How to take element-wise logarithm of a matrix in sympy?

Question

Working with a sympy Matrix or numpy array of sympy symbols, how does one take the element-wise logarithm?

For example, if I have:

m=sympy.Matrix(sympy.symbols('a b c d'))

Then np.abs(m) works fine, but np.log(m) does not work ("AttributeError: log").

Any solutions?

@Bitwise See [this issue on github](https://github.com/numpy/numpy/issues/1611). Apparently, you can't use `numpy.log` on object arrays (e.g. sympy arrays). — senshin, Jan 16 '14 at 17:58
@senshin thanks. So this means that there is no way to take the logarithm of a sympy array/matrix? — Bitwise, Jan 16 '14 at 18:53
@Bitwise Are we talking about an actual matrix logarithm (inverse of the matrix exponential) or an element-wise logarithm? I ask because the matrix `m` you've defined is not square (it's 1-by-4), so it doesn't have a matrix log. — senshin, Jan 16 '14 at 18:56

score 8 · Accepted Answer · answered Jan 17 '14 at 01:05

8

Use Matrix.applyfunc:

In [6]: M = sympy.Matrix(sympy.symbols('a b c d'))

In [7]: M.applyfunc(sympy.log)
Out[7]:
⎡log(a)⎤
⎢      ⎥
⎢log(b)⎥
⎢      ⎥
⎢log(c)⎥
⎢      ⎥
⎣log(d)⎦

You can't use np.log because that does a numeric log, but you want the symbolic version, i.e., sympy.log.

answered Jan 17 '14 at 01:05

asmeurer

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Hey, just saw you are the lead developer of sympy - respect! Good job. It would be great if the matrix vectorization was more streamlined similar to Matlab symbolic toolbox. – Bitwise Jan 17 '14 at 01:39
Well, I didn't write most of the code, though. There have been a ton of contributors. – asmeurer Jan 17 '14 at 02:30
If you have any suggestion to make it better, let us know. – asmeurer Jan 17 '14 at 02:31
is there a way to pass in the base for log? – lingxiao Oct 06 '15 at 06:25
The base is given as a second argument to log, but for now, it just divides by `log(base)`, so `log(x, y)` just gives `log(x)/log(y)`. So in this case you could use `M.applyfunc(sympy.log)/sympy.log(base)`. – asmeurer Oct 07 '15 at 17:25

score 1 · Answer 2 · answered Jan 16 '14 at 19:08

If you want an elementwise logarithm, and your matrices are all going to be single-column, you should just be able to use a list comprehension:

>>> m = sympy.Matrix(sympy.symbols('a b c d'))
>>> logm = sympy.Matrix([sympy.log(x) for x in m])
>>> logm
Matrix([
[log(a)],
[log(b)],
[log(c)],
[log(d)]])

This is kind of ugly, but you could wrap it in a function for ease, e.g.:

>>> def sp_log(m):
    return sympy.Matrix([sympy.log(x) for x in m])

>>> sp_log(m)
Matrix([
[log(a)],
[log(b)],
[log(c)],
[log(d)]])

Thanks - so no vectorized solution I guess. I hoped sympy would be a good replacement for Matlab symbolic stuff but I see sympy isn't there yet in terms of handling matrices. — Bitwise, Jan 16 '14 at 19:37

How to take element-wise logarithm of a matrix in sympy?

2 Answers2