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how to project a matrix onto another matrix...

Asked by: LeeHoYeung 535
linearalgebra
January 31 2014
0  3

ProjOfEigenVector := MatrixMatrixMultiply(BeProjected, (Transpose(OrthoBasis).MatrixInverse(MatrixMatrixMultiply(OrthoBasis, Transpose(OrthoBasis)), method = pseudo).OrthoBasis));

i use definition of this 

# P=(A*B’).inv(B*B’).B

#P=A*(B’).inv(B*B’).B)

however, no matter whatever matrix A pass into this equation in order to project onto B,

it still return the original matrix A

how can this definition be used to project a matrix onto another matrix?

how to correctly to project a matrix onto another matrix

Maple Player app for iPad crashes when I run an ap...

Asked by: johndoe11 5
January 29 2014
1  3

I'm trying to create a small app for Maple Player to graph solids of revolution. When I run the app in the desktop version of Maple T.A it works, but when I move it into the Maple Player App it crashes. Any ideas?

How do I solve a nonlinear differential equation b...

Asked by: kiyanoosh 15
numeric
January 29 2014
2  7

hi, I am new here I want to solve these toe coupled equations with the following boundary condition numerically:

  1)  diff(f(eta),eta$3)+(1)/(2)*f(eta)*diff(f(eta),eta$2)-Pi*(2*f(eta)*(diff(f(eta),eta))*

(diff(f(eta),eta,eta))+f(eta)^2*(diff(f(eta),eta,eta,eta))+eta*(diff(f(eta),eta))^2*(diff(f(eta),eta$2)))-K*

(diff(f(eta),eta)-1)=0

2)   diff(theta(eta),eta,eta)+(1)/(2)*Pr*f(eta)*(diff(theta(eta),eta))=0

boundary conditions: 1)  f(0) = 0   2)  D(f)(0) = 0   3)  D(f)(infinity=10) = 1

                               1) theta(infinity=10) = 1      2) theta(0)=0

Pi=0.1    K=0.2

Virtual User Summit

by: eithne 2072 Maple , MapleSim
January 29 2014
6  0

Maplesoft is holding its first ever Virtual User Summit on Feb. 27.  You’ll be able to watch presentations by both Maplesoft and Maplesoft customers, ask questions, have discussions in the lounge with other attendees, and even enter a draw, all from the comfort of your own home or office.

Here’s the agenda.  We’ll release more detailed information on speakers and session times in the next couple of weeks.

For more information and to register:  Maplesoft Virtual User Conference

We're looking forward to seeing you there. (Well, "seeing you" :-))

eithne

Doubt related to Eval!...

Asked by: Murilo V 10
eval
January 29 2014
1  6

Does anybody know why the answer of a equation i am getting on maple is coming with "eval" written?

Example:

 

the answer should be a number ...

Why does it happen?

 

 

solve the system of equations...

Asked by: yangtheary 290
solve
January 28 2014
0  1

solve the system of equations (10a+3b+4c+d+e=0,11b+2c+2d+3e+f=0,15c+4d+5e+4f+g=0,2a+b-3c+12d-3e+f+g=0,6a-5b+3c-d+17e+f=0,3a+2b-3c+4d+e-16f+2g=0,4a-6b+c+d+3e+19g=0)

How do I get this particular trig expansion...

Asked by: DJJerome1976 540
trigonometric-identities
January 28 2014
2  25

I would like to express 2*sin(x+Pi/4) in the form sqrt(2)*sin(x)+sqrt(2)*cos(x). I've tried many variations using simplify/expand/combine/etc. to no avail. Any ideas?

How to save in Maple 17 ? ...

Asked by: kamrul126 5
January 28 2014
1  7

I have the  following simple code in Maple:

x:=2*y

save x, "file1.mpl";

This code works successfully in Maple 13 and 14. However, does not work in Maple 17.  I do not understand why this happens. Can anyone help me to save a procedure in Maple 17.

 

Error, (in dsolve/numeric/bvp) initial Newton iter...

