From 65d76d888748c1b56aa33daab7a21805e5cba824 Mon Sep 17 00:00:00 2001 From: Americo Cunha <36556019+americocunhajr@users.noreply.github.com> Date: Tue, 17 Sep 2024 16:13:18 -0300 Subject: [PATCH] Add files via upload --- ..._Truss10_MassMin_FrequencyBounds_BoxPlot.m | 29 +- .../Main_Truss10_MassMin_FrequencyBounds_CE.m | 4 +- .../Main_Truss10_MassMin_FrequencyBounds_GA.m | 4 +- ...Main_Truss10_MassMin_FrequencyBounds_SQP.m | 4 +- ...Main_Truss10_MassMin_YieldStress_BoxPlot.m | 31 +- .../Main_Truss10_MassMin_YieldStress_CE.m | 2 +- .../Main_Truss10_MassMin_YieldStress_GA.m | 2 +- .../Main_Truss10_MassMin_YieldStress_SQP.m | 2 +- ..._Truss37_MassMin_FrequencyBounds_BoxPlot.m | 301 ++++++++++++++++ .../Main_Truss37_MassMin_FrequencyBounds_CE.m | 168 +++++++++ .../Main_Truss37_MassMin_FrequencyBounds_GA.m | 171 ++++++++++ ...Main_Truss37_MassMin_FrequencyBounds_SQP.m | 170 ++++++++++ CROSS-OPT-1.0/PlotTruss10.m | 74 ++-- CROSS-OPT-1.0/PlotTruss37.m | 192 +++++++++++ CROSS-OPT-1.0/TrussFrequencyBounds10.m | 77 +++++ CROSS-OPT-1.0/TrussFrequencyBounds37.m | 118 +++++++ CROSS-OPT-1.0/TrussMass10.m | 30 ++ CROSS-OPT-1.0/TrussMass37.m | 102 ++++++ CROSS-OPT-1.0/inferno.m | 321 ++++++++++++++++++ CROSS-OPT-1.0/magma.m | 321 ++++++++++++++++++ CROSS-OPT-1.0/plasma.m | 320 +++++++++++++++++ CROSS-OPT-1.0/viridis.m | 321 ++++++++++++++++++ 22 files changed, 2704 insertions(+), 60 deletions(-) create mode 100644 CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m create mode 100644 CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_CE.m create mode 100644 CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_GA.m create mode 100644 CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_SQP.m create mode 100644 CROSS-OPT-1.0/PlotTruss37.m create mode 100644 CROSS-OPT-1.0/TrussFrequencyBounds10.m create mode 100644 CROSS-OPT-1.0/TrussFrequencyBounds37.m create mode 100644 CROSS-OPT-1.0/TrussMass10.m create mode 100644 CROSS-OPT-1.0/TrussMass37.m create mode 100644 CROSS-OPT-1.0/inferno.m create mode 100644 CROSS-OPT-1.0/magma.m create mode 100644 CROSS-OPT-1.0/plasma.m create mode 100644 CROSS-OPT-1.0/viridis.m diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_BoxPlot.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_BoxPlot.m index 12d3d27..7416f9a 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_BoxPlot.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_BoxPlot.m @@ -6,7 +6,7 @@ % Americo Cunha Jr % % Originally programmed in: Jun 25, 2024 -% Last updated in: Aug 22, 2024 +% Last updated in: Sep 15, 2024 % ----------------------------------------------------------------- %  Mass minimization with frequency constraints for a 10 bars % truss structure. Box plot calculation for CE, GA and SQP. @@ -65,8 +65,8 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); -nonlcon = @(x)TrussFrequencyBounds(x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds10(x,MyTruss); % number of variables Nvars = 10; @@ -80,7 +80,7 @@ sigma0 = 5*(ub-lb); % number of box plot samples -Nbp = 5; +Nbp = 64; % boxplot for CE % ------------------------------------------------------------------ @@ -176,10 +176,10 @@ % optional parameters opt = optimoptions('fmincon','Display','off','Algorithm','sqp'); -% random initial guess -x0 = lb + (ub-lb).*rand(1,Nvars); - while t < Nbp + % random initial guess + x0 = lb + (ub-lb).*rand(1,Nvars); + % SPQ solver [Xopt,Fopt,ExitFlag,SQPstr] = fmincon(fun,x0,[],[],[],[],lb,ub,nonlcon,opt); @@ -199,6 +199,21 @@ % ------------------------------------------------------------------ +% save simulation results +% ----------------------------------------------------------- +tic +disp(' ') +disp(' --- saving simulation results --- '); +disp(' '); +disp(' ... '); +disp(' '); + +save('Truss10_MassMin_FrequencyBounds_BoxPlot.mat'); + +toc +% ----------------------------------------------------------- + + % post processing % ------------------------------------------------------------------ disp(' ') diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_CE.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_CE.m index 622dc5e..2339147 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_CE.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_CE.m @@ -64,8 +64,8 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); -nonlcon = @(x)TrussFrequencyBounds(x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds10(x,MyTruss); % number of variables Nvars = 10; diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_GA.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_GA.m index e89baa6..ca95abc 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_GA.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_GA.m @@ -64,8 +64,8 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); -nonlcon = @(x)TrussFrequencyBounds(x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds10(x,MyTruss); % number of variables Nvars = 10; diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_SQP.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_SQP.m index ea809e8..1a4a28f 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_SQP.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_FrequencyBounds_SQP.m @@ -64,8 +64,8 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); -nonlcon = @(x)TrussFrequencyBounds(x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds10(x,MyTruss); % number of variables Nvars = 10; diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_BoxPlot.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_BoxPlot.m index 6a46582..a4cd855 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_BoxPlot.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_BoxPlot.m @@ -73,7 +73,7 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); nonlcon = @(x)TrussYieldStress(x,MyTruss); % number of variables @@ -88,7 +88,7 @@ sigma0 = 5*(ub-lb); % number of box plot samples -Nbp = 125; +Nbp = 64; % boxplot for CE % ------------------------------------------------------------------ @@ -184,16 +184,16 @@ % optional parameters opt = optimoptions('fmincon','Display','off','Algorithm','sqp'); -% random initial guess -x0 = lb + (ub-lb).*rand(1,Nvars); - while t < Nbp + % random initial guess + x0 = lb + (ub-lb).*rand(1,Nvars); + % SPQ solver [Xopt,Fopt,ExitFlag,SQPstr] = fmincon(fun,x0,[],[],[],[],lb,ub,nonlcon,opt); - + % update solver running counter Nrun_SQP = Nrun_SQP + 1; - + % check constraint violation if max(nonlcon(Xopt)) <= opt.TolCon t = t + 1; @@ -207,6 +207,21 @@ % ------------------------------------------------------------------ +% save simulation results +% ------------------------------------------------------------------ +tic +disp(' ') +disp(' --- saving simulation results --- '); +disp(' '); +disp(' ... '); +disp(' '); + +save('Truss10_MassMin_YieldStress_BoxPlot.mat'); + +toc +% ------------------------------------------------------------------ + + % post processing % ------------------------------------------------------------------ disp(' ') @@ -218,7 +233,7 @@ figure x = [Fopt_SQP Fopt_GA Fopt_CE]; boxplot(x,'Notch','off','Labels',{'SQP','GA','CE'}); -ylabel('Truss Mass (kg)','FontSize',20,'FontName', 'Helvetica') +ylabel('Truss Mass (kg)','FontSize',20,'FontName', 'Helvetica') title("Number samples: " + Nbp, 'FontSize',20,'FontName', 'Helvetica') set(gca, 'FontName', 'Helvetica'); set(gca, 'FontSize', 18); diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_CE.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_CE.m index 1ec9762..b28f000 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_CE.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_CE.m @@ -72,7 +72,7 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); nonlcon = @(x)TrussYieldStress(x,MyTruss); % number of variables diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_GA.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_GA.m index b64a6fd..02893c7 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_GA.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_GA.m @@ -72,7 +72,7 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); nonlcon = @(x)TrussYieldStress(x,MyTruss); % number of variables diff --git a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_SQP.m b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_SQP.m index 0459ad9..93d4a47 100644 --- a/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_SQP.m +++ b/CROSS-OPT-1.0/Main_Truss10_MassMin_YieldStress_SQP.m @@ -72,7 +72,7 @@ MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs % objective and constraint functions -fun = @(x)TrussMass (x,MyTruss); +fun = @(x)TrussMass10 (x,MyTruss); nonlcon = @(x)TrussYieldStress(x,MyTruss); % number of variables diff --git a/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m new file mode 100644 index 0000000..53b2b91 --- /dev/null +++ b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m @@ -0,0 +1,301 @@ +% ----------------------------------------------------------------- +% Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Jun 25, 2024 +% Last updated in: Sep 15, 2024 +% ----------------------------------------------------------------- +%  Mass minimization with frequency constraints for a 37 bars +% truss structure. Box plot calculation for CE, GA and SQP. +% ----------------------------------------------------------------- + + +clc; clear; close all; + +disp(' ---------------------------------------------- ') +disp(' Main_Truss37_MassMin_FrequencyBounds_BoxPlot.m ') +disp(' ---------------------------------------------- ') + +% random number generator (fix the seed for reproducibility) +rng_stream = RandStream('mt19937ar','Seed',30081984); +RandStream.setGlobalStream(rng_stream); + +% truss parameters +a = 1.0; % bar length (m) +h = 1.0; % truss height (m) +rho = 7800.0; % material density (kg/m^3) +E = 210.0e9; % elastic modulus (Pa) +AddedMass = 10.0; % added mass (kg) +omegaTresh = 2*pi*[20 40 60]'; % treshold frequencies (rad/s) + +% sctruct with the truss parameters +MyTruss.a = a; % bar length (m) +MyTruss.h = h; % truss height (m) +MyTruss.rho = rho; % material density (kg/m^3) +MyTruss.E = E; % elastic modulus (Pa) +MyTruss.AddedMass = AddedMass; % added mass (kg) +MyTruss.omegaTresh = omegaTresh; % treshold frequencies (rad/s) +MyTruss.FixedDoFs = [1 2 40]; % Diriclet boundary condition DoFs +MyTruss.NODES = [ 0 0; % nodes coordinates + a 0; + a h; + 2*a 0; + 2*a h; + 3*a 0; + 3*a h; + 4*a 0; + 4*a h; + 5*a 0; + 5*a h; + 6*a 0; + 6*a h; + 7*a 0; + 7*a h; + 8*a 0; + 8*a h; + 9*a 0; + 9*a h; + 10*a 0]; +MyTruss.ELEM = [ 1 3; % element nodes + 2 3; + 3 4; + 3 5; + 4 5; + 5 6; + 5 7; + 6 7; + 7 8; + 7 9; + 8 9; + 9 10; + 9 11; + 10 11; + 10 13; + 11 13; + 12 13; + 12 15; + 13 15; + 14 15; + 14 17; + 15 17; + 16 17; + 16 19; + 17 19; + 18 19; + 19 20; + 1 2; + 2 4; + 4 6; + 6 8; + 8 10; + 10 12; + 12 14; + 14 16; + 16 18; + 18 20]; +MyTruss.SYMBARS = {[ 1 27]; % symmetrical bars + [ 2 26]; + [ 3 24]; + [ 4 25]; + [ 5 23]; + [ 6 21]; + [ 7 22]; + [ 8 20]; + [ 9 18]; + [10 19]; + [11 17]; + [12 15]; + [13 16]; + [14 14]; + 28:37}; +MyTruss.Nnodes = size(MyTruss.NODES,1); % # of nodes +MyTruss.Nelem = size(MyTruss.ELEM ,1); % # of elements +MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs + +% number of design variables of each kind +NvarsA = size(MyTruss.SYMBARS,1); +NvarsH = 5; +MyTruss.NvarsA = NvarsA; +MyTruss.NvarsH = NvarsH; +Nvars = NvarsA + NvarsH; + +% objective and constraint functions +fun = @(x)TrussMass37 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds37(x,MyTruss); + +% lower and upper bounds for design variables +lb_A = 100.0*ones(1,NvarsA)*1e-6; % unit: m^2 +ub_A = 1000.0*ones(1,NvarsA)*1e-6; % unit: m^2 +lb_H = 0.1*ones(1,NvarsH); % unit: m +ub_H = 10.0*ones(1,NvarsH); % unit: m +lb = [lb_A lb_H]; +ub = [ub_A ub_H]; + +% initial mean and standard deviation +xmean0 = 0.5*(ub+lb); +sigma0 = 5*(ub-lb); + +% number of box plot samples +Nbp = 64; + +% boxplot for CE +% ------------------------------------------------------------------ +tic +disp(' ') +disp(' --------------- ') +disp(' CE Box Plot ... ') +disp(' --------------- ') +disp(' ') + + t = 0; + Nrun_CE = 0; + Xopt_CE = zeros(Nbp,Nvars); + Fopt_CE = zeros(Nbp,1); +Fcount_CE = zeros(Nbp,1); + +% optional parameters +CEstr.Verbose = 0; + +while t < Nbp + % CE solver + [Xopt,Fopt,ExitFlag,CEstr] = CEopt(fun,[],[],lb,ub,nonlcon,CEstr); + + % update solver running counter + Nrun_CE = Nrun_CE + 1; + + % check constraint violation + if max(nonlcon(Xopt)) <= CEstr.TolCon + t = t + 1; + Xopt_CE(t,:) = Xopt; + Fopt_CE(t,:) = Fopt; + Fcount_CE(t,:) = CEstr.Fcount; + end +end +Xopt_CE_m = median(Xopt_CE) +toc +% ------------------------------------------------------------------ + + +% boxplot for GA +% ------------------------------------------------------------------ +tic +disp(' ') +disp(' --------------- ') +disp(' GA Box Plot ... ') +disp(' --------------- ') +disp(' ') + + t = 0; + Nrun_GA = 0; + Xopt_GA = zeros(Nbp,Nvars); + Fopt_GA = zeros(Nbp,1); +Fcount_GA = zeros(Nbp,1); + +% optional parameters +opt = optimoptions('ga','Display','off'); + +while t < Nbp + % GA solver + [Xopt,Fopt,ExitFlag,GAstr] = ga(fun,Nvars,[],[],[],[],lb,ub,nonlcon,opt); + + % update solver running counter + Nrun_GA = Nrun_GA + 1; + + % check constraint violation + if max(nonlcon(Xopt)) <= opt.TolCon + t = t + 1; + Xopt_GA(t,:) = Xopt; + Fopt_GA(t,:) = Fopt; + Fcount_GA(t,:) = GAstr.funccount; + end +end +Xopt_GA_m = median(Xopt_GA) +toc +% ------------------------------------------------------------------ + + +% boxplot for SQP +% ------------------------------------------------------------------ +tic +disp(' ') +disp(' ---------------- ') +disp(' SQP Box Plot ... ') +disp(' ---------------- ') +disp(' ') + + t = 0; + Nrun_SQP = 0; + Xopt_SQP = zeros(Nbp,Nvars); + Fopt_SQP = zeros(Nbp,1); +Fcount_SQP = zeros(Nbp,1); + +% optional parameters +opt = optimoptions('fmincon','Display','off','Algorithm','sqp'); + +while t < Nbp + % random initial guess + x0 = lb + (ub-lb).