I am having trouble with integrating a matrix element-wise with respect to two variables (r and z) using dblquad.

I used two for-loops (inside a nested function) to create a 2D-matrix called Az(m,l) and I want to integrate all elements of that matrix between the same boundaries (rmin,rmax,zmin and zmax). The best option I could think of is using dblquad together with for loops to integrate every element independently, but other suggestions are also welcome. I placed my code below.

_____________________________________________________________

function [Bz, Rho, Zeta]=MagField3 (I,rmin,rmax,zmin,zmax,rhomin,rhomax,zetamin,zetamax,n)

rho = (linspace(rhomax,rhomin,n))'; % One column of rho-values

Rho = repmat(rho,1,n); % Build square matrix

zeta = linspace(zetamin,zetamax,n); % One row of zeta-values

Zeta = repmat(zeta,n,1); % Build square matrix

mu = 4*pi*10^-7; % Magnetic permeability

k = zeros(n); %Preallocation

K = zeros(n);

E = zeros(n);

Bz = zeros(n);

function Az = AAz(r,z)

for m = linspace(1,n,n)

for l = linspace(1,n,n)

Az = zeros(n);

k(m,l) = sqrt((4.*r.*Rho(m,l))./((r+Rho(m,l)).^2+(Zeta(m,l)-z).^2));

[K(m,l),E(m,l)] = ellipke(k(m,l).^2);

Az(m,l) = (I*mu./(2*pi*sqrt((r+Rho(m,l)).^2+(Zeta(m,l)-z).^2))).*(K(m,l)+((r.^2-Rho(m,l).^2-(Zeta(m,l)-z).^2)./((r-Rho(m,l)).^2+(Zeta(m,l)-z).^2)).*E(m,l));

end

end

end

for m = linspace(1,n,n)

for l = linspace(1,n,n)

Bz(m,l) = dblquad(@(r,z)AAz(m,l),rmin,rmax,zmin,zmax);

end

end

end

______________________________________________________________

However, when I run the program I receive this error message:

________________________________________________________

??? Index exceeds matrix dimensions.

Error in ==> quad at 85

if ~isfinite(y(7))

Error in ==> dblquad>innerintegral at 84

Q(i) = quadf(intfcn, xmin, xmax, tol, trace, y(i), varargin{:});

Error in ==> quad at 77

y = f(x, varargin{:});

Error in ==> dblquad at 60

Q = quadf(@innerintegral, ymin, ymax, tol, trace, intfcn, ...

Error in ==> MagField3 at 30

Bz(m,l) = dblquad(@(r,z)AAz(m,l),rmin,rmax,zmin,zmax);

________________________________________________________

I am new to Matlab, so it is possible that I am making a very basic mistake. Can anyone help me with this?

Thanks in advance!

Bram

"Bram " <BramCERN@hotmail.com> wrote in message <i2tv00$lq5$1@fred.mathworks.com>...

> Hi there,

>

> I am having trouble with integrating a matrix element-wise with respect to two variables (r and z) using dblquad.

>

> I used two for-loops (inside a nested function) to create a 2D-matrix called Az(m,l) and I want to integrate all elements of that matrix between the same boundaries (rmin,rmax,zmin and zmax). The best option I could think of is using dblquad together with for loops to integrate every element independently, but other suggestions are also welcome. I placed my code below.

>

> _____________________________________________________________

> function [Bz, Rho, Zeta]=MagField3 (I,rmin,rmax,zmin,zmax,rhomin,rhomax,zetamin,zetamax,n)

>

> rho = (linspace(rhomax,rhomin,n))'; % One column of rho-values

> Rho = repmat(rho,1,n); % Build square matrix

>

> zeta = linspace(zetamin,zetamax,n); % One row of zeta-values

> Zeta = repmat(zeta,n,1); % Build square matrix

>

> mu = 4*pi*10^-7; % Magnetic permeability

>

> k = zeros(n); %Preallocation

> K = zeros(n);

> E = zeros(n);

> Bz = zeros(n);

>

> function Az = AAz(r,z)

> for m = linspace(1,n,n)

> for l = linspace(1,n,n)

> Az = zeros(n);

> k(m,l) = sqrt((4.*r.*Rho(m,l))./((r+Rho(m,l)).^2+(Zeta(m,l)-z).^2));

> [K(m,l),E(m,l)] = ellipke(k(m,l).^2);

> Az(m,l) = (I*mu./(2*pi*sqrt((r+Rho(m,l)).^2+(Zeta(m,l)-z).^2))).*(K(m,l)+((r.^2-Rho(m,l).^2-(Zeta(m,l)-z).^2)./((r-Rho(m,l)).^2+(Zeta(m,l)-z).^2)).*E(m,l));

> end

> end

> end

>

> for m = linspace(1,n,n)

> for l = linspace(1,n,n)

> Bz(m,l) = dblquad(@(r,z)AAz(m,l),rmin,rmax,zmin,zmax);

> end

> end

>

> end

> ______________________________________________________________

>

> However, when I run the program I receive this error message:

> ________________________________________________________

> ??? Index exceeds matrix dimensions.

