Hi everybody, I’m Helena

I have a function with the following general characteristics:

y= const*M*[Int_def (from a to b) [f(x)*g(x, M)*p(x, t, M,K)]dx]

::::::::::::::::::::::::::::::::::::::::::::::::::

y= dependent variable

a= 1.76E-7

b= 1.76E-9

x= integration variable

M= unknown parameter

K= unknown parameter

t= independent variable

::::::::::::::::::::::::::::::::::::::::::::::::::

... and I'm trying to fit it to my experimental data (421 values), to determine the best values for M and K. In order to do that I’m using the package Statistic and the NonlinearFit command from maple, however, it seems that NonlinearFit cannot fit the model (y(t)) to the experimental data. It gives an error: “Error, (in Statistics:-NonlinearFit) integration range or variable must be specified in the second argument, got HFloat(1.0) = 0 .. 1” for which I could not find any explanation or solution on the internet. Could you please give me some advice or ideas about how can I solve this problem?

Thank you so much in advance for your attention and help.

Hi, I would like to represent the piecewise function as a Bar Graph. I can only get a line Graph. Thanks in advance.
 

Download Ch1_3_Functions_Exam8.mw

 Recently I often drew some graphs in Graph Theory  by Maple. I tried to use DrawGraph, but  I found that evey edge only meets straight line  style in this package.

For example: 

How do I draw some edges with curve syle in graph? like following:

Thanks!

In answer to a previous question (https://www.mapleprimes.com/questions/228965-How-Can-I-Save-A-Record) acer introduced me to the .mla archives as a possible store location for variables.

I have been working with this and now end up having 4 .mla files (called results1.mla...results4.mla) that each hold output from some lengthy batch running of maple. Each of these has two tables with values called Beams and Beams2 (same name in each of these archives). While named the same the content is different.

My question is: How do I get at each of these? As acer explained, the content (i.e. the tables Beams and Beams2) is mapped into the namespace of the Maple session once libname includes the directory where the .mla files sit. They are actually in the same directory as the associated Maple programs so they mask each other.

I tried to juggle libname prepending the .mla file I want to the rest; but that does not seem to work (I always get the same data). I do need the data all in one worksheet for collating and postprocessing and display.

TIA,

M.D.

Hi everybody:

How can I solve this system of nonlinear equations without use the fsolve command?

eq[1] := -3*c[0]+3*c[1] = c[0]*(1-259*d[0]*(1/192)+43*d[1]*(1/64)-11*d[2]*(1/64)+(1/64)*d[3])-23/6;
eq[2] := -3*d[0]+3*d[1] = d[0]*(-2+23*c[0]*(1/80)+139*c[1]*(1/320)-17*c[2]*(1/160)+3*c[3]*(1/320))-1;
eq[3] := -4*c[0]*(1/3)+c[2]+(1/3)*c[3] = (8*c[0]*(1/27)+4*c[1]*(1/9)+2*c[2]*(1/9)+(1/27)*c[3])*(1-2657*d[0]*(1/5184)-343*d[1]*(1/1728)-185*d[2]*(1/1728)-79*d[3]*(1/5184))-3;
eq[4] := -4*d[0]*(1/3)+d[2]+(1/3)*d[3] = (8*d[0]*(1/27)+4*d[1]*(1/9)+2*d[2]*(1/9)+(1/27)*d[3])*(-2+109*c[0]*(1/8640)+553*c[1]*(1/1440)+559*c[2]*(1/2880)+37*c[3]*(1/1080))-5/6;
eq[5] := -(1/3)*c[0]-c[1]+4*c[3]*(1/3) = ((1/27)*c[0]+2*c[1]*(1/9)+4*c[2]*(1/9)+8*c[3]*(1/27))*(1-673*d[0]*(1/5184)-455*d[1]*(1/1728)-505*d[2]*(1/1728)-767*d[3]*(1/5184))-49/27;
eq[6] := -(1/3)*d[0]-d[1]+4*d[3]*(1/3) = ((1/27)*d[0]+2*d[1]*(1/9)+4*d[2]*(1/9)+8*d[3]*(1/27))*(-2-173*c[0]*(1/4320)+241*c[1]*(1/2880)+59*c[2]*(1/180)+2191*c[3]*(1/8640))-11/36;
eq[7] := c[0] = 1;
eq[8] := d[0] = 0;

tnx...

I'm trying to Graph a Piecewise Defined Function.

j(x) = piecewise(x < 0, x^2 + 1, 0 <= x, x - 1);

It doesn't provide a plot option.

