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Commit ab81f3e0 authored by Antoine Cyril David Hoffmann's avatar Antoine Cyril David Hoffmann
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scripts update

parent 03d92523
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...@@ -54,19 +54,22 @@ if (abs(CO) == 2) %Sugama operator ...@@ -54,19 +54,22 @@ if (abs(CO) == 2) %Sugama operator
elseif (abs(CO) == 3) %pitch angle operator elseif (abs(CO) == 3) %pitch angle operator
INITIAL.mat_file = ['''../../../iCa/gk_pitchangle_8_P_20_J_10_N_150_kpm_8.0.h5''']; INITIAL.mat_file = ['''../../../iCa/gk_pitchangle_8_P_20_J_10_N_150_kpm_8.0.h5'''];
elseif (CO == 4) % Full Coulomb GK elseif (CO == 4) % Full Coulomb GK
disp('Warning, FCGK not implemented yet') INITIAL.mat_file = ['''../../../iCa/gk_coulomb_P_6_J_3_N_150_kpm_8.0.h5'''];
elseif (CO == -1) % DGDK elseif (CO == -1) % DGDK
disp('Warning, DGDK not debugged') disp('Warning, DGDK not debugged')
end end
% Naming and creating input file % Naming and creating input file
if (CO == -3); CONAME = 'PADK'; switch abs(CO)
elseif(CO == -2); CONAME = 'SGDK'; case 0; CONAME = 'LB';
elseif(CO == -1); CONAME = 'DGDK'; case 1; CONAME = 'DG';
elseif(CO == 0); CONAME = 'LBDK'; case 2; CONAME = 'SG';
elseif(CO == 1); CONAME = 'DGGK'; case 3; CONAME = 'PA';
elseif(CO == 2); CONAME = 'SGGK'; case 4; CONAME = 'FC';
elseif(CO == 3); CONAME = 'PAGK'; otherwise; CONAME ='UK';
end
if (CO <= 0); CONAME = [CONAME,'DK'];
else; CONAME = [CONAME,'GK'];
end end
if (CLOS == 0); CLOSNAME = 'Trunc.'; if (CLOS == 0); CLOSNAME = 'Trunc.';
elseif(CLOS == 1); CLOSNAME = 'Clos. 1'; elseif(CLOS == 1); CLOSNAME = 'Clos. 1';
......
...@@ -34,6 +34,7 @@ rp_=[... ...@@ -34,6 +34,7 @@ rp_=[...
5e-2, 1e-3;... 5e-2, 1e-3;...
1e-2, 1e-3;... 1e-2, 1e-3;...
1e-2, 1e-4;... 1e-2, 1e-4;...
1e-2, 5e-4;...
]; ];
figure; set(gcf, 'Position', [100, 100, 900, 400]) figure; set(gcf, 'Position', [100, 100, 900, 400])
grid on; xlim([5e-4,5e0]); ylim([5e-5,5e+0]); grid on; xlim([5e-4,5e0]); ylim([5e-5,5e+0]);
...@@ -72,6 +73,12 @@ mu_ = [3e-3 1e-3 1e-4]; ...@@ -72,6 +73,12 @@ mu_ = [3e-3 1e-3 1e-4];
nu_ = [1e-2 1e-2 1e-2]; nu_ = [1e-2 1e-2 1e-2];
plot(nu_,mu_,'x--','DisplayName','N=150, L=100, P,J=2,1'); plot(nu_,mu_,'x--','DisplayName','N=150, L=100, P,J=2,1');
% HD_study/150x75_L_100_P_4_J_2_eta_0.6_nu_1e-02_DGGK_CLOS_0_mu_3e-02/
mu_ = [3e-3 5e-4];
nu_ = [1e-2 1e-2];
plot(nu_,mu_,'x--','DisplayName','N=150, L=100, P,J=4,2');
% HD_study/150x75_L_100_P_2_J_1_eta_0.6_nu_5e-02_DGGK_CLOS_0_mu_3e-02/ % HD_study/150x75_L_100_P_2_J_1_eta_0.6_nu_5e-02_DGGK_CLOS_0_mu_3e-02/
mu_ = [3e-3 1e-3]; mu_ = [3e-3 1e-3];
nu_ = [5e-2 5e-2]; nu_ = [5e-2 5e-2];
......
