Good news is that regular Maple already has (another, completely separate) copy of several of these f11 NAG Library routines embedded within it. These work right from the LinearAlgebra package in the Maple Library, without the Connector or any extra NAG download or install.

> restart:

> with(LinearAlgebra):

> a := Vector[row](22,[1.0,1.0,-1.0,2.0,2.0,
>                      3.0,-2.0,1.0,-2.0,1.0,1.0],
>                  datatype=float[8]):

> irow := Vector[row](22,[1,1,2,2,2,3,3,4,4,4,4],
>                  datatype=integer[kernelopts('wordsize')/8]):

> icol := Vector[row](22,[2,3,1,3,4,1,4,1,2,3,4],
>                  datatype=integer[kernelopts('wordsize')/8]):

> A:=Matrix(4,4,storage=sparse,datatype=float[8]):
> for i from 1 to 11 do
>    A[irow[i],icol[i]]:=a[i];
> end do:

> A;
                             [ 0.   1.  1.   0.]
                             [                 ]
                             [-1.   0.  2.   2.]
                             [                 ]
                             [ 3.   0.  0.  -2.]
                             [                 ]
                             [ 1.  -2.  1.   1.]

> V:=Vector(4,(i)->i,datatype=float[8]);
                                       [1.]
                                       [  ]
                                       [2.]
                                  V := [  ]
                                       [3.]
                                       [  ]
                                       [4.]

> infolevel[LinearAlgebra]:=6:

> X:=LinearSolve(A,V);

LinearSolve: using method SparseIterative
LinearSolve: using method   SparseIterative
LinearSolve: calling external function
LinearSolve: using CGS method
LinearSolve: preconditioning with incomplete LU factorization
LinearSolve: level of fill =  0
LinearSolve: using complete pivoting strategy
LinearSolve: dimension of workspaces for preconditioner =  30
LinearSolve: using infinity norm in stopping criteria
LinearSolve: setting maximum iterations to  200
LinearSolve: setting tolerance to  0.10e-7
LinearSolve: NAG hw_f11zaf
LinearSolve: NAG hw_f11daf
LinearSolve: NAG hw_f11dcf
LinearSolve: number of iterations 1
LinearSolve: residual computed last as HFloat(4.440892098500626e-16)
                             [                   -16]
                             [4.44089209850063 10   ]
                             [                      ]
                             [     -1.50000000000000]
                        X := [                      ]
                             [      2.50000000000000]
                             [                      ]
                             [     -1.50000000000000]

> A.X-V;

unknown: hw_SpMatVecMulRR
                          [                     0.]
                          [                       ]
                          [                     0.]
                          [                       ]
                          [                    -16]
                          [-4.44089209850063 10   ]
                          [                       ]
                          [                     0.]

As you can see, the above uses f11daf, followed by f11dcf. Those are Fortran Library versions of the C Library functions f11dac and f11dcc.

There isn't an easy way to preserve the "incomplete LU factorization" results from f11daf, and to re-use such in multiple successive calls to f11dcf. Instead, both f11daf and f11dcf would get called together, each time LinearSolve got called. So if one has multiple RHS Vectors then it's better to solve them all at once, so as to factorize the Matrix only once. (An alternative would involve poking into the LinearAlgebra routine which does the individual external-calls to the compiled wrappers to f11daf and  f11dcf, and replicating the set-up of workspaces, external calls, etc, relevent to this real nonsymmetric sparse case.)

The SparseIterative method for nonsymmetric, numeric Matrices can also be forced in the call to LinearSolve, and some options specified. Eg,

   method=SparseIterative,methodoptions=[....]

Note that I did not have to use a triple of Vectors, `irow`, and `icol` and `a` above. I could have formed sparse nonsymmetric Matrix `A` in any fashion I wanted. Yes, it is true that the nonzero entries and their indices of a datatype=float[8] Matrix with storage=sparse are internally stored in three contiguous portions of memory: 2 arrays of hardware integers and one of hardware doubles. But there's no easy way to access those at the Maple Library command level without making an external call to a function which picks out those as three Vectors (using the "external API").

I better repeat the important bit: all the above works in Maple 14, 13, 12, etc, right from the LinearAlgebra package in the Maple Library, without the Connector or any extra NAG download or install. It should work in plain, installed Maple.

Now on to your more specific question about the Connector (if you still need to know, in light of the above).

You need a copy of the NAG C Library in order to run the commands in the Maple-NAG Connector product. (See point 1 of this help-page section "Before You Begin" for a mention of this fact.) See here, at NAG's own website, for some detail on obtaining the Mark 8 NAG C Library. (Their latest, the Mark 9, might not work.)

