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Where is the problem in my loop which increases th...

Asked by: mehdibgh 240
performance integration memory
September 01 2022
0  6

In part of my program, I have a loop that the iterative calculations are performed there. During running the program when it comes to the loop the memory usage become full in a short period of time and I face the memory shortage. Since my program is so long and huge, I only can show the loop part of it here, you may look at where is the problem of high memory usage in loop and how to deal with it. Any comment will be appreciated.

I again note that, this segment can not be run independently since it is a part of big program. I put it just to see and mmake comment if any.

> 

M := 3; Nm := 1
> 

w0 := Matrix(M+Nm, 1)
> 

wd0 := Matrix(M+Nm, 1)
> 

taim := 1
> 

F0 := convert([seq(Quadrature(Quadrature(simplify(add(add(W[i, j, 4, r]*LegendreP(i, 1)*LegendreP(j, 0), i = 0 .. II), j = 0 .. JJ)), `ζ__1` = -1 .. 1, method = romberg[3]), `η__1` = -1 .. 1, method = romberg[3]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)
> 

T := 1/(2*Pi*`ω__km`[M][2])
> 

dt := (1/10)*T

0.1123479896110e-4

 (1)
> 

for i to M do tau[i](t) := tau[i] end do
> 

for i to Nm do p[i](t) := p[i] end do
> 

`α__N` := .5; `β__N` := .25; a__0 := 1/(`β__N`*dt^2); a__1 := `α__N`/(`β__N`*dt); a__2 := 1/(`β__N`*dt); a__3 := 1/(2*`β__N`)-1; a__4 := `α__N`/`β__N`-1; a__5 := dt*(`α__N`/(2*`β__N`)-1); a__6 := dt*(1-`α__N`); a__7 := `α__N`*dt
> 

q := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

dq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

ddq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

q(1 .. M+Nm, 1) := w0
> 

dq(1 .. M+Nm, 1) := wd0
> 

for i to M do tau[i] := q(i, 1) end do
> 

for i to Nm do p[i] := q(M+i, 1) end do
> 

ddq(1 .. M+Nm, 1) := 1/ML.(diff((diff(sin(`ω__b`*t__0), t__0))*LinearAlgebra:-Transpose(F0), t__0)-CL.dq(1 .. M+Nm, 1 .. 1)-KL.q(1 .. M+Nm, 1 .. 1)-eqMNL)
> 

t__0 := dt
> 

V := LinearAlgebra:-Transpose(convert([seq(Tau[i], i = 1 .. M), seq(P[i], i = 1 .. Nm)], Matrix))
> 

Qn__2 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))
> 

Qn__3 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

External force

 
> 

`ω__b` := 25

> 

``

> 

F := diff((diff(sin(`ω__b`*t), t))*LinearAlgebra:-Transpose(convert(F0, Matrix)), t)

> 

``
> 

s := 1
> 

k__d := 100000
> 

with(Student[NumericalAnalysis]); dt
> 

``

Loop

 
> 

for t from t__0 by dt to taim do EQ := KL.V+a__0*ML.V+a__1*CL.V-ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))-CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))-F-Qn__2-Qn__3; G := Matrix(M+Nm, proc (i, j) options operator, arrow; (diff(EQ[i], V[j, 1]))[1] end proc); G1 := 1/G; if t = t__0 then X[1] := 1/(CL*a__1+ML*a__0+KL).(F+ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))+CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))) else X[1] := q(1 .. M+Nm, s .. s) end if; for k to 11 do X[k+1] := eval(V-G1.EQ, Equate(V, X[k])) end do; q(1 .. M+Nm, s+1 .. s+1) := X[k]; ddq(1 .. M+Nm, s+1 .. s+1) := a__0*(q(1 .. M+Nm, s+1 .. s+1)-q(1 .. M+Nm, s .. s))-a__2*dq(1 .. M+Nm, s .. s)-a__3*ddq(1 .. M+Nm, s .. s); dq(1 .. M+Nm, s+1 .. s+1) := dq(1 .. M+Nm, s .. s)+a__6*ddq(1 .. M+Nm, s .. s)+a__7*ddq(1 .. M+Nm, s+1 .. s+1); Wxy2 := add(add(add(h*W[i, j, 2, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Wxy3 := add(add(add(h*W[i, j, 3, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Plt := plots:-implicitplot(Wxy2-Wxy3, `&zeta;__2` = -1 .. 1, `&eta;__2` = -1 .. 1, color = red, thickness = 2, gridrefine = 3); j := 111111; Hvs2 := 1; for i while i <= j do Pnt[i] := op([1, i], Plt); if Wxy2-Wxy3 = 0 then j := 0 elif convert(Pnt[i], string)[1] = "C" then j := 0 else a__e[i] := (1/2)*abs(max(Column(Pnt[i], 1))-min(Column(Pnt[i], 1))); if a__e[i] = 0 then a__e[i] = 0.1e-5 end if; b__e[i] := (1/2)*abs(max(Column(Pnt[i], 2))-min(Column(Pnt[i], 2))); if b__e[i] = 0 then b__e[i] = 0.1e-5 end if; xc[i] := (max(Column(Pnt[i], 1))+min(Column(Pnt[i], 1)))*(1/2); yc[i] := (max(Column(Pnt[i], 2))+min(Column(Pnt[i], 2)))*(1/2); Hv2[i] := ((`&zeta;__2`-xc[i])/a__e[i])^2+((`&eta;__2`-yc[i])/b__e[i])^2-1; Hvs2 := Hv2[i]*Hvs2 end if end do; Qn__2 := LinearAlgebra:-Transpose(convert([(1/2)*k__d*Grid:-Seq(Quadrature(Quadrature(Heaviside(-Hvs2)*abs(Wxy2-Wxy3)*add(add(W[i, j, 2, r]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`), i = 0 .. II), j = 0 .. JJ), `&zeta;__2` = -1 .. 1, method = romberg[5]), `&eta;__2` = -1 .. 1, method = romberg[5]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)); Qn__3 := -Qn__2; s := s+1 end do