Download piecewisegraph.mw

Download funct_misrep.mw

data := [[0., 9.1300, 0.931e-1, 0.899e-1, .1000, 0.], [30.0000, 8.9300, .1270, .1230, .2270, 0.49e-2], [60.0000, 8.6000, .1510, .1390, .4920, 0.153e-1], [90.0000, 8.2800, .1540, .1490, .7780, 0.249e-1], [120.0000, 7.9700, .1540, .1570, 1.0700, 0.329e-1], [150.0000, 7.8600, .1540, .1600, 1.1700, 0.348e-1], [180.0000, 7.8100, .1530, .1530, 1.2100, 0.404e-1], [210.0000, 7.7700, .1400, .1420, 1.2800, 0.432e-1]];
des := [diff(y1(t), t) = -k1*y1(t)-k2*y1(t), diff(y2(t), t) = k2*y1(t)-k3*y2(t), diff(y3(t), t) = k1*y1(t)+k3*y2(t)-k4*y3(t), diff(y4(t), t) = k4*y3(t)-k5*y2(t)*y4(t)+k6*y5(t), diff(y5(t), t) = k5*y2(t)*y4(t)-k6*y5(t)];
ics := seq((y || i)(0) = data[1, i+1], i = 1 .. 5):
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous(ics Assign seq

  lparlpary verbarverbar irpar(0) equals data(1comma i + 1)comma 

  i equals 1 periodperiod 5rparcolon, 

  Typesetting:-merror("unable to match delimiters")))
res := dsolve({ics, des[]}, numeric, parameters = [k1, k2, k3, k4, k5, k6]);
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
timeList := [0, 30, 60, 90, 120, 150, 180, 210];
              [0, 30, 60, 90, 120, 150, 180, 210]
sse := proc (k1, k2, k3, k4, k5, k6) res(parameters = [k1, k2, k3, k4, k5, k6]); add((rhs(select(has, res(timeList[i]), y1)[])-data[i, 2])^2+(rhs(select(has, res(timeList[i]), y2)[])-data[i, 3])^2+(rhs(select(has, res(timeList[i]), y3)[])-data[i, 4])^2+(rhs(select(has, res(timeList[i]), y4)[])-data[i, 5])^2+(rhs(select(has, res(timeList[i]), y5)[])-data[i, 6])^2, i = 2 .. 8) end proc;
proc(k1, k2, k3, k4, k5, k6)  ...  end;
c := GlobalOptimization:-GlobalSolve(('sse')(k1, k2, k3, k4, k5, k6), k1 = 0 .. 1, k2 = 0 .. 1, k3 = 0 .. 1, k4 = 0 .. 1, k5 = 0 .. 1, k6 = 0 .. 1, timelimit = 10); [.219132447080011505, [k1 = 0.852482740113834e-3, k2 = 0.52683998680924474e-4, k3 = 0., k4 = 0.5113239298267808e-1, k5 = 0.4363021255887466e-2, k6 = 0.]];
Error, `GlobalOptimization` does not evaluate to a module
[0.219132447080011505, [k1 = 0.000852482740113834, 

  k2 = 0.000052683998680924474, k3 = 0., 

  k4 = 0.05113239298267808, k5 = 0.004363021255887466, k6 = 0.]]

res(parameters = c[2]):  p:=Array(1..5):  for n from 1 to 5 do     p[n]:=plots:-display(plots:-odeplot(res, [t, (y || n)(t)], t = 0 .. 210),plots:-pointplot([seq([data[i, 1], data[i, n+1]], i = 1 .. 8)]));  end do; plots:-display(p) ;
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous(res(parameters 

  equals c(2))colon  pAssignArray(1periodperiod5)colon  for n 

  from 1 to 5 do     p(n)Assignplotscolon - displaylparplotscolon

   - odeplotlparrescomma lsqbtcomma lpary verbarverbar nrpar(t)

  rsqbcomma t equals 0 periodperiod 210rparcommaplotscolon - 

  pointplot((seq((data(icomma 1)comma data(icomma n + 1))comma i 

  equals 1 periodperiod 8)))rparsemi  end dosemi plotscolon - 

  display(p) , Typesetting:-merror("unable to match delimiters")))

 I cannot solve this equation. Please help me

How can I use maple to get the numerical solution of this non-autonomous system

sys_ode := diff(x(t), t) = ax(t)-bx(t)y(t)+2sin(t), diff(y(t), t) = -cy(t)+dx(t)y(t)

where a,b,c,d is parameters, they can take any value.

Hi! 

I'm having a weird issue. :( 

DEplot command worked when I initially ran the executed it, but then when I executed the entire worksheet, it didn't plot. Instead I just get this output. 

This is the entire worksheet so far without the output. 

If someone could please help me, I would greatly appreciate it!!!!!

restart;
with(DEtools);

eq1 := diff(y(x), x) = 3*x*y(x);

dsolve(eq1, y(x));

ini1 := y(0) = 3;

dsolve({eq1, ini1}, y(x));

ini2 := y(1) = -3;

dsolve({eq1, ini2}, y(x));

eq2 := y(x)*diff(y(x), x) = -x;

dsolve(eq2, y(x));

dsolve({eq2, ini1}, y(x));

restart;
with(plots);

eq := diff(y(x), x) = 3*x*y(x);

ini := y(0) = 5;


dsolve({eq, ini}, y(x));




sol := rhs(%);

plot(sol, x = -2 .. 2, y = 0 .. 10);
DEplot(eq, y(x), x = -2 .. 2, y = 0 .. 10, [[ini]]);

Does anyone use MTM toobox and why?

