15.6 Array Objects

Numeric provides an array type that represents a grid of items. An array object a has a specified number of dimensions, known as its rank, up to some arbitrarily high limit (normally 40, when Numeric is built with default options). A scalar (i.e., a single number) has rank 0, a vector has rank 1, a matrix has rank 2, and so forth.

15.6.1 Type Codes

The values that occupy cells in the grid of an array object, known as the elements of the array, are homogeneous, meaning they are all of the same type, and all element values are stored within one memory area. This contrasts with a list or tuple, where the items may be of different types and each is stored as a separate Python object. This means a Numeric array occupies far less memory than a Python list or tuple with the same number of items. The type of a's elements is encoded as a's type code, a one-character string, as shown in Table 15-3. Factory functions that build array instances, covered in Section 15.6.6 later in this chapter, take a typecode argument that is one of the values in Table 15-3.

Table 15-3. Type codes for Numeric arrays

Type code	C type	Python type	Synonym
'c'	char	str (length 1)	Character
'b'	unsigned char	int	UnsignedInt8
'1'	signed char	int	Int8
's'	short	int	Int16
'i'	int	int	Int32
'l'	long	int	Int
'f'	float	float	Float32
'F'	two floats	complex	Complex32
'd'	double	float	Float
'D'	two doubles	complex	Complex
'O'	PyObject*	any	PyObject

Numeric supplies readable attribute names for each type code, as shown in the last column of Table 15-3. Numeric also supplies, on all platforms, the names Int0, Float0, Float8, Float16, Float64, Complex0, Complex8, Complex16, and Complex64. In each case, the name refers to the smallest type of the requested kind with at least that many bits. For example, Float8 is the smallest floating-point type of at least 8 bits (generally the same as Float32, but some platforms may provide very small floating-point types), while Complex0 is the smallest complex type. On some platforms, but not all, Numeric also supplies the names Int64, Int128, Float128, and Complex128, with similar meanings. These names are not supplied on all platforms because not all platforms provide numbers with that many bits. The next release of Numeric will also support unsigned integer types.

A type code of 'O' indicates that elements are references to Python objects. In this case, elements can be of different types. This lets you use Numeric array objects as Python containers, for advanced array-processing tasks that may have nothing to do with numeric processing. When you build an array a with one of Numeric's factory functions, you can either specify a's type code explicitly or accept a default data-dependent type code.

To get the type code of an array a, call a.typecode( ). a's type code determines how many bytes each element of a takes up in memory. Call a.itemsize( ) to get this information. When the type code is 'O', the item size is small (e.g., 4 bytes on a 32-bit platform), but this size accounts only for the reference held in each of a's cells. The objects indicated by the references are stored elsewhere as separate Python objects; each such object may occupy an arbitrary amount of extra memory, which is not accounted for in the item size of an array with type code 'O'.

15.6.2 Shape and Indexing

Each array object a has an attribute a.shape, which is a tuple of integer values. len(a.shape) is a's rank, so for example, a one-dimensional array of numbers (also known as a vector) has rank 1, and a.shape has just one item. More generally, each item of a.shape is the length of the corresponding dimension of a. a's number of elements, known as its size, is the product of all items of a.shape. Each dimension of a is also known as an axis. Axis indices are from 0 up, as usual in Python. Negative axis indices are allowed and count from the right, so -1 is the last (rightmost) axis.

Each array a is a Python sequence. Each item a[i] of a is a subarray of a, meaning it is an array with a rank one less than a's:

a[i].shape=  =a.shape[1:]

For example, if a is a two-dimensional matrix (a is of rank 2), a[i], for any valid index i, is a one-dimensional subarray of a corresponding to a row of the matrix. When a's rank is 1 or 0, a's items are a's elements. Since a is a sequence, you can index a with normal indexing syntax to access or change a's items. Note that a's items are a's subarrays; only for an array of rank 1 or 0 are the array's items the same thing as the array's elements.

You can also use a in a for loop, as for any other sequence. For example:

for x in a:
    process(x)

means the same thing as:

for i in range(len(a)):
    x = a[i]
    process(x)

In these examples, each item x of a in the for loop is a subarray of a. For example, if a is a two-dimensional matrix, each x in either of these loops is a one-dimensional subarray of a corresponding to a row of the matrix.

You can also index a by a tuple. For example, if a's rank is at least 2, you can write a[i][j] as a[i,j] for any valid i and j, for rebinding as well as for access. Tuple indexing is faster and more convenient. You do not need to use parentheses inside the brackets in order to indicate that you are indexing a by a tuple: it suffices to write the indices one after the other, separated by commas. In other words, a[i,j] means the same thing as a[(i,j)], but the syntax without the parentheses is more natural and readable.