*rand(1,Nvars); + + % SPQ solver + [Xopt,Fopt,ExitFlag,SQPstr] = fmincon(fun,x0,[],[],[],[],lb,ub,nonlcon,opt); + + % update solver running counter + Nrun_SQP = Nrun_SQP + 1; + + % check constraint violation + if max(nonlcon(Xopt)) <= opt.TolCon + t = t + 1; + Xopt_SQP(t,:) = Xopt; + Fopt_SQP(t,:) = Fopt; + Fcount_SQP(t,:) = SQPstr.funcCount; + end +end +Xopt_SPQ_m = median(Xopt_SQP) +toc +% ------------------------------------------------------------------ + + +% save simulation results +% ----------------------------------------------------------- +tic +disp(' ') +disp(' --- saving simulation results --- '); +disp(' '); +disp(' ... '); +disp(' '); + +save('Truss37_MassMin_FrequencyBounds_BoxPlot.mat'); + +toc +% ----------------------------------------------------------- + + +% post processing +% ------------------------------------------------------------------ +disp(' ') +disp(' ------------------- ') +disp(' Post processing ... ') +disp(' ------------------- ') +disp(' ') + +figure +x = [Fopt_SQP Fopt_GA Fopt_CE]; +boxplot(x,'Notch','off','Labels',{'SQP','GA','CE'}); +ylabel('Truss Mass (kg)','FontSize',20,'FontName', 'Helvetica') +title("Number samples: " + Nbp, 'FontSize',20,'FontName', 'Helvetica') +set(gca, 'FontName', 'Helvetica'); +set(gca, 'FontSize', 18); +box on + +figure +x = [Fcount_SQP Fcount_GA Fcount_CE]; +boxplot(x,'Notch','off','Labels',{'SQP','GA','CE'}); +ylabel('Function Evaluations','FontSize',20,'FontName', 'Helvetica') +title("Number samples: " + Nbp, 'FontSize',20,'FontName', 'Helvetica') +set(gca, 'FontName', 'Helvetica'); +set(gca, 'FontSize', 18); +box on +% ------------------------------------------------------------------ diff --git a/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_CE.m b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_CE.m new file mode 100644 index 0000000..8c8fef3 --- /dev/null +++ b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_CE.m @@ -0,0 +1,168 @@ +% ----------------------------------------------------------------- +% Main_Truss37_MassMin_FrequencyBounds_CE.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% Mass minimization with frequency constraints for a 37 bars +% truss structure using the cross-entropy method. +% ----------------------------------------------------------------- + +clc; clear; close all; + +disp(' ----------------------------------------- ') +disp(' Main_Truss37_MassMin_FrequencyBounds_CE.m ') +disp(' ----------------------------------------- ') + +% random number generator (fix the seed for reproducibility) +%rng_stream = RandStream('mt19937ar','Seed',30081984); +%RandStream.setGlobalStream(rng_stream); + +% truss parameters +a = 1.0; % bar length (m) +h = 1.0; % truss height (m) +rho = 7800.0; % material density (kg/m^3) +E = 210.0e9; % elastic modulus (Pa) +AddedMass = 10.0; % added mass (kg) +omegaTresh = 2*pi*[20 40 60]'; % treshold frequencies (rad/s) + +% sctruct with the truss parameters +MyTruss.a = a; % bar length (m) +MyTruss.h = h; % truss height (m) +MyTruss.rho = rho; % material density (kg/m^3) +MyTruss.E = E; % elastic modulus (Pa) +MyTruss.AddedMass = AddedMass; % added mass (kg) +MyTruss.omegaTresh = omegaTresh; % treshold frequencies (rad/s) +MyTruss.FixedDoFs = [1 2 40]; % Diriclet boundary condition DoFs +MyTruss.NODES = [ 0 0; % nodes coordinates + a 0; + a h; + 2*a 0; + 2*a h; + 3*a 0; + 3*a h; + 4*a 0; + 4*a h; + 5*a 0; + 5*a h; + 6*a 0; + 6*a h; + 7*a 0; + 7*a h; + 8*a 0; + 8*a h; + 9*a 0; + 9*a h; + 10*a 0]; +MyTruss.ELEM = [ 1 3; % element nodes + 2 3; + 3 4; + 3 5; + 4 5; + 5 6; + 5 7; + 6 7; + 7 8; + 7 9; + 8 9; + 9 10; + 9 11; + 10 11; + 10 13; + 11 13; + 12 13; + 12 15; + 13 15; + 14 15; + 14 17; + 15 17; + 16 17; + 16 19; + 17 19; + 18 19; + 19 20; + 1 2; + 2 4; + 4 6; + 6 8; + 8 10; + 10 12; + 12 14; + 14 16; + 16 18; + 18 20]; +MyTruss.SYMBARS = {[ 1 27]; % symmetrical bars + [ 2 26]; + [ 3 24]; + [ 4 25]; + [ 5 23]; + [ 6 21]; + [ 7 22]; + [ 8 20]; + [ 9 18]; + [10 19]; + [11 17]; + [12 15]; + [13 16]; + [14 14]; + 28:37}; +MyTruss.Nnodes = size(MyTruss.NODES,1); % # of nodes +MyTruss.Nelem = size(MyTruss.ELEM ,1); % # of elements +MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs + +% number of design variables of each kind +NvarsA = size(MyTruss.SYMBARS,1); +NvarsH = 5; +MyTruss.NvarsA = NvarsA; +MyTruss.NvarsH = NvarsH; + +% objective and constraint functions +fun = @(x)TrussMass37 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds37(x,MyTruss); + +% lower and upper bounds for design variables +lb_A = 100.0*ones(1,NvarsA)*1e-6; % unit: m^2 +ub_A = 1000.0*ones(1,NvarsA)*1e-6; % unit: m^2 +lb_H = 0.1*ones(1,NvarsH); % unit: m +ub_H = 10.0*ones(1,NvarsH); % unit: m +lb = [lb_A lb_H]; +ub = [ub_A ub_H]; + +% initial mean and standard deviation +xmean0 = 0.5*(ub+lb); +sigma0 = 5*(ub-lb); + +% CE solver +tic +[Xopt,Fopt,ExitFlag,CEstr] = CEopt(fun,[],[],lb,ub,nonlcon); +toc + +% check constraint violation +disp(' ') +disp(' Check if inequality constraints are <= 0') +disp(' ') +G = nonlcon(Xopt); +for i=1:length(G) + fprintf(' G(%d) = %5.2f\n',i,G(i)); +end +disp(' ') +if sum(G > CEstr.TolCon) ~= 0 + disp(' One or more constraints violated :-( ') +else + disp(' All constraints respected :-) ') +end + +% display optimized mass +fprintf('\n Original truss mass (kg): %5.2f',fun(xmean0)); +fprintf('\n Optimized truss mass (kg): %5.2f',Fopt ); +disp(' ') + +% plot the nominal truss structure +PlotTruss37([xmean0(1:NvarsA)*5e3 xmean0(NvarsA+1:end)],MyTruss,'Non-optimal Truss Structure'); + +% plot the optimal truss structure +PlotTruss37([ Xopt(1:NvarsA)*5e3 Xopt(NvarsA+1:end)],MyTruss,'Optimal Truss Structure'); diff --git a/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_GA.m b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_GA.m new file mode 100644 index 0000000..5e308e2 --- /dev/null +++ b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_GA.m @@ -0,0 +1,171 @@ +% ----------------------------------------------------------------- +% Main_Truss37_MassMin_FrequencyBounds_GA.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% Mass minimization with frequency constraints for a 37 bars +% truss structure using genetic algorithm. +% ----------------------------------------------------------------- + +clc; clear; close all; + +disp(' ----------------------------------------- ') +disp(' Main_Truss37_MassMin_FrequencyBounds_GA.m ') +disp(' ----------------------------------------- ') + +% random number generator (fix the seed for reproducibility) +%rng_stream = RandStream('mt19937ar','Seed',30081984); +%RandStream.setGlobalStream(rng_stream); + +% truss parameters +a = 1.0; % bar length (m) +h = 1.0; % truss height (m) +rho = 7800.0; % material density (kg/m^3) +E = 210.0e9; % elastic modulus (Pa) +AddedMass = 10.0; % added mass (kg) +omegaTresh = 2*pi*[20 40 60]'; % treshold frequencies (rad/s) + +% sctruct with the truss parameters +MyTruss.a = a; % bar length (m) +MyTruss.h = h; % truss height (m) +MyTruss.rho = rho; % material density (kg/m^3) +MyTruss.E = E; % elastic modulus (Pa) +MyTruss.AddedMass = AddedMass; % added mass (kg) +MyTruss.omegaTresh = omegaTresh; % treshold frequencies (rad/s) +MyTruss.FixedDoFs = [1 2 40]; % Diriclet boundary condition DoFs +MyTruss.NODES = [ 0 0; % nodes coordinates + a 0; + a h; + 2*a 0; + 2*a h; + 3*a 0; + 3*a h; + 4*a 0; + 4*a h; + 5*a 0; + 5*a h; + 6*a 0; + 6*a h; + 7*a 0; + 7*a h; + 8*a 0; + 8*a h; + 9*a 0; + 9*a h; + 10*a 0]; +MyTruss.ELEM = [ 1 3; % element nodes + 2 3; + 3 4; + 3 5; + 4 5; + 5 6; + 5 7; + 6 7; + 7 8; + 7 9; + 8 9; + 9 10; + 9 11; + 10 11; + 10 13; + 11 13; + 12 13; + 12 15; + 13 15; + 14 15; + 14 17; + 15 17; + 16 17; + 16 19; + 17 19; + 18 19; + 19 20; + 1 2; + 2 4; + 4 6; + 6 8; + 8 10; + 10 12; + 12 14; + 14 16; + 16 18; + 18 20]; +MyTruss.SYMBARS = {[ 1 27]; % symmetrical bars + [ 2 26]; + [ 3 24]; + [ 4 25]; + [ 5 23]; + [ 6 21]; + [ 7 22]; + [ 8 20]; + [ 9 18]; + [10 19]; + [11 17]; + [12 15]; + [13 16]; + [14 14]; + 28:37}; +MyTruss.Nnodes = size(MyTruss.NODES,1); % # of nodes +MyTruss.Nelem = size(MyTruss.ELEM ,1); % # of elements +MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs + +% number of design variables of each kind +NvarsA = size(MyTruss.SYMBARS,1); +NvarsH = 5; +MyTruss.NvarsA = NvarsA; +MyTruss.NvarsH = NvarsH; +Nvars = NvarsA + NvarsH; + +% objective and constraint functions +fun = @(x)TrussMass37 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds37(x,MyTruss); + +% lower and upper bounds for design variables +lb_A = 100.0*ones(1,NvarsA)*1e-6; % unit: m^2 +ub_A = 1000.0*ones(1,NvarsA)*1e-6; % unit: m^2 +lb_H = 0.1*ones(1,NvarsH); % unit: m +ub_H = 10.0*ones(1,NvarsH); % unit: m +lb = [lb_A lb_H]; +ub = [ub_A ub_H]; + +% initial mean +xmean0 = 0.5*(ub+lb); + +% optional parameters +opt = optimoptions('ga','Display','iter'); + +% GA solver +tic +[Xopt,Fopt,ExitFlag,GAstr] = ga(fun,Nvars,[],[],[],[],lb,ub,nonlcon,opt); +toc + +% check constraint violation +disp(' ') +disp(' Check if inequality constraints are <= 0') +disp(' ') +G = nonlcon(Xopt); +for i=1:length(G) + fprintf(' G(%d) = %5.2f\n',i,G(i)); +end +disp(' ') +if sum(G > opt.TolCon) ~= 0 + disp(' One or more constraints violated :-( ') +else + disp(' All constraints respected :-) ') +end + +% display optimized mass +fprintf('\n Original truss mass (kg): %5.2f',fun(xmean0)); +fprintf('\n Optimized truss mass (kg): %5.2f',Fopt ); +disp(' ') + +% plot the nominal truss structure +PlotTruss37([xmean0(1:NvarsA)*5e3 xmean0(NvarsA+1:end)],MyTruss,'Non-optimal Truss Structure'); + +% plot the optimal truss structure +PlotTruss37([ Xopt(1:NvarsA)*5e3 Xopt(NvarsA+1:end)],MyTruss,'Optimal Truss Structure'); diff --git a/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_SQP.m b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_SQP.m new file mode 100644 index 0000000..a199371 --- /dev/null +++ b/CROSS-OPT-1.0/Main_Truss37_MassMin_FrequencyBounds_SQP.m @@ -0,0 +1,170 @@ +% ----------------------------------------------------------------- +% Main_Truss37_MassMin_FrequencyBounds_SQP.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% Mass minimization with frequency constraints for a 37 bars +% truss structure using sequential quadratic programming. +% ----------------------------------------------------------------- + +clc; clear; close all; + +disp(' ------------------------------------------ ') +disp(' Main_Truss37_MassMin_FrequencyBounds_SQP.m ') +disp(' ------------------------------------------ ') + +% random number generator (fix the seed for reproducibility) +%rng_stream = RandStream('mt19937ar','Seed',30081984); +%RandStream.setGlobalStream(rng_stream); + +% truss parameters +a = 1.0; % bar length (m) +h = 1.0; % truss height (m) +rho = 7800.0; % material density (kg/m^3) +E = 210.0e9; % elastic modulus (Pa) +AddedMass = 10.0; % added mass (kg) +omegaTresh = 2*pi*[20 40 60]'; % treshold frequencies (rad/s) + +% sctruct with the truss parameters +MyTruss.a = a; % bar length (m) +MyTruss.h = h; % truss height (m) +MyTruss.rho = rho; % material density (kg/m^3) +MyTruss.E = E; % elastic modulus (Pa) +MyTruss.AddedMass = AddedMass; % added mass (kg) +MyTruss.omegaTresh = omegaTresh; % treshold frequencies (rad/s) +MyTruss.FixedDoFs = [1 2 40]; % Diriclet boundary condition DoFs +MyTruss.NODES = [ 0 0; % nodes coordinates + a 0; + a h; + 2*a 0; + 2*a h; + 3*a 0; + 3*a h; + 4*a 0; + 4*a h; + 5*a 0; + 5*a h; + 6*a 0; + 6*a h; + 7*a 0; + 7*a h; + 8*a 0; + 8*a h; + 9*a 0; + 9*a h; + 10*a 0]; +MyTruss.ELEM = [ 1 3; % element nodes + 2 3; + 3 4; + 3 5; + 4 5; + 5 6; + 5 7; + 6 7; + 7 8; + 7 9; + 8 9; + 9 10; + 9 11; + 10 11; + 10 13; + 11 13; + 12 13; + 12 15; + 13 15; + 14 15; + 14 17; + 15 17; + 16 17; + 16 19; + 17 19; + 18 19; + 19 20; + 1 2; + 2 4; + 4 6; + 6 8; + 8 10; + 10 12; + 12 14; + 14 16; + 16 18; + 18 20]; +MyTruss.SYMBARS = {[ 1 27]; % symmetrical bars + [ 2 26]; + [ 3 24]; + [ 4 25]; + [ 5 23]; + [ 6 21]; + [ 7 22]; + [ 8 20]; + [ 9 18]; + [10 19]; + [11 17]; + [12 15]; + [13 16]; + [14 14]; + 