# Arrays¶

Numba has support for fast indexing and understands NumPy arrays and infers types for various calls of the NumPy API.

Limitations:

Unfortunately, there are a few pitfalls. We hope to resolve these in the future, and to document them in the meantime:

Operation Example
Boundschecking array[N], with N < 0 or N > array.shape[0]
Wraparound array[-1]

## Array Expressions¶

Numba implements array expressions which provide a single pass over the data with a fused expression. It also implements native slicing and stack-allocated NumPy array views, which means slicing is very fast compared to slicing in Python. It also means one can now slice an array in a nopython context. Lets try a diffusion in numba with loops and with array expressions:

from numba import *
import numpy as np

mu = 0.1
Lx, Ly = 101, 101
N = 1000

@autojit
def diffuse_loops(iter_num):
u = np.zeros((Lx, Ly), dtype=np.float64)
temp_u = np.zeros_like(u)
temp_u[Lx / 2, Ly / 2] = 1000.0

for n in range(iter_num):
for i in range(1, Lx - 1):
for j in range(1, Ly - 1):
u[i, j] = mu * (temp_u[i + 1, j] + temp_u[i - 1, j] +
temp_u[i, j + 1] + temp_u[i, j - 1] -
4 * temp_u[i, j])

temp = u
u = temp_u
temp_u = temp

return u

@autojit
def diffuse_array_expressions(iter_num):
u = np.zeros((Lx, Ly), dtype=np.float64)
temp_u = np.zeros_like(u)
temp_u[Lx / 2, Ly / 2] = 1000.0

for i in range(iter_num):
u[1:-1, 1:-1] = mu * (temp_u[2:, 1:-1] + temp_u[:-2, 1:-1] +
temp_u[1:-1, 2:] + temp_u[1:-1, :-2] -
4 * temp_u[1:-1, 1:-1])

temp = u
u = temp_u
temp_u = temp

return u


Note

Correct handling of overlapping memory between the left-hand and right-hand side of expressions is not supported yet.

Array expressions also support broadcasting, raising an error if shapes do not match:

@autojit
def matrix_vector(M, v):
return np.sum(M * v, axis=1)

M = np.arange(90).reshape(9, 10)
v = np.arange(10)
print matrix_vector(M, v)
print np.dot(M, v)


Prints:

[ 285  735 1185 1635 2085 2535 2985 3435 3885]
[ 285  735 1185 1635 2085 2535 2985 3435 3885]

Calling the function with incompatible shapes gives the following:

In [0]: matrix_vector(M, np.arange(8))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
...
ValueError: Shape mismatch while broadcasting

Note

Errors raised in a nopython context print an error message and abort the program.

### New Arrays¶

Expressions not containing a left-hand side automatically create a new array:

@autojit
def square(a):
return a * a

print square(np.arange(10)) # array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])


Allocating new arrays is however not support yet in nopython mode:

@autojit(nopython=True)
def square(a):
return a * a

print square(np.arange(10)) # NumbaError: 1:0: Cannot allocate new memory in nopython context


### Math¶

All NumPy math functions supported on scalars is also supported for arrays. This includes most unary ufuncs:

@autojit
def tan(a):
return np.sin(a) / np.cos(a)


## Universal Functions (ufuncs)¶

Numba’s vectorize allows Numba functions taking scalar input arguments to be used as NumPy ufuncs (see http://docs.scipy.org/doc/numpy/reference/ufuncs.html).

For the example codes we will assume the user has run the following import:

from numba.vectorize import Vectorize, vectorize


### ufunc Definition¶

Ufunc arguments are scalars of a NumPy array. Function definitions can be arbitrary mathematical expressions.

def my_ufunc(a, b):
return a+b+sqrt(a*cos(b))


Compilation requires type information. Numba assumes no knowledge of type when building native ufuncs. We must therefore define argument and return dtypes for the defined ufunc. We can add many and various dtypes for a given BasicVectorize ufuncs, using Numba types, to create different versions of the code depending on the inputs.

v = Vectorize(my_ufunc)


Above we are using signed and unsigned 32-bit ints, a float f4, and a double f8.

To compile our ufunc we issue the following command

basic_ufunc = v.build_ufunc()


bv.build_ufunc() returns a python callable list of functions which are compiled by Numba. This work is normally accomplished by PyUFunc_FromFuncAndData and Numba takes care of it.* We’ve now registered a set of overload functions ready be used as NumPy ufuncs.

Lastly, we call basic_ufunc with two NumPy array as arguments

data = np.array(np.random.random(100))
result = basic_ufunc(data, data)


Since we defined a binary ufunc, we can use the various ufunc methods such as reduce, accumulate, etc:

data = np.array(np.arange(100), dtype=np.int32)
print basic_ufunc.reduce(data)
print basic_ufunc.accumulate(data)


### Building ufuncs using @vectorize¶

An alternative syntax is available through the use of the vectorize decorator:

from numba import *
import math

pi = math.pi

@vectorize([f4(f4), f8(f8)], target='cpu')
def sinc(x):
if x == 0.0:
return 1.0
else:
return math.sin(x*pi)/(pi*x)


The vectorize decorator takes a list of function signature and an optional target keyword argument (default to ‘cpu’). The example above generate a sinc ufunc that is overloaded to accept float and double. This syntax replaces calls to Vectorize.add and Vectorize.build_ufunc.

## Generalized Ufuncs¶

The numba.vectorize module also provides support for generalized ufuncs. Traditional ufuncs perfom element-wise operations, whereas generalized ufuncs operate on entire sub-arrays. Unlike other Numba Vectorize classes, the GUVectorize constructor takes an additional signature which specifies the shapes of the inner arrays we want to operate on.

### Imports¶

from numba import float32, float64, int32
from numba.vectorize import GUVectorize
import numpy as np


### Generalized ufunc Definition¶

GUVectorize ufunc arguments are vectors of a NumPy array. Function definitions can be arbitrary expressions.

def matmulcore(A, B, C):
m, n = A.shape
n, p = B.shape
for i in range(m):
for j in range(p):
C[i, j] = 0
for k in range(n):
C[i, j] += A[i, k] * B[k, j]


Compilation requires type information. Numba assumes no knowledge of type when building native ufuncs. We must therefore define argument and return dtypes for the defined ufunc. We can add as many dtypes as we need, which do not need to be uniform, i.e. we can specify a gufunc taking an array of ints and an array of doubles while producing an array of complex numbers. The gufunc will dispatch to the right implementation depending on the argument types.

We can define our gufunc as follows:

gufunc = GUVectorize(matmulcore, '(m,n),(n,p)->(m,p)')


Above we are using a float float32, a double float64, and a signed 32-bit int. The GUVectorize calls PyDynUFunc_FromFuncAndDataAndSignature which requires a the signature: (m,n),(n,p)->(m,p) in the constructor. This signature defines the “core dimensions” of the generalized ufunc.

We can compile the ufunc as follows:

gufunc = gufunc.build_ufunc()


We can now use the gufunc with two NumPy matrices:

matrix_ct = 10
A = np.arange(matrix_ct * 2 * 4, dtype=np.float32).reshape(matrix_ct, 2, 4)
B = np.arange(matrix_ct * 4 * 5, dtype=np.float32).reshape(matrix_ct, 4, 5)
C = gufunc(A, B)


Notice that we don’t have a third argument in the gufunc call but the generalized ufunc definition above has three arguments. The last argument of the generalized ufunc is the output, which is automatically allocated with the shape specified in the signature.