I am programming a procedure in Maple. This procedure receive a list of vector fields (from the ``DifferentialGeometry'' package). I want that in the output they appear, together with the performed computations, the name of the vector fields introduced by the user.
During the procedure I refer to them by the name I have given to the parameter, but I don't actually know the "names of the variables". Is there a way to recover them? I have being looking for in the Maple documentation and in the DGinfo help, but I didn't get anything.
EXAMPLE ADDED
I have simplified the problem to the following. Consider the code:
with(DifferentialGeometry);
DGsetup([x, u], M);
X := evalDG(D_u*x+2*D_x);
myproc := proc (var)
return evalDG(var+D_u)
end proc;
myproc(X)
The output is
But I want modify the code in such a way that the output were something like
X+D_u is 2 D_x + (1+x) D_u
That is, I want to use the name ("X") of the variable in the output, not only the value (2 D_x + x D_u).
Thank you for your time.
Here is one way of handling your example.
restart;
with(DifferentialGeometry):
DGsetup([x, u], M):
myproc := proc(var::uneval) local evar;
evar := eval(var);
return evalDG(var+D_u) = evalDG(evar+D_u);
end proc:
X := evalDG(D_u*x+2*D_x):
myproc(X);
X + D_u = 2 D_u + (1 + x) D_u
Here is a variant on that idea, with two such parameters on the procedure, but also handling then in a more general manner.
restart;
with(DifferentialGeometry):
DGsetup([x, u], M):
myproc := proc(var1::uneval, var2::uneval)
local evars, res;
evars := [var1=eval(var1), var2=eval(var2)];
res := var1 + var2 + D_u;
return res = evalDG(eval(res, evars));
end proc:
X1 := evalDG(D_u*x+2*D_x):
X2 := evalDG(D_u*x+3*D_x):
myproc(X1, X2);
X1 + X2 + D_u = 5 D_x + (1 + 2 x) D_x
Related
Well, there was a debate on the below code between me and my friend. We're a bit confused about the output it produce. Can someone clarify the call-by-reference and call-by value result for the below piece of code?
program params;
var i: integer;
a: array[1..2] of integer;
procedure p(x,y: integer);
begin
x := x + 1;
i := i + 1;
y := y + 1;
end;
begin
a[1] := 1;
a[2] := 2;
i := 1;
p( a[i],a[i] );
output( a[1],a[2] );
end.
The resulting output of this program in the case that the
parameters are transmitted to procedure p by value-result and by reference.
Call by Value
x and y in p are local variables initialized with the actual parameters, while i is a global variable, so the call p( a[i],a[i] ) is equivalent to:
x := 1 /* The value of a[i] */
y := 1 /* The value of a[i] */
x := 2 /* x + 1 */
i := 2 /* i + 1 */
y := 2 /* y + 1 */
and at the end the values 1, 2 are printed since they are the values of a[1], a[2] which weren't changed.
Call by Reference
Both x and y in p are alias for a[1] and (again) a[1] (since i = 1 when the procedure is called), so the call is equivalent to:
a[1] := 2 /* a[1] + 1 */
i := 2 /* i + 1 */
a[1] := 3 /* a[1] + 1 */
and at the end the values 3, 2 are printed.
Call by Name
Call by Name is equivalent to Call by Reference when simple variables are passed as parameters, but is different when you pass an expression that denotes a memory location, like a subscript. In this case the actual parameter is re-evaluated each time it is encountered. So in this case, this is the effect of the call of p( a[i],a[i] ):
a[1] := 2 /* since i = 1, the result is equal to a[1] + 1 */
i := 2 /* i + 1 */
a[2] := 3 /* since i is now 2, the result is equal to a[2] + 1 */
and at the end the values 2, 3 are printed. In practice the implementation calls an anonymous function (a “thunk”), each time it must evaluate a parameter.
Call by Value Result
Just to complete the discussion, here is the case for the value-result parameter passing, in which x and y are initialized at the beginning of the procedure execution with the values of the actual parameters, and, at the end of the execution of the procedure, are copied back to the original variables addresses:
x := 1 /* The value of a[i] */
y := 1 /* The value of a[i] */
x := 2 /* x + 1 */
i := 2 /* i + 1 */
y := 2 /* y + 1 */
a[1] := 2 /* the value of x is copied back to a[1] */
a[1] := 2 /* the value of y is copied back to a[1] (not a[2]!) */
and at the end the values 2, 2 are printed.
