Table performance / general performance / vectorizing - matlab

Question

I implemented a 4D Interpolation in matlab, where performance is really important. The interpolation method is a nearest neighbor interpolation based on a delaunay triangulation. As I am quite new to matlab coding, I want to ask, if I should use arrays or cells instead of tables, because of their poor performance. Also the general question, if you see anything, where I can speed up my code. I already saved the mat files in v6 so this is not an option. Below the text you see the code of the main program. After that the code for the 2D interpolation.
the tables I loaded in consist of 7 coloums filled with AeroDataId, X_C coordinate, CP (pressure derivative), Mach number, lift coefficient, ReynoldsNumber and Transition. One AeroDataId belongs to in the most cases 280 x_c coordinates with the different pressure coefficients.
Filtering all the data seems to be faster than using sql queries.
clc
close
clear
%% ReynoldsNumbers and Transitions known in the database
ReynoldsNumbers=[1e6;1.5e6;2.5e6;5e6;8e6;14e6;25e6;50e6;100e6];
Transition=[0;0.1;0.2;0.3;0.4;0.5;0.6;0.7;0.8;0.9];
%% parameters
Ma=0.85;
C_l=0.345;
Tl=0.15;
Re=55e6;
AirfoilId=0;
delta=0.015;
delta_ini=0.15;
%% try to find the neighbours of the parameters, which already exist in the database
tic
Re_u=ReynoldsNumbers(ReynoldsNumbers==Re);
Tl_u=Transition(Transition==Tl);
Tl_o=[];
Re_o=[];
if isempty(Re_u)
Re_u_index=nearestpoint(Re,ReynoldsNumbers,'previous');
Re_o_index=nearestpoint(Re,ReynoldsNumbers,'next');
Re_o=ReynoldsNumbers(Re_o_index);
Re_u=ReynoldsNumbers(Re_u_index);
if Re < 1e6
Re_u=1e6;
Re_o=1.5e6;
elseif Re > 100e6
Re_u=50e6;
Re_o=100e6;
end
end
if isempty(Tl_u)
Tl_u_index=nearestpoint(Tl,Transition,'previous');
Tl_o_index=nearestpoint(Tl,Transition,'next');
Tl_u=Transition(Tl_u_index);
Tl_o=Transition(Tl_o_index);
end
toc
%% load data based on the airfoilId size of new_upper_airfoil 25000000x7 table
if AirfoilId==0
load('new_upper_airfoil_all_0');
load('new_lower_airfoil_all_0');
elseif AirfoilId==1
load('new_upper_airfoil_all_1');
load('new_lower_airfoil_all_1');
elseif AirfoilId==2
load('new_upper_airfoil_all_2');
load('new_lower_airfoil_all_2');
end
%% no need to to make all the interpolation with the whole data, only a specific delta
new_upper_airfoil=new_upper_airfoil_all(new_upper_airfoil_all.Ma < (Ma+delta_ini) & new_upper_airfoil_all.Ma > (Ma-delta_ini) & new_upper_airfoil_all.CL_res < (C_l+delta_ini) & new_upper_airfoil_all.CL_res > (C_l-delta_ini),2:7);
new_lower_airfoil=new_lower_airfoil_all(new_lower_airfoil_all.Ma < (Ma+delta_ini) & new_lower_airfoil_all.Ma > (Ma-delta_ini) & new_lower_airfoil_all.CL_res < (C_l+delta_ini) & new_lower_airfoil_all.CL_res > (C_l-delta_ini),2:7);