Asked by: aylin 25
ode
January 27 2014
1  3

Dear Experts,

When I run this code in maple I am facing with "Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging".

restart:
 
 unprotect('gamma');
 lambda:=5*10^5:
 mu:=0.003:
 beta:=4*10^(-10):
 delta:=0.2:
 alpha:=0.043:
 sigma:=alpha+delta:
 k:=6.24:
 gamma:=0.65:
 A[1]:=1:
 A[2]:=1:

ics := x[1](0)=1.7*10^8, x[2](0)=0,x[3](0)=400,psi[1](50)=0,psi[2](50)=0,psi[3](50)=0:

ode1:=diff(x[1](t), t)=lambda-mu*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)+delta*x[2](t),
 diff(x[2](t), t) =(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-sigma*x[2](t),
 diff(x[3](t), t) =(1+psi[3](t)*k*x[2](t)/A[2])*k*x[2](t)-gamma*x[3](t),
 diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*x[3](t)^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-mu+beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*x[3](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
> diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*k^2*x[2](t)-psi[1](t)*delta+psi[2](t)*sigma-psi[3](t)*(psi[3](t)*k^2/A[2]*x[2](t)+(1+psi[3](t)*k*x[2](t)/A[2])*k),
> diff(psi[3](t), t) = 1/A[1]*beta^2*x[1](t)^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*x[1](t)^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*gamma;

sol:=dsolve([ode1,ics],numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Please help me to solve this equation on Maple.




Fourier Transform result not understood...

Asked by: Jan GvK 20
fourier-transform
January 27 2014
0  0

Hello,

I understand that the question is not really Maple related, but I still hope for some help.


See the worksheet below. I defined a pure sine wave and determined the complex Fourier coefficients for it which I used to plot the amplitude and power spectra. It is easy to see the relations in terms of amplitude and power between the time and frequency signal.

The Fourier Transform of the sine wave logically shows the Dirac distribution, but I can't see the relation in terms of amplitude and power to the original time signal. Taking the integral of the transformed signal (A) wil result in a step of Pi at w=-1 and again at w=1. What am I missing here?

Thanks

> 

restart; with(inttrans); with(plots); with(DynamicSystems)

 

Define a signal:

 

> 

T := 2*Pi;

2*Pi

  

sin(t)

 (1)

 

Determine the waveform power:

 

> 

F := (int(f^2, t))/T+C:
> 

C := simplify(solve(subs(t = 0, F) = 0, C)):
> 

eval((int(f^2, t = -(1/2)*T .. (1/2)*T))/T)

1/2

 (2)
> 

plot([f, f^2, F], t = -Pi .. Pi, gridlines = true)

 

 

Determine the complex Fourier series coefficients and plot the spectra:

 

> 

q := proc (n) options operator, arrow; (int(f*exp(-(2*I)*n*Pi*t/T), t = -(1/2)*T .. (1/2)*T))/T end proc:
> 

simplify(q(n))

I*sin(Pi*n)/(Pi*(n^2-1))

 (3)
> 

ComplexCoefficients := evalf(`<,>`(seq(q(n), n = -1 .. 1)))

ComplexCoefficients := Vector(3, {(1) = .5000000000*I, (2) = 0., (3) = -.5000000000*I})

 (4)
> 

B := evalf(`<,>`(seq(sqrt(Re(q(n))^2+Im(q(n))^2), n = -3 .. 3))):

 
> 

C := evalf(`<,>`(seq(Re(q(n))^2+Im(q(n))^2, n = -3 .. 3))); -1; DiscretePlot(C, -3, 1, titlefont = ["ARIAL", "bold", 14], title = "Power Spectrum", color = "Red", gridlines = true, style = stem)

 

So, the signal power for f of 1/2 can be found directly within the power spectrum plot "(2*1/(4))."

 

I would expect to be able to directly see the amplitude and power relation to the time signal from the Fourier Transform of f but i can't.

 

> 

A := fourier(f, t, w);

I*Pi*(Dirac(w+1)-Dirac(w-1))

 (5)


Download 20140127MaplePrime.mw

 

 

How to solve a differential equation on Maple? ...

Asked by: saraha 5
January 27 2014
1  17

I have to solve a system composed of a mass, a spring and a damper, represented by this equation :

m (d2x/dt2) + c (dx/dt) + k x(t) = F(t)

with m the mass, t the time, c the constant of the damper, k the constant of the spring, F an external force applied to the mass and x(t) the movement of the mass m at time t.

Please help me to solve this equation on Maple.

Disability question -- voice input into Maple work...

Asked by: rahe 23
January 26 2014
2  0

I am using Maple worksheets in a class. I have a student who finds it difficult to spend much time at the keyboard because of a joint disorder. I am looking for alternate input methods such as Dragon or the Dictate Facility on MacBooks which might help her out. Any suggestions would be appreciated. 

Thanks,

-Maury

Differential Equation with Homogeneous Coefficient...

