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MaplePrimes Questions

view matrix as 2-d image instead of 1-d text...

Asked by: WmEllis 15
matrix
July 28 2019
3  6

In Maply 2018, inputting (entering in red text)

A := <<1,2,3>|<6,7,8>>;

produces output (in blue text)

A := Matrix(3, 2, {(1, 1) = 1, (1, 2) = 6, (2, 1) = 2, (2, 2) = 7, (3, 1) = 3, (3, 2) = 8}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

What must I do to make the output appear appear instead as a standard 2-d array, with big brackets to the left and right, 1st column = <1,2,3>; 2nd column = <6,7,8>?

Thank you.

 

Unexpected solution to PDE...

Asked by: Rouben Rostamian 8541
pde differential-equations elliptic
July 28 2019
3  2

We solve Laplace's equation in the domain a < r and r < b, c < t and t < d
in polar coordinates subject to prescribed Dirichlet data.

Maple produces a solution in the form of an infinite sum,
but that solution fails to satisfy the boundary condition
on the domain's outer arc.  Is this a bug or am I missing
something?

> 

restart;
> 

kernelopts(version);

`Maple 2019.1, X86 64 LINUX, May 21 2019, Build ID 1399874`

> 

with(plots):
> 

pde := diff(u(r,t),r,r) + diff(u(r,t),r)/r + diff(u(r,t),t,t)/r^2 = 0;

diff(diff(u(r, t), r), r)+(diff(u(r, t), r))/r+(diff(diff(u(r, t), t), t))/r^2 = 0

> 

a, b, c, d := 1, 2, Pi/6, Pi/2;

1, 2, (1/6)*Pi, (1/2)*Pi

> 

bc := u(r,c)=c, u(r,d)=0, u(a,t)=0, u(b,t)=t;

u(r, (1/6)*Pi) = (1/6)*Pi, u(r, (1/2)*Pi) = 0, u(1, t) = 0, u(2, t) = t

We plot the boundary data on the domain's outer arc:

> 

p1 := plots:-spacecurve([b*cos(t), b*sin(t), t], t=c..d, color=red, thickness=5);

Solve the PDE:

> 

pdsol := pdsolve({pde, bc});

u(r, t) = Sum((1/6)*cos(3*signum(n1-1/4)*(-1+4*n1)*t)*(2*Pi*sin((1/2)*signum(n1-1/4)*Pi)*abs(n1-1/4)-6*Pi*sin((3/2)*signum(n1-1/4)*Pi)*abs(n1-1/4)+cos((3/2)*signum(n1-1/4)*Pi)-cos((1/2)*signum(n1-1/4)*Pi))*signum(n1-1/4)*8^(signum(n1-1/4)*(4*n1+1))*(r^((-3+12*n1)*signum(n1-1/4))-r^((3-12*n1)*signum(n1-1/4)))/(abs(n1-1/4)*Pi*(-1+4*n1)*(16777216^(signum(n1-1/4)*n1)-64^signum(n1-1/4))), n1 = 0 .. infinity)+Sum(-(1/3)*((-1)^n-1)*sin(n*Pi*ln(r)/ln(2))*(exp((1/6)*Pi*n*(Pi+6*t)/ln(2))-exp((1/6)*Pi*n*(7*Pi-6*t)/ln(2)))/(n*(exp((1/3)*n*Pi^2/ln(2))-exp(n*Pi^2/ln(2)))), n = 1 .. infinity)

Truncate the infinite sum at 20 terms, and plot the result:

> 

eval(rhs(pdsol), infinity=20):
value(%):
p2 := plot3d([r*cos(t), r*sin(t), %], r=a..b, t=c..d);

Here is the combined plot of the solution and the boundary condition.
We see that the proposed solution completely misses the boundary condition.

> 

plots:-display([p1,p2], orientation=[25,72,0]);


 

Download mw.mw

I Have a problem in Do loop...

Asked by: amrramadaneg 76
do-loop limit
July 28 2019
0  2

Dears, greeting for all

I have a problem, I try to explain it by a figure

This formula does not work.

I need to substitute n=0 to give G_n+1 as a function of the parameter s, then find the limit. 

.where G_n is a function in s.

this is the result

 

how to express eigenvector or eigenvalues in terms...