...@@ -7,8 +7,10 @@ outfile =''; ...@@ -7,8 +7,10 @@ outfile ='';
outfile =''; outfile ='';
outfile =''; outfile ='';
outfile =''; outfile ='';
outfile ='HD_study/300x150_L_100_P_2_J_1_eta_0.6_nu_5e-01_DGGK_mu_2e-03'; outfile ='';
% outfile ='HD_study/150x75_L_100_P_4_J_2_eta_0.6_nu_1e-02_DGGK_mu_3e-03'; outfile ='';
outfile ='';
outfile ='HD_study/150x75_L_100_P_4_J_2_eta_0.6_nu_1e-02_DGGK_mu_3e-03';
BASIC.RESDIR = ['../results/',outfile,'/']; BASIC.RESDIR = ['../results/',outfile,'/'];
BASIC.MISCDIR = ['/misc/HeLaZ_outputs/results/',outfile,'/']; BASIC.MISCDIR = ['/misc/HeLaZ_outputs/results/',outfile,'/'];
CMD = ['cp ', BASIC.RESDIR,'outputs* ',BASIC.MISCDIR]; disp(CMD); CMD = ['cp ', BASIC.RESDIR,'outputs* ',BASIC.MISCDIR]; disp(CMD);
...@@ -19,7 +21,9 @@ outfile =''; ...@@ -19,7 +21,9 @@ outfile ='';
outfile =''; outfile ='';
outfile =''; outfile ='';
outfile =''; outfile ='';
outfile ='/marconi_scratch/userexternal/ahoffman/HeLaZ/results/test_3D_marconi/100x50_L_60_P_2_J_1_eta_Inf_nu_1e-01_DGGK_mu_0e+00/out.txt'; outfile ='';
outfile ='';
outfile ='/marconi_scratch/userexternal/ahoffman/HeLaZ/results/test_3D_marconi/100x50x20_L_60_q0_1_P_2_J_1_eta_0.6_nu_1e-01_DGGK_mu_2e-02/out.txt';
BASIC.RESDIR = ['../',outfile(46:end-8),'/']; BASIC.RESDIR = ['../',outfile(46:end-8),'/'];
BASIC.MISCDIR = ['/misc/HeLaZ_outputs/',outfile(46:end-8),'/']; BASIC.MISCDIR = ['/misc/HeLaZ_outputs/',outfile(46:end-8),'/'];
end end
...@@ -74,7 +78,7 @@ t0 =00; iz = 1; ix = 1; iy = 1; ...@@ -74,7 +78,7 @@ t0 =00; iz = 1; ix = 1; iy = 1;
skip_ = 1; DELAY = 1e-2*skip_; skip_ = 1; DELAY = 1e-2*skip_;
[~, it03D] = min(abs(Ts3D-t0)); FRAMES_3D = it03D:skip_:numel(Ts3D); [~, it03D] = min(abs(Ts3D-t0)); FRAMES_3D = it03D:skip_:numel(Ts3D);
[~, it05D] = min(abs(Ts5D-t0)); FRAMES_5D = it05D:skip_:numel(Ts5D); [~, it05D] = min(abs(Ts5D-t0)); FRAMES_5D = it05D:skip_:numel(Ts5D);
INTERP = 0; T = Ts3D; FRAMES = FRAMES_3D; INTERP = 1; T = Ts3D; FRAMES = FRAMES_3D;
% Field to plot % Field to plot
% FIELD = dens_e; NAME = 'ne'; FIELDNAME = 'n_e'; % FIELD = dens_e; NAME = 'ne'; FIELDNAME = 'n_e';
% FIELD = dens_i; NAME = 'ni'; FIELDNAME = 'n_i'; % FIELD = dens_i; NAME = 'ni'; FIELDNAME = 'n_i';
......
