+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html)
+--- Forum: General Forum (/forum-4.html)
+--- Thread: New Sum of Powers Log Function (/thread-16557.html)
Pages: 1 2
RE: New Sum of Powers Log Function - Albert Chan - 04-02-2021 01:29 AM
(04-01-2021 11:55 PM)Namir Wrote: I am looking to solve for x given all other parameters--n, s, scale.
I guess the only sure way is to actually do the sum.
Because of the power-law nature of functions, we should use log scale, like before.
I have no idea what should be the right guess for it, so I just start with g=1.
Note that guess is evaluated twice. This is a fluke of mpmath, to simplify code.
The branched solver(s) re-calculated from the same guess again.
Code:
from mpmath import *
def show(x): print float(x); return x
nbx_to_s = lambda n,b,x: 1+fsum(k**(x*b**(n-k)) for k in xrange(2,n+1))
nbs_to_x = lambda n,b,s,g=1.: findroot(lambda x: log(nbx_to_s(n,b,show(x))/s), g, tol=1e-4)>>> n, b = 100, 0.8
>>> s = nbx_to_s(n, b, 1.6) # = 2238.0808062735837
>>> x = nbs_to_x(n, b, s)
1.0
1.0
1.25
1.69268857579
1.59352468855
1.5999199506
1.60000007609
1.6
>>> s = nbx_to_s(n, b, 16) # = 1.0000003500527855e+32
>>> x = nbs_to_x(n, b, s)
1.0
1.0
1.25
23.7615084486
15.9522719123
15.999999997
16.0
16.0
RE: New Sum of Powers Log Function - Albert Chan - 04-02-2021 01:18 PM
(04-02-2021 01:29 AM)Albert Chan Wrote: Note that guess is evaluated twice. This is a fluke of mpmath, to simplify code.
The branched solver(s) re-calculated from the same guess again.
This is the patch to fix this issue.
C:\python\Lib\site-packages\mpmath\calculus\optimization.py, findroot():
Right before entering solver, i.e. below comment "use solver"
Code:
# use solver
f0, p = f, [tuple(x0), fx] # cache previous result
def f(*x):
if x!=p[0]: p[0]=x; p[1]=f0(*x)
return p[1]What is shocking is the patch may save more than 1 call.
Example, copied from help(findroot):
>>> f = [lambda x1, x2: x1**2 + x2, lambda x1, x2: 5*x1**2 - 3*x1 + 2*x2 - 3]
>>> findroot(f, (0, 0))
[-0.618033988749895]
[-0.381966011250105]
Patched findroot reduced f calls, from 24, down to 17
Code:
01 0.0 0.0
02 1.45519152284e-11 0.0
03 0.0 1.45519152284e-11
04 -1.00000000001 1.45519152285e-11
05 -0.500000000005 7.27595761425e-12
06 -0.49999999999 7.27595761425e-12
07 -0.500000000005 2.18278728426e-11
08 -0.625 -0.374999999999
09 -0.624999999986 -0.374999999999
10 -0.625 -0.374999999985
11 -0.618055555556 -0.381944444445
12 -0.618055555541 -0.381944444445
13 -0.618055555556 -0.38194444443
14 -0.618033988958 -0.381966011042
15 -0.618033988943 -0.381966011042
16 -0.618033988958 -0.381966011028
17 -0.61803398875 -0.38196601125RE: New Sum of Powers Log Function - Namir - 04-04-2021 03:41 PM
Thanks Albert. Will be looking at your recent feedback.