args is a standard key word with minimize, just look it up to see how it
works.
Say, you have F(a, d, c, m ,e, f) as a function.
If you give the ‚starting guess‘ as x0 = (1, ,2, 3), it will minimize the
function by varying the first three variables in the parameter list of F,
that is a, d, c.
Balance parameters you have to give with the args keyword.
If you read the minimizer operations instructions, it will tell you how
minimizer hands over the values in args to your function F. And your F must
‚understand this‘.
On Sat 20. Aug 2022 at 13:24 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
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>>>>>>> send an email to sympy+unsubscr...@googlegroups.com.
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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>
>>>>>>> .
>>>>>>
>>>>>>
>>>>>>> --
>>>>>> 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%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
>>>>> 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%2B1XYLNg4ScH5bK%3DeW7%3DVL_2%2BWdWT4kf5ud41LR5hh%2BJkCJR2g%40mail.gmail.com
>>>>> <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
>>>> 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/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>
>> .
>>
> --
> 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%2B1XYLP8YcB6puF4Tg0BVOUKv8wCHnE1o113AeKXoMZnJ-NfpA%40mail.gmail.com
> <https://groups.google.com/d/msgid/sympy/CA%2B1XYLP8YcB6puF4Tg0BVOUKv8wCHnE1o113AeKXoMZnJ-NfpA%40mail.gmail.com?utm_medium=email&utm_source=footer>
> .
>
--
Best regards,
Peter Stahlecker
--
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