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 >>> > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/8fb2dae4-9f46-4c1b-b96f-83033278c27d%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6JmFnSvc2Z_9T7_hOHmXmpY_3ZkzdaR6QU6fXVs8oUz6g%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