28:37}; +MyTruss.Nnodes = size(MyTruss.NODES,1); % # of nodes +MyTruss.Nelem = size(MyTruss.ELEM ,1); % # of elements +MyTruss.Ndofs = 2*MyTruss.Nnodes; % # of DoFs + +% number of design variables of each kind +NvarsA = size(MyTruss.SYMBARS,1); +NvarsH = 5; +MyTruss.NvarsA = NvarsA; +MyTruss.NvarsH = NvarsH; + +% objective and constraint functions +fun = @(x)TrussMass37 (x,MyTruss); +nonlcon = @(x)TrussFrequencyBounds37(x,MyTruss); + +% lower and upper bounds for design variables +lb_A = 100.0*ones(1,NvarsA)*1e-6; % unit: m^2 +ub_A = 1000.0*ones(1,NvarsA)*1e-6; % unit: m^2 +lb_H = 0.1*ones(1,NvarsH); % unit: m +ub_H = 10.0*ones(1,NvarsH); % unit: m +lb = [lb_A lb_H]; +ub = [ub_A ub_H]; + +% initial guess +x0 = 0.5*(ub+lb); + +% optional parameters +opt = optimoptions('fmincon','Display','iter','Algorithm','sqp'); + +% SQP solver +tic +[Xopt,Fopt,ExitFlag,SQPstr] = fmincon(fun,x0,[],[],[],[],lb,ub,nonlcon,opt); +toc + +% check constraint violation +disp(' ') +disp(' Check if inequality constraints are <= 0') +disp(' ') +G = nonlcon(Xopt); +for i=1:length(G) + fprintf(' G(%d) = %5.2f\n',i,G(i)); +end +disp(' ') +if sum(G > opt.TolCon) ~= 0 + disp(' One or more constraints violated :-( ') +else + disp(' All constraints respected :-) ') +end + +% display optimized mass +fprintf('\n Original truss mass (kg): %5.2f',fun(x0)); +fprintf('\n Optimized truss mass (kg): %5.2f',Fopt ); +disp(' ') + +% plot the nominal truss structure +PlotTruss37([x0(1:NvarsA)*5e3 x0(NvarsA+1:end)],MyTruss,'Non-optimal Truss Structure'); + +% plot the optimal truss structure +PlotTruss37([ Xopt(1:NvarsA)*5e3 Xopt(NvarsA+1:end)],MyTruss,'Optimal Truss Structure'); diff --git a/CROSS-OPT-1.0/PlotTruss10.m b/CROSS-OPT-1.0/PlotTruss10.m index 2490ae0..2cbe44c 100644 --- a/CROSS-OPT-1.0/PlotTruss10.m +++ b/CROSS-OPT-1.0/PlotTruss10.m @@ -6,20 +6,22 @@ % Americo Cunha Jr % % Originally programmed in: Apr 04, 2024 -% Last updated in: Aug 29, 2024 +% Last updated in: Sep 14, 2024 % ----------------------------------------------------------------- % Plot a 10 bars truss given the elements cross-section area. % ----------------------------------------------------------------- -function PlotTruss10(x,MyTruss,MyTitle) +function PlotTruss10(Area,MyTruss,MyTitle) % truss structure parameters h = MyTruss.h; NODES = MyTruss.NODES; ELEM = MyTruss.ELEM; + Nelem = MyTruss.Nelem; % custom color grayColor = [.7 .7 .7]; + % Open figure figure('DefaultAxesFontSize',10) clf hold on @@ -44,23 +46,25 @@ function PlotTruss10(x,MyTruss,MyTitle) patch(a21,a22,grayColor,'EdgeColor','none'); plot([a21(2) a21(3)],[a22(2) a22(3)],'k','linewidth',2.5); - for i = 1:length(x) + % Draw bars and nodes + for i = 1:Nelem patch('Faces' ,ELEM(i,:),... - 'Vertices' ,NODES,... + 'Vertices' ,NODES ,... 'EdgeColor' ,grayColor,... - 'LineWidth' ,x(i)); - + 'LineWidth' ,Area(i)); + patch('Faces' ,ELEM(i,:),... - 'Vertices' ,NODES,... - 'EdgeColor' ,'none',... - 'FaceColor' ,'none', ... - 'MarkerEdgeColor','blue',... - 'Marker' ,'o',... - 'MarkerFaceColor','white',... - 'MarkerSize' ,10,... + 'Vertices' ,NODES ,... + 'EdgeColor' ,'none' ,... + 'FaceColor' ,'none' ,... + 'MarkerEdgeColor','blue' ,... + 'Marker' ,'o' ,... + 'MarkerFaceColor','white' ,... + 'MarkerSize' ,10 ,... 'LineWidth' ,3); end + % Draw added mass for i = 1:4 plot([NODES(i,1)],[NODES(i,2)] , ... 'Marker' , 'o', ... @@ -74,41 +78,39 @@ function PlotTruss10(x,MyTruss,MyTitle) title(MyTitle,'FontSize',18) pause(1) end -%------------------------------------------------------------ - +% ------------------------------------------------------------ -%------------------------------------------------------------ - function [X,Y] = hatch_coordinates(xlim, ylim, xstep, ystep, merge) - %// function [X,Y] = hatch_coordinates(xlim,ylim,xstep,ystep,merge) - %// - %// Return coordinates for plotting a hatch pattern - %// The angle of the lines can be adjusted by varying the - % ratio xstep/ystep - %// xlim and ylim are vectors with two elements, - % where the first element needs to be smaller than the second. +% ------------------------------------------------------------ +% This function returns the coordinates for plotting a hatch +% pattern. The angle of the lines can be adjusted by varying +% the ratio xstep/ystep. xlim and ylim are vectors with two +% elements, where the first element needs to be smaller than +% the second. +% ------------------------------------------------------------ +function [X,Y] = hatch_coordinates(xlim,ylim,xstep,ystep,merge) - % // set default options + % set default options if nargin < 3 ; xstep = 1 ; end if nargin < 4 ; ystep = xstep ; end if nargin < 5 ; merge = true ; end - % // define base grid + % define base grid xpos = xlim(1):xstep:xlim(2) ; nx = numel(xpos) ; ypos = ylim(1):ystep:ylim(2) ; ny = numel(ypos) ; - % // Create the coordinates + % Create the coordinates nanline = NaN*ones(1,nx+ny-3) ; - X = [ [ xpos(1)*ones(1,ny-2) xpos(1:end-1) ] ; ... - [ xpos(2:end) xpos(end)*ones(1,ny-2) ] ; ... - nanline ] ; - Y = [ [ypos(end-1:-1:1) ylim(1)*ones(1,nx-2) ] ; ... - [ypos(end)*ones(1,nx-1) ypos(end-1:-1:2)] ; ... - nanline ] ; + X = [ [xpos(1)*ones(1,ny-2) xpos(1:end-1)]; ... + [xpos(2:end) xpos(end)*ones(1,ny-2)]; ... + nanline]; + Y = [ [ypos(end-1:-1:1) ylim(1)*ones(1,nx-2)]; ... + [ypos(end)*ones(1,nx-1) ypos(end-1:-1:2)]; ... + nanline]; - % // merge if asked too + % merge if asked too if merge X = X(:) ; Y = Y(:) ; end - end - %------------------------------------------------------------ \ No newline at end of file +end +% ------------------------------------------------------------ \ No newline at end of file diff --git a/CROSS-OPT-1.0/PlotTruss37.m b/CROSS-OPT-1.0/PlotTruss37.m new file mode 100644 index 0000000..8600184 --- /dev/null +++ b/CROSS-OPT-1.0/PlotTruss37.m @@ -0,0 +1,192 @@ +% ----------------------------------------------------------------- +% PlotTruss37.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 13, 2024 +% ----------------------------------------------------------------- +% Plot a 37 bars truss given the elements cross-section area. +% ----------------------------------------------------------------- +function PlotTruss37(x,MyTruss,MyTitle) + + % truss structure parameters + a = MyTruss.a; + ELEM = MyTruss.ELEM; + SYMBARS = MyTruss.SYMBARS; + Nelem = MyTruss.Nelem; + + % number of design variables + NvarsA = MyTruss.NvarsA; + NvarsH = MyTruss.NvarsH; + + % design variables vectors + Area = zeros(Nelem,1); + for i=1:NvarsA + % area design variables + Area(SYMBARS{i}) = x(i); + end + if NvarsH > 0 + % height design variables + Height = x(NvarsA+1:end); + + % mesh points in global coordinates (Nnodes x 2) + NODES = [ 0 0; + a 0; + a Height(1); + 2*a 0; + 2*a Height(2); + 3*a 0; + 3*a Height(3); + 4*a 0; + 4*a Height(4); + 5*a 0; + 5*a Height(5); + 6*a 0; + 6*a Height(4); + 7*a 0; + 7*a Height(3); + 8*a 0; + 8*a Height(2); + 9*a 0; + 9*a Height(1); + 10*a 0]; + else + % mesh points in global coordinates (Nnodes x 2) + NODES = MyTruss.NODES; + end + + % custom color + grayColor = [.7 .7 .7]; + + % Open figure + figure('DefaultAxesFontSize',10) + clf + hold on + + % Support 1 + xl1 = [-0.3 0.3]; + yl1 = [-0.1 -0.075]; + [X1,Y1] = hatch_coordinates(xl1, yl1, 0.025); + plot(X1,Y1,'Color', grayColor,'linewidth',0.01); + a11 = [0; -0.3; 0.3]; + a12 = [0; -0.075; -0.075]; + patch(a11,a12,grayColor,'EdgeColor','none'); + plot([a11(2) a11(3)],[a12(2) a12(3)],'k','linewidth',2.5); + + % Support 2 + xl1 = [9.7 10.3]; + yl1 = [-0.135 -0.11]; + [X1,Y1] = hatch_coordinates(xl1, yl1, 0.025); + plot(X1,Y1,'Color', grayColor,'linewidth',0.01); + a21 = [10; 9.7; 10.3]; + a22 = [0; -0.075; -0.075]; + patch(a21,a22,grayColor,'EdgeColor','none'); + plot([a21(2) a21(3)],[a22(2) a22(3)],'k','linewidth',2.5); + plot([a21(2) a21(3)],[-0.11 -0.11] ,'k','linewidth',2.5); + f = [1 2]; + v = [9.8 -0.0925; 10.2 -0.0925]; + patch( 'Faces' ,f,... + 'Vertices' ,v,... + 'EdgeColor' ,'none',... + 'FaceColor' ,'none', ... + 'MarkerEdgeColor','k',... + 'Marker' ,'o',... + 'MarkerFaceColor','white',... + 'MarkerSize' ,10,... + 'LineWidth' ,0.01); + + % Custom color scheme + mycolor = plasma(NvarsA-1); + + % Draw vertical and top horizontal bars + for i=1:NvarsA-1 + idx1 = SYMBARS{i}(1); + patch('Faces' ,ELEM(idx1,:) ,... + 'Vertices' ,NODES ,... + 'EdgeColor',mycolor(i,:),... + 'FaceColor','none' ,... + 'LineWidth',Area(i)); + + idx2 = SYMBARS{i}(2); + patch('Faces' ,ELEM(idx2,:) ,... + 'Vertices' ,NODES ,... + 'EdgeColor',mycolor(i,:),... + 'FaceColor','none' ,... + 'LineWidth',Area(i)); + end + + % Draw horizontal bars at the bottom + for i = SYMBARS{NvarsA} + patch('Faces' ,ELEM(i,:),... + 'Vertices' ,NODES ,... + 'EdgeColor',grayColor,... + 'FaceColor','none' ,... + 'LineWidth',Area(i)); + end + + % Draw nodes + for i=1:Nelem + patch('Faces' ,ELEM(i,:),... + 'Vertices' ,NODES,... + 'EdgeColor' ,'none',... + 'FaceColor' ,'none', ... + 'MarkerEdgeColor','b',... + 'Marker' ,'o',... + 'MarkerFaceColor','white',... + 'MarkerSize' ,10,... + 'LineWidth' ,3); + end + + % Draw added mass + for i = 2:2:18 + plot([NODES(i,1)],[NODES(i,2)], ... + 'Marker' , 'o',... + 'MarkerEdgeColor' ,[0.9290 0.6940 0.1250],... + 'LineWidth' , 3.1 , .... + 'MarkerSize' , 15); + end + + set(gca,'xtick',[],'ytick',[]) + set(gca,'XColor', 'none','YColor','none') + title(MyTitle,'FontSize',18) + pause(1) +end +% ------------------------------------------------------------ + +% ------------------------------------------------------------ +% This function returns the coordinates for plotting a hatch +% pattern. The angle of the lines can be adjusted by varying +% the ratio xstep/ystep. xlim and ylim are vectors with two +% elements, where the first element needs to be smaller than +% the second. +% ------------------------------------------------------------ +function [X,Y] = hatch_coordinates(xlim,ylim,xstep,ystep,merge) + + % set default options + if nargin < 3 ; xstep = 1 ; end + if nargin < 4 ; ystep = xstep ; end + if nargin < 5 ; merge = true ; end + + % define base grid + xpos = xlim(1):xstep:xlim(2) ; nx = numel(xpos) ; + ypos = ylim(1):ystep:ylim(2) ; ny = numel(ypos) ; + + % Create the coordinates + nanline = NaN*ones(1,nx+ny-3) ; + X = [ [xpos(1)*ones(1,ny-2) xpos(1:end-1)]; ... + [xpos(2:end) xpos(end)*ones(1,ny-2)]; ... + nanline]; + Y = [ [ypos(end-1:-1:1) ylim(1)*ones(1,nx-2)]; ... + [ypos(end)*ones(1,nx-1) ypos(end-1:-1:2)]; ... + nanline]; + + % merge if asked too + if merge + X = X(:) ; + Y = Y(:) ; + end +end +% ------------------------------------------------------------ \ No newline at end of file diff --git a/CROSS-OPT-1.0/TrussFrequencyBounds10.m b/CROSS-OPT-1.0/TrussFrequencyBounds10.m new file mode 100644 index 0000000..3d52d4a --- /dev/null +++ b/CROSS-OPT-1.0/TrussFrequencyBounds10.m @@ -0,0 +1,77 @@ +% ----------------------------------------------------------------- +% TrussFrequencyBounds10.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% This function computes the frequency bounds for a truss +% ----------------------------------------------------------------- +function [G,H] = TrussFrequencyBounds10(Area,MyTruss) + + % truss structure parameters + rho = MyTruss.rho; + E = MyTruss.E; + AddedMass = MyTruss.AddedMass; + omegaTresh = MyTruss.omegaTresh; + FixedDoFs = MyTruss.FixedDoFs; + NODES = MyTruss.NODES; + ELEM = MyTruss.ELEM; + Nelem = MyTruss.Nelem; + Ndofs = MyTruss.Ndofs; + + % preallocate memory for constraints + Nconstr = length(omegaTresh); + G = zeros(1,Nconstr); % inequality constraints + H = []; % equality constraint + + % preallocate memory for FEM matrices + M = zeros(Ndofs,Ndofs); + K = zeros(Ndofs,Ndofs); + + % assembly global matrices + for e = 1:Nelem + % distance between nodes + dx = NODES(ELEM(e,2),1) - NODES(ELEM(e,1),1); + dy = NODES(ELEM(e,2),2) - NODES(ELEM(e,1),2); + l = sqrt(dx^2+dy^2); + % strain-displacement matrix + c = dx/l; + s = dy/l; + B = [-c -s c s]; + % element DoFs + eDof = [2*ELEM(e,1)-1, 2*ELEM(e,1),... + 2*ELEM(e,2)-1, 2*ELEM(e,2)]; + % local stiffness matrix + Ke = (E*Area(e)/l)*(B'*B); + % local mass matrix + Me = (rho*Area(e)*l/6)*[2 0 1 0;... + 0 2 0 1;... + 1 0 2 0;... + 0 1 0 2]; + % update global matrices + K(eDof,eDof) = K(eDof,eDof) + Ke; + M(eDof,eDof) = M(eDof,eDof) + Me; + end + + % update mass matrix with the added mass + M = M + AddedMass*eye(Ndofs,Ndofs); + + % free DoFs coordinates + FreeDoFs = setdiff(1:Ndofs,FixedDoFs); + + % solve the generalized eigenvalue problem + omega2 = eig(K(FreeDoFs,FreeDoFs),M(FreeDoFs,FreeDoFs)); + + % sort frequencies (rad/s) + omega = sort(sqrt(omega2)); + + % frequency constraints + for j = 1:Nconstr + G(j) = 1 - omega(j)/omegaTresh(j); + end +end +% ----------------------------------------------------------------- \ No newline at end of file diff --git a/CROSS-OPT-1.0/TrussFrequencyBounds37.m b/CROSS-OPT-1.0/TrussFrequencyBounds37.m new file mode 100644 index 0000000..307402f --- /dev/null +++ b/CROSS-OPT-1.0/TrussFrequencyBounds37.m @@ -0,0 +1,118 @@ +% ----------------------------------------------------------------- +% TrussFrequencyBounds37.