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
> <javascript:>> 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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