# 5 Multicomponent, complex, and user type arrays

## 5.1 Multicomponent and complex arrays

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;

### 5.1.1 Extracting components

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;
    }

### 5.1.2 Special support for complex arrays

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 (Single-argument math functions) for details.

### 5.1.3 Zipping together expressions

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]));

## 5.2 Creating arrays of a user type

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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