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% This function computes the frequency bounds for a truss +% ----------------------------------------------------------------- +function [G,H] = TrussFrequencyBounds37(x,MyTruss) + + % truss structure parameters + a = MyTruss.a; + rho = MyTruss.rho; + E = MyTruss.E; + AddedMass = MyTruss.AddedMass; + omegaTresh = MyTruss.omegaTresh; + FixedDoFs = MyTruss.FixedDoFs; + ELEM = MyTruss.ELEM; + SYMBARS = MyTruss.SYMBARS; + Nelem = MyTruss.Nelem; + Ndofs = MyTruss.Ndofs; + + % number of design variables + NvarsA = MyTruss.NvarsA; + NvarsH = MyTruss.NvarsH; + + % design variables vectors + Area = zeros(Nelem,1); + for i=1:NvarsA + % area design variables + Area(SYMBARS{i}) = x(i); + end + if NvarsH > 0 + % height design variables + Height = x(NvarsA+1:end); + + % mesh points in global coordinates (Nnodes x 2) + NODES = [ 0 0; + a 0; + a Height(1); + 2*a 0; + 2*a Height(2); + 3*a 0; + 3*a Height(3); + 4*a 0; + 4*a Height(4); + 5*a 0; + 5*a Height(5); + 6*a 0; + 6*a Height(4); + 7*a 0; + 7*a Height(3); + 8*a 0; + 8*a Height(2); + 9*a 0; + 9*a Height(1); + 10*a 0]; + else + % mesh points in global coordinates (Nnodes x 2) + NODES = MyTruss.NODES; + end + + % preallocate memory for constraints + Nconstr = length(omegaTresh); + G = zeros(1,Nconstr); % inequality constraints + H = []; % equality constraint + + % preallocate memory for FEM matrices + M = zeros(Ndofs,Ndofs); + K = zeros(Ndofs,Ndofs); + + % assembly global matrices + for e = 1:Nelem + % distance between nodes + dx = NODES(ELEM(e,2),1) - NODES(ELEM(e,1),1); + dy = NODES(ELEM(e,2),2) - NODES(ELEM(e,1),2); + l = sqrt(dx^2+dy^2); + % strain-displacement matrix + c = dx/l; + s = dy/l; + B = [-c -s c s]; + % element DoFs + eDof = [2*ELEM(e,1)-1, 2*ELEM(e,1),... + 2*ELEM(e,2)-1, 2*ELEM(e,2)]; + % local stiffness matrix + Ke = (E*Area(e)/l)*(B'*B); + % local mass matrix + Me = (rho*Area(e)*l/6)*[2 0 1 0;... + 0 2 0 1;... + 1 0 2 0;... + 0 1 0 2]; + % update global matrices + K(eDof,eDof) = K(eDof,eDof) + Ke; + M(eDof,eDof) = M(eDof,eDof) + Me; + end + + % update mass matrix with the added mass + M = M + AddedMass*eye(Ndofs,Ndofs); + + % free DoFs coordinates + FreeDoFs = setdiff(1:Ndofs,FixedDoFs); + + % solve the generalized eigenvalue problem + omega2 = eig(K(FreeDoFs,FreeDoFs),M(FreeDoFs,FreeDoFs)); + + % sort frequencies (rad/s) + omega = sort(sqrt(omega2)); + + % frequency constraints + for j = 1:Nconstr + G(j) = 1 - omega(j)/omegaTresh(j); + end +end +% ----------------------------------------------------------------- \ No newline at end of file diff --git a/CROSS-OPT-1.0/TrussMass10.m b/CROSS-OPT-1.0/TrussMass10.m new file mode 100644 index 0000000..2e167c9 --- /dev/null +++ b/CROSS-OPT-1.0/TrussMass10.m @@ -0,0 +1,30 @@ +% ----------------------------------------------------------------- +% TrussMass10.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% This function computes the mass of a 10 bars truss structure. +% ----------------------------------------------------------------- +function Mass = TrussMass10(Area,MyTruss) + + % truss structure parameters + rho = MyTruss.rho; + NODES = MyTruss.NODES; + ELEM = MyTruss.ELEM; + Nelem = MyTruss.Nelem; + + % compute the mass + Mass = 0.0; + for e = 1:Nelem + dx = NODES(ELEM(e,2),1) - NODES(ELEM(e,1),1); + dy = NODES(ELEM(e,2),2) - NODES(ELEM(e,1),2); + l = sqrt(dx^2+dy^2); + Mass = Mass + rho*Area(e)*l; + end +end +% ----------------------------------------------------------------- \ No newline at end of file diff --git a/CROSS-OPT-1.0/TrussMass37.m b/CROSS-OPT-1.0/TrussMass37.m new file mode 100644 index 0000000..1267ebe --- /dev/null +++ b/CROSS-OPT-1.0/TrussMass37.m @@ -0,0 +1,102 @@ +% ----------------------------------------------------------------- +% TrussMass10.m +% ----------------------------------------------------------------- +% programmers: Marcos Vinicius Issa +% Anderson Pereira +% Americo Cunha Jr +% +% Originally programmed in: Apr 04, 2024 +% Last updated in: Sep 14, 2024 +% ----------------------------------------------------------------- +% This function computes the mass of a 37 bars truss structure. +% ----------------------------------------------------------------- +function Mass = TrussMass37(x,MyTruss) + + % truss structure parameters + a = MyTruss.a; + rho = MyTruss.rho; + ELEM = MyTruss.ELEM; + Nelem = MyTruss.Nelem; + SYMBARS = MyTruss.SYMBARS; + + % number of design variables + NvarsA = MyTruss.NvarsA; + NvarsH = MyTruss.NvarsH; + + % design variables vectors + Area = zeros(Nelem,1); + for i=1:NvarsA + % area design variables + Area(SYMBARS{i}) = x(i); + end + if NvarsH > 0 + + % height design variables + Height = x(NvarsA+1:end); + + % mesh points in global coordinates (Nnodes x 2) + NODES = [ 0 0; + a 0; + a Height(1); + 2*a 0; + 2*a Height(2); + 3*a 0; + 3*a Height(3); + 4*a 0; + 4*a Height(4); + 5*a 0; + 5*a Height(5); + 6*a 0; + 6*a Height(4); + 7*a 0; + 7*a Height(3); + 8*a 0; + 8*a Height(2); + 9*a 0; + 9*a Height(1); + 10*a 0]; + else + % mesh points in global coordinates (Nnodes x 2) + NODES = MyTruss.NODES; + end + +% A([1 27]) = x(6); +% A([2 26]) = x(7); +% A(26) = x(7); +% A(3) = x(8); +% A(24) = x(8); +% A(4) = x(9); +% A(25) = x(9); +% A(5) = x(10); +% A(23) = x(10); +% A(6) = x(11); +% A(21) = x(11); +% A(7) = x(12); +% A(22) = x(12); +% A(8,:) = x(13); +% A(20,:) = x(13); +% A(9,:) = x(14); +% A(18,:) = x(14); +% A(10,:) = x(15); +% A(19,:) = x(15); +% A(11,:) = x(16); +% A(17,:) = x(16); +% A(12,:) = x(17); +% A(15,:) = x(17); +% A(13,:) = x(18); +% A(16,:) = x(18); +% A(14,:) = x(19); +% for i=28:37 +% A(i,:) = 4e-3; +% end + + % compute the mass + Mass = 0.0; + for e = 1:Nelem + dx = NODES(ELEM(e,2),1) - NODES(ELEM(e,1),1); + dy = NODES(ELEM(e,2),2) - NODES(ELEM(e,1),2); + l = sqrt(dx^2+dy^2); + Mass = Mass + rho*Area(e)*l; + end +end +% ----------------------------------------------------------------- \ No newline at end of file diff --git a/CROSS-OPT-1.0/inferno.m b/CROSS-OPT-1.0/inferno.m new file mode 100644 index 0000000..2131bb1 --- /dev/null +++ b/CROSS-OPT-1.0/inferno.m @@ -0,0 +1,321 @@ +function map = inferno(N) +% Perceptually uniform sequential colormap from MatPlotLib. +% +% Copyright (c) 2017-2020 Stephen Cobeldick +% +%%% Syntax: +% map = inferno +% map = inferno(N) +% +% Colormap designed by Eric Firing, Nathaniel J. Smith, and Stefan van der Walt. +% +% For MatPlotLib 2.0 improved colormaps were created in the perceptually +% uniform colorspace CAM02-UCS. The new colormaps are introduced here: +% +% The RGB data is from here: +% +% Note VIRIDIS replaces the awful JET as the MatPlotLib default colormap. +% +%% Examples %% +% +%%% Plot the scheme's RGB values: +% rgbplot(inferno(256)) +% +%%% New colors for the COLORMAP example: +% load spine +% image(X) +% colormap(inferno) +% +%%% New colors for the SURF example: +% [X,Y,Z] = peaks(30), +% surfc(X,Y,Z) +% colormap(inferno) +% axis([-3,3,-3,3,-10,5]) +% +%% Input and Output Arguments %% +% +%%% Inputs (*=default): +% N = NumericScalar, N>=0, an integer to define the colormap length. +% = *[], use the length of the current figure's colormap (see COLORMAP). +% +%%% Outputs: +% map = NumericMatrix, size Nx3, a colormap of RGB values between 0 and 1. +% +% See also CIVIDIS INFERNO MAGMA PLASMA TWILIGHT TAB10 SET LINES COLORMAP PARULA + +if nargin<1 || isnumeric(N)&&isequal(N,[]) + N = size(get(gcf,'colormap'),1); +else + assert(isscalar(N)&&isfinite(N)&&isreal(N),... + 'SC:inferno:N:NotRealFiniteScalarNumeric',... + 'First argument must be a real finite numeric scalar.') +end +% +raw = [[ 1.46159096e-03, 4.66127766e-04, 1.38655200e-02], + [ 2.26726368e-03, 1.26992553e-03, 1.85703520e-02], + [ 3.29899092e-03, 2.24934863e-03, 2.42390508e-02], + [ 4.54690615e-03, 3.39180156e-03, 3.09092475e-02], + [ 6.00552565e-03, 4.69194561e-03, 3.85578980e-02], + [ 7.67578856e-03, 6.13611626e-03, 4.68360336e-02], + [ 9.56051094e-03, 7.71344131e-03, 5.51430756e-02], + [ 1.16634769e-02, 9.41675403e-03, 6.34598080e-02], + [ 1.39950388e-02, 1.12247138e-02, 7.18616890e-02], + [ 1.65605595e-02, 1.31362262e-02, 8.02817951e-02], + [ 1.93732295e-02, 1.51325789e-02, 8.87668094e-02], + [ 2.24468865e-02, 1.71991484e-02, 9.73274383e-02], + [ 2.57927373e-02, 1.93306298e-02, 1.05929835e-01], + [ 2.94324251e-02, 2.15030771e-02, 1.14621328e-01], + [ 3.33852235e-02, 2.37024271e-02, 1.23397286e-01], + [ 3.76684211e-02, 2.59207864e-02, 1.32232108e-01], + [ 4.22525554e-02, 2.81385015e-02, 1.41140519e-01], + [ 4.69146287e-02, 3.03236129e-02, 1.50163867e-01], + [ 5.16437624e-02, 3.24736172e-02, 1.59254277e-01], + [ 5.64491009e-02, 3.45691867e-02, 1.68413539e-01], + [ 6.13397200e-02, 3.65900213e-02, 1.77642172e-01], + [ 6.63312620e-02, 3.85036268e-02, 1.86961588e-01], + [ 7.14289181e-02, 4.02939095e-02, 1.96353558e-01], + [ 7.66367560e-02, 4.19053329e-02, 2.05798788e-01], + [ 8.19620773e-02, 4.33278666e-02, 2.15289113e-01], + [ 8.74113897e-02, 4.45561662e-02, 2.24813479e-01], + [ 9.29901526e-02, 4.55829503e-02, 2.34357604e-01], + [ 9.87024972e-02, 4.64018731e-02, 2.43903700e-01], + [ 1.04550936e-01, 4.70080541e-02, 2.53430300e-01], + [ 1.10536084e-01, 4.73986708e-02, 2.62912235e-01], + [ 1.16656423e-01, 4.75735920e-02, 2.72320803e-01], + [ 1.22908126e-01, 4.75360183e-02, 2.81624170e-01], + [ 1.29284984e-01, 4.72930838e-02, 2.90788012e-01], + [ 1.35778450e-01, 4.68563678e-02, 2.99776404e-01], + [ 1.42377819e-01, 4.62422566e-02, 3.08552910e-01], + [ 1.49072957e-01, 4.54676444e-02, 3.17085139e-01], + [ 1.55849711e-01, 4.45588056e-02, 3.25338414e-01], + [ 1.62688939e-01, 4.35542881e-02, 3.33276678e-01], + [ 1.69575148e-01, 4.24893149e-02, 3.40874188e-01], + [ 1.76493202e-01, 4.14017089e-02, 3.48110606e-01], + [ 1.83428775e-01, 4.03288858e-02, 3.54971391e-01], + [ 1.90367453e-01, 3.93088888e-02, 3.61446945e-01], + [ 1.97297425e-01, 3.84001825e-02, 3.67534629e-01], + [ 2.04209298e-01, 3.76322609e-02, 3.73237557e-01], + [ 2.11095463e-01, 3.70296488e-02, 3.78563264e-01], + [ 2.17948648e-01, 3.66146049e-02, 3.83522415e-01], + [ 2.24762908e-01, 3.64049901e-02, 3.88128944e-01], + [ 2.31538148e-01, 3.64052511e-02, 3.92400150e-01], + [ 2.38272961e-01, 3.66209949e-02, 3.96353388e-01], + [ 2.44966911e-01, 3.70545017e-02, 4.00006615e-01], + [ 2.51620354e-01, 3.77052832e-02, 4.03377897e-01], + [ 2.58234265e-01, 3.85706153e-02, 4.06485031e-01], + [ 2.64809649e-01, 3.96468666e-02, 4.09345373e-01], + [ 2.71346664e-01, 4.09215821e-02, 4.11976086e-01], + [ 2.77849829e-01, 4.23528741e-02, 4.14392106e-01], + [ 2.84321318e-01, 4.39325787e-02, 4.16607861e-01], + [ 2.90763373e-01, 4.56437598e-02, 4.18636756e-01], + [ 2.97178251e-01, 4.74700293e-02, 4.20491164e-01], + [ 3.03568182e-01, 4.93958927e-02, 4.22182449e-01], + [ 3.09935342e-01, 5.14069729e-02, 4.23720999e-01], + [ 3.16281835e-01, 5.34901321e-02, 4.25116277e-01], + [ 3.22609671e-01, 5.56335178e-02, 4.26376869e-01], + [ 3.28920763e-01, 5.78265505e-02, 4.27510546e-01], + [ 3.35216916e-01, 6.00598734e-02, 4.28524320e-01], + [ 3.41499828e-01, 6.23252772e-02, 4.29424503e-01], + [ 3.47771086e-01, 6.46156100e-02, 4.30216765e-01], + [ 3.54032169e-01, 6.69246832e-02, 4.30906186e-01], + [ 3.60284449e-01, 6.92471753e-02, 4.31497309e-01], + [ 3.66529195e-01, 7.15785403e-02, 4.31994185e-01], + [ 3.72767575e-01, 7.39149211e-02, 4.32400419e-01], + [ 3.79000659e-01, 7.62530701e-02, 4.32719214e-01], + [ 3.85228383e-01, 7.85914864e-02, 4.32954973e-01], + [ 3.91452659e-01, 8.09267058e-02, 4.33108763e-01], + [ 3.97674379e-01, 8.32568129e-02, 4.33182647e-01], + [ 4.03894278e-01, 8.55803445e-02, 4.33178526e-01], + [ 4.10113015e-01, 8.78961593e-02, 4.33098056e-01], + [ 4.16331169e-01, 9.02033992e-02, 4.32942678e-01], + [ 4.22549249e-01, 9.25014543e-02, 4.32713635e-01], + [ 4.28767696e-01, 9.47899342e-02, 4.32411996e-01], + [ 4.34986885e-01, 9.70686417e-02, 4.32038673e-01], + [ 4.41207124e-01, 9.93375510e-02, 4.31594438e-01], + [ 4.47428382e-01, 1.01597079e-01, 4.31080497e-01], + [ 4.53650614e-01, 1.03847716e-01, 4.30497898e-01], + [ 4.59874623e-01, 1.06089165e-01, 4.29845789e-01], + [ 4.66100494e-01, 1.08321923e-01, 4.29124507e-01], + [ 4.72328255e-01, 1.10546584e-01, 4.28334320e-01], + [ 4.78557889e-01, 1.12763831e-01, 4.27475431e-01], + [ 4.84789325e-01, 1.14974430e-01, 4.26547991e-01], + [ 4.91022448e-01, 1.17179219e-01, 4.25552106e-01], + [ 4.97257069e-01, 1.19379132e-01, 4.24487908e-01], + [ 5.03492698e-01, 1.21575414e-01, 4.23356110e-01], + [ 5.09729541e-01, 1.23768654e-01, 4.22155676e-01], + [ 5.15967304e-01, 1.25959947e-01, 4.20886594e-01], + [ 5.22205646e-01, 1.28150439e-01, 4.19548848e-01], + [ 5.28444192e-01, 1.30341324e-01, 4.18142411e-01], + [ 5.34682523e-01, 1.32533845e-01, 4.16667258e-01], + [ 5.40920186e-01, 1.34729286e-01, 4.15123366e-01], + [ 5.47156706e-01, 1.36928959e-01, 4.13510662e-01], + [ 5.53391649e-01, 1.39134147e-01, 4.11828882e-01], + [ 5.59624442e-01, 1.41346265e-01, 4.10078028e-01], + [ 5.65854477e-01, 1.43566769e-01, 4.08258132e-01], + [ 5.72081108e-01, 