Problem of function libraries in lambdify

[Emile59]

Hello,

I am currently developping a python program to tranform a symbolic expression computed by `sympy` into a `numpy` array containing all the numerical values. I instantiate the symbolic expression with the `sympy.lambdify` function.

Some of the symbolic expressions contain Bessel functions, and I pass `scipy.special.jv/jy` etc. as parameters in the `lambdify` function. Here is the single code (appart from the program) :

    m = Symbol('m')
    expr= -1.06048319593874*(-(3.14159265358979*m*besselj(27.9937791601866*m, 4.46681007624482*sqrt(-I)) - 0.501286290793831*sqrt(-I)*besselj(27.9937791601866*m + 1, 4.46681007624482*sqrt(-I)))*bessely(27.9937791601866*m, 6.81776274795262*sqrt(-I))/(3.14159265358979*m*bessely(27.9937791601866*m, 4.46681007624482*sqrt(-I)) - 0.501286290793831*sqrt(-I)*bessely(27.9937791601866*m + 1, 4.46681007624482*sqrt(-I))) + besselj(27.9937791601866*m, 6.81776274795262*sqrt(-I)))*sin(0.942966379693359*m)*cos(1.5707963267949*m)/m
    nm = 5
    vm = arange(nm) +1
    bessel = {'besselj':jv,'besselk':kv,'besseli':iv,'bessely':yv}
    libraries = [bessel, "numpy"]    
    result = lambdify(m, expr, modules=libraries)(vm)

    In[1] : result
    Out[1]:
    array([ -7.51212638e-030 -3.22606326e-030j,
             4.81143544e-046 +1.04405860e-046j,
             1.97977798e-097 +3.02047228e-098j,
             3.84986092e-124 +4.73598141e-125j,
             1.12934434e-181 +1.21145535e-182j])

The result is as I expected : a 5 rows 1-d array with each integer value of the symbol `m`.

The problem is when I try to implement it in the program. Here is the implementation :

    expr = list_symbolic_expr[index]
    vcm = arange(Dim_col[0]) +1   #Dim_col = list of integer range values to instantiate                    
    m = Symbol(str(Var_col[0])) #Var_col = list of symbolic integer parameters
    print expr, m
    smat = lambdify(m, expr, modules=libraries)(vcm)

Here is the error when using `scipy.special` bessel functions :

    In [2]: run Get_System_Num
    Out [2]:
    -1.06048319593874*(-(3.14159265358979*m*besselj(27.9937791601866*m, 4.46681007624482*sqrt(-I)) - 0.501286290793831*sqrt(-I)*besselj(27.9937791601866*m + 1, 4.46681007624482*sqrt(-I)))*bessely(27.9937791601866*m, 6.81776274795262*sqrt(-I))/(3.14159265358979*m*bessely(27.9937791601866*m, 4.46681007624482*sqrt(-I)) - 0.501286290793831*sqrt(-I)*bessely(27.9937791601866*m + 1, 4.46681007624482*sqrt(-I))) + besselj(27.9937791601866*m, 6.81776274795262*sqrt(-I)))*sin(0.942966379693359*m)*cos(1.5707963267949*m)/m m
      File "Numeric\Get_System_Num.py", line 183, in get_Mat
        smat = lambdify(m, expr, modules=libraries)(vcm)
   
      File "<string>", line 1, in <lambda>
   
    TypeError: ufunc 'jv' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''

Here is the error when using `sympy.special` bessel functions :

      File "Numeric\Get_System_Num.py", line 183, in get_Mat
        smat = lambdify(m, expr, modules=libraries)(vcm)
   
      File "<string>", line 1, in <lambda>
   
      File "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\core\function.py", line 375, in __new__
        result = super(Function, cls).__new__(cls, *args, **options)
   
      File "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\core\function.py", line 199, in __new__
        evaluated = cls.eval(*args)
   
      File "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\functions\special\bessel.py", line 161, in eval
        if nu.is_integer:
   
    AttributeError: 'numpy.ndarray' object has no attribute 'is_integer'

When I try to lambdify this simple expression : `17469169.5935065*sin(0.942966379693359*m)*cos(1.5707963267949*m)/m`, with "numpy" as module argument, it gives :    `'float' object has no attribute 'sin'`

I have also tried the packaged module 'numexpr' without success, as it stops on this other expression : `0.058**(46.6321243523316*k)`, saying :

