Cannot do mpmath.sqrtm() in sympy

[Yuxiang Wang]

Dear all,

I have the following code to extract the square root of a symmetric second-order tensor.

from sympy import symbols, Matrix, mpmath
import numpy as np

F11, F12, F13, F21, F22, F23, F31, F32, F33 = symbols('F11, F12, F13, F21, F22, F23, F31, F32, F33', real=True)
F = np.array([[F11, F12, F13], [F21, F22, F23], [F31, F32, F33]])
B = F.dot(F.T)
mpmath.sqrtm(Matrix(B))

However, it gave me the error:

TypeError                                 Traceback (most recent call last)
<ipython-input-14-439fed475a57> in <module>()
      5 F = np.array([[F11, F12, F13], [F21, F22, F23], [F31, F32, F33]])
      6 B = F.dot(F.T)
----> 7 mpmath.sqrtm(Matrix(B))

X:\WinPython3\python-3.4.2.amd64\lib\site-packages\sympy\mpmath\matrices\calculus.py in sqrtm(ctx, A, _may_rotate)
    308 
    309         """
--> 310         A = ctx.matrix(A)
    311         # Trivial
    312         if A*0 == A:

X:\WinPython3\python-3.4.2.amd64\lib\site-packages\sympy\mpmath\matrices\matrices.py in __init__(self, *args, **kwargs)
    326                     A[i,j] = convert(A[i,j])
    327         elif hasattr(args[0], 'tolist'):
--> 328             A = self.ctx.matrix(args[0].tolist())
    329             self.__data = A._matrix__data
    330             self.__rows = A._matrix__rows

X:\WinPython3\python-3.4.2.amd64\lib\site-packages\sympy\mpmath\matrices\matrices.py in __init__(self, *args, **kwargs)
    299                 for i, row in enumerate(A):
    300                     for j, a in enumerate(row):
--> 301                         self[i, j] = convert(a)
    302             else:
    303                 # interpret list as row vector

X:\WinPython3\python-3.4.2.amd64\lib\site-packages\sympy\mpmath\ctx_mp_python.py in convert(ctx, x, strings)
    660         if hasattr(x, '_mpmath_'):
    661             return ctx.convert(x._mpmath_(prec, rounding))
--> 662         return ctx._convert_fallback(x, strings)
    663 
    664     def isnan(ctx, x):

X:\WinPython3\python-3.4.2.amd64\lib\site-packages\sympy\mpmath\ctx_mp.py in _convert_fallback(ctx, x, strings)
    612             else:
    613                 raise ValueError("can only create mpf from zero-width interval")
--> 614         raise TypeError("cannot create mpf from " + repr(x))
    615 
    616     def mpmathify(ctx, *args, **kwargs):

TypeError: cannot create mpf from F11**2 + F12**2 + F13**2

May I ask why that is happening? Is this a limitation of sympy or that I am doing something wrong?

Thank you!

Shawn

[Tim Lahey]

Hi,

mpmath is for multi-precision math, not symbolic math. It's expecting
numbers, not symbols. I don't think there's a square root routine for
symbolic matrices implemented.

Cheers,

Tim.

On 24 Nov 2014, at 14:05, Yuxiang Wang wrote:

> Dear all,
>
> I have the following code to extract the square root of a symmetric
> second-order tensor.
>

> from sympy import symbols, Matrix, mpmathimport numpy as np

>
> F11, F12, F13, F21, F22, F23, F31, F32, F33 = symbols('F11, F12, F13,
> F21, F22, F23, F31, F32, F33', real=True)
> F = np.array([[F11, F12, F13], [F21, F22, F23], [F31, F32, F33]])
> B = F.dot(F.T)
> mpmath.sqrtm(Matrix(B))
>
> However, it gave me the error:
>
> TypeError Traceback (most recent call
> last)<ipython-input-14-439fed475a57> in <module>()
> 5 F = np.array([[F11, F12, F13], [F21, F22, F23], [F31, F32, F33]])

> 6 B = F.dot(F.T)----> 7 mpmath.sqrtm(Matrix(B))

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[Yuxiang Wang]

Hi Tim,

Thank you for your response!

And thanks for letting me know that symbolic square root matrix routine was not implemented. 

I will try to do the following:

1) Get eigenvectors first;

2) Take square root of the eigenvalues;

3) Re-construct the square root matrix from the original eigenvectors and the sqrt of eigenvalues.

Thanks again!

Shawn

[Aaron Meurer]

It seems sqrt(Matrix) (where sqrt is sympy.sqrt) is unevaluated, but
if you do Matrix(B)**(S(1)/2) it tries to evaluate it (but it hangs).

You shouldn't use NumPy if you are dealing with symbolic matrices.
There is no advantage to using NumPy at that point, vs. sympy.Matrix.

Aaron Meurer

> https://groups.google.com/d/msgid/sympy/79209aad-242d-4e63-9d65-b8c2d581aaf8%40googlegroups.com.

[Yuxiang Wang]

Hi Aaron,

Thank you for the response!

I tried to use numpy.ndarray because I got other orders of tensors, so I wanted to be consistent. But it seems that Matrix object can be higher-order too, so I'll try to use them. Thanks for the tip!

Shawn

[Chris Smith]

To take the sqrt of each element in B, use B.applyfunc(sqrt).

[Yuxiang Wang]

Chris,

Thanks for responding! I was actually doing the square-root of the matrix, rather than the element-wise. But thanks still!

-Shawn