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5.1 Multicomponent and complex arrays Multicomponent Array's 5.2 Creating arrays of a user type Array's of your own type
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Multicomponent arrays have elements which are vectors. Examples of such arrays are vector fields, colour images (which contain, say, RGB tuples), and multispectral images. Complex-valued arrays can also be regarded as multicomponent arrays, since each element is a 2-tuple of real values.
Here are some examples of multicomponent arrays:
// A 3-dimensional array; each element is a length 3 vector of float Array<TinyVector<float,3>,3> A; // A complex 2-dimensional array Array<complex<double>,2> B; // A 2-dimensional image containing RGB tuples struct RGB24 { unsigned char r, g, b; }; Array<RGB24,2> C; |
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Blitz++ provides some special support for such arrays. The most important is the ability to extract a single component. For example:
Array<TinyVector<float,3>,2> A(128,128); Array<float,2> B = A.extractComponent(float(), 1, 3); B = 0; |
The call to extractComponent
returns an array of floats; this array
is a view of the second component of each element of A. The arguments of
extractComponent
are: (1) the type of the component (in this example,
float); (2) the component number to extract (numbered 0, 1, ... N-1); and
(3) the number of components in the array.
This is a little bit messy, so Blitz++ provides a handy shortcut using
operator[]
:
Array<TinyVector<float,3>,2> A(128,128); A[1] = 0; |
The number inside the square brackets is the component number. However, for
this operation to work, Blitz++ has to already know how many components
there are, and what type they are. It knows this already for
TinyVector
and complex<T>
. If you use your own type, though,
you will have to tell Blitz++ this information using the macro
BZ_DECLARE_MULTICOMPONENT_TYPE()
. This macro has three arguments:
BZ_DECLARE_MULTICOMPONENT_TYPE(T_element, T_componentType, numComponents) |
T_element
is the element type of the array. T_componentType
is the type of the components of that element. numComponents
is the
number of components in each element.
An example will clarify this. Suppose we wanted to make a colour image,
stored in 24-bit HSV (hue-saturation-value) format. We can make a class
HSV24
which represents a single pixel:
#include <blitz/array.h> using namespace blitz; class HSV24 { public: // These constants will makes the code below cleaner; we can // refer to the components by name, rather than number. static const int hue=0, saturation=1, value=2; HSV24() { } HSV24(int hue, int saturation, int value) : h_(hue), s_(saturation), v_(value) { } // Some other stuff here, obviously private: unsigned char h_, s_, v_; }; |
Right after the class declaration, we will invoke the macro
BZ_DECLARE_MULTICOMPONENT_TYPE
to tell Blitz++ about HSV24:
// HSV24 has 3 components of type unsigned char BZ_DECLARE_MULTICOMPONENT_TYPE(HSV24, unsigned char, 3); |
Now we can create HSV images and modify the individual components:
int main() { Array<HSV24,2> A(128,128); // A 128x128 HSV image ... // Extract a greyscale version of the image Array<unsigned char,2> A_greyscale = A[HSV24::value]; // Bump up the saturation component to get a // pastel effect A[HSV24::saturation] *= 1.3; // Brighten up the middle of the image Range middle(32,96); A[HSV24::value](middle,middle) *= 1.2; } |
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Since complex arrays are used frequently, Blitz++ provides two special methods for getting the real and imaginary components:
Array<complex<float>,2> A(32,32); real(A) = 1.0; imag(A) = 0.0; |
The function real(A)
returns an array view of the real component;
imag(A)
returns a view of the imaginary component.
Note: Blitz++ provides numerous math functions defined over complex-valued
arrays, such as conj
, polar
, arg
, abs
,
cos
, pow
, etc. See the section on math functions
(3.8 Single-argument math functions) for details.
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Blitz++ provides a function zip()
which lets you combine two or more
expressions into a single component. For example, you can combine two real
expressions into a complex expression, or three integer expressions into an
HSV24 expression. The function has this syntax:
resultexpr zip(expr1, expr2, T_element) resultexpr zip(expr1, expr2, expr3, T_element) ** not available yet resultexpr zip(expr1, expr2, expr3, expr4, T_element) ** not available yet |
The types resultexpr
, expr1
and expr2
are array
expressions. The third argument is the type you want to create. For
example:
int N = 16; Array<complex<float>,1> A(N); Array<float,1> theta(N); ... A = zip(cos(theta), sin(theta), complex<float>()); |
The above line is equivalent to:
for (int i=0; i < N; ++i) A[i] = complex<float>(cos(theta[i]), sin(theta[i])); |
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You can use the Array
class with types you have created yourself, or
types from another library. If you want to do arithmetic on the array,
whatever operators you use on the arrays have to be defined on the
underlying type.
For example, here's a simple class for doing fixed point computations in the interval [0,1]:
#include <blitz/array.h> #include <blitz/numinquire.h> // for huge() using namespace blitz; // A simple fixed point arithmetic class which represents a point // in the interval [0,1]. class FixedPoint { public: // The type to use for the mantissa typedef unsigned int T_mantissa; FixedPoint() { } FixedPoint(T_mantissa mantissa) { mantissa_ = mantissa; } FixedPoint(double value) { assert((value >= 0.0) && (value <= 1.0)); mantissa_ = static_cast<T_mantissa>(value * huge(T_mantissa())); } FixedPoint operator+(FixedPoint x) { return FixedPoint(mantissa_ + x.mantissa_); } double value() const { return mantissa_ / double(huge(T_mantissa())); } private: T_mantissa mantissa_; }; ostream& operator<<(ostream& os, const FixedPoint& a) { os << a.value(); return os; } |
The function huge(T)
returns the largest representable value for type
T; in the example above, it's equal to UINT_MAX
.
The FixedPoint
class declares three useful operations: conversion
from double
, addition, and outputing to an ostream
. We can
use all of these operations on an Array<FixedPoint>
object:
#include <fixed-point.h> // FixedPoint class int main() { // Create an array using the FixedPoint class: Array<FixedPoint, 2> A(4,4), B(4,4); A = 0.5, 0.3, 0.8, 0.2, 0.1, 0.3, 0.2, 0.9, 0.0, 1.0, 0.7, 0.4, 0.2, 0.3, 0.8, 0.4; B = A + 0.05; cout << "B = " << B << endl; return 0; } |
Note that the array A
is initialized using a comma-delimited list of
double
; this makes use of the constructor FixedPoint(double)
.
The assignment B = A + 0.05
uses
FixedPoint::operator+(FixedPoint)
, with an implicit conversion from
double
to FixedPoint
. Formatting the array B
onto the
standard output stream is done using the output operator defined for
FixedPoint
.
Here's the program output:
B = 4 x 4 [ 0.55 0.35 0.85 0.25 0.15 0.35 0.25 0.95 0.05 0.05 0.75 0.45 0.25 0.35 0.85 0.45 ] |
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