For a discussion of the different ways of passing parameters, see for instance this.
procedure p(x, y: integer);
begin
end;
In this case the varaibles passed as parameters are never modified. They are copied either to two registers (likely x: EAX and y: ECX) or to the stack. (depending on the compiler ABI)
procedure p(var x, y: integer);
begin
end;
In this case the original parameters are modified. x and y are pointers to the original variables passed as parameters.
i was "finding Pi" with Monte Carlo Method, but the answer was incorrect. The oryginal code was:
RandomTools[MersenneTwister]: with(Statistics):
tries := 10000:
s := 0;
for i to tries do
if GenerateFloat()^2+GenerateFloat()^2 < 1 then s := s+1 end if;
end do:
evalf(4*s/tries)
It gives answer aroud 2.8-2.85
when I change the code to
s := 0;
x := Array([seq(GenerateFloat(), i = 1 .. tries)]);
y := Array([seq(GenerateFloat(), i = 1 .. tries)]);
for i to tries do
if x[i]^2+y[i]^2 < 1 then s := s+1 end if;
end do:
evalf(4*s/tries)
Then the answer is correct. I have no idea why i can't generate number in "for" loop.
I've founded that the mean of it is the same, but the variance is different.
For:
tries := 100000;
A := Array([seq(GenerateFloat(), i = 1 .. 2*tries)]);
s1 := Array([seq(A[i]^2+A[tries+i]^2, i = 1 .. tries)]);
Mean(s1);
Variance(s1);
s2 := Array([seq(GenerateFloat()^2+GenerateFloat()^2, i = 1 .. tries)]);
Mean(s2);
Variance(s2);
output is:
0.6702112097021581
0.17845439723457215
0.664707674135025
0.35463131700965245
What's wrong with it? GenerateFloat() should be as uniform as possible.
Automatic simplification is turning your,
GenerateFloat()^2+GenerateFloat()^2
into,
2*GenerateFloat()^2
before GenerateFloat() is evaluated.
One simple change to get it to work as you expected would be separate them. Eg,
restart:
with(RandomTools[MersenneTwister]):
tries := 10^4:
s := 0:
for i to tries do
t1,t2 := GenerateFloat(),GenerateFloat();
if t1^2+t2^2 < 1 then s := s+1 end if;
end do:
evalf(4*s/tries);
Another way is to use a slightly different construction which doesn't automatically simplify. Consider, single right quotes (uneval quotes) don't stop automatic simplification (which is a definition of the term if you want).
'f()^2 + f()^2';
2
2 f()
But the following does not automatically simplify,
a:=1:
'f()^2 + a*f()^2';
2 2
f() + a f()
Therefore another easy workaround is,
restart:
with(RandomTools[MersenneTwister]):
tries := 10^4:
s := 0:
a := 1;
for i to tries do
if GenerateFloat()^2 + a*GenerateFloat()^2 < 1 then s := s+1 end if;
end do:
evalf(4*s/tries);
I'm experincing a very weird and erratical behaviour in Lazarus 0.9.30.2 version FPC 2.4.4. as shown in the code snippet below after calling NormalizeVEctor procedure in objects, e1 and ne1 becomes the same value whereas I was intending to preserve the original value of vector in e1 and ne1 will represent the normalized value of that vector.
var
e1,e2, ne1, ne2, bisector, speed,res :QVector2D;
begin
e1 := QVector2D.Create;
e2 := QVector2D.Create;
ne1 := QVector2D.Create;
ne2 := QVector2D.Create;
.....
.....
ne1 := e1;
ne2 := e2;
ne1.NormalizeVector; ne2.NormalizeVector;// ne1 = e1 are the same values
bisector := SubtractVector(ne2,ne1);
QVector declaration is as shown below
QVector2D = class(TPersistent)
public
Vector :TVector3D;
function length: Single;
function NormalizeVector:QVEctor2D;
end;
A Maple expression (for example, x^3+x*y) can be converted to Matlab by
with(CodeGeneration):
Matlab(x^3+x*y);
However, in Matlab, there are two kinds of product: A*B and A.*B. The above way will give x^3+x*y. Is there a convenient way to get the result x.^3+x.*y?
The language definition for Maple's CodeGeneration[Matlab] can be extended to handle various instances of the elementwise tilde (~) operator.
Since 'x*~y' seems to automatically simplify to `~`[`*`](x, ` $`, y), and since there appears to be a hard-coded error emitted by the presence of the name " $", then that name is substituted by NULL in the usage code below.