1.45797150e-01, 4.06369246e-01], + [ 5.78303656e-01, 1.48038934e-01, 4.04411444e-01], + [ 5.84521407e-01, 1.50293679e-01, 4.02384829e-01], + [ 5.90733615e-01, 1.52562977e-01, 4.00289528e-01], + [ 5.96939751e-01, 1.54848232e-01, 3.98124897e-01], + [ 6.03138930e-01, 1.57151161e-01, 3.95891308e-01], + [ 6.09330184e-01, 1.59473549e-01, 3.93589349e-01], + [ 6.15512627e-01, 1.61817111e-01, 3.91219295e-01], + [ 6.21685340e-01, 1.64183582e-01, 3.88781456e-01], + [ 6.27847374e-01, 1.66574724e-01, 3.86276180e-01], + [ 6.33997746e-01, 1.68992314e-01, 3.83703854e-01], + [ 6.40135447e-01, 1.71438150e-01, 3.81064906e-01], + [ 6.46259648e-01, 1.73913876e-01, 3.78358969e-01], + [ 6.52369348e-01, 1.76421271e-01, 3.75586209e-01], + [ 6.58463166e-01, 1.78962399e-01, 3.72748214e-01], + [ 6.64539964e-01, 1.81539111e-01, 3.69845599e-01], + [ 6.70598572e-01, 1.84153268e-01, 3.66879025e-01], + [ 6.76637795e-01, 1.86806728e-01, 3.63849195e-01], + [ 6.82656407e-01, 1.89501352e-01, 3.60756856e-01], + [ 6.88653158e-01, 1.92238994e-01, 3.57602797e-01], + [ 6.94626769e-01, 1.95021500e-01, 3.54387853e-01], + [ 7.00575937e-01, 1.97850703e-01, 3.51112900e-01], + [ 7.06499709e-01, 2.00728196e-01, 3.47776863e-01], + [ 7.12396345e-01, 2.03656029e-01, 3.44382594e-01], + [ 7.18264447e-01, 2.06635993e-01, 3.40931208e-01], + [ 7.24102613e-01, 2.09669834e-01, 3.37423766e-01], + [ 7.29909422e-01, 2.12759270e-01, 3.33861367e-01], + [ 7.35683432e-01, 2.15905976e-01, 3.30245147e-01], + [ 7.41423185e-01, 2.19111589e-01, 3.26576275e-01], + [ 7.47127207e-01, 2.22377697e-01, 3.22855952e-01], + [ 7.52794009e-01, 2.25705837e-01, 3.19085410e-01], + [ 7.58422090e-01, 2.29097492e-01, 3.15265910e-01], + [ 7.64009940e-01, 2.32554083e-01, 3.11398734e-01], + [ 7.69556038e-01, 2.36076967e-01, 3.07485188e-01], + [ 7.75058888e-01, 2.39667435e-01, 3.03526312e-01], + [ 7.80517023e-01, 2.43326720e-01, 2.99522665e-01], + [ 7.85928794e-01, 2.47055968e-01, 2.95476756e-01], + [ 7.91292674e-01, 2.50856232e-01, 2.91389943e-01], + [ 7.96607144e-01, 2.54728485e-01, 2.87263585e-01], + [ 8.01870689e-01, 2.58673610e-01, 2.83099033e-01], + [ 8.07081807e-01, 2.62692401e-01, 2.78897629e-01], + [ 8.12239008e-01, 2.66785558e-01, 2.74660698e-01], + [ 8.17340818e-01, 2.70953688e-01, 2.70389545e-01], + [ 8.22385784e-01, 2.75197300e-01, 2.66085445e-01], + [ 8.27372474e-01, 2.79516805e-01, 2.61749643e-01], + [ 8.32299481e-01, 2.83912516e-01, 2.57383341e-01], + [ 8.37165425e-01, 2.88384647e-01, 2.52987700e-01], + [ 8.41968959e-01, 2.92933312e-01, 2.48563825e-01], + [ 8.46708768e-01, 2.97558528e-01, 2.44112767e-01], + [ 8.51383572e-01, 3.02260213e-01, 2.39635512e-01], + [ 8.55992130e-01, 3.07038188e-01, 2.35132978e-01], + [ 8.60533241e-01, 3.11892183e-01, 2.30606009e-01], + [ 8.65005747e-01, 3.16821833e-01, 2.26055368e-01], + [ 8.69408534e-01, 3.21826685e-01, 2.21481734e-01], + [ 8.73740530e-01, 3.26906201e-01, 2.16885699e-01], + [ 8.78000715e-01, 3.32059760e-01, 2.12267762e-01], + [ 8.82188112e-01, 3.37286663e-01, 2.07628326e-01], + [ 8.86301795e-01, 3.42586137e-01, 2.02967696e-01], + [ 8.90340885e-01, 3.47957340e-01, 1.98286080e-01], + [ 8.94304553e-01, 3.53399363e-01, 1.93583583e-01], + [ 8.98192017e-01, 3.58911240e-01, 1.88860212e-01], + [ 9.02002544e-01, 3.64491949e-01, 1.84115876e-01], + [ 9.05735448e-01, 3.70140419e-01, 1.79350388e-01], + [ 9.09390090e-01, 3.75855533e-01, 1.74563472e-01], + [ 9.12965874e-01, 3.81636138e-01, 1.69754764e-01], + [ 9.16462251e-01, 3.87481044e-01, 1.64923826e-01], + [ 9.19878710e-01, 3.93389034e-01, 1.60070152e-01], + [ 9.23214783e-01, 3.99358867e-01, 1.55193185e-01], + [ 9.26470039e-01, 4.05389282e-01, 1.50292329e-01], + [ 9.29644083e-01, 4.11479007e-01, 1.45366973e-01], + [ 9.32736555e-01, 4.17626756e-01, 1.40416519e-01], + [ 9.35747126e-01, 4.23831237e-01, 1.35440416e-01], + [ 9.38675494e-01, 4.30091162e-01, 1.30438175e-01], + [ 9.41521384e-01, 4.36405243e-01, 1.25409440e-01], + [ 9.44284543e-01, 4.42772199e-01, 1.20354038e-01], + [ 9.46964741e-01, 4.49190757e-01, 1.15272059e-01], + [ 9.49561766e-01, 4.55659658e-01, 1.10163947e-01], + [ 9.52075421e-01, 4.62177656e-01, 1.05030614e-01], + [ 9.54505523e-01, 4.68743522e-01, 9.98735931e-02], + [ 9.56851903e-01, 4.75356048e-01, 9.46952268e-02], + [ 9.59114397e-01, 4.82014044e-01, 8.94989073e-02], + [ 9.61292850e-01, 4.88716345e-01, 8.42893891e-02], + [ 9.63387110e-01, 4.95461806e-01, 7.90731907e-02], + [ 9.65397031e-01, 5.02249309e-01, 7.38591143e-02], + [ 9.67322465e-01, 5.09077761e-01, 6.86589199e-02], + [ 9.69163264e-01, 5.15946092e-01, 6.34881971e-02], + [ 9.70919277e-01, 5.22853259e-01, 5.83674890e-02], + [ 9.72590351e-01, 5.29798246e-01, 5.33237243e-02], + [ 9.74176327e-01, 5.36780059e-01, 4.83920090e-02], + [ 9.75677038e-01, 5.43797733e-01, 4.36177922e-02], + [ 9.77092313e-01, 5.50850323e-01, 3.90500131e-02], + [ 9.78421971e-01, 5.57936911e-01, 3.49306227e-02], + [ 9.79665824e-01, 5.65056600e-01, 3.14091591e-02], + [ 9.80823673e-01, 5.72208516e-01, 2.85075931e-02], + [ 9.81895311e-01, 5.79391803e-01, 2.62497353e-02], + [ 9.82880522e-01, 5.86605627e-01, 2.46613416e-02], + [ 9.83779081e-01, 5.93849168e-01, 2.37702263e-02], + [ 9.84590755e-01, 6.01121626e-01, 2.36063833e-02], + [ 9.85315301e-01, 6.08422211e-01, 2.42021174e-02], + [ 9.85952471e-01, 6.15750147e-01, 2.55921853e-02], + [ 9.86502013e-01, 6.23104667e-01, 2.78139496e-02], + [ 9.86963670e-01, 6.30485011e-01, 3.09075459e-02], + [ 9.87337182e-01, 6.37890424e-01, 3.49160639e-02], + [ 9.87622296e-01, 6.45320152e-01, 3.98857472e-02], + [ 9.87818759e-01, 6.52773439e-01, 4.55808037e-02], + [ 9.87926330e-01, 6.60249526e-01, 5.17503867e-02], + [ 9.87944783e-01, 6.67747641e-01, 5.83286889e-02], + [ 9.87873910e-01, 6.75267000e-01, 6.52570167e-02], + [ 9.87713535e-01, 6.82806802e-01, 7.24892330e-02], + [ 9.87463516e-01, 6.90366218e-01, 7.99897176e-02], + [ 9.87123759e-01, 6.97944391e-01, 8.77314215e-02], + [ 9.86694229e-01, 7.05540424e-01, 9.56941797e-02], + [ 9.86174970e-01, 7.13153375e-01, 1.03863324e-01], + [ 9.85565739e-01, 7.20782460e-01, 1.12228756e-01], + [ 9.84865203e-01, 7.28427497e-01, 1.20784651e-01], + [ 9.84075129e-01, 7.36086521e-01, 1.29526579e-01], + [ 9.83195992e-01, 7.43758326e-01, 1.38453063e-01], + [ 9.82228463e-01, 7.51441596e-01, 1.47564573e-01], + [ 9.81173457e-01, 7.59134892e-01, 1.56863224e-01], + [ 9.80032178e-01, 7.66836624e-01, 1.66352544e-01], + [ 9.78806183e-01, 7.74545028e-01, 1.76037298e-01], + [ 9.77497453e-01, 7.82258138e-01, 1.85923357e-01], + [ 9.76108474e-01, 7.89973753e-01, 1.96017589e-01], + [ 9.74637842e-01, 7.97691563e-01, 2.06331925e-01], + [ 9.73087939e-01, 8.05409333e-01, 2.16876839e-01], + [ 9.71467822e-01, 8.13121725e-01, 2.27658046e-01], + [ 9.69783146e-01, 8.20825143e-01, 2.38685942e-01], + [ 9.68040817e-01, 8.28515491e-01, 2.49971582e-01], + [ 9.66242589e-01, 8.36190976e-01, 2.61533898e-01], + [ 9.64393924e-01, 8.43848069e-01, 2.73391112e-01], + [ 9.62516656e-01, 8.51476340e-01, 2.85545675e-01], + [ 9.60625545e-01, 8.59068716e-01, 2.98010219e-01], + [ 9.58720088e-01, 8.66624355e-01, 3.10820466e-01], + [ 9.56834075e-01, 8.74128569e-01, 3.23973947e-01], + [ 9.54997177e-01, 8.81568926e-01, 3.37475479e-01], + [ 9.53215092e-01, 8.88942277e-01, 3.51368713e-01], + [ 9.51546225e-01, 8.96225909e-01, 3.65627005e-01], + [ 9.50018481e-01, 9.03409063e-01, 3.80271225e-01], + [ 9.48683391e-01, 9.10472964e-01, 3.95289169e-01], + [ 9.47594362e-01, 9.17399053e-01, 4.10665194e-01], + [ 9.46809163e-01, 9.24168246e-01, 4.26373236e-01], + [ 9.46391536e-01, 9.30760752e-01, 4.42367495e-01], + [ 9.46402951e-01, 9.37158971e-01, 4.58591507e-01], + [ 9.46902568e-01, 9.43347775e-01, 4.74969778e-01], + [ 9.47936825e-01, 9.49317522e-01, 4.91426053e-01], + [ 9.49544830e-01, 9.55062900e-01, 5.07859649e-01], + [ 9.51740304e-01, 9.60586693e-01, 5.24203026e-01], + [ 9.54529281e-01, 9.65895868e-01, 5.40360752e-01], + [ 9.57896053e-01, 9.71003330e-01, 5.56275090e-01], + [ 9.61812020e-01, 9.75924241e-01, 5.71925382e-01], + [ 9.66248822e-01, 9.80678193e-01, 5.87205773e-01], + [ 9.71161622e-01, 9.85282161e-01, 6.02154330e-01], + [ 9.76510983e-01, 9.89753437e-01, 6.16760413e-01], + [ 9.82257307e-01, 9.94108844e-01, 6.31017009e-01], + [ 9.88362068e-01, 9.98364143e-01, 6.44924005e-01]]; +% +num = size(raw,1); +% With small extrapolation when N>num: +vec = linspace(0,num+1,N+2); +map = interp1(1:num,raw,vec(2:N+1),'linear','extrap'); +% Interpolation only for all values of N: +%map = interp1(1:num,raw,linspace(1,num,N),'spline') +% Range limits: +map = max(0,min(1,map)); +% +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file diff --git a/CROSS-OPT-1.0/magma.m b/CROSS-OPT-1.0/magma.m new file mode 100644 index 0000000..a4e876b --- /dev/null +++ b/CROSS-OPT-1.0/magma.m @@ -0,0 +1,321 @@ +function map = magma(N) +% Perceptually uniform sequential colormap from MatPlotLib. +% +% Copyright (c) 2017-2020 Stephen Cobeldick +% +%%% Syntax: +% map = magma +% map = magma(N) +% +% Colormap designed by Eric Firing, Nathaniel J. Smith, and Stefan van der Walt. +% +% For MatPlotLib 2.0 improved colormaps were created in the perceptually +% uniform colorspace CAM02-UCS. The new colormaps are introduced here: +% +% The RGB data is from here: +% +% Note VIRIDIS replaces the awful JET as the MatPlotLib default colormap. +% +%% Examples %% +% +%%% Plot the scheme's RGB values: +% rgbplot(magma(256)) +% +%%% New colors for the COLORMAP example: +% load spine +% image(X) +% colormap(magma) +% +%%% New colors for the SURF example: +% [X,Y,Z] = peaks(30), +% surfc(X,Y,Z) +% colormap(magma) +% axis([-3,3,-3,3,-10,5]) +% +%% Input and Output Arguments %% +% +%%% Inputs (*=default): +% N = NumericScalar, N>=0, an integer to define the colormap length. +% = *[], use the length of the current figure's colormap (see COLORMAP). +% +%%% Outputs: +% map = NumericMatrix, size Nx3, a colormap of RGB values between 0 and 1. +% +% See also CIVIDIS INFERNO MAGMA PLASMA TWILIGHT TAB10 SET LINES COLORMAP PARULA + +if nargin<1 || isnumeric(N)&&isequal(N,[]) + N = size(get(gcf,'colormap'),1); +else + assert(isscalar(N)&&isfinite(N)&&isreal(N),... + 'SC:magma:N:NotRealFiniteScalarNumeric',... + 'First argument must be a real finite numeric scalar.') +end +% +raw = [[ 1.46159096e-03, 4.66127766e-04, 1.38655200e-02], + [ 2.25764007e-03, 1.29495431e-03, 1.83311461e-02], + [ 3.27943222e-03, 2.30452991e-03, 2.37083291e-02], + [ 4.51230222e-03, 3.49037666e-03, 2.99647059e-02], + [ 5.94976987e-03, 4.84285000e-03, 3.71296695e-02], + [ 7.58798550e-03, 6.35613622e-03, 4.49730774e-02], + [ 9.42604390e-03, 8.02185006e-03, 5.28443561e-02], + [ 1.14654337e-02, 9.82831486e-03, 6.07496380e-02], + [ 1.37075706e-02, 1.17705913e-02, 6.86665843e-02], + [ 1.61557566e-02, 1.38404966e-02, 7.66026660e-02], + [ 1.88153670e-02, 1.60262753e-02, 8.45844897e-02], + [ 2.16919340e-02, 1.83201254e-02, 9.26101050e-02], + [ 2.47917814e-02, 2.07147875e-02, 1.00675555e-01], + [ 2.81228154e-02, 2.32009284e-02, 1.08786954e-01], + [ 3.16955304e-02, 2.57651161e-02, 1.16964722e-01], + [ 3.55204468e-02, 2.83974570e-02, 1.25209396e-01], + [ 3.96084872e-02, 3.10895652e-02, 1.33515085e-01], + [ 4.38295350e-02, 3.38299885e-02, 1.41886249e-01], + [ 4.80616391e-02, 3.66066101e-02, 1.50326989e-01], + [ 5.23204388e-02, 3.94066020e-02, 1.58841025e-01], + [ 5.66148978e-02, 4.21598925e-02, 1.67445592e-01], + [ 6.09493930e-02, 4.47944924e-02, 1.76128834e-01], + [ 6.53301801e-02, 4.73177796e-02, 1.84891506e-01], + [ 6.97637296e-02, 4.97264666e-02, 1.93735088e-01], + [ 7.42565152e-02, 5.20167766e-02, 2.02660374e-01], + [ 7.88150034e-02, 5.41844801e-02, 2.11667355e-01], + [ 8.34456313e-02, 5.62249365e-02, 2.20755099e-01], + [ 8.81547730e-02, 5.81331465e-02, 2.29921611e-01], + [ 9.29486914e-02, 5.99038167e-02, 2.39163669e-01], + [ 9.78334770e-02, 6.15314414e-02, 2.48476662e-01], + [ 1.02814972e-01, 6.30104053e-02, 2.57854400e-01], + [ 1.07898679e-01, 6.43351102e-02, 2.67288933e-01], + [ 1.13094451e-01, 6.54920358e-02, 2.76783978e-01], + [ 1.18405035e-01, 6.64791593e-02, 2.86320656e-01], + [ 1.23832651e-01, 6.72946449e-02, 2.95879431e-01], + [ 1.29380192e-01, 6.79349264e-02, 3.05442931e-01], + [ 1.35053322e-01, 6.83912798e-02, 3.14999890e-01], + [ 1.40857952e-01, 6.86540710e-02, 3.24537640e-01], + [ 1.46785234e-01, 6.87382323e-02, 3.34011109e-01], + [ 1.52839217e-01, 6.86368599e-02, 3.43404450e-01], + [ 1.59017511e-01, 6.83540225e-02, 3.52688028e-01], + [ 1.65308131e-01, 6.79108689e-02, 3.61816426e-01], + [ 1.71713033e-01, 6.73053260e-02, 3.70770827e-01], + [ 1.78211730e-01, 6.65758073e-02, 3.79497161e-01], + [ 1.84800877e-01, 6.57324381e-02, 3.87972507e-01], + [ 1.91459745e-01, 6.48183312e-02, 3.96151969e-01], + [ 1.98176877e-01, 6.38624166e-02, 4.04008953e-01], + [ 2.04934882e-01, 6.29066192e-02, 4.11514273e-01], + [ 2.11718061e-01, 6.19917876e-02, 4.18646741e-01], + [ 2.18511590e-01, 6.11584918e-02, 4.25391816e-01], + [ 2.25302032e-01, 6.04451843e-02, 4.31741767e-01], + [ 2.32076515e-01, 5.98886855e-02, 4.37694665e-01], + [ 2.38825991e-01, 5.95170384e-02, 4.43255999e-01], + [ 2.45543175e-01, 5.93524384e-02, 