The underlying Chapter F11 sparse linear algebra functions of the NAG C Library are proprietary to NAG Ltd, UK, and as such won't run from the Maple-NAG Connector without a valid license to accompany that NAG C Library. This means that one has to purchase a NAG C Library license (from NAG), over and above the usual Maple license, in order to run such license-locked commands from the Connector.

The Connector is a bridge between these two distinct commercial products: Maple, and the NAG C Library. You need both products, and valid licenses for both products, in order to use the Connector in full.

Not all NAG C Library commands invoke license-locked NAG C Library functions. But the f11 ones are locked, if I recall correctly.

acer

restart:
st:=time():
evalf(Int(exp(-t)/(mul(-3+2*exp(-.1*(1-.1)^i*t), i = 0 .. 4)), t = 0 .. infinity));
time()-st;
                         -0.5821551499
                             25.803

restart:
st:=time():
evalf(Int(unapply(exp(-t)/(mul(-3+2*exp(-.1*(1-.1)^i*t), i = 0 .. 4)),t), 0 .. infinity));
time()-st;
                         -0.5821551499
                             0.031

restart:
st:=time():
evalf(Int(exp(-t)/(mul(-3+2*exp(-.1*(1-.1)^i*t), i = 0 .. 4)), t=0 .. infinity,
          method=_d01amc));
time()-st;
                         -0.5821551499
                             0.032

What I suspect is going on is that a lot of computational effort is (by default) being put into determining whether the integrand is singular in the given range. By forcing a method, or concealing the expression form of the integrand inside a procedure, some or all of this checking might be bypassed. (And, naturally, that would only be safe when one knows something of the qualitative behavior of the integrand.) That's my conjecture, anyway, though one could trace through `evalf/int/control` or something to see.

acer

Quite often French curves are sold alongside "ship's curves" for drafting. My understanding is that all this sort of thing predates the kind of math that we'd nowadays associate with such curves or their construction.

I found this ["A History of Curves and Surfaces in SAGD" by Gerald Farin] link interesting. It suggests that ship builders used to keep the large curved ribs used in building ships hulls, as templates. This goes with the notion that the curves would be built by hand, and that it predates the mathematicalization of such curves. It's plausible then, that smaller French curve construction might also have originally been by-hand. That linked paper does make a hint that Pascal and Monge might have somehow been involved in the methodology, but doesn't give detail on that. The link goes on to talk about Bezier and others who subsequently established the math behind such processes.

acer

Is this (post, or parent thread) close enough that you can hammer it to fit?

Or do you just need the -c option of the `maple` script? With that option (or multiple instances of it!) you can initialize the session, etc. Eg.  'maple -c "assign(...)"

% maple -s -c "assign(x,4)"

    |\^/|     Maple 14 (SUN SPARC SOLARIS)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2010
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> x;
                                       4

acer

You'd want to set the system to 'FPS', so that simplification of units results in units of feet for the dimension of length.

Apart from the three ways shown below, you could alternatively use the right-click context-sensitive menu action Units -> Simplify on the output.

> restart:

> Units:-UseSystem('FPS');

> Z := 5*Unit('ft'):
> simplify(Z^2);

                                      [  2]
                                   25 [ft ]

> restart:

> Units:-UseSystem('FPS');
> with(Units:-Standard):

> Z := 5*Unit('ft'):
> Z^2;

                                      [  2]
                                   25 [ft ]

> restart:

> Units:-UseSystem('FPS');

> Z := 5*Unit('ft'):
> Z^2:
> combine(%, 'units');

                                      [  2]
                                   25 [ft ]

acer

There is a predefined system of units whose base units for mass and length are gram and centimeter (see here). There are other ways to change the default units for any given dimension, but let us know if this is not adequate for you.

Maple will keep Pi as an exact quantity by default. One can use the `evalf` command to approximate it to floating-point. By default, Maple will use the `Digits` environment variable to control the working precision (see here). One can also set the display precision for Standard GUI output (see here). It's usually better to let Maple use at least its default setting of Digits=10 for computation (and to separately control only the final display) than it is to downgrade the computation precision to something as low as Digits=5 (which might allow too much roundoff error for you on more complicated expressions). Below I use `evalf[5]` on just the final result, as a programmatic way to adjust the final displayed float value.

