vertical dimensions mismatch ode45

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Imene Yed
Imene Yed 2021-5-22
编辑： Sulaymon Eshkabilov 2021-5-23
I'm trying to solve a system of ODE with 43 equations and 156 constants ,here is my code:
clear all,clc
%temperature
T=17000
%constante k:
k1=2.36 *(1e-12)*(T/300)^(-0.29)*exp(17.60/T)
k2 =3.24 *(1e-12) *(T/300)^(-0.66)
k3=3.50 *(1e-12)*(T/300)^(-0.53)* exp(3.20/T)
..
k156=...
%initial conditions
[IC1,IC2,IC3,IC4,IC5,IC6,IC7,IC8,IC9,IC10...,IC43]=deal(10^19)
IC=[IC1 IC2 IC3 IC4 IC5 IC6 IC7 IC8 IC9 IC10 IC11 ..... IC43]
%time
t0 = 0;
tf = 1E-7;
t1 = 5E-12;
f= @(t,n) [k1*n(2)*n(42)+k15*n(5)*n(9)+k16*n(5)*n(26)+k25*n(4)*n(26)+k29*n(4)*n(9)+k33*n(4)*n(11)+...
.. ]
%resolving
[t,n]= ode45(f,[0 5E-12 1E-7], IC )
plot(t,n)
error: vertical dimensions mismatch (13x1 vs 1x2)
error: called from
conc>@<anonymous> at line 246 column 506
starting_stepsize at line 53 column 5
ode45 at line 196 column 25
conc at line 247 column 6
  16 个评论
显示 14更早的评论
Torsten
Torsten 2021-5-22
global k1 k2 k3 ...
...
[T,N] = ode45(@fun,[0.0 5.0e-12 1e-7],IC);
plot(T,N)
end
function dn = fun(t,n)
global k1 k2 ...
dn = zeros(43,1);
dn(1) = k1*n(2)*n(42) + k15*n(5)...; % 72 characters long, then skip
dn(2) = -k1*n(2)*n(42) -k5*n(5)*n(15) ...; % 72 characters long, then skip
...
end
Imene Yed
Imene Yed 2021-5-22
thnk you so much I will try it then I will tell you if it works ,anyway thank you for all your answers.

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采纳的回答

Sulaymon Eshkabilov
Hi,
While defining your fcn handle, you have omitted several empty spaces that created additonal elements in your fcn handle (f). Now all errs are removed and it is works. Your system response is very unstable. You need to take care of your initial conditions. Here is the corrected fcn handle:
...
IC = 1e19*ones(1,43); % Test: IC = 1e9*ones(1,43)
%%
F=@(t,n)([k1*n(2)*n(42)+k15*n(5)*n(9)+k16*n(5)*n(26)+k25*n(4)*n(26)+k29*n(4)*n(9)+k33*n(4)*n(11)+k39*n(7)*n(26)+k40*n(7)*n(27)+k43*n(7)*n(9)+k44*n(7)*n(12)+k48*n(9)*n(9)+k59*n(11)*n(42)+k72*n(2)*n(24)+k104*n(3)*n(5)+k105*n(3)*n(8)+k106*n(3)*n(25)+k117*n(18)*n(2)+k119*n(3)*n(43)+k122*n(11)*n(43)+k124*n(13)*n(43)+k130*n(22)*n(43)-k4*n(1)*n(37)-k8*n(1)*n(15)-k9*n(1)*n(26)-k10*n(1)*n(24)-k11*n(1)*n