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<H1> 5. Multicomponent, complex, and user type arrays </H1>
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<BLOCKQUOTE><TABLE BORDER=0 CELLSPACING=0> 
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="blitz_5.html#SEC122">5.1 Multicomponent and complex arrays</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Multicomponent Array's</TD></TR>
<TR><TD ALIGN="left" VALIGN="TOP"><A HREF="blitz_5.html#SEC126">5.2 Creating arrays of a user type</A></TD><TD>&nbsp;&nbsp;</TD><TD ALIGN="left" VALIGN="TOP">Array's of your own type</TD></TR>
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<P>

<A NAME="Array multi"></A>
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<H2> 5.1 Multicomponent and complex arrays </H2>
<!--docid::SEC122::-->
<P>

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.
</P><P>

Here are some examples of multicomponent arrays:
</P><P>

<A NAME="IDX312"></A>
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>// A 3-dimensional array; each element is a length 3 vector of float
Array&#60;TinyVector&#60;float,3&#62;,3&#62; A;  

// A complex 2-dimensional array
Array&#60;complex&#60;double&#62;,2&#62; B;

// A 2-dimensional image containing RGB tuples
struct RGB24 {
  unsigned char r, g, b;
};

Array&#60;RGB24,2&#62; C;
</pre></td></tr></table></P><P>

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<H3> 5.1.1 Extracting components </H3>
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<P>

<A NAME="IDX313"></A>
<A NAME="IDX314"></A>
</P><P>

Blitz++ provides some special support for such arrays.  The most important
is the ability to extract a single component.  For example:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>Array&#60;TinyVector&#60;float,3&#62;,2&#62; A(128,128);
Array&#60;float,2&#62; B = A.extractComponent(float(), 1, 3);
B = 0;
</pre></td></tr></table></P><P>

The call to <CODE>extractComponent</CODE> returns an array of floats; this array
is a view of the second component of each element of A.  The arguments of
<CODE>extractComponent</CODE> 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.
</P><P>

This is a little bit messy, so Blitz++ provides a handy shortcut using
<CODE>operator[]</CODE>:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>Array&#60;TinyVector&#60;float,3&#62;,2&#62; A(128,128);
A[1] = 0;
</pre></td></tr></table></P><P>

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
<CODE>TinyVector</CODE> and <CODE>complex&#60;T&#62;</CODE>.  If you use your own type, though,
you will have to tell Blitz++ this information using the macro
<CODE>BZ_DECLARE_MULTICOMPONENT_TYPE()</CODE>.  This macro has three arguments:
</P><P>

<A NAME="IDX315"></A>
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>BZ_DECLARE_MULTICOMPONENT_TYPE(T_element, T_componentType, numComponents)
</pre></td></tr></table></P><P>

<CODE>T_element</CODE> is the element type of the array.  <CODE>T_componentType</CODE>
is the type of the components of that element.  <CODE>numComponents</CODE> is the
number of components in each element.
</P><P>

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
<CODE>HSV24</CODE> which represents a single pixel:
</P><P>

<A NAME="IDX316"></A>
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>#include &#60;blitz/array.h&#62;

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_;
};
</pre></td></tr></table></P><P>

Right after the class declaration, we will invoke the macro
<CODE>BZ_DECLARE_MULTICOMPONENT_TYPE</CODE> to tell Blitz++ about HSV24:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>// HSV24 has 3 components of type unsigned char
BZ_DECLARE_MULTICOMPONENT_TYPE(HSV24, unsigned char, 3);
</pre></td></tr></table></P><P>

Now we can create HSV images and modify the individual components:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>int main()
{
    Array&#60;HSV24,2&#62; A(128,128);   // A 128x128 HSV image
    ...

