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<html>
<title>Blitz++ Class Reference: Vector&lt;T&gt;</title>
<body>

<h1>Blitz++ Class Reference: Vector&lt;T&gt;</h1>

<table border cellpadding=10 align=top>
<tr valign=top><td>
<h3>Sections</h3>
<ul>
<li><a href="#summary">Summary</a></li>
<li><a href="#synopsis">Synopsis</a></li>
<li><a href="#template">Template parameter</a></li>
<li><a href="#publictype">Public types</a></li>
<li><a href="#construct">Constructors</a></li>
<li><a href="#member">Member functions</a></li>
<li><a href="#memberops">Member operators</a></li>
<li><a href="#ops">Operators</a></li>
<li><a href="#global">Global math functions</a></li>
<li><a href="#global2">Other global functions</a></li>
<li><a href="#example">Example</a></li>
</ul>
</td>
<td>
<h3>Related topics and classes</h3>
<ul>
<li>The <a href="range.html">Range</a> class</li>
<!-- <li>Aliasing and the <a href="restrict.html">restrict</a> keyword</li> -->
<!-- <li>Data/view model</li> -->
<!-- <li>Expression templates</li> -->
<!-- <li>Type promotion</li> -->
<!-- <li>Performance benchmarks</li> -->
<!-- <li>where/elsewhere/endwhere</li> -->
<!-- <li>Matrix&lt;T&gt;</li> -->
<!-- <li>FFTServer&lt;T&gt;</li> -->
</ul>
</td>

<td align=center>
<h3>Inheritance diagram</h3>
MemoryBlockReference&lt;T&gt;<br>
|<br>
Vector&lt;T&gt;
</td>
</table>

<a name="summary">
<!-- <h2>Summary</h2> -->

<a name="synopsis">
<h2>Synopsis</h2>

<pre>
#include &lt;blitz/vector.h&gt;
using namespace blitz;
Vector&lt;double&gt; x(100);
</pre>

<a name="template">
<h2>Template parameter</h2>

<p>
The template parameter of Vector&lt;T&gt; is the element type of the 
vector.  This should an integral, floating point, or complex type.  
These choices of <b>T</b> should work: 
<ul>
<li>bool, char, unsigned char, short int, short unsigned int, int, unsigned int,
long, unsigned long</li>
<li>float, double, long double</li>
<li>complex&lt;float&gt;, complex&lt;double&gt;, and 
complex&lt;long double&gt;</li>
</ul>
Other types
may work provided they have the necessary numeric semantics.
</p>

<a name="publictype">
<h2>Public types</h2>

<p>Vector&lt;T&gt; declares several publicly accessible
types.  They may be accessed using the scope (::) operator: e.g.
<pre>
Vector&lt;double&gt; x(50);                       // Create a vector of length 50
Vector&lt;double&gt;::T_iterator z = x.begin();   // Get an iterator for x
</pre>

<table border cellpadding=2>
<tr>
<th>
Type
</th>
<th>
Description
</th>
</tr>
<tr align=left>
<td>
<b>T_numtype</b></td>
<td>The numeric type of the vector elements (e.g. double)</td>
</tr>

<tr align=left><td>
<b>T_vector</b></td>
<td>Complete type of the vector itself (e.g. Vector&lt;double&gt;)</td></tr>

<tr align=left><td>
<b>T_iterator</b></td>
<td>STL-like iterator to be used on this vector (see begin(), end())
** Not yet supported</td>
</tr>

<tr align=left><td>
<b>T_constIterator</b></td>
<td>STL-like const iterator to be used on this vector (see begin(), end())
** Not yet supported</td>
</tr>
</table>

<a name="construct">
<h2>Constructors</h2>

<ul>
<li><b>Vector()</b><br><br>
Default constructor.  No memory is allocated; the length of the vector is
zero. The
vector may subsequently be resized using resize(), or used to refer to another
vector's data using reference().<br></li>