(20)-k12*n(1)*n(35)-k13*n(1)*n(22)-k61*n(2)*n(1)-k64*n(1)*n(13)-k65*n(1)*n(4)-k66*n(1)*n(9)-k67*n(1)*n(5)-k68*n(1)*n(1)-k69*n(1)*n(7)-k73*n(1)*n(27)-k74*n(1)*n(11)-k75*n(1)*n(23)-k76*n(1)*n(21)-k77*n(1)*n(19)-k118*n(1)*n(43)-k132*n(1)*n(42)-k136*n(1)*n(3)-k137*n(1)*n(12)-k138*n(1)*n(14)-k139*n(1)*n(6)-2*k164*n(7)*n(1)*n(1)+k164*n(7)*n(1)^(2)-k163*n(1)*n(15)*n(4)+k163*n(1)*n(15)*n(4)-k165*n(1)*n(32)*n(4)+k165*n(1)*n(32)*n(4);
-k1*n(2)*n(42)-k5*n(2)*n(15)-k6*n(2)*n(30)-k7*n(2)*n(36)-k61*n(2)*n(1)-k62*n(2)*n(7)-k63*n(2)*n(4)-k72*n(2)*n(24)-k117*n(18)*n(2)+k45*n(7)*n(11)+k73*n(1)*n(27)+k74*n(1)*n(11)+k75*n(1)*n(23)+k76*n(1)*n(21)+k77*n(1)*n(19)+k118*n(1)*n(43)+k122*n(11)*n(43);
k32*n(4)*n(12)+k132*n(1)*n(42)-k14*n(3)*n(24)-k104*n(3)*n(5)-k105*n(3)*n(8)-k106*n(3)*n(25)-k119*n(3)*n(43)-k136*n(1)*n(3)-k140*n(3)*n(4)-k141*n(3)*n(15)-k142*n(3)*n(7);
k2*n(5)*n(42)+k8*n(1)*n(15)+k10*n(1)*n(24)+k13*n(1)*n(22)+k14*n(3)*n(24)+k35*n(7)*n(15)+k36*n(7)*n(19)+k37*n(7)*n(24)+k38*n(7)*n(32)+k52*n(15)*n(24)+k53*n(15)*n(20)+k55*n(15)*n(22)+k56*n(15)*n(26)+k78*n(5)*n(9)+k79*n(5)*n(22)+k80*n(5)*n(30)+k81*n(5)*n(15)+k84*n(6)*n(15)+k85*n(6)*n(26)+k104*n(3)*n(5)+2*k107*n(5)*n(6)+k108*n(5)*n(18)+k109*n(6)*n(8)+k120*n(6)*n(43)+2*k126*n(15)*n(43)+k128*n(19)*n(43)+k130*n(22)*n(43)+k131*n(24)*n(43)+k162*n(42)*n(4)*n(15)-k19*n(4)*n(24)-k20*n(4)*n(32)-k21*n(4)*n(30)-k22*n(4)*n(30)-k23*n(4)*n(20)-k24*n(4)*n(36)-k25*n(4)*n(26)-k26*n(4)*n(26)-k27*n(4)*n(13)-k28*n(4)*n(35)-k29*n(4)*n(9)-k30*n(4)*n(21)-k31*n(4)*n(14)-k32*n(4)*n(12)-k33*n(4)*n(11)-k63*n(2)*n(4)-k65*n(1)*n(4)-2*k70*n(4)*n(4)-k82*n(4)*n(21)-k83*n(4)*n(23)-k133*n(4)*n(42)-k140*n(3)*n(4)-k143*n(4)*n(6)-k144*n(4)*n(12)-k161*n(42)*n(4)*n(15)-k162*n(42)*n(4)*n(15)-k163*n(1)*n(15)*n(4)-k165*n(1)*n(32)*n(4);
k5*n(2)*n(15)+k34*n(8)*n(15)+k82*n(4)*n(21)+k83*n(4)*n(23)+k128*n(19)*n(43)-k19*n(4)*n(24)-k20*n(4)*n(32)-k21*n(4)*n(30)-k22*n(4)*n(30)-k23*n(4)*n(20)-k24*n(4)*n(36)-k25*n(4)*n(26)-k26*n(4)*n(26)-k27*n(4)*n(13)-k28*n(4)*n(35)-k29*n(4)*n(9)-k30*n(4)*n(21)-k31*n(4)*n(14)-k32*n(4)*n(12)-k33*n(4)*n(11)-k63*n(2)*n(4)-k65*n(1)*n(4)-2*k70*n(4)*n(4)-k82*n(4)*n(21)-k83*n(4)*n(23)-k133*n(4)*n(42)-k140*n(3)*n(4)-k143*n(4)*n(6)-k144*n(4)*n(12)-k161*n(42)*n(4)*n(15)-k162*n(42)*n(4)*n(15)-k163*n(1)*n(15)*n(4)-k165*n(1)*n(32)*n(4);