If the result of indexing is a single number, Numeric implicitly converts the result from a rank-zero array to a scalar quantity of the appropriate Python type. In other words, as a result of such an indexing you get a number, not an array with one number in it. While this makes it convenient to pass array elements to other non-Numeric software, it also has unfortunate consequences, and this behavior will change in numarray. With the present behavior, special-casing is required. For example:

a[i].shape=  =a.shape[1:]

does not execute correctly as Python code when a's rank is 1. In this case, a[i] is just a number, and numbers don't have a shape attribute. Thus, an AttributeError exception results.

15.6.3 Storage

An array object a is usually stored in a continuous memory area, with the elements one after the other in what is traditionally called row-major order. This means that, for example, when a's rank is 2, the elements of a's first row (a[0]) come first, immediately followed by those of a's second row (a[1]), and so on.

An array can be noncontiguous when it shares some of the storage of a larger array, as covered in the following section Section 15.6.4. For example, if a's rank is 2, the slice b=a[:,0] is the first column of a, and is stored noncontiguously because it occupies some of the same storage as a. In other words, b[0] occupies the same storage as a[0,0], while b[1] occupies the same storage as a[1,0], which cannot be adjacent to the memory occupied by a[0,0] when a has more than one column.

Numeric handles both contiguous and noncontiguous arrays transparently in most cases. In the rest of this chapter, I will point out the rare exceptions where a contiguous array is needed. When you want to copy a noncontiguous array b into a new contiguous array c, use method copy, covered in Section 15.6.7 later in this chapter.

15.6.4 Slicing

Arrays may share some or all of their data with other arrays. Numeric shares data between arrays whenever feasible. If you want Numeric to copy data, explicitly ask for a copy. Data sharing particularly applies to slices. For built-in Python lists and standard library array objects, slices are copies, but for Numeric array objects, slices share data with the array they're sliced from:

from Numeric import *
alist=range(10)
list_slice=alist[3:7]
list_slice[2]=22
print list_slice, alist       # prints: [3,4,22,6] [0,1,2,3,4,5,6,7,8,9]
anarray=array(alist)
arr_slice=anarray[3:7]
arr_slice[2]=33
print arr_slice, anarray      # prints: [ 3 4 33 6] [ 0 1 2 3 4 33 6 7 8 9]

Rebinding an item of list_slice does not affect the list alist that list_slice is sliced from, since for built-in lists, slicing performs a copy. However, because for Numeric arrays, slicing shares data, assigning to an item of arr_slice does affect the array object anarray that arr_slice is sliced from. This behavior may be unexpected for a beginner, but was chosen to enable high performance.

15.6.4.1 Slicing examples

You can use a tuple to slice an array, just as you can to index it. For arrays, slicing and indexing blend into each other. Each item in a slicing tuple can be an integer, and the slice has one fewer axis than the array being sliced. Slicing removes the axis for which you give a number by selecting the indicated plane of the array.

A slicing tuple item can also be a slice expression; the general syntax is start:stop:step, and you can omit one or more of the three parts (see Section 4.6 in Chapter 4, and function slice in Chapter 8, for details on slice semantics and defaults). Here are some example slicings:

# a is [[ 0, 1, 2, 3, 4, 5],
#       [10,11,12,13,14,15],
#       [20,21,22,23,24,25],
#       [30,31,32,33,34,35],
#       [40,41,42,43,44,45],
#       [50,51,52,53,54,55]]
a[0,2:4)                        # array([2,3])
a[3:,3:]                        # array([[33,34,35],
                                #        [43,44,45],
                                #        [53,54,55]])
a[:,4]                          # array([4,14,24,34,44,54])
a[2::2,::2]                     # array([[20,22,24],
                                #        [40,42,44]])

A slicing-tuple item can also use an ellipsis (...) to indicate that the following items in the slicing tuple apply to the last (rightmost) axes of the array you're slicing. For example, consider slicing an array b of rank 3:

b.shape                            # (4,2,3)
b[1].shape                         # (2,3)
b[...,1].shape                     # (4,2)

When we slice with b[1] (equivalent to indexing), we give an integer index for axis 0, and therefore we select a specific plane along b's axis 0. By selecting a specific plane, we remove that axis from the result's shape. Therefore, the result's shape is b.shape[1:]. When we slice with b[...,1], we select a specific plane along b's axis -1 (the rightmost axis of b). Again, by selecting a specific plane, we remove that axis from the result's shape. Therefore, the result's shape in this case is b.shape[:-1].

