I am thinking of passing results of sympy expression as string and pars it to replace log or exp to np.log,... and use it without lambdifed form. Am I going in right way. Show quoted text Zohreh Karimzadeh
Contact me on +989102116325 and at z.karimza...@gmail.com 🌧️🌍🌱 On Sat, 20 Aug 2022, 10:56 Zohreh Karimzadeh, <z.karimza...@gmail.com> wrote: > I am thinking of passing results of sympy expression as string and pars it > to replace log or exp to np.log,... and use it without lambdifed form. > > Zohreh Karimzadeh > > Contact me on > +989102116325 > and at > z.karimza...@gmail.com > 🌧️🌍🌱 > > > On Sat, 20 Aug 2022, 10:54 Zohreh Karimzadeh, <z.karimza...@gmail.com> > wrote: > >> You mean I should make independent variables acceptable as args to >> minimizer,? >> >> Zohreh Karimzadeh >> >> Contact me on >> +989102116325 >> and at >> z.karimza...@gmail.com >> 🌧️🌍🌱 >> >> >> On Sat, 20 Aug 2022, 09:35 Peter Stahlecker, <peter.stahlec...@gmail.com> >> wrote: >> >>> But would then this not be a simpler way, without any lambdify ? >>> >>> def func_to_be_minimized(alpha, beta, gamma, eta, L, K, VA): >>> …… >>> …… >>> return np.sum(…….) >>> >>> X0 = (…..) >>> args = (L. K, VA) >>> resultat = minimize(func_to_be_minimized, X0, args = args, bounds =…) >>> >>> args contains the variables of your function, which will not be >>> minimized. >>> >>> You may have to play around with args = (L. K, VA) a bit, because >>> minimize ‚hands over‘ whatever is in args to your function in a certain >>> way, and your function must accept them this way. (I never know exactly how >>> to do it, as I do not use it often at all, so I just play around until it >>> works) >>> >>> >>> >>> On Sat 20. Aug 2022 at 11:48 Zohreh Karimzadeh <z.karimza...@gmail.com> >>> wrote: >>> >>>> Exactly >>>> >>>> Zohreh Karimzadeh >>>> >>>> Contact me on >>>> +989102116325 >>>> and at >>>> z.karimza...@gmail.com >>>> 🌧️🌍🌱 >>>> >>>> >>>> On Sat, 20 Aug 2022, 06:15 Peter Stahlecker, < >>>> peter.stahlec...@gmail.com> wrote: >>>> >>>>> Maybe a dumb question from my part: >>>>> >>>>> do I understand you correctly: >>>>> >>>>> For *given* L, K, VA you try to find the alpha, beta, gamma, eta >>>>> which minimize >>>>> the function np.sum(….) ? >>>>> >>>>> Is my understanding correct? >>>>> >>>>> On Fri 19. Aug 2022 at 22:11 Zohreh Karimzadeh <z.karimza...@gmail.com> >>>>> wrote: >>>>> >>>>>> I am new at python and using your comment seems hard to me could >>>>>> possibly let me know know it by example or any key words if is there. >>>>>> >>>>>> Zohreh Karimzadeh >>>>>> >>>>>> Contact me on >>>>>> +989102116325 >>>>>> and at >>>>>> z.karimza...@gmail.com >>>>>> 🌧️🌍🌱 >>>>>> >>>>>> >>>>>> On Fri, 19 Aug 2022, 00:03 Aaron Meurer, <asmeu...@gmail.com> wrote: >>>>>> >>>>>>> Instead of generating a separate lambdified function for every >>>>>>> input, you may find it simpler to lambdify a single function with your >>>>>>> params as extra symbolic parameters, then pass those in using the args() >>>>>>> argument to minimize(). >>>>>>> >>>>>>> Aaron Meurer >>>>>>> >>>>>>> On Thu, Aug 18, 2022 at 4:35 AM Zohreh Karimzadeh < >>>>>>> z.karimza...