k133*n(4)*n(42)+k161*n(42)*n(4)*n(15)-k84*n(6)*n(15)-k85*n(6)*n(26)-k107*n(5)*n(6)-k109*n(6)*n(8)-k120*n(6)*n(43)-k139*n(1)*n(6)-k143*n(4)*n(6)-k145*n(6)*n(24)-k146*n(6)*n(22)-k147*n(6)*n(7);
k3*n(8)*n(42)+k9*n(1)*n(26)+k11*n(1)*n(20)+k18*n(5)*n(20)+k19*n(4)*n(24)+k23*n(4)*n(20)+k26*n(4)*n(26)+k30*n(4)*n(21)+2*k60*n(21)*n(42)+k86*n(8)*n(15)+k87*n(8)*n(9)+k88*n(8)*n(22)+k89*n(8)*n(26)+k90*n(8)*n(24)+k105*n(3)*n(8)+k109*n(6)*n(8)+k110*n(8)*n(18)+k111*n(8)*n(12)+k112*n(8)*n(28)+k113*n(8)*n(14)+2*k129*n(20)*n(43)+k131*n(24)*n(43)+2*k159*n(20)*n(42)-k35*n(7)*n(15)-k36*n(7)*n(19)-k37*n(7)*n(24)-k38*n(7)*n(32)-k39*n(7)*n(26)-k40*n(7)*n(27)-k41*n(7)*n(13)-k42*n(7)*n(14)-k43*n(7)*n(9)-k44*n(7)*n(12)-k45*n(7)*n(11)-k46*n(7)*n(35)-k62*n(2)*n(7)-k69*n(1)*n(7)-k71*n(8)*n(7)-k91*n(7)*n(21)-k142*n(3)*n(7)-k147*n(6)*n(7)-k164*n(7)*n(1)*n(1);
k91*n(7)*n(21)-k3*n(8)*n(42)-k34*n(8)*n(15)-k71*n(8)*n(7)-k86*n(8)*n(15)-k87*n(8)*n(9)-k88*n(8)*n(22)-k89*n(8)*n(26)-k90*n(8)*n(24)-k105*n(3)*n(8)-k109*n(6)*n(8)-k110*n(8)*n(18)-k111*n(8)*n(12)-k112*n(8)*n(28)-k113*n(8)*n(14);
k9*n(1)*n(26)+k12*n(1)*n(35)+k13*n(1)*n(22)+k27*n(4)*n(13)+k41*n(7)*n(13)+k68*n(1)*n(1)+k74*n(1)*n(11)+k94*n(11)*n(24)+k111*n(8)*n(12)+k115*n(12)*n(25)+k121*n(9)*n(43)+k123*n(12)*n(43)+k124*n(13)*n(43)+k136*n(1)*n(3)+k153*n(10)*n(42)+k154*n(10)^(2)+k155*n(10)*n(1)-k15*n(5)*n(9)-k29*n(4)*n(9)-k43*n(7)*n(9)-k47*n(9)*n(15)-2*k48*n(9)*n(9)-k49*n(9)*n(19)-k66*n(1)*n(9)-k78*n(5)*n(9)-k87*n(8)*n(9)-k92*n(9)*n(23)-k93*n(9)*n(27)-k121*n(9)*n(43)-k134*n(9)*n(42)-k148*n(9)*n(12)-k150*n(9)*n(42);
k150*n(9)*n(42)-k153*n(10)*n(42)-k154*n(10)^(2)-k155*n(10)*n(1);
k61*n(2)*n(1)+k78*n(5)*n(9)+k87*n(8)*n(9)+k92*n(9)*n(23)+k93*n(9)*n(27)-k33*n(4)*n(11)-k45*n(7)*n(11)-k50*n(11)*n(15)-k59*n(11)*n(42)-k74*n(1)*n(11)-k94*n(11)*n(24)-k122*n(11)*n(43);
-k32*n(4)*n(12)-k44*n(7)*n(12)-k111*n(8)*n(12)-k115*n(12)*n(25)-k123*n(12)*n(43)-k137*n(1)*n(12)-k144*n(4)*n(12)-k148*n(9)*n(12)-k149*n(12)*n(13)+k31*n(4)*n(14)+k42*n(7)*n(14)+k134*n(9)*n(42);
k48*n(9)*n(9)+k66*n(1)*n(9)+k113*n(8)*n(14)+k114*n(14)*n(25)+k125*n(14)*n(43)+k137*n(1)*n(12)-k27*n(4)*n(13)-k41*n(7)*n(13)-k64*n(1)*n(13)-k124*n(13)*n(43)-k135*n(13)*n(42)-k149*n(12)*n(13);
k135*n(13)*n(42)-k31*n(4)*n(14)-k42*n(7)*n(14)-k113*n(8)*n(14)-k114*n(14)*n(25)-k125*n(14)*n(43)-k138*n(1)*n(14);