``

Download HighMemUseProb.mw

Rotate graph on x and y components...

Asked by: kencom1 115
plotting
August 30 2022
0  3

Good day everyone, 

Can I plot the graph of the sheet attached below such that x will be on the vertical component and y will be on the horizontal component? Can this be done on Maple? Anyone with useful information should please help.

plot_graph.mw

Why extracting a n*1 matrix from n*m matrix gives...

Asked by: mehdibgh 240
matrix vector indexing
August 24 2022
0  1

I am trying to do the following computation. I  extracted n*1 matrix from n*n matrix which unbelievably gives vector?

How I can do the following multiplication without using convert command? Or how to extract n*1 matrix (not vector) from n*n matrix without using convert?

> 

``
> 

restart
> 

``
> 

``
> 

A := Matrix(4, 4, {(1, 1) = m[1, 1], (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = m[2, 1], (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = m[3, 1], (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = m[4, 1], (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

A := Matrix(4, 4, {(1, 1) = 0, (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = 0, (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = 0, (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = 0, (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

 (1)
> 

A(1 .. 4, 1) := Matrix(4, 1):
> 

A

Matrix([[0, m[1, 2], m[1, 3], m[1, 4]], [0, m[2, 2], m[2, 3], m[2, 4]], [0, m[3, 2], m[3, 3], m[3, 4]], [0, m[4, 2], m[4, 3], m[4, 4]]])

 (2)
> 

B := A(1 .. 4, 2)

B := Vector(4, {(1) = m[1, 2], (2) = m[2, 2], (3) = m[3, 2], (4) = m[4, 2]})

 (3)
> 

A.B

4

 (4)
> 

F := Matrix(4, 1, {(1, 1) = 0.4279668887e-7, (2, 1) = -0.3901148183e-7, (3, 1) = 0.3900685346e-7, (4, 1) = 0.})
> 

Typesetting:-delayDotProduct(A, B)-F

Error, (in rtable/Sum) invalid input: dimensions do not match: Vector[column](1 .. 4) cannot be added to Matrix(1 .. 4, 1 .. 1)

  
> 

A.convert(B, Matrix)-F

Matrix(4, 1, {(1, 1) = m[1, 2]*m[2, 2]+m[1, 3]*m[3, 2]+m[1, 4]*m[4, 2]-0.4279668887e-7, (2, 1) = m[2, 2]^2+m[2, 3]*m[3, 2]+m[2, 4]*m[4, 2]+0.3901148183e-7, (3, 1) = m[3, 2]*m[2, 2]+m[3, 3]*m[3, 2]+m[3, 4]*m[4, 2]-0.3900685346e-7, (4, 1) = m[2, 2]*m[4, 2]+m[3, 2]*m[4, 3]+m[4, 2]*m[4, 4]})

 (5)

``

Download soalzarb.mw

How can the multiplication of two functions be con...

Asked by: moh111 20
multiplication
August 22 2022
2  13

If i have p := 8*T(x, 7)*T(x, 2)+4*T(x, 5)*T(x, 1)+6*T(x, 3)*T(x, 3)+7*T(x, 1)*T(x, 4)

 I want to convert the the multiplication functions like T(x, 7)*T(x, 2) into summation T(x, 7)+T(x, 2)

How to plot sequencially points created in a loop ...

Asked by: mehdibgh 240
August 19 2022
1  7

I want to plot a number created in a loop to monitor how it varies while keeping all previous ones on the figure. This is simply done in Matlab by hold on command, but I dont know how it is possible in Maple?

for i to 22 do
plot([i], [i^.5], style = point) :
end do

Note I want to monitor points during the loop running not after it finishes.

Why romberg method do not work for integration if...