A slicing-tuple item can also be the pseudo-index NewAxis. The resulting slice has an additional axis at the point at which you use NewAxis, with a value of 1 in the corresponding item of the shape tuple. Continuing the previous example:

b[NewAxis,...,NewAxis].shape       # (1,4,2,3,1)

Here, rather than selecting and thus removing some of b's axes, we have added two new axes, one at the start of the shape and one at the end, thanks to the ellipsis.

Axis removal and addition can both occur in the same slicing. For example:

b[NewAxis,:,0,:,NewAxis].shape     # (1,4,3,1)

Here, we both add new axes at the start and end of the shape, and select a specific index from the middle axis (axis 1) of b by giving an index for that axis. Therefore, axis 1 of b is removed from the result's shape. The colons (:) used as the second and fourth items in the slicing tuple in this example are slice expressions with both start and stop omitted, meaning that all of the corresponding axis is included in the slice. In all these examples, all slices share some or all of b's data. Slicing affects only the shape of the resulting array. No data is copied, and no operations are performed on the data.

15.6.4.2 Assigning to array slices

Assignment to array slices is less flexible than assignment to list slices. Normally, you can assign to an array slice only another array of the same shape as the slice. However, if the right-hand side of the assignment is not an array, Numeric implicitly creates a temporary array from it. Each element of the right-hand side is coerced to the left-hand side's type. If the right-hand side array is not the same shape as the left-hand side slice, broadcasting applies, as covered in Section 15.6.8 later in this chapter. So, for example, you can assign a scalar (a single number) to any slice of a numeric array. In this case, the right-hand side number is coerced, then broadcast (replicated) as needed to make the assignment succeed.

When you assign to an array slice (or indexing) a right-hand side of a type different from that of the left-hand side, Numeric coerces the values to the left-hand side's type, for example by truncating floating-point numbers to integers. This does not apply if the right-hand side values are complex. Full coercion does not apply to in-place operators, which can only cast the right-hand side values upwards (for example, an integer right-hand side may be used for in-place operations with a floating-point left-hand side, but not vice versa), as covered in Section 15.6.8.2 later in this chapter.

15.6.5 Truth Values

Although an array object a is a Python sequence, in recent versions of Numeric a does not follow Python's normal rule for truth values of sequences, where bool(a) depends only on len(a) and not on a's elements (i.e., the rule by which any sequence is false only when empty, otherwise it is true). Rather, a is false when a has no elements or all of a's elements are numeric 0. This lets you test for element-wise equality of arrays in the natural way:

if a=  =b:

Without this proviso, such an if condition would be satisfied by any non-empty comparable arrays a and b.

Do remember, however, that you have to be explicit when you want to test whether a has any items or whether a has any elements, as these are two different conditions:

a = Numeric.array( [ [  ], [  ], [  ] ] )
if a: print 'a is true'
else: print 'a is false'                       # prints: a is false
if len(a): print 'a has some items'
else: print 'a has no items'                   # prints: a has some items
if Numeric.size(a): print 'a has some elements'
else: print 'a has no elements'                # prints: a has no elements

In most cases, the best way to compare arrays of numbers is for approximate equality with function allclose, covered later in this chapter.

15.6.6 Factory Functions

Numeric supplies numerous factory functions that create array objects.

array(data,typecode=None,copy=True,savespace=False)

Returns a new array object a. a's shape depends on data. When data is a number, a has rank 0 and a.shape is the empty tuple ( ). When data is a sequence of numbers, a has rank 1 and a.shape is the singleton tuple (len(data),). When data is a sequence of sequences of numbers, all of data's items must have the same length, a has rank 2, and a.shape is the pair (len(data),len(data[0])). This idea generalizes to any nesting level of data as a sequence of sequences, up to the arbitrarily high limit on rank mentioned earlier in this chapter. If data is nested over that limit, array raises TypeError. (This is unlikely to be a problem in practice, as an array of rank at least 40, with each axis of length at least 2, would have well over a million of millions of elements).

typecode can be any of the values shown in Table 15-2 or None. When typecode is None, array chooses a default type code depending on the types of the elements of data. When any one or more elements in data are long integer values or are neither numbers nor plain strings (e.g., None or Unicode strings), the type code is PyObject. When all elements are plain strings, the type code is Character. When any one or more elements (but not all) are plain strings, all others are numbers (not long integers), and typecode is None, array raises TypeError. You must explicitly pass 'O' or PyObject as argument typecode if you want to have array build an array from some plain strings and some non-long integers. When all elements are numbers (not long integers), the default type code depends on the widest numeric type among the elements. When any of the elements is a complex, the type code is Complex. When no elements are complex but some are floating-point values, the type code is Float. When all elements are integers, the type code is Int.

Function array, by default, returns an array object a that doesn't share data with others. If data is an array object, and you explicitly pass a false value for argument copy, array returns an array object a that shares data with data, if feasible.

