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Thread Subject:
Urgent....D operator in matlab

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 00:36:21

Message: 1 of 11

Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in Bessel function:
                                            1+sigma*D/alpha^2
where D is the differential opeartor "d/dt"

Subject: Urgent....D operator in matlab

From: TideMan

Date: 7 Apr, 2010 00:44:52

Message: 2 of 11

On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
>                                             1+sigma*D/alpha^2
> where D is the differential opeartor "d/dt"

I know nothing about Mathematica, but to numerically differentiate in
Matlab, use:
help diff
help gradient

BTW, your equation makes no sense to me.
By my way of reckoning, D must have an argument of some sort.

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 01:08:24

Message: 3 of 11

TideMan <mulgor@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa661b@r1g2000yqb.googlegroups.com>...
> On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> >                                             1+sigma*D/alpha^2
> > where D is the differential opeartor "d/dt"
>
> I know nothing about Mathematica, but to numerically differentiate in
> Matlab, use:
> help diff
> help gradient
>
> BTW, your equation makes no sense to me.
> By my way of reckoning, D must have an argument of some sort.


A bessel function ratio is defined as following:
B = 1
for ctr = 1:inf %here inf can be replaced with any finite number for approximation
         num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
         den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
          B = B*num/den
end

alpha0 and alpha1 are zeros of zero - order and first order bessel function.
The final value of B is the bessel function ratio that I am trying to calculate.

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 01:37:05

Message: 4 of 11

"kumar vishwajeet" <kwzeet@gmail.com> wrote in message <hpglu8$e9a$1@fred.mathworks.com>...
> TideMan <mulgor@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa661b@r1g2000yqb.googlegroups.com>...
> > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> > >                                             1+sigma*D/alpha^2
> > > where D is the differential opeartor "d/dt"
> >
> > I know nothing about Mathematica, but to numerically differentiate in
> > Matlab, use:
> > help diff
> > help gradient
> >
> > BTW, your equation makes no sense to me.
> > By my way of reckoning, D must have an argument of some sort.
>
>
> A bessel function ratio is defined as following:
> B = 1
> for ctr = 1:inf %here inf can be replaced with any finite number for approximation
> num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> B = B*num/den
> end
>
> alpha0 and alpha1 are zeros of zero - order and first order bessel function.
> The final value of B is the bessel function ratio that I am trying to calculate.


Follow this link:-
http://mathworld.wolfram.com/DifferentialOperator.html
I want a similar 'D" operator in MATLAB

Subject: Urgent....D operator in matlab

From: TideMan

Date: 7 Apr, 2010 01:45:20

Message: 5 of 11

On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> TideMan <mul...@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
> > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> > >                                             1+sigma*D/alpha^2
> > > where D is the differential opeartor "d/dt"
>
> > I know nothing about Mathematica, but to numerically differentiate in
> > Matlab, use:
> > help diff
> > help gradient
>
> > BTW, your equation makes no sense to me.
> > By my way of reckoning, D must have an argument of some sort.
>
> A bessel function ratio is defined as following:
> B = 1
> for ctr = 1:inf  %here inf can be replaced with any finite number for approximation
>          num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
>          den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
>           B = B*num/den
> end
>
> alpha0 and alpha1 are zeros of zero - order and first order bessel function.
> The final value of B is the bessel function ratio that I am trying to calculate.

So when you write:
D/(alpha1(ctr)*alpha1(ctr))
you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
t.
Is that correct?
If so, that's pretty weird notation.

And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
numerically or symbolically?

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 02:00:20

Message: 6 of 11

TideMan <mulgor@gmail.com> wrote in message <b94018b6-814f-473c-8316-990881bdac94@w17g2000yqj.googlegroups.com>...
> On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > TideMan <mul...@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
> > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> > > >                                             1+sigma*D/alpha^2
> > > > where D is the differential opeartor "d/dt"
> >
> > > I know nothing about Mathematica, but to numerically differentiate in
> > > Matlab, use:
> > > help diff
> > > help gradient
> >
> > > BTW, your equation makes no sense to me.
> > > By my way of reckoning, D must have an argument of some sort.
> >
> > A bessel function ratio is defined as following:
> > B = 1
> > for ctr = 1:inf  %here inf can be replaced with any finite number for approximation
> >          num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> >          den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> >           B = B*num/den
> > end
> >
> > alpha0 and alpha1 are zeros of zero - order and first order bessel function.
> > The final value of B is the bessel function ratio that I am trying to calculate.
>
> So when you write:
> D/(alpha1(ctr)*alpha1(ctr))
> you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
> you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
> t.
> Is that correct?
> If so, that's pretty weird notation.
>
> And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
> numerically or symbolically?

