Make matrices type-stable, not allowing mixed types in one matrix. Always use the type of the context.
Therefore, specifying an element type by the "force_type" argument does not make sense.
It did not work properly before either, the data was not stored in the given type:
```
>>> M = mpmath.matrix(mpmath.matrix([[0,1,2]]), force_type=bool)
>>> M
matrix(
[['0.0', '1.0', '1.0']])
>>> type(M[0,0])
<class 'mpmath.ctx_mp_python.mpf'>
>>> M._matrix__data
{(0, 1): mpf('1.0'), (0, 2): mpf('1.0')}
```
Now the argument is removed and gives a warning instead:
>>> mpmath.matrix(mpmath.matrix([[0,1,2]]), force_type=bool)
/mpmath/mpmath/matrices/matrices.py:288: UserWarning: The force_type argument was removed, it did not work properly anyway. If you want to force floating-point or interval computations, use the respective methods from `fp` or `mp` instead, e.g., `fp.matrix()` or `iv.matrix()`. If you want to truncate values to integer, use .apply(int) instead.
warnings.warn("The force_type argument was removed, it did not work"
matrix([['0.0', '1.0', '2.0']])
Non-interval datatypes were not converted to intervals, resulting in unexpected behavior. For example, M[i, j] didn't return mpi interval objects, but mpf floats, so M[i, j] * M[k, l] and, under certain conditions, M * M, was not performed as interval multiplication.
This could have unexpected consequences, as outlined below.
"Exact" computation for reference:
>>> import mpmath
>>> x = mpmath.convert('1.00000000000001') # 1.0000...001 rounded to the next mpf floating point value
>>> mpmath.mp.dps=1000
>>> x*x # Good approximation of x*x
mpf('1.00000000000001998401444325291756783368705994138804689654360263219301518944348572404123842716217041015625')
Interval arithmetic should return an interval containing that value, with some uncertainty.
Restart python to reset mp.dps.
Before this commit, the following occurs:
>>> import mpmath
>>> x = mpmath.convert('1.00000000000001')
>>> x
mpf('1.00000000000001')
>>> A = mpmath.matrix([[x]])
>>> B = mpmath.iv.matrix(A)
>>> C = mpmath.iv.matrix([[x]])
>>> A*A
matrix(
[['1.00000000000002']])
>>> B*B
matrix(
[['[1.000000000000019984, 1.000000000000019984]']])
>>> (B*B)[0,0].delta
mpi('0.0', '0.0')
>>> C*C
matrix(
[['[1.000000000000019984, 1.0000000000000202061]']])
B*B is wrong, the interval width must be nonzero at the default precision of 15 digits.
B*B is different from C*C, although both were initialized from the same numerical value and computed the same way.
After this commit, the result is valid:
>>> B*B
matrix(
[['[1.000000000000019984, 1.0000000000000202061]']])
>>> (B*B)[0,0].delta
mpi('2.2204460492503131e-16', '2.2204460492503131e-16')
Some more insight:
Old incorrect behavior:
>>> mpmath.iv.matrix(mpmath.eye(1))[0,0]
mpf('1.0')
New correct behavior:
>>> mpmath.iv.matrix(mpmath.eye(1))[0,0]
mpf('1.0')
>>> mpmath.iv.eye(1)[0,0]
mpi('1.0', '1.0')
>>> import mpmath
>>> mpmath.iv.matrix(mpmath.eye(1))
matrix(
[['[1.0, 1.0]']])
>>> mpmath.iv.matrix(mpmath.eye(1))[0,0]
mpi('1.0', '1.0')
>>> mpmath.fp.matrix(mpmath.eye(1))[0,0]
1.0
>>> mpmath.matrix(mpmath.eye(1))[0,0]
mpf('1.0')
The type now exactly matches the type returned by the context's matrix functions such as eye():
>>> mpmath.matrix(mpmath.eye(1))[0,0]
mpf('1.0')
>>> mpmath.eye(1)[0,0]
mpf('1.0')
>>> mpmath.iv.matrix(mpmath.eye(1))[0,0]
mpi('1.0', '1.0')
>>> mpmath.iv.eye(1)[0,0]
mpi('1.0', '1.0')
>>> mpmath.fp.matrix(mpmath.eye(1))[0,0]
1.0
>>> mpmath.fp.eye(1)[0,0]
1.0
This reverts c98b4d6. I believe, for platform-independent
Python library these tests are not needed, even if we add
gmpy-enabled tests. Right now this only enlarge the build
matrix and slowdown the testing process...
fredrik