Asked by: mehdibgh 240
integration numeric heaviside
August 15 2022
0  4

I am trying to find a fast method for integration of a function composed of several Heavisides. I used Quadrature-Romberg, but no success. What is the problem with it and what method do you recommend instead?

``

> 

restart
> 

``
> 

A := Heaviside(zeta__2-.6429162216568)*Heaviside(eta__2+.5050000000000-10.98537767108*sqrt(492.5151416233-zeta__2^2))+Heaviside(zeta__2-.9999999999936)*Heaviside(eta__2+.9875792458758+3.881485663812*10^9*sqrt(9.765625000000*10^22-zeta__2^2))+Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2-.4637698986762+2.327456686822*10^11*sqrt(2.777777777778*10^24-zeta__2^2))-Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2-.4637698986762-2.327456686822*10^11*sqrt(2.777777777778*10^24-zeta__2^2))+Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.1619291800251+3.018371923484*10^11*sqrt(4.000000000000*10^24-zeta__2^2))-Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.1619291800251-3.018371923484*10^11*sqrt(4.000000000000*10^24-zeta__2^2))+Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.7243706106403+1.382194833711*10^11*sqrt(1.562500000000*10^24-zeta__2^2))-Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.7243706106403-1.382194833711*10^11*sqrt(1.562500000000*10^24-zeta__2^2))+Heaviside(zeta__2-1.000000000000)*Heaviside(eta__2+.9875792458758-3.881485663812*10^9*sqrt(9.765625000000*10^22-zeta__2^2))-Heaviside(zeta__2-1.000000000000)*Heaviside(eta__2+.9875792458758+3.881485663812*10^9*sqrt(9.765625000000*10^22-zeta__2^2))+Heaviside(zeta__2-1.000000000000)*Heaviside(eta__2-.8341191288491-1.298592148442*10^10*sqrt(9.706617486471*10^21-zeta__2^2))-Heaviside(zeta__2-1.000000000000)*Heaviside(eta__2-.8341191288491+1.298592148442*10^10*sqrt(9.706617486471*10^21-zeta__2^2))-Heaviside(zeta__2-.9999999999796)*Heaviside(eta__2-.8341191288491-1.298592148442*10^10*sqrt(9.706617486471*10^21-zeta__2^2))-Heaviside(zeta__2-.5527964251744)*Heaviside(eta__2+.5050000000000-10.98537767108*sqrt(492.5151416233-zeta__2^2))+Heaviside(zeta__2-.5527964251744)*Heaviside(eta__2+.5050000000000+10.98537767108*sqrt(492.5151416233-zeta__2^2))+Heaviside(zeta__2-.7684252323012)*Heaviside(eta__2-.5050000000000-8.127372424924*sqrt(269.5813999936-zeta__2^2))-Heaviside(zeta__2-.6466146460206)*Heaviside(eta__2-.5050000000000-8.127372424924*sqrt(269.5813999936-zeta__2^2))-Heaviside(zeta__2-.7684252323012)*Heaviside(eta__2-.5050000000000+8.127372424924*sqrt(269.5813999936-zeta__2^2))+Heaviside(zeta__2-.6466146460206)*Heaviside(eta__2-.5050000000000+8.127372424924*sqrt(269.5813999936-zeta__2^2))-Heaviside(zeta__2-.9999999999936)*Heaviside(eta__2+.9875792458758-3.881485663812*10^9*sqrt(9.765625000000*10^22-zeta__2^2))+Heaviside(zeta__2-.9999999999796)*Heaviside(eta__2-.8341191288491+1.298592148442*10^10*sqrt(9.706617486471*10^21-zeta__2^2))+Heaviside(zeta__2+.9999999999972)*Heaviside(eta__2+.9842650870048-1.085166413462*10^10*sqrt(4.756242568371*10^23-zeta__2^2))-Heaviside(zeta__2+.9999999999972)*Heaviside(eta__2+.9842650870048+1.085166413462*10^10*sqrt(4.756242568371*10^23-zeta__2^2))+Heaviside(zeta__2+.9999999999990)*Heaviside(eta__2+.1619291800251-3.018371923484*10^11*sqrt(4.000000000000*10^24-zeta__2^2))-Heaviside(zeta__2+.9999999999990)*Heaviside(eta__2+.1619291800251+3.018371923484*10^11*sqrt(4.000000000000*10^24-zeta__2^2))+Heaviside(zeta__2+.9999999999988)*Heaviside(eta__2-.4637698986762-2.327456686822*10^11*sqrt(2.777777777778*10^24-zeta__2^2))-Heaviside(zeta__2+.9999999999988)*Heaviside(eta__2-.4637698986762+2.327456686822*10^11*sqrt(2.777777777778*10^24-zeta__2^2))+Heaviside(zeta__2+.9999999999984)*Heaviside(eta__2+.7243706106403-1.382194833711*10^11*sqrt(1.562500000000*10^24-zeta__2^2))-Heaviside(zeta__2+.9999999999984)*Heaviside(eta__2+.7243706106403+1.382194833711*10^11*sqrt(1.562500000000*10^24-zeta__2^2))+Heaviside(zeta__2+.9999999999984)*Heaviside(eta__2-.9031048925918-8.123652892875*10^10*sqrt(1.562500000000*10^24-zeta__2^2))-Heaviside(zeta__2+.9999999999984)*Heaviside(eta__2-.9031048925918+8.123652892875*10^10*sqrt(1.562500000000*10^24-zeta__2^2))-Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.9842650870048-1.085166413462*10^10*sqrt(4.756242568371*10^23-zeta__2^2))+Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2+.9842650870048+1.085166413462*10^10*sqrt(4.756242568371*10^23-zeta__2^2))-Heaviside(zeta__2-.6429162216568)*Heaviside(eta__2+.5050000000000+10.98537767108*sqrt(492.5151416233-zeta__2^2))-Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2-.9031048925918-8.123652892875*10^10*sqrt(1.562500000000*10^24-zeta__2^2))+Heaviside(zeta__2+1.000000000000)*Heaviside(eta__2-.9031048925918+8.123652892875*10^10*sqrt(1.562500000000*10^24-zeta__2^2)):
> 