@gmail.com> wrote: >>>>>>> >>>>>>>> the following code is ok when expression is passed as : >>>>>>>> >>>>>>>> import numpy as np >>>>>>>> from scipy.optimize import minimize, curve_fit >>>>>>>> from lmfit import Model, Parameters >>>>>>>> >>>>>>>> L = np.array([0.299, 0.295, 0.290, 0.284, 0.279, 0.273, 0.268, 0.262, >>>>>>>> 0.256, 0.250]) >>>>>>>> K = np.array([2.954, 3.056, 3.119, 3.163, 3.215, 3.274, 3.351, 3.410, >>>>>>>> 3.446, 3.416]) >>>>>>>> VA = np.array([0.919, 0.727, 0.928, 0.629, 0.656, 0.854, 0.955, 0.981, >>>>>>>> 0.908, 0.794]) >>>>>>>> >>>>>>>> >>>>>>>> def f(param): >>>>>>>> gamma = param[0] >>>>>>>> alpha = param[1] >>>>>>>> beta = param[2] >>>>>>>> eta = param[3] >>>>>>>> VA_est = gamma - (1 / eta) * np.log(alpha * L ** -eta + beta * K >>>>>>>> ** -eta) >>>>>>>> >>>>>>>> return np.sum((np.log(VA) - VA_est) ** 2) >>>>>>>> >>>>>>>> >>>>>>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>>>>>> x0 = (1, 0.01, 0.98, 1) >>>>>>>> result = minimize(f, x0, bounds=bnds) >>>>>>>> print(result.message) >>>>>>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>>>>>> >>>>>>>> but when the expression is passed as the following way: >>>>>>>> >>>>>>>> import numpy as np >>>>>>>> import sympy as sp >>>>>>>> from scipy.optimize import minimize, curve_fit >>>>>>>> from lmfit import Model, Parameters >>>>>>>> >>>>>>>> L = np.array([0.299, 0.295, 0.290, 0.284, 0.279, 0.273, 0.268, 0.262, >>>>>>>> 0.256, 0.250]) >>>>>>>> K = np.array([2.954, 3.056, 3.119, 3.163, 3.215, 3.274, 3.351, 3.410, >>>>>>>> 3.446, 3.416]) >>>>>>>> VA = np.array([0.919, 0.727, 0.928, 0.629, 0.656, 0.854, 0.955, 0.981, >>>>>>>> 0.908, 0.794]) >>>>>>>> >>>>>>>> >>>>>>>> def f(param): >>>>>>>> gamma, alpha, beta, eta = sp.symbols('gamma, alpha, beta, eta') >>>>>>>> gamma = param[0] >>>>>>>> alpha = param[1] >>>>>>>> beta = param[2] >>>>>>>> eta = param[3] >>>>>>>> Vi_est = gamma - (1 / eta) * sp.log(alpha * L ** -eta + beta * K >>>>>>>> ** -eta) >>>>>>>> Vlam_est = sp.lambdify((gamma, alpha, beta, eta), Vi_est) >>>>>>>> >>>>>>>> return np.sum((np.log(VA) - Vlam_est) ** 2) >>>>>>>> >>>>>>>> >>>>>>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>>>>>> x0 = (1, 0.01, 0.98, 1) >>>>>>>> >>>>>>>> result = minimize(f, x0, bounds=bnds) >>>>>>>> >>>>>>>> print(result.message) >>>>>>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>>>>>> >>>>>>>> >>>>>>>> I face difficulty: >>>>>>>> ********************************************* >>>>>>>> Traceback (most recent call last): >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>>>>>> line 70, in wrapper >>>>>>>> retval = cfunc(*args, **kwargs) >>>>>>>> TypeError: unhashable type: 'numpy.ndarray' >>>>>>>> >>>>>>>> During handling of the above exception, another exception occurred: >>>>>>>> >>>>>>>> Traceback (most recent call last): >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>>>>>> line 70, in wrapper >>>>>>>> retval = cfunc(*args, **kwargs) >>>>>>>> TypeError: unhashable type: 'numpy.ndarray' >>>>>>>> >>>>>>>> During handling of the above exception, another