<br><li>
<b>Vector(size_t length)</b><br><br>
Create a new vector of the given length.  Memory is allocated using
<b>new</b>.  Elements are not initialized.<br></li>

<br><li>
<b>Vector(Vector&lt;T_numtype&gt;& x)</b><br><br>
Creates a reference (or alias) to the data of vector x.  Both x and this
vector now refer to the same underlying data, so any changes made to the
data via x will be visible in this vector.  (Note: T_numtype is a publicly
declared typedef for the template parameter).<br></li>

<br><li>
<b>Vector(Vector&lt;T_numtype&gt;& x, <a href="range.html">Range</a> r)</b><br><br>
Creates a reference (or alias) to a portion of the data of vector x.  
The range object specifies an interval of the index set.  For example,
<pre>
Vector&lt;double&gt; x(50);                // Create a vector of length 50
Vector&lt;double&gt; y(x, Range(10,20));  // y is now of length 11, and
                                     // refers to elements 10-20 of x
y[5] = 3;                            // y[5] is aliased to x[15]
</pre>
</li>

<li>
<b>Vector(size_t length, T_numtype initValue)</b><br><br>
Creates a new vector of the given length, and initializes all elements
to initValue.  Memory is allocated using <b>new</b>.</li>

<br><br><li>
<b>Vector(size_t length, T_numtype firstValue, T_numtype inc)</b><br><br>
Creates a new vector of the given length, and initializes the elements
to [ firstValue, firstValue + inc, firstValue + 2 * inc, ...,
firstValue + (length-1) * inc ].  Memory is allocated using <b>new</b>.</li>

<br><br><li>
<b>Vector(<a href="range.html">Range</a> r)</b><br><br>
Creates a vector and initializes the elements to the range r.  For
example,
<pre>
Vector&lt;int&gt; z(Range(0,5));    // z = [ 0, 1, 2, 3, 4, 5 ]
</pre>
</li>

<li>
<b>Vector(size_t length, Random&lt;P_distribution&gt;& random)</b><br><br>
Creates a vector and initializes its elements with random numbers.
For example,
<pre>
#include &lt;blitz/rand-normal.h&gt;
Random&lt;Normal&gt; gaussianNoise(0.0, 2.5);     // Zero-mean, variance 2.5
Vector&lt;double&gt; x(50, gaussianNoise);  
</pre>
</li>

<li>
<b>Vector(size_t length, T_numtype* [restrict] data, int stride = 1)</b><br><br>
Creates a vector which refers to the given data.  The <a href="restrict.html">
NCEG <b>restrict</b></a>
keyword can be used only with compilers which support it.  The stride
parameter gives the spacing of elements: in the created vector, element 
<b>i</b> will be <b>data[i * stride]</b>.  When the vector object is
destroyed, the memory is not freed (i.e. the vector does not assume
ownership of the data).</li>

<br><br><li>
<b>Vector(<i>vector expression</i>)</b><br><br>
Creates a vector of appropriate length and stores the result of
<i>vector expression</i> in it.  (See the explanation of expression
templates).   Examples:
<pre>
// Create a vector of length 16 containing a sampled cosine (full period)
Vector&lt;double&gt; x(cos(Range(0,15) * 2 * M_PI / 16.0));

// Create a new vector containing an approximation of the derivative
// of x.
Range I(1,15);
double delta = 1 / 16.;    // Spacing between samples
Vector&lt;double&gt; y = (x(I) - x(I-1)) / delta;
</pre>
</li>

</ul>



<a name="member">
<h2>Member functions</h2>

<ul>
<li>
<b>T_iterator      begin()</b>    ** NOT YET SUPPORTED<br><br>
Returns an STL-compliant iterator positioned at the beginning of the vector's
data.  T_iterator is a public type declared by Vector&lt;T_numtype&gt;, and
should be used to specify the type of the iterator:
<pre>
Vector&lt;double&gt; x(50);
Vector&lt;double&gt;::T_iterator iter = x.begin();
</pre>
Since T_iterator is STL-compliant, it may be used with the standard
template library routines.  [GIVE EXAMPLES]  See also end().
</li>