plot3d(A, zeta__2 = -1 .. 1, eta__2 = -1 .. 1, color = green)

 
> 

Digits := 22:
> 

with(Student[NumericalAnalysis]):
> 

Quadrature(Quadrature(A, zeta__2 = -1 .. 1, method = romberg[8]), eta__4 = -1 .. 1, method = romberg[8])

Float(undefined)*Heaviside(eta__2+1212964270000000000001.)+Float(undefined)*Heaviside(eta__2-1279401131003415700657.)-0.1513022270849353690226e-1*Heaviside(eta__2-133.8411610374164929382)+Float(undefined)*Heaviside(eta__2-7483906296259851792359.)+Float(undefined)*Heaviside(eta__2+7483906296259851792361.)+Float(undefined)*Heaviside(eta__2-0.1015456611625000000000e24)+Float(undefined)*Heaviside(eta__2+0.1015456611625000000000e24)+Float(undefined)*Heaviside(eta__2+0.3879094478488497112464e24)+Float(undefined)*Heaviside(eta__2+1279401131003415700655.)-0.4538512794872905686682e-1*Heaviside(eta__2-133.8360207224718595497)+0.4538512794872905686682e-1*Heaviside(eta__2+132.8260207224718595497)+0.4538512794872905686682e-1*Heaviside(eta__2+132.8042477794001150390)-0.4538512794872905686682e-1*Heaviside(eta__2-133.8253766167816064928)-0.4538512794872905686682e-1*Heaviside(eta__2-243.1883998382669648802)+0.1513022270849353690226e-1*Heaviside(eta__2+132.8311610374164929382)+Float(undefined)*Heaviside(eta__2-0.1727743542500000000000e24)-0.1513022270849353690226e-1*Heaviside(eta__2-243.2027260661341424950)+0.1513022270849353690226e-1*Heaviside(eta__2+244.2127260661341424950)+0.4538512794872905686682e-1*Heaviside(eta__2+244.1983998382669648802)-0.4538512794872905686682e-1*Heaviside(eta__2-243.1980716456433769010)+0.4538512794872905686682e-1*Heaviside(eta__2+244.2080716456433769010)+0.4538512794872905686682e-1*Heaviside(eta__2+132.8153766167816064928)+0.1513022270849353690226e-1*Heaviside(eta__2+132.8098727970154075001)+Float(undefined)*Heaviside(eta__2-0.3879094478488497112464e24)-0.4538512794872905686682e-1*Heaviside(eta__2-243.2072595071292620415)+Float(undefined)*Heaviside(eta__2+0.6036743846000000000000e24)+Float(undefined)*Heaviside(eta__2-0.6036743846000000000000e24)+Float(undefined)*Heaviside(eta__2+0.1727743542500000000000e24)-0.1916322521366165064753e-1*Heaviside(eta__2-133.8307592537082147847)+0.1916322521366165064753e-1*Heaviside(eta__2+132.8207592537082147847)-0.1916322521366165064753e-1*Heaviside(eta__2-243.2116719753798543789)+0.1916322521366165064753e-1*Heaviside(eta__2+244.2216719753798543789)-0.4538512794872905686682e-1*Heaviside(eta__2-133.8026340889186250133)+0.4538512794872905686682e-1*Heaviside(eta__2+132.7926340889186250133)-0.4538512794872905686682e-1*Heaviside(eta__2-133.8142477794001150390)-0.1513022270849353690226e-1*Heaviside(eta__2-133.8198727970154075001)+0.4538512794872905686682e-1*Heaviside(eta__2+244.2172595071292620415)-0.1903631769101229216919e-1*Heaviside(eta__2-133.8085015485931455736)+0.1903631769101229216919e-1*Heaviside(eta__2+132.7985015485931455736)+0.1903531841918040745676e-1*Heaviside(eta__2+244.2032962387251632874)-0.1903531841918040745676e-1*Heaviside(eta__2-243.1932962387251632874)+Float(undefined)*Heaviside(eta__2-1212964269999999999999.)