> restart:
> with(CodeGeneration): with(LanguageDefinition):
> LanguageDefinition:-Define("NewMatlab", extend="Matlab",
> AddFunction("`~`[`^`]", [Vector,integer]::Vector,
> proc(X,Y)
> Printer:-Print(X,".^",Y)
> end proc,
> numeric=double),
> AddFunction("`~`[`*`]", [Vector,integer]::Vector,
> proc(X,Y)
> Printer:-Print(X,".*",Y)
> end proc,
> numeric=double));
> expr:=''x^~y + x^~3 + x*~y'':
> Translate(subs(` $`=NULL, expr ), language="NewMatlab");
cg = x.^y + x.^3 + x.*y;
> p := proc(x,y)
> x^~y + x^~3 + x*~y;
> end proc:
> f := subs(` $`=NULL, eval(p) ):
> Translate(f, language="NewMatlab");
function freturn = f(x, y)
freturn = x.^y + x.^3 + x.*y;
For whatever it's worth, Maple 2015 can do this translation directly, without the extra help kindly provided by acer:
> f := (x,y)->x^~y + x^~3 + x*~y:
> CodeGeneration:-Matlab(f);
function freturn = f(x, y)
freturn = x .^ y + x .^ 3 + x .* y;
If the Matlab(x^3+x*y) expression gives out the code x^3+x*y in written format, then you can simply convert it into x.^3+x.y , just by using "Find & Replace" option of any notepad application. Just find all "" and "^" , and then replace them with ".*" and ".^" .
Hope this helps.
I'd like to create a function My`Print[args__] that prints the names of the symbols that I pass it, along with their values. The problem is that before the symbols are passed to My`Print, they're evaluated. So My`Print never gets to see the symbol names.
One solution is to surround every argument that I pass to My`Print with Unevaluated[], but this seems messy. Is there a way of defining a MACRO such that when I type My`Print[args__], the Mathematica Kernel sees My`Print[Unevaluated /# args__]?
You need to set the attribute HoldAll on your function, with SetAttribute[my`print].
Here's a possible implementation:
Clear[my`print]
SetAttributes[my`print, HoldAll]
my`print[args__] :=
Scan[
Function[x, Print[Unevaluated[x], " = ", x], {HoldAll}],
Hold[args]
]
I used lowercase names to avoid conflicts with built-ins or functions from packages.
EDIT:
Just to make it explicit: I have two functions here. One will print the value of a single symbol, and is implemented as a Function inside. You can just use this on its own if it's sufficient. The other is the actual my`print function. Note that both need to have the HoldAll attribute.
ClearAll[My`Print]
SetAttributes[My`Print, HoldAll]
My`Print[args___] :=
Do[
Print[
Extract[Hold[args], i, HoldForm], "=", List[args][[i]]
], {i, Length[List[args]]}
]
ape = 20;
nut := 20 ape;
mouse = cat + nut;
My`Print[ape, nut, mouse]
(* ==>
ape=20
nut=400
mouse=400+cat
*)
SetAttributes[MyPrint, HoldAll];
MyPrint[var_] :=
Module[
{varname = ToString[Hold[var]]},
Print[StringTake[varname, {6, StringLength[varname] - 1}],
" = ", Evaluate[var]]
]
Coming late to the party - one can use Listability to get a rather elegant (IMO) solution avoiding explicit loops or evaluation control constructs:
ClearAll[prn];
SetAttributes[prn, {HoldAll, Listable}];
prn[arg_] := Print[HoldForm[arg], " = ", arg];
prn[args___] := prn[{args}]
Stealing the test case from #Sjoerd,
In[21]:= prn[ape,nut,mouse]
During evaluation of In[21]:= ape = 20
During evaluation of In[21]:= nut = 400
During evaluation of In[21]:= mouse = 400+cat
Out[21]= {Null,Null,Null}
Here is another variation of My`Print to add to the mix:
ClearAll[My`Print]
SetAttributes[My`Print, HoldAll]
My`Print[expr_] := Print[HoldForm[expr], " = ", expr]
My`Print[exprs___] := Scan[My`Print, Hold[exprs]]
... and another...
ClearAll[My`Print]
SetAttributes[My`Print, HoldAll]
My`Print[args___] :=
Replace[
Unevaluated # CompoundExpression # args
, a_ :> Print[HoldForm[a], " = ", a]
, {1}
]
Either way, the use is the same:
$x = 23;
f[x_] := 1 + x
My`Print[$x, $x + 1, f[1]]
(* prints:
$x = 23
$x+1 = 24
f[1] = 2
*)
In addition to the other answers consider the functions DownValues, OwnValues and UpValues:
In[1] := f[x_] := x^2
In[2] := f[x_, y_] := (x + y)^2
In[3] := DownValues[f]
Out[3] = {HoldPattern[f[x_]] :> x^2, HoldPattern[f[x_, y_]] :> (x + y)^2}
http://reference.wolfram.com/mathematica/ref/DownValues.html