k17*n(5)*n(32)+k19*n(4)*n(24)+k20*n(4)*n(32)+k21*n(4)*n(30)+k57*n(24)*n(24)+k70*n(4)*n(4)+k77*n(1)*n(19)+k97*n(19)*n(32)+k98*n(19)*n(24)+k108*n(5)*n(18)+k110*n(8)*n(18)+k116*n(18)*n(25)+k117*n(18)*n(2)+k127*n(18)*n(43)+k143*n(4)*n(6)+2*k156*n(18)*n(15)+2*k157*n(18)*n(16)+2*k158*n(18)*n(17)+k161*n(42)*n(4)*n(15)-k5*n(2)*n(15)-k8*n(1)*n(15)-k34*n(8)*n(15)-k35*n(7)*n(15)-k47*n(9)*n(15)-k50*n(11)*n(15)-k51*n(15)*n(37)-k52*n(15)*n(24)-k53*n(15)*n(20)-k54*n(15)*n(27)-k55*n(15)*n(22)-k56*n(15)*n(26)-k81*n(5)*n(15)-k84*n(6)*n(15)-k86*n(8)*n(15)-k95*n(15)*n(21)-k96*n(15)*n(23)-k126*n(15)*n(43)-k141*n(3)*n(15)-k151*n(15)*n(42)-k152*n(15)*n(42)-k156*n(18)*n(15)-k161*n(42)*n(4)*n(15)-k162*n(42)*n(4)*n(15)-k163*n(1)*n(15)*n(4);
k151*n(42)*n(15)-k157*n(16)*n(18);
k152*n(42)*n(15)-k158*n(17)*n(18);
k84*n(6)*n(15)+k162*n(42)*n(4)*n(15)-k108*n(5)*n(18)-k110*n(8)*n(18)-k116*n(18)*n(25)-k117*n(18)*n(2)-k127*n(18)*n(43)-k156*n(18)*n(15)-k157*n(18)*n(16)-k158*n(18)*n(17);
k81*n(5)*n(15)+k86*n(8)*n(15)+k95*n(15)*n(21)+k96*n(15)*n(23)-k36*n(7)*n(19)-k49*n(9)*n(19)-k77*n(1)*n(19)-k97*n(19)*n(32)-k98*n(19)*n(24)-k128*n(19)*n(43);
k21*n(4)*n(30)+k37*n(7)*n(24)+k39*n(7)*n(26)+k57*n(24)*n(24)+k76*n(1)*n(21)+k82*n(4)*n(21)+k91*n(7)*n(21)+k95*n(15)*n(21)+k99*n(21)*n(26)+k100*n(21)*n(22)-k11*n(1)*n(20)-k18*n(5)*n(20)-k23*n(4)*n(20)-k53*n(15)*n(20)-k129*n(20)*n(43)-k159*n(20)*n(42)-k160*n(20)*n(42);
k40*n(7)*n(27)+k71*n(8)*n(7)+k160*n(20)*n(42)-k30*n(4)*n(21)-k60*n(21)*n(42)-k76*n(1)*n(21)-k82*n(4)*n(21)-k91*n(7)*n(21)-k95*n(15)*n(21)-k99*n(21)*n(26)-k100*n(21)*n(22);
k4*n(1)*n(37)+k5*n(2)*n(15)+k8*n(1)*n(15)+k24*n(4)*n(36)+k26*n(4)*n(26)+k27*n(4)*n(13)+k28*n(4)*n(35)+k29*n(4)*n(9)+k31*n(4)*n(14)+k32*n(4)*n(12)+2*k47*n(9)*n(15)+k49*n(9)*n(19)+k50*n(11)*n(15)+k54*n(15)*n(27)+k58*n(24)*n(37)+k65*n(1)*n(4)+k75*n(1)*n(23)+k83*n(4)*n(23)+k92*n(9)*n(23)+k96*n(15)*n(23)+k102*n(24)*n(23)+k139*n(1)*n(6)+k140*n(3)*n(4)-k13*n(1)*n(22)-k55*n(15)*n(22)-k79*n(5)*n(22)-k88*n(8)*n(22)-k100*n(21)*n(22)-k101*n(22)*n(27)-k130*n(22)*n(43)-k146*n(6)*n(22);
k7*n(2)*n(36)+k15*n(5)*n(9)+k33*n(4)*n(11)+k49*n(9)*n(19)+k50*n(11)*n(15)+k63*n(2)*n(4)+k67*n(1)*n(5)+k79*n(5)*n(22)+k88*n(8)*n(22)+k100*n(21)*n(22)+k101*n(22)*n(27)-k75*n(1)*n(23)-k83*n(4)*n(23)-k92*n(9)*n(23)-k96*n(15)*n(23)-k102*n(24)*n(23);