%% filter data for the first 2D - Interpoaltion and execute it
new_upper_airfoil1=new_upper_airfoil(new_upper_airfoil.ReynoldsNumber==Re_u & new_upper_airfoil.Transition==Tl_u,1:4);
new_lower_airfoil1=new_lower_airfoil(new_lower_airfoil.ReynoldsNumber==Re_u & new_lower_airfoil.Transition==Tl_u,1:4);
DV1=delaunay_nearest(new_upper_airfoil1, new_lower_airfoil1, Ma, C_l, delta);
DV_1=table(DV1.X_C, DV1.CP, repmat(Re_u,280,1),repmat(Tl_u,280,1),'VariableNames',{'X_C','CP','Re','Tl'});
%% secound
if ~isempty(Tl_o)
new_upper_airfoil2=new_upper_airfoil(new_upper_airfoil.ReynoldsNumber==Re_u & new_upper_airfoil.Transition==Tl_o,1:4);
new_lower_airfoil2=new_lower_airfoil(new_lower_airfoil.ReynoldsNumber==Re_u & new_lower_airfoil.Transition==Tl_o,1:4);
DV2=delaunay_nearest(new_upper_airfoil2, new_lower_airfoil2, Ma, C_l, delta);
DV_2=table(DV2.X_C, DV2.CP, repmat(Re_u,280,1), repmat(Tl_o,280,1),'VariableNames',{'X_C','CP','Re','Tl'});
else
DV_2=[];
end
%% third
if ~isempty(Re_o)
new_upper_airfoil3=new_upper_airfoil(new_upper_airfoil.ReynoldsNumber==Re_o & new_upper_airfoil.Transition==Tl_u,1:4);
new_lower_airfoil3=new_lower_airfoil(new_lower_airfoil.ReynoldsNumber==Re_o & new_lower_airfoil.Transition==Tl_u,1:4);
DV3=delaunay_nearest(new_upper_airfoil3, new_lower_airfoil3, Ma, C_l, delta);
DV_3=table(DV3.X_C, DV3.CP, repmat(Re_o,280,1),repmat(Tl_u,280,1),'VariableNames',{'X_C','CP','Re','Tl'});
else
DV_3=[];
end
%% fourth
if ~isempty(Re_o) && ~isempty(Tl_o)
new_upper_airfoil4=new_upper_airfoil(new_upper_airfoil.ReynoldsNumber==Re_o & new_upper_airfoil.Transition==Tl_o,1:4);
new_lower_airfoil4=new_lower_airfoil(new_lower_airfoil.ReynoldsNumber==Re_o & new_lower_airfoil.Transition==Tl_o,1:4);
DV4=delaunay_nearest(new_upper_airfoil4, new_lower_airfoil4, Ma, C_l, delta);
DV_4=table(DV4.X_C, DV4.CP, repmat(Re_o,280,1),repmat(Tl_o,280,1),'VariableNames',{'X_C','CP','Re','Tl'});
else
DV_4=[];
end
%% Interpolation of the 4 2D Interpolations
DV_inter=[DV_1;DV_2;DV_3;DV_4];
if size(DV_inter,1)==280
DV=DV_1(:,1:2);
% figure
% hold on
% plot(DV.X_C,-DV.CP,'bl-');
% grid on;
% xlabel('X_C');
% ylabel('Cp');
%
else
%% interpolation with inverse distance weighted interpoaltion
load('x_c0');
DV=zeros(281,2);
for x_c=1:1:280
x_c_inter=x_c0(x_c);
Find=DV_inter(DV_inter.X_C==x_c_inter,:);
cp_inter=IDW(Find.Re, Find.Tl,Find.CP,Re,Tl,-2,'ng',2);
DV(x_c,:)=[x_c_inter,cp_inter];
end
DV(281,:)=DV(1,:);
figure
hold on
plot(DV(:,1),-DV(:,2),'r-');
grid on;
xlabel('X_C');
ylabel('Cp');
end
function DV = delaunay_nearest(new_upper_airfoil,new_lower_airfoil,Ma,C_l,delta)
Error=true;
load('x_c0');
while(Error)
%% build table for the pressure distribution
DV=array2table(zeros(280,2),'VariableNames',{'X_C','CP'});