4.48435938e-01], + [ 2.52220252e-01, 5.94147119e-02, 4.53247729e-01], + [ 2.58857304e-01, 5.97055998e-02, 4.57709924e-01], + [ 2.65446744e-01, 6.02368754e-02, 4.61840297e-01], + [ 2.71994089e-01, 6.09935552e-02, 4.65660375e-01], + [ 2.78493300e-01, 6.19778136e-02, 4.69190328e-01], + [ 2.84951097e-01, 6.31676261e-02, 4.72450879e-01], + [ 2.91365817e-01, 6.45534486e-02, 4.75462193e-01], + [ 2.97740413e-01, 6.61170432e-02, 4.78243482e-01], + [ 3.04080941e-01, 6.78353452e-02, 4.80811572e-01], + [ 3.10382027e-01, 6.97024767e-02, 4.83186340e-01], + [ 3.16654235e-01, 7.16895272e-02, 4.85380429e-01], + [ 3.22899126e-01, 7.37819504e-02, 4.87408399e-01], + [ 3.29114038e-01, 7.59715081e-02, 4.89286796e-01], + [ 3.35307503e-01, 7.82361045e-02, 4.91024144e-01], + [ 3.41481725e-01, 8.05635079e-02, 4.92631321e-01], + [ 3.47635742e-01, 8.29463512e-02, 4.94120923e-01], + [ 3.53773161e-01, 8.53726329e-02, 4.95501096e-01], + [ 3.59897941e-01, 8.78311772e-02, 4.96778331e-01], + [ 3.66011928e-01, 9.03143031e-02, 4.97959963e-01], + [ 3.72116205e-01, 9.28159917e-02, 4.99053326e-01], + [ 3.78210547e-01, 9.53322947e-02, 5.00066568e-01], + [ 3.84299445e-01, 9.78549106e-02, 5.01001964e-01], + [ 3.90384361e-01, 1.00379466e-01, 5.01864236e-01], + [ 3.96466670e-01, 1.02902194e-01, 5.02657590e-01], + [ 4.02547663e-01, 1.05419865e-01, 5.03385761e-01], + [ 4.08628505e-01, 1.07929771e-01, 5.04052118e-01], + [ 4.14708664e-01, 1.10431177e-01, 5.04661843e-01], + [ 4.20791157e-01, 1.12920210e-01, 5.05214935e-01], + [ 4.26876965e-01, 1.15395258e-01, 5.05713602e-01], + [ 4.32967001e-01, 1.17854987e-01, 5.06159754e-01], + [ 4.39062114e-01, 1.20298314e-01, 5.06555026e-01], + [ 4.45163096e-01, 1.22724371e-01, 5.06900806e-01], + [ 4.51270678e-01, 1.25132484e-01, 5.07198258e-01], + [ 4.57385535e-01, 1.27522145e-01, 5.07448336e-01], + [ 4.63508291e-01, 1.29892998e-01, 5.07651812e-01], + [ 4.69639514e-01, 1.32244819e-01, 5.07809282e-01], + [ 4.75779723e-01, 1.34577500e-01, 5.07921193e-01], + [ 4.81928997e-01, 1.36891390e-01, 5.07988509e-01], + [ 4.88088169e-01, 1.39186217e-01, 5.08010737e-01], + [ 4.94257673e-01, 1.41462106e-01, 5.07987836e-01], + [ 5.00437834e-01, 1.43719323e-01, 5.07919772e-01], + [ 5.06628929e-01, 1.45958202e-01, 5.07806420e-01], + [ 5.12831195e-01, 1.48179144e-01, 5.07647570e-01], + [ 5.19044825e-01, 1.50382611e-01, 5.07442938e-01], + [ 5.25269968e-01, 1.52569121e-01, 5.07192172e-01], + [ 5.31506735e-01, 1.54739247e-01, 5.06894860e-01], + [ 5.37755194e-01, 1.56893613e-01, 5.06550538e-01], + [ 5.44015371e-01, 1.59032895e-01, 5.06158696e-01], + [ 5.50287252e-01, 1.61157816e-01, 5.05718782e-01], + [ 5.56570783e-01, 1.63269149e-01, 5.05230210e-01], + [ 5.62865867e-01, 1.65367714e-01, 5.04692365e-01], + [ 5.69172368e-01, 1.67454379e-01, 5.04104606e-01], + [ 5.75490107e-01, 1.69530062e-01, 5.03466273e-01], + [ 5.81818864e-01, 1.71595728e-01, 5.02776690e-01], + [ 5.88158375e-01, 1.73652392e-01, 5.02035167e-01], + [ 5.94508337e-01, 1.75701122e-01, 5.01241011e-01], + [ 6.00868399e-01, 1.77743036e-01, 5.00393522e-01], + [ 6.07238169e-01, 1.79779309e-01, 4.99491999e-01], + [ 6.13617209e-01, 1.81811170e-01, 4.98535746e-01], + [ 6.20005032e-01, 1.83839907e-01, 4.97524075e-01], + [ 6.26401108e-01, 1.85866869e-01, 4.96456304e-01], + [ 6.32804854e-01, 1.87893468e-01, 4.95331769e-01], + [ 6.39215638e-01, 1.89921182e-01, 4.94149821e-01], + [ 6.45632778e-01, 1.91951556e-01, 4.92909832e-01], + [ 6.52055535e-01, 1.93986210e-01, 4.91611196e-01], + [ 6.58483116e-01, 1.96026835e-01, 4.90253338e-01], + [ 6.64914668e-01, 1.98075202e-01, 4.88835712e-01], + [ 6.71349279e-01, 2.00133166e-01, 4.87357807e-01], + [ 6.77785975e-01, 2.02202663e-01, 4.85819154e-01], + [ 6.84223712e-01, 2.04285721e-01, 4.84219325e-01], + [ 6.90661380e-01, 2.06384461e-01, 4.82557941e-01], + [ 6.97097796e-01, 2.08501100e-01, 4.80834678e-01], + [ 7.03531700e-01, 2.10637956e-01, 4.79049270e-01], + [ 7.09961888e-01, 2.12797337e-01, 4.77201121e-01], + [ 7.16387038e-01, 2.14981693e-01, 4.75289780e-01], + [ 7.22805451e-01, 2.17193831e-01, 4.73315708e-01], + [ 7.29215521e-01, 2.19436516e-01, 4.71278924e-01], + [ 7.35615545e-01, 2.21712634e-01, 4.69179541e-01], + [ 7.42003713e-01, 2.24025196e-01, 4.67017774e-01], + [ 7.48378107e-01, 2.26377345e-01, 4.64793954e-01], + [ 7.54736692e-01, 2.28772352e-01, 4.62508534e-01], + [ 7.61077312e-01, 2.31213625e-01, 4.60162106e-01], + [ 7.67397681e-01, 2.33704708e-01, 4.57755411e-01], + [ 7.73695380e-01, 2.36249283e-01, 4.55289354e-01], + [ 7.79967847e-01, 2.38851170e-01, 4.52765022e-01], + [ 7.86212372e-01, 2.41514325e-01, 4.50183695e-01], + [ 7.92426972e-01, 2.44242250e-01, 4.47543155e-01], + [ 7.98607760e-01, 2.47039798e-01, 4.44848441e-01], + [ 8.04751511e-01, 2.49911350e-01, 4.42101615e-01], + [ 8.10854841e-01, 2.52861399e-01, 4.39304963e-01], + [ 8.16914186e-01, 2.55894550e-01, 4.36461074e-01], + [ 8.22925797e-01, 2.59015505e-01, 4.33572874e-01], + [ 8.28885740e-01, 2.62229049e-01, 4.30643647e-01], + [ 8.34790818e-01, 2.65539703e-01, 4.27671352e-01], + [ 8.40635680e-01, 2.68952874e-01, 4.24665620e-01], + [ 8.46415804e-01, 2.72473491e-01, 4.21631064e-01], + [ 8.52126490e-01, 2.76106469e-01, 4.18572767e-01], + [ 8.57762870e-01, 2.79856666e-01, 4.15496319e-01], + [ 8.63320397e-01, 2.83729003e-01, 4.12402889e-01], + [ 8.68793368e-01, 2.87728205e-01, 4.09303002e-01], + [ 8.74176342e-01, 2.91858679e-01, 4.06205397e-01], + [ 8.79463944e-01, 2.96124596e-01, 4.03118034e-01], + [ 8.84650824e-01, 3.00530090e-01, 4.00047060e-01], + [ 8.89731418e-01, 3.05078817e-01, 3.97001559e-01], + [ 8.94700194e-01, 3.09773445e-01, 3.93994634e-01], + [ 8.99551884e-01, 3.14616425e-01, 3.91036674e-01], + [ 9.04281297e-01, 3.19609981e-01, 3.88136889e-01], + [ 9.08883524e-01, 3.24755126e-01, 3.85308008e-01], + [ 9.13354091e-01, 3.30051947e-01, 3.82563414e-01], + [ 9.17688852e-01, 3.35500068e-01, 3.79915138e-01], + [ 9.21884187e-01, 3.41098112e-01, 3.77375977e-01], + [ 9.25937102e-01, 3.46843685e-01, 3.74959077e-01], + [ 9.29845090e-01, 3.52733817e-01, 3.72676513e-01], + [ 9.33606454e-01, 3.58764377e-01, 3.70540883e-01], + [ 9.37220874e-01, 3.64929312e-01, 3.68566525e-01], + [ 9.40687443e-01, 3.71224168e-01, 3.66761699e-01], + [ 9.44006448e-01, 3.77642889e-01, 3.65136328e-01], + [ 9.47179528e-01, 3.84177874e-01, 3.63701130e-01], + [ 9.50210150e-01, 3.90819546e-01, 3.62467694e-01], + [ 9.53099077e-01, 3.97562894e-01, 3.61438431e-01], + [ 9.55849237e-01, 4.04400213e-01, 3.60619076e-01], + [ 9.58464079e-01, 4.11323666e-01, 3.60014232e-01], + [ 9.60949221e-01, 4.18323245e-01, 3.59629789e-01], + [ 9.63310281e-01, 4.25389724e-01, 3.59469020e-01], + [ 9.65549351e-01, 4.32518707e-01, 3.59529151e-01], + [ 9.67671128e-01, 4.39702976e-01, 3.59810172e-01], + [ 9.69680441e-01, 4.46935635e-01, 3.60311120e-01], + [ 9.71582181e-01, 4.54210170e-01, 3.61030156e-01], + [ 9.73381238e-01, 4.61520484e-01, 3.61964652e-01], + [ 9.75082439e-01, 4.68860936e-01, 3.63111292e-01], + [ 9.76690494e-01, 4.76226350e-01, 3.64466162e-01], + [ 9.78209957e-01, 4.83612031e-01, 3.66024854e-01], + [ 9.79645181e-01, 4.91013764e-01, 3.67782559e-01], + [ 9.81000291e-01, 4.98427800e-01, 3.69734157e-01], + [ 9.82279159e-01, 5.05850848e-01, 3.71874301e-01], + [ 9.83485387e-01, 5.13280054e-01, 3.74197501e-01], + [ 9.84622298e-01, 5.20712972e-01, 3.76698186e-01], + [ 9.85692925e-01, 5.28147545e-01, 3.79370774e-01], + [ 9.86700017e-01, 5.35582070e-01, 3.82209724e-01], + [ 9.87646038e-01, 5.43015173e-01, 3.85209578e-01], + [ 9.88533173e-01, 5.50445778e-01, 3.88365009e-01], + [ 9.89363341e-01, 5.57873075e-01, 3.91670846e-01], + [ 9.90138201e-01, 5.65296495e-01, 3.95122099e-01], + [ 9.90871208e-01, 5.72706259e-01, 3.98713971e-01], + [ 9.91558165e-01, 5.80106828e-01, 4.02441058e-01], + [ 9.92195728e-01, 5.87501706e-01, 4.06298792e-01], + [ 9.92784669e-01, 5.94891088e-01, 4.10282976e-01], + [ 9.93325561e-01, 6.02275297e-01, 4.14389658e-01], + [ 9.93834412e-01, 6.09643540e-01, 4.18613221e-01], + [ 9.94308514e-01, 6.16998953e-01, 4.22949672e-01], + [ 9.94737698e-01, 6.24349657e-01, 4.27396771e-01], + [ 9.95121854e-01, 6.31696376e-01, 4.31951492e-01], + [ 9.95480469e-01, 6.39026596e-01, 4.36607159e-01], + [ 9.95809924e-01, 6.46343897e-01, 4.41360951e-01], + [ 9.96095703e-01, 6.53658756e-01, 4.46213021e-01], + [ 9.96341406e-01, 6.60969379e-01, 4.51160201e-01], + [ 9.96579803e-01, 6.68255621e-01, 4.56191814e-01], + [ 9.96774784e-01, 6.75541484e-01, 4.61314158e-01], + [ 9.96925427e-01, 6.82827953e-01, 4.66525689e-01], + [ 9.97077185e-01, 6.90087897e-01, 4.71811461e-01], + [ 9.97186253e-01, 6.97348991e-01, 4.77181727e-01], + [ 9.97253982e-01, 7.04610791e-01, 4.82634651e-01], + [ 9.97325180e-01, 7.11847714e-01, 4.88154375e-01], + [ 9.97350983e-01, 7.19089119e-01, 4.93754665e-01], + [ 9.97350583e-01, 7.26324415e-01, 4.99427972e-01], + [ 9.97341259e-01, 7.33544671e-01, 5.05166839e-01], + [ 9.97284689e-01, 7.40771893e-01, 5.10983331e-01], + [ 9.97228367e-01, 7.47980563e-01, 5.16859378e-01], + [ 9.97138480e-01, 7.55189852e-01, 5.22805996e-01], + [ 9.97019342e-01, 7.62397883e-01, 5.28820775e-01], + [ 9.96898254e-01, 7.69590975e-01, 5.34892341e-01], + [ 9.96726862e-01, 7.76794860e-01, 5.41038571e-01], + [ 9.96570645e-01, 7.83976508e-01, 5.47232992e-01], + [ 9.96369065e-01, 7.91167346e-01, 5.53498939e-01], + [ 9.96162309e-01, 7.98347709e-01, 5.59819643e-01], + [ 9.95932448e-01, 8.05527126e-01, 5.66201824e-01], + [ 9.95680107e-01, 8.12705773e-01, 5.72644795e-01], + [ 9.95423973e-01, 8.19875302e-01, 5.79140130e-01], + [ 9.95131288e-01, 8.27051773e-01, 5.85701463e-01], + [ 9.94851089e-01, 8.34212826e-01, 5.92307093e-01], + [ 9.94523666e-01, 8.41386618e-01, 5.98982818e-01], + [ 9.94221900e-01, 8.48540474e-01, 6.05695903e-01], + [ 9.93865767e-01, 8.55711038e-01, 6.12481798e-01], + [ 9.93545285e-01, 8.62858846e-01, 6.19299300e-01], + [ 9.93169558e-01, 8.70024467e-01, 6.26189463e-01], + [ 9.92830963e-01, 8.77168404e-01, 6.33109148e-01], + [ 9.92439881e-01, 8.84329694e-01, 6.40099465e-01], + [ 9.92089454e-01, 8.91469549e-01, 6.47116021e-01], + [ 9.91687744e-01, 8.98627050e-01, 6.54201544e-01], + [ 9.91331929e-01, 9.05762748e-01, 6.61308839e-01], + [ 9.90929685e-01, 9.12915010e-01, 6.68481201e-01], + [ 9.90569914e-01, 9.20048699e-01, 6.75674592e-01], + [ 9.90174637e-01, 9.27195612e-01, 6.82925602e-01], + [ 9.89814839e-01, 9.34328540e-01, 6.90198194e-01], + [ 9.89433736e-01, 9.41470354e-01, 6.97518628e-01], + [ 9.89077438e-01, 9.48604077e-01, 7.04862519e-01], + [ 9.88717064e-01, 9.55741520e-01, 7.12242232e-01], + [ 9.88367028e-01, 9.62878026e-01, 7.19648627e-01], + [ 9.88032885e-01, 9.70012413e-01, 7.27076773e-01], + [ 9.87690702e-01, 9.77154231e-01, 7.34536205e-01], + [ 9.87386827e-01, 9.84287561e-01, 7.42001547e-01], + [ 9.87052509e-01, 9.91437853e-01, 7.49504188e-01]]; +% +num = size(raw,1); +% With small extrapolation when N>num: +vec = linspace(0,num+1,N+2); +map = interp1(1:num,raw,vec(2:N+1),'linear','extrap'); +% Interpolation only for all values of N: +%map = interp1(1:num,raw,linspace(1,num,N),'spline') +% Range limits: +map = max(0,min(1,map)); +% +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file diff --git a/CROSS-OPT-1.0/plasma.m b/CROSS-OPT-1.0/plasma.m new file mode 100644 index 0000000..b3bcac7 --- /dev/null +++ b/CROSS-OPT-1.0/plasma.m @@ -0,0 +1,320 @@ +function map = plasma(N) +% Perceptually uniform sequential colormap from MatPlotLib. +% +% Copyright (c) 2017-2020 Stephen Cobeldick +% +%%% Syntax: +% map = plasma +% map = plasma(N) +% +% Colormap designed by Eric Firing, Nathaniel J. Smith, and Stefan van der Walt. +% +% For MatPlotLib 2.0 improved colormaps were created in the perceptually +% uniform colorspace CAM02-UCS. The new colormaps are introduced here: +% +% The RGB data is from here: +% +% Note VIRIDIS replaces the awful JET as the MatPlotLib default colormap. +% +%% Examples %% +% +%%% Plot the scheme's RGB values: +% rgbplot(plasma(256)) +% +%%% New colors for the COLORMAP example: +% load spine +% image(X) +% colormap(plasma) +% +%%% New colors for the SURF example: +% [X,Y,Z] = peaks(30), +% surfc(X,Y,Z) +% colormap(plasma) +% axis([-3,3,-3,3,-10,5]) +% +%% Input and Output Arguments %% +% +%%% Inputs (*=default): +% N = NumericScalar, N>=0, an integer to define the colormap length. +% = *[], use the length of the current figure's colormap (see COLORMAP). +% +%%% Outputs: +% map = NumericMatrix, size Nx3, a colormap of RGB values between 0 and 1. +% +% See also CIVIDIS INFERNO MAGMA PLASMA TWILIGHT TAB10 SET LINES COLORMAP PARULA + +if nargin<1 || isnumeric(N)&&isequal(N,[]) + N = size(get(gcf,'colormap'),1); +else + assert(isscalar(N)&&isfinite(N)&&isreal(N),... + 'SC:plasma:N:NotRealFiniteScalarNumeric',... + 'First argument must be a real finite numeric scalar.') +end +% +raw = [[ 5.03832136e-02, 2.98028976e-02, 5.27974883e-01], + [ 6.35363639e-02, 2.84259729e-02, 5.33123681e-01], + [ 7.53531234e-02, 2.72063728e-02, 5.38007001e-01], + [ 8.62217979e-02, 2.61253206e-02, 5.42657691e-01], + [ 9.63786097e-02, 2.51650976e-02, 5.47103487e-01], + [ 1.05979704e-01, 2.43092436e-02, 5.51367851e-01], + [ 