Asked by: Ratch 216
dsolve coefficients
January 26 2014
1  6

Can anyone tell me how to use dsolve to find the solution to the problem in the attachment.  It is faily easy to do using substitution for homogeneous coefficients, but dsolve seems to put out a very complicated solution to the problem.

> 

with(DEtools):
> 

2*x*y(x)+(x^2+y(x)^2)*(diff(y(x), x))

2*x*y(x)+(x^2+y(x)^2)*(diff(y(x), x))

 (1)
> 

dsolve(%)

y(x) = ((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)-2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3))/_C1^(1/2), y(x) = (-(1/4)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)))/_C1^(1/2), y(x) = (-(1/4)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)))/_C1^(1/2)

 (2)
> 

NULL

 

Download DEprob.mw

export matrix for matlab...

Asked by: arashsaeedi 5
student matrix
January 26 2014
1  1

I have 2 problem with my jacobian matrix:

first: i can not evaluate 11*11 jacobian matrix. at last i can evaluate 10*10 matrix. can i solve this?
second: i want to export my matrix for matlab but i see this error : {export matrix"cannot convert matrix element to float[8] data type"}
so how i can use this matrix in my matlab code?
 my jacobian matrix:


with(VectorCalculus); Jacobian([VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(2.68, ex), VectorCalculus:-`-`(VectorCalculus:-`*`(2, vx))), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.500000001, e^VectorCalculus:-`*`(1.666666667, sqrt(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))^2), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb^2)))))), VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))), VectorCalculus:-`+`(VectorCalculus:-`*`(rx, 1/sqrt(VectorCalculus:-`+`(rx^2, ry^2))), VectorCalculus:-`*`(1/2, VectorCalculus:-`*`(VectorCalculus:-`+`(VectorCalculus:-`*`(2, rx), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb(ex)))), 1/sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))))), ln(e)), 1/sqrt(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))^2), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb^2)))))), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(50.00000000, e^VectorCalculus:-`-`(VectorCalculus:-`*`(5.000000000, sqrt(VectorCalculus:-`+`(Rx^2, Ry^2))))), Rx), ln(e)), 1/sqrt(VectorCalculus:-`+`(Rx^2, Ry^2)))), VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(2.68, ey), VectorCalculus:-`-`(VectorCalculus:-`*`(2, vy))), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(3.500000001, e^VectorCalculus:-`*`(1.666666667, sqrt(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))^2), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb^2)))))), VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))), VectorCalculus:-`+`(VectorCalculus:-`*`(ry, 1/sqrt(VectorCalculus:-`+`(rx^2, ry^2))), VectorCalculus:-`*`(1/2, VectorCalculus:-`*`(VectorCalculus:-`+`(VectorCalculus:-`*`(2, ry), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb(ey)))), 1/sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))))), ln(e)), 1/sqrt(VectorCalculus:-`+`(VectorCalculus:-`-`(VectorCalculus:-`+`(sqrt(VectorCalculus:-`+`(rx^2, ry^2)), sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(rx, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ex))))^2, VectorCalculus:-`+`(ry, VectorCalculus:-`-`(VectorCalculus:-`*`(2, vb(ey))))^2)))^2), VectorCalculus:-`-`(VectorCalculus:-`*`(4, vb^2)))))), VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(VectorCalculus:-`*`(50.00000000, e^VectorCalculus:-`-`(VectorCalculus:-`*`(5.000000000, sqrt(VectorCalculus:-`+`(Rx^2, Ry^2))))), Ry), ln(e)), 1/sqrt(VectorCalculus:-`+`(Rx^2, Ry^2)))), 1, 1, 1, 1, 1, 1, 1, 1, 1], [vx, vy, ex, ey, rx, ry, Ex, Ey, vb, Rx, Ry])

Matrix evaluation differ on i386 and amd64 platfor...

Asked by: flaminio 10
matrix linux
January 25 2014
2  9

THE FOLLOWING CODE 

restart;

A:=Matrix([[ a , b ], [ c , d ]]);

a:=1; b:=0; c:=0; d:=1;

A; 

produces differents results under MAPLE 16  linux i386 and under MAPLE 16  linux amd64

in the first case the last evalution has the following printed output:

Matrix([[a,b],[c,d]])

on the second machine the printed output is

Matrix([[1,0],[0,1]])

Does anybody has an explication; I thought that the "coorect behaviour was the first one since tables use last-name evalutation. But now I am puzzled.

 

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