 (1)
> 

int(int(A, zeta__2 = -1 .. 1), eta__2 = -1 .. 1)

.4238607655960000000000

 (2)
> 

``

Download romberg.mw

How to solve a set of equaions using fsolve?...

Asked by: mehdibgh 240
matrix indexing fsolve
July 28 2022
0  11

I have a set of equations gathered in a vector. The number of equations varies each time. Here in this example it is 4. How you suggest so solve them with fsolve? I tried to use seq but faced error.

> 

restart
> 

EQ := Matrix(4, 1, {(1, 1) = 32.1640740637930*Tau[1]-0.172224519601111e-4*Tau[2]-0.270626540730518e-3*Tau[3]+0.1570620334e-9*P[1]+0.3715450960e-14*sin(t), (2, 1) = -0.172224519601111e-4*Tau[1]+32.1667045885952*Tau[2]+0.587369829416537e-4*Tau[3]-0.1589565489e-8*P[1]+0.1004220091e-12*sin(t), (3, 1) = -0.270626540730518e-3*Tau[1]+0.587369829416537e-4*Tau[2]+32.1816411689934*Tau[3]-0.7419658527e-8*P[1]+0.5201228088e-12*sin(t), (4, 1) = 0.1570620334e-9*Tau[1]-0.1589565489e-8*Tau[2]-0.7419658527e-8*Tau[3]+601.876235436204*P[1]})
> 

V := Matrix(1, 4, {(1, 1) = Tau[1], (1, 2) = Tau[2], (1, 3) = Tau[3], (1, 4) = P[1]})
> 

q := 0
> 

X := Matrix(4, 1, {(1, 1) = -0.1156532164e-15*sin(t), (2, 1) = -0.3121894613e-14*sin(t), (3, 1) = -0.1616209235e-13*sin(t), (4, 1) = -0.2074537757e-24*sin(t)})
> 

t := 1
> 

Xf := fsolve({seq(EQ[r], r = 1 .. 4)}, {seq(V[r] = q .. X[r], r = 1 .. 4)})

Error, Matrix index out of range``

``

Download SoalNewton.mw

Why GenerateMatrix produces wrong results?...

Asked by: mehdibgh 240
linearalgebra generatematrix
June 22 2022
1  1

Why GenerateMatrix produces wrong results?

``

> 

restart
> 

N := 2:
> 

a := 1:
> 

with(ArrayTools):
> 

``
> 

Qa := [-0.5379667864e-1*(diff(tau[1, 1](t), t, t))+7.862351349*10^(-11)*tau[2, 1](t)-8.050993899*10^(-12)*(diff(tau[2, 1](t), t, t))+.1166068042*(diff(tau[1, 2](t), t))+2.181309895*10^(-11)*(diff(tau[2, 2](t), t))+.5309519363*tau[1, 1](t) = 0, -1.265965258*10^(-11)*(diff(tau[1, 1](t), t, t))+.4884414390*tau[2, 1](t)-0.4948946475e-1*(diff(tau[2, 1](t), t, t))+2.738892495*10^(-11)*(diff(tau[1, 2](t), t))+.1340883970*(diff(tau[2, 2](t), t))+1.246469610*10^(-10)*tau[1, 1](t) = 0, 3.649366137*10^(-10)*tau[2, 2](t)-9.135908950*10^(-12)*(diff(tau[2, 2](t), t, t))-5.160677740*10^(-11)*(diff(tau[2, 1](t), t))+1.953765755*tau[1, 2](t)-0.4948946473e-1*(diff(tau[1, 2](t), t, t))-.3476543209*(diff(tau[1, 1](t), t)) = 0, 2.246672656*tau[2, 2](t)-0.5690888318e-1*(diff(tau[2, 2](t), t, t))-.3198194887*(diff(tau[2, 1](t), t))+4.602903411*10^(-10)*tau[1, 2](t)-1.159417294*10^(-11)*(diff(tau[1, 2](t), t, t))-8.175817372*10^(-11)*(diff(tau[1, 1](t), t)) = 0]
> 

Q1 := [seq(seq(diff(tau[i, j](t), t), i = 1 .. M), j = 1 .. N)]

[diff(tau[1, 1](t), t), diff(tau[2, 1](t), t), diff(tau[1, 2](t), t), diff(tau[2, 2](t), t)]

 (1)
> 

with(LinearAlgebra):
> 

CR := GenerateMatrix(simplify(Qa), Q1)

