itpp Namespace Reference

itpp namespace More...

Classes
class	Array
	General array class. More...
class	bin
	Binary arithmetic (boolean) class. More...
class	bfstream_base
	Base class for binary file classesThis class serves as a base class for the classes bofstream, bifstream, and bfstream. It controls the endianity (i.e. the byte order of multibyte numbers on the disk) of the inhereted classes. More...
class	bofstream
	Binary Outfile Class. More...
class	bifstream
	Binary Infile Class. More...
class	bfstream
	Binary in/out-file Class. More...
class	Circular_Buffer
	General circular buffer class. More...
class	Factory
	Base class for class factories. More...
class	GF2mat_sparse_alist
	Parameterized "alist" representation of sparse GF(2) matrix. More...
class	GF2mat
	Class for dense GF(2) matrices. More...
class	it_file_base
	Base class for it_ifile and it_file. More...
class	it_ifile
	The IT++ file format reading class. More...
class	it_file
	The IT++ file format reading and writing class. More...
class	Name
	Automatic naming when savingAn easy way to give a variable a name and optionally description when saving. Usage: More...
class	it_file_base_old
	Base class for it_ifile_old and it_file_old. More...
class	it_ifile_old
	The old (version 2) IT++ file format reading class. More...
class	it_file_old
	The old (version 2) IT++ file format reading and writing class. More...
class	Mat
	Matrix Class (Templated) More...
class	Parser
	Argument Parser Class. More...
class	Random_Generator
	Base class for random (stochastic) sources. More...
class	Bernoulli_RNG
	Bernoulli distribution. More...
class	I_Uniform_RNG
	Integer uniform distributionExample: Generation of random uniformly distributed integers in the interval [0,10]. More...
class	Uniform_RNG
	Uniform distribution. More...
class	Exponential_RNG
	Exponential distribution. More...
class	Normal_RNG
	Normal distributionNormal (Gaussian) random variables, using a simplified Ziggurat method. More...
class	Gamma_RNG
	Gamma distributionGenerate samples from Gamma(alpha,beta) density, according to the following equation: . More...
class	Laplace_RNG
	Laplacian distribution. More...
class	Complex_Normal_RNG
	A Complex Normal Source. More...
class	AR1_Normal_RNG
	Filtered normal distribution. More...
class	Weibull_RNG
	Weibull distribution. More...
class	Rayleigh_RNG
	Rayleigh distribution. More...
class	Rice_RNG
	Rice distribution. More...
class	Sparse_Mat
	Templated Sparse Matrix Class. More...
class	Sort
	Class for sorting of vectors. More...
class	Stack
	General stack class. More...
class	Sparse_Vec
	Templated sparse vector class. More...
class	Timer
	A virtual base class for timers. More...
class	CPU_Timer
	A CPU time timer classMeasures the time spent by the CPU on the current process. If two processes are running concurrently, one real seconds equal 5 CPU seconds per process. The resolution is not very good (in the order of 0.01 seconds). More...
class	Real_Timer
	A real time timer classMeasures real time. More...
class	Vec
	Vector Class (Templated) More...
class	BCH
	Class for binary, narrow-sense BCH codes. More...
class	Fading_Generator
	Fading generator class. More...
class	Independent_Fading_Generator
	Independent (random) fading generator class. More...
class	Static_Fading_Generator
	Static fading generator class. More...
class	Correlated_Fading_Generator
	Correlated (random) fading generator class. More...
class	Rice_Fading_Generator
	Rice type fading generator class. More...
class	FIR_Fading_Generator
	FIR type Fading generator class. More...
class	IFFT_Fading_Generator
	IFFT type Fading generator class. More...
class	Channel_Specification
	General specification of a time-domain multipath channel. More...
class	TDL_Channel
	Tapped Delay Line (TDL) channel model. More...
class	BSC
	A Binary Symetric Channel with crossover probability p. More...
class	AWGN_Channel
	Ordinary AWGN Channel for cvec or vec inputs and outputs. More...
class	Channel_Code
	Generic Channel Code class. More...
class	Dummy_Code
	Dummy Channel Code class. More...
class	Convolutional_Code
	Binary Convolutional rate 1/n class. More...
class	CRC_Code
	Cyclic Redundancy Check Codes. More...
class	Extended_Golay
	Extended Golay code (24,12,8). More...
class	BERC
	Bit Error Rate Counter (BERC) Class. More...
class	BLERC
	Class for counting block error rates. More...
class	EXIT
	EXtrinsic Information Transfer (EXIT) chart. More...
class	GF
	Galois Field GF(q). More...
class	GFX
	Polynomials over GF(q)[x], where q=2^m, m=1,...,16. More...
class	Hamming_Code
	Binary Hamming codes. More...
class	Block_Interleaver
	Block Interleaver Class. More...
class	Cross_Interleaver
	Cross Interleaver Class. More...
class	Sequence_Interleaver
	Sequence Interleaver Class. More...
class	LDPC_Parity
	LDPC parity check matrix generic class. More...
class	LDPC_Parity_Unstructured
	Pure abstract class for unstructured LDPC matrices. More...
class	LDPC_Parity_Irregular
	Irregular LDPC code generator class. More...
class	LDPC_Parity_Regular
	Regular LDPC code generator class. More...
class	BLDPC_Parity
	Block LDPC code parity-check matrix. More...
class	LDPC_Generator
	LDPC Generator pure virtual base class. More...
class	LDPC_Generator_Systematic
	Systematic LDPC Generator class. More...
class	BLDPC_Generator
	Block LDPC Generator class. More...
class	LDPC_Code
	Low-density parity check (LDPC) codec. More...
class	LLR_calc_unit
	Log-likelihood algebra calculation unit. More...
class	Modulator
	General modulator for 1D or 2D signal constellations. More...
