I'm teaching a math bio class where I need to plot a life history graph. The matrix equation is new=A*old, where A is a square matrix. I want to create a matrix of the population at each iteration (for say 10 iterations) and plot each column separately. I'm having trouble figuring it out and would appreciate some help.
One way is to define the matrix a and the list p of
vectors of populations, initially containing just the vector
of initial populations:
sage: a = matrix(RR, 2, [1.02, -0.01, 0.03, 1.03])
sage: p = [vector(RR, 2, [300, 200])]
then extend the list by applying a number of times the matrix to the last vector:
sage: for k in range(20):
....: p.append(a * p[-1])
then observe the evolution of populations:
sage: p
[(300.000000000000, 200.000000000000),
(304.000000000000, 215.000000000000),
(307.930000000000, 230.570000000000),
(311.782900000000, 246.725000000000),
(315.551308000000, 263.480237000000),
(319.227531790000, 280.851183350000),
(322.803570592300, 298.853544804200),
(326.271106556104, 317.503258266095),
(329.621496104565, 336.816489210761),
(332.845761134549, 356.809628770221),
(335.934580069538, 377.499290467364),
(338.878278766255, 398.902306583471),
(341.666821275745, 421.035724143963),
(344.289800459820, 443.916800506554),
(346.736428463951, 467.562998535545),
(348.995527047875, 491.991981345530),
(351.055517775377, 517.221606597332),
(352.904412064911, 543.269920328514),
(354.529801102924, 570.155150300316),
(355.918845621980, 597.895698842414),
(357.058265545995, 626.510135176345)]
or plot it as a set of points:
sage: point2d(p)
Launched png viewer for Graphics object consisting of 1 graphics primitive
or one could color the first point in red:
sage: point2d(p[0], color='red') + point2d(p[1:])
Launched png viewer for Graphics object consisting of 2 graphics primitives
or one could use line2d instead of point2d,
or one could use animate to animate the evolution.
If you want to plot the evolution of each population:
sage: x, y = zip(*p)
sage: px = list_plot(x, color='green')
sage: py = list_plot(y, color='purple')
sage: px
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: py
Launched png viewer for Graphics object consisting of 1 graphics primitive
sage: px + py
Launched png viewer for Graphics object consisting of 2 graphics primitives
How do I plot each column separately? This gives the first column vs the second column. Suppose I want to plot the column entries from the first column on the y-axis and the index on the x-axis.
We need much more input to help seriously, like the size of the matrix, a concrete example of A, an example of picture you want to obtain.
Waiting for more details, here is a sample of what you can easily get:
sage: A = matrix([[2,1],[1,1]])
sage: A
[2 1]
[1 1]
sage: C = matrix([[2],[3]])
sage: C
[2]
[3]
sage: A * C
[7]
[5]
sage: L = []
sage: L = [C]
sage: for i in range(10):
....: C = A*C
....: L.append(C)
sage: L
[
[2] [7] [19] [50] [131] [343] [898] [2351] [6155] [16114]
[3], [5], [12], [31], [ 81], [212], [555], [1453], [3804], [ 9959],
[42187]
[26073]
]
Asked: 2018-04-15 20:08:56 +0100
Seen: 180 times
Last updated: Apr 16 '18
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