<br><br><li>
<b>T_constIterator begin()  const</b>    ** NOT YET SUPPORTED<br><br>
Returns an STL-compliant const iterator positioned at the beginning of
the vector's data.  A const iterator has read-only access to the vector
elements.  T_constIterator is a public type declared by Vector&lt;T_numtype&gt;,
and should be used to specify the type of the iterator:
<pre>
Vector&lt;int&gt; z(50,0,1);       // Creates the vector [ 0 1 2 ... 49 ]
const Vector&lt;int&gt;& zref = z; // Create a const reference to z
Vector&lt;int&gt;::T_constIterator iter = zref.begin();
</pre>
Since T_constIterator is STL-compliant, it may be used with the
standard template library routines.  [GIVE EXAMPLES]  See also end().<br><br>

The begin() method is const-overloaded.  By default, a non-const iterator
is returned.  A const iterator is returned only when the vector itself
is const.
</li>

<br><br><li>
<b>T_vector        copy()   const</b><br><br>
Returns a copy of the vector.  A new block of memory is allocated, and
the vector copy is guaranteed to have unit stride.
</li>

<br><br><li>
<b>T_iterator      end()</b><br><br>
Returns an STL-compliant iterator positioned at the end of the
vector's data.  See begin() above.
</li>

<br><br><li>
<b>T_constIterator end()    const</b><br><br>
Returns an STL-compliant const iterator positioned at the end of the
vector's data.  See begin() above.
</li>

<br><br><li>
<b>T_numtype * [<i>restrict</i>] data()<br>
const T_numtype * [<i>restrict</i>] data() const</b><br><br>
Obtain a pointer to the beginning of the vector data.  This method
should be used with caution, since it has the potential to
cause data corruption and/or segment violations if used improperly.
The vector data is not necessarily stored contiguously; the
spacing between vector elements can be obtained via the stride()
member function.  Here is an example:
<pre>
Vector&lt;float&gt; x(10,0,1);          // Creates [ 0 1 2 3 4 5 6 7 8 9 ]
float* xptr = x.data();           // Get a pointer to the vector data
int length = x.length();          // Obtain the length of the vector (10)
int stride = x.stride();          // Note that stride may be negative

for (int i=0; i < length; ++i)
    xptr[i * stride] = 7;         // Set each element to 7

// Now the vector contains [ 7 7 7 7 7 7 7 7 7 7 ]
// Note that "x = 7;" would accomplish the same result.
</pre>
The <a href="restrict.html">NCEG restrict</a> keyword is applicable 
only if the compiler supports it.<br><br>

The data() method is const-overloaded: if the vector is const, then 
data() returns a const T_numtype* pointer.
</li>

<br><br><li>
<b>size_t          length() const</b><br><br>
Returns the length of the vector.</li>

<br><br><li>
<b>void            makeUnique()</b><br><br>
If the vector's elements are referenced (or aliased) by another vector,
a copy is made, and on return the vector refers to the new copy.
</li>

<br><br><li>
<b>void            reference(T_vector& x)</b><br><br>
Makes the vector an alias for vector x.  After this member function is
used, both the vector and x refer to the same underlying data.</li>

<br><br><li>
<b>void            resize(size_t length)</b><br><br>
If length is different than the current length of the vector, the
vector is resized.  The current contents are lost.
</li>

<br><br><li>
<b>void            resizeAndPreserve(size_t newLength)</b><br><br>
Allocates a new vector of size newLength, and copies as much of
the current vector as will fit into the new vector.  If the new
vector is larger than the previous vector, then the unused elements
are left uninitialized.</li>

<br><br><li>
<b>Vector&lt;T_numtype&gt; reverse()</b><br><br>
Returns a view of the vector in reverse order.  This is done using
a negative stride.</li>