By default, an array object with a numeric type code is implicitly cast up when operated with numbers of wider numeric types. When you do not need this implicit casting, you can save some memory by explicitly passing a true value for argument savespace to the array factory function, to set the resulting array object a into space-saving mode. For example:

array(range(4),typecode='b')+2.0    # array([2.,3.,4.,5.])
array(range(4),typecode='b',savespace=True)+2.0     
# array([2,3,4,5])
array(range(4),typecode='b',savespace=True)+258.7   
# array([2,3,4,5])

The first statement creates an array of floating-point values, as savespace is not specified and thus each element is implicitly cast up to a float when added to 2.0. The second and third statements create arrays of 8-bit integers, since savespace is specified. Therefore, instead of implicit casting up of the array's element, we get implicit casting down of the float added to each element. 258.7 is cast down to 2: the fractional part .7 is lost because of the cast to an integer, and the resulting 258 becomes 2 because, since the cast is to 8-bit integers, only the lowest 8 bits are kept. The savespace mode can be very useful for large arrays, but be careful lest you suffer unexpected loss of precision when using it.

arrayrange([start,]stop[,step=1],typecode=None)

Like array(range(start,stop,step),typecode), but faster. See built-in function range, covered in Chapter 8, for details about start, stop, and step. arrayrange allows float values for these arguments, not just int values. Be careful when exploiting this feature, since the approximations inherent in floating-point arithmetic may lead to a result with one more or fewer items than you might expect. arange is a synonym of arrayrange.

fromstring(data,count=None,typecode=Int)

Returns a one-dimensional array a of shape (count,) with data copied from the bytes of string data. When count is None, len(data) must be a multiple of typecode's item size, and a's shape is (len(data)/a.itemsize( ),). When count is not None, len(data) must be greater than or equal to count*a.itemsize( ), and fromstring ignores data's trailing bytes, if any.

Together with methods a.tostring and a.byteswapped (covered in the following section Section 15.6.7), function fromstring allows binary input/output of array objects. When you need to save arrays and later reload them, and don't need to use the saved form in non-Python programs, it's simpler and faster to use module cPickle, covered in Chapter 11. Many experienced users prefer to use a portable self-describing file format such as netCDF (see http://met-www.cit.cornell.edu/noon/ncmodule.html).

identity(n,typecode=Int)

Returns a two-dimensional array a of shape (n,n). a's elements are 0, except those on the main diagonal (a[j,j] for j in range(n)), which are 1.

ones(shapetuple,typecode=Int,savespace=False)

Returns an array a such that a.shape= =shapetuple. All of a's elements are 1.

zeros(shapetuple,typecode=Int,savespace=False)

Returns an array a such that a.shape= =shapetuple. All of a's elements are 0.

Note that, by default, identity, ones, and zeros all return arrays whose type is Int. Be sure to specify explicitly a different type code, such as Float, if that is what you really want. For example, be sure to avoid the following common mistake:

a = zeros(3)
a[0] = 0.3                    # a is array([0,0,0])

Since a is Int in this snippet, the 0.3 we assign to one of its items gets truncated to the integer 0. Instead, you typically want something closer to the following:

a = zeros(3,Float)
a[0] = 0.3                    # a is array([0.3,0.,0.])

Here, we have explicitly specified Float as the type code for a, and therefore no truncation occurs when we assign 0.3 to one of a's items.

15.6.7 Attributes and Methods

For most array manipulations, Numeric supplies functions you can call with array arguments. You can also use Python lists as arguments; this polymorphism offers flexibility that is not available for functionality packaged up as array attributes and methods. Each array object a also supplies some methods and attributes, for direct access to functionality that would not benefit from polymorphic possibilities.

a.astype(typecode)

Returns a new array b with the same shape as a. b's elements are a's elements coerced to the type indicated by typecode. b does not share a's data, even if typecode equals a.typecode( ).

a.byteswapped(  )

Returns a new array object b with the same type code and shape as a. Each element of b is copied from the corresponding element of a, inverting the order of the bytes in the value. This swapping transforms each value from little-endian to big-endian or vice versa. Together with function fromstring and method a.tostring, this helps when you have binary data from one kind of machine and need them for the other kind (for example, Intel platforms are little-endian, while Sun platforms are big-endian).

a.copy(  )

Returns a new contiguous array object b, identical to a, but not sharing a's data.

a .flat is an attribute that contains an array with rank of one less than a and of the same size as a, sharing a's data. Indexing or slicing a.flat lets you access or change a's elements through this alternate view of a. Trying to access a.flat raises a TypeError exception if a is noncontiguous. When a is contiguous, a.flat is in row-major order. This means that, for example, when a's shape is (7,4) (i.e., a is a two-dimensional matrix with seven rows and four columns), a.flat[i] is the same as a[divmod(i,4)] for all i in range(28).