class	QAM
	M-ary QAM modulator with square lattice. More...
class	PSK
	M-ary PSK modulator. More...
class	QPSK
	QPSK modulator. More...
class	BPSK_c
	BPSK modulator with complex symbols. More...
class	BPSK
	BPSK modulator with real symbols. More...
class	PAM_c
	M-ary PAM modulator with complex symbols. More...
class	PAM
	M-ary PAM modulator with real symbols. More...
class	Modulator_ND
	Base class for an N-dimensional (ND) vector (MIMO) modulator. More...
class	Modulator_NRD
	Base class for N-dimensional vector (MIMO) channel modulators/demodulators with real-valued components. More...
class	Modulator_NCD
	Base class for vector (MIMO) channel modulator/demodulators with complex valued components. More...
class	ND_UPAM
	Real-valued MIMO channel with uniform PAM along each dimension. More...
class	ND_UQAM
	Complex MIMO channel with uniform QAM per dimension. More...
class	ND_UPSK
class	Multilateration
	Multilateration class for 3D indoor localization More...
class	OFDM
	Class for modulating and demodulation of OFDM signals using the FFT. More...
class	Pulse_Shape
	General FIR Pulse Shape. More...
class	Raised_Cosine
	Raised Cosine (RC) Pulse Shaper. More...
class	Root_Raised_Cosine
	(Square) Root Raised Cosine (RRC) Pulse Shaper More...
class	Punctured_Convolutional_Code
	Binary Punctured Convolutional Code Class. More...
class	Rec_Syst_Conv_Code
	A Recursive Systematic Convolutional Encoder/Decoder class. More...
class	Reed_Solomon
	Reed-Solomon Codes. More...
class	LFSR
	Binary Linear Feedback Shift Register (LFSR) More...
class	Gold
	Gold Sequences. More...
class	SISO
	Soft Input Soft Output (SISO) modules. More...
class	Spread_1d
	Spreading of float symbols to float output. More...
class	Spread_2d
	Spreading of complex symbols to complex output. More...
class	Multicode_Spread_1d
	Multicode spreading of float symbols. More...
class	Multicode_Spread_2d
	Multicode spreading of complex symbols to complex output. More...
class	STC
	Space Time block Codes (STC) class. More...
class	Turbo_Codec
	Turbo encoder/decoder Class. More...
class	Punctured_Turbo_Codec
	Punctured turbo encoder/decoder Class. More...
class	CFix
	Complex fixed-point data type. More...
class	CFixed
	Templated complex fixed-point data type. More...
class	Fix
	Fixed-point data type. More...
class	Fix_Base
	Base class for fixed-point data types. More...
class	Fix_Factory
	Class factory for fixed-point data types Fix and CFix. More...
class	Fixed
	Templated fixed-point data type. More...
class	Newton_Search
	Newton Search. More...
class	Line_Search
	Line Search. More...
class	Base_Event
	Base Event Class. More...
struct	Compare_Base_Event_Times
	Compare to events, Returns true if expire time of event1 is larger than the expire time of event2. More...
class	Event_Queue
	Event Queue class. More...
class	Event
	An Event class that executes a function when the event expires. More...
class	Data_Event
	An Event class that executes a function with some data as input when the event expires. More...
class	Front_Drop_Queue
	ADD DOCUMENTATION HERE. More...
class	Packet
class	L3_Packet_Info
class	Link_Packet
class	ACK
class	Packet_Channel
	ADD DOCUMENTATION HERE. More...
class	ACK_Channel
	ADD DOCUMENTATION HERE. More...
class	Packet_Generator
class	Poisson_Packet_Generator
class	Constant_Rate_Packet_Generator
class	Burst_WWW_Packet_Generator
class	Sink
class	Selective_Repeat_ARQ_Sender
class	Selective_Repeat_ARQ_Receiver
class	Signal
	Signals and slots. More...
class	Base_Slot
	Base Slot class. More...
class	Slot
	Slot Class. More...
class	TTimer
class	Sequence_Number
class	TCP_Segment
class	TCP_Packet
class	TCP_Sender
class	TCP_Receiver_Buffer
class	TCP_Receiver
class	TCP_Server_Application
class	TCP_Client_Application
class	Fast_ICA
	Fast_ICA Fast Independent Component Analysis (Fast ICA)The software is based upon original FastICA for Matlab from A. Hyvarinen. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks, 10(3), pp. 626-634, 1999. More...
class	Filter
	Virtual Filter Base Class.The class is templated as follows: More...
class	MA_Filter
	Moving Average Filter Base Class.This class implements a moving average (MA) filter according to where b is the filter coefficients, x is the input and y is the output. More...
class	AR_Filter
	Autoregressive (AR) Filter Base Class.This class implements a autoregressive (AR) filter according to where a is the filter coefficients, x is the input and y is the output. More...
class	ARMA_Filter
	Autoregressive Moving Average (ARMA) Filter Base Class.This class implements a autoregressive moving average (ARMA) filter according to . More...
class	Freq_Filt
	Freq_Filt Frequency domain filtering using the overlap-add techniqueThe Freq_Filt class implements an FFT based filter using the overlap-add technique. The data is filtered by first transforming the input sequence into the frequency domain with an efficient FFT implementation (i.e. FFTW) and then multiplied with a Fourier transformed version of the impulse response. The resulting data is then inversed Fourier transformed to return a filtered time domain signal. More...
class	Sine_Source
	Sine-wave source. More...
class	Square_Source
	Square-wave source. More...
class	Triangle_Source
	Triangle-wave source. More...
class	Sawtooth_Source
	Sawtooth-wave source. More...
class	Impulse_Source
	Impulse source. More...
class	Pattern_Source
	Pattern source. More...
class	Audio_Stream_Description
	Description of audio stream. More...