<br><br><li>
<b>int             stride() const</b><br><br>
Returns the distance between vector elements in memory.  This
will normally be 1 (referred to as <i>unit stride</i>).</li>

</ul>

<a name="memberops">
<h2>Member operators</h2>

<pre>
T_numtype        operator()(unsigned i) const
T_numtype&       operator()(unsigned i)
T_numtype        operator[](unsigned i) const
T_numtype&       operator[](unsigned i)
T_vector         operator()(Range r)
T_vector         operator[](Range r)
T_pick           operator[](Vector&lt;int&gt;)        ** Currently broken
</pre>

<a name="ops">

<h3>Iostream operators</h3>

<pre>
ostream& operator>>(ostream& os, const <i>vector expression</i>&);
</pre>
Formats a vector or vector expression for output.  In future releases,
several output formats will be supported.

<h3>Arithmetic operators</h3>

Arithmetic operators are implemented using expression templates.  These
assignment operators are supported:

<pre>
operator=(<i>vector expression</i>)
operator+=(<i>vector expression</i>)
operator-=(<i>vector expression</i>)
operator*=(<i>vector expression</i>)
operator/=(<i>vector expression</i>)
operator%=(<i>vector expression</i>)
operator^=(<i>vector expression</i>)
operator&=(<i>vector expression</i>)
operator|=(<i>vector expression</i>)
operator>>=(<i>vector expression</i>)
operator=(<i>vector expression</i>)
</pre>

<p>
A <i>vector expression</i> can be any combination of these operators
and operands, as well as use of the math functions listed later.
</p>

<h4>Vector expression operators</h4>
<pre>
+ - * / % ^ & | >> << 
> < >= <= == != && ||
</pre>

<h4>Vector expression operands</h4>
<ul>
<li>Vector&lt;T_numtype&gt;</li>
<li>Vector&lt;T_numtype2&gt; (A vector of a different type)</li>
<li>VectorPick&lt;T_numtype&gt;</li>
<li><a href="range.html">Range</a></li>
<li>Random  ** NOT YET FULLY SUPPORTED</li>
<li>Scalar constants (int,float,double,long double)</li>
<li>Complex constants (complex&lt;float&gt;, complex&lt;double&gt;, 
    complex&lt;long double&gt;)</li>
</ul>

<p>
Arithmetic type promotion for vectors is identical to type promotion
for built-in types. For example, adding a double constant to a 
Vector&lt;int&gt; will result in a Vector&lt;double&gt;; multiplying
a Vector&lt;long double&gt; by a Vector&lt;float&gt; will result in
a Vector&lt;long double&gt;.  Generally, the result is promoted to
which ever type preserves the greatest precision.</p>

<p>Note that division and multiplication of integers may result in
truncation and/or wraparound, since the result remains an integer
type.  The solution is to cast the elements of one of the vectors 
as floating-point types; see <b>cast&lt;T2&gt;</b> below.
** the cast() function is not yet implemented</p>

<pre>
Vector&lt;int&gt; x(5), y(5);
Vector&lt;double&gt; z(5);

// ...

z = x / y;      // Calculated using integer math, then cast as double
                // Results in truncation

z = x / cast&lt;double&gt;(y);   // Calculated using floating point 

</pre>

<a name="global">
<!-- <h2>Global functions</h2> -->

<h3>Single-operand math functions</h3>

<h5>Notes</h5>
<ul>
<li>Single operand math functions are evaluated using expression templates.</li>
<li>If used on an integer vector, most of the functions below will return
the answer type as a double.</li>
</ul>

<table border cellpadding=2>
<tr align=center><th>Function</th><th>Description</th><th>Real vectors</th><th>Complex vectors</th><th>Availability</th></tr>
<tr><td>abs</td><td>Absolute value</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>acos</td><td>Inverse cosine.  Elements must be in the range [-1,+1].  The resulting elements lie in [-Pi,+Pi].</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>acosh</td><td>Inverse hyperbolic cosine</td> <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>