%% another smaller delta for the interpolation (if too small the exception will be catched and the interpolation is restarted with a higher delta
new_upper_airfoil_loop=new_upper_airfoil(new_upper_airfoil.Ma < (Ma+delta) & new_upper_airfoil.Ma > (Ma-delta) & new_upper_airfoil.CL_res < (C_l+delta) & new_upper_airfoil.CL_res > (C_l-delta),:);
new_lower_airfoil_loop=new_lower_airfoil(new_lower_airfoil.Ma < (Ma+delta) & new_lower_airfoil.Ma > (Ma-delta) & new_lower_airfoil.CL_res < (C_l+delta) & new_lower_airfoil.CL_res > (C_l-delta),:);
%% try to build the delaunay triangulation
try
DT=delaunayTriangulation(new_upper_airfoil_loop.Ma,new_upper_airfoil_loop.CL_res);
% figure
% hold on;
% triplot(DT);
% plot(Ma,C_l,'ro');
%% find nearest neighbor
pointindex=dsearchn(DT.Points,[Ma,C_l]);
point=DT.Points(pointindex,:);
Error=0;
catch
delta=delta+0.005;
disp('Die Deltas wurden um 0.005 erhöht, da der Bereich der Daten zu klein war.');
continue;
end
%% search for the nearest neighbor
new_upper_airfoil_loop=new_upper_airfoil_loop(new_upper_airfoil_loop.Ma==point(1,1) & new_upper_airfoil_loop.CL_res==point(1,2),1:2);
new_lower_airfoil_loop=new_lower_airfoil_loop(new_lower_airfoil_loop.Ma==point(1,1) & new_lower_airfoil_loop.CL_res==point(1,2),1:2);
%% 2D Interpolation for all 280 points of the airfoil with the same x/c coordinates
for x_c=1:1:280
x_c_inter=x_c0(x_c);
%% upper_airfoil
if x_c < 146
FIND=new_upper_airfoil_loop(abs(new_upper_airfoil_loop.X_C-x_c_inter)<0.0005,:);
if(isempty(FIND))
leftNeighborIndex=nearestpoint(x_c_inter,new_upper_airfoil_loop.X_C,'previous');
if isnan(leftNeighborIndex)
leftNeighborIndex=1;
end
rightNeighborIndex=leftNeighborIndex+1;
if rightNeighborIndex > height(new_upper_airfoil_loop)
rightNeighborIndex=leftNeighborIndex-1;
end
average=interp1([new_upper_airfoil_loop.X_C(leftNeighborIndex,:),new_upper_airfoil_loop.X_C(rightNeighborIndex,:)], [new_upper_airfoil_loop.CP(leftNeighborIndex,:),new_upper_airfoil_loop.CP(rightNeighborIndex,:)], x_c_inter, 'linear','extrap');
FIND.X_C(1,:)=x_c_inter;
FIND.CP(1,:)=average;
DV(x_c,:)=FIND;
else
FIND.X_C(1,1)=x_c_inter;
DV(x_c,:)=FIND(1,:);
end
end
%% lower airfoil
if x_c > 145
FIND=new_lower_airfoil_loop(abs(new_lower_airfoil_loop.X_C-x_c_inter)<0.00008,:);
if(isempty(FIND))
leftNeighborIndex=nearestpoint(x_c_inter,new_lower_airfoil_loop.X_C,'previous');
if isnan(leftNeighborIndex)
leftNeighborIndex=height(new_lower_airfoil_loop);
end
rightNeighborIndex=leftNeighborIndex-1;
average=interp1([new_lower_airfoil_loop.X_C(leftNeighborIndex,:),new_lower_airfoil_loop.X_C(rightNeighborIndex,:)], [new_lower_airfoil_loop.CP(leftNeighborIndex,:),new_lower_airfoil_loop.CP(rightNeighborIndex,:)], x_c_inter, 'linear','extrap');
FIND.X_C(1,:)=x_c_inter;
FIND.CP(1,:)=average;
DV(x_c,:)=FIND;
else
FIND.X_C(1,1)=x_c_inter;
DV(x_c,:)=FIND(1,:);
end
end
end
end
end