Frequently Asked Questions¶
- General questions about NumPy
- General questions about SciPy
- NumPy vs. SciPy vs. other packages
- Python version support
- Basic NumPy/SciPy usage
- What is the preferred way to check for an empty (zero element) array?
- I want to load data from a text file. How do I make this code more efficient?
- What is the difference between matrices and arrays?
- Why not just have a separate operator for matrix multiplication?
- How do I find the indices of an array where some condition is true?
- How do I count the number of times each value appears in an array of integers?
- Advanced NumPy usage
- Where to get help
NumPy is a Python extension module that provides efficient operation on arrays of homogeneous data. It allows python to serve as a high-level language for manipulating numerical data, much like IDL, MATLAB, or Yorick.
As always, you should choose the programming tools that suit your problem and your environment. Advantages many people cite are that it is open-source, it doesn’t cost anything, it uses the general-purpose language (Python) rather than a sui generis programming language, and it is relatively easy to connect existing C and Fortran code to the Python interpreter.
A NumPy array is a multidimensional array of objects all of the same type. In memory, it is an object which points to a block of memory, keeps track of the type of data stored in that memory, keeps track of how many dimensions there are and how large each one is, and - importantly - the spacing between elements along each axis.
For example, you might have a NumPy array that represents the numbers from zero to nine, stored as 32-bit integers, one right after another, in a single block of memory. (for comparison, each Python integer needs to have some type information stored alongside it). You might also have the array of even numbers from zero to eight, stored in the same block of memory, but with a gap of four bytes (one 32-bit integer) between elements. This is called striding, and it means that you can often create a new array referring to a subset of the elements in an array without copying any data. Such subsets are called views. This is an efficiency gain, obviously, but it also allows modification of selected elements of an array in various ways.
An important constraint on NumPy arrays is that for a given axis, all the elements must be spaced by the same number of bytes in memory. NumPy cannot use double-indirection to access array elements, so indexing modes that would require this must produce copies. This constraint makes it possible for all the inner loops in NumPy’s internals to be written in efficient C code.
NumPy arrays offer a number of other possibilities, including using a memory-mapped disk file as the storage space for an array, and record arrays, where each element can have a custom, compound data type.
Python’s lists are efficient general-purpose containers. They support (fairly) efficient insertion, deletion, appending, and concatenation, and Python’s list comprehensions make them easy to construct and manipulate. However, they have certain limitations: they don’t support “vectorized” operations like elementwise addition and multiplication, and the fact that they can contain objects of differing types mean that Python must store type information for every element, and must execute type dispatching code when operating on each element. This also means that very few list operations can be carried out by efficient C loops – each iteration would require type checks and other Python API bookkeeping.
The short version is that Numeric was the original package that provided efficient homogeneous numeric arrays for Python, but some developers felt it lacked certain essential features, so they began developing an independent implementation called numarray. Having two incompatible implementations of array was clearly a disaster in the making, so NumPy was designed to be an improvement on both.
Neither Numeric nor numarray is currently supported. NumPy has been the standard array package for a number of years now. If you use Numeric or numarray, you should upgrade; NumPy is explicitly designed to have all the capabilities of both (and already boasts new features found in neither of its predecessor packages). There are tools available to ease the upgrade process; only C code should require much modification.
SciPy is a set of open source (BSD licensed) scientific and numerical tools for Python. It currently supports special functions, integration, ordinary differential equation (ODE) solvers, gradient optimization, parallel programming tools, an expression-to-C++ compiler for fast execution, and others. A good rule of thumb is that if it’s covered in a general textbook on numerical computing (for example, the well-known Numerical Recipes series), it’s probably implemented in scipy.
SciPy is freely available. It is distributed as open source software, meaning that you have complete access to the source code and can use it in any way allowed by its liberal BSD license.
SciPy’s license is free for both commercial and non-commercial use, the terms of the BSD license. (TODO: Link)
Actually, the time-critical loops are usually implemented in C or Fortran. Much of SciPy is a thin layer of code on top of the scientific routines that are freely available at http://www.netlib.org/. Netlib is a huge repository of incredibly valuable and robust scientific algorithms written in C and Fortran. It would be silly to rewrite these algorithms and would take years to debug them. SciPy uses a variety of methods to generate “wrappers” around these algorithms so that they can be used in Python. Some wrappers were generated by hand coding them in C. The rest were generated using either SWIG or f2py. Some of the newer contributions to SciPy are either written entirely or wrapped with Cython.
A second answer is that for difficult problems, a better algorithm can make a tremendous difference in the time it takes to solve a problem. So using scipy’s built-in algorithms may be much faster than a simple algorithm coded in C.
