Filling a matrix with functions

[Oscar Alberto Castillo Felisola]

Hi. I know that one can define a function by declaring

sage: f = function('f', t,r)

However, I'm interested in declaring a matrix filled with different functions. Of course, for a small matrix I can do it by hand, but for "huge" matrices it is boring and make no sense.

Is it possible to do what I need?

[Harald Schilly]

On Tuesday, March 24, 2015 at 11:05:21 AM UTC+1, Oscar Alberto Castillo Felisola wrote:

but for "huge" matrices it is boring and make no sense.

Can you describe a rule or pattern how this matrix should be filled? 

[Oscar Alberto Castillo Felisola]

I'd like to obtain something like

f11 = function('f11', t,r)
f12 = function('f12', t,r)
f21 = function('f21', t,r)
f22 = function('f22', t,r)
M = matrix(2,2, [[f11, f12], [f21, f22]])

Note that in principle all the functions depend on the same variables.

If the assignation of functions could be used as components of a metric of sagemanifold, would be even better.

[Harald Schilly]

On Tuesday, March 24, 2015 at 12:49:57 PM UTC+1, Oscar Alberto Castillo Felisola wrote:

I'd like to obtain something like

f11 = function('f11', t,r)
f12 = function('f12', t,r)
f21 = function('f21', t,r)
f22 = function('f22', t,r)
M = matrix(2,2, [[f11, f12], [f21, f22]])

 

Since this is doable via a functional mapping from the indices to the desired objects, you can use the matrix to do this via the lambda operator:

sage: var("t r")
(t, r)
sage: matrix(5, 5, lambda x,y : function("f%s%s" % (x,y), t, r))
[f00(t, r) f01(t, r) f02(t, r) f03(t, r) f04(t, r)]
[f10(t, r) f11(t, r) f12(t, r) f13(t, r) f14(t, r)]
[f20(t, r) f21(t, r) f22(t, r) f23(t, r) f24(t, r)]
[f30(t, r) f31(t, r) f32(t, r) f33(t, r) f34(t, r)]
[f40(t, r) f41(t, r) f42(t, r) f43(t, r) f44(t, r)]

It's zero-based indexed, as everything else in Python, but you can fix it easily. Hope this helps.

-- Harald

[Oscar Alberto Castillo Felisola]

Thank you very much Harald!