<tr><td>arg</td>
<td>Argument (phase/angle) of a complex vector. Result is a scalar vector whose elements lie in [-Pi, +Pi].</td>
<td></td>
<td>Y</td>
<td>all<sup>b</sup></td></tr>

<tr><td>asin</td><td>Inverse sine.  Elements must be in the range [-1,+1].  The resulting elements lie in [-Pi,+Pi].</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>asinh</td><td>Inverse hyperbolic sine</td>     <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>
<tr><td>atan</td><td>Inverse tangent.  Resulting elements lie in [-Pi,+Pi].</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>atanh</td><td>Inverse hyperbolic tangent</td>     <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>
<tr><td>cast&lt;T2&gt;</td><td>Cast vector elements to type T2<br>** NOT YET AVAILABLE</td><td>Y</td><td>Y</td><td>some<sup>e</sup></td></tr>
<tr><td>cbrt</td><td>Cubic root</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>
<tr><td>ceil</td><td>Smallest floating integer not less than element</td>     <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>
<tr><td>class</td><td>Floating-point classification.  Result is an integer
vector with elements taking values FP_PLUS_NORM,
FP_MINUS_NORM, FP_PLUS_ZERO, FP_MINUS_ZERO, FP_PLUS_INF, FP_MINUS_INF,
FP_PLUS_DENORM, FP_MINUS_DENORM, FP_SNAN, FP_QNAN as defined in &lt;float.h&gt;
</td>
     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>

<tr><td>conj</td>
<td>Complex conjugate</td>
<td></td>
<td>Y</td>
<td>all<sup>b</sup></td></tr>

<tr><td>cos</td><td>Cosine.  Resulting elements lie in [-1,+1].</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>cosh</td><td>Hyperbolic cosine</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>exp</td><td>Exponential.</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>expm1</td><td>Exponential minus one: exp(x)-1</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>erf</td><td>Error function</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>erfc</td><td>Complementary error function (1-erf(x)).</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>fabs</td><td>Same as <b>abs</b></td>     <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>
<tr><td>finite</td><td>Nonzero if finite.  Result is integer.</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>
<tr><td>floor</td><td>Largest floating int not greater than x</td>     <td>Y</td>     <td></td>  <td>all</td><td>     </td></tr>
<tr><td>ilogb</td><td>Integer unbiased exponent</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>

<tr><td>imag</td>
<td>Imaginary portion of a complex vector. Result is a scalar vector which
may be used as an lvalue.</td>
<td></td>
<td>Y</td>
<td>all<sup>b</sup></td></tr>

<tr><td>isnan</td><td>Nonzero if x is NaNS (Signalling Not a Number) or NaNQ (Quiet Not A Number).  Result is integer.</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>
<tr><td>itrunc</td><td>Truncate and convert to integer.  Result is integer.</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>

<tr><td>inv</td>
<td>Inverse of a complex number</td>
<td></td>
<td>Y</td>
<td>all<sup>b</sup></td></tr>

<tr><td>j0</td><td>Bessel function first kind, order 0</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>j1</td><td>Bessel function first kind, order 1<br>
See also y0(x), y1(x), jn(x,y) and yn(x,y).
</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>lgamma</td><td>Log absolute gamma</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>log</td><td>Natural logarithm</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>logb</td><td>Unbiased exponent (IEEE)</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>log1p</td><td>Natural logarithm of (1+x)</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>log10</td><td>Logarithm base 10</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>nearest</td><td>Nearest floating point integer to x.</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>

<tr><td>norm</td>
<td>Norm (magnitude) of a complex vector. Result is a scalar vector.</td>
<td></td>
<td>Y</td>
<td>all<sup>b</sup></td></tr>

<tr><td>real</td>
<td>Real portion of a complex vector. Result is a scalar vector which may
be used as an lvalue.</td>
<td></td>
<td>Y</td>  
<td>all<sup>b</sup></td></tr>