for NU = [0.01] for NU = [0.1]
for ETAN = [2.0] for ETAN = [2.0]
for CO = [3] for CO = [1]
%clear all; %clear all;
addpath(genpath('../matlab')) % ... add addpath(genpath('../matlab')) % ... add
default_plots_options default_plots_options
...@@ -33,12 +33,10 @@ SPSCP = 0; % Sampling per time unit for checkpoints ...@@ -33,12 +33,10 @@ SPSCP = 0; % Sampling per time unit for checkpoints
RESTART = 0; % To restart from last checkpoint RESTART = 0; % To restart from last checkpoint
JOB2LOAD= 00; JOB2LOAD= 00;
%% OPTIONS %% OPTIONS
% SIMID = 'v2.7_lin_analysis'; % Name of the simulation SIMID = 'v3.1_lin_analysis'; % Name of the simulation
SIMID = 'kobayashi_2015_fig2'; % Name of the simulation
% SIMID = 'v2.6_lin_analysis'; % Name of the simulation
NON_LIN = 0 *(1-KXEQ0); % activate non-linearity (is cancelled if KXEQ0 = 1) NON_LIN = 0 *(1-KXEQ0); % activate non-linearity (is cancelled if KXEQ0 = 1)
% Collision operator % Collision operator
% (0 : L.Bernstein, 1 : Dougherty, 2: Sugama, 3 : Full Couloumb ; +/- for GK/DK) % (0 : L.Bernstein, 1 : Dougherty, 2: Sugama, 3 : Pitch angle, 4 : Full Couloumb ; +/- for GK/DK)
% CO = 2; % CO = 2;
INIT_ZF = 0; ZF_AMP = 0.0; INIT_ZF = 0; ZF_AMP = 0.0;
CLOS = 0; % Closure model (0: =0 truncation, 1: semi coll, 2: Copy closure J+1 = J, P+2 = P) CLOS = 0; % Closure model (0: =0 truncation, 1: semi coll, 2: Copy closure J+1 = J, P+2 = P)
...@@ -63,15 +61,18 @@ JOBNUM = 00; ...@@ -63,15 +61,18 @@ JOBNUM = 00;
KPAR = 0.0; % Parellel wave vector component KPAR = 0.0; % Parellel wave vector component
HD_CO = 0.5; % Hyper diffusivity cutoff ratio HD_CO = 0.5; % Hyper diffusivity cutoff ratio
kmax = N*pi/L;% Highest fourier mode kmax = N*pi/L;% Highest fourier mode
MU = NU_HYP/(HD_CO*kmax)^4 % Hyperdiffusivity coefficient MU = NU_HYP/(HD_CO*kmax)^4; % Hyperdiffusivity coefficient
Nz = 1; % number of perpendicular planes (parallel grid)
q0 = 1.0; % safety factor
shear = 0.0; % magnetic shear
eps = 0.0; % inverse aspect ratio
%% PARAMETER SCANS %% PARAMETER SCANS
if 1 if 1
%% Parameter scan over PJ %% Parameter scan over PJ
% PA = [2 4 6 10]; % PA = [2 4 6 10];
% JA = [1 2 3 5]; % JA = [1 2 3 5];
PA = [2]; PA = [6];
JA = [1]; JA = [3];
DTA= DT*ones(size(JA));%./sqrt(JA); DTA= DT*ones(size(JA));%./sqrt(JA);
% DTA= DT; % DTA= DT;
mup_ = MU_P; mup_ = MU_P;
...@@ -87,23 +88,21 @@ for i = 1:Nparam ...@@ -87,23 +88,21 @@ for i = 1:Nparam
PMAXE = PA(i); PMAXI = PA(i); PMAXE = PA(i); PMAXI = PA(i);
JMAXE = JA(i); JMAXI = JA(i); JMAXE = JA(i); JMAXI = JA(i);
DT = DTA(i); DT = DTA(i);
% MU_P = mup_/PMAXE^2;
% MU_J = muj_/JMAXE^3;
setup setup
% Run linear simulation % Run linear simulation
% system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 1 ./../../../bin/helaz 1 1; cd ../../../wk']) % system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 1 ./../../../bin/helaz_3 1 1; cd ../../../wk'])