exception occurred: >>>>>>>> >>>>>>>> Traceback (most recent call last): >>>>>>>> File >>>>>>>> "F:\Zohreh\MainZohreh\postdoc-field\CSU\pythonProject\fit_test_2.py", >>>>>>>> line >>>>>>>> 26, in <module> >>>>>>>> result = minimize(f, x0, bounds=bnds) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_minimize.py", >>>>>>>> line 692, in minimize >>>>>>>> res = _minimize_lbfgsb(fun, x0, args, jac, bounds, >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_lbfgsb_py.py", >>>>>>>> line 308, in _minimize_lbfgsb >>>>>>>> sf = _prepare_scalar_function(fun, x0, jac=jac, args=args, >>>>>>>> epsilon=eps, >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_optimize.py", >>>>>>>> line 263, in _prepare_scalar_function >>>>>>>> sf = ScalarFunction(fun, x0, args, grad, hess, >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>>>>>> line 158, in __init__ >>>>>>>> self._update_fun() >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>>>>>> line 251, in _update_fun >>>>>>>> self._update_fun_impl() >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>>>>>> line 155, in update_fun >>>>>>>> self.f = fun_wrapped(self.x) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\scipy\optimize\_differentiable_functions.py", >>>>>>>> line 137, in fun_wrapped >>>>>>>> fx = fun(np.copy(x), *args) >>>>>>>> File >>>>>>>> "F:\Zohreh\MainZohreh\postdoc-field\CSU\pythonProject\fit_test_2.py", >>>>>>>> line >>>>>>>> 17, in f >>>>>>>> Vi_est = gamma - (1 / eta) * sp.log(alpha * L ** -eta + beta * >>>>>>>> K ** -eta) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>>>>>> line 74, in wrapper >>>>>>>> retval = func(*args, **kwargs) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\function.py", >>>>>>>> line 476, in __new__ >>>>>>>> result = super().__new__(cls, *args, **options) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\cache.py", >>>>>>>> line 74, in wrapper >>>>>>>> retval = func(*args, **kwargs) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\core\function.py", >>>>>>>> line 288, in __new__ >>>>>>>> evaluated = cls.eval(*args) >>>>>>>> File >>>>>>>> "C:\Users\Zohreh\AppData\Roaming\Python\Python310\site-packages\sympy\functions\elementary\exponential.py", >>>>>>>> line 718, in eval >>>>>>>> coeff = arg.as_coefficient(I) >>>>>>>> AttributeError: 'ImmutableDenseNDimArray' object has no attribute >>>>>>>> 'as_coefficient' >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Zohreh Karimzadeh >>>>>>>> https://www.researchgate.net/profile/Zohreh-Karimzadeh >>>>>>>> Skype Name 49a52224a8b6b38b >>>>>>>> Twitter Account @zohrehkarimzad1 >>>>>>>> z.karimza...@gmail.com >>>>>>>> +989102116325 >>>>>>>> >>>>>>>> ((((((((((((((((Value Water))))))))))))))) >>>>>>>> >>>>>>>> Zohreh Karimzadeh >>>>>>>> *https://www.researchgate.net/profile/Zohreh-Karimzadeh* >>>>>>>> <https://www.researchgate.net/profile/Zohreh-Karimzadeh> >>>>>>>> Skype Name 49a52224a8b6b38b >>>>>>>> Twitter Account @zohrehkarimzad1 >>>>>>>> z.karimza...@gmail.com >>>>>>>> +989102116325 >>>>>>>> >>>>>>>> ((((((((((((((((Value Water))))))))))))))) >>>>>>>> >>>>>>>> >>>>>>>> On Thu, Aug 18, 2022 at 10:42 AM Peter Stahlecker < >>>>>>>> peter.stahlec...