CR := Matrix(4, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = .1166068042, (1, 4) = 0.2181309895e-10, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0.2738892495e-10, (2, 4) = .1340883970, (3, 1) = -.3476543209, (3, 2) = -0.5160677740e-10, (3, 3) = 0, (3, 4) = 0, (4, 1) = -0.8175817372e-10, (4, 2) = -.3198194887, (4, 3) = 0, (4, 4) = 0}), Vector(4, {(1) = 0.5379667864e-1*(diff(diff(tau[1, 1](t), t), t))-0.7862351349e-10*tau[2, 1](t)+0.8050993899e-11*(diff(diff(tau[2, 1](t), t), t))-.5309519363*tau[1, 1](t), (2) = 0.1265965258e-10*(diff(diff(tau[1, 1](t), t), t))-.4884414390*tau[2, 1](t)+0.4948946475e-1*(diff(diff(tau[2, 1](t), t), t))-0.1246469610e-9*tau[1, 1](t), (3) = -0.3649366137e-9*tau[2, 2](t)+0.9135908950e-11*(diff(diff(tau[2, 2](t), t), t))-1.953765755*tau[1, 2](t)+0.4948946473e-1*(diff(diff(tau[1, 2](t), t), t)), (4) = -2.246672656*tau[2, 2](t)+0.5690888318e-1*(diff(diff(tau[2, 2](t), t), t))-0.4602903411e-9*tau[1, 2](t)+0.1159417294e-10*(diff(diff(tau[1, 2](t), t), t))})

 (2)
> 

``
> 

``
> 

``

Download GenMatrix.mw

Do you know why increasing the number of applicati...

Asked by: mehdibgh 240
integration numeric romberg
June 11 2022
0  5

Do you know why increasing the number of applications of trapezoidal rule results infinity and imaginary part?

I want get result for Romberg Integration Method with 6 Applications of Trapezoidal Rule.