system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 6 ./../../../bin/helaz 1 6; cd ../../../wk']) system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 6 ./../../../bin/helaz_3 1 6; cd ../../../wk'])
% system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 6 ./../../../bin/helaz 2 3; cd ../../../wk']) % system(['cd ../results/',SIMID,'/',PARAMS,'/; mpirun -np 6 ./../../../bin/helaz_3 2 3; cd ../../../wk'])
% Load and process results % Load and process results
%% %%
filename = ['../results/',SIMID,'/',PARAMS,'/outputs_00.h5']; filename = ['../results/',SIMID,'/',PARAMS,'/outputs_00.h5'];
load_results load_results
tend = Ts2D(end); tstart = 0.4*tend; tend = Ts3D(end); tstart = 0.4*tend;
[~,itstart] = min(abs(Ts2D-tstart)); [~,itstart] = min(abs(Ts3D-tstart));
[~,itend] = min(abs(Ts2D-tend)); [~,itend] = min(abs(Ts3D-tend));
for ikx = 1:N/2+1 for ikx = 1:N/2+1
gamma_Ni00(i,ikx) = (LinearFit_s(Ts2D(itstart:itend)',(squeeze(abs(Ni00(ikx,1,itstart:itend)))))); gamma_Ni00(i,ikx) = (LinearFit_s(Ts3D(itstart:itend)',(squeeze(abs(Ni00(ikx,1,itstart:itend))))));
Ni00_ST(i,ikx,1:numel(Ts2D)) = squeeze((Ni00(ikx,1,:))); Ni00_ST(i,ikx,1:numel(Ts3D)) = squeeze((Ni00(ikx,1,:)));
end end
tend = Ts5D(end); tstart = 0.4*tend; tend = Ts5D(end); tstart = 0.4*tend;
[~,itstart] = min(abs(Ts5D-tstart)); [~,itstart] = min(abs(Ts5D-tstart));
......
...@@ -6,10 +6,10 @@ CLUSTER.TIME = '99:00:00'; % allocation time hh:mm:ss ...@@ -6,10 +6,10 @@ CLUSTER.TIME = '99:00:00'; % allocation time hh:mm:ss
%% PHYSICAL PARAMETERS %% PHYSICAL PARAMETERS
NU = 0.1; % Collision frequency NU = 0.1; % Collision frequency
ETAN = 1.0/0.6; % Density gradient drive (R/Ln) ETAN = 1.0/0.6; % Density gradient drive (R/Ln)
NU_HYP = 0.1; NU_HYP = 1.0;
%% GRID AND GEOMETRY PARAMETERS %% GRID AND GEOMETRY PARAMETERS
N = 100; % Frequency gridpoints (Nkx = N/2) N = 50; % Frequency gridpoints (Nkx = N/2)
L = 60; % Size of the squared frequency domain L = 30; % Size of the squared frequency domain
Nz = 10; % number of perpendicular planes (parallel grid) Nz = 10; % number of perpendicular planes (parallel grid)
q0 = 1.0; % safety factor q0 = 1.0; % safety factor
shear = 0.0; % magnetic shear shear = 0.0; % magnetic shear
...@@ -17,7 +17,7 @@ eps = 0.0; % inverse aspect ratio ...@@ -17,7 +17,7 @@ eps = 0.0; % inverse aspect ratio
P = 2; P = 2;
J = 1; J = 1;
%% TIME PARAMETERS %% TIME PARAMETERS
TMAX = 200; % Maximal time unit TMAX = 500; % Maximal time unit
DT = 1e-2; % Time step DT = 1e-2; % Time step
SPS0D = 1; % Sampling per time unit for profiler SPS0D = 1; % Sampling per time unit for profiler
SPS2D = 1; % Sampling per time unit for 2D arrays SPS2D = 1; % Sampling per time unit for 2D arrays
......