@gmail.com> wrote: >>>>>>>> >>>>>>>>> I use lambdify quite a bit, on rather large expressions. >>>>>>>>> Basically, it always works like this for me: >>>>>>>>> >>>>>>>>> import sympy as sm >>>>>>>>> x1, x2, …, xn = sm.symbols(‚x1, x2, ….., xn‘) >>>>>>>>> …. >>>>>>>>> … >>>>>>>>> expr = some expression of generally with me: sm.sin, sm.cos, >>>>>>>>> sm.exp, sm.sqrt, >>>>>>>>> sm.Heaviside, etc.. >>>>>>>>> This expression may have 50,000 terms, may be an (axb) matrix, >>>>>>>>> whatever. >>>>>>>>> >>>>>>>>> expr_lam = sm.lambdify([x1, x2, …,xn], expr) >>>>>>>>> >>>>>>>>> Now I can evaluate expr_lam(…) like I would evaluate any numpy >>>>>>>>> function. >>>>>>>>> >>>>>>>>> I have no idea, what expr_lam looks like, I would not know how to >>>>>>>>> look at it. >>>>>>>>> I assume, it converts sm.sin(..) to np.sin(…), etc >>>>>>>>> >>>>>>>>> This is how it works for me. >>>>>>>>> As I do not really understand your points, like ‚dynamically >>>>>>>>> created‘, ‚parse and subs‘, this may be of not help at all for you. >>>>>>>>> >>>>>>>>> Peter >>>>>>>>> >>>>>>>>> >>>>>>>>> On Thu 18. Aug 2022 at 09:21 Zohreh Karimzadeh < >>>>>>>>> z.karimza...@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> Before run I import sp.sqrt or sp.exp but after run they get >>>>>>>>>> disappeared. My expression is big and dynamically created and not >>>>>>>>>> possible to parse and subs np.exp or sp.exp. >>>>>>>>>> >>>>>>>>>> Zohreh Karimzadeh >>>>>>>>>> >>>>>>>>>> Contact me on >>>>>>>>>> +989102116325 >>>>>>>>>> and at >>>>>>>>>> z.karimza...@gmail.com >>>>>>>>>> 🌧️🌍🌱 >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Thu, 18 Aug 2022, 01:17 Aaron Meurer, <asmeu...@gmail.com> >>>>>>>>>> wrote: >>>>>>>>>> >>>>>>>>>>> Your expression uses "sqrt" but you haven't imported it from >>>>>>>>>>> anywhere, since you only did "import sympy as sp". You need to use >>>>>>>>>>> sp.sqrt. >>>>>>>>>>> >>>>>>>>>>> Aaron Meurer >>>>>>>>>>> >>>>>>>>>>> On Wed, Aug 17, 2022 at 11:02 AM Zohreh Karimzadeh < >>>>>>>>>>> z.karimza...@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> Here is my code: >>>>>>>>>>>> >>>>>>>>>>>> import matplotlib.pyplot as plt >>>>>>>>>>>> import numpy as np >>>>>>>>>>>> import sympy as sp >>>>>>>>>>>> import pandas as pd >>>>>>>>>>>> #exp_NaCl path: >>>>>>>>>>>> F:\Zohreh\MainZohreh\postdoc-field\CSU\Duplicat_Pure >>>>>>>>>>>> df = >>>>>>>>>>>> pd.read_excel(r'F:\Zohreh\MainZohreh\postdoc-field\CSU\Duplicat_Pure\data.xlsx', >>>>>>>>>>>> sheet_name='NaCl_exp') >>>>>>>>>>>> XNa = df['XNa'] >>>>>>>>>>>> XCl = df['XCl'] >>>>>>>>>>>> Xwater = df['Xwater'] >>>>>>>>>>>> Y = df['gama_x'] >>>>>>>>>>>> L=['WwaterNaCl', 'UwaterNaCl', 'VwaterNaCl', 'XCl', 'XNa', >>>>>>>>>>>> 'Xwater', 'BNaCl'] >>>>>>>>>>>> for j in range(len(L)): >>>>>>>>>>>> locals()[L[j]] = sp.symbols(L[j]) >>>>>>>>>>>> expr = >>>>>>>>>>>> -0.0118343195266272*BNaCl*XCl*XNa*(-2*(9.19238815542512*sqrt(XNa) >>>>>>>>>>>> + 9.19238815542512*sqrt(XCl + XNa) + >>>>>>>>>>>> 1)*exp(-9.19238815542512*sqrt(XNa) - 