Plotting error: Need to plot the evolution of symbolic matrix?

syms t

PHI=[ 1, t, t/3 - (2*exp(-3*t))/9 + 2/9, (2*t)/3 + (2*exp(-3*t))/9 - 2/9;

0, 1, (5*exp(-3*t))/12 - (3*exp(t))/4 + 1/3, 2/3 - exp(t)/4 - (5*exp(-3*t))/12;

0, 0, exp(-3*t)/4 + (3*exp(t))/4, exp(t)/4 - exp(-3*t)/4;

0, 0, (3*exp(t))/4 - (3*exp(-3*t))/4, (3*exp(-3*t))/4 + exp(t)/4];

N=norm(PHI);

ezplot(N,[0,1])

Answer 1

[Star Strider]

Try this:

PHI = @(t) [ 1, t, t/3-(2*exp(-3*t))/9+2/9, (2*t)/3+(2*exp(-3*t))/9-2/9;
    0, 1, (5*exp(-3*t))/12-(3*exp(t))/4+1/3, 2/3-exp(t)/4-(5*exp(-3*t))/12;
    0, 0, exp(-3*t)/4+(3*exp(t))/4, exp(t)/4-exp(-3*t)/4;
    0, 0, (3*exp(t))/4-(3*exp(-3*t))/4, (3*exp(-3*t))/4+exp(t)/4];
N = @(t) norm(PHI(t));

t = linspace(0, 1, 50);
for k = 1:numel(t)
    Nt(k) = N(t(k));
end

figure
plot(t, Nt)
grid

[Shauvik Das]

Thank you :)

[Star Strider]

As always, my pleasure!

[Shauvik Das]

syms t

PHI=[ 1, -t, -t/3 - (2*exp(-3*(-t)))/9 + 2/9, (2*-t)/3 + (2*exp(-3*(-t)))/9 - 2/9;

0, 1, (5*exp(-3*(-t)))/12 - (3*exp(-t))/4 + 1/3, 2/3 - exp(-t)/4 - (5*exp(-3*(-t)))/12;

0, 0, exp(-3*(-t))/4 + (3*exp(-t))/4, exp(-t)/4 - exp(-3*(-t))/4;

0, 0, (3*exp(-t))/4 - (3*exp(-3*(-t)))/4, (3*exp(-3*(-t)))/4 + exp(-t)/4];

PHIT=transpose (PHI);

B=[0;1;2;1];

BT=transpose (B);

GRAMi = PHI*B*BT*PHIT

GRAMfinal=int(GRAMi,t, 0, t)

A= det(GRAMfinal)

N = @(t) (A(t));

t = linspace(0, 1, 50);

for k = 1:numel(t)

Nt(k) = N(t(k));

end

figure

plot(t, Nt)

grid

%% Not sure why is it not plotting determinant of the matrix in the same way.

[Star Strider]

Try this:

PHI = @(t) [ 1, t, t/3-(2*exp(-3*t))/9+2/9, (2*t)/3+(2*exp(-3*t))/9-2/9;
    0, 1, (5*exp(-3*t))/12-(3*exp(t))/4+1/3, 2/3-exp(t)/4-(5*exp(-3*t))/12;
    0, 0, exp(-3*t)/4+(3*exp(t))/4, exp(t)/4-exp(-3*t)/4;
    0, 0, (3*exp(t))/4-(3*exp(-3*t))/4, (3*exp(-3*t))/4+exp(t)/4];

PHIT = @(t) transpose(PHI(t));
B=[0;1;2;1];
BT=transpose(B);
GRAMi = @(t) PHI(t)*B*BT*PHIT(t);
GRAMfinal = @(t) integral(GRAMi, 0, t, 'ArrayValued',1)
A = @(t) det(GRAMfinal(t));
N = @(t) (A(t));

t = linspace(0, 1, 50);
for k = 1:numel(t)
    Nt(k) = N(t(k));
end

figure
plot(t, Nt)
grid

That ran without error for me, and appears to do what you want.