No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)). The following expansion will make it clear:-
1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity can be written as:
1+a1*D+a2*D+a3*D+................ till infinity
where ai = sigma/(alpha1(ctr)*alpha1(ctr))
So I am trying to find a replacement for D in MATLAB.

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 02:27:07

Message: 7 of 11

"kumar vishwajeet" <kwzeet@gmail.com> wrote in message <hpgovk$pd4$1@fred.mathworks.com>...
> TideMan <mulgor@gmail.com> wrote in message <b94018b6-814f-473c-8316-990881bdac94@w17g2000yqj.googlegroups.com>...
> > On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > TideMan <mul...@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
> > > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > > > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> > > > >                                             1+sigma*D/alpha^2
> > > > > where D is the differential opeartor "d/dt"
> > >
> > > > I know nothing about Mathematica, but to numerically differentiate in
> > > > Matlab, use:
> > > > help diff
> > > > help gradient
> > >
> > > > BTW, your equation makes no sense to me.
> > > > By my way of reckoning, D must have an argument of some sort.
> > >
> > > A bessel function ratio is defined as following:
> > > B = 1
> > > for ctr = 1:inf  %here inf can be replaced with any finite number for approximation
> > >          num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> > >          den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> > >           B = B*num/den
> > > end
> > >
> > > alpha0 and alpha1 are zeros of zero - order and first order bessel function.
> > > The final value of B is the bessel function ratio that I am trying to calculate.
> >
> > So when you write:
> > D/(alpha1(ctr)*alpha1(ctr))
> > you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
> > you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
> > t.
> > Is that correct?
> > If so, that's pretty weird notation.
> >
> > And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
> > numerically or symbolically?
>
> No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)). The following expansion will make it clear:-
> 1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity can be written as:
> 1+a1*D+a2*D^2+a3*D^3+................ till infinity
> where ai = sigma/(alpha1(ctr)*alpha1(ctr))
> So I am trying to find a replacement for D in MATLAB.

Subject: Urgent....D operator in matlab

From: kumar vishwajeet

Date: 7 Apr, 2010 02:28:07

Message: 8 of 11

"kumar vishwajeet" <kwzeet@gmail.com> wrote in message <hpgovk$pd4$1@fred.mathworks.com>...
> TideMan <mulgor@gmail.com> wrote in message <b94018b6-814f-473c-8316-990881bdac94@w17g2000yqj.googlegroups.com>...
> > On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > TideMan <mul...@gmail.com> wrote in message <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
> > > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> > > > > Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in  Bessel function:
> > > > >                                             1+sigma*D/alpha^2
> > > > > where D is the differential opeartor "d/dt"
> > >
> > > > I know nothing about Mathematica, but to numerically differentiate in
> > > > Matlab, use:
> > > > help diff
> > > > help gradient
> > >
> > > > BTW, your equation makes no sense to me.
> > > > By my way of reckoning, D must have an argument of some sort.
> > >
> > > A bessel function ratio is defined as following:
> > > B = 1
> > > for ctr = 1:inf  %here inf can be replaced with any finite number for approximation
> > >          num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> > >          den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> > >           B = B*num/den
> > > end
> > >
> > > alpha0 and alpha1 are zeros of zero - order and first order bessel function.
> > > The final value of B is the bessel function ratio that I am trying to calculate.
> >
> > So when you write:
> > D/(alpha1(ctr)*alpha1(ctr))
> > you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
> > you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
> > t.
> > Is that correct?
> > If so, that's pretty weird notation.
> >
> > And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
> > numerically or symbolically?
>
> No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)). The following expansion will make it clear:-
> 1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity can be written as:
> 1+a1*D+a2*D+a3*D+................ till infinity
> where ai = sigma/(alpha1(ctr)*alpha1(ctr))
> So I am trying to find a replacement for D in MATLAB.

