# Items tagged with vectorvector Tagged Items Feed

### Spacial Matrix Prodution...

July 18 2014
0 0

Hi all

I have a mathematical problem and I asked it in various sites but the answers till yet are not correct.

Assume that we have:

T[m]:=t->t^m:
b[n,m]:=unapply(piecewise(t>=(n-1)*tj/N and t<n*tj/N, T[m](N*t-(n-1)*tj), 0), t):

where n,N,tj are known constants. furthermore assume that we want to comute the following integral:

for following approximations:

I have written the following code but it seems to be incorrect:

V1:=Vector([seq(seq(b[n,m](t),m=0..1),n=1..3)]);
V:=evalf(V1.Transpose(V1));

the original program is :

taaylor.mws

I will be so grateful if any one can help me to solve it by maple

Ph.D Candidate

Applied Mathematics Department

### Plotting data on a sphere...

July 17 2014
3 31

I have 3 column vectors:

phi contains the number of radians from the North Pole

theta contains the number of radians from the Greenwich meridian

D contains number data corresponding to the point (phi,theta) on the sphere.

How do I plot:

a) a contour plot on the surface of the sphere where each point at (phi, theta) has a corresponding data value D?

b) a plot where the height above the surface at (phi, theta) is some linear function of D such as radius*D*constant?

### Vector math and conditional functions...

July 17 2014
1 4

Level: Idiot (Me)

I have a matrix of 3 columns and lots of rows M

• First column is latitude in degrees
• Second column is longitude in degrees
• Third column is data

So I set lambda:=M(..,1) and phi_g:=M(..,2) giving me two column vectors.

I want to convert lambda and phi_g to polar coordinates theta and phi

theta:=90-lambda produces "Error, (in rtable/Sum) invalid arguments"

WHY?

I also want to convert phi_g to phi where phi=phi_g when phi_g is 0...180 and phi=phi_g +360 when phi_g <0

How do I create a conditional function like this?

### Vector Field to "normal" function...

July 14 2014
1 8

Hello everyone.

I have a vector field in 2d-cartesian coordinates which I would like to convert to a "normal" function, that is f(x, y) where when you put x and y in, you get the magnitude of the vector at that point.

Example vector field:

This one is very hard to handle by hand which is why I want to use Maple for it.

I tried VectorCalculus[Norm] but it gave me this:

### Vectors of lists...

June 30 2014
0 5

restart;

Vector([a, b]);  <a, b>;  # Identical results

a:=[1, 2]:  b:=[3, 4]:

Vector([a, b]), <a, b>;   # Different results. Why?

### How to listplot two vectors on the same graph...

June 26 2014
0 4

How to listplot two vectors on the same graph?

That means having two lines.

### how to plot the data in vector...

June 25 2014
0 2

in maple 12 or 15

assume

result := Vector(10);

for i from 1 to 10 do

result[i] := i;

od;

how to plot it against i?

after tried plot(result(x), x=1..10);

### How do I make a surface between arbitrary points?...

May 26 2014
1 4

Hi,

I have a file with arbitrary points which I want to connect with a surface. I have seen similar problems on this site but I can't fix my problem with the answers that are given, mainly because my points are just plain vectors. Can anybody help me?
These are my points/vectors:

v1 := `<,>`(15, 6, 14.89);
v2 := `<,>`(15, 8, 14.72);
v3 := `<,>`(15, 10, 14.79);
v4 := `<,>`(15, 12, 14.95);
v5 := `<,>`(15, 14, 15.17);
v6 := `<,>`(15, 16, 15.43);
w1 := `<,>`(15/2, 4, 9.78);
w2 := `<,>`(15/2, 6, 9.95);
w3 := `<,>`(15/2, 8, 9.85);
x1 := `<,>`(15*(1/3), 4, 8.71);
x2 := `<,>`(15*(1/3), 6, 8.44);
y1 := `<,>`(15/4, 4, 8.31);

I can only plot the different points with

with(plots);
pointplot3d({v1, v2, v3, v4, v5, v6, w1, w2, w3, x1, x2, y1}, scaling = CONSTRAINED, symbolsize = 20, color = red, axes = normal, labels = ["L/h", "n", "kg/m"]);

I hope someone can help me!