class	SND_In_File
	Class to read audio data from au file. More...
class	SND_Out_File
	A class to write SND-files (the .au format) More...
class	SND_IO_File
	A class for doing both input and output of audio samples. More...
class	Audio_Sample< enc_mulaw8 >
	uLaw-encoded Audio samples. More...
class	Audio_Sample< enc_linear8 >
	8-bit PCM encoded audio samples. More...
class	Audio_Sample< enc_linear16 >
	16-bit PCM encoded audio samples More...
class	Sample_24
	Small class to represent 24-bit PCM samples. More...
class	Audio_Sample< enc_linear24 >
	24-bit PCM encoded audio samples. More...
class	Audio_Sample< enc_linear32 >
	32-bit PCM encoded audio samples. More...
class	Audio_Sample< enc_float >
	Audio samples encoded as floats. More...
class	Audio_Sample< enc_double >
	Audio samples encoded as doubles. More...
class	Audio_Sample< enc_alaw8 >
	aLaw-encoded Audio samples. More...
class	GMM
	Gaussian Mixture Model Class. More...
class	Vector_Quantizer
	Class for vector quantization. More...
class	Scalar_Quantizer
	Class for vector quantization. More...
class	Histogram
	Histogram computation class. More...
class	Stat
	A class for sampling a signal and calculating statistics. More...
class	MOG_diag
	Diagonal Mixture of Gaussians (MOG) class. More...
class	MOG_diag_EM_sup
	support class for MOG_diag_ML() and MOG_diag_MAP() More...
class	MOG_diag_kmeans_sup
	support class for MOG_diag_kmeans() More...
class	MOG_generic
	Generic Mixture of Gaussians (MOG) class. Used as a base for other MOG classes. More...

Typedefs
typedef Sparse_Vec< bin >	GF2vec_sparse
	Sparse GF(2) vector.
typedef Sparse_Mat< bin >	GF2mat_sparse
	Sparse GF(2) matrix.
typedef Normal_RNG	Gauss_RNG
	Gauss_RNG is the same as Normal Source.
typedef AR1_Normal_RNG	AR1_Gauss_RNG
	AR1_Gauss_RNG is the same as AR1_Normal_RNG.
typedef Vec< CFix >	cfixvec
	Typedef for complex fixed-point vector type.
typedef Mat< CFix >	cfixmat
	Typedef for complex fixed-point matrix type.
typedef CFixed< 1, TC, WRAP >	cfixed1
	Typedefs for CFixed (cfixed1, cfixed2, ..., cfixed64)
typedef Vec< Fix >	fixvec
	Typedef for fixed-point vector type.
typedef Mat< Fix >	fixmat
	Typedef for fixed-point matrix type.
typedef int64_t	fixrep
	Representation for fixed-point data types.
typedef Fixed< 1, TC, WRAP >	fixed1
	Typedefs for Fixed (fixed1, fixed2, ..., fixed64)
typedef Fixed< 1, US, WRAP >	ufixed1
	Typedefs for unsigned Fixed (ufixed1, ufixed2, ..., ufixed64)
typedef Fixed< 1, TC, SAT >	sfixed1
	Typedefs for saturated Fixed (sfixed1, sfixed2, ..., sfixed64)
typedef Fixed< 1, US, SAT >	sufixed1
	Typedefs for saturated unsigned Fixed (sufixed1, sufixed2, ..., sufixed64)
typedef double	Ttype
	64-bit floating point time

Enumerations
enum	error_msg_style { Full, Minimum }
	Style of assert, error and warning messages.
enum	SORTING_METHOD { INTROSORT = 0, QUICKSORT = 1, HEAPSORT = 2, INSERTSORT = 3 }
	Sorting algorithms that can be used in a Sort class. More...
enum	CHANNEL_PROFILE {   ITU_Vehicular_A, ITU_Vehicular_B, ITU_Pedestrian_A, ITU_Pedestrian_B,   COST207_RA, COST207_RA6, COST207_TU, COST207_TU6alt,   COST207_TU12, COST207_TU12alt, COST207_BU, COST207_BU6alt,   COST207_BU12, COST207_BU12alt, COST207_HT, COST207_HT6alt,   COST207_HT12, COST207_HT12alt, COST259_TUx, COST259_RAx,   COST259_HTx }
	Predefined channel profiles. Includes LOS and Doppler spectrum settings.
enum	FADING_TYPE { Independent, Static, Correlated }
	Fading generator type: Independent (default), Static or Correlated.
enum	CORRELATED_METHOD { Rice_MEDS, IFFT, FIR }
	Correlated fading generation methods: Rice_MEDS (default), IFFT or FIR.
enum	RICE_METHOD { MEDS }
	Rice fading generation methods: MEDS.
enum	DOPPLER_SPECTRUM {   Jakes = 0, J = 0, Classic = 0, C = 0,   GaussI = 1, Gauss1 = 1, GI = 1, G1 = 1,   GaussII = 2, Gauss2 = 2, GII = 2, G2 = 2 }
	Predefined Doppler spectra.
enum	CONVOLUTIONAL_CODE_TYPE { MFD, ODS }
	Type of Convolutional Code.
enum	CONVOLUTIONAL_CODE_METHOD { Trunc, Tail, Tailbite }
	Encoding and decoding methods for Convolutional codes.
enum	Soft_Method { LOGMAP, APPROX }
	Soft demodulation methods. More...
enum	e_mode { TC, US }
	Sign encoding modes (aligned with SystemC) More...
enum	o_mode {   SAT, SAT_ZERO, SAT_SYM, WRAP,   WRAP_SM }
	Overflow modes (aligned with SystemC) More...
enum	q_mode {   RND, RND_ZERO, RND_MIN_INF, RND_INF,   RND_CONV, RND_CONV_ODD, TRN, TRN_ZERO }
	Quantization modes (aligned with SystemC) More...
enum	output_mode { OUTPUT_FIX, OUTPUT_FIX_SHIFT, OUTPUT_FLOAT, OUTPUT_FLOAT_SHIFT }
	Output modes. More...
enum	Newton_Search_Method { BFGS }
	Newton Search method.
enum	Line_Search_Method { Soft, Exact }
	Line Search method.
enum	Audio_Encoding {   enc_unknown = 0, enc_mulaw8 = 1, enc_alaw8 = 27, enc_linear8 = 2,   enc_linear16 = 3, enc_linear24 = 4, enc_linear32 = 5, enc_float = 6,   enc_double = 7 }
	Supported encoding types for audio samples. More...

