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] > <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 > >>> > > -- > > 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] <javascript:>. > > To post to this group, send email to [email protected] > <javascript:>. > > 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/a9c5f7ba-1c2d-4673-a8d4-b1253c150054%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