### Shift vector components...

May 25 2014
1 3

Hello;

Suppose we have a vector as follows:

Plex:=[u,v,w,x,y,z]

Could anyone help me to reproduce the following vectors via a "for" loop?

[ v, u, w, x, y, z]

[ w, v, u, x, y, z]

[ x, w, v, u, y, z]

[ y, x, w, v, u, z]

I have a simple Matlab script which can do what I intend. So, my question is how can I implement this script in Maple?

Plex=[u,v,w,x,y,z]

for i=2:5

Plex=[Plex(i) Plex];

Plex(i+1)=[];

disp(Plex)

end

### fitting multiple data curves...

May 09 2014
1 1

i have a non linear equation that depends on three variables e, theta and z.

i have done calculations to calculate e while varying theta and z. theta varied among the vector [0, Pi/4, Pi/3, Pi/2] and z was varying between 1 and 20

when plotting my data it gives the following plot where z is represented on the x-axis and each curve correspond to one theta

i am currently able of fitting one plot to one equation i would like to fit the data points using the nonlinearfit function and to only get one equation for all the plots. is that possible in maple or not

### How to plot columns from a given 3x3 matrix...

May 07 2014
1 9

So if you are given a 3x3 matrix i was just wondering how to use plot3d and plot the 3 column vectors given by it?  Thanks.

### Error, (in rtable/Power) singular matrix...

May 04 2014
0 2

Hi,

I have an error how can I fix the error. Thank you.

Matrix_Fred:=proc(N,d,lambda)
local Kernel,K,Fredholm,phi,MatA,eq2,eq3,eq4,Vct_basis,fct,sys,M,b,M1,Vect_beta,W,i,beta,alpha,eq5,eq6,x,Subs1,Fredholm_stencil,Stencil,w,V,sys1,sys2,Subs2,sys3,Sol_phi;
Fredholm:=phi(x)=f(x)+lambda*int(Kernel(x,y)*phi(y),y=-a..a);
Kernel:=(x,y)->ln(abs(x-y));
eq2:=int(Kernel(x,y)*phi(y),y=-a..a)=sum(int(Kernel(x,y)*phi(y),y=n*h..(n+d)*h),n=-N..N-d);
Vct_basis:=[seq(x^i,i=0..d+1)];
fct:=[seq(unapply('Vct_basis[i]','x'),i=1..d+2)];
sys:=[seq(eq3(fct[i]),i=1..d+1)];
w := [seq(beta[i,n],i=1..d+1)];
M,b := GenerateMatrix(sys,w);
M1:=-M; V:=-b;
Vect_beta:=(M1)^(-1).V;
for i from 1 to d+1 do
beta[i,n]:=Vect_beta[i];
end do;
x:=m*h;
for i from 1 to d+1 do
alpha[m,n,i]:=unapply(beta[i,n],n,m);
end do;
eq5:=lhs(eq2)=sum(rhs(eq4), n=-N..N-d);
eq6:=subs(x=m*h,subs(lhs(eq5)=rhs(eq5) ,Fredholm)):
Subs1 :=[seq(phi(m*h)=phi[m], m=-N..N)];
Fredholm_stencil:=subs(Subs1,eq6):
Stencil[1] := unapply(Fredholm_stencil,m,lambda,phi,f);
sys1 := [seq(Stencil[1](m,lambda,phi,f),m=-N..N)]:
sys2:=subs(Subs1,sys1):
Subs2:=[seq(f(m*h)=f[m], m=-N..N)]:
sys3:=subs(Subs2,sys2):
Sol_phi := [seq(phi[i],i=-N..N)]; # The unknown vector must be computed.
MatA := GenerateMatrix(convert(sys3,list),Sol_phi)[1];
return MatA;
end proc:

d:=1; N:=2; lambda:=3/Pi;
Matrix_Fred(N,d,lambda);
1
2
3
--
Pi
Error, (in rtable/Power) singular matrix

### How to take away each element in a Vector in turn...

April 08 2014
0 3

Hi say I have the vector V1.