9.19238815542512*sqrt(XCl + >>>>>>>>>>>> XNa)) + 2)/((XCl + XNa)*(sqrt(XNa) + sqrt(XCl + XNa))**2) + >>>>>>>>>>>> 0.00591715976331361*BNaCl*XCl*(-2*(9.19238815542512*sqrt(XNa) + >>>>>>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + >>>>>>>>>>>> 1)*exp(-9.19238815542512*sqrt(XNa) - 9.19238815542512*sqrt(XCl + >>>>>>>>>>>> XNa)) + 2)/(sqrt(XNa) + sqrt(XCl + XNa))**2 + >>>>>>>>>>>> 0.00591715976331361*BNaCl*XNa*(-2*(9.19238815542512*sqrt(XNa) + >>>>>>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + >>>>>>>>>>>> 1)*exp(-9.19238815542512*sqrt(XNa) - 9.19238815542512*sqrt(XCl + >>>>>>>>>>>> XNa)) + 2)/(sqrt(XNa) + sqrt(XCl + XNa))**2 - >>>>>>>>>>>> 1.0*Cl*WwaterNaCl*Xwater*(0.5*XCl + 0.5*XNa + 0.5)/XCl - >>>>>>>>>>>> 0.5*Cl*WwaterNaCl/XCl - 4.0*UwaterNaCl*XCl*XNa*Xwater + >>>>>>>>>>>> 2.0*UwaterNaCl*XCl*Xwater + 2.0*UwaterNaCl*XNa*Xwater - >>>>>>>>>>>> 4.0*UwaterNaCl*XNa - 6.0*VwaterNaCl*XCl*XNa*Xwater**2 - >>>>>>>>>>>> 4.0*VwaterNaCl*XCl*Xwater**2 + 2.0*VwaterNaCl*XNa*Xwater**2 - >>>>>>>>>>>> 1.0*WwaterNaCl*Xwater*(0.5*XCl + 0.5*XNa + 0.5) + >>>>>>>>>>>> 2.0*WwaterNaCl*Xwater - 0.5*WwaterNaCl - >>>>>>>>>>>> 1.45739430799067*(0.707106781186548*sqrt(XNa) + >>>>>>>>>>>> 0.707106781186548*sqrt(XCl + XNa))*(-XCl - XNa + >>>>>>>>>>>> 1)/(9.19238815542512*sqrt(XNa) + 9.19238815542512*sqrt(XCl + XNa) >>>>>>>>>>>> + 1) - 1.45739430799067*(0.707106781186548*sqrt(XNa) + >>>>>>>>>>>> 0.707106781186548*sqrt(XCl + XNa))*(-1.4142135623731*sqrt(XNa) - >>>>>>>>>>>> 1.4142135623731*sqrt(XCl + XNa) + 1)/(9.19238815542512*sqrt(XNa) + >>>>>>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1) - >>>>>>>>>>>> 0.448429017843282*log(9.19238815542512*sqrt(XNa) + >>>>>>>>>>>> 9.19238815542512*sqrt(XCl + XNa) + 1) >>>>>>>>>>>> model_func = sp.lambdify(L, expr ) >>>>>>>>>>>> >>>>>>>>>>>> def f(param): >>>>>>>>>>>> BNaCl = param[0] >>>>>>>>>>>> UwaterNaCl = param[1] >>>>>>>>>>>> VwaterNaCl = param[2] >>>>>>>>>>>> WwaterNaCl = param[3] >>>>>>>>>>>> Y_est = model_func >>>>>>>>>>>> return np.sum((np.log(Y) - Y_est)**2) >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> bnds = [(1, np.inf), (0, 1), (0, 1), (-1, np.inf)] >>>>>>>>>>>> x0 = (1, 0.01, 0.98, 1) >>>>>>>>>>>> con = {"type": "eq", "fun": c} >>>>>>>>>>>> >>>>>>>>>>>> result = minimize(f, x0, bounds=bnds) >>>>>>>>>>>> >>>>>>>>>>>> print(result.fun) >>>>>>>>>>>> print(result.message) >>>>>>>>>>>> print(result.x[0], result.x[1], result.x[2], result.x[3]) >>>>>>>>>>>> >>>>>>>>>>>> while I got : >>>>>>>>>>>> NameError: name 'sqrt' is not defined >>>>>>>>>>>> >>>>>>>>>>>> Zohreh Karimzadeh >>>>>>>>>>>> *https://www.researchgate.net/profile/Zohreh-Karimzadeh* >>>>>>>>>>>> <https://www.researchgate.net/profile/Zohreh-Karimzadeh> >>>>>>>>>>>> Skype Name 49a52224a8b6b38b >>>>>>>>>>>> Twitter Account @zohrehkarimzad1 >>>>>>>>>>>> z.karimza...@gmail.com >>>>>>>>>>>> +989102116325 >>>>>>>>>>>> >>>>>>>>>>>> ((((((((((((((((Value Water))))))))))))))) >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> On Wed, Aug 17, 2022 at 7:46 PM Peter Stahlecker < >>>>>>>>>>>> peter.stahlec...