Asked by: LeeHoYeung 535
linear-algebra eigenvalues fibonacci
July 28 2019
0  3

how to express eigenvector or eigenvalues in terms of fibonacci or lucas or golden ratio?

fibonacci ratio has many 

f(n)/f(n-1) , all eigenvector can not divided by any one of them

 

how to verify lambda calculus is computable and re...

Asked by: LeeHoYeung 535
July 28 2019
0  2

how to verify lambda calculus is computable and realizable in maple?

is it possible to realize lambda calculus into algebra ?

how to use β-reduction to convert algebra function into lambda calculus?

is there a way to convert back ?

how to combine multiple lambda calculus into one lambda calculus and check computable and then convert back to algebra function?

Passing variable number of arguments...

Asked by: Stretto 260
proc
July 27 2019
2  1

I'm starting to use procs a lot just because they are more general and can more easily handle complex functionality.

 

I usually have to pass a function to them and that function may or may not take a series of arguments.

 

e.g.,

 

f := (x,y,a)->a*x*y;

g := proc(q, ...)

    q(x,y,...)

end proc;

 

g(f, 3);

 

Here 3 should be passed for a(using ... to represent it).

 

If I pass a function

 

h := (x,y)->x*y

then it would be g(f)

 

I could possibly use nops, ops, arrays, etc... but looking for the right solution.

 

Generation of numbers with Cauchy distribution in ...

Asked by: DimaBrt 105
cauchy sample statistics
July 27 2019
0  2

Hello. To generate nine numbers with Cauchy distribution C(0,1) I use Sample(Random Variable(Cauchy(0, 1)), 9). Is there a way to make all generated numbers belong to the interval (-1,1)?

how to make diff(y(x),x) display as y'(x) in works...

Asked by: nm 11493
July 27 2019
2  1

I spend some time searching and reading help. But not able to find if this is possible.

I use worksheet only (i.e. not 2D document). I have my display set as

 

I'd like diff(y(x),x) to display as y'(x) in output.

I know I can do this 

PDEtools:-declare(y(x), prime = x);

And that will make diff(y(x),x) display as y'  but I want y'(x). And the same for diff(y(x),x$2) to display as y''(x). And to be clear, y(x) will still display as y(x).  I am mainly interested in making the derivative display a little nicer if possible.

Is there a way to do this?

I am using 2019.1 on windows 10.

 

Wrong values for Eigenvalues, depending on Digits ...

Asked by: Dobrica 20
linearalgebra datatype digits
July 27 2019
4  3

Hello!

I want to calculate Eigenvalues. Depending on values for digits and which datatype I choose Maple sometimes returns zero as Eigenvalues. Maybe there is a problem with the used routines: CLAPACK sw_dgeevx_, CLAPACK sw_zgeevx_.

Thank you for your suggestions!
 

``

> 

 

Problems LinearAlgebra:-Eigenvalues, Digits, ':-datatype' = ':-sfloat', ':-datatype' = ':-complex'( ':-sfloat' )

 
> 

restart;

> 

interface( ':-displayprecision' = 5 ):
 
> 

infolevel['LinearAlgebra'] := 5;
myPlatform := kernelopts( ':-platform' );
myVersion := kernelopts( ':-version' );

5

 

"windows"

 

`Maple 2018.2, X86 64 WINDOWS, Nov 16 2018, Build ID 1362973`

(1.1)

Example 1

 
> 

A1 := Matrix( 5, 5, [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [-10201/1000, 30199/10000, -5049/250, 97/50, -48/5]] );

Matrix(5, 5, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 1, (5, 1) = -10201/1000, (5, 2) = 30199/10000, (5, 3) = -5049/250, (5, 4) = 97/50, (5, 5) = -48/5})

(1.1.1)
> 

LinearAlgebra:-Eigenvalues( A1 );

CharacteristicPolynomial: working on determinant of minor 2
CharacteristicPolynomial: working on determinant of minor 3
CharacteristicPolynomial: working on determinant of minor 4
CharacteristicPolynomial: working on determinant of minor 5

 

Vector(5, {(1) = -10, (2) = 1/10+I, (3) = 1/10-I, (4) = 1/10+I, (5) = 1/10-I})