Trying to access the a.real and a.imag attributes raises a TypeError exception unless a's type code is complex. When a's type code is complex, each of a.real and a.imag is a noncontiguous array with the same shape as a and a float type code, sharing data with a. By accessing or modifying a.real or a.imag, you access or modify the real or imaginary parts of a's complex-number elements. imaginary is a synonym of imag.

a.iscontiguous(  )

Returns True if a's data occupies contiguous storage, otherwise False. This matters particularly when interfacing to C-coded extensions. a.copy( ) makes a contiguous copy of a. Noncontiguous arrays arise when slicing or transposing arrays, as well as for attributes a.real and a.imag of an array a with a complex type code.

a.itemsize(  )

Returns the number of bytes of memory used by each of a's elements (not by each of a's items, which are subarrays of a).

a.savespace(flag=True)

Sets or resets the space-saving mode of array a, depending on the truth value of flag. When flag is true, a.savespace(flag) sets a's space-saving mode so that a's elements are not implicitly cast up when operated with arrays of wider numeric types. For more details on this, see the discussion of savespace for function array earlier in this chapter. When flag is false, a.savespace(flag) resets a's space-saving mode so that a's elements are implicitly cast up when needed.

The a.shape attribute is a tuple with one item per axis of a, giving the length of that axis. You can assign a sequence of integers to a.shape to change the shape of a, but a's size (the total number of elements) must remain the same. When you assign to a.shape another sequence s, one of s's items can be -1, meaning that the length along that axis is whatever is needed to keep a's size unchanged. However, the product of the other items of s must evenly divide a's size, or else the reshaping raises an exception. When you need to change the total number of elements in a, call function resize (covered in Section 15.6.9 later in this chapter).

a.spacesaver(  )

Returns True if space-saving mode is on for array a, otherwise False. See the discussion of savespace for function array earlier in this chapter.

a.tolist(  )

Returns a list L equivalent to a. For example, if a.shape is (2,3) and a's type code is 'd', L is a list of two lists of three float values each. In other words, for each valid i and j, L[i][j]= =a[i,j]. Note that list(a) converts only the top-level (axis 0) of array a into a list, and thus is not equivalent to a.tolist( ) if a's rank is 2 or more. For example:

a=array([[1,2,3],[4,5,6]],typecode='d')
print a.shape             # prints: (2,3)
print a                   # prints: [[1. 2. 3.]
                          #          [4. 5. 6.]]
print list(a)             
# prints: [array([1.,2.,3.]), array([4.,5.,6.])]
print a.tolist(  )          
# prints: [[1.0,2.0,3.0],[4.0,5.0,6.0]]

a.tostring(  )

Returns a binary string s whose bytes are a copy of the bytes of a's elements.

a.typecode(  )

Returns the type code of a as a one-character string.

15.6.8 Operations on Arrays

Arithmetic operators +, -, *, /, %, and **, comparison operators >, >=, <, <=, = =, and !=, and bitwise operators &, |, ^, and ~ (all covered in Chapter 4) also apply to arrays. If both operands a and b are arrays with equal shapes and type codes, the result is a new array c with the same shape and type code. Each element of c is the result of the operator on corresponding elements of a and b (element-wise operation).

Arrays do not follow sequence semantics for * (replication) and + (concatenation), but rather use * and + for element-wise arithmetic. Similarly, * does not mean matrix multiplication, but element-wise multiplication. Numeric supplies functions to perform replication, concatenation, and matrix multiplication; all operators on arrays perform element-wise operations.

When the type codes of a and b differ, the narrower numeric type is converted to the wider one, like for other Python numeric operations. As usual, operations between numeric and non-numeric values are disallowed. In the case of arrays, you can inhibit casting up by setting an array into space-saving mode with method savespace. Use space-saving mode with care, since it can result in silent loss of significant data. For more details on this, see the discussion of savespace for function array earlier in this chapter.

15.6.8.1 Broadcasting

Element-wise operations between arrays of different shapes are generally not possible: attempting such operations raises an exception. Numeric allows some such operations by broadcasting (replicating) a smaller array up to the shape of the larger one when feasible. To make broadcasting efficient, the replication is only conceptual: Numeric does not need to physically copy the data being broadcast (i.e., you need not worry that performance will be degraded because an operation involves broadcasting).

The simplest case of broadcasting is when one operand, a, is a scalar (an array of rank 0), while b, the other operand, is an array. In this case, Numeric conceptually builds a temporary array t, with shape b.shape, where each element of t equals a. Numeric then performs the requested operation between t and b. In practice, therefore, when you operate an array b with a scalar a, as in a+b or b+a, the resulting array has the same shape as b, and each element is the result of applying the operator to the corresponding element of b and the single number a.