Functions
bin	mxArray2bin (const mxArray *in)
	Convert the matlab-format mxArray to bin.
short	mxArray2short (const mxArray *in)
	Convert the matlab-format mxArray to short.
int	mxArray2int (const mxArray *in)
	Convert the matlab-format mxArray to int.
double	mxArray2double (const mxArray *in)
	Convert the matlab-format mxArray to double.
std::complex< double >	mxArray2double_complex (const mxArray *in)
	Convert the matlab-format mxArray to complex<double>
std::string	mxArray2string (const mxArray *in)
	Convert the matlab-format mxArray to string.
bvec	mxArray2bvec (const mxArray *in)
	Convert the matlab-format mxArray to bvec.
svec	mxArray2svec (const mxArray *in)
	Convert the matlab-format mxArray to svec.
ivec	mxArray2ivec (const mxArray *in)
	Convert the matlab-format mxArray to ivec.
vec	mxArray2vec (const mxArray *in)
	Convert the matlab-format mxArray to vec.
cvec	mxArray2cvec (const mxArray *in)
	Convert the matlab-format mxArray to cvec.
bmat	mxArray2bmat (const mxArray *in)
	Convert the matlab-format mxArray to bmat.
smat	mxArray2smat (const mxArray *in)
	Convert the matlab-format mxArray to smat.
imat	mxArray2imat (const mxArray *in)
	Convert the matlab-format mxArray to imat.
mat	mxArray2mat (const mxArray *in)
	Convert the matlab-format mxArray to mat.
cmat	mxArray2cmat (const mxArray *in)
	Convert the matlab-format mxArray to cmat.
void	bin2mxArray (const bin &in, mxArray *out)
	Convert bin to the matlab-format mxArray.
void	short2mxArray (const short &in, mxArray *out)
	Convert short to the matlab-format mxArray.
void	int2mxArray (const int &in, mxArray *out)
	Convert int to the matlab-format mxArray.
void	double2mxArray (const double &in, mxArray *out)
	Convert double to the matlab-format mxArray.
void	double_complex2mxArray (const std::complex< double > &in, mxArray *out)
	Convert complex<double> to the matlab-format mxArray.
void	string2mxArray (const std::string &in, mxArray *&out)
	Convert string to the matlab-format mxArray.
void	bvec2mxArray (const bvec &in, mxArray *out)
	Convert bvec to the matlab-format mxArray.
void	svec2mxArray (const svec &in, mxArray *out)
	Convert svec to the matlab-format mxArray.
void	ivec2mxArray (const ivec &in, mxArray *out)
	Convert ivec to the matlab-format mxArray.
void	vec2mxArray (const vec &in, mxArray *out)
	Convert vec to the matlab-format mxArray.
void	cvec2mxArray (const cvec &in, mxArray *out)
	Convert cvec to the matlab-format mxArray.
void	bmat2mxArray (const bmat &in, mxArray *out)
	Convert bmat to the matlab-format mxArray.
void	smat2mxArray (const smat &in, mxArray *out)
	Convert smat to the matlab-format mxArray.
void	imat2mxArray (const imat &in, mxArray *out)
	Convert imat to the matlab-format mxArray.
void	mat2mxArray (const mat &in, mxArray *out)
	Convert mat to the matlab-format mxArray.
void	cmat2mxArray (const cmat &in, mxArray *out)
	Convert cmat to the matlab-format mxArray.
void	mxArray2Csvec (const mxArray *in, short *out)
	Convert the matlab-format mxArray to C-format pointer to short.
void	mxArray2Civec (const mxArray *in, int *out)
	Convert the matlab-format mxArray to C-format pointer to int.
void	mxArray2Cvec (const mxArray *in, double *out)
	Convert the matlab-format mxArray to C-format pointer to double.
void	mxArray2Ccvec (const mxArray *in, double *out_real, double *out_imag)
	Convert the matlab-format mxArray to C-format pointers to double (real and imaginary parts)
void	mxArray2Csmat (const mxArray *in, short **out)
	Convert the matlab-format mxArray to C-format pointer to pointer to short.
void	mxArray2Cimat (const mxArray *in, int **out)
	Convert the matlab-format mxArray to C-format pointer to pointer to int.
void	mxArray2Cmat (const mxArray *in, double **out)
	Convert the matlab-format mxArray to C-format pointer to pointer to double.
void	mxArray2Ccmat (const mxArray *in, double **out_real, double **out_imag)
	Convert the matlab-format mxArray to C-format pointer to pointer to double (real and imaginary parts)
void	Csvec2mxArray (short *in, mxArray *out)
	Convert C-format pointer to short to matlab-format mxArray.
void	Civec2mxArray (int *in, mxArray *out)
	Convert C-format pointer to int to matlab-format mxArray.
void	Cvec2mxArray (double *in, mxArray *out)
	Convert C-format pointer to double to matlab-format mxArray.
void	Ccvec2mxArray (double *in_real, double *in_imag, mxArray *out)
	Convert C-format pointers to double (real and imaginary parts) to matlab-format mxArray.