Sorry..I mean
1+a1*D+a2*D^2+a3*D^3+................ till infinity

Subject: Urgent....D operator in matlab

From: Steven Lord

Date: 7 Apr, 2010 14:22:31

Message: 9 of 11


"kumar vishwajeet" <kwzeet@gmail.com> wrote in message
news:hpgqjn$gv4$1@fred.mathworks.com...
> "kumar vishwajeet" <kwzeet@gmail.com> wrote in message
> <hpgovk$pd4$1@fred.mathworks.com>...
>> TideMan <mulgor@gmail.com> wrote in message
>> <b94018b6-814f-473c-8316-990881bdac94@w17g2000yqj.googlegroups.com>...
>> > On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
>> > > TideMan <mul...@gmail.com> wrote in message
>> > > <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
>> > > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
>> > > > > Does anyone know about differential operator in MATLAB
>> > > > > corresponding to "D" operator in Mathematica. I am not looking
>> > > > > for diff() function. I just want to use d/dt corresponding to
>> > > > > "d/dx" used in mathematica. I want to use this "d/dt" operator in
>> > > > > Bessel function:
>> > > > > 1+sigma*D/alpha^2
>> > > > > where D is the differential opeartor "d/dt"
>> > >
>> > > > I know nothing about Mathematica, but to numerically differentiate
>> > > > in
>> > > > Matlab, use:
>> > > > help diff
>> > > > help gradient
>> > >
>> > > > BTW, your equation makes no sense to me.
>> > > > By my way of reckoning, D must have an argument of some sort.
>> > >
>> > > A bessel function ratio is defined as following:
>> > > B = 1
>> > > for ctr = 1:inf %here inf can be replaced with any finite number for
>> > > approximation
>> > > num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
>> > > den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
>> > > B = B*num/den
>> > > end
>> > >
>> > > alpha0 and alpha1 are zeros of zero - order and first order bessel
>> > > function.
>> > > The final value of B is the bessel function ratio that I am trying to
>> > > calculate.
>> >
>> > So when you write:
>> > D/(alpha1(ctr)*alpha1(ctr))
>> > you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
>> > you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
>> > t.
>> > Is that correct?
>> > If so, that's pretty weird notation.
>> >
>> > And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
>> > numerically or symbolically?
>>
>> No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)).
>> The following expansion will make it clear:-
>> 1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity
>> can be written as:
>> 1+a1*D+a2*D+a3*D+................ till infinity
>> where ai = sigma/(alpha1(ctr)*alpha1(ctr))
>> So I am trying to find a replacement for D in MATLAB.
>
> Sorry..I mean
> 1+a1*D+a2*D^2+a3*D^3+................ till infinity

You can't have just a "naked" derivative operator -- you have to apply it to
some function. If you have a symbolic function created using Symbolic Math
Toolbox, then DIFF is the correct function to use ... as long as you use it
on a sym object, which will invoke the DIFF _method_ for sym objects rather
than the numeric DIFF _function_ which computes a difference.

syms t
f = sin(t)+cos(t);
derivative = f; % the "0th" derivative is F itself
n = 20;
a = 1:n;
total = sym(ones(1, n+1));
for k = 1:n
    derivative = diff(derivative, t);
    total(k+1) = a(k)*derivative;
end
sumOfDerivatives = sum(total)

Note I've done it this way so you can see each term that contributes to the
sum -- if you want you can simply add each term to the running total inside
the loop.

Note that if you want you could put this code in a function that accepts f
and the symbolic variable with which to differentiate; that way you could
apply it like the "naked" (1+sum(a(k)*D^k)) operator you described above.

--
Steve Lord
slord@mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ

Subject: Urgent....D operator in matlab

From: Loren Shure

Date: 7 Apr, 2010 16:03:36

Message: 10 of 11

In article <hpgk25$igs$1@fred.mathworks.com>, kwzeet@gmail.com says...
> Does anyone know about differential operator in MATLAB corresponding to "D" operator in Mathematica. I am not looking for diff() function. I just want to use d/dt corresponding to "d/dx" used in mathematica. I want to use this "d/dt" operator in Bessel function:
> 1+sigma*D/alpha^2
> where D is the differential opeartor "d/dt"
>

Perhaps you can use diff on a sym object from the Symbolic Math Toolbox.