> 

restart
> 

with(Student[NumericalAnalysis]):
> 

``
> 

fff := (eta__1^2-1.)^2*(zeta__1^2-1.)^2*(-5.6584306313*10^(-8)*eta__1^4*zeta__1^4-1.0454641424*10^(-8)*eta__1*zeta__1^4+5.6161016651*10^(-9)*eta__1^3*zeta__1^4+1.0615594865*10^(-8)*eta__1^5*zeta__1^4+5.4851856568*10^(-9)*eta__1^3*zeta__1^2-1.4132765167*10^(-8)*eta__1^5*zeta__1^2-7.8157365683*10^(-7)*zeta__1*eta__1^4+2.9373057668*10^(-8)*eta__1^5*zeta__1^5-7.032574429*10^(-8)*eta__1^3*zeta__1^5-5.2577413654*10^(-8)*eta__1^5*zeta__1^3+2.3272955826*10^(-8)*eta__1^5*zeta__1+1.5782217112*10^(-7)*eta__1^3*zeta__1^3+2.1771522925*10^(-8)*eta__1*zeta__1^5-8.3051507888*10^(-8)*eta__1^3*zeta__1-2.2997952126*10^(-8)*eta__1*zeta__1^3+0.22608138853e-5*eta__1^4-0.53519692056e-5*eta__1^2+0.62041471332e-4+0.54946587424e-4*zeta__1^2-0.10412827312e-5*zeta__1^4-0.53422910417e-5*zeta__1^3+0.12053033309e-3*zeta__1-4.5961086182*10^(-8)*eta__1^2*zeta__1^4-1.6404108106*10^(-7)*zeta__1^2*eta__1-1.5606093643*10^(-7)*zeta__1*eta__1^2-4.168658171*10^(-7)*zeta__1*eta__1-0.5430102455e-5*eta__1^2*zeta__1^5+0.87015148204e-5*eta__1^2*zeta__1^3+0.25592467903e-5*eta__1^4*zeta__1^5-0.4071733639e-5*eta__1^4*zeta__1^3-0.44664222239e-5*eta__1^4*zeta__1^2+0.84495460425e-5*eta__1^2*zeta__1^2+7.5007400675*10^(-7)*zeta__1^5-6.6427826628*10^(-9)*eta__1^3+3.5821686059*10^(-9)*eta__1^5-2.4361928132*10^(-7)*eta__1)/(-0.32350168299e-2*eta__1^5-0.40854298828e-3*zeta__1^8-0.57170204466e-1*eta__1^8+.26989142602*zeta__1^7+.34307133883*eta__1^6+.14111119517*eta__1^4-0.48267577378e-1*zeta__1^9-1.082755589*eta__1^2-1.3163499567*zeta__1^2+0.75042415188e-3*eta__1^7-0.40463518464e-2*zeta__1^6+.66506159208*zeta__1^4+.58641863992*zeta__1^3-0.18089939414e-3*eta__1^9-.60151130424*zeta__1^5+0.49423587807e-2*eta__1^3-0.22768667085e-2*eta__1-.20653118433*zeta__1-.15635457174*eta__1^8*zeta__1+.64029273264*eta__1^8*zeta__1^3-1.8403657443*eta__1^6*zeta__1^7-0.48478855017e-1*eta__1^8*zeta__1^4-0.22007436935e-2*eta__1^2*zeta__1^8+0.56271163518e-2*eta__1^4*zeta__1^8-.22701198791*eta__1^6*zeta__1^6-0.18753531811e-2*eta__1*zeta__1^9+0.63616448215e-2*eta__1^3*zeta__1^9-0.70972300998e-2*eta__1^5*zeta__1^9+0.26109384594e-2*eta__1^7*zeta__1^9+0.37597513815e-2*eta__1^9*zeta__1^7-.81152175007*eta__1^8*zeta__1^5+.32758358916*eta__1^8*zeta__1^7+.60516338422*eta__1^6*zeta__1-2.7777061884*eta__1^6*zeta__1^3+3.8764153863*eta__1^6*zeta__1^5+0.14976271107e-3*eta__1*zeta__1^8+0.64408301026e-3*eta__1^3*zeta__1^8-0.17374541537e-2*eta__1^5*zeta__1^8+0.9436084324e-3*eta__1^7*zeta__1^8-0.95617026598e-3*eta__1*zeta__1^6-0.79980551762e-3*eta__1^3*zeta__1^6-0.43427014208e-2*eta__1^7*zeta__1^6+0.52833995188e-2*eta__1^5*zeta__1^6-0.39563328597e-2*eta__1^7*zeta__1^2-0.30978282387e-2*zeta__1*eta__1+3.4563944947*eta__1^2*zeta__1^5-2.669958003*eta__1^2*zeta__1^3-5.9197768267*eta__1^4*zeta__1^5+4.2209528188*eta__1^4*zeta__1^3+.1920464905*eta__1^4*zeta__1^2+1.9334990569*eta__1^2*zeta__1^2+0.66050016962e-2*eta__1^7*zeta__1^4+.80614880365*eta__1^6*zeta__1^4-.9191903249*eta__1^6*zeta__1^2-1.724981418*zeta__1^7*eta__1^2+2.9678721471*zeta__1^7*eta__1^4-.94779423754*zeta__1*eta__1^4+.46301464814*zeta__1^6*eta__1^4-.22761063366*zeta__1^6*eta__1^2-0.85894534062e-2*eta__1^5*zeta__1^4+0.8278524871e-2*eta__1^5*zeta__1^2+0.46097207851e-2*eta__1^3*zeta__1^4-0.93963570584e-2*eta__1^3*zeta__1^2-0.81381430978e-3*eta__1*zeta__1^4-.62093209055*eta__1^2*zeta__1^4-.80179945016*eta__1^4*zeta__1^4+.70551660939*zeta__1*eta__1^2+0.38970885732e-2*zeta__1^2*eta__1+0.10746052526e-1*eta__1*zeta__1^7-0.40389225121e-1*eta__1^3*zeta__1^7+0.52300044044e-1*eta__1^5*zeta__1^7+.10999473421*eta__1^8*zeta__1^2-0.45528793761e-1*eta__1^7*zeta__1^3+0.57167454208e-1*eta__1^7*zeta__1^5+0.11770764739e-2*eta__1^9*zeta__1^2-0.18114547653e-2*eta__1^9*zeta__1^4+0.81527768559e-3*eta__1^9*zeta__1^6+0.13191002642e-1*eta__1*zeta__1^3+0.14324735033e-1*eta__1^3*zeta__1-0.18963873748e-1*eta__1*zeta__1^5-0.56315405543e-1*eta__1^3*zeta__1^3-0.21374958034e-1*eta__1^5*zeta__1+0.7601825081e-1*eta__1^3*zeta__1^5+.65574325943+0.80855499912e-1*eta__1^5*zeta__1^3-.10468335582*eta__1^5*zeta__1^5-0.26416622831e-1*eta__1^7*zeta__1^7-0.20189726843e-2*eta__1^9*zeta__1+0.77976967502e-2*eta__1^9*zeta__1^3-0.95384754473e-2*eta__1^9*zeta__1^5+.13649316215*eta__1^6*zeta__1^9+.23302831691*eta__1^2*zeta__1^9-.32125390168*eta__1^4*zeta__1^9+0.12167023924e-1*eta__1^7*zeta__1-0.301782967e-2*eta__1^6*zeta__1^8-0.43456747248e-2*eta__1^8*zeta__1^6):
> 

plot3d(sqrt(fff), zeta__1 = -1 .. 1, eta__1 = -1 .. 1, color = green)

 
> 

``
> 

Quadrature(Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[3]), eta__1 = -1 .. 1, method = romberg[3])

0.2745463666e-1+0.*I

 (1)
> 

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[4]), eta__1 = -1 .. 1, method = romberg[4])

0.3314502549e-1+0.*I

 (2)
> 

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[5]), eta__1 = -1 .. 1, method = romberg[5])

0.3621732017e-1+0.*I

 (3)
> 

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[6]), eta__1 = -1 .. 1, method = romberg[6])

Float(undefined)+Float(undefined)*I

 (4)
> 

``

Download question.mw

How to speed up the calculation of the double inte...

