How can I get the Standard Errors of the covariance matrix in Maple?
I can simulate a covariance matrix in Maple as follows:

restart:
with(Statistics):
with(LinearAlgebra):

R := RandomMatrix(4, 4, generator = -15 .. 15, outputoptions = [datatype = float[8]]);
CovarianceMatrix(R);

but how do I find the standard errors?

I write this system but I have 2 error

restart; params := [z = 0,

Omega = 2.2758,

tau = 13.8, T2 = 200,

omega0 = 1,

r = .7071,

s = 2.2758,

omega = .5]

sys1 := {diff(q(t), t) = -2*Omega*v(t)-s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*(y(t)-x(t))-q(t)/T2,

diff(v(t), t) = Omega*q(t)-v(t)/T2,

diff(x(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)+y(t)/T1,

diff(y(t), t) = -2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*q(t)-y(t)/T1};

ICs1 := {q(-20) = 0, v(-20) = 0, x(-20) = 1, y(-20) = 0}

ans1 := dsolve(`union`(eval(sys1, params), ICs1), numeric, output = listprocedure); plots:-odeplot(ans1, [[t, x(t)], [t, y(t)], [t, q(t)], [t, v(t)]], t = -20 .. 20, legend = [x, y, q, v])

Error, invalid input: eval received params, which is not valid for its 2nd argument, eqns
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

Hello everybody

I'm new at using Maple

so what I'm trying to do is " solve system of differential equations numerically " and plot the result 

I use the floweing code

PDEtools[declare]((u, v, w)(t), prime = t)

> params := z = 0;

Omega= 2.2758;

tau = 13.8;

T2 = 200; s = 1;

r = 0.7071;

\[CapitalDelta] = 1.7758;

s = 2.2758;

Eta= 1.05457173*10^-34;

omega = 0.5; k = 1666666.667;

> sys1 := {diff(u(t), t) = Omega*v(t)-u(t)/T2,

diff(v(t), t) = -Omega*u*{t}-2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*w(t)-v(t)/T2,

diff(w(t), t) = 2*s*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(k*z-omega*t)*v(t)};

Cs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

> ans1 := dsolve*RealRange(Open({ICs1, sys1}), {u(t), v(t), w(t)});
%;
Error, (in RealRange) invalid arguments

plot([u(t),t=-20..20])
plot([v(t),t=-20..20])
plot([w(t),t=-20..20])

:::::::::

also I need to use the result of v(t) in another equation as,

x=2*v(t)*cos(k*z-omega*t)

How I can do that ?

Hi There,

Can any one correct me the mistake in the following differentiation:

Above command gives the following error:

Error, (in simpl/abs) abs is not differentiable at non-real arguments

I am struggling to get a single output value for my piece wise function. I am trying to plot this piecewise function. All the B-values and L value are previously defined.

My end goal is to plot the function.

Unfortunately, I cannot get the piecewise function to output a single value. I have tried s(2) which gives me the entire piecewise function with the correct numbers plugged in.

Here is the file in its full form.

damshw9.mw

Hi All,

I tried to convert the following hypergeometric function into BesselJ function. But I failed to do so. Could any one let me know the  reference or procedure to convert the Hypergeom function into bessel function.

Following is the integral I am intended to do.

Result:

I need to convert the result into equivalent bessel function.

If at all there is a way to co-relate the generalized corelation between bessel function <-> hypergeom function.

Direct me to any books you come across.

Thanks

Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks

Here is the question:Prior to this question I was given f(z)=z^2+1, N(z)=(z^2-1)/(2z), T(z)=z-I/z+I such that T(N^k (z))=(T(z))^2^k. And L is a set of number on the real axis. Now the question is that given we have two regions of the complext plane as follow:

R₊ = {z : N^k{z) -> i as k -> ∞}; R_- = {z : N^k(z) -> -i as k -> ∞}.

Draw a diagram to illustrate these regions, the line L and the roots i and -i. We call R₊ the basin of attractionfor the root +i, and similarly R_-is the basin of attraction for the root -i.

 Show that if z is on the set L (the common boundary of the two regions R₊ and R_{_}, then N^k(z) stays on L for all values of k. (This is easy once you identify what L is.) So in this case iteration does not produce a root at all.

