Users Guide

Table of Contents

• Introduction
• Predefined Data Types
  • Predefined Scalar Types
  • Prepared Vector Types
  • Prepared Matrix Types
• Using Vectors
  • Defining a Vector
  • Vector Manipulation
  • Vector Converters
  • Vector Functions
• Using Matrices
  • Matrix Converters
• The Array Class
• Random Vectors, Matrices, and Generators
  • Random Vectors and Matrices
  • Random Number Generators (RNG)
• Deterministic Sources
• Filter Classes and Functions
• Signal Processing Functions
• Timer Classes
• Reading and Writing to Files

Introduction

The itbase library is the core of IT++ and it contains classes and functions for mathematics with scalars, vectors, and matrices. This document does not cover all the aspects of the itbase library. It does however explain the most important things you need to know in order to start using IT++. Once you are more familiar with the itbase library you will find the online reference manual more useful.

Predefined Data Types

Predefined Scalar Types

Apart from the standard C++ types e.g. char, short, int, long, double, float, and long long, the following types are specific for IT++:

• complex<double>: Contains real and imaginary parts of type double
• bin: Used for binary (0,1) data

Prepared Vector Types

A vector can in principle be of arbitrary type (that support addition, subtraction, multiplication and division), since the general vector class Vec<TYPE> is templated. However, the most commonly used vector types are predefined. These predefined vector types are:

• vec: Basic vector type containing double
• cvec: Vector type containing complex<double>
• ivec: Vector type containing int
• bvec: Vector type containing bin
• svec: Vector type containing short

The general vector class is used to define the specialized classes above. The vec class is actually a Vec<double>. We urge you to use these predefined classes instead of Vec<TYPE> when ever possible.

Prepared Matrix Types

The general matrix class is called Mat<TYPE>. These predefined matrix types are:

• mat: Basic matrix type containing double
• cmat: Matrix type containing complex<double>
• imat: Matrix type containing int
• bmat: Matrix type containing bin
• smat: Matrix type containing short

As with vector, the general matrix class is used to define the specialized classes above. The mat class is thus a Mat<double>. We urge you to use these predefined classes instead of Mat<TYPE> whenever possible.

Using Vectors

Vectors and matrices in IT++ are very similar. We therefore begin to describe the vector class in detail and then briefly explain the differences regarding matrices in the next section.

Defining a Vector

A vector containing elements of type double is defined with:

vec my_vector;

However, this will not assign a size (memory) to the vector. To assign size 10 to the vector we may use:

vec my_vector(10);

or

vec my_vector;
my_vector.set_size(10,false);

where the second parameter in the set_size call (true or false) determines if you want to copy the contents of the old data area into the new resized one, or not. This may be useful when down-sizing a vector, but in this case it is not. It is also equivalent to use

my_vector.set_length(10,false);

instead of set_size.

Observe that a declared vector (or matrix) is not cleared (the element values are undefined). To clear a vector we simply write

my_vector.clear();

or

my_vector.zeros();

To fill the vector with ones we write

my_vector.ones();

It is possible to retrieve the length (size) of a vector in any of the following ways:

length_of_vector = my_vector.length();
length_of_vector = my_vector.size();
length_of_vector = length(my_vector);

To assign values to a vector

vec  a = "0 0.7 5 9.3";        // that is a = [0 0.7 5 9.3]
ivec b = "0:5";                // that is b = [0 1 2 3 4 5]
vec  c = "3:2.5:13";           // that is c = [3 5.5 8 10.5 13]
ivec d = "1:3:5,0:2:4";        // that is d = [1 3 5 0 2 4]
vec e("1.2,3.4,5.6");          // that is e = [1.2 3.4 5.6]
vec f;
f.set("1.0 2.0 3.0 4.0");      // that is f = [1.0 2.0 3.0 4.0]
vec g;
g = f;                         // that is g is a copy of f

A comma or a space character separates the vector elements. When assigning or retrieving a specific vector element use

a(i) = 3.14;
double p = a(i);

for element number i. Vector elements are numbered such that a(0) denotes the first element. It is also possible to use square brackets as in the C language, i.e.

a[i] = 3.14;
double p = a[i];

Parts or a vector are retrieved by

a.left(3);   // a vector containing the first 3 elements of a
a.right(2);  // a vector containing the last 2 elements of a
a.mid(1,2);  // a vector containing the 2 elements starting with a(1)
a(2,4);      // a vector containing all elements from a(2) to a(4)
a(2,-1);     // a vector containing all elements from a(2) to the end of a

Alternatively you can use get() methods instead of () or [] operators, e.g.

a.get(4);
a.get(5,-1);