<tr><td>rint</td><td>Round to floating point integer, using the current 
floating-point rounding mode.  Rounding mode is read and set by
the functions fp_read_rnd() and fp_swap_rnd().  (See system man pages)</td>       <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>rsqrt</td><td>Reciprocal square root (i.e. 1.0/sqrt(x))</td>     <td>Y</td>     <td></td>  <td>some<sup>d</sup></td><td>     </td></tr>
<tr><td>sin</td><td>Sine.  Resulting elements lie in [-1,+1].</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>sinh</td><td>Hyperbolic sine</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>sqr</td><td>Square: equivalent to x*x</td>     <td>Y</td>     <td>Y</td>  <td>all<sup>e</sup></td><td>     </td></tr>
<tr><td>sqrt</td><td>Square root</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>tan</td><td>Tangent</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>tanh</td><td>Hyperbolic tangent</td>     <td>Y</td>     <td>Y</td>  <td>all</td><td>     </td></tr>
<tr><td>trunc</td><td>Nearest floating-point integer in the direction of zero</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>uitrunc</td><td>Truncate and convert to unsigned.  Result is unsigned integer.</td>     <td>Y</td>     <td></td> <td>some<sup>d</sup></td>  </tr>
<tr><td>y0</td><td>Bessel function 2nd kind, order 0</td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
<tr><td>y1</td><td>Bessel function 2nd kind, order 1
<br>See also yn(x,y) below</br></td>     <td>Y</td>     <td></td>  <td>some<sup>c</sup></td><td>     </td></tr>
</table>

<sup>a</sup>ANSI C math function<br>
<sup>b</sup>ANSI C++ math function<br>
<sup>c</sup>IEEE 754 standard required function<br>
<sup>d</sup>IEEE 754 recommended function<br>
<sup>e</sup>Nonstandard function specific to Blitz++<br>
<br>

<h3>Global math functions with two operands</h3>

** These functions are not yet implemented **
<pre>

All the two operand math functions are provided in three forms:<br>
atan2(double,vector)
atan2(vector,double)
atan2(vector,vector)
copysign(vector,double)
drem(d,d)
fmod(d,d)
frexp(d, Vector&lt;int&gt;& e)  NOT INCLUDED
hypot(d,d)
jn(int, d)                      NOT INCLUDED
ldexp(d,i)                      NOT INCLUDED
modf(d, Vector&lt;int&gt;& e)   NOT INCLUDED
max(d, d)
min(d, d)
nextafter(d, d)
polar(d,d)                      NOT INCLUDED
pow(d,d)
remainder(d,d)
scalb(d,d)
unordered(d,d)
yn(int,d)                       NOT INCLUDED
</pre>

<a name="global2">
<h2>Other global functions</h2>

(These functions <i>are</i> available)

<pre>
accumulate
<!-- convolve -->
dot 
delta
<!-- even -->
<!-- innerProduct  (same as dot) -->
<!-- imag -->
<!-- inversePermute -->
<!-- kronecker -->
<!-- kurtosis -->
max
maxIndex
maxValue
mean
min
minIndex
minValue
norm
<!-- odd -->
<!-- outerProduct  (same as kronecker) -->
<!-- permute -->
<!-- real -->
reverse
<!-- skewness -->
<!-- sort -->
sum
<!-- variance -->
</pre>

<h2>The <i>where</i> function</h2>

<p>
The <i>where(X,Y,Z)</i> function provides the same functionality as
the operator X ? Y : Z.  If X is logical true, then Y is returned;
otherwise, Z is returned.
</p>

<p>
The <i>where</i> function is implemented using expression templates.
The arguments X, Y, and Z can each be vectors, vector expressions,
<a href="range.html">Range</a>, or Vector picks.
</p>

<a name="example">
<h2>Example</h2>

Please see the files in the <a href="../examples/"><b>Blitz++/examples</b></a> directory.
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