void	Csmat2mxArray (short **in, mxArray *out)
	Convert C-format pointer to pointer to short to matlab-format mxArray.
void	Cimat2mxArray (int **in, mxArray *out)
	Convert C-format pointer to pointer to int to matlab-format mxArray.
void	Cmat2mxArray (double **in, mxArray *out)
	Convert C-format pointer to pointer to double to matlab-format mxArray.
void	Ccmat2mxArray (double **in_real, double **in_imag, mxArray *out)
	Convert C-format pointer to pointer to double (real and imaginary parts) to matlab-format mxArray.
template<class T >
const Array< T >	concat (const Array< T > &a, const T &e)
	Append element e to the end of the Array a.
template<class T >
const Array< T >	concat (const T &e, const Array< T > &a)
	Append element e to the beginning of the Array a.
template<class T >
const Array< T >	concat (const Array< T > &a1, const Array< T > &a2)
	Concat Arrays a1 and a2.
template<class T >
const Array< T >	concat (const Array< T > &a1, const Array< T > &a2, const Array< T > &a3)
	Concat Arrays a1, a2 and a3.
double	besselj (int nu, double x)
	Bessel function of first kind of order nu for nu integer.
vec	besselj (int nu, const vec &x)
	Bessel function of first kind of order nu for nu integer.
double	besselj (double nu, double x)
	Bessel function of first kind of order nu. nu is real.
vec	besselj (double nu, const vec &x)
	Bessel function of first kind of order nu. nu is real.
double	bessely (int nu, double x)
	Bessel function of second kind of order nu. nu is integer.
vec	bessely (int nu, const vec &x)
	Bessel function of second kind of order nu. nu is integer.
double	bessely (double nu, double x)
	Bessel function of second kind of order nu. nu is real.
vec	bessely (double nu, const vec &x)
	Bessel function of second kind of order nu. nu is real.
double	besseli (double nu, double x)
	Modified Bessel function of first kind of order nu. nu is double. x is double.
vec	besseli (double nu, const vec &x)
	Modified Bessel function of first kind of order nu. nu is double. x is double.
double	besselk (int nu, double x)
	Modified Bessel function of second kind of order nu. nu is double. x is double.
vec	besselk (int nu, const vec &x)
	Modified Bessel function of second kind of order nu. nu is double. x is double.
std::ostream &	operator<< (std::ostream &output, const bin &inbin)
	Output stream of bin.
std::istream &	operator>> (std::istream &input, bin &outbin)
	Input stream of bin.
bin	abs (const bin &inbin)
	absolute value of bin
template<typename T1 , typename T2 >
void	read_endian (T1 &st, T2 &data, bool switch_endian=false)
	Read binary data and optionally switch endianness.
template<typename T1 , typename T2 >
void	write_endian (T1 &st, T2 data, bool switch_endian=false)
	Write binary data and optionally switch endianness.
bool	exist (const std::string &name)
	Checks if a file named name already exists on the disk.
template<class T >
bvec	to_bvec (const Vec< T > &v)
	Converts a Vec<T> to bvec.
template<class T >
svec	to_svec (const Vec< T > &v)
	Converts a Vec<T> to svec.
template<class T >
ivec	to_ivec (const Vec< T > &v)
	Converts a Vec<T> to ivec.
template<class T >
vec	to_vec (const Vec< T > &v)
	Converts a Vec<T> to vec.
template<class T >
cvec	to_cvec (const Vec< T > &v)
	Converts a Vec<T> to cvec.
template<class T >
cvec	to_cvec (const Vec< T > &real, const Vec< T > &imag)
	Converts real and imaginary Vec<T> to cvec.
ivec	to_ivec (int s)
	Converts an int to ivec.
vec	to_vec (double s)
	Converts an double to vec.
cvec	to_cvec (double real, double imag)
	Converts real and imaginary double to cvec.
template<class T >
bmat	to_bmat (const Mat< T > &m)
	Converts a Mat<T> to bmat.
template<class T >
smat	to_smat (const Mat< T > &m)
	Converts a Mat<T> to smat.
template<class T >
imat	to_imat (const Mat< T > &m)
	Converts a Mat<T> to imat.
template<class T >
mat	to_mat (const Mat< T > &m)
	Converts a Mat<T> to mat.
template<class T >
cmat	to_cmat (const Mat< T > &m)
	Converts a Mat<T> to cmat.
template<class T >
cmat	to_cmat (const Mat< T > &real, const Mat< T > &imag)
	Converts real and imaginary Mat<T> to cmat.
ITPP_EXPORT bvec	dec2bin (int length, int index)
	Convert a decimal int index to bvec using length bits in the representation.
ITPP_EXPORT void	dec2bin (int index, bvec &v)
	Convert a decimal int index to bvec. Value returned in v.
ITPP_EXPORT bvec	dec2bin (int index, bool msb_first=true)
	Convert a decimal int index to bvec with the first bit as MSB if msb_first == true.
ITPP_EXPORT int	bin2dec (const bvec &inbvec, bool msb_first=true)
	Convert a bvec to decimal int with the first bit as MSB if msb_first == true.
ITPP_EXPORT bvec	oct2bin (const ivec &octalindex, short keepzeros=0)
	Convert ivec of octal form to bvec.
ITPP_EXPORT ivec	bin2oct (const bvec &inbits)
	Convert bvec to octal ivec.
ITPP_EXPORT ivec	bin2pol (const bvec &inbvec)
	Convert bvec to polar binary representation as ivec.
ITPP_EXPORT bvec	pol2bin (const ivec &inpol)
	Convert binary polar ivec to bvec.
double	rad_to_deg (double x)
	Convert radians to degrees.
double	deg_to_rad (double x)
	Convert degrees to radians.
ITPP_EXPORT double	round (double x)
	Round to nearest integer, return result in double.