I discovered this through the eig help search and found the MATLAB format of [V, D] = eig(Matrix) for eigenvectors and eigenvalues as a single function call with output a nice shortcut vs two calls to LinearAlgebra[Eigenvalues], LinearAlegebra[Eigenvectors]

But, is the overhead and overmapping of standard maple functions worth it?   I find very little descriptions about the Maple Toolbox, specifically the MTM package.

Hi everyone:

how can I obtain the B from A?

A:=u[1, 0](t)*v[1, 3](t)+u[1, 1](t)*v[1, 2](t)+u[1, 2](t)*v[1, 1](t)+u[1, 3](t)*v[1, 0](t)
B:=u[1, 0](t)*v[1, 3](tau)+u[1, 1](t)*v[1, 2](tau)+u[1, 2](t)*v[1, 1](tau)+u[1, 3](t)*v[1, 0](tau)

tnx... 

Good day house.

Please I don't know why the solve command does not display any results in the following code. Kindly assist. Thank you in anticipation.

restart;
omega := v/h;
t := sum(a[j]*x^j, j = 0 .. 6)+a[7]*cos(omega*x)+a[8]*sin(omega*x);
r1 := diff(t, x$2);
r2 := diff(t, x$4);
c1 := eval(t, x = q+2*h) = y[n+2];
c2 := eval(r1, x = q) = f[n];
c3 := eval(r1, x = q+h) = f[n+1];
c4 := eval(r1, x = q+2*h) = f[n+2];
c5 := eval(r1, x = q+3*h) = f[n+3];
c6 := eval(r2, x = q) = g[n];
c7 := eval(r2, x = q+h) = g[n+1];
c8 := eval(r2, x = q+2*h) = g[n+2];
c9 := eval(r2, x = q+3*h) = g[n+3];
b1 := seq(a[i], i = 0 .. 8);
`k≔solve`({c1, c2, c3, c4, c5, c6, c7, c8, c9}, {a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]});

Please I found out that the MatrixInverse on the assignment statement P3 does not run for about three days now. Please kindly help to simplify the code. Thank you and kind regards.

restart; omega := v/h;
r := a[0]+a[1]*x+a[2]*sinh(omega*x)+a[3]*cosh(omega*x)+a[4]*cos(omega*x)+a[5]*sin(omega*x);
b := diff(r, x);

c := eval(b, x = q) = f[n];
d := eval(r, x = q+3*h) = y[n+3]; e := eval(b, x = q+3*h) = f[n+3];
g := eval(b, x = q+2*h) = f[n+2];
i := eval(b, x = q+h) = f[n+1];
j := eval(b, x = q+4*h) = f[n+4];
k := solve({c, d, e, g, i, j}, {a[0], a[1], a[2], a[3], a[4], a[5]});
Warning,  computation interrupted
assign(k);
cf := r;
s4 := y[n+4] = simplify(eval(cf, x = q+4*h));
s3 := y[n+2] = simplify(eval(cf, x = q+2*h));
s2 := y[n+1] = simplify(eval(cf, x = q+h));
s1 := y[n] = simplify(eval(cf, x = q));

with(LinearAlgebra);
with(plots);
h := 1;
YN_1 := seq(y[n+k], k = 1 .. 4);
A1, a0 := GenerateMatrix([s1, s2, s3, s4], [YN_1]);
eval(A1);
YN := seq(y[n-k], k = 3 .. 0, -1);
A0, b1 := GenerateMatrix([s1, s2, s3, s4], [YN]);
eval(A0);
FN_1 := seq(f[n+k], k = 1 .. 4);
B1, b2 := GenerateMatrix([s1, s2, s3, s4], [FN_1]);
eval(B1);
FN := seq(f[n-k], k = 3 .. 0, -1);
B0, b3 := GenerateMatrix([s1, s2, s3, s4], [FN]);
eval(B0);
ScalarMultiply(R, A1)-A0;
det := Determinant(ScalarMultiply(R, A1)-A0);
P1 := A1-ScalarMultiply(B1, z);
P2 := combine(simplify(P1, size), trig);
P3 := MatrixInverse(P2);
P4 := A0-ScalarMultiply(B0, z);
P5 := MatrixMatrixMultiply(P3, P4);
P6 := Eigenvalues(P5);
f := P6[4];
T := unapply(f, z);
implicitplot(f, z = -5 .. 5, v = -5 .. 5, filled = true, grid = [5, 5], gridrefine = 8, labels = [z, v], coloring = [blue, white]);