DerApproximator

DerApproximator Description

DerApproximator is a Python library for finite-differences derivatives approximation.Example:from DerApproximator import *print get_d1(lambda x: (x**2).sum(), [1,2,3])print get_d1(lambda x: x**2, [1,2,3])Expected output: [ 1.99999993 3.99999998 5.99999996][[ 2. 0. 0. ][ 0. 3.99999996 0. ][ 0. 0. 5.99999996]] * check_d1 checks user-provided routing for obtaining 1st derivatives of a functionExample:from numpy import *from DerApproximator import *func = lambda x: (x**4).sum()func_d = lambda x: 40 * x**3x = arange(1.0, 6.0)r = check_d1(func, func_d, x)func = lambda x: x**4func_d = lambda x: 40 * diag(x**3)x = arange(1.0, 6.0)r = check_d1(func, func_d, x)Expected output:func num user-supplied numerical RD0 +4.000e+01 +4.000e+00 31 +3.200e+02 +3.200e+01 32 +1.080e+03 +1.080e+02 33 +2.560e+03 +2.560e+02 34 +5.000e+03 +5.000e+02 3max(abs(d_user - d_numerical)) = 4499.9999861(is registered in func number 4)func num i,j: dfunc[i]/dx[j] user-supplied numerical RD0 0 / 0 +4.000e+01 +4.000e+00 36 1 / 1 +3.200e+02 +3.200e+01 312 2 / 2 +1.080e+03 +1.080e+02 318 3 / 3 +2.560e+03 +2.560e+02 324 4 / 4 +5.000e+03 +5.000e+02 3max(abs(d_user - d_numerical)) = 4499.9999861(is registered in func number 24) * Default diffInt is 1.5e-8, you can overwrite it by"diffInt"argument for get_d1 and check_d1. Another one argument is stencil, default value 2 for DerApproximator, FuncDesigner and OpenOpt NSP is 2, i.e. (f(x+diffInt)-f(x-diffInt)) / (2*diffInt), for OpenOpt NLP default is 1, i.e. (f(x+diffInt)-f(x)) / diffInt.Example:from numpy import *from DerApproximator import get_d1func = lambda x: (x**4).sum()x = arange(1.0, 6.0)r1 = get_d1(func, x, stencil = 1, diffInt = 1e-5)print(r1)r2 = get_d1(func, x, stencil = 2, diffInt = 1e-5)print(r2)Expected output:[ 4.00005999 32.00024 108.00054 256.00095998 500.00149998][ 4. 32. 108. 256. 499.99999998] * If it turns out that f(x+diffInt) is NaN (not a number) or f(x-diffInt) is NaN, than only one side will be involved into calculations. BTW this is a typical situation for lots of numerical optimization problems, and currently functions approx_fprime and check_grad from scipy.optimize are even more primitive - they have only one stencil and no handling of NaNs.Product's homepage Requirements: · Python · NumPy What's New in This Release: [ read full changelog ] · Add parameter exactShape (prevents flattering operations on result). �.You can free download DerApproximator from Softpedia now.