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 <[email protected]> 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 <[email protected]> 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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