More generally, broadcasting can also apply when both operands a and b are arrays. Conceptually, broadcasting works according to rather complicated general rules:

Broadcasting's rules are complicated because of their generality, but most typical applications of broadcasting are in simple cases. For example, say we compute a+b, and a.shape is (5,3) (a matrix of five rows, three columns). Further, say typical values for b.shape include ( ) (a scalar), (3,) (a one-dimensional vector with three elements), and (5,1) (a matrix with five rows, one column). In each of these cases, b is broadcast up to a temporary array t with shape (5,3) by replicating b's elements along the needed axis (both axes, when b is a scalar), and Numeric computes a+t. The simplest and most frequent case, of course, is when b.shape is (5,3), the same shape as a's. In this case, no broadcasting is needed.

15.6.8.2 In-place operations

Arrays support in-place operations through augmented assignment operators +=, -=, and so on. The left-hand side array or slice cannot be broadcast, but the right-hand side can be. Similarly, the left-hand side cannot be cast up, but the right-hand side can be. In other words, in-place operations treat the left-hand side as rigid in both shape and type, but the right-hand side is subject to the normal, more lenient rules.

15.6.9 Functions

Numeric defines several functions that operate on arrays, or polymorphically on Python sequences, conceptually forming temporary arrays from non-array operands.

allclose(x,y,rtol=1.e-5,atol=1.e-8)

Returns True when every element of x is close to the corresponding element of y, otherwise False. Two elements ex and ey are defined to be close if:

abs(ex-ey)<atol+rtol*abs(ey)

In other words, ex and ey are close if both are tiny (less than atol) or if the relative difference is small (less than rtol). allclose is generally a better way to check array equality than = =, since floating-point arithmetic requires some comparison tolerance. However, allclose is not applicable to complex arrays, only to floating-point and integer arrays. To compare two complex arrays x and y for approximate equality, you can use:

allclose(x.real, y.real) and allclose(x.imag, y.imag)

argmax(a,axis=-1)
argmin(a,axis=-1)

argmax returns a new integer array m whose shape tuple is a.shape minus the indicated axis. Each element of m is the index of a maximal element of a along axis. argmin is similar, but indicates minimal elements rather than maximal ones.

argsort(a,axis=-1)

Returns a new integer array m with the same shape as a. Each vector of m along axis is the index sequence needed to sort the corresponding axis of a. In particular, if a has rank 1, the most common case, take(a,argsort(a))= =sort(a). For example:

x = [52, 115, 99, 111, 114, 101, 97, 110, 100, 55]
print Numeric.argsort(x)   # prints: [0 9 6 2 8 5 7 3 4 1]
print Numeric.sort(x)      
# prints: [52 55 97 99 100 101 110 111 114 115]
print Numeric.take(x, Numeric.argsort(x))
# prints: [52 55 97 99 100 101 110 111 114 115]

Here, the result of Numeric.argsort(x) tells us that x's smallest element is x[0], the second smallest is x[9], the third smallest is x[6], and so on. The call to Numeric.take in the last print statement takes x's elements exactly in this order, and therefore produces the same sorted array as the call to Numeric.sort in the second print statement.

array2string(a,max_line_width=None,precision=None,
             suppress_small=None,separator=' ',
            array_output=False)

Returns a string representation s of array a, showing elements within brackets, separated by string separator. The last dimension is horizontal, the penultimate one vertical, and further dimensions are denoted by bracket nesting. If array_output is true, s starts with 'array(' and ends with ')'. s ends with ",'X')" instead if X, which is a's type code, is not Float, Complex, or Int, which lets you later use eval(s) if separator is ','.

Lines longer than max_line_width (by default, 77) are broken up. precision determines how many digits are used per element (by default, 8). If suppress_small is true, very small numbers are shown as 0. You can change these defaults by binding attributes of module sys named output_line_width, float_output_precision, and float_output_suppress_small.

str(a) is like array2string(a). repr(a) is like array2string(a,separator=', ',array_output=True).

average(a,axis=0,weights=None,returned=False)

Returns a's average along axis. When axis is None, returns the average of all a's elements. When weights is not None, weights must be an array with a's shape, or a one-dimensional array with the length of a's given axis, and average computes a weighted average. When returned is true, returns a pair: the first item is the average, the second item is the sum of weights (the count of values, when weights is None).

choose(a,values)

Returns an array c with the same shape as a. values is a sequence. a's elements are integers between 0, included, and len(values), excluded. Each element of c is the item of values whose index is the corresponding element of a. For example:

print Numeric.choose(Numeric.identity(3),'ox')   
# prints: [[x o o]
#          [o x o]
#          [o o x]]

clip(m,min,max)