The SciPy development team works hard to make SciPy as reliable as possible, but, as in any software product, bugs do occur. If you find bugs that affect your software, please tell us by entering a ticket in the SciPy bug tracker, or NumPy bug tracker, as appropriate.
Drop us a mail on the mailing lists. We are keen for more people to help out writing code, unit tests, documentation (including translations into other languages), and helping out with the website.
In an ideal world, NumPy would contain nothing but the array data type and the most basic operations: indexing, sorting, reshaping, basic elementwise functions, et cetera. All numerical code would reside in SciPy. However, one of NumPy’s important goals is compatibility, so NumPy tries to retain all features supported by either of its predecessors. Thus NumPy contains some linear algebra functions, even though these more properly belong in SciPy. In any case, SciPy contains more fully-featured versions of the linear algebra modules, as well as many other numerical algorithms. If you are doing scientific computing with python, you should probably install both NumPy and SciPy. Most new features belong in SciPy rather than NumPy.
Plotting functionality is beyond the scope of NumPy and SciPy, which focus on numerical objects and algorithms. Several packages exist that integrate closely with NumPy to produce high quality plots, such as the immensely popular Matplotlib and the extensible, modular toolkit Chaco.
Like 2D plotting, 3D graphics is beyond the scope of NumPy and SciPy, but just as in the 2D case, packages exist that integrate with NumPy. Matplotlib provides basic 3D plotting in the mplot3d subpackage, whereas Mayavi provides a wide range of high-quality 3D visualization features, utilizing the powerful VTK engine.
One of the design goals of NumPy was to make it buildable without a Fortran compiler, and if you don’t have LAPACK available NumPy will use its own implementation. SciPy requires a Fortran compiler to be built, and heavily depends on wrapped Fortran code.
The linalg modules in NumPy and SciPy have some common functions but with different docstrings, and scipy.linalg contains functions not found in numpy.linalg, such as functions related to LU decomposition and the Schur decomposition, multiple ways of calculating the pseudoinverse, and matrix transcendentals like the matrix logarithm. Some functions that exist in both have augmented functionality in scipy.linalg; for example scipy.linalg.eig() can take a second matrix argument for solving generalized eigenvalue problems.
NumPy and SciPy support the Python 2.x series, beginning with version 2.4, as well as Python 3.1 and newer. The first release of NumPy to support Python 3 was NumPy 1.5.0. Python 3 support in SciPy starts with version 0.9.0.
No. Simply put, Jython runs on top of the Java Virtual Machine and has no way to interface with extensions written in C for the standard Python (CPython) interpreter.
Some users have reported success in using NumPy with Ironclad on 32-bit Windows. The current status of Ironclad support for SciPy is unknown, but there are several complicating factors (namely the Fortran compiler situation on Windows) that make it less feasible than NumPy.
If you are certain a variable is an array, then use the size attribute. If the variable may be a list or other sequence type, use len(). The size attribute is preferable to len because:
>>> a = numpy.zeros((1,0)) >>> a.size 0
>>> len(a) 1
Use numpy.loadtxt(). Even if your text file has header and footer lines or comments, loadtxt can almost certainly read it; it is convenient and efficient.
If you find this still too slow, you should consider changing to a more efficient file format than plain text. There are a large number of alternatives, depending on your needs (and on which version of NumPy/SciPy you are using):
- Text files: slow, huge, portable, human-readable; built into NumPy
- Raw binary: no metadata, totally unportable, fast; built into NumPy
- pickle: somewhat slow, somewhat portable (may be incompatible with different NumPy versions); built into NumPy
- MATLAB format: portable; built into SciPy (scipy.io.loadmat())
- HDF5: high-powered kitchen-sink format; both PyTables and h5py provide a NumPy friendly interface on top of the core HDF5 library written in C.
- FITS: standard kitchen-sink format in astronomy; pyfits provides a convenient python interface.
- .npy: NumPy native binary data format, simple, efficient, portable; built into NumPy as of 1.0.5.
NumPy’s basic data type is the multidimensional array. These can be one-dimensional (that is, one index, like a list or a vector), two-dimensional (two indices, like an image), three-dimensional, or more (zero-dimensional arrays exist and are a slightly strange corner case). They support various operations, including addition, subtraction, multiplication, exponentiation, and so on - but all of these are elementwise operations. If you want matrix multiplication between two two-dimensional arrays, the function numpy.dot() does this. It also works fine for getting the matrix product of a two-dimensional array and a one-dimensional array, in either direction, or two one-dimensional arrays. If you want some kind of matrix multiplication-like operation on higher-dimensional arrays (tensor contraction), you need to think which indices you want to be contracting over. Some combination of tensordot() and rollaxis() should do what you want.
