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## FuncDesigner 0.51

Nov 30, -1
Submit date:
Feb 15, 2015
Publisher:
Dmitrey Kroshko
File size:
322

### FuncDesigner 0.51

 FuncDesigner is an open source CAS (Computer Algebra System) written in Python. Below are three examples, so you can understand how the project works.Example: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[0] * c[1] + c[-1] / (a * c.size)f3 = f1*f2 + 2*a + sin(b) * (1+2*c.size + 3*f2.size)f = 2*a*b*c + f1*f2 + f3 + dot(a+c, b+c)point = {a:1, b:2, c:[3, 4, 5]} # however, you'd better use numpy arrays instead of Python listsprint(f(point))print(f.D(point))print(f.D(point, a))print(f.D(point, [b]))print(f.D(point, fixedVars = [a, c]))Expected output:[ 140.9337138 110.16255336 80.67870244]{a: array([ 69.75779959, 88.89020412, 109.93551537]), b: array([-23.10565554, -39.41138045, -59.08378522]), c: array([[ 6.19249888, 38.261221 , 38.261221 ], [ 29.68377935, -0.18961959, 29.68377935], [ 23.03059873, 23.03059873, -6.22406763]])}[ 69.75779959 88.89020412 109.93551537]{b: array([-23.10565554, -39.41138045, -59.08378522])}{b: array([-23.10565554, -39.41138045, -59.08378522])} * You can use "for" cycle in FuncDesigner codeExample: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[0] * c[1] + c[-1] / (a * c.size)f3 = f1*f2 + 2*a + sin(b) * (1+2*c.size + 3*f2.size)F = sin(f2)*f3 + 1M = 15for i in range(M): F = 0.5*F + 0.4*f3*cos(f1+2*f2)point = {a:1, b:2, c:[3, 4, 5]} # however, you'd better use numpy arrays instead of Python listsprint(F(point))print(F.D(point))print(F.D(point, a))print(F.D(point, [b]))print(F.D(point, fixedVars = [a, c]))[ 4.63468686 0.30782902 1.21725266]{a: array([-436.83015952, 204.25331181, 186.38788436]), b: array([ 562.63390316, -273.23484496, -256.32464645]), c: array([[ 395.96975635, 167.24928464, 55.74976155], [ -74.80518167, -129.34496329, -19.94804845], [ -57.42472654, -45.93978123, -66.30049589]])}[-436.83015952 204.25331181 186.38788436]{b: array([ 562.63390316, -273.23484496, -256.32464645])}{b: array([ 562.63390316, -273.23484496, -256.32464645])}Example:from FuncDesigner import *from openopt import NLPa, b, c = oovars('a', 'b', 'c')f = sum(a*[1, 2])**2+b**2+c**2startPoint = {a:[100, 12], b:2, c:40} # however, you'd better use numpy arrays instead of Python listsp = NLP(f, startPoint)p.constraints = [(2*c+a-10)**2 < 1.5 + 0.1*b, (a-10)**28.9, a+b > [ 7.97999836, 7.8552538 ], a < 9, (c-2)**2 < 1, b < -1.02, c > 1.01, ((b + c * log10(a).sum() - 1) ** 2).eq(0)]r = p.solve('ralg')print r.xfExpected output:...objFunValue: 717.75631 (feasible, max constraint = 7.44605e-07){a: array([ 8.99999792, 8.87525277]), b: array([-1.01999971]), c: array([ 1.0613562])}

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