Returns an array c with the same type code and shape as a. Each element ec of c is the corresponding element ea of a, where min<=ea<=max. Where ea<min, ec is min; where ea>max, ec is max. For example:

print Numeric.clip(Numeric.arange(10),2,7)  
# prints: [2 2 2 3 4 5 6 7 7 7]

compress(condition,a,axis=0)

Returns an array c with the same type code and rank as a. c includes only the elements of a for which the item of condition, corresponding along the given axis, is true. For example, compress((1,0,1),a) = = take(a,(0,2),0) since (1,0,1) has true values only at indices 0 and 2. Here's how to get only the even numbers from an array:

a = Numeric.arange(10)
print Numeric.compress(a%2=  =0, a)   # prints: [0 2 4 6 8]

concatenate(arrays, axis=0)

arrays is a sequence of arrays, all with the same shape except possibly along the given axis. concatenate returns an array that is the concatenation of the arrays along the given axis. In particular, concatenate((s,)*n) has the same sequence replication semantics that s*n would have if s were a generic Python sequence rather than an array. For example:

print Numeric.concatenate([Numeric.arange(5),
                           Numeric.arange(3)])
# prints: [0 1 2 3 4 0 1 2]

convolve(a,b,mode=2)

Returns an array c with rank 1, the linear convolution of rank 1 arrays a and b. Linear convolution is defined over unbounded sequences. convolve conceptually extends a and b to infinite length by padding with 0, then clips the infinite-length result to its central part, yielding c. When mode is 2, the default, convolve clips only the padding, so c's shape is (len(a)+len(b)-1,). Otherwise, convolve clips more. Say len(a) is greater than or equal to len(b): when mode is 0, len(c) is len(a)-len(b)+1; when mode is 1, len(c) is len(a). When len(a) is less than len(b), the effect is symmetrical. For example:

a = Numeric.arange(6)
b = Numeric.arange(4)
print Numeric.convolve(a, b)          
# prints: [0 0 1 4 10 16 22 22 15]
print Numeric.convolve(a, b, 1)       
# prints: [0 1 4 10 16 22]
print Numeric.convolve(a, b, 0)       # prints: [4 10 16]

cross_correlate(a,b,mode=0)

Like convolve(a,b[::-1],mode).

diagonal(a,k=0,axis1=0,axis2=1)

Returns the elements of a whose index along axis1 and index along axis2 differ by k. When a has rank 2, this means the main diagonal when k equals 0, subdiagonals above the main one when k is greater than 0, and subdiagonals below the main one when k is less than 0. For example:

# a is [[0 1 2 3]
#       [4 5 6 7]
#       [8 9 10 11]
#       [12 13 14 15]]
print Numeric.diagonal(a)        # prints: [0 5 10 15]
print Numeric.diagonal(a,1)      # prints: [1 6 11]
print Numeric.diagonal(a,-1)     # prints: [4 9 14]

As shown, diagonal(a) is the main diagonal, diagonal(a,1) the subdiagonal just above the main one, and diagonal(a,-1) the subdiagonal just below the main one.

indices(shapetuple,typecode=None)

Returns an integer array x of shape (len(shapetuple),)+shapetuple. Each element of subarray x[i] is equal to the element's i index in the subarray. For example:

print Numeric.indices((2,4))     # prints: [[[0 0 0 0]
                                 #           [1 1 1 1]]
                                 #          [[0 1 2 3]
                                 #           [0 1 2 3]]]

innerproduct(a,b)

Returns an array m with the result of the inner product of a and b, like matrixmultiply(a,transpose(b)). a.shape[-1] must equal b.shape[-1], and m.shape is the tuple a.shape[:-1]+b.shape[0:-1:-1].

matrixmultiply(a,b)

Returns an array m with a times b in the matrix-multiplication sense, rather than element-wise multiplication. a.shape[-1] must equal b.shape[0], and m.shape is the tuple a.shape[:-1]+b.shape[1:].

nonzero(a)

Returns the indices of those elements of a that are not equal to 0, like the expression:

array([i for i in range(len(a)) if a[i] != 0])

a must be a sequence or one-dimensional array.