...@@ -18,13 +18,13 @@ NP_P = 2; % MPI processes along p ...@@ -18,13 +18,13 @@ NP_P = 2; % MPI processes along p
NP_KX = 24; % MPI processes along kx NP_KX = 24; % MPI processes along kx
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PHYSICAL PARAMETERS %% PHYSICAL PARAMETERS
NU = 0.05; % Collision frequency NU = 0.1; % Collision frequency
ETAN = 1.0/0.6; % Density gradient drive (R/Ln) ETAN = 1.0/0.6; % Density gradient drive (R/Ln)
NU_HYP = 10.0; NU_HYP = 1.0;
%% GRID PARAMETERS %% GRID PARAMETERS
N = 300; % Frequency gridpoints (Nkx = N/2) N = 100; % Frequency gridpoints (Nkx = N/2)
L = 100; % Size of the squared frequency domain L = 60; % Size of the squared frequency domain
Nz = 1; % number of perpendicular planes (parallel grid) Nz = 20; % number of perpendicular planes (parallel grid)
q0 = 1.0; % q factor () q0 = 1.0; % q factor ()
shear = 0.0; % magnetic shear shear = 0.0; % magnetic shear
eps = 0.0; % inverse aspect ratio eps = 0.0; % inverse aspect ratio
...@@ -43,11 +43,11 @@ JOB2LOAD= 0; ...@@ -43,11 +43,11 @@ JOB2LOAD= 0;
%% OPTIONS AND NAMING %% OPTIONS AND NAMING
% Collision operator % Collision operator
% (0 : L.Bernstein, 1 : Dougherty, 2: Sugama, 3 : Pitch angle ; +/- for GK/DK) % (0 : L.Bernstein, 1 : Dougherty, 2: Sugama, 3 : Pitch angle ; +/- for GK/DK)
CO = 2; CO = 1;
CLOS = 0; % Closure model (0: =0 truncation) CLOS = 0; % Closure model (0: =0 truncation)
NL_CLOS = 0; % nonlinear closure model (-2: nmax = jmax, -1: nmax = jmax-j, >=0 : nmax = NL_CLOS) NL_CLOS = 0; % nonlinear closure model (-2: nmax = jmax, -1: nmax = jmax-j, >=0 : nmax = NL_CLOS)
% SIMID = 'test_3D_marconi'; % Name of the simulation SIMID = 'test_3D_marconi'; % Name of the simulation
SIMID = 'HD_study'; % Name of the simulation % SIMID = 'HD_study'; % Name of the simulation
% SIMID = ['v3.0_P_',num2str(P),'_J_',num2str(J)]; % Name of the simulation % SIMID = ['v3.0_P_',num2str(P),'_J_',num2str(J)]; % Name of the simulation
NON_LIN = 1; % activate non-linearity (is cancelled if KXEQ0 = 1) NON_LIN = 1; % activate non-linearity (is cancelled if KXEQ0 = 1)
% INIT options % INIT options
......
MAT = results.iCa; % MAT = results.iCa;
figure % figure
suptitle('DGGK,P=6,J=3'); % suptitle('FCGK,P=6,J=3');
subplot(221) % subplot(221)
imagesc(log(abs(MAT))); % imagesc(log(abs(MAT)));
title('log abs') % title('log abs')
subplot(222) % subplot(222)
imagesc(imag(MAT)); colormap(bluewhitered) % imagesc(imag(MAT)); colormap(bluewhitered)
title('imag'); colorbar % title('imag'); colorbar
subplot(223) % subplot(223)
imagesc(imag(MAT)>0); % imagesc(imag(MAT)>0);
title('imag$>$0'); % title('imag$>$0');
subplot(224) % subplot(224)
imagesc(imag(MAT)<0); % imagesc(imag(MAT)<0);
title('imag$<$0'); % title('imag$<$0');
%
%
%% SGGK %% SGGK
P_ = 20; J_ = 10; P_ = 20; J_ = 10;
mat_file_name = '/home/ahoffman/HeLaZ/iCa/gk_sugama_P_20_J_10_N_150_kpm_8.0.h5'; mat_file_name = '/home/ahoffman/HeLaZ/iCa/gk_sugama_P_20_J_10_N_150_kpm_8.0.h5';
