;
|
||||||
|
else
|
||||||
|
idx = find(obj.valid_from_idx==true_from_state_idx,1,'first');
|
||||||
|
dirac(idx) = 1;
|
||||||
|
obj.true_to_state_idx(symbol) = obj.valid_to_idx(idx);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% ===================================================================
|
||||||
|
% TRAINING MODE (weight update)
|
||||||
|
% ===================================================================
|
||||||
|
if training
|
||||||
|
% --- Softmax and CE
|
||||||
|
v_shift = -(v_tilde - min(v_tilde));
|
||||||
|
v_shift = min(v_shift,100);
|
||||||
|
expv = exp(v_shift);
|
||||||
|
p = expv./(sum(expv)+eps);
|
||||||
|
CE_symbol(symbol) = -log(p(dirac==1)+eps);
|
||||||
|
|
||||||
|
% --- CE smoothing and adaptive μ
|
||||||
|
if sym_idx>obj.L
|
||||||
|
CE_smooth(symbol)=0.01*CE_symbol(symbol)+0.99*CE_symbol(symbol-1);
|
||||||
|
else
|
||||||
|
CE_smooth(symbol)=CE_symbol(symbol);
|
||||||
|
end
|
||||||
|
CE_accum=CE_accum+CE_symbol(symbol);
|
||||||
|
|
||||||
|
% --- Gradient update
|
||||||
|
dmp=(dirac-p)';
|
||||||
|
dL_Dw=(yk).*dmp;
|
||||||
|
if sym_idx>=obj.L
|
||||||
|
if obj.adaptive_mu
|
||||||
|
mu_eff=CE_smooth(symbol);
|
||||||
|
mu_eff=max(min(mu_eff,0.2),1e-4);
|
||||||
|
else
|
||||||
|
mu_eff=mu;
|
||||||
|
end
|
||||||
|
obj.w=obj.w - mu_eff.*dL_Dw;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% ===================================================================
|
||||||
|
% DECODING MODE (Viterbi only)
|
||||||
|
% ===================================================================
|
||||||
|
% Compare-Select (always executed)
|
||||||
|
vmat=inf(obj.nStates,obj.nStates);
|
||||||
|
vmat(obj.valid)=v_tilde;
|
||||||
|
[pm_next,pred(symbol,:)]=min(vmat,[],2);
|
||||||
|
pm_next=pm_next-min(pm_next);
|
||||||
|
pm=pm_next;
|
||||||
|
pm_sto(:,symbol)=pm;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% --- Traceback
|
||||||
|
[~,s_end]=min(pm);
|
||||||
|
vpath=zeros(symbol,1,'uint32');
|
||||||
|
vpath(symbol)=s_end;
|
||||||
|
for n=symbol:-1:2
|
||||||
|
vpath(n-1)=pred(n,vpath(n));
|
||||||
|
end
|
||||||
|
|
||||||
|
y_ref=d(start_symbol:end);
|
||||||
|
y=obj.first_sym(vpath);
|
||||||
|
|
||||||
|
% --- BER/CE reporting and plots
|
||||||
|
if training
|
||||||
|
err=sum(y~=y_ref(1:length(y)));
|
||||||
|
ser=err/length(y);
|
||||||
|
try
|
||||||
|
ref_bits=PAMmapper(obj.S,0).demap(y_ref(1:length(y)));
|
||||||
|
eq_bits=PAMmapper(obj.S,0).demap(y);
|
||||||
|
[~,~,ber,~]=calc_ber(ref_bits,eq_bits,"skip_front",10,"skip_end",10,"returnErrorLocation",1);
|
||||||
|
fprintf('Epoch %d - BER: %.2e\n',epoch,ber);
|
||||||
|
obj.ber(epoch)=ber;
|
||||||
|
catch
|
||||||
|
fprintf('Epoch %d - SER: %.2e\n',epoch,ser);
|
||||||
|
obj.ber(epoch)=ser;
|
||||||
|
end
|
||||||
|
obj.ce(epoch)=CE_accum/symbol;
|
||||||
|
|
||||||
|
if debug && mod(epoch,10)==1 && showPlots
|
||||||
|
figure(10);clf
|
||||||
|
subplot(3,2,1:2);
|
||||||
|
if obj.use_gpu, wm=gather(obj.w); else, wm=obj.w; end
|
||||||
|
imagesc(wm);axis xy;colorbar;title('Filter W');
|
||||||
|
subplot(3,2,3);
|
||||||
|
vtilde_mat=NaN(obj.nStates,obj.nStates);
|
||||||
|
vtilde_mat(obj.valid)=gather(v_tilde); % gather just in case
|
||||||
|
imagesc(vtilde_mat);axis xy;colorbar;title('Path Metrics (v\_tilde)');
|
||||||
|
subplot(3,2,4);
|
||||||
|
plot(1:symbol,gather(pm_sto));title('Path Metric Evolution');
|
||||||
|
subplot(3,2,5);hold on;
|
||||||
|
scatter(1:symbol,CE_symbol,1,'.');
|
||||||
|
scatter(1:symbol,CE_smooth,1,'.');
|
||||||
|
title('Cross Entropy');
|
||||||
|
subplot(3,2,6);hold on;
|
||||||
|
yyaxis left
|
||||||
|
scatter(1:length(obj.ce),obj.ce,10,'s','filled');
|
||||||
|
ylabel('Cross Entropy');
|
||||||
|
yyaxis right
|
||||||
|