However, some users find that they are doing so many matrix multiplications that always having to write dot as a prefix is too cumbersome, or they really want to keep row and column vectors separate. For these users, there is a matrix class. This is simply a transparent wrapper around arrays that forces arrays to be at least two-dimensional, and that overloads the multiplication and exponentiation operations. Multiplication becomes matrix multiplication, and exponentiation becomes matrix exponentiation. If you want elementwise multiplication, use numpy.multiply().
The function asmatrix() converts an array into a matrix (without ever copying any data); asarray() converts matrices to arrays. asanyarray() makes sure that the result is either a matrix or an array (but not, say, a list). Unfortunately, a few of NumPy’s many functions use asarray() when they should use asanyarray(), so from time to time you may find your matrices accidentally get converted into arrays. Just use asmatrix() on the output of these operations, and consider filing a bug.
Unfortunately Python does not allow extension modules to define new operators, and there is no operator we can overload for this purpose. This is however the subject of PEP 225, which (if accepted) would add several operators to the Python language. A summary of a discussion of PEP 225’s relative merits at SciPy 2008 can be found in this archived post to the Python-dev mailing list.
The prefered idiom for doing this is to use the function numpy.nonzero() , or the nonzero() method of an array. Given an array a, the condition a > 3 returns a boolean array and since False is interpreted as 0 in Python and NumPy, np.nonzero(a > 3) yields the indices of a where the condition is true.
>>> import numpy as np >>> a = np.array([[1,2,3],[4,5,6],[7,8,9]]) >>> a > 3 array([[False, False, False], [ True, True, True], [ True, True, True]], dtype=bool) >>> np.nonzero(a > 3) (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
The nonzero() method of the boolean array can also be called.
>>> (a > 3).nonzero() (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))
Use numpy.bincount(). The resulting array is
>>> arr = numpy.array([0, 5, 4, 0, 4, 4, 3, 0, 0, 5, 2, 1, 1, 9]) >>> numpy.bincount(arr)
The argument to bincount() must consist of positive integers or booleans. Negative integers are not supported.
nan, short for “not a number”, is a special floating point value defined by the IEEE-754 specification along with inf (infinity) and other values and behaviours. In theory, IEEE nan was specifically designed to address the problem of missing values, but the reality is that different platforms behave differently, making life more difficult. On some platforms, the presence of nan slows calculations 10-100 times. For integer data, no nan value exists. Some platforms, notably older Crays and VAX machines, don’t support nan whatsoever.
Despite all these issues NumPy (and SciPy) endeavor to support IEEE-754 behaviour (based on NumPy’s predecessor numarray). The most significant challenge is a lack of cross-platform support within Python itself. Because NumPy is written to take advantage of C99, which supports IEEE-754, it can side-step such issues internally, but users may still face problems when, for example, comparing values within Python interpreter. In fact, NumPy currently assumes IEEE-754 behavior of the underlying floats, a decision that may have to be revisited when the VAX community rises up in rebellion.
Those wishing to avoid potential headaches will be interested in an alternative solution which has a long history in NumPy’s predecessors – masked arrays. Masked arrays are standard arrays with a second “mask” array of the same shape to indicate whether the value is present or missing. Masked arrays are the domain of the numpy.ma module, and continue the cross-platform Numeric/numarray tradition. See “Cookbook/Matplotlib/Plotting values with masked arrays” (TODO) for example, to avoid plotting missing data in Matplotlib. Despite their additional memory requirement, masked arrays are faster than nans on many floating point units. See also the NumPy developer’s wiki page on masked arrays.
>>> A = numpy.zeros(3) >>> A[[0,1,1,2]] += 1 >>> A array([ 1., 1., 1.])
One might, quite reasonably, have expected A to contain [1,2,1]. Unfortunately this is not what is implemented in NumPy. More, the Python Reference Manual specifies that
>>> x = x + y
>>> x += y
should result in x having the same value (though not necessarily the same identity). More, even if the NumPy developers wanted to modify this behaviour, Python does not provide an overloadable __indexed_iadd__() function; the code acts like
>>> tmp = A.__getitem__([0,1,1,2]) >>> tmp.__iadd__(1) >>> A.__setitem__([0,1,1,2],tmp)
This leads to other peculiarities sometimes; if the indexing operation is actually able to provide a view rather than a copy, the __iadd__() writes to the array, then the view is copied into the array, so that the array is written to twice.