1.15123641e-01, 2.35562500e-02, 5.55467728e-01], + [ 1.23902903e-01, 2.28781011e-02, 5.59423480e-01], + [ 1.32380720e-01, 2.22583774e-02, 5.63250116e-01], + [ 1.40603076e-01, 2.16866674e-02, 5.66959485e-01], + [ 1.48606527e-01, 2.11535876e-02, 5.70561711e-01], + [ 1.56420649e-01, 2.06507174e-02, 5.74065446e-01], + [ 1.64069722e-01, 2.01705326e-02, 5.77478074e-01], + [ 1.71573925e-01, 1.97063415e-02, 5.80805890e-01], + [ 1.78950212e-01, 1.92522243e-02, 5.84054243e-01], + [ 1.86212958e-01, 1.88029767e-02, 5.87227661e-01], + [ 1.93374449e-01, 1.83540593e-02, 5.90329954e-01], + [ 2.00445260e-01, 1.79015512e-02, 5.93364304e-01], + [ 2.07434551e-01, 1.74421086e-02, 5.96333341e-01], + [ 2.14350298e-01, 1.69729276e-02, 5.99239207e-01], + [ 2.21196750e-01, 1.64970484e-02, 6.02083323e-01], + [ 2.27982971e-01, 1.60071509e-02, 6.04867403e-01], + [ 2.34714537e-01, 1.55015065e-02, 6.07592438e-01], + [ 2.41396253e-01, 1.49791041e-02, 6.10259089e-01], + [ 2.48032377e-01, 1.44393586e-02, 6.12867743e-01], + [ 2.54626690e-01, 1.38820918e-02, 6.15418537e-01], + [ 2.61182562e-01, 1.33075156e-02, 6.17911385e-01], + [ 2.67702993e-01, 1.27162163e-02, 6.20345997e-01], + [ 2.74190665e-01, 1.21091423e-02, 6.22721903e-01], + [ 2.80647969e-01, 1.14875915e-02, 6.25038468e-01], + [ 2.87076059e-01, 1.08554862e-02, 6.27294975e-01], + [ 2.93477695e-01, 1.02128849e-02, 6.29490490e-01], + [ 2.99855122e-01, 9.56079551e-03, 6.31623923e-01], + [ 3.06209825e-01, 8.90185346e-03, 6.33694102e-01], + [ 3.12543124e-01, 8.23900704e-03, 6.35699759e-01], + [ 3.18856183e-01, 7.57551051e-03, 6.37639537e-01], + [ 3.25150025e-01, 6.91491734e-03, 6.39512001e-01], + [ 3.31425547e-01, 6.26107379e-03, 6.41315649e-01], + [ 3.37683446e-01, 5.61830889e-03, 6.43048936e-01], + [ 3.43924591e-01, 4.99053080e-03, 6.44710195e-01], + [ 3.50149699e-01, 4.38202557e-03, 6.46297711e-01], + [ 3.56359209e-01, 3.79781761e-03, 6.47809772e-01], + [ 3.62553473e-01, 3.24319591e-03, 6.49244641e-01], + [ 3.68732762e-01, 2.72370721e-03, 6.50600561e-01], + [ 3.74897270e-01, 2.24514897e-03, 6.51875762e-01], + [ 3.81047116e-01, 1.81356205e-03, 6.53068467e-01], + [ 3.87182639e-01, 1.43446923e-03, 6.54176761e-01], + [ 3.93304010e-01, 1.11388259e-03, 6.55198755e-01], + [ 3.99410821e-01, 8.59420809e-04, 6.56132835e-01], + [ 4.05502914e-01, 6.78091517e-04, 6.56977276e-01], + [ 4.11580082e-01, 5.77101735e-04, 6.57730380e-01], + [ 4.17642063e-01, 5.63847476e-04, 6.58390492e-01], + [ 4.23688549e-01, 6.45902780e-04, 6.58956004e-01], + [ 4.29719186e-01, 8.31008207e-04, 6.59425363e-01], + [ 4.35733575e-01, 1.12705875e-03, 6.59797077e-01], + [ 4.41732123e-01, 1.53984779e-03, 6.60069009e-01], + [ 4.47713600e-01, 2.07954744e-03, 6.60240367e-01], + [ 4.53677394e-01, 2.75470302e-03, 6.60309966e-01], + [ 4.59622938e-01, 3.57374415e-03, 6.60276655e-01], + [ 4.65549631e-01, 4.54518084e-03, 6.60139383e-01], + [ 4.71456847e-01, 5.67758762e-03, 6.59897210e-01], + [ 4.77343929e-01, 6.97958743e-03, 6.59549311e-01], + [ 4.83210198e-01, 8.45983494e-03, 6.59094989e-01], + [ 4.89054951e-01, 1.01269996e-02, 6.58533677e-01], + [ 4.94877466e-01, 1.19897486e-02, 6.57864946e-01], + [ 5.00677687e-01, 1.40550640e-02, 6.57087561e-01], + [ 5.06454143e-01, 1.63333443e-02, 6.56202294e-01], + [ 5.12206035e-01, 1.88332232e-02, 6.55209222e-01], + [ 5.17932580e-01, 2.15631918e-02, 6.54108545e-01], + [ 5.23632990e-01, 2.45316468e-02, 6.52900629e-01], + [ 5.29306474e-01, 2.77468735e-02, 6.51586010e-01], + [ 5.34952244e-01, 3.12170300e-02, 6.50165396e-01], + [ 5.40569510e-01, 3.49501310e-02, 6.48639668e-01], + [ 5.46157494e-01, 3.89540334e-02, 6.47009884e-01], + [ 5.51715423e-01, 4.31364795e-02, 6.45277275e-01], + [ 5.57242538e-01, 4.73307585e-02, 6.43443250e-01], + [ 5.62738096e-01, 5.15448092e-02, 6.41509389e-01], + [ 5.68201372e-01, 5.57776706e-02, 6.39477440e-01], + [ 5.73631859e-01, 6.00281369e-02, 6.37348841e-01], + [ 5.79028682e-01, 6.42955547e-02, 6.35126108e-01], + [ 5.84391137e-01, 6.85790261e-02, 6.32811608e-01], + [ 5.89718606e-01, 7.28775875e-02, 6.30407727e-01], + [ 5.95010505e-01, 7.71902878e-02, 6.27916992e-01], + [ 6.00266283e-01, 8.15161895e-02, 6.25342058e-01], + [ 6.05485428e-01, 8.58543713e-02, 6.22685703e-01], + [ 6.10667469e-01, 9.02039303e-02, 6.19950811e-01], + [ 6.15811974e-01, 9.45639838e-02, 6.17140367e-01], + [ 6.20918555e-01, 9.89336721e-02, 6.14257440e-01], + [ 6.25986869e-01, 1.03312160e-01, 6.11305174e-01], + [ 6.31016615e-01, 1.07698641e-01, 6.08286774e-01], + [ 6.36007543e-01, 1.12092335e-01, 6.05205491e-01], + [ 6.40959444e-01, 1.16492495e-01, 6.02064611e-01], + [ 6.45872158e-01, 1.20898405e-01, 5.98867442e-01], + [ 6.50745571e-01, 1.25309384e-01, 5.95617300e-01], + [ 6.55579615e-01, 1.29724785e-01, 5.92317494e-01], + [ 6.60374266e-01, 1.34143997e-01, 5.88971318e-01], + [ 6.65129493e-01, 1.38566428e-01, 5.85582301e-01], + [ 6.69845385e-01, 1.42991540e-01, 5.82153572e-01], + [ 6.74522060e-01, 1.47418835e-01, 5.78688247e-01], + [ 6.79159664e-01, 1.51847851e-01, 5.75189431e-01], + [ 6.83758384e-01, 1.56278163e-01, 5.71660158e-01], + [ 6.88318440e-01, 1.60709387e-01, 5.68103380e-01], + [ 6.92840088e-01, 1.65141174e-01, 5.64521958e-01], + [ 6.97323615e-01, 1.69573215e-01, 5.60918659e-01], + [ 7.01769334e-01, 1.74005236e-01, 5.57296144e-01], + [ 7.06177590e-01, 1.78437000e-01, 5.53656970e-01], + [ 7.10548747e-01, 1.82868306e-01, 5.50003579e-01], + [ 7.14883195e-01, 1.87298986e-01, 5.46338299e-01], + [ 7.19181339e-01, 1.91728906e-01, 5.42663338e-01], + [ 7.23443604e-01, 1.96157962e-01, 5.38980786e-01], + [ 7.27670428e-01, 2.00586086e-01, 5.35292612e-01], + [ 7.31862231e-01, 2.05013174e-01, 5.31600995e-01], + [ 7.36019424e-01, 2.09439071e-01, 5.27908434e-01], + [ 7.40142557e-01, 2.13863965e-01, 5.24215533e-01], + [ 7.44232102e-01, 2.18287899e-01, 5.20523766e-01], + [ 7.48288533e-01, 2.22710942e-01, 5.16834495e-01], + [ 7.52312321e-01, 2.27133187e-01, 5.13148963e-01], + [ 7.56303937e-01, 2.31554749e-01, 5.09468305e-01], + [ 7.60263849e-01, 2.35975765e-01, 5.05793543e-01], + [ 7.64192516e-01, 2.40396394e-01, 5.02125599e-01], + [ 7.68090391e-01, 2.44816813e-01, 4.98465290e-01], + [ 7.71957916e-01, 2.49237220e-01, 4.94813338e-01], + [ 7.75795522e-01, 2.53657797e-01, 4.91170517e-01], + [ 7.79603614e-01, 2.58078397e-01, 4.87539124e-01], + [ 7.83382636e-01, 2.62499662e-01, 4.83917732e-01], + [ 7.87132978e-01, 2.66921859e-01, 4.80306702e-01], + [ 7.90855015e-01, 2.71345267e-01, 4.76706319e-01], + [ 7.94549101e-01, 2.75770179e-01, 4.73116798e-01], + [ 7.98215577e-01, 2.80196901e-01, 4.69538286e-01], + [ 8.01854758e-01, 2.84625750e-01, 4.65970871e-01], + [ 8.05466945e-01, 2.89057057e-01, 4.62414580e-01], + [ 8.09052419e-01, 2.93491117e-01, 4.58869577e-01], + [ 8.12611506e-01, 2.97927865e-01, 4.55337565e-01], + [ 8.16144382e-01, 3.02368130e-01, 4.51816385e-01], + [ 8.19651255e-01, 3.06812282e-01, 4.48305861e-01], + [ 8.23132309e-01, 3.11260703e-01, 4.44805781e-01], + [ 8.26587706e-01, 3.15713782e-01, 4.41315901e-01], + [ 8.30017584e-01, 3.20171913e-01, 4.37835947e-01], + [ 8.33422053e-01, 3.24635499e-01, 4.34365616e-01], + [ 8.36801237e-01, 3.29104836e-01, 4.30905052e-01], + [ 8.40155276e-01, 3.33580106e-01, 4.27454836e-01], + [ 8.43484103e-01, 3.38062109e-01, 4.24013059e-01], + [ 8.46787726e-01, 3.42551272e-01, 4.20579333e-01], + [ 8.50066132e-01, 3.47048028e-01, 4.17153264e-01], + [ 8.53319279e-01, 3.51552815e-01, 4.13734445e-01], + [ 8.56547103e-01, 3.56066072e-01, 4.10322469e-01], + [ 8.59749520e-01, 3.60588229e-01, 4.06916975e-01], + [ 8.62926559e-01, 3.65119408e-01, 4.03518809e-01], + [ 8.66077920e-01, 3.69660446e-01, 4.00126027e-01], + [ 8.69203436e-01, 3.74211795e-01, 3.96738211e-01], + [ 8.72302917e-01, 3.78773910e-01, 3.93354947e-01], + [ 8.75376149e-01, 3.83347243e-01, 3.89975832e-01], + [ 8.78422895e-01, 3.87932249e-01, 3.86600468e-01], + [ 8.81442916e-01, 3.92529339e-01, 3.83228622e-01], + [ 8.84435982e-01, 3.97138877e-01, 3.79860246e-01], + [ 8.87401682e-01, 4.01761511e-01, 3.76494232e-01], + [ 8.90339687e-01, 4.06397694e-01, 3.73130228e-01], + [ 8.93249647e-01, 4.11047871e-01, 3.69767893e-01], + [ 8.96131191e-01, 4.15712489e-01, 3.66406907e-01], + [ 8.98983931e-01, 4.20391986e-01, 3.63046965e-01], + [ 9.01807455e-01, 4.25086807e-01, 3.59687758e-01], + [ 9.04601295e-01, 4.29797442e-01, 3.56328796e-01], + [ 9.07364995e-01, 4.34524335e-01, 3.52969777e-01], + [ 9.10098088e-01, 4.39267908e-01, 3.49610469e-01], + [ 9.12800095e-01, 4.44028574e-01, 3.46250656e-01], + [ 9.15470518e-01, 4.48806744e-01, 3.42890148e-01], + [ 9.18108848e-01, 4.53602818e-01, 3.39528771e-01], + [ 9.20714383e-01, 4.58417420e-01, 3.36165582e-01], + [ 9.23286660e-01, 4.63250828e-01, 3.32800827e-01], + [ 9.25825146e-01, 4.68103387e-01, 3.29434512e-01], + [ 9.28329275e-01, 4.72975465e-01, 3.26066550e-01], + [ 9.30798469e-01, 4.77867420e-01, 3.22696876e-01], + [ 9.33232140e-01, 4.82779603e-01, 3.19325444e-01], + [ 9.35629684e-01, 4.87712357e-01, 3.15952211e-01], + [ 9.37990034e-01, 4.92666544e-01, 3.12575440e-01], + [ 9.40312939e-01, 4.97642038e-01, 3.09196628e-01], + [ 9.42597771e-01, 5.02639147e-01, 3.05815824e-01], + [ 9.44843893e-01, 5.07658169e-01, 3.02433101e-01], + [ 9.47050662e-01, 5.12699390e-01, 2.99048555e-01], + [ 9.49217427e-01, 5.17763087e-01, 2.95662308e-01], + [ 9.51343530e-01, 5.22849522e-01, 2.92274506e-01], + [ 9.53427725e-01, 5.27959550e-01, 2.88883445e-01], + [ 9.55469640e-01, 5.33093083e-01, 2.85490391e-01], + [ 9.57468770e-01, 5.38250172e-01, 2.82096149e-01], + [ 9.59424430e-01, 5.43431038e-01, 2.78700990e-01], + [ 9.61335930e-01, 5.48635890e-01, 2.75305214e-01], + [ 9.63202573e-01, 5.53864931e-01, 2.71909159e-01], + [ 9.65023656e-01, 5.59118349e-01, 2.68513200e-01], + [ 9.66798470e-01, 5.64396327e-01, 2.65117752e-01], + [ 9.68525639e-01, 5.69699633e-01, 2.61721488e-01], + [ 9.70204593e-01, 5.75028270e-01, 2.58325424e-01], + [ 9.71835007e-01, 5.80382015e-01, 2.54931256e-01], + [ 9.73416145e-01, 5.85761012e-01, 2.51539615e-01], + [ 9.74947262e-01, 5.91165394e-01, 2.48151200e-01], + [ 9.76427606e-01, 5.96595287e-01, 2.44766775e-01], + [ 9.77856416e-01, 6.02050811e-01, 2.41387186e-01], + [ 9.79232922e-01, 6.07532077e-01, 2.38013359e-01], + [ 9.80556344e-01, 6.13039190e-01, 2.34646316e-01], + [ 9.81825890e-01, 6.18572250e-01, 2.31287178e-01], + [ 9.83040742e-01, 6.24131362e-01, 2.27937141e-01], + [ 9.84198924e-01, 6.29717516e-01, 2.24595006e-01], + [ 9.85300760e-01, 6.35329876e-01, 2.21264889e-01], + [ 9.86345421e-01, 6.40968508e-01, 2.17948456e-01], + [ 9.87332067e-01, 6.46633475e-01, 2.14647532e-01], + [ 9.88259846e-01, 6.52324832e-01, 2.11364122e-01], + [ 9.89127893e-01, 6.58042630e-01, 2.08100426e-01], + [ 9.89935328e-01, 6.63786914e-01, 2.04858855e-01], + [ 9.90681261e-01, 6.69557720e-01, 2.01642049e-01], + [ 9.91364787e-01, 6.75355082e-01, 1.98452900e-01], + [ 9.91984990e-01, 6.81179025e-01, 1.95294567e-01], + [ 9.92540939e-01, 6.87029567e-01, 1.92170500e-01], + [ 9.93031693e-01, 6.92906719e-01, 1.89084459e-01], + [ 9.93456302e-01, 6.98810484e-01, 1.86040537e-01], + [ 9.93813802e-01, 7.04740854e-01, 1.83043180e-01], + [ 9.94103226e-01, 7.10697814e-01, 1.80097207e-01], + [ 9.94323596e-01, 7.16681336e-01, 1.77207826e-01], + [ 9.94473934e-01, 7.22691379e-01, 1.74380656e-01], + [ 9.94553260e-01, 7.28727890e-01, 1.71621733e-01], + [ 9.94560594e-01, 7.34790799e-01, 1.68937522e-01], + [ 9.94494964e-01, 7.40880020e-01, 1.66334918e-01], + [ 9.94355411e-01, 7.46995448e-01, 1.63821243e-01], + [ 9.94140989e-01, 7.53136955e-01, 1.61404226e-01], + [ 9.93850778e-01, 7.59304390e-01, 1.59091984e-01], + [ 9.93482190e-01, 7.65498551e-01, 1.56890625e-01], + [ 9.93033251e-01, 7.71719833e-01, 1.54807583e-01], + [ 9.92505214e-01, 7.77966775e-01, 1.52854862e-01], + [ 9.91897270e-01, 7.84239120e-01, 1.51041581e-01], + [ 9.91208680e-01, 7.90536569e-01, 1.49376885e-01], + [ 9.90438793e-01, 7.96858775e-01, 1.47869810e-01], + [ 9.89587065e-01, 8.03205337e-01, 1.46529128e-01], + [ 9.88647741e-01, 8.09578605e-01, 1.45357284e-01], + [ 9.87620557e-01, 8.15977942e-01, 1.44362644e-01], + [ 9.86509366e-01, 8.22400620e-01, 1.43556679e-01], + [ 9.85314198e-01, 8.28845980e-01, 1.42945116e-01], + [ 9.84031139e-01, 8.35315360e-01, 1.42528388e-01], + [ 9.82652820e-01, 8.41811730e-01, 1.42302653e-01], + [ 9.81190389e-01, 8.48328902e-01, 1.42278607e-01], + [ 9.79643637e-01, 8.54866468e-01, 1.42453425e-01], + [ 9.77994918e-01, 8.61432314e-01, 1.42808191e-01], + [ 9.76264977e-01, 8.68015998e-01, 1.43350944e-01], + [ 9.74443038e-01, 8.74622194e-01, 1.44061156e-01], + [ 9.72530009e-01, 8.81250063e-01, 1.44922913e-01], + [ 9.70532932e-01, 8.87896125e-01, 1.45918663e-01], + [ 9.68443477e-01, 8.94563989e-01, 1.47014438e-01], + [ 9.66271225e-01, 9.01249365e-01, 1.48179639e-01], + [ 9.64021057e-01, 9.07950379e-01, 1.49370428e-01], + [ 9.61681481e-01, 9.14672479e-01, 1.50520343e-01], + [ 9.59275646e-01, 9.21406537e-01, 1.51566019e-01], + [ 9.56808068e-01, 9.28152065e-01, 1.52409489e-01], + [ 9.54286813e-01, 9.34907730e-01, 1.52921158e-01], + [ 9.51726083e-01, 9.41670605e-01, 1.52925363e-01], + [ 9.49150533e-01, 9.48434900e-01, 1.52177604e-01], + [ 