k20*n(4)*n(32)+k22*2*n(4)*n(30)+k23*n(4)*n(20)+k24*n(4)*n(36)+k25*n(4)*n(26)+k34*n(8)*n(15)+k35*n(7)*n(15)+k51*n(15)*n(37)+k106*n(3)*n(25)+k114*n(14)*n(25)+k115*n(12)*n(25)+k116*n(18)*n(25)+k147*n(6)*n(7)-k10*n(1)*n(24)-k14*n(3)*n(24)-k19*n(4)*n(24)-k37*n(7)*n(24)-k52*n(15)*n(24)-k57*2*n(24)*n(24)-k58*n(24)*n(37)-k72*n(2)*n(24)-k90*n(8)*n(24)-k94*n(11)*n(24)-k98*n(19)*n(24)-k102*n(24)*n(23)-k103*n(24)*n(27)-k131*n(24)*n(43)-k145*n(6)*n(24);
k6*n(2)*n(30)+k16*n(5)*n(26)+k17*n(5)*n(32)+k18*n(5)*n(20)+k30*n(4)*n(21)+k36*n(7)*n(19)+k54*n(15)*n(27)+k72*n(2)*n(24)+k90*n(8)*n(24)+k94*n(11)*n(24)+k98*n(19)*n(24)+k102*n(24)*n(23)+k103*n(24)*n(27)-k106*n(3)*n(25)-k114*n(14)*n(25)-k115*n(12)*n(25)-k116*n(18)*n(25);
k4*n(1)*n(37)+k6*n(2)*n(30)+k7*n(2)*n(36)+k10*n(1)*n(24)+k11*n(1)*n(20)+k12*n(1)*n(35)+k28*n(4)*n(35)+k41*n(7)*n(13)+k42*n(7)*n(14)+k43*n(7)*n(9)+k45*n(7)*n(11)+k46*2*n(7)*n(35)+k69*n(1)*n(7)+k73*n(1)*n(27)+k93*n(9)*n(27)+k101*n(22)*n(27)+k103*n(24)*n(27)+k112*n(8)*n(28)+k142*n(3)*n(7)+k164*n(7)*n(1)*n(1)-k9*n(1)*n(26)-k16*n(5)*n(26)-k25*n(4)*n(26)-k26*n(4)*n(26)-k39*n(7)*n(26)-k56*n(15)*n(26)-k85*n(6)*n(26)-k89*n(8)*n(26)-k99*n(21)*n(26);
k62*n(2)*n(7)+k89*n(8)*n(26)+k99*n(21)*n(26)-k40*n(7)*n(27)-k54*n(15)*n(27)-k73*n(1)*n(27)-k93*n(9)*n(27)-k101*n(22)*n(27)-k103*n(24)*n(27);
k14*n(3)*n(24)+k44*n(7)*n(12)+k85*n(6)*n(26)-k112*n(8)*n(28);
k163*n(1)*n(15)*n(4);
k38*n(7)*n(32)+k53*n(15)*n(20)+k58*n(24)*n(37)-k6*n(2)*n(30)-k21*n(4)*n(30)-k22*n(4)*n(30)-k80*n(5)*n(30);
k80*n(5)*n(30);
k52*n(15)*n(24)+k145*n(6)*n(24)-k17*n(5)*n(32)-k20*n(4)*n(32)-k38*n(7)*n(32)-k97*n(19)*n(32)-k165*n(1)*n(32)*n(4);
k97*n(19)*n(32);
k51*n(15)*n(37)+k55*n(15)*n(22)+k141*n(3)*n(15)+k146*n(6)*n(22);
-k12*n(1)*n(35)-k28*n(4)*n(35)-k46*n(7)*n(35);
-k7*n(2)*n(36)-k24*n(4)*n(36);
-k4*n(1)*n(37)-k51*n(15)*n(37)-k58*n(24)*n(37)+k56*n(15)*n(26);
k165*n(1)*n(32)*n(4);
k144*n(4)*n(12);
k64*n(1)*n(13)+k138*n(1)*n(14)+k148*n(9)*n(12);
k149*n(12)*n(13);