@gmail.com> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> I use lambdify(....) a lot, but always like this: >>>>>>>>>>>>> >>>>>>>>>>>>> x = sympy.symbols('x') >>>>>>>>>>>>> expr = symy.S(10.) * sympy.sqrt(x) >>>>>>>>>>>>> expr_lam = sympy.lambdify([x], expr) >>>>>>>>>>>>> >>>>>>>>>>>>> a = expr_lam(10.) >>>>>>>>>>>>> >>>>>>>>>>>>> This seems to work for me. >>>>>>>>>>>>> >>>>>>>>>>>>> On Wed 17. Aug 2022 at 20:38, Zohreh Karimzadeh < >>>>>>>>>>>>> z.karimza...@gmail.com> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> Dear sympy group >>>>>>>>>>>>>> Thanks for your sympy. >>>>>>>>>>>>>> >>>>>>>>>>>>>> I am working on a code, after creating my big expression >>>>>>>>>>>>>> using sympy it includes sqrt. >>>>>>>>>>>>>> >>>>>>>>>>>>>> I need to lambdify my expression to make it consistent with >>>>>>>>>>>>>> numpy and other suffs. >>>>>>>>>>>>>> >>>>>>>>>>>>>> expr =10 * sp.sqrt(sp.symbols('x')) >>>>>>>>>>>>>> >>>>>>>>>>>>>> model_func = sp.lambdify('x', expr) >>>>>>>>>>>>>> >>>>>>>>>>>>>> But I found my expression after lambdifying becomes >>>>>>>>>>>>>> somethings like this: >>>>>>>>>>>>>> >>>>>>>>>>>>>> 10*sqrt(x) >>>>>>>>>>>>>> >>>>>>>>>>>>>> while I need : >>>>>>>>>>>>>> >>>>>>>>>>>>>> 10*numpy.sqrt(x) >>>>>>>>>>>>>> >>>>>>>>>>>>>> Could possibly let me know how get sqrt to work with numpy? >>>>>>>>>>>>>> >>>>>>>>>>>>>> Regards, >>>>>>>>>>>>>> >>>>>>>>>>>>>> Zohreh >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> -- >>>>>>>>>>>>>> You received this message because you are subscribed to the >>>>>>>>>>>>>> Google Groups "sympy" group. >>>>>>>>>>>>>> To unsubscribe from this group and stop receiving emails from >>>>>>>>>>>>>> it, send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>>>>>>> To view this discussion on the web visit >>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/1f0b313f-31c5-402e-991e-142a556016f4n%40googlegroups.com >>>>>>>>>>>>>> <https://groups.google.com/d/msgid/sympy/1f0b313f-31c5-402e-991e-142a556016f4n%40googlegroups.com?utm_medium=email&utm_source=footer> >>>>>>>>>>>>>> . >>>>>>>>>>>>>> >>>>>>>>>>>>> -- >>>>>>>>>>>>> Best regards, >>>>>>>>>>>>> >>>>>>>>>>>>> Peter Stahlecker >>>>>>>>>>>>> >>>>>>>>>>>>> -- >>>>>>>>>>>>> You received this message because you are subscribed to the >>>>>>>>>>>>> Google Groups "sympy" group. >>>>>>>>>>>>> To unsubscribe from this group and stop receiving emails from >>>>>>>>>>>>> it, send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>>>>>> To view this discussion on the web visit >>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/CABKqA0ZoGwsadsk4SWCbJVMbCDwXcO_gNGumJH00GAeEFod7Cw%40mail.gmail.com >>>>>>>>>>>>> <https://groups.google.com/d/msgid/sympy/CABKqA0ZoGwsadsk4SWCbJVMbCDwXcO_gNGumJH00GAeEFod7Cw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>>>>>>> . >>>>>>>>>>>>> >>>>>>>>>>>> -- >>>>>>>>>>>> You received this message because you are subscribed to the >>>>>>>>>>>> Google Groups "sympy" group. >>>>>>>>>>>> To unsubscribe from this group and stop receiving emails from >>>>>>>>>>>> it, send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>>>>> To view this