    // Extract a greyscale version of the image
    Array&#60;unsigned char,2&#62; 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;
}
</pre></td></tr></table></P><P>

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<H3> 5.1.2 Special support for complex arrays </H3>
<!--docid::SEC124::-->
<P>

<A NAME="IDX317"></A>
<A NAME="IDX318"></A>
</P><P>

Since complex arrays are used frequently, Blitz++ provides two special
methods for getting the real and imaginary components:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>Array&#60;complex&#60;float&#62;,2&#62; A(32,32);

real(A) = 1.0;
imag(A) = 0.0;
</pre></td></tr></table></P><P>

The function <CODE>real(A)</CODE> returns an array view of the real component;
<CODE>imag(A)</CODE> returns a view of the imaginary component.
</P><P>

Note: Blitz++ provides numerous math functions defined over complex-valued
arrays, such as <CODE>conj</CODE>, <CODE>polar</CODE>, <CODE>arg</CODE>, <CODE>abs</CODE>,
<CODE>cos</CODE>, <CODE>pow</CODE>, etc.  See the section on math functions
(<A HREF="blitz_3.html#SEC92">3.8 Single-argument math functions</A>) for details.
</P><P>

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<H3> 5.1.3 Zipping together expressions </H3>
<!--docid::SEC125::-->
<P>

Blitz++ provides a function <CODE>zip()</CODE> 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:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>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
</pre></td></tr></table></P><P>

The types <CODE>resultexpr</CODE>, <CODE>expr1</CODE> and <CODE>expr2</CODE> are array
expressions.  The third argument is the type you want to create.  For
example:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>int N = 16;
Array&#60;complex&#60;float&#62;,1&#62; A(N);
Array&#60;float,1&#62; theta(N);

 ...

A = zip(cos(theta), sin(theta), complex&#60;float&#62;());
</pre></td></tr></table></P><P>

The above line is equivalent to:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=example><pre>for (int i=0; i &#60; N; ++i)
   A[i] = complex&#60;float&#62;(cos(theta[i]), sin(theta[i]));
</pre></td></tr></table></P><P>

<A NAME="Array usertype"></A>
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<H2> 5.2 Creating arrays of a user type </H2>
<!--docid::SEC126::-->
<P>

You can use the <CODE>Array</CODE> 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.
</P><P>

For example, here's a simple class for doing fixed point computations in the
interval [0,1]:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre>#include &#60;blitz/array.h&#62;
#include &#60;blitz/numinquire.h&#62; // 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 &#62;= 0.0) &#38;&#38; (value &#60;= 1.0));
        mantissa_ = static_cast&#60;T_mantissa&#62;(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&#38; operator&#60;&#60;(ostream&#38; os, const FixedPoint&#38; a)
{
    os &#60;&#60; a.value();
    return os;
}

</FONT></pre></td></tr></table></P><P>

The function <CODE>huge(T)</CODE> returns the largest representable value for type
T; in the example above, it's equal to <CODE>UINT_MAX</CODE>.
</P><P>

The <CODE>FixedPoint</CODE> class declares three useful operations: conversion
from <CODE>double</CODE>, addition, and outputing to an <CODE>ostream</CODE>.  We can
use all of these operations on an <CODE>Array&#60;FixedPoint&#62;</CODE> object:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre>
#include &#60;fixed-point.h&#62; // FixedPoint class

int main()
{
    // Create an array using the FixedPoint class:

    Array&#60;FixedPoint, 2&#62; 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 &#60;&#60; "B = " &#60;&#60; B &#60;&#60; endl;

    return 0;
}
</FONT></pre></td></tr></table></P><P>

Note that the array <CODE>A</CODE> is initialized using a comma-delimited list of
<CODE>double</CODE>; this makes use of the constructor <CODE>FixedPoint(double)</CODE>.
The assignment <CODE>B = A + 0.05</CODE> uses
<CODE>FixedPoint::operator+(FixedPoint)</CODE>, with an implicit conversion from
<CODE>double</CODE> to <CODE>FixedPoint</CODE>.  Formatting the array <CODE>B</CODE> onto the
standard output stream is done using the output operator defined for
<CODE>FixedPoint</CODE>.
</P><P>

Here's the program output:
</P><P>

<TABLE><tr><td>&nbsp;</td><td class=smallexample><FONT SIZE=-1><pre>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 ]

</FONT></pre></td></tr></table></P><P>

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