>

> Error in ==> quad at 85

> if ~isfinite(y(7))

>

> Error in ==> dblquad>innerintegral at 84

> Q(i) = quadf(intfcn, xmin, xmax, tol, trace, y(i), varargin{:});

>

> Error in ==> quad at 77

> y = f(x, varargin{:});

>

> Error in ==> dblquad at 60

> Q = quadf(@innerintegral, ymin, ymax, tol, trace, intfcn, ...

>

> Error in ==> MagField3 at 30

> Bz(m,l) = dblquad(@(r,z)AAz(m,l),rmin,rmax,zmin,zmax);

> ________________________________________________________

>

> I am new to Matlab, so it is possible that I am making a very basic mistake. Can anyone help me with this?

>

> Thanks in advance!

>

> Bram

- - - - - - - - - -

Bram, I call to your attention the statement in dblquad documentation that says, "fun(x,y) [referring to the integrand] must accept a vector x and a scalar y and return a vector of values of the integrand."

In your code you are apparently making the assumption that the r variable as called by dblquad is a scalar and therefore that the resulting value for Az(m,l) will also be a scalar for each m and l value. As you can see from the above quotation, that is not the way dblquad works. Your integrand function must be prepared to accept the variable r as a vector of values and return a like-sized vector of values for the corresponding Az values. You have no way of knowing in advance how long that vector might be, and it may vary from call to call, depending as it does on the needs of dblquad in dealing with the particular integrand values you hand to it. The integrand function you write must be able to handle this kind of variability in the calls it receives from dblquad.

This means that for each pair of indices m and l you must allow the values for Az to be computed in accordance with the demands made upon it by dblquad independently of all other paired values of m and l. In other words you must have an outer double loop that computes the double integral for each m and l. Within that loop the integration must be allowed to be completed over the specified r-z range before going on to the next pair of m and l values. Your attempt to have an Az matrix furnishing integrands for all m and l pairs simultaneously as dblquad proceeds with its integration in a parallel fashion will not work.

Roger Stafford

You can think of your watch list as threads that you have bookmarked.

You can add tags, authors, threads, and even search results to your watch list. This way you can easily keep track of topics that you're interested in. To view your watch list, click on the "My Newsreader" link.

To add items to your watch list, click the "add to watch list" link at the bottom of any page.

To add search criteria to your watch list, search for the desired term in the search box. Click on the "Add this search to my watch list" link on the search results page.

You can also add a tag to your watch list by searching for the tag with the directive "tag:tag_name" where tag_name is the name of the tag you would like to watch.

To add an author to your watch list, go to the author's profile page and click on the "Add this author to my watch list" link at the top of the page. You can also add an author to your watch list by going to a thread that the author has posted to and clicking on the "Add this author to my watch list" link. You will be notified whenever the author makes a post.

To add a thread to your watch list, go to the thread page and click the "Add this thread to my watch list" link at the top of the page.

*No tags are associated with this thread.*

A tag is like a keyword or category label associated with each thread. Tags make it easier for you to find threads of interest.

Anyone can tag a thread. Tags are public and visible to everyone.

Got questions?

Get answers.

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi test

Learn moreDiscover what MATLAB ^{®} can do for your career.

Opportunities for recent engineering grads.

Apply TodayThe newsgroups are a worldwide forum that is open to everyone. Newsgroups are used to discuss a huge range of topics, make announcements, and trade files.

Discussions are threaded, or grouped in a way that allows you to read a posted message and all of its replies in chronological order. This makes it easy to follow the thread of the conversation, and to see what’s already been said before you post your own reply or make a new posting.

Newsgroup content is distributed by servers hosted by various organizations on the Internet. Messages are exchanged and managed using open-standard protocols. No single entity “owns” the newsgroups.

There are thousands of newsgroups, each addressing a single topic or area of interest. The MATLAB Central Newsreader posts and displays messages in the comp.soft-sys.matlab newsgroup.

**MATLAB Central**

You can use the integrated newsreader at the MATLAB Central website to read and post messages in this newsgroup. MATLAB Central is hosted by MathWorks.

Messages posted through the MATLAB Central Newsreader are seen by everyone using the newsgroups, regardless of how they access the newsgroups. There are several advantages to using MATLAB Central.

**One Account**

Your MATLAB Central account is tied to your MathWorks Account for easy access.

**Use the Email Address of Your Choice**

The MATLAB Central Newsreader allows you to define an alternative email address as your posting address, avoiding clutter in your primary mailbox and reducing spam.

**Spam Control**

Most newsgroup spam is filtered out by the MATLAB Central Newsreader.

**Tagging**

Messages can be tagged with a relevant label by any signed-in user. Tags can be used as keywords to find particular files of interest, or as a way to categorize your bookmarked postings. You may choose to allow others to view your tags, and you can view or search others’ tags as well as those of the community at large. Tagging provides a way to see both the big trends and the smaller, more obscure ideas and applications.

**Watch lists**

Setting up watch lists allows you to be notified of updates made to postings selected by author, thread, or any search variable. Your watch list notifications can be sent by email (daily digest or immediate), displayed in My Newsreader, or sent via RSS feed.

- Use a newsreader through your school, employer, or internet service provider
- Pay for newsgroup access from a commercial provider
- Use Google Groups
- Mathforum.org provides a newsreader with access to the comp.soft sys.matlab newsgroup
- Run your own server. For typical instructions, see: http://www.slyck.com/ng.php?page=2

You can also select a location from the following list:

- Canada (English)
- United States (English)

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)