scatter(1:length(obj.ber),obj.ber,10,'d','filled');
|
||||||
|
set(gca,'YScale','log');
|
||||||
|
ylabel('BER (log)');
|
||||||
|
xlabel('Epoch');grid on;
|
||||||
|
title('Convergence');
|
||||||
|
drawnow;
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% ==============================================================
|
||||||
|
% Helper: Sequence → key (always scalar)
|
||||||
|
% ==============================================================
|
||||||
|
function key = seq2key(obj, seq)
|
||||||
|
[~, idx] = ismember(flip(seq), obj.constellation);
|
||||||
|
pow = (obj.nSym .^ (0:obj.L-1)).';
|
||||||
|
key = 1 + sum((idx(:) - 1) .* pow);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
@@ -23,7 +23,7 @@ try
|
|||||||
|
|
||||||
if options.mode == "load_run_id" || options.append_to_db
|
if options.mode == "load_run_id" || options.append_to_db
|
||||||
% Initialize database connection
|
% Initialize database connection
|
||||||
database = DBHandler("dataBase", [options.dataBase], "type", options.database_type );
|
database = DBHandler("dataBase", [options.dataBase], "type", options.database_type, 'user',"silas","password","silas","server","134.245.243.254");
|
||||||
|
|
||||||
if 0
|
if 0
|
||||||
% 2. Check if an equalizer configuration with the same hash exists
|
% 2. Check if an equalizer configuration with the same hash exists
|
||||||
@@ -95,7 +95,7 @@ try
|
|||||||
adaption= 1;
|
adaption= 1;
|
||||||
use_dd_mode = 1;
|
use_dd_mode = 1;
|
||||||
|
|
||||||
use_ffe = 1;
|
use_ffe = 0;
|
||||||
use_dfe = 0;
|
use_dfe = 0;
|
||||||
use_vnle_mlse = 0;
|
use_vnle_mlse = 0;
|
||||||
use_dbtgt = 0;
|
use_dbtgt = 0;
|
||||||
|
|||||||
34
Functions/Theory/Dissertation/dispersion_around_zdw.m
Normal file
34
Functions/Theory/Dissertation/dispersion_around_zdw.m
Normal file
@@ -0,0 +1,34 @@
|
|||||||
|
|
||||||
|
% plot_dispersion_models
|
||||||
|
% ------------------------------------------------------------
|
||||||
|
% Visualizes exact and linearized chromatic dispersion D(λ)
|
||||||
|
% around the zero-dispersion wavelength (ZDW).
|
||||||
|
%
|
||||||
|
% Inputs:
|
||||||
|
% lambda0_nm - ZDW in nm
|
||||||
|
% S0 - dispersion slope at ZDW [ps/(nm^2·km)]
|
||||||
|
% ------------------------------------------------------------
|
||||||
|
|
||||||
|
lambda0_nm = 1310;
|
||||||
|
S0 = 0.08;
|
||||||
|
% wavelength axis around ZDW
|
||||||
|
lambda_nm = linspace(lambda0_nm-40, lambda0_nm+40, 400);
|
||||||
|
|
||||||
|
% exact dispersion model
|
||||||
|
D_exact = (S0/4) .* ( ...
|
||||||
|
lambda_nm - (lambda0_nm^4)./(lambda_nm.^3) );
|
||||||
|
|
||||||
|
% linearized model around ZDW
|
||||||
|
D_lin = S0 .* (lambda_nm - lambda0_nm);
|
||||||
|
|
||||||
|
% plot
|
||||||
|
figure('Color','w'); hold on;
|
||||||
|
plot(lambda_nm, D_exact, 'LineWidth',2, 'DisplayName','Exact model');
|
||||||
|
plot(lambda_nm, D_lin, '--', 'LineWidth',2, 'DisplayName','Linearized model');
|
||||||
|
|
||||||
|
xlabel('Wavelength \lambda [nm]');
|
||||||
|
ylabel('Dispersion D(\lambda) [ps/(nm·km)]');
|
||||||
|
title('Chromatic Dispersion Around the ZDW');
|
||||||
|
legend('Location','best');
|
||||||
|
grid on; box on;
|
||||||
|
|
||||||
@@ -9,7 +9,7 @@ L = 1; % km
|
|||||||
|
|
||||||
% Dispersion berechnen (lineare Näherung)
|
% Dispersion berechnen (lineare Näherung)
|
||||||
D = S0 .* ( lambda - Lambda0 ) * L;
|
D = S0 .* ( lambda - Lambda0 ) * L;
|
||||||
% D = (S0./4) .* ( lambda - (Lambda0.^4)./(lambda^3) ) * L;
|
D = (S0./4) .* ( lambda - (Lambda0.^4)./(lambda^3) ) * L;
|
||||||
|
|
||||||
%% 2D-Konturplot nur mit Linien und Text
|
%% 2D-Konturplot nur mit Linien und Text
|
||||||
figure('Color','w');
|
figure('Color','w');
|
||||||
|
|||||||
Reference in New Issue
Block a user