(1.1.2)
> 

A11 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(5, 5, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 1.00000, (5, 1) = -10.20100, (5, 2) = 3.01990, (5, 3) = -20.19600, (5, 4) = 1.94000, (5, 5) = -9.60000})

(1.1.3)
> 

Digits := 89;
LinearAlgebra:-Eigenvalues( A11 );

Digits := 89

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881249354686)

(1.1.4)
> 

Digits := 90;
LinearAlgebra:-Eigenvalues( A11 );

Digits := 90

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881249352150)

(1.1.5)
> 

A12 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(5, 5, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (1, 5) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (2, 5) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (3, 5) = 0.+0.*I, (4, 1) = 0.+0.*I, (4, 2) = 0.+0.*I, (4, 3) = 0.+0.*I, (4, 4) = 0.+0.*I, (4, 5) = 1.00000+0.*I, (5, 1) = -10.20100+0.*I, (5, 2) = 3.01990+0.*I, (5, 3) = -20.19600+0.*I, (5, 4) = 1.94000+0.*I, (5, 5) = -9.60000+0.*I})

(1.1.6)
> 

Digits := 100;
LinearAlgebra:-Eigenvalues( A12 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881249345038)

(1.1.7)
> 

Digits := 250;
LinearAlgebra:-Eigenvalues( A12 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881342643606)

(1.1.8)
> 

 

> 

 

Example 2

 
> 

A2 := Matrix(3, 3, [[0, 1, 0], [0, 0, 1], [3375, -675, 45]]);

Matrix(3, 3, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (3, 1) = 3375, (3, 2) = -675, (3, 3) = 45})

(1.2.1)
> 

LinearAlgebra:-Eigenvalues( A2 );

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 3 x 3 matrix

IntegerCharacteristicPolynomial: Using prime 33554393
IntegerCharacteristicPolynomial: Using prime 33554383
IntegerCharacteristicPolynomial: Used total of  2  prime(s)

 

Vector(3, {(1) = 15, (2) = 15, (3) = 15})

(1.2.2)
> 

A21 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(3, 3, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (3, 1) = 3375.00000, (3, 2) = -675.00000, (3, 3) = 45.00000})

(1.2.3)
> 

Digits := 77;
LinearAlgebra:-Eigenvalues( A21 );

Digits := 77

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881342621686)

(1.2.4)
> 

Digits := 78;
LinearAlgebra:-Eigenvalues( A21 );

Digits := 78

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881342617230)

(1.2.5)
> 

A22 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(3, 3, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (3, 1) = 3375.00000+0.*I, (3, 2) = -675.00000+0.*I, (3, 3) = 45.00000+0.*I})

(1.2.6)
> 

Digits := 58;
LinearAlgebra:-Eigenvalues( A22 );

Digits := 58

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881342614934)

(1.2.7)
> 

Digits := 59;
LinearAlgebra:-Eigenvalues( A22 );

Digits := 59

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881325525942)

(1.2.8)
> 

 

> 

 

Example 3

 
> 

A3 := Matrix(4, 4, [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-48841, 8840, -842, 40]]);

Matrix(4, 4, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (4, 1) = -48841, (4, 2) = 8840, (4, 3) = -842, (4, 4) = 40})

(1.3.1)
> 

LinearAlgebra:-Eigenvalues( A3 );

IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix
IntegerCharacteristicPolynomial: Using prime 33554393

IntegerCharacteristicPolynomial: Using prime 33554383
IntegerCharacteristicPolynomial: Used total of  2  prime(s)

 

Vector(4, {(1) = 10+11*I, (2) = 10-11*I, (3) = 10+11*I, (4) = 10-11*I})

(1.3.2)
> 

A31 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(4, 4, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (4, 1) = -48841.00000, (4, 2) = 8840.00000, (4, 3) = -842.00000, (4, 4) = 40.00000})

(1.3.3)
> 

Digits := 75;
LinearAlgebra:-Eigenvalues( A31 );

Digits := 75

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881324662046)

(1.3.4)
> 

Digits := 76;
LinearAlgebra:-Eigenvalues( A31 );

Digits := 76

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881324657710)

(1.3.5)
> 

A32 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(4, 4, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (4, 1) = -48841.00000+0.*I, (4, 2) = 8840.00000+0.*I, (4, 3) = -842.00000+0.*I, (4, 4) = 40.00000+0.*I})