k118*n(1)*n(43)+k119*n(3)*n(43)+k120*n(6)*n(43)+k121*n(12)*n(43)+k123*n(12)*n(43)+k125*n(14)*n(43)+k127*n(18)*n(43)+k136*n(1)*n(3)+k137*n(1)*n(12)+k138*n(1)*n(14)+k139*n(1)*n(6)+k140*n(3)*n(4)+k141*n(3)*n(15)+k142*n(3)*n(7)+k143*n(4)*n(6)+k144*n(4)*n(12)+k145*n(6)*n(24)+k146*n(6)*n(22)+k147*n(6)*n(7)+k148*n(9)*n(12)+k149*n(12)*n(13)+k150*n(9)*n(42)+k151*n(15)*n(42)+k152*n(15)*n(42)+k153*n(10)*n(42)+k156*n(18)*n(15)+k157*n(18)*n(16)+k158*n(18)*n(17)+k159*n(20)*n(42)+2*k160*n(20)*n(42)-k1*n(2)*n(42)-k2*n(5)*n(42)-k3*n(8)*n(42)-k59*n(11)*n(42)-k60*n(21)*n(42)-k132*n(1)*n(42)-k133*n(4)*n(42)-k134*n(9)*n(42)-k135*n(13)*n(42)-k150*n(9)*n(42)-k151*n(15)*n(42)-k152*n(15)*n(42)-k153*n(10)*n(42)-k159*n(20)*n(42)-k160*n(20)*n(42)-k161*n(42)*n(4)*n(15)-k162*n(42)*n(4)*n(15);
-k118*n(1)*n(43)-k119*n(3)*n(43)-k120*n(6)*n(43)-k121*n(9)*n(43)-k122*n(11)*n(43)-k123*n(12)*n(43)-k124*n(13)*n(43)-k125*n(14)*n(43)-k126*n(15)*n(43)-k127*n(18)*n(43)-k128*n(19)*n(43)-k129*n(20)*n(43)-k130*n(22)*n(43)-k131*n(24)*n(43)+k1*n(2)*n(42)+k2*n(5)*n(42)+k3*n(8)*n(42)+k61*n(2)*n(1)+k62*n(2)*n(7)+k63*n(2)*n(4)+k64*n(1)*n(13)+k65*n(1)*n(4)+k66*n(1)*n(9)+k67*n(1)*n(5)+k68*n(1)*n(1)+k69*n(1)*n(7)+k70*n(4)*n(4)+k71*n(8)*n(7)+k132*n(1)*n(42)+k133*n(4)*n(42)+k134*n(9)*n(42)+k135*n(13)*n(42)]);
[t,n]= ode45(F,[0:5e-12:1e-7],IC);
plot(t,n)
Good luck.
  5 个评论
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Sulaymon Eshkabilov
Sulaymon Eshkabilov 2021-5-22
Without knowledge of your system's physical nature or process, just based on your developed simulation model, it is clear that you need to choose your initial conditions very carefully and choose the parameter values. Since you are dealing with very large values and your system behaviour is quite unstable that means you need to be careful with "+" and "-" signs in your system model. It is likely that we tend to overlook "-" sign while re-writing a system of differential equations. Thus, please note this issue, as well. One more important point is ODE solver's accuracy can be improved by tighting its relative and absolute error tolerances that can be adjusted by using odeset(). You may also select appropriate solver's step size. Note that by tighting the error tolerances and step sizes the calculation time will also increase significantly.
These are my general observations of your system's sim. model.
So far, I see that it is fairly large system and very interesting exercise.
Good luck and have fun!
Imene Yed
Imene Yed 2021-5-22
Thank you so much sir for your answers !!!!!

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