If you have a vector called index_list containing indexes (ivec) you may write

// these give a vector containing elements with indexes in index_list
a(index_list);
a.get(index_list);

If you have a bvec called e.g. bin_list you may write

// these give a vector containing all elements a(i) for which bin_list(i) equals 1
a(bin_list);
a.get(bin_list);

Have a look at the following example:

#include <itpp/itbase.h>
using namespace itpp;
using namespace std;

int main() {
  vec a = linspace(0,1,11);
  ivec index_list = "3 5 2 2";
  bvec bin_list = "1 0 1 0 1 0 1 0 1 0 1";

  cout << "a = " << a << endl;
  cout << "a(index_list) = " << a(index_list) << endl;
  cout << "a.get(bin_list) = " << a.get(bin_list) << endl;
}

When you run this program you will see

a = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0]
a(index_list) = [0.3 0.5 0.2 0.2]
a.get(bin_list) = [0.0 0.2 0.4 0.6 0.8 1.0]

Vector Manipulation

Below follows a listing of the most common vector manipulation commands that are available. All examples are given for an ivec denoted my_ivec, but of course this will work for other vector types as well.

• shift_right:

  // Shift in scalar data (10) at position 0
  my_ivec.shift_right(10);
  
  // Shift in vector at position 0
  my_ivec.shift_right("10 4");

• shift_left:

  // Shift in scalar data (10) at position Size()-1
  my_ivec.shift_left(10);
  
  // Shift in vector at position Size()-1
  my_ivec.shift_left("10 4");

• set_subvector:

  // Replace part of vector from position (10) with the vector "11 13"
  my_ivec.set_subvector(10,"11 13");

• del:

  // Delete element at index (10), making vector size one less
  my_ivec.del(10);

• ins:

  // Insert element at index (10), making vector size one extra
  my_ivec.ins(10);

• split:

  // Splits vector at pos (10). Returns first part, keep second part.
  ivec first_part = my_ivec.split(10);

• elem_mult:

  // Multiply two vectors element wise.
  ivec my_product = elem_mult(my_invec1,my_ivec2);

• elem_div:

  // Dividide two vectors element wise.
  ivec my_product = elem_div(my_invec1,my_ivec2);

• Calculation: +, -, *, /

  a = my_ivec1 + my_ivec2;  // Addition of vectors
  a = my_ivec + 10;         // Addition of vector and scalar
  a = my_ivec1 - my_ivec2;  // Subtraction of vectors
  a = my_ivec - 10;         // Subtraction of vector and scalar
  a = my_ivec * 10;         // Multiplication of vector and scalar
  a = my_ivec / 10;         // Division of vector and scalar

• Calculation: +=, -=, *=, /=, |=

  a += my_ivec;  // Addition of vectors (a = a+my_ivec)
  my_ivec += 10; // Addition of vector and scalar (10)
  a -= my_ivec;  // Subtraction of vectors (a = a-my_ivec)
  my_ivec -= 10; // Subtraction of vector and scalar (10)
  my_ivec *= 10; // Multiplication of vector and scalar (10)
  my_ivec /= 10; // Divsion of vector and scalar (10)
  my_ivec |= a;  // Element wise division

• concat

  a = concat(my_ivec1, my_ivec2);  // concatenation of two vectors

Vector Converters

In order to convert e.g an ivec to a vec we can write some thing like my_vec = to_vec(my_ivec). The following converters are available:

• to_bvec,
• to_svec,
• to_ivec,
• to_vec,
• to_cvec.

Vector Functions

There are several functions that operate on vectors. Some examples are: max, max_index, min, min_index, product, energy, geometric_mean, mean, median, norm, round, variance, ceil_i, floor_i, round_i, find.

Examples of functions that generate different kinds of vectors are: linspace, ones_b, ones_c, ones_i, ones zeros_b. There are several more than these. Please refer to the IT++ reference manual for a description of these.

Using Matrices

Matrices are two-dimensional arrays, and most of their functionality is similar to that of vectors. The predefined matrix types are:

• mat,
• cmat,
• imat,
• smat,
• bmat.

Below follows some examples that are specific for matrices only:

• Define a matrix of type double with 3 rows and 4 columns

  mat a(3,4);

• Define a matrix of type int with 2 rows and 3 columns. A comma (,) or space is used to separate columns and a semicolon (;) is used to separate rows.

  imat a = "1 2 3;4 5 6";

• Access to rows and columns with get_row and get_col

  a.get_row(1); // Returns the second row of the matrix b
  a.get_col(0); // Returns the first column of the matrix b

• Set rows and columns with set_row and set_col

  a.set_row(1,"9 8 7"); // Set second row to "9 8 7"
  a.set_col(0,"7 2");   // Set first column to "7 2"

• The size of a matrix

  // Set the size. "false" means "do not copy"
  a.set_size(4,5,false);
  int nr_of_rows = a.rows();    // return the number of rows
  int nr_of_columns = a.cols(); // return the number of columns

• Access to parts of a matrix

  a(r,c); // Access to a single element.
  a(i);   // Access to a single element. Linear addressing, by rows.
  
  // Returns the sub-matrix from rows r1 to r2 and columns c1 to c2.
  a(r1,r2,c1,c2);

• Copy rows and columns

  // Copy row number "from" to row number "to"
  a.copy_row(to,from)
  
  // Copy column number "from" to column number "to"
  a.copy_col(to,from)

• Swap rows and columns

  // Swap rows number r1 and r2
  a.swap_rows(r1,r2)
  
  // Swap columns number c1 and c2
  a.swap_cols(c1,c2)

• Horizontal and vertical concatenation

  // Equivalent to the MATLAB command c = [a b]
  c = concat_horizontal(a,b);
  
  // Equivalent to the MATLAB command c = [a;b]
  c = concat_vertical(a,b);

Matrix Converters

The following converters are available:

• to_mat,
• to_imat,
• to_cmat,
• to_bmat.

The Array Class

The itbase library contains, among other things, the Array class. An Array can contain any type of data. Below is an example of an Array containing vectors (vec):

#include <itpp/itbase.h>

using namespace itpp;
using namespace std;

int main() {
  Array<vec> my_vec_array(2);
  my_vec_array(0) = linspace(0,1,4);
  my_vec_array(1) = "0.1 0.2 0.3 0.4 0.3 0.2 0.1";
  cout << "my_vec_array = " << my_vec_array << endl;

  return 0;
}

Random Vectors, Matrices, and Generators

Random Vectors and Matrices

Random vectors and matrices are easily obtained by using these predefined functions:

• randb: Generates a random bit vector or matrix
• randu: Generates a random uniform vector or matrix
• randi: Generates a random index vector or matrix
• randray: Generates a random Rayleigh vector or matrix
• randrice: Generates a random Rice vector or matrix
• randexp: Generates a random Exponential vector or matrix
• randn: Generates a random Gaussian vector or matrix
• randn_c: Generates a random complex Gaussian vector or matrix

Random Number Generators (RNG)

The following discrete valued random number generators are available. More information about these can be found in the IT++ reference manual.

• Bernoulli_RNG
• I_Uniform_RNG

The following continuous valued random number generators are available.

• Uniform_RNG
• Exponential_RNG
• Normal_RNG
• Complex_Normal_RNG
• AR1_Normal_RNG
• Weibull_RNG
• Rayleigh_RNG
• Rice_RNG

Deterministic Sources

The following deterministic sources are available:

• Sine_Source
• Square_Source
• Triangle_Source
• Sawtooth_Source
• Impulse_Source
• Pattern_Source

Filter Classes and Functions

The following filter classes are available:

• AR_Filter
• MA_Filter
• ARMA_Filter
• Freq_Filt

The following filter functions are available:

• filter

Signal Processing Functions

The following signal processing functions are available:

• a2k, k2a, a2lar, k2lar, lpc, levinsson, lerouxguegen
• fft, ifft, fft_real, ifft_real
• dct, idct
• spectrum
• cov, xcorr
• chirp
• dht, dht2, dwht, dhwt2, self_dht, self_dwht
• filter_spectrum
• filter_whiteness

Timer Classes

The Real_Timer class can be used to measure execution time of a program as in the following example:

#include <itpp/itbase.h>

using namespace itpp;
using namespace std;

int main() {
  long sum = 0;
  Real_Timer my_timer;

  my_timer.tic();
  for (int i=0; i<10000000; i++) {
    sum += i;
  }
  my_timer.toc_print();

  cout << "The sum is " << sum << endl;

  return 0;
}

Reading and Writing to Files

The following example saves the variable a to the file my_file_name.it:

#include <itpp/itbase.h>

using namespace itpp;

int main() {
  it_file my_file("my_file_name.it");
  vec a = "1.0 2.0 3.0 4.0";
  my_file << Name("a") << a;

  return 0;
}

The following example reads the variable a from the file my_file_name.it and prints it:

#include <itpp/itbase.h>

using namespace itpp;
using namespace std;

int main() {
  it_file my_file("my_file_name.it");
  vec a;
  my_file >> Name("a") >> a;
  cout << "a = " << a << endl;

  return 0;
}

Note that *.it files can be read and written in Matlab/Octave by using the itload.m and itsave.m functions.

Also available is the class it_ifile that can only be used for reading of files.