So basically my problem is that the fact I'm not very familar with the commands to draw such diagram, and I don't know much about Newton's method to compute complex roots. It would be appreciated if anyone can help me how to get start with the question. Thanks.

Following previous question at

http://www.mapleprimes.com/questions/149581-Improve-Algorithm-Dsolve

and also

http://www.mapleprimes.com/questions/149243-BVP-With-Constraining-Integrals

I wrote the following code

***********************

restart:

gama1:=0:


phi0:=0.00789:


rhocu:=2/(1-zet^2)*int((1-eta)*rho(eta)*c(eta)*u(eta),eta=0..1-zet):

eq1:=diff(u(eta),eta,eta)+1/(mu(eta)/mu1[w])+((1/(eta-1)+1/mu(eta)*(mu_phi*diff(phi(eta),eta)))*diff(u(eta),eta)):
eq2:=diff(T(eta),eta,eta)+1/(k(eta)/k1[w])*(2/(1-zet^2)*rho(eta)*c(eta)*u(eta)/(p2*10000)+( (a[k1]+2*b[k1]*phi(eta))/(1+a[k1]*phi1[w]+b[k1]*phi1[w]^2)*diff(phi(eta),eta)-k(eta)/k1[w]/(1-eta)*diff(T(eta),eta) )):
eq3:=diff(phi(eta),eta)-phi(eta)/(N[bt]*(1-gama1*T(eta))^2)*diff(T(eta),eta):
mu:=unapply(mu1[bf]*(1+a[mu1]*phi(eta)+b[mu1]*phi(eta)^2),eta):
k:=unapply(k1[bf]*(1+a[k1]*phi(eta)+b[k1]*phi(eta)^2),eta):
rhop:=3880:
rhobf:=998.2:
cp:=773:
cbf:=4182:
rho:=unapply(  phi(eta)*rhop+(1-phi(eta))*rhobf ,eta):
c:=unapply(  (phi(eta)*rhop*cp+(1-phi(eta))*rhobf*cbf )/rho(eta) ,eta):
mu_phi:=mu1[bf]*(a[mu1]+2*b[mu1]*phi(eta)):

a[mu1]:=39.11:
b[mu1]:=533.9:
mu1[bf]:=9.93/10000:
a[k1]:=7.47:
b[k1]:=0:
k1[bf]:=0.597:
zet:=0.5:
#phi(0):=1:
#u(0):=0:
phi1[w]:=phi0:
N[bt]:=0.2:
mu1[w]:=mu(0):
k1[w]:=k(0):

eq1:=subs(phi(0)=phi0,u(0)=0,eq1):
eq2:=subs(phi(0)=phi0,u(0)=0,eq2):
eq3:=subs(phi(0)=phi0,u(0)=0,eq3):

p:=proc(pp2) global res,F0,F1,F2:
if not type([pp2],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve({eq1=0,subs(p2=pp2,eq2)=0,eq3=0,u(0)=0,u(1-zet)=0,phi(0)=phi0,T(0)=0,D(T)(0)=1}, numeric,output=listprocedure):
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
evalf(2/(1-zet^2)*Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*( F1(eta)*rhop*cp+(1-F1(eta))*rhobf*cbf )/(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))-pp2*10000:
end proc:


s1:=Student:-NumericalAnalysis:-Secant(p(pp2),pp2=[6,7],tolerance=1e-6);

                   HFloat(6.600456858832996)

p2:=%:



ruu:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))):
phb:=evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet))) :
TTb:=evalf(2/(1-zet^2)*(Int((1-eta)*F2(eta),eta=0..1-zet))):
rhouu:=evalf(2/(1-zet^2)*(Int((1-eta)*(F1(eta)*rhop+(1-F1(eta))*rhobf)*F0(eta),eta=0..1-zet))):
with(plots):
res(parameters=[R0,R1]):
odeplot(res,[[eta,u(eta)/ruu],[eta,phi(eta)/phb],[eta,T(eta)/TTb]],0..zet);

*************************************

as you can see at the second line of the code, the value of phi0:=0.00789. however, I want to modify the code in a way that phi0 is calculated with the following addition constraint

evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta)*F1(eta),eta=0..1-zet))) / evalf(2/(1-zet^2)*(Int((1-eta)*F0(eta),eta=0..1-zet)))-0.02=0

I would be most grateful if you could help me in this problem.