put(a,indices,values)

a must be a contiguous array. indices is a sequence of integers, taken as indices into a.flat. values is a sequence of values that can be converted to a's type code (if shorter than indices, values is repeated as needed). Each element of a indicated by an item in indices is replaced by the corresponding item in values. put is therefore similar to (but faster than) the loop:

for i,v in zip(indices,values*len(indices)):
    a.flat[i]=v

putmask(a,mask,values)

a must be a contiguous array. mask is a sequence with the same length as a.flat. values is a sequence of values that can be converted to a's type code (if shorter than mask, values is repeated as needed). Each element of a corresponding to a true item in mask is replaced by the corresponding item in values. putmask is therefore similar to (but faster than) the loop:

for i,v in zip(xrange(len(mask)),values*len(mask)):
    if mask[i]: a.flat[i]=v

rank(a)

Returns the rank of a, just like len(array(a,copy=False).shape).

ravel(a)

Returns the flat form of a, just like array(a,copy=False).flat.

repeat(a,repeat,axis=0)

Returns an array with the same type code and rank as a, where each of a's elements is repeated along axis as many times as the value of the corresponding element of repeat. repeat is an integer, or an integer sequence of length a.shape[axis].

reshape(a,shapetuple)

Returns an array r with shape shapetuple, sharing a's data. r=reshape(a,shapetuple) is just like r=a;r.shape=shapetuple. The product of shapetuple's items must equal the product of a.shape's, but one of shapetuple's items may be -1 to ask for adaptation of that axis's length. For example:

print Numeric.reshape(range(12),(3,-1))     
# prints: [[0 1 2 3]
#          [4 5 6 7]
#          [8 9 10 11]]

resize(a,shapetuple)

Returns an array r with shape shapetuple and data copied from a. If r's size is smaller than a's size, r.flat is copied from the start of ravel(a); if r's size is larger, the data in ravel(a) is replicated as many times as needed. In particular, resize(s,(n*len(s),)) has the sequence replication semantics that s*n would have if s were a generic Python sequence rather than an array. For example:

print Numeric.resize(range(5),(3,4))        
# prints: [[0 1 2 3]
#          [4 0 1 2]
#          [3 4 0 1]]

searchsorted(a,values)

a must be a sorted rank 1 array. searchsorted returns an array of integers s with the same shape as values. Each element of s is the index in a where the corresponding element of values would fit in the sorted order of a. For example:

print Numeric.searchsorted([0,1],
    [0.2,-0.3,0.5,1.3,1.0,0.0,0.3])
# prints: [1 0 1 2 1 0 1]

This specific idiom returns an array with 0 in correspondence to each element x of values when x is less than or equal to 0; 1 when x is greater than 0 and less than or equal to 1; and 2 when x is greater than 1. With slight generalization, and with appropriate thresholds as the elements of sorted array a, this idiom allows very fast classification of what subrange each element x of values falls into.

shape(a)

Returns the shape of a, just like array(a,copy=False).shape.

size(a,axis=None)

When axis is None, returns the total number of elements in a. Otherwise, returns the number of elements of a along axis, like array(a,copy=False).shape[axis].

sort(a,axis=-1)

Returns an array s with the same type code and shape as a, with elements along each plane of the given axis reordered so that the plane is sorted in increasing order. For example:

# x is [[0 1 2 3]
#       [4 0 1 2]
#       [3 4 0 1]]
print Numeric.sort(x)       # prints: [[0 1 2 3]
                            #          [0 1 2 4]
                            #          [0 1 3 4]]
print Numeric.sort(x,0)     # prints: [[0 0 0 1]
                            #          [3 1 1 2]
                            #          [4 4 2 3]]

sort(x) returns a result where each row is sorted. sort(x,0) returns a result where each column is sorted.

swapaxes(a,axis1,axis2)

Returns an array s with the same type code, rank, and size as a, sharing a's data. s's shape is the same as a, but with the lengths of axes axis1 and axis2 swapped. In other words, s=swapaxes(a,axis1,axis2) is like:

swapped_shape=range(length(a.shape))
swapped_shape[axis1]=axis2
swapped_shape[axis2]=axis1
s=transpose(a,swapped_shape)

take(a,indices,axis=0)

Returns an array t with the same type code and rank as a, containing the subset of a's elements that would be in a slice along axis comprising the given indices. For example, after t=take(a,(1,3)), t.shape= =(2,)+a.shape[1:], and t's elements are those in the second and fourth rows of a.

trace(a,k=0)

Returns the sum of a's elements along the k diagonal, like sum(diagonal(a,k)).

transpose(a,axes=None)

Returns an array t, with the same type code, rank, and size as a, sharing a's data. t's axes are permuted with respect to a's by the axis indices in sequence axes. When axes is None, t's axes invert the order of a's, as if axes were a.shape[::-1].

where(condition,x,y)

Returns an array w with the same shape as condition. Where an element of condition is true, the corresponding element of w is the corresponding element of x; otherwise it is the corresponding element of y. For example, clip(a,min,max) is the same as where(greater(a,max),max,where(greater(a,min),a,min)).