ITPP_EXPORT vec	round (const vec &x)
	Round to nearest integer.
ITPP_EXPORT mat	round (const mat &x)
	Round to nearest integer.
ITPP_EXPORT int	round_i (double x)
	Round to nearest integer.
ITPP_EXPORT ivec	round_i (const vec &x)
	Round to nearest integer and return ivec.
ITPP_EXPORT imat	round_i (const mat &x)
	Round to nearest integer and return imat.
vec	ceil (const vec &x)
	Round to nearest upper integer.
mat	ceil (const mat &x)
	Round to nearest upper integer.
int	ceil_i (double x)
	The nearest larger integer.
ITPP_EXPORT ivec	ceil_i (const vec &x)
	Round to nearest upper integer.
ITPP_EXPORT imat	ceil_i (const mat &x)
	Round to nearest upper integer.
vec	floor (const vec &x)
	Round to nearest lower integer.
mat	floor (const mat &x)
	Round to nearest lower integer.
int	floor_i (double x)
	The nearest smaller integer.
ITPP_EXPORT ivec	floor_i (const vec &x)
	Round to nearest lower integer.
ITPP_EXPORT imat	floor_i (const mat &x)
	Round to nearest lower integer.
double	round_to_zero (double x, double threshold=1e-14)
	Round x to zero if abs(x) is smaller than threshold.
std::complex< double >	round_to_zero (const std::complex< double > &x, double threshold=1e-14)
	Round each part of x smaller than threshold to zero.
vec	round_to_zero (const vec &x, double threshold=1e-14)
	Round each element to zero if element < threshold.
mat	round_to_zero (const mat &x, double threshold=1e-14)
	Round each element to zero if element < threshold.
ITPP_EXPORT cvec	round_to_zero (const cvec &x, double threshold=1e-14)
	Round each element to zero if element < threshold.
ITPP_EXPORT cmat	round_to_zero (const cmat &x, double threshold=1e-14)
	Round each element to zero if element < threshold.
double	round_to_infty (const double in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for numbers greater than threshold.
std::complex< double >	round_to_infty (const std::complex< double > &in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for complex numbers whose real and imaginary parts are greater than threshold.
vec	round_to_infty (const vec &in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for vectors greater than threshold.
mat	round_to_infty (const mat &in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for matrices greater than threshold.
ITPP_EXPORT cvec	round_to_infty (const cvec &in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for complex vectors greater than threshold.
ITPP_EXPORT cmat	round_to_infty (const cmat &in, const double threshold=1e9)
	Remove trailing digits, found after the decimal point, for complex matrices greater than threshold.
int	gray_code (int x)
	Convert to Gray Code.
template<typename T >
std::string	to_str (const T &i)
	Convert anything to string.
ITPP_EXPORT std::string	to_str (const double &i, const int precision)
	Convert double to string.
void	copy_vector (int n, const double *x, double *y)
void	copy_vector (int n, const std::complex< double > *x, std::complex< double > *y)
void	copy_vector (int n, const double *x, int incx, double *y, int incy)
void	copy_vector (int n, const std::complex< double > *x, int incx, std::complex< double > *y, int incy)
void	swap_vector (int n, double *x, double *y)
void	swap_vector (int n, std::complex< double > *x, std::complex< double > *y)
void	swap_vector (int n, double *x, int incx, double *y, int incy)
void	swap_vector (int n, std::complex< double > *x, int incx, std::complex< double > *y, int incy)
void	scal_vector (int n, double alpha, double *x)
void	scal_vector (int n, std::complex< double > alpha, std::complex< double > *x)
void	scal_vector (int n, double alpha, double *x, int incx)
void	scal_vector (int n, std::complex< double > alpha, std::complex< double > *x, int incx)
void	axpy_vector (int n, double alpha, const double *x, double *y)
void	axpy_vector (int n, std::complex< double > alpha, const std::complex< double > *x, std::complex< double > *y)
void	axpy_vector (int n, double alpha, const double *x, int incx, double *y, int incy)
void	axpy_vector (int n, std::complex< double > alpha, const std::complex< double > *x, int incx, std::complex< double > *y, int incy)
template<class T >
void	create_elements (T *&ptr, int n, const Factory &)
	Create an n-length array of T to be used as Array, Vec or Mat elements.
template<>
void	create_elements< unsigned char > (unsigned char *&ptr, int n, const Factory &)
	Specialization for unsigned char data arrays (used in GF2Mat)
template<>
void	create_elements< bin > (bin *&ptr, int n, const Factory &)
	Specialization for binary data arrays.
template<>
void	create_elements< short int > (short int *&ptr, int n, const Factory &)
	Specialization for short integer data arrays.
template<>
void	create_elements< int > (int *&ptr, int n, const Factory &)
	Specialization for integer data arrays.
template<>
void	create_elements< double > (double *&ptr, int n, const Factory &)
	Specialization for 16-byte aligned double data arrays.
template<>
void	create_elements< std::complex< double > > (std::complex< double > *&ptr, int n, const Factory &)
	Specialization for 16-byte aligned complex double data arrays.
template<class T >
void	destroy_elements (T *&ptr, int n)
	Destroy an array of Array, Vec or Mat elements.
template<>
void	destroy_elements< unsigned char > (unsigned char *&ptr, int)
	Specialization for unsigned char data arrays (used in GF2Mat)
template<>
void	destroy_elements< bin > (bin *&ptr, int)
	Specialization for binary data arrays.
template<>
void	destroy_elements< short int > (short int *&ptr, int)
	Specialization for short integer data arrays.
template<>
void	destroy_elements< int > (int *&ptr, int)
	Specialization for integer data arrays.
template<>
void	destroy_elements< double > (double *&ptr, int)
	Specialisation for 16-byte aligned double data arrays.
template<>
void	destroy_elements< std::complex< double > > (std::complex< double > *&ptr, int)
	Specialisation for 16-byte aligned complex double data arrays.
template<class T >
void	create_elements (Array< T > *&ptr, int n, const Factory &f)
	Create an n-length array of Array<T> to be used as Array elements.
template<class T >
void	create_elements (Mat< T > *&ptr, int n, const Factory &f)
	Create an n-length array of Mat<T> to be used as Array elements.
template<class T >
void	create_elements (Vec< T > *&ptr, int n, const Factory &f)
	Create an n-length array of Vec<T> to be used as Array elements.
void	sub_v_vT_m (mat &m, const vec &v)
	Calculates m=m-v*v'*m.
void	sub_m_v_vT (mat &m, const vec &v)
	Calculates m=m-m*v*v'.