> restart:

> with(Units:-Standard):
> Units:-UseSystem(CGS);

> wirediameter:=.40*Unit(inch):
> wirelength:=1000*Unit(ft):
> wirevolume:=(wirediameter/2)^2 * Pi * wirelength: 
> wireweight:=61*Unit(lb):
> wiredensity:=evalf(wireweight/wirevolume):

> evalf[5](wiredensity);

                         [   g     ]
                  1.1197 [ ------- ]
                         [     3   ]
                         [   cm    ]

acer

Is this an attempt to phish for HD SNs associated with valid Maple licenses? (Isn't/wasn't HD SN an alternative to NIC SN for authentication?) Sorry if that sounds callous, but we live in troubled times.

acer

@turloughmack I apologize if I misinterpreted. The option price nomenclature part is technical jargon, and seems to obscure the fact that your difficulties seem to be with the coding aspects (which really are not specific to just that discipline). The jargon can obscure the question.

It might be better for legibility if you could use a notation that matched Maple's 1D notation, when posting the code as plaintext. For example, if your names are indexed then an entry for f might be f[i+1,j] and not f_i+1,j (which is what one might physically type, as 2D input). This is key, since even this interpretation might not be what you want. It seems that you might want the (i+1)th instance of a Vector f. In that case you could have a table of N Vectors f[i], with each member Vector having entries f[i][j], j=1..m. Or you might prefer to create an N by m Matrix f where each row represents a Vector and the indexing would be f[i,j].

It was pointed out in response to your earlier Question that square brackets are for list creation, and that you'd probably need round brackets as expression delimiters. But square brackets are still used above in the assignments of a[j], b[j], and c[j]. Is there a reason for that?

You've used `m` mostly, but in your setup of f[N] it appears that you really mean `M` (which is 10, as is N). Is that right? Is m supposed to be M, or vice versa?

Is this getting there?

restart:

a := j -> 1/2*(r-q)*j*Deltat - 1/2*sigma^2*j^2*Deltat:
b := j -> 1 + sigma^2*j^2*Deltat + r*Deltat:
c := j -> -1/2*(r-q)*j*Deltat - 1/2*sigma^2*j^2*Deltat:

r:= 0.05: Deltat:= T/N: DeltaS:=S/M: T:=0.4: q:=0: K:=1.1: S:=2: M:=10: N:=10:

thematrix := Matrix(M,M,scan=band[1,1],
            [[seq(a(j),j=1..M-1)],
             [seq(b(j),j=1..M)],
             [seq(c(j),j=1..M-1)]]):

f[N]:=Vector(M,(j)->max(K-j,DeltaS,0)):

thismatrix:=eval(thematrix,sigma=0.9):

for i from N to 2 by -1 do
 f[i-1] := LinearAlgebra:-LinearSolve(thismatrix,f[i]);
end do:

f[1];

invthismatrix:=thismatrix^(-1):
invthismatrix^9 . f[N];

It might be slightly more numerically stable to do the repeated LinearSolve, over MatrixInverse. But at this size problem any efficiency concerns and tweaks (re-using the LU decomposition, done just once) would make the code less clear for a negligible benefit I suspect.

Maybe the brute force way would do: find the x,y (err, Q1,Q2) values at the intersections. Then just draw eight curves instead of four. And have some of the eight get the dashed line style. See ?plot,option on chenging the line style.

Instead of creating all curves in a single plot structure right away, you could assign each to a name. Ie, P1:=plot3(....,Q1=-1..X, Q2=-1...1) where X is the Q1-coordinate of the intersection point. Analogously for the other curves, but some with the line style specified as an option. Then use plots:-display to show them all superimposed.

acer

What precisely do you mean by "prints itself"? Do you mean that calling it will produce as output the same result as would evaluating (or printing) it?

I have set interface(prettyprint=1) for these examples below.

> f:=proc() print(eval(procname)); end proc;
                 f := proc() print(eval(procname)) end proc;

> f();
proc() print(eval(procname)) end proc;

Note that the above does not work when the procedure is anonymous. But for that case, one can use the new (as of Maple 14, see here) `thisproc`,

> f:=proc() print(eval(procname)); end proc:

> %(); # NULL output, ie. it didn't succeed

> proc() print(eval(thisproc)); end proc;
proc() print(eval(thisproc)) end proc;

> %();
proc() print(eval(thisproc)) end proc;

It occurs to me that perhaps you instead mean that you want the result of calling `f` to simply be the name of f.

> f:=proc(x)
>    debugopts('callstack')[2];
> end proc:

> f();
                               f

> g:=proc() f(); end proc:
> g();
                               f

I found that callstack useful when coding a redefined version of (the protected) `userinfo` which would display results to a Text Component. This worked even when the code was run in a Maplet or other "hidden" facility, and it worked without having (access) to change or edit the original routine sources. The task was harder still -- to find out how the current parent procedure had been called. I'd meant to blog it...

