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
On Monday, November 24, 2014 3:22:34 PM UTC-5, Aaron Meurer wrote:
>
> 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
>
> On Mon, Nov 24, 2014 at 12:23 PM, Yuxiang Wang
> <wangyux...@gmail.com <javascript:>> wrote:
> > 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
> >
> >
> > On Monday, November 24, 2014 2:17:08 PM UTC-5, Tim Lahey wrote:
> >>
> >> 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))
> >> >
> >> >
> >> >
> 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
> >> >
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