SGGK_self = h5read(mat_file_name,'/00149/Caapj/Ciipj'); SGGK_self = h5read(mat_file_name,'/00000/Caapj/Ciipj');
SGGK_ei = h5read(mat_file_name,'/00000/Ceipj/CeipjF')+h5read(mat_file_name,'/00000/Ceipj/CeipjT'); SGGK_ei = h5read(mat_file_name,'/00000/Ceipj/CeipjF')+h5read(mat_file_name,'/00000/Ceipj/CeipjT');
SGGK_ie = h5read(mat_file_name,'/00000/Ciepj/CiepjF')+h5read(mat_file_name,'/00000/Ciepj/CiepjT'); SGGK_ie = h5read(mat_file_name,'/00000/Ciepj/CiepjF')+h5read(mat_file_name,'/00000/Ciepj/CiepjT');
figure figure
MAT = 1i*SGGK_self; suptitle('SGGK ii,P=20,J=10, k=8'); MAT = 1i*SGGK_self; suptitle('SGGK ii,P=20,J=10, k=0');
% MAT = 1i*SGGK_ei; suptitle('SGGK ei,P=20,J=10'); % MAT = 1i*SGGK_ei; suptitle('SGGK ei,P=20,J=10');
% MAT = 1i*SGGK_ie; suptitle('SGGK ie,P=20,J=10'); % MAT = 1i*SGGK_ie; suptitle('SGGK ie,P=20,J=10');
subplot(221) subplot(221)
...@@ -42,13 +42,38 @@ subplot(224) ...@@ -42,13 +42,38 @@ subplot(224)
%% PAGK %% PAGK
P_ = 20; J_ = 10; P_ = 20; J_ = 10;
mat_file_name = '/home/ahoffman/HeLaZ/iCa/gk_pitchangle_8_P_20_J_10_N_150_kpm_8.0.h5'; mat_file_name = '/home/ahoffman/HeLaZ/iCa/gk_pitchangle_8_P_20_J_10_N_150_kpm_8.0.h5';
PAGK_self = h5read(mat_file_name,'/00149/Caapj/Ceepj'); PAGK_self = h5read(mat_file_name,'/00000/Caapj/Ceepj');
% PAGK_ei = h5read(mat_file_name,'/00000/Ceipj/CeipjF')+h5read(mat_file_name,'/00000/Ceipj/CeipjT'); % PAGK_ei = h5read(mat_file_name,'/00000/Ceipj/CeipjF')+h5read(mat_file_name,'/00000/Ceipj/CeipjT');
% PAGK_ie = h5read(mat_file_name,'/00000/Ciepj/CiepjF')+h5read(mat_file_name,'/00000/Ciepj/CiepjT'); % PAGK_ie = h5read(mat_file_name,'/00000/Ciepj/CiepjF')+h5read(mat_file_name,'/00000/Ciepj/CiepjT');
figure figure
MAT = 1i*PAGK_self; suptitle('PAGK ii,P=20,J=10, k=8'); MAT = 1i*PAGK_self; suptitle('PAGK ii,P=20,J=10, k=0');
subplot(221)
imagesc(abs(MAT));
title('log abs')
subplot(222)
imagesc(imag(MAT)); colormap(bluewhitered)
title('imag'); colorbar
subplot(223)
imagesc(imag(MAT)>0);
title('imag$>$0');
subplot(224)
imagesc(imag(MAT)<0);
title('imag$<$0');
%% SGGK
P_ = 6; J_ = 3;
mat_file_name = '/home/ahoffman/HeLaZ/iCa/gk_coulomb_P_6_J_3_N_150_kpm_8.0.h5';
FCGK_self = h5read(mat_file_name,'/00000/Caapj/Ciipj');
FCGK_ei = h5read(mat_file_name,'/00000/Ceipj/CeipjF')+h5read(mat_file_name,'/00000/Ceipj/CeipjT');
FCGK_ie = h5read(mat_file_name,'/00000/Ciepj/CiepjF')+h5read(mat_file_name,'/00000/Ciepj/CiepjT');
figure
MAT = 1i*FCGK_self; suptitle('FCGK ii,P=20,J=10, k=0');
% MAT = 1i*SGGK_ei; suptitle('FCGK ei,P=20,J=10');
% MAT = 1i*SGGK_ie; suptitle('FCGK ie,P=20,J=10');
subplot(221) subplot(221)
imagesc(abs(MAT)); imagesc(abs(MAT));
title('log abs') title('log abs')
...@@ -61,3 +86,4 @@ subplot(223) ...@@ -61,3 +86,4 @@ subplot(223)
subplot(224) subplot(224)
imagesc(imag(MAT)<0); imagesc(imag(MAT)<0);
title('imag$<$0'); title('imag$<$0');
\ No newline at end of file
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