Thanks for your attention in advance

Amir

[> restart;
[> OPTIMAL:=proc(f,Condition::set)
local vars,L,S,SS,k,m,K,Fmax,Fmin,sol_min,sol_MIN,sol_max,sol_MAX;
vars:=indets(f,name) union indets(Condition,name);
L:=map(convert,Condition,equality);
K:=combinat[choose](L);
S:=NULL:
for k to nops(k) do if solve(K[k])<>NULL then
extrema(f,K[k],vars,'s||k'):S:=S,a||values(s||k):fi od:
SS:={}
for k to nops([s]) do
if type(s[k],set) then SS:=SS union evalc(s[k]) fi od;
SS:=remove(has,SS,l);
S:=NULL:
for k to nops(ss) do if type(SS[k],set(equation)) and
map(evalb,evalf(simplify(subs(SS[k],Condition))))={true}
then S:=S,vatue(ss[k]) fi od;
SS =[s];
Fmax:=-infinity:
for k to nops(SS) do
if evalf(simplify(subs(ss[k],f)))>evalf(Fmax)
then Fmax:=simplify(value(subs(SS[k],f)));sol_max:=SS[k]; fi;od;
sol_MAX:=sol_max:
for k to nops(SS) do
if Fmax=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_max)<>{} then
sol_MAX:=sol_MAX,Ss[k] fi od;
‘Fmax'=simplify(expand(Fmax)),sol_MAX:
Fmin:=infinity:
for k to nops(SS) do
if evalf(simplify((subs(SS[k],f))))<evalf(Fmin)
then Fmin:=simplify((subs(SS[k],f)));sol_min:=SS[k]; fi;od;
sol_MIN:=sol_min:
for k to nops(SS) do
if Fmin=simplify(value(subs(SS[k],f)))
and (SS[k] minus sol_min)<>{} then
sol_MIN:=sol_MlN,SS[k] fi od;
RETURN('F[min]'=simplify(expand(Fmin)),sol_MlN,
'F[max]'=simplify(expand(Fmax)),sol_max);
end: ↵

" Error, unable to match delimiters"
  Please, help me.
I don't understand. Thank you, thank you.

So i have to plot 3 ODEs. How would I go about plotting dx/dt=10(y-x) AND dy/dt=x(28-x)-y AND dz/dt= xy-8z/3. Any help at all would be appreciated.

I have a column vector that looks like this:

"GOOG.NASDAQ_GOOG"
"GOOG.NASDAQ_AAPL"
"GOOG.NASDAQ_ZN"
"GOOG.NASDAQ_ZOOM"
....

However, I need it to be in this format:

GOOG.NASDAQ_GOOG.4,GOOG.NASDAQ_AAPL.4,GOOG.NASDAQ_ZN.4,GOOG.NASDAQ_ZOOM.4 etc

It appears to be very simple but I cant figure out how to do it in Maple.

LL_101)_Quandl_Get_D.mw

I have two procedures X() and P() which both are working. (See attached worksheet )

LL_100)_Quandl_Get_D.mwLL_100)_Quandl_Get_D.mw

When I put:

z := X(P());
Do(%DataTable0 = z);

I get an error:

Attempted to set unknown property 'value' on component 'DataTable0'

why??

Hello there,

I have some troubles with plotting implicit functions , aswell with plotting polar ones.

When I ask the plot of my function it's not ''smooth'' , it has edgdes everywhere that aren't suposed to be there (I think).

These are 2 examples:

K:=x^2*(x^2+y^2)=a^2*y^2;a:=1;
implicitplot(K,x=-2..3,y=-6..6,colour=red);

K:=(x^2+y^2)^3=a^3*x*(x^2*3*y^2);

implicitplot(K,x=-6..6,y=-6..6,colour=red);

Can somebody help me out on how to draw them smoothly?

Maybe I have to change settings?

Thanks alot!

Thanks