GF2mat	gf2dense_eye (int m)
	GF(2) Identity matrix.
GF2mat	operator* (const GF2mat &X, const GF2mat &Y)
	GF(2) matrix multiplication.
bvec	operator* (const GF2mat &X, const bvec &y)
	GF(2) matrix multiplication with "regular" binary vector.
GF2mat	mult_trans (const GF2mat &X, const GF2mat &Y)
	Multiplication X*Y' where X and Y are GF(2) matrices.
GF2mat	operator+ (const GF2mat &X, const GF2mat &Y)
	GF(2) matrix addition.
std::ostream &	operator<< (std::ostream &os, const GF2mat &X)
	Output stream (plain text) operator for dense GF(2) matrices.
it_file &	operator<< (it_file &f, const GF2mat &X)
it_ifile &	operator>> (it_ifile &f, GF2mat &X)
template<typename T , typename Ftn >
Vec< T >	apply_functor (Ftn f, const Vec< T > &v)
	Help function to apply function object to Vec<T>
template<typename T >
Vec< T >	apply_function (T(*f)(T), const Vec< T > &v)
	Help function to call for a function: Vec<T> function(Vec<T>)
template<typename T >
Vec< T >	apply_function (T(*f)(const T &), const Vec< T > &v)
	Help function to call for a function: Vec<T> function(const Vec<T>&)
template<typename T , typename Ftn >
Mat< T >	apply_functor (Ftn f, const Mat< T > &m)
	Help function to apply function object to Mat<T>
template<typename T >
Mat< T >	apply_function (T(*f)(T), const Mat< T > &m)
	Help function to call for a function: Mat<T> function(Mat<T>&)
template<typename T >
Mat< T >	apply_function (T(*f)(const T &), const Mat< T > &m)
	Help function to call for a function: Mat<T> function(const Mat<T>&)
template<typename T >
Vec< T >	apply_function (T(*f)(T, T), const T &x, const Vec< T > &v)
	Help function to call for a function: Vec<T> function(T, Vec<T>)
template<typename T >
Vec< T >	apply_function (T(*f)(const T &, const T &), const T &x, const Vec< T > &v)
	Help function to call for a function: Vec<T> function(const T&, const Vec<T>&)
template<typename T >
Mat< T >	apply_function (T(*f)(T, T), const T &x, const Mat< T > &m)
	Help function to call for a function: Mat<T> function(T, Mat<T>)
template<typename T >
Mat< T >	apply_function (T(*f)(const T &, const T &), const T &x, const Mat< T > &m)
	Help function to call for a function: Mat<T> function(const T&, const Mat<T>&)
template<typename T >
Vec< T >	apply_function (T(*f)(T, T), const Vec< T > &v, const T &x)
	Help function to call for a function: Vec<T> function(Vec<T>, T)
template<typename T >
Vec< T >	apply_function (T(*f)(const T &, const T &), const Vec< T > &v, const T &x)
	Help function to call for a function: Vec<T> function(const Vec<T>&, const T&)
template<typename T >
Mat< T >	apply_function (T(*f)(T, T), const Mat< T > &m, const T &x)
	Help function to call for a function: Mat<T> function(Mat<T>, T)
template<typename T >
Mat< T >	apply_function (T(*f)(const T &, const T &), const Mat< T > &m, const T &x)
	Help function to call for a function: Mat<T> function(const Mat<T>&, const T&)
void	it_assert_f (std::string ass, std::string msg, std::string file, int line)
	Helper function for the it_assert and it_assert_debug macros.
void	it_error_f (std::string msg, std::string file, int line)
	Helper function for the it_error and it_error_if macros.
void	it_info_f (std::string msg)
	Helper function for the it_info and it_info_debug macros.
void	it_warning_f (std::string msg, std::string file, int line)
	Helper function for the it_warning macro.
void	it_enable_warnings ()
	Enable warnings.
void	it_disable_warnings ()
	Disable warnings.
void	it_redirect_warnings (std::ostream *warn_stream)
	Redirect warnings to the ostream warn_stream.
void	it_error_msg_style (error_msg_style style)
	Set preferred style of assert, error and warning messages.
ITPP_EXPORT void	it_enable_exceptions (bool on)
	Enable/disable using exceptions for error handling.