9.46602270e-01, 9.55189860e-01, 1.50327944e-01], + [ 9.44151742e-01, 9.61916487e-01, 1.46860789e-01], + [ 9.41896120e-01, 9.68589814e-01, 1.40955606e-01], + [ 9.40015097e-01, 9.75158357e-01, 1.31325517e-01]]; +% +num = size(raw,1); +% With small extrapolation when N>num: +vec = linspace(0,num+1,N+2); +map = interp1(1:num,raw,vec(2:N+1),'linear','extrap'); +% Interpolation only for all values of N: +%map = interp1(1:num,raw,linspace(1,num,N),'spline') +% Range limits: +map = max(0,min(1,map)); +% +end \ No newline at end of file diff --git a/CROSS-OPT-1.0/viridis.m b/CROSS-OPT-1.0/viridis.m new file mode 100644 index 0000000..0add810 --- /dev/null +++ b/CROSS-OPT-1.0/viridis.m @@ -0,0 +1,321 @@ +function map = viridis(N) +% Perceptually uniform sequential colormap from MatPlotLib. +% +% Copyright (c) 2017-2020 Stephen Cobeldick +% +%%% Syntax: +% map = viridis +% map = viridis(N) +% +% Colormap designed by Eric Firing, Nathaniel J. Smith, and Stefan van der Walt. +% +% For MatPlotLib 2.0 improved colormaps were created in the perceptually +% uniform colorspace CAM02-UCS. The new colormaps are introduced here: +% +% The RGB data is from here: +% +% Note VIRIDIS replaces the awful JET as the MatPlotLib default colormap. +% +%% Examples %% +% +%%% Plot the scheme's RGB values: +% rgbplot(viridis(256)) +% +%%% New colors for the COLORMAP example: +% load spine +% image(X) +% colormap(viridis) +% +%%% New colors for the SURF example: +% [X,Y,Z] = peaks(30); +% surfc(X,Y,Z) +% colormap(viridis) +% axis([-3,3,-3,3,-10,5]) +% +%% Input and Output Arguments %% +% +%%% Inputs (*=default): +% N = NumericScalar, N>=0, an integer to define the colormap length. +% = *[], use the length of the current figure's colormap (see COLORMAP). +% +%%% Outputs: +% map = NumericMatrix, size Nx3, a colormap of RGB values between 0 and 1. +% +% See also CIVIDIS INFERNO MAGMA PLASMA TWILIGHT TAB10 SET LINES COLORMAP PARULA + +if nargin<1 || isnumeric(N)&&isequal(N,[]) + N = size(get(gcf,'colormap'),1); +else + assert(isscalar(N)&&isfinite(N)&&isreal(N),... + 'SC:viridis:N:NotRealFiniteScalarNumeric',... + 'First argument must be a real finite numeric scalar.') +end +% +raw = [[ 0.26700401, 0.00487433, 0.32941519], + [ 0.26851048, 0.00960483, 0.33542652], + [ 0.26994384, 0.01462494, 0.34137895], + [ 0.27130489, 0.01994186, 0.34726862], + [ 0.27259384, 0.02556309, 0.35309303], + [ 0.27380934, 0.03149748, 0.35885256], + [ 0.27495242, 0.03775181, 0.36454323], + [ 0.27602238, 0.04416723, 0.37016418], + [ 0.2770184 , 0.05034437, 0.37571452], + [ 0.27794143, 0.05632444, 0.38119074], + [ 0.27879067, 0.06214536, 0.38659204], + [ 0.2795655 , 0.06783587, 0.39191723], + [ 0.28026658, 0.07341724, 0.39716349], + [ 0.28089358, 0.07890703, 0.40232944], + [ 0.28144581, 0.0843197 , 0.40741404], + [ 0.28192358, 0.08966622, 0.41241521], + [ 0.28232739, 0.09495545, 0.41733086], + [ 0.28265633, 0.10019576, 0.42216032], + [ 0.28291049, 0.10539345, 0.42690202], + [ 0.28309095, 0.11055307, 0.43155375], + [ 0.28319704, 0.11567966, 0.43611482], + [ 0.28322882, 0.12077701, 0.44058404], + [ 0.28318684, 0.12584799, 0.44496 ], + [ 0.283072 , 0.13089477, 0.44924127], + [ 0.28288389, 0.13592005, 0.45342734], + [ 0.28262297, 0.14092556, 0.45751726], + [ 0.28229037, 0.14591233, 0.46150995], + [ 0.28188676, 0.15088147, 0.46540474], + [ 0.28141228, 0.15583425, 0.46920128], + [ 0.28086773, 0.16077132, 0.47289909], + [ 0.28025468, 0.16569272, 0.47649762], + [ 0.27957399, 0.17059884, 0.47999675], + [ 0.27882618, 0.1754902 , 0.48339654], + [ 0.27801236, 0.18036684, 0.48669702], + [ 0.27713437, 0.18522836, 0.48989831], + [ 0.27619376, 0.19007447, 0.49300074], + [ 0.27519116, 0.1949054 , 0.49600488], + [ 0.27412802, 0.19972086, 0.49891131], + [ 0.27300596, 0.20452049, 0.50172076], + [ 0.27182812, 0.20930306, 0.50443413], + [ 0.27059473, 0.21406899, 0.50705243], + [ 0.26930756, 0.21881782, 0.50957678], + [ 0.26796846, 0.22354911, 0.5120084 ], + [ 0.26657984, 0.2282621 , 0.5143487 ], + [ 0.2651445 , 0.23295593, 0.5165993 ], + [ 0.2636632 , 0.23763078, 0.51876163], + [ 0.26213801, 0.24228619, 0.52083736], + [ 0.26057103, 0.2469217 , 0.52282822], + [ 0.25896451, 0.25153685, 0.52473609], + [ 0.25732244, 0.2561304 , 0.52656332], + [ 0.25564519, 0.26070284, 0.52831152], + [ 0.25393498, 0.26525384, 0.52998273], + [ 0.25219404, 0.26978306, 0.53157905], + [ 0.25042462, 0.27429024, 0.53310261], + [ 0.24862899, 0.27877509, 0.53455561], + [ 0.2468114 , 0.28323662, 0.53594093], + [ 0.24497208, 0.28767547, 0.53726018], + [ 0.24311324, 0.29209154, 0.53851561], + [ 0.24123708, 0.29648471, 0.53970946], + [ 0.23934575, 0.30085494, 0.54084398], + [ 0.23744138, 0.30520222, 0.5419214 ], + [ 0.23552606, 0.30952657, 0.54294396], + [ 0.23360277, 0.31382773, 0.54391424], + [ 0.2316735 , 0.3181058 , 0.54483444], + [ 0.22973926, 0.32236127, 0.54570633], + [ 0.22780192, 0.32659432, 0.546532 ], + [ 0.2258633 , 0.33080515, 0.54731353], + [ 0.22392515, 0.334994 , 0.54805291], + [ 0.22198915, 0.33916114, 0.54875211], + [ 0.22005691, 0.34330688, 0.54941304], + [ 0.21812995, 0.34743154, 0.55003755], + [ 0.21620971, 0.35153548, 0.55062743], + [ 0.21429757, 0.35561907, 0.5511844 ], + [ 0.21239477, 0.35968273, 0.55171011], + [ 0.2105031 , 0.36372671, 0.55220646], + [ 0.20862342, 0.36775151, 0.55267486], + [ 0.20675628, 0.37175775, 0.55311653], + [ 0.20490257, 0.37574589, 0.55353282], + [ 0.20306309, 0.37971644, 0.55392505], + [ 0.20123854, 0.38366989, 0.55429441], + [ 0.1994295 , 0.38760678, 0.55464205], + [ 0.1976365 , 0.39152762, 0.55496905], + [ 0.19585993, 0.39543297, 0.55527637], + [ 0.19410009, 0.39932336, 0.55556494], + [ 0.19235719, 0.40319934, 0.55583559], + [ 0.19063135, 0.40706148, 0.55608907], + [ 0.18892259, 0.41091033, 0.55632606], + [ 0.18723083, 0.41474645, 0.55654717], + [ 0.18555593, 0.4185704 , 0.55675292], + [ 0.18389763, 0.42238275, 0.55694377], + [ 0.18225561, 0.42618405, 0.5571201 ], + [ 0.18062949, 0.42997486, 0.55728221], + [ 0.17901879, 0.43375572, 0.55743035], + [ 0.17742298, 0.4375272 , 0.55756466], + [ 0.17584148, 0.44128981, 0.55768526], + [ 0.17427363, 0.4450441 , 0.55779216], + [ 0.17271876, 0.4487906 , 0.55788532], + [ 0.17117615, 0.4525298 , 0.55796464], + [ 0.16964573, 0.45626209, 0.55803034], + [ 0.16812641, 0.45998802, 0.55808199], + [ 0.1666171 , 0.46370813, 0.55811913], + [ 0.16511703, 0.4674229 , 0.55814141], + [ 0.16362543, 0.47113278, 0.55814842], + [ 0.16214155, 0.47483821, 0.55813967], + [ 0.16066467, 0.47853961, 0.55811466], + [ 0.15919413, 0.4822374 , 0.5580728 ], + [ 0.15772933, 0.48593197, 0.55801347], + [ 0.15626973, 0.4896237 , 0.557936 ], + [ 0.15481488, 0.49331293, 0.55783967], + [ 0.15336445, 0.49700003, 0.55772371], + [ 0.1519182 , 0.50068529, 0.55758733], + [ 0.15047605, 0.50436904, 0.55742968], + [ 0.14903918, 0.50805136, 0.5572505 ], + [ 0.14760731, 0.51173263, 0.55704861], + [ 0.14618026, 0.51541316, 0.55682271], + [ 0.14475863, 0.51909319, 0.55657181], + [ 0.14334327, 0.52277292, 0.55629491], + [ 0.14193527, 0.52645254, 0.55599097], + [ 0.14053599, 0.53013219, 0.55565893], + [ 0.13914708, 0.53381201, 0.55529773], + [ 0.13777048, 0.53749213, 0.55490625], + [ 0.1364085 , 0.54117264, 0.55448339], + [ 0.13506561, 0.54485335, 0.55402906], + [ 0.13374299, 0.54853458, 0.55354108], + [ 0.13244401, 0.55221637, 0.55301828], + [ 0.13117249, 0.55589872, 0.55245948], + [ 0.1299327 , 0.55958162, 0.55186354], + [ 0.12872938, 0.56326503, 0.55122927], + [ 0.12756771, 0.56694891, 0.55055551], + [ 0.12645338, 0.57063316, 0.5498411 ], + [ 0.12539383, 0.57431754, 0.54908564], + [ 0.12439474, 0.57800205, 0.5482874 ], + [ 0.12346281, 0.58168661, 0.54744498], + [ 0.12260562, 0.58537105, 0.54655722], + [ 0.12183122, 0.58905521, 0.54562298], + [ 0.12114807, 0.59273889, 0.54464114], + [ 0.12056501, 0.59642187, 0.54361058], + [ 0.12009154, 0.60010387, 0.54253043], + [ 0.11973756, 0.60378459, 0.54139999], + [ 0.11951163, 0.60746388, 0.54021751], + [ 0.11942341, 0.61114146, 0.53898192], + [ 0.11948255, 0.61481702, 0.53769219], + [ 0.11969858, 0.61849025, 0.53634733], + [ 0.12008079, 0.62216081, 0.53494633], + [ 0.12063824, 0.62582833, 0.53348834], + [ 0.12137972, 0.62949242, 0.53197275], + [ 0.12231244, 0.63315277, 0.53039808], + [ 0.12344358, 0.63680899, 0.52876343], + [ 0.12477953, 0.64046069, 0.52706792], + [ 0.12632581, 0.64410744, 0.52531069], + [ 0.12808703, 0.64774881, 0.52349092], + [ 0.13006688, 0.65138436, 0.52160791], + [ 0.13226797, 0.65501363, 0.51966086], + [ 0.13469183, 0.65863619, 0.5176488 ], + [ 0.13733921, 0.66225157, 0.51557101], + [ 0.14020991, 0.66585927, 0.5134268 ], + [ 0.14330291, 0.66945881, 0.51121549], + [ 0.1466164 , 0.67304968, 0.50893644], + [ 0.15014782, 0.67663139, 0.5065889 ], + [ 0.15389405, 0.68020343, 0.50417217], + [ 0.15785146, 0.68376525, 0.50168574], + [ 0.16201598, 0.68731632, 0.49912906], + [ 0.1663832 , 0.69085611, 0.49650163], + [ 0.1709484 , 0.69438405, 0.49380294], + [ 0.17570671, 0.6978996 , 0.49103252], + [ 0.18065314, 0.70140222, 0.48818938], + [ 0.18578266, 0.70489133, 0.48527326], + [ 0.19109018, 0.70836635, 0.48228395], + [ 0.19657063, 0.71182668, 0.47922108], + [ 0.20221902, 0.71527175, 0.47608431], + [ 0.20803045, 0.71870095, 0.4728733 ], + [ 0.21400015, 0.72211371, 0.46958774], + [ 0.22012381, 0.72550945, 0.46622638], + [ 0.2263969 , 0.72888753, 0.46278934], + [ 0.23281498, 0.73224735, 0.45927675], + [ 0.2393739 , 0.73558828, 0.45568838], + [ 0.24606968, 0.73890972, 0.45202405], + [ 0.25289851, 0.74221104, 0.44828355], + [ 0.25985676, 0.74549162, 0.44446673], + [ 0.26694127, 0.74875084, 0.44057284], + [ 0.27414922, 0.75198807, 0.4366009 ], + [ 0.28147681, 0.75520266, 0.43255207], + [ 0.28892102, 0.75839399, 0.42842626], + [ 0.29647899, 0.76156142, 0.42422341], + [ 0.30414796, 0.76470433, 0.41994346], + [ 0.31192534, 0.76782207, 0.41558638], + [ 0.3198086 , 0.77091403, 0.41115215], + [ 0.3277958 , 0.77397953, 0.40664011], + [ 0.33588539, 0.7770179 , 0.40204917], + [ 0.34407411, 0.78002855, 0.39738103], + [ 0.35235985, 0.78301086, 0.39263579], + [ 0.36074053, 0.78596419, 0.38781353], + [ 0.3692142 , 0.78888793, 0.38291438], + [ 0.37777892, 0.79178146, 0.3779385 ], + [ 0.38643282, 0.79464415, 0.37288606], + [ 0.39517408, 0.79747541, 0.36775726], + [ 0.40400101, 0.80027461, 0.36255223], + [ 0.4129135 , 0.80304099, 0.35726893], + [ 0.42190813, 0.80577412, 0.35191009], + [ 0.43098317, 0.80847343, 0.34647607], + [ 0.44013691, 0.81113836, 0.3409673 ], + [ 0.44936763, 0.81376835, 0.33538426], + [ 0.45867362, 0.81636288, 0.32972749], + [ 0.46805314, 0.81892143, 0.32399761], + [ 0.47750446, 0.82144351, 0.31819529], + [ 0.4870258 , 0.82392862, 0.31232133], + [ 0.49661536, 0.82637633, 0.30637661], + [ 0.5062713 , 0.82878621, 0.30036211], + [ 0.51599182, 0.83115784, 0.29427888], + [ 0.52577622, 0.83349064, 0.2881265 ], + [ 0.5356211 , 0.83578452, 0.28190832], + [ 0.5455244 , 0.83803918, 0.27562602], + [ 0.55548397, 0.84025437, 0.26928147], + [ 0.5654976 , 0.8424299 , 0.26287683], + [ 0.57556297, 0.84456561, 0.25641457], + [ 0.58567772, 0.84666139, 0.24989748], + [ 0.59583934, 0.84871722, 0.24332878], + [ 0.60604528, 0.8507331 , 0.23671214], + [ 0.61629283, 0.85270912, 0.23005179], + [ 0.62657923, 0.85464543, 0.22335258], + [ 0.63690157, 0.85654226, 0.21662012], + [ 0.64725685, 0.85839991, 0.20986086], + [ 0.65764197, 0.86021878, 0.20308229], + [ 0.66805369, 0.86199932, 0.19629307], + [ 0.67848868, 0.86374211, 0.18950326], + [ 0.68894351, 0.86544779, 0.18272455], + [ 0.69941463, 0.86711711, 0.17597055], + [ 0.70989842, 0.86875092, 0.16925712], + [ 0.72039115, 0.87035015, 0.16260273], + [ 0.73088902, 0.87191584, 0.15602894], + [ 0.74138803, 0.87344918, 0.14956101], + [ 0.75188414, 0.87495143, 0.14322828], + [ 0.76237342, 0.87642392, 0.13706449], + [ 0.77285183, 0.87786808, 0.13110864], + [ 0.78331535, 0.87928545, 0.12540538], + [ 0.79375994, 0.88067763, 0.12000532], + [ 0.80418159, 0.88204632, 0.11496505], + [ 0.81457634, 0.88339329, 0.11034678], + [ 0.82494028, 0.88472036, 0.10621724], + [ 0.83526959, 0.88602943, 0.1026459 ], + [ 0.84556056, 0.88732243, 0.09970219], + [ 0.8558096 , 0.88860134, 0.09745186], + [ 0.86601325, 0.88986815, 0.09595277], + [ 0.87616824, 0.89112487, 0.09525046], + [ 0.88627146, 0.89237353, 0.09537439], + [ 0.89632002, 0.89361614, 0.09633538], + [ 0.90631121, 0.89485467, 0.09812496], + [ 0.91624212, 0.89609127, 0.1007168 ], + [ 0.92610579, 0.89732977, 0.10407067], + [ 0.93590444, 0.8985704 , 0.10813094], + [ 0.94563626, 0.899815 , 0.11283773], + [ 0.95529972, 0.90106534, 0.11812832], + [ 0.96489353, 0.90232311, 0.12394051], + [ 0.97441665, 0.90358991, 0.13021494], + [ 0.98386829, 0.90486726, 0.13689671], + [ 0.99324789, 0.90615657, 0.1439362 ]]; +% +num = size(raw,1); +% With small extrapolation when N>num: +vec = linspace(0,num+1,N+2); +map = interp1(1:num,raw,vec(2:N+1),'linear','extrap'); +% Interpolation only for all values of N: +%map = interp1(1:num,raw,linspace(1,num,N),'spline') +% Range limits: +map = max(0,min(1,map)); +% +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file