      File "C:\Users\Emile\Anaconda2\lib\site-packages\numexpr\necompiler.py", line 756, in evaluate
        signature = [(name, getType(arg)) for (name, arg) in zip(names, arguments)]
   
      File "C:\Users\Emile\Anaconda2\lib\site-packages\numexpr\necompiler.py", line 654, in getType
        raise ValueError("unknown type %s" % a.dtype.name)
   
    ValueError: unknown type object

It seems that `lambdify` cannot interprete properly the input value in the bessel function in the program code (wether it is with scipy or sympy bessel functions), as the input value seems to be an array object, while it is not a problem in the single code. Yet I do not see the difference between them. There is also a problem about defining the modules, even if numpy and bessel functions are correctly specified.
So I really don't know the nature of this problem, and I can't even track it as the exception raised comes from inside sympy and I don't know how to put flags in sympy functions.
Thank you for reading this, and I hope someone may help me on this topic. Please tell me if more information are needed to illustrate this problem.

[Aaron Meurer]

The only thing that I can see that would be different here is the size
of the input array. What is Dim_col[0]? Note that for me, anything >=
8 gives nan in the result (due to precision loss). It looks like the
default behavior of the "safe" casting has changed in recent versions
of numpy (https://docs.scipy.org/doc/numpy/reference/generated/numpy.can_cast.html),
so the version of numpy you are using is important. What versions of
numpy and scipy are you using?

>
>
>
> Here is the error when using `sympy.special` bessel functions :
>
>
> File "Numeric\Get_System_Num.py", line 183, in get_Mat
> smat = lambdify(m, expr, modules=libraries)(vcm)
>
> File "<string>", line 1, in <lambda>
>
> File
> "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\core\function.py", line
> 375, in __new__
> result = super(Function, cls).__new__(cls, *args, **options)
>
> File
> "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\core\function.py", line
> 199, in __new__
> evaluated = cls.eval(*args)
>
> File
> "C:\Users\Emile\Anaconda2\lib\site-packages\sympy\functions\special\bessel.py",
> line 161, in eval
> if nu.is_integer:
>
> AttributeError: 'numpy.ndarray' object has no attribute 'is_integer'

No, this won't work. You can't use NumPy arrays as input to SymPy
functions. SymPy functions only work with SymPy expressions. If you
want to use a NumPy array you have to lambdify the expression first to
use the numpy and scipy functions.

>
>
> When I try to lambdify this simple expression :
> `17469169.5935065*sin(0.942966379693359*m)*cos(1.5707963267949*m)/m`, with
> "numpy" as module argument, it gives : `'float' object has no attribute
> 'sin'`

I can't reproduce this. What is the input to the lambdified function?

>
> I have also tried the packaged module 'numexpr' without success, as it stops
> on this other expression : `0.058**(46.6321243523316*k)`, saying :
>
> File
> "C:\Users\Emile\Anaconda2\lib\site-packages\numexpr\necompiler.py", line
> 756, in evaluate
> signature = [(name, getType(arg)) for (name, arg) in zip(names,
> arguments)]
>
> File
> "C:\Users\Emile\Anaconda2\lib\site-packages\numexpr\necompiler.py", line
> 654, in getType
> raise ValueError("unknown type %s" % a.dtype.name)
>
> ValueError: unknown type object

I also can't reproduce this.

Aaron Meurer

>
>
>
> It seems that `lambdify` cannot interprete properly the input value in the
> bessel function in the program code (wether it is with scipy or sympy bessel
> functions), as the input value seems to be an array object, while it is not
> a problem in the single code. Yet I do not see the difference between them.
> There is also a problem about defining the modules, even if numpy and bessel
> functions are correctly specified.
> So I really don't know the nature of this problem, and I can't even track it
> as the exception raised comes from inside sympy and I don't know how to put
> flags in sympy functions.
> Thank you for reading this, and I hope someone may help me on this topic.
> Please tell me if more information are needed to illustrate this problem.
>
>

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[Emile59]

Hello,
Thank you very much for your help. I have also posted on stack overflow, and i added the rest of the get_system_num class, so I invite you to check it. I use these versions :

• for numpy : 1.9.2
  
• for scipy : 0.15.1
  
• for sympy : 0.7.6.1
  

with Python 2.7.10 |Anaconda 2.4.0 (64-bit)|

I forgot to precise indeed that Dim_row and Dim_col are list of integers and Var_row and Var_dim are lists of symbols.

The problem is the syntax works on an isolated case, meaning when I declare the expressions and symbols directly, but not when I extract them from a pre-computed list of symbolic expressions.