Another way to get this simpler effect of printing only the current procedure's own name might be,

> f:=proc() op(1,''procname''); end proc:

> f();
                               f

Do either of those two interpretations of "prints itself" come close to your intended meaning?

acer

Hey Axel, I see you're still musing over that usenet post. One might easily get Maple to convert the following roots of that quintic to radicals, by just calling `solve` with its Explicit option.

> seq(cos(i*Pi/11),i in [1,3,5,7,9]);

           /1    \     /3    \     /5    \      /4    \      /2    \
        cos|-- Pi|, cos|-- Pi|, cos|-- Pi|, -cos|-- Pi|, -cos|-- Pi|
           \11   /     \11   /     \11   /      \11   /      \11   /

But these roots of that sextic look like they are going to be a little tougher... ;)

seq(cos(i*Pi/13),i in [1,3,5,7,9,11]);

    /1    \     /3    \     /5    \      /6    \      /4    \  
 cos|-- Pi|, cos|-- Pi|, cos|-- Pi|, -cos|-- Pi|, -cos|-- Pi|, 
    \13   /     \13   /     \13   /      \13   /      \13   /  

       /2    \
   -cos|-- Pi|
       \13   /

acer

As 1D Maple notation input, your expression would need a star or a dot (* or .) between the bracketed terms in order to denote multiplication. For example, (a+b)*(a-b).

As 2D Math input, it would need either a star of a dot (typed in as * or .) for explicitly denoted multiplication or a space for implicitly denoted multiplication. For example .

Without any of these, the first set of bracketed terms get interpreted as (a sum of functions), and the entire expression as one big function application. The 1D and 2D parsers support a distributed function call syntax. Without the multiplication sign (or space for 2D input) the following are all parsed as function application:

> (sin+cos)(x);
                        sin(x) + cos(x)

> (sin+f)(x);
                         sin(x) + f(x)

> (f+g)(x-y);
                      f(x - y) + g(x - y)

> (a+b)(x-y);
                      a(x - y) + b(x - y)

> (a+b)(a-b);
                      a(a - b) + b(a - b)

The first term of even that last result is not the same as a*(a-b). No, it is `a` applied as a function, with argument a-b. There's no reason to prevent the parser from recognizing that an as-yet undefined operator `a` might be applied to the sum of names of other operators. Maple is so much more than just mere math.

Some people have expressed the opinion that Maple's relatively new implicit multiplication syntax (denoted by a space between terms, in 2D Math input) makes for visually confusing documents which obscure these syntax distinctions and lead inexperienced users to make this mistake more often.

acer

You should not be using the (officially) deprecated linalg package. You should use the newer LinearAlgebra package.

For transposition either use the LinearAlgebra:-Transpose command, or raise the Matrix or Vector to the %T power (eg. V^%T).

Remember that Maple is case-sensitive.

Also, use Matrix and Vector, not the deprecated matrix and vector commands.

You can extract a column using the shorter syntax E[1..-1,j]. So E[1..-1,5] would extract the 5th column of a Matrix E.

See ?rtable_indexing

acer

If this is an assignment for which you are supposed to explicitly demonstrate the solving method in action, then see dskoog's Answer.

If, on the other hand, you just want to apply a known method to solve your moderately sized numeric problem then you could use the LinearSolve command with the method=LU options. (Linear solving via LU dcomposition is pretty much just Gaussian elimination in disguise since the L factor provides a way to store the pivoting info. Generally, G.E. of an augmented system would get you half-way there, and you'd back-sub for the second stage. By doing LU and then both forward- and backward-sub'ing the whole task is done. The LinearSolve command would just do all those steps for you, internally.)

The quoted size of your problem makes me think that maybe you just want the system solved. Hence the method=LU and LinearSolve suggestion.

 X := LinearAlgebra:-LinearSolve(A, B, method=LU);

acer

Yes, use Re() and Im(), and not op().

And use I*Im(expr) if you want the imaginary component of expr, as opposed to the "imaginary part". The term "imaginary part" is being used to denote the real number b in a complex number a+b*I, say.

> Xi := sqrt(I);

                               1  (1/2)   1    (1/2)
                         Xi := - 2      + - I 2     
                               2          2         

> Bs := Matrix([[Re(Xi), I*Im(Xi)], [I*Im(Xi), Re(Xi)]]);

                             [ 1  (1/2)   1    (1/2)]
                             [ - 2        - I 2     ]
                             [ 2          2         ]
                       Bs := [                      ]
                             [1    (1/2)   1  (1/2) ]
                             [- I 2        - 2      ]
                             [2            2        ]

Use capitalized Matrix, not matrix.

acer