(1.3.6)
> 

Digits := 100;
LinearAlgebra:-Eigenvalues( A32 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881324648198)

(1.3.7)
> 

Digits := 250;
LinearAlgebra:-Eigenvalues( A32 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881327288182)

(1.3.8)
> 

 

> 

 

Example 4

 
> 

A4 := Matrix(8, 8, [[0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1050625/20736, 529925/1296, -15417673/10368, 3622249/1296, -55468465/20736, 93265/108, -1345/8, 52/3]]);

Matrix(8, 8, {(1, 1) = 0, (1, 2) = 1, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 1, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 1, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 1, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 1, (5, 7) = 0, (5, 8) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 1, (6, 8) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 1, (8, 1) = -1050625/20736, (8, 2) = 529925/1296, (8, 3) = -15417673/10368, (8, 4) = 3622249/1296, (8, 5) = -55468465/20736, (8, 6) = 93265/108, (8, 7) = -1345/8, (8, 8) = 52/3})

(1.4.1)
> 

LinearAlgebra:-Eigenvalues( A4 );

CharacteristicPolynomial: working on determinant of minor 2
CharacteristicPolynomial: working on determinant of minor 3

CharacteristicPolynomial: working on determinant of minor 4
CharacteristicPolynomial: working on determinant of minor 5
CharacteristicPolynomial: working on determinant of minor 6
CharacteristicPolynomial: working on determinant of minor 7
CharacteristicPolynomial: working on determinant of minor 8

 

Vector(8, {(1) = 1/3-(1/4)*I, (2) = 1/3+(1/4)*I, (3) = 4-5*I, (4) = 4+5*I, (5) = 1/3-(1/4)*I, (6) = 1/3+(1/4)*I, (7) = 4-5*I, (8) = 4+5*I})

(1.4.2)
> 

A41 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-sfloat' );

Matrix(8, 8, {(1, 1) = 0., (1, 2) = 1.00000, (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (1, 6) = 0., (1, 7) = 0., (1, 8) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 1.00000, (2, 4) = 0., (2, 5) = 0., (2, 6) = 0., (2, 7) = 0., (2, 8) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 1.00000, (3, 5) = 0., (3, 6) = 0., (3, 7) = 0., (3, 8) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 1.00000, (4, 6) = 0., (4, 7) = 0., (4, 8) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0., (5, 6) = 1.00000, (5, 7) = 0., (5, 8) = 0., (6, 1) = 0., (6, 2) = 0., (6, 3) = 0., (6, 4) = 0., (6, 5) = 0., (6, 6) = 0., (6, 7) = 1.00000, (6, 8) = 0., (7, 1) = 0., (7, 2) = 0., (7, 3) = 0., (7, 4) = 0., (7, 5) = 0., (7, 6) = 0., (7, 7) = 0., (7, 8) = 1.00000, (8, 1) = -50.66671, (8, 2) = 408.89275, (8, 3) = -1487.04408, (8, 4) = 2794.94522, (8, 5) = -2674.98384, (8, 6) = 863.56481, (8, 7) = -168.12500, (8, 8) = 17.33333})

 (1.4.3)
> 

Digits := 74;
LinearAlgebra:-Eigenvalues( A41 );

Digits := 74

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881317242630)

(1.4.4)
> 

Digits := 75;
LinearAlgebra:-Eigenvalues( A41 );

Digits := 75

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_dgeevx_

 

Vector[column](%id = 18446745881317239134)

(1.4.5)
> 

A42 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );

Matrix(8, 8, {(1, 1) = 0.+0.*I, (1, 2) = 1.00000+0.*I, (1, 3) = 0.+0.*I, (1, 4) = 0.+0.*I, (1, 5) = 0.+0.*I, (1, 6) = 0.+0.*I, (1, 7) = 0.+0.*I, (1, 8) = 0.+0.*I, (2, 1) = 0.+0.*I, (2, 2) = 0.+0.*I, (2, 3) = 1.00000+0.*I, (2, 4) = 0.+0.*I, (2, 5) = 0.+0.*I, (2, 6) = 0.+0.*I, (2, 7) = 0.+0.*I, (2, 8) = 0.+0.*I, (3, 1) = 0.+0.*I, (3, 2) = 0.+0.*I, (3, 3) = 0.+0.*I, (3, 4) = 1.00000+0.*I, (3, 5) = 0.+0.*I, (3, 6) = 0.+0.*I, (3, 7) = 0.+0.*I, (3, 8) = 0.+0.*I, (4, 1) = 0.+0.*I, (4, 2) = 0.+0.*I, (4, 3) = 0.+0.*I, (4, 4) = 0.+0.*I, (4, 5) = 1.00000+0.*I, (4, 6) = 0.+0.*I, (4, 7) = 0.+0.*I, (4, 8) = 0.+0.*I, (5, 1) = 0.+0.*I, (5, 2) = 0.+0.*I, (5, 3) = 0.+0.*I, (5, 4) = 0.+0.*I, (5, 5) = 0.+0.*I, (5, 6) = 1.00000+0.*I, (5, 7) = 0.+0.*I, (5, 8) = 0.+0.*I, (6, 1) = 0.+0.*I, (6, 2) = 0.+0.*I, (6, 3) = 0.+0.*I, (6, 4) = 0.+0.*I, (6, 5) = 0.+0.*I, (6, 6) = 0.+0.*I, (6, 7) = 1.00000+0.*I, (6, 8) = 0.+0.*I, (7, 1) = 0.+0.*I, (7, 2) = 0.+0.*I, (7, 3) = 0.+0.*I, (7, 4) = 0.+0.*I, (7, 5) = 0.+0.*I, (7, 6) = 0.+0.*I, (7, 7) = 0.+0.*I, (7, 8) = 1.00000+0.*I, (8, 1) = -50.66671+0.*I, (8, 2) = 408.89275+0.*I, (8, 3) = -1487.04408+0.*I, (8, 4) = 2794.94522+0.*I, (8, 5) = -2674.98384+0.*I, (8, 6) = 863.56481+0.*I, (8, 7) = -168.12500+0.*I, (8, 8) = 17.33333+0.*I})

 (1.4.6)
> 

Digits := 100;
LinearAlgebra:-Eigenvalues( A42 );

Digits := 100

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881317227806)

(1.4.7)
> 

Digits := 250;
LinearAlgebra:-Eigenvalues( A42 );

Digits := 250

 

Eigenvalues: calling external function
Eigenvalues: initializing the output object
Eigenvalues: using software external library
Eigenvalues: CLAPACK sw_zgeevx_

 

Vector[column](%id = 18446745881356880102)

(1.4.8)
> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

> 

 

``


 

Download Problems_LinearAlgebra_Eigenvalues.mw

has anyone tried to use Peter Fritzone's book with...

Asked by: wswain 240
parameter modelica simulation
July 27 2019
0  4

has anyone tried to use Peter Fritzone's book with maplesim helloworld modelica??

 

The simple approach from Peter (creating a custom modelica component) is to getting started by running a simple simulation where x_dot(t) = - a*x,  where the normal form is x(t) = x^-a for logarithmic type decay.

plot of x(t) should be a decay curve.  

 

Maple Code

A:-LinkModel = fine, connects

 

SimData := A:-Simulate(outputs = x, returntype = datapoints, tf = 2);

Error, invalid input: Simulate expects value for keyword parameter [outputs, output] to be of type {list(algebraic), list(anyfunc(identical(t)))}, but received x
 

***********

Simcode

 

Model Main;

