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
>>>>>>>>
>>>>>>>> --
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>>>>>>>> Groups "sympy" group.
>>>>>>>> To unsubscribe from this group and stop receiving emails from it,
>>>>>>>> send an email to sympy+unsubscr...@googlegroups.com.
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>>>>>>>> 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>
>>>>>>>> .
>>>>>>>>
>>>>>>> --
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>>>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLMK-fgpxc71GYzue5gJvd%3Dfj2sV6Dvhj8zrmVpPhiVk%2Bw%40mail.gmail.com?utm_medium=email&utm_source=footer>
>>>>>>> .
>>>>>>
>>>>>>
>>>>>>> --
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>>>>>> send an email to sympy+unsubscr...@googlegroups.com.
>>>>>> To view this discussion on the web visit
>>>>>> https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2BBQo_nWKJtbxPmi40V0Y6OgAaT78jSNSWKnwW8L3qmZQ%40mail.gmail.com
>>>>>> <https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2BBQo_nWKJtbxPmi40V0Y6OgAaT78jSNSWKnwW8L3qmZQ%40mail.gmail.com?utm_medium=email&utm_source=footer>
>>>>>> .
>>>>>>
>>>>> --
>>>>> You received this message because you are subscribed to the Google
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>>>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLNg4ScH5bK%3DeW7%3DVL_2%2BWdWT4kf5ud41LR5hh%2BJkCJR2g%40mail.gmail.com?utm_medium=email&utm_source=footer>
>>>>> .
>>>>>
>>>> --
>>>> Best regards,
>>>>
>>>> Peter Stahlecker
>>>>
>>> --
>>>> You received this message because you are subscribed to the Google
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>>>> 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/CABKqA0aP_Rx9rDQ-%2BumFq_9W8C4LDTRMGrFif_5GZ_dRTpA2VA%40mail.gmail.com
>>>> <https://groups.google.com/d/msgid/sympy/CABKqA0aP_Rx9rDQ-%2BumFq_9W8C4LDTRMGrFif_5GZ_dRTpA2VA%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%2B1XYLOmpYg0iHjow4D5hvp_%3DFSfmKEgaWBiDFoweEX4Vo4jxw%40mail.gmail.com
>>> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLOmpYg0iHjow4D5hvp_%3DFSfmKEgaWBiDFoweEX4Vo4jxw%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/CABKqA0YJ7gvfrAKV4%2B%2BWU%3Dd_MP_%2BUMDAeRh434KdFesS%3DxiAvA%40mail.gmail.com
>> <https://groups.google.com/d/msgid/sympy/CABKqA0YJ7gvfrAKV4%2B%2BWU%3Dd_MP_%2BUMDAeRh434KdFesS%3DxiAvA%40mail.gmail.com?utm_medium=email&utm_source=footer>
>> .
>>
>
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