discussion on the web visit >>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLPRvXZ6jiJbUS_xpWNKqMuUH7Kt5evue%2BwKEwDMvGekBQ%40mail.gmail.com >>>>>>>>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLPRvXZ6jiJbUS_xpWNKqMuUH7Kt5evue%2BwKEwDMvGekBQ%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>>>>>> . >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> -- >>>>>>>>>>> You received this message because you are subscribed to the >>>>>>>>>>> Google Groups "sympy" group. >>>>>>>>>>> To unsubscribe from this group and stop receiving emails from >>>>>>>>>>> it, send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>>>> To view this discussion on the web visit >>>>>>>>>>> https://groups.google.com/d/msgid/sympy/CAKgW%3D6JfUmU7Uu%2BSrcA1STxVvWWm7bGWE%3Dit8CTchksTC0Qk7g%40mail.gmail.com >>>>>>>>>>> <https://groups.google.com/d/msgid/sympy/CAKgW%3D6JfUmU7Uu%2BSrcA1STxVvWWm7bGWE%3Dit8CTchksTC0Qk7g%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>>>>> . >>>>>>>>>>> >>>>>>>>>> -- >>>>>>>>>> You received this message because you are subscribed to the >>>>>>>>>> Google Groups "sympy" group. >>>>>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>>>>> send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>>> To view this discussion on the web visit >>>>>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLPiCR%3DS2Fac3FZtjMpspqB7BRKtYEi45BVWPjkizVbNvw%40mail.gmail.com >>>>>>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLPiCR%3DS2Fac3FZtjMpspqB7BRKtYEi45BVWPjkizVbNvw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>>>> . >>>>>>>>>> >>>>>>>>> -- >>>>>>>>> Best regards, >>>>>>>>> >>>>>>>>> Peter Stahlecker >>>>>>>>> >>>>>>>>> -- >>>>>>>>> You received this message because you are subscribed to the Google >>>>>>>>> Groups "sympy" group. >>>>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>>>> send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>>> To view this discussion on the web visit >>>>>>>>> https://groups.google.com/d/msgid/sympy/CABKqA0b%3DF0akMH4oyg5%2By9dGvgrf_vvVJTnVhVduMP1f%2Bp1pFw%40mail.gmail.com >>>>>>>>> <https://groups.google.com/d/msgid/sympy/CABKqA0b%3DF0akMH4oyg5%2By9dGvgrf_vvVJTnVhVduMP1f%2Bp1pFw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>>> . >>>>>>>>> >>>>>>>> -- >>>>>>>> You received this message because you are subscribed to the Google >>>>>>>> Groups "sympy" group. >>>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>>> send an email to sympy+unsubscr...@googlegroups.com. >>>>>>>> To view this discussion on the web visit >>>>>>>> https://groups.google.com/d/msgid/sympy/CA%2B1XYLMK-fgpxc71GYzue5gJvd%3Dfj2sV6Dvhj8zrmVpPhiVk%2Bw%40mail.gmail.com >>>>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLMK-fgpxc71GYzue5gJvd%3Dfj2sV6Dvhj8zrmVpPhiVk%2Bw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>>>>>>> . >>>>>>> >>>>>>> >>>>>>>> -- >>>>>>> You received this message because you are subscribed to the Google >>>>>>> Groups "sympy" group. >>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>> send an 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