IEEE 754 Floating Point Special Values¶
Special values defined in numpy: nan, inf,
NaNs can be used as a poor-man’s mask (if you don’t care what the original value was)
Note: cannot use equality to test NaNs. E.g.:
>>> myarr = np.array([1., 0., np.nan, 3.]) >>> np.where(myarr == np.nan) >>> np.nan == np.nan # is always False! Use special numpy functions instead. False >>> myarr[myarr == np.nan] = 0. # doesn't work >>> myarr array([ 1., 0., NaN, 3.]) >>> myarr[np.isnan(myarr)] = 0. # use this instead find >>> myarr array([ 1., 0., 0., 3.])
Other related special value functions:
isinf(): True if value is inf isfinite(): True if not nan or inf nan_to_num(): Map nan to 0, inf to max float, -inf to min float
The following corresponds to the usual functions except that nans are excluded from the results:
nansum() nanmax() nanmin() nanargmax() nanargmin() >>> x = np.arange(10.) >>> x = np.nan >>> x.sum() nan >>> np.nansum(x) 42.0
How numpy handles numerical exceptions¶
The default is to
underflow. But this can be changed, and it can be
set individually for different kinds of exceptions. The different behaviors
- ‘ignore’ : Take no action when the exception occurs.
- ‘warn’ : Print a RuntimeWarning (via the Python
- ‘raise’ : Raise a FloatingPointError.
- ‘call’ : Call a function specified using the seterrcall function.
- ‘print’ : Print a warning directly to
- ‘log’ : Record error in a Log object specified by seterrcall.
These behaviors can be set for all kinds of errors or specific ones:
- all : apply to all numeric exceptions
- invalid : when NaNs are generated
- divide : divide by zero (for integers as well!)
- overflow : floating point overflows
- underflow : floating point underflows
Note that integer divide-by-zero is handled by the same machinery. These behaviors are set on a per-thread basis.
>>> oldsettings = np.seterr(all='warn') >>> np.zeros(5,dtype=np.float32)/0. invalid value encountered in divide >>> j = np.seterr(under='ignore') >>> np.array([1.e-100])**10 >>> j = np.seterr(invalid='raise') >>> np.sqrt(np.array([-1.])) FloatingPointError: invalid value encountered in sqrt >>> def errorhandler(errstr, errflag): ... print("saw stupid error!") >>> np.seterrcall(errorhandler) <function err_handler at 0x...> >>> j = np.seterr(all='call') >>> np.zeros(5, dtype=np.int32)/0 FloatingPointError: invalid value encountered in divide saw stupid error! >>> j = np.seterr(**oldsettings) # restore previous ... # error-handling settings
Interfacing to C¶
Only a survey of the choices. Little detail on how each works.
- Bare metal, wrap your own C-code manually.
- No dependencies on other tools
- Lots of learning overhead:
- need to learn basics of Python C API
- need to learn basics of numpy C API
- need to learn how to handle reference counting and love it.
- Reference counting often difficult to get right.
- getting it wrong leads to memory leaks, and worse, segfaults
- API will change for Python 3.0!
- avoid learning C API’s
- no dealing with reference counting
- can code in pseudo python and generate C code
- can also interface to existing C code
- should shield you from changes to Python C api
- has become the de-facto standard within the scientific Python community
- fast indexing support for arrays
- Can write code in non-standard form which may become obsolete
- Not as flexible as manual wrapping
part of Python standard library
good for interfacing to existing sharable libraries, particularly Windows DLLs
avoids API/reference counting issues
good numpy support: arrays have all these in their ctypes attribute:a.ctypes.data a.ctypes.get_strides a.ctypes.data_as a.ctypes.shape a.ctypes.get_as_parameter a.ctypes.shape_as a.ctypes.get_data a.ctypes.strides a.ctypes.get_shape a.ctypes.strides_as
- can’t use for writing code to be turned into C extensions, only a wrapper tool.
- SWIG (automatic wrapper generator)
- around a long time
- multiple scripting language support
- C++ support
- Good for wrapping large (many functions) existing C libraries
- generates lots of code between Python and the C code
- can cause performance problems that are nearly impossible to optimize out
- interface files can be hard to write
- doesn’t necessarily avoid reference counting issues or needing to know API’s
- can turn many numpy expressions into C code
- dynamic compiling and loading of generated C code
- can embed pure C code in Python module and have weave extract, generate interfaces and compile, etc.
- Future very uncertain: it’s the only part of Scipy not ported to Python 3 and is effectively deprecated in favor of Cython.
- Turns pure python into efficient machine code through jit-like optimizations
- very fast when it optimizes well
- Only on intel (windows?)
- Doesn’t do much for numpy?
Interfacing to Fortran:¶
The clear choice to wrap Fortran code is f2py.
Pyfort is an older alternative, but not supported any longer. Fwrap is a newer project that looked promising but isn’t being developed any longer.
Interfacing to C++:¶
- SIP (used mainly in PyQT)