Asked by: mehdibgh 240
performance integration legendrep
June 03 2022
1  1

I want to calculate the double integral of the following expression which includes sum of several Legendre polynomial terms, but the speed is so low. Any suggestion to speed up the calculation?

NULL

> 

Restart:
> 

NULL
> 

II := 9:
> 

JJ := 9:
> 

M := 9:
> 

NULL
> 

`&Delta;P1` := add(add(add(add(add(add(add(-(LegendreP(i, zeta__1)*LegendreP(j, eta__1)*(diff(diff(tau[r](t), t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*(diff(tau[r](t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*tau[r](t))/sqrt(LegendreP(m, zeta__1)*LegendreP(j, eta__1)+LegendreP(i, zeta__1)*LegendreP(l, eta__1)), i = 1 .. II), j = 1 .. JJ), k = 1 .. II), m = 1 .. II), l = 1 .. JJ), n = 1 .. JJ), r = 1 .. M):
> 

A := int(int(`&Delta;P1`, zeta__1 = -1 .. 1), eta__1 = -1 .. 1):
> 

A

``

Download Soal.mw

Maple seems to plot incorrectly...

Asked by: ProfG 15
floor plotting
May 11 2022
3  8

The function n->ceil(sqrt(4*n))-floor(sqrt(2*n))-1 counts the number of squares strictly between 2n and 4n.

Maple 2016 gives the same output as what I get when I create a plot here: plot(ceil(sqrt(4*n))-floor(sqrt(2*n))-1,n=10..100)

Note, however, that Maple does not plot at least the point of interest (72.4), which is nevertheless an element of the graph:

[10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2], [16, 2], [17, 3], [18, 2], [19, 2], [20, 2], [21, 3], [22, 3], [23, 3], [24, 3], [25, 2], [26, 3], [27, 3], [28, 3], [29, 3], [30, 3], [31, 4], [32, 3], [33, 3], [34, 3], [35, 3], [36, 3], [37, 4], [38, 4], [39, 4], [40, 4], [41, 3], [42, 3], [43, 4], [44, 4], [45, 4], [46, 4], [47, 4], [48, 4], [49, 4], [50, 4], [51, 4], [52, 4], [53, 4], [54, 4], [55, 4], [56, 4], [57, 5], [58, 5], [59, 5], [60, 5], [61, 4], [62, 4], [63, 4], [64, 4], [65, 5], [66, 5], [67, 5], [68, 5], [69, 5], [70, 5], [71, 5], [72, 4], [73, 5], [74, 5], [75, 5], [76, 5], [77, 5], [78, 5], [79, 5], [80, 5], [81, 5], [82, 6], [83, 6], [84, 6], [85, 5], [86, 5], [87, 5], [88, 5], [89, 5], [90, 5], [91, 6], [92, 6], [93, 6], [94, 6], [95, 6], [96, 6], [97, 6], [98, 5], [99, 5], [100, 5]

What's going wrong here?
Regards
Prof.G

How do I get explict answer to system of ODEs...

Asked by: soneye 20
ode dsolve explicit
March 04 2022
4  5

Dear Colleagues,

I am trying to solve the following system of ode

odeSystem := {diff(y1(x), x) = -x*y2(x)-(1+x)*y3(x), diff(y2(x), x) = -x*y1(x)-(1+x)*y4(x), diff(y3(x), x) = -x*y1(x)-(1+x)*y4(x)-5*x*cos((1/2)*x^2), diff(y4(x), x) = -x*y2(x)-(1+x)*y3(x)+5*x*sin((1/2)*x^2), y1(0) = 5, y2(0) = 1, y3(0) = -1, y4(0) = 0};
systemSol := dsolve(odeSystem);

However, the result displayed is not explicit and contains integral sign. Please, I need help to obtain explicit result.

Thank you.

Is there any way to find the equation of intersect...

Asked by: mehdibgh 240
February 22 2022
2  9

I have two surfaces f=f(x,y) and g=g(x,y), is there any way to find the equation of intersection curve of them in maple?

contact.mw

error when using dslove...

Asked by: Ngu? Van Thái 10
ode syntax numeric
February 15 2022
2  1

i use dslove command to solve system of differential equations but got an error, i checked the error but i don't know where i went wrong, please help me!

error: Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

HOI.mw

pdsolve error code...

Asked by: kencom1 115
pde numeric pdsolve
February 12 2022
0  1

Good day everyone,

I am running a maple code for a pde and is given the error code "Error, (in pdsolve/numeric/process_IBCs) initial/boundary condition must be given in terms of the dependent variables of the problem only ([W]), got ((D@@2)[1](W))(0, tau) = 0". The link is attached below.

pde.mw

Thanks in advance.

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