### What is NumPy?¶

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, for example, IDL or MATLAB.

### Why should I use NumPy rather than IDL, MATLAB, or Octave?¶

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 a general-purpose programming language (Python), which is very popular and has high-quality libraries for almost any task available, and it is relatively easy to connect existing C and Fortran code to the Python interpreter.

### What is a NumPy array?¶

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.

### What advantages do NumPy arrays offer over (nested) Python lists?¶

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.

### What’s the story behind Numeric, numarray, and NumPy?¶

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.

### What is SciPy?¶

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.

### How much does it cost?¶

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.

### What are SciPy’s licensing terms?¶

SciPy’s license is free for both commercial and non-commercial use, per the terms of the BSD license here.

### How can SciPy be fast if it is written in an interpreted language like Python?¶

Actually, the time-critical loops are usually implemented in C, C++, or Fortran. Parts of SciPy are thin layers 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.

### I’ve found a bug. What do I do?¶

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.

### How can I get involved in SciPy?¶

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.

### Is there commercial support available?¶

Yes, commercial support is offered for SciPy by a number of companies, for example Anaconda, Enthought, and Quansight.

## NumPy vs. SciPy vs. other packages¶

### What is the difference between NumPy and SciPy?¶

In an ideal world, NumPy would contain nothing but the array data type and the most basic operations: indexing, sorting, reshaping, basic elementwise functions, etc. 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 and Fourier transforms, 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.

### How do I make plots using NumPy/SciPy?¶

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 and Pandas to produce high quality plots, such as the immensely popular Matplotlib. Other popular options are Bokeh, Plotly, Altair, and Chaco.

### How do I make 3D plots/visualizations using NumPy/SciPy?¶

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.

### Why both `numpy.linalg` and `scipy.linalg`? What’s the difference?¶

`scipy.linalg` is a more complete wrapping of Fortran LAPACK using f2py.

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.

## Python version support¶

### Do NumPy and SciPytill support Python 2.7?¶

The last version of NumPy to support Python 2.7 is NumPy 1.16.x. The last SciPy version to do so is SciPy 1.2.x. The first release of NumPy to support Python 3.x was NumPy 1.5.0. Python 3 support in SciPy was introduced in SciPy 0.9.0.

### Does NumPy/SciPy work with PyPy?¶

In general, yes. Recent improvements in PyPy have made the scientific Python stack work with PyPy. The NumPy and SciPy projects run PyPy in continuous integration and aim to further improve support over time. Since much of NumPy and SciPy is implemented as C extension modules, the code may not run any faster (for most cases it’s significantly slower still, however, PyPy is actively working on improving this). As always when benchmarking, your experience is the best guide.

### Does NumPy/SciPy work with Jython or C#/.NET?¶

No, neither is supported. Jython never worked, because it 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 years ago, there was an effort to make NumPy and SciPy compatible with .NET. Some users at the time reported success in using NumPy with Ironclad on 32-bit Windows.

## Basic NumPy/SciPy usage¶

### What is the preferred way to check for an empty (zero-element) array?¶

If you are certain a variable is an array, then use the size attribute. If the variable is a list or other sequence type, use `len()`. The size attribute is preferable to len because:

```>>> a = numpy.zeros((1,0))
>>> a.size
0
```

whereas

```>>> len(a)
1
```

### I want to load data from a text file. How do I make this code more efficient?¶

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 can try pandas (it has a faster csv reader for example). If that doesn’t help, 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

• pickle: somewhat slow, somewhat portable (may be incompatible with different NumPy versions); built into NumPy

• 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; the astropy library provides a convenient Python interface through its io.fits package

• .npy: NumPy native binary data format, simple, efficient, portable; built into NumPy as of 1.0.5

### What is the difference between matrices and arrays?¶

Note: NumPy matrices will be deprecated, do not use them for new code. The rest of the answer below is kept for historical reasons.

NumPy’s basic data type is the multidimensional array. These can be 1-D (that is, one index, like a list or a vector), 2-D (two indices, like an image), 3-D, or more (0-D arrays exist and are slightly strange corner cases). 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 2-D arrays, the function `numpy.dot()` or the built-in Python operator `@` do this. It also works fine for getting the matrix product of a 2-D array and a 1-D array, in either direction, or two 1-D arrays. If you want some kind of matrix multiplication-like operation on higher-dimensional arrays (tensor contraction), you need to think over which indices you want to be contracting. 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 2-D, 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 getting converted into arrays. Just use `asmatrix()` on the output of these operations and consider filing a bug.

### Why not just have a separate operator for matrix multiplication?¶

From Python 3.5, the `@` symbol will be defined as a matrix multiplication operator, and NumPy and SciPy will make use of this. This addition was the subject of PEP 465. The separate matrix and array types exist to work around the lack of this operator in earlier versions of Python.

### How do I find the indices of an array where some condition is true?¶

The preferred 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]))
```

### How do I count the number of times each value appears in an array of integers?¶

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.

### Does NumPy support `nan`?¶

`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.

Despite all these issues NumPy (and SciPy) endeavor to support IEEE-754 behavior (based on NumPy’s predecessor numarray). The most significant challenge is the 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 the Python interpreter.

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 documentation on masked arrays.

Another good option is to use pandas - it uses `nan` in a similar way to NumPy for floating-point data, and since pandas 0.25.0 also supports missing integer values.

### Why doesn’t A[[0, 1, 1, 2]] += 1 do what I think it should?¶

This comes up from time to time on the mailing list. See here for one extensive discussion.

```>>> 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. Moreover, the Python Reference Manual specifies that

```>>> x = x + y
```

and

```>>> x += y
```

should result in `x` having the same value (though not necessarily the same identity). Moreover, even if the NumPy developers wanted to modify this behavior, Python does not provide an overloadable `__indexed_iadd__()` function; the code acts like

```>>> tmp = A.__getitem__([0,1,1,2])
>>> 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.

However, do not despair! NumPy does contain functionality for this type of behavior, and it can be obtained by using the ufunc `at()`, which is an attribute of the addition (`np.add`), subtraction (`np.subtract`), multiplication (`np.multiply`), and division (`np.divide`) ufuncs between a matrix and a scalar:

```>>> A = numpy.zeros(3)
>>> numpy.add.at(A, [0, 1, 1, 2], 1)
>>> A
array([ 1.,  2.,  1.])
```

## Where to get help¶

You can ask questions with the SciPy tag on StackOverflow, or on the scipy-user mailing list. Search for an answer first, because someone may already have found a solution to your problem, and using that will save everyone time.