V1:=Vector([a,b,c,d,e,f,g]):

and function myfun.

how do i use it as the input to the function my fun, by taking away each element in turn?
myfun(V1[2..]);              # 1st element removed
myfun(V1[[1,3..]]);         # 2nd element removed
myfun(V1[[1,2,4..]]);      # 3rd element removed

and so go

is there a more efficient way?

Many thanks,

### Operations with Vectors - Scalar and Vector...

April 06 2014 Maple 18
2 1

Addition, subtraction, scalar product, vector, projections and graphs with physics packages and plots. With this you can begin to start the physics course for engineering.

Operaciones_con_Vect.mw   (in spanish)

Lenin Araujo Castillo

Physics Pure

Computer Science

### Minimization Process...

April 04 2014
1 12

Hi all

I have the following segment of maple program which belongs to time delay systems dynamic. here C=X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P, is a matrix(vector) which comes from reordering the system terms and my goal is to minimizing J:=X.E.Transpose(X)+U.E.Transpose(U), subject to constraint C=0, but i don't know how to do so.

I will be so grateful if anyone can guide me

best wishes

Ph.D Candidate

Applied Mathematics Department

 > restart: with(Optimization): with(LinearAlgebra): macro(LA= LinearAlgebra): L:=1:  r:=2:  tau:= 1: interface(rtablesize= 2*r+1): Z:= Matrix(      2*r+1, 2*r+1,      [tau,       seq(evalf((L/(2*(iz-1)*Pi))*sin(2*(iz-1)*Pi*tau/L)), iz= 2..r+1),       seq(evalf((L/(2*(iz-1-r)*Pi))*(1-cos(2*(iz-1-r)*Pi*tau/L))), iz= r+2..2*r+1)       ],      scan= columns,      datatype= float[8] );                          Dtau00:= < 1 >: Dtau01:= Vector[row](r): Dtau02:= Vector[row](r): Dtau10:= Vector(r): Dtau20:= Vector(r): Dtau1:= LA:-DiagonalMatrix([seq(evalf(cos(2*i*Pi*tau/L)), i= 1..r)]): Dtau2:= LA:-DiagonalMatrix([seq(evalf(sin(2*i*Pi*tau/L)), i= 1..r)]): Dtau3:= -Dtau2: Dtau4:= copy(Dtau1): Dtau:= < < Dtau00 | Dtau01 | Dtau02 >,          < Dtau10 | Dtau1  | Dtau2  >,          < Dtau20 | Dtau3  | Dtau4  > >;   P00:= < L/2 >: P01:= Vector[row](r): P02:= Vector[row](r, j-> evalf(-L/j/Pi), datatype= float[8]): P10:= Vector(r): P20:= Vector(r, i-> evalf(L/2/i/Pi)): P1:= Matrix(r,r): P2:= LA:-DiagonalMatrix(P20): P3:= LA:-DiagonalMatrix(-P20): P4:= Matrix(r,r): P:= < < P00 | P01 | P02 >,       < P10 | P1  | P2  >,       < P20 | P3  | P4  > >; interface(rtablesize=2*r+1):    # optionally J:=Vector([L, L/2 \$ 2*r]):      # Matrix([[...]]) would also work here E:=DiagonalMatrix(J); X:=  Vector[row](2*r+1,symbol=a); U:=Vector[row](2*r+1,symbol=b); X0:= Vector[row](2*r+1,[1]); G:=Vector[row](2*r+1,[1]); C:=simplify(X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P);
 (1)
 > J:=X.E.Transpose(X)+U.E.Transpose(U);
 (2)
 > Minimize(J,{C=0});
 Error, (in Optimization:-NLPSolve) invalid arguments
 > #XP:=-.015+X[1]+add(X[l+1]*f1(l)+X[r+l+1]*f2(l), l= 1..r): #plot([XP,T1], t= 0..1);#,legend= "Solution Of x(t) with r=50"):
 >
 >
 >
 >

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