Imports

public HelloWorld HelloWorld1 annotation(Placement(transformation(origin={100.0,200.0},extent={{-20.0,-20.0},{20.0,20.0}},rotation=0)));
    annotation(
            Diagram(coordinateSystem(preserveAspectRatio=true, extent={{0,0},{200.0,200.0}}),graphics),
            Icon(coordinateSystem(preserveAspectRatio=true, extent={{0,0},{200.0,200.0}}),graphics={Rectangle(extent={{0,0},{200.0,200.0}}, lineColor={0,0,0})}),
            uses(Modelica(version="3.2.3")),
            experiment(
              StartTime = 0,
              StopTime = 2.0,
              __Maplesoft_solver = "ck45",
              __Maplesoft_adaptive = true,
              Tolerance = 0.1e-4,
              __Maplesoft_tolerance_abs = 0.1e-4,
              __Maplesoft_step_size = 0.1e-2,
              __Maplesoft_min_step_size = 0,
              __Maplesoft_max_step_size = 0,
              __Maplesoft_plot_points = 2000,
              __Maplesoft_numeric_jacobian = false,
              __Maplesoft_constraint_iterations = 50,
              __Maplesoft_event_iterations = 100,
              __Maplesoft_algebraic_error_control = false,
              __Maplesoft_algebraic_error_relaxation_factor = 1,
              __Maplesoft_rate_hysteresis = 0.1e-9,
              __Maplesoft_reduce_events = false,
              __Maplesoft_integration_diagnostics = false,
              __Maplesoft_compiler = true,
              __Maplesoft_compiler_optimize = true,
              __Maplesoft_scale_method = "none",
              __Maplesoft_plot_event_points = true
            )
    );

 

end Main;

class HelloWorld
    Real x (start =1);
    parameter Real a = 1;
equation
    der(x) = -a*x;
end HelloWorld;

How do you find Fourier Transform of non-integer p...

Asked by: Nadeem_Malik 20
fourier inttrans
July 27 2019
0  5

 

Dear Maple users,

I want to find an expression for the Fourier Transform (FT) of an expression like  f(t)=exp(-t^2)/t^a, where a>0 is a constant.

I note that integer values of a (postive or negative) is ok; but non-integer fails. See sheet attached where I have tried 1 or 2 cases, a=0, 1, 0.3, etc.

So the questions are:

(1) how can I find the FT of the above for typical non-integer values of a>0 ?

(2) how can I find the FT of the above for general a -- i.e. declare a as a parameter?

 

Thanks

Nadeem


 

with(inttrans)

fourier(exp(-t^2), t, w)

exp(-(1/4)*w^2)*Pi^(1/2)

 (1)

fourier(t*exp(-t^2), t, w)

-((1/2)*I)*w*exp(-(1/4)*w^2)*Pi^(1/2)

 (2)

fourier(exp(-t^2)/t, t, w)

-I*Pi*erf((1/2)*w)

 (3)

fourier(t^.3*exp(-t^2), t, w)

fourier(t^(3/10)*exp(-t^2), t, w)

 (4)

fourier(exp(-t^2)/t^.3, t, w)

fourier(exp(-t^2)/t^(3/10), t, w)

 (5)

``


 

Download Sheet_fourier_1.mw

i want to plot a few equation with animate plot or...

Asked by: kambiz1199 170
animate plotting
July 27 2019
1  7

hi 

i want to plot this equations , i want to show that step by step and remind previous . i plot with animte plot but it do not show the previous

 

restart;
with(plottools);
co := blue;
with(plots);

t := 1;
for i from 20 by -1 to 0 do t := t+1; a[i] := -i*x/t+i; p[i] := plot(a[i], x = 0 .. 20, y = 0 .. 20, color = co, thickness = 3) end do;

plots[animate](plot, [a[k], x = 0 .. 20, y = 0 .. 20], k = [seq(i, i = 1 .. 20)]);

Elliptical PDEs...

Asked by: Oliveira 210
pde numeric pdsolve
July 27 2019
2  3

pde := (diff(u(r, theta), r) + r * diff(u(r, theta), r, r) + diff(u(r, theta), theta, theta) / r ) / r:
iv := u( 1, theta) = 0, u( 3, theta) = theta, u( r, 0) = 10, u( r, Pi/2) = 0:
           Maple 2019 returns a symbolic solution for PDE:
pdsolve([pde, iv], u(r, theta));
   But for the numeric option, it returns a message saying that Maple is unable to handle elliptical PDEs.
pdsolve(pde, {iv}, numeric, time = t, range = 1 .. 3);

Error, (in pdsolve/numeric) unable to handle elliptic PDEs
I found it strange.

Oliveira.

FUNCTIONAL FORM OF INTERPOLATON...

Asked by: radaar 202
optimization interpolation
July 27 2019
0  1

How to get the functional form of interpolation in the given example below

 

GP.mw

Fractional differential equation...

Asked by: Sina Sadighi 5
fractional-derivative
July 27 2019
1  1

Hi

please help me, how could I write this? 

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