symbolic arrays
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From: Gideon Simpson on 26 Apr 2010 11:27 Is it possible to define symbolic variables of arrays? I want to do syms a(1) a(2) a(3)... so that I can compute the jacobian of a vector valued function.
From: Steven Lord on 26 Apr 2010 13:08 "Gideon Simpson" <gideon.simpson(a)gmail.com> wrote in message news:hr4bca$k7g$1(a)fred.mathworks.com... > Is it possible to define symbolic variables of arrays? > > I want to do > > syms a(1) a(2) a(3)... > > so that I can compute the jacobian of a vector valued function. A = sym(zeros(4)); for k = 1:numel(A) A(k) = sym(sprintf('a%d', k)); end A -- Steve Lord slord(a)mathworks.com comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ
From: Alan Weiss on 26 Apr 2010 13:42 On 4/26/2010 1:08 PM, Steven Lord wrote: > "Gideon Simpson"<gideon.simpson(a)gmail.com> wrote in message > news:hr4bca$k7g$1(a)fred.mathworks.com... >> Is it possible to define symbolic variables of arrays? >> >> I want to do >> >> syms a(1) a(2) a(3)... >> >> so that I can compute the jacobian of a vector valued function. > > A = sym(zeros(4)); > for k = 1:numel(A) > A(k) = sym(sprintf('a%d', k)); > end > A > You might also want to see a doc example on computing symbolic jacobians: http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brn4nh7.html#brv_i_1 Or view a similar demo: http://www.mathworks.com/products/optimization/demos.html?file=/products/demos/shipping/optim/symbolic_optim_demo.html Alan Weiss MATLAB mathematical toolbox documentation
From: Gideon Simpson on 2 May 2010 13:13 Alan Weiss <aweiss(a)mathworks.com> wrote in message <hr4j9a$k5i$1(a)fred.mathworks.com>... > On 4/26/2010 1:08 PM, Steven Lord wrote: > > "Gideon Simpson"<gideon.simpson(a)gmail.com> wrote in message > > news:hr4bca$k7g$1(a)fred.mathworks.com... > >> Is it possible to define symbolic variables of arrays? > >> > >> I want to do > >> > >> syms a(1) a(2) a(3)... > >> > >> so that I can compute the jacobian of a vector valued function. > > > > A = sym(zeros(4)); > > for k = 1:numel(A) > > A(k) = sym(sprintf('a%d', k)); > > end > > A > > > You might also want to see a doc example on computing symbolic jacobians: > http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brn4nh7.html#brv_i_1 > > Or view a similar demo: > http://www.mathworks.com/products/optimization/demos.html?file=/products/demos/shipping/optim/symbolic_optim_demo.html > > Alan Weiss > MATLAB mathematical toolbox documentation This isn't quite working as I had wished. Suppose my function is f(x_1, x_2) = x_1^2 + 3 *x_1 x_2 - sin(x_2) and I intend to define x as a 2d column vector, and wish to compute the jacobian of f. if I try: x = sym(zeros(2,1)); for k = 1:numel(x) x(k) = sym(sprintf('x(%i)',k)); end f = x(1)^2 + 3 * x(1) * x(2) - sin(x(2)) But if I now do jacobian(f, x) I get: [ diff(3*x(1)*x(2) - sin(x(2)) + x(1)^2, x(1)), diff(3*x(1)*x(2) - sin(x(2)) + x(1)^2, x(2))] Obviously, I can switch to having my variables be x1, x2, as in the examples, but suppose I want to avoid that. Is it possible?
From: Alan Weiss on 3 May 2010 15:36 "Gideon Simpson" <gideon.simpson(a)gmail.com> wrote in message <hrkbqu$sui$1(a)fred.mathworks.com>... > Alan Weiss <aweiss(a)mathworks.com> wrote in message <hr4j9a$k5i$1(a)fred.mathworks.com>... > > On 4/26/2010 1:08 PM, Steven Lord wrote: > > > "Gideon Simpson"<gideon.simpson(a)gmail.com> wrote in message > > > news:hr4bca$k7g$1(a)fred.mathworks.com... > > >> Is it possible to define symbolic variables of arrays? > > >> > > >> I want to do > > >> > > >> syms a(1) a(2) a(3)... > > >> > > >> so that I can compute the jacobian of a vector valued function. > > > > > > A = sym(zeros(4)); > > > for k = 1:numel(A) > > > A(k) = sym(sprintf('a%d', k)); > > > end > > > A > > > > > You might also want to see a doc example on computing symbolic jacobians: > > http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brn4nh7.html#brv_i_1 > > > > Or view a similar demo: > > http://www.mathworks.com/products/optimization/demos.html?file=/products/demos/shipping/optim/symbolic_optim_demo.html > > > > Alan Weiss > > MATLAB mathematical toolbox documentation > > This isn't quite working as I had wished. Suppose my function is > > f(x_1, x_2) = x_1^2 + 3 *x_1 x_2 - sin(x_2) > > and I intend to define x as a 2d column vector, and wish to compute the jacobian of f. > > if I try: > > x = sym(zeros(2,1)); > > for k = 1:numel(x) > x(k) = sym(sprintf('x(%i)',k)); > end > > f = x(1)^2 + 3 * x(1) * x(2) - sin(x(2)) > > But if I now do > > jacobian(f, x) > > I get: > > [ diff(3*x(1)*x(2) - sin(x(2)) + x(1)^2, x(1)), diff(3*x(1)*x(2) - sin(x(2)) + x(1)^2, x(2))] > > > Obviously, I can switch to having my variables be x1, x2, as in the examples, but suppose I want to avoid that. Is it possible? I am not sure it is possible. The basic data type for symbolic variables is complex scalar. When you make a vector out of these scalars, I believe the scalars should each have a different name. So a vector of scalars x = [x1,x2,...,xn], for example, has x(2) = x2. I believe trying to do it your way has x(2) essentially undefined. But I could be wrong. In any case, it certainly works to define each element of a symbolic vector as a separate symbolic scalar, so I suggest you employ that technique for now. Alan Weiss MATLAB mathematical toolbox documentation
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