FuncDesigner .503

Developer: License / Value : Very last Up to date : Classification A lot more programs BSD License / FREE August 2nd, 2013, eleven : fifty seven GMT [ look at background ] ROOT / Science

FuncDesigner is a CAS ( Personal computer  Algebra System ) created in Python and accredited unde the BSD license.

Case in point :

from FuncDesigner import *

a, b, c = oovars('a', 'b', 'c')

f1, f2 = sin(a) + cos(b) - log2(c) + sqrt(b), sum(c) + c * cosh(b) / arctan(a) + c[] * c[ 1 ] + c[- one ] / (a * c. dimensions )

f3 = f1*f2 + 2 *a + sin(b) * ( 1 + two *c. dimensions + three *f2. dimension )

f = 2 *a*b*c + f1*f2 + f3 + dot(a+c, b+c)

stage = a: 1, b: two, c:[ three, four, five ] # nonetheless, you would better use numpy arrays alternatively of Python lists

print(f( stage ))

print(f.D( position ))

print(f.D( place, a))

print(f.D( place, [b]))

print(f.D( place, fixedVars = [a, c]))

Envisioned output:
[ a hundred and forty.9337138 one hundred ten.16255336 eighty.67870244]
a: array([ 69.75779959, 88.89020412, 109.93551537]), b: array([-23.10565554, -39.41138045, - 59.08378522]),
c: array([[ six.19249888, 38.261221, 38.261221 ],
[ 29.68377935, -.18961959, 29.68377935],
[ 23.03059873, 23.03059873, - six.22406763]])
[ sixty nine.75779959 88.89020412 109.93551537]
b: array([-23.10565554, -39.41138045, - fifty nine.08378522])
b: array([-23.10565554, -39.41138045, - fifty nine.08378522])

 * You can use "for" cycle in FuncDesigner code

Case in point :

from FuncDesigner import *

a, b, c = oovars('a', 'b', 'c')

f1, f2 = sin(a) + cos(b) - log2(c) + sqrt(b), sum(c) + c * cosh(b) / arctan(a) + c[] * c[ 1 ] + c[- one ] / (a * c. size )

f3 = f1*f2 + two *a + sin(b) * ( one + 2 *c. size + three *f2. dimension )

F = sin(f2)*f3 + one

M = fifteen

for i in variety (M): F =. 5 *F +. 4 *f3*cos(f1+ two *f2)

point = a: one, b: two, c:[ 3, 4, five ] # on the other hand, you would greater use numpy arrays as a substitute of Python lists

print(F( stage ))

print(F.D( level ))

print(F.D( place, a))

print(F.D( position, [b]))

print(F.D( point, fixedVars = [a, c]))

[ 4.63468686.30782902 one.21725266]
a: array([-436.83015952, 204.25331181, 186.38788436]), b: array([ 562.63390316, -273.23484496, -256.32464645]),
c: array([[ 395.96975635, 167.24928464, fifty five.74976155],
 [ - seventy four.80518167, -129.34496329, -19.94804845],
 [ - 57.42472654, - forty five.93978123, - sixty six.30049589]])
[-436.83015952 204.25331181 186.38788436]
b: array([ 562.63390316, -273.23484496, -256.32464645])
b: array([ 562.63390316, -273.23484496, -256.32464645])

 * If some your functions experienced been created on other languages (C, Fortran, etc ), or are beyond FuncDesigner Ad abilities due to any other motive (has "for"/" when " loops, routines for resolving programs of nonlinear, mb differential equations and many others ), you can outline your individual oofun with wrapper close to the operate, and the missing derivatives will be covered up by finite- variances derivatives approximation through DerApproximator.
 * FuncDesigner as well as DerApproximator was excluded from OpenOpt framework as unbiased Python module.
 OpenOpt can optimize FuncDesigner designs with no needs to provide 1st derivatives.

Instance :

from FuncDesigner import *

from openopt import NLP

a, b, c = oovars('a', 'b', 'c')

f = sum(a*[ one, two ])** 2 +b** two +c** two

startPoint = a:[ one hundred, 12 ], b: two, c: 40 # nonetheless, you would much better use numpy arrays as an alternative of Python lists

p = NLP(f, startPoint)

p.constraints = [( two *c+a- 10 )** two < 1.5 + 0.1*b, (a-10)**28.9, a+b> [ seven.97999836, seven.8552538 ],

a < 9, (c-2)**2 < 1, b < -1.02, c> 1.01, ((b + c * log10(a).sum() - one ) ** 2 ).eq()]

r = p. fix ('ralg')

print r.xf

Envisioned output:
...
objFunValue: 717.75631 ( possible, max constraint = seven.44605e-07)
a: array([ eight.99999792, 8.87525277]), b: array([- one.01999971]), c: array([ 1.0613562])


Product's homepage

Necessities :

· Python
· NumPy

What is New in This Launch : [ examine entire changelog ]

· Interalg now performs numerous times ( at times orders) speedier on ( probably multidimensional) integration difficulties (IP) and on some optimization problems
· Include modeling dense (MI)(QC)QP in FuncDesigner (alpha- variation, rendering may get the job done slowly and gradually however )
· Bugfix for cplex wrapper
· Some advancements for FuncDesigner interval examination (and thus interalg)
· Increase FuncDesigner interval investigation for tan in range (-pi/ 2,pi/ 2 )
· Some other bugfixes and improvements
· (Proprietary) FuncDesigner stochastic addon now is offered as standalone pyc-file, became obtainable for Python3 as very well

Via: FuncDesigner 0.503