--
Loren
http://blogs.mathworks.com/loren
http://matlabwiki.mathworks.com/MATLAB_FAQ

Subject: Urgent....D operator in matlab

From: riccardo

Date: 7 Apr, 2010 16:23:08

Message: 11 of 11

"Steven Lord" <slord@mathworks.com> wrote in message <hpi4ec$e9a$1@fred.mathworks.com>...
>
> "kumar vishwajeet" <kwzeet@gmail.com> wrote in message
> news:hpgqjn$gv4$1@fred.mathworks.com...
> > "kumar vishwajeet" <kwzeet@gmail.com> wrote in message
> > <hpgovk$pd4$1@fred.mathworks.com>...
> >> TideMan <mulgor@gmail.com> wrote in message
> >> <b94018b6-814f-473c-8316-990881bdac94@w17g2000yqj.googlegroups.com>...
> >> > On Apr 7, 1:08 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> >> > > TideMan <mul...@gmail.com> wrote in message
> >> > > <b787b93d-3173-4ca1-9a48-d75f6afa6...@r1g2000yqb.googlegroups.com>...
> >> > > > On Apr 7, 12:36 pm, "kumar vishwajeet" <kwz...@gmail.com> wrote:
> >> > > > > Does anyone know about differential operator in MATLAB
> >> > > > > corresponding to "D" operator in Mathematica. I am not looking
> >> > > > > for diff() function. I just want to use d/dt corresponding to
> >> > > > > "d/dx" used in mathematica. I want to use this "d/dt" operator in
> >> > > > > Bessel function:
> >> > > > > 1+sigma*D/alpha^2
> >> > > > > where D is the differential opeartor "d/dt"
> >> > >
> >> > > > I know nothing about Mathematica, but to numerically differentiate
> >> > > > in
> >> > > > Matlab, use:
> >> > > > help diff
> >> > > > help gradient
> >> > >
> >> > > > BTW, your equation makes no sense to me.
> >> > > > By my way of reckoning, D must have an argument of some sort.
> >> > >
> >> > > A bessel function ratio is defined as following:
> >> > > B = 1
> >> > > for ctr = 1:inf %here inf can be replaced with any finite number for
> >> > > approximation
> >> > > num = 1+sigma*D/(alpha1(ctr)*alpha1(ctr))
> >> > > den = 1+sigma*D/(alpha0(ctr)*alpha0(ctr))
> >> > > B = B*num/den
> >> > > end
> >> > >
> >> > > alpha0 and alpha1 are zeros of zero - order and first order bessel
> >> > > function.
> >> > > The final value of B is the bessel function ratio that I am trying to
> >> > > calculate.
> >> >
> >> > So when you write:
> >> > D/(alpha1(ctr)*alpha1(ctr))
> >> > you don't mean the quotient of D and (alpha1(ctr)*alpha1(ctr)),
> >> > you mean the derivative of (alpha1(ctr)*alpha1(ctr)) with respect to
> >> > t.
> >> > Is that correct?
> >> > If so, that's pretty weird notation.
> >> >
> >> > And are you trying to differentiate (alpha1(ctr)*alpha1(ctr))
> >> > numerically or symbolically?
> >>
> >> No I am not trying to divide or differentiate (alpha1(ctr)*alpha1(ctr)).
> >> The following expansion will make it clear:-
> >> 1+a1*d/dx+a2*(d/dx)^2+a3*(d/dx)^3+a4*(d/dx)^4+...........till infinity
> >> can be written as:
> >> 1+a1*D+a2*D+a3*D+................ till infinity
> >> where ai = sigma/(alpha1(ctr)*alpha1(ctr))
> >> So I am trying to find a replacement for D in MATLAB.
> >
> > Sorry..I mean
> > 1+a1*D+a2*D^2+a3*D^3+................ till infinity
>
> You can't have just a "naked" derivative operator -- you have to apply it to
> some function. If you have a symbolic function created using Symbolic Math
> Toolbox, then DIFF is the correct function to use ... as long as you use it
> on a sym object, which will invoke the DIFF _method_ for sym objects rather
> than the numeric DIFF _function_ which computes a difference.
>
> syms t
> f = sin(t)+cos(t);
> derivative = f; % the "0th" derivative is F itself
> n = 20;
> a = 1:n;
> total = sym(ones(1, n+1));
> for k = 1:n
> derivative = diff(derivative, t);
> total(k+1) = a(k)*derivative;
> end
> sumOfDerivatives = sum(total)
>
> Note I've done it this way so you can see each term that contributes to the
> sum -- if you want you can simply add each term to the running total inside
> the loop.
>
> Note that if you want you could put this code in a function that accepts f
> and the symbolic variable with which to differentiate; that way you could
> apply it like the "naked" (1+sum(a(k)*D^k)) operator you described above.
>
> --
> Steve Lord
> slord@mathworks.com
> comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
>

Perhaps the OP question can be rephrased as "can I do Operational Calculus in Matlab?".
I'd say the Symbolic Math Toolbox should be a decent candidate for that.

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