it_ifile &	operator>> (it_ifile &f, char &v)
	Read the char variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, bool &v)
	Read the bool variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, bin &v)
	Read the binary variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, short &v)
	Read the short variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, int &v)
	Read the integer variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, float &v)
	Read the float variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, double &v)
	Read the double variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, std::complex< float > &v)
	Read the float complex variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, std::complex< double > &v)
	Read the double complex variable v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, bvec &v)
	Read the bvec v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, svec &v)
	Read the svec v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, ivec &v)
	Read the ivec v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, vec &v)
	Read the vec v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, cvec &v)
	Read the cvec v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, std::string &str)
	Read the string str from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, bmat &m)
	Read the bmat m from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, smat &m)
	Read the smat m from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, imat &m)
	Read the imat m from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, mat &m)
	Read the mat m from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, cmat &m)
	Read the cmat m from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< bin > &v)
	Read the binary Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< short > &v)
	Read the short integer Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< int > &v)
	Read the integer Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< float > &v)
	Read the float Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< double > &v)
	Read the double Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< std::complex< float > > &v)
	Read the float complex Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< std::complex< double > > &v)
	Read the double complex Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< bvec > &v)
	Read the bvec Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< svec > &v)
	Read the svec Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< ivec > &v)
	Read the ivec Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< vec > &v)
	Read the vec Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< cvec > &v)
	Read the cvec Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< std::string > &v)
	Read the string Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< bmat > &v)
	Read the bmat Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< smat > &v)
	Read the bmat Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< imat > &v)
	Read the imat Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< mat > &v)
	Read the mat Array v from the it_ifile pointer.
it_ifile &	operator>> (it_ifile &f, Array< cmat > &v)
	Read the cmat Array v from the it_ifile pointer.
it_file &	operator<< (it_file &f, char x)
	Write the char variable x to the it_file pointer.
it_file &	operator<< (it_file &f, bool x)
	Write the bool variable x to the it_file pointer.
it_file &	operator<< (it_file &f, bin x)
	Write the binary variable x to the it_file pointer.
it_file &	operator<< (it_file &f, short x)
	Write the short variable x to the it_file pointer.
it_file &	operator<< (it_file &f, int x)
	Write the integer variable x to the it_file pointer.
it_file &	operator<< (it_file &f, float x)
	Write the float variable x to the it_file pointer.
it_file &	operator<< (it_file &f, double x)
	Write the double variable x to the it_file pointer.
it_file &	operator<< (it_file &f, std::complex< float > x)
	Write the float complex variable x to the it_file pointer.
it_file &	operator<< (it_file &f, std::complex< double > x)
	Write the double complex variable x to the it_file pointer.
it_file &	operator<< (it_file &f, const bvec &v)
	Write the bvec v to the it_file pointer.
it_file &	operator<< (it_file &f, const svec &v)
	Write the svec v to the it_file pointer.
it_file &	operator<< (it_file &f, const ivec &v)
	Write the ivec v to the it_file pointer.
it_file &	operator<< (it_file &f, const vec &v)
	Write the vec v to the it_file pointer.
it_file &	operator<< (it_file &f, const cvec &v)
	Write the cvec v to the it_file pointer.
it_file &	operator<< (it_file &f, const std::string &str)
	Write the string str to the it_file pointer.
it_file &	operator<< (it_file &f, const bmat &m)
	Write the bmat m to the it_file pointer.
it_file &	operator<< (it_file &f, const smat &m)
	Write the smat m to the it_file pointer.
it_file &	operator<< (it_file &f, const imat &m)
	Write the imat m to the it_file pointer.
it_file &	operator<< (it_file &f, const mat &m)
	Write the mat m to the it_file pointer.
it_file &	operator<< (it_file &f, const cmat &m)
	Write the cmat m to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< bin > &v)
	Write the bin Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< short > &v)
	Write the short int Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< int > &v)
	Write the int Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< float > &v)
	Write the float Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< double > &v)
	Write the double Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< std::complex< float > > &v)
	Write the float complex Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< std::complex< double > > &v)
	Write the double complex Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< bvec > &v)
	Write the bvec Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< svec > &v)
	Write the svec Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< ivec > &v)
	Write the ivec Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< vec > &v)
	Write the vec Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< cvec > &v)
	Write the cvec Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< std::string > &v)
	Write the string Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< bmat > &v)
	Write the bmat Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< smat > &v)
	Write the smat Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< imat > &v)
	Write the imat Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< mat > &v)
	Write the mat Array v to the it_file pointer.
it_file &	operator<< (it_file &f, const Array< cmat > &v)
	Write the cmat Array v to the it_file pointer.
it_ifile_old &	operator>> (it_ifile_old &f, char &v)
	Read the char variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, bin &v)
	Read the binary variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, short &v)
	Read the short variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, int &v)
	Read the integer variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, double &v)
	Read the double variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, float &v)
	Read the float variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, std::complex< float > &v)
	Read the float complex variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, std::complex< double > &v)
	Read the double complex variable v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, vec &v)
	Read the vec v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, ivec &v)
	Read the ivec v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, bvec &v)
	Read the bvec v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, cvec &v)
	Read the cvec v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, std::string &str)
	Read the string str from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, mat &m)
	Read the mat m from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, imat &m)
	Read the imat m from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, bmat &m)
	Read the bmat m from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, cmat &m)
	Read the cmat m from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< float > &v)
	Read the float Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< double > &v)
	Read the double Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< int > &v)
	Read the integer Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< bin > &v)
	Read the binary Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< std::complex< float > > &v)
	Read the float complex Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< std::complex< double > > &v)
	Read the double complex Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< vec > &v)
	Read the vec Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< ivec > &v)
	Read the ivec Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< bvec > &v)
	Read the bvec Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< cvec > &v)
	Read the cvec Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< std::string > &v)
	Read the string Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< mat > &v)
	Read the mat Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< imat > &v)
	Read the imat Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< bmat > &v)
	Read the bmat Array v from the it_ifile_old pointer.
it_ifile_old &	operator>> (it_ifile_old &f, Array< cmat > &v)
	Read the cmat Array v from the it_ifile_old pointer.
it_file_old &	operator<< (it_file_old &f, char x)
	Write the char variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, bin x)
	Write the binary variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, short x)
	Write the short variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, int x)
	Write the integer variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, float x)
	Write the float variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, double x)
	Write the double variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, std::complex< float > x)
	Write the float complex variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, std::complex< double > x)
	Write the double complex variable x to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const vec &v)
	Write the vec v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const ivec &v)
	Write the ivec v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const bvec &v)
	Write the bvec v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const cvec &v)
	