We certainly could. The question would then be what the scope of the method
should be. Should it only handle systems that can be expressed as Ax = b?
Or should it behave like `CoefficientArrays
<http://reference.wolfram.com/mathematica/ref/CoefficientArrays.html>`
mentioned above, and handle Ax + Bx^2 + Cx^3 + D = 0? Either way, I think
it should error if the form can't be matched exactly (i.e. don't linearize,
just express a linear, or polynomial, system as matrices).
On Saturday, June 14, 2014 6:44:21 PM UTC-5, Aaron Meurer wrote:
>
> Oh, of course. B is on the rhs. This is probably more natural to me too.
>
> Should we make a convenience function that does this? I think this use
> of jacobian would be lost on most people.
>
> Aaron Meurer
>
> On Sat, Jun 14, 2014 at 6:29 PM, James Crist <cris...@umn.edu
> <javascript:>> wrote:
> > It's just the convention I'm most used to. Systems that can be expressed
> as
> > A*x = B I usually solve for x, or if A isn't square, the least squares
> > solution x. In both cases you need A and B in this form. I suppose Ax +
> B
> > could seem more natural though.
> >
> > On Friday, June 13, 2014 6:45:48 PM UTC-5, Aaron Meurer wrote:
> >>
> >> That's a clever trick. I should have thought of that.
> >>
> >> Is there any reason you let system = A*x - B instead of A*x + B? The
> >> latter seems more natural.
> >>
> >> Aaron Meurer
> >>
> >> On Sat, Jun 7, 2014 at 12:28 AM, James Crist <cris...@umn.edu> wrote:
> >> > I just answered this on gitter earlier today, but you can just take
> the
> >> > jacobian of the system to get its matrix form. For example:
> >> >
> >> > In [1]: from sympy import *
> >> >
> >> > In [2]: a, b, c, d = symbols('a, b, c, d')
> >> >
> >> > In [3]: x1, x2, x3, x4 = symbols('x1:5')
> >> >
> >> > In [4]: x = Matrix([x1, x2, x3, x4])
> >> >
> >> > In [5]: system = Matrix([a*x1 + b*x2 + c,
> >> > ...: c*x1 + d*x3 + 2,
> >> > ...: c*x3 + b*x4 + a])
> >> >
> >> > In [6]: A = system.jacobian(x)
> >> >
> >> > In [7]: B = A*x - system
> >> >
> >> > In [8]: A
> >> > Out[8]:
> >> > Matrix([
> >> > [a, b, 0, 0],
> >> > [c, 0, d, 0],
> >> > [0, 0, c, b]])
> >> >
> >> > In [9]: B
> >> > Out[9]:
> >> > Matrix([
> >> > [-c],
> >> > [-2],
> >> > [-a]])
> >> >
> >> > In [10]: assert A*x - B == system
> >> >
> >> > The functionality I'm adding for my GSoC for linearizing a system of
> >> > equations will also be able to return these matrices in a convenient
> >> > form.
> >> > But it's not terribly difficult to solve for these arrangements using
> >> > the
> >> > current functionality.
> >> >
> >> >
> >> >
> >> >
> >> >
> >> >
> >> >
> >> > On Thursday, June 5, 2014 4:22:52 PM UTC-5, Andrei Berceanu wrote:
> >> >>
> >> >> Was this implemented into sympy at any point? It could be the
> >> >> equivalent
> >> >> of Mathematica's CoefficientArrays function.
> >> >>
> >> >> On Thursday, November 14, 2013 5:56:22 AM UTC+1, Chris Smith wrote:
> >> >>>
> >> >>> I forgot that as_independent, without the as_Add=True flag will
> treat
> >> >>> Muls differently. The following will be more robust:
> >> >>>
> >> >>> def eqs2matrix(eqs, syms, augment=False):
> >> >>> """
> >> >>> >>> s
> >> >>> [x + 2*y == 4, 2*c + y/2 == 0]
> >> >>> >>> eqs2matrix(s, (x, c))
> >> >>> (Matrix([
> >> >>> [1, 0],
> >> >>> [0, 2]]), Matrix([
> >> >>> [-2*y + 4],
> >> >>> [ -y/2]]))
> >> >>> >>> eqs2matrix([2*c*(x+y)-4],(x, y))
> >> >>> (Matrix([[2*c, 2*c]]), Matrix([[4]]))
> >> >>> """
> >> >>> s = Matrix([si.lhs - si.rhs if isinstance(si, Equality) else si
> >> >>> for
> >> >>> si in eqs])
> >> >>> sym = syms
> >> >>> j = s.jacobian(sym)
> >> >>> rhs = -(s - j*Matrix(sym))
> >> >>> rhs.simplify()
> >> >>> if augment:
> >> >>> j.col_insert(0, rhs)
> >> >>> else:
> >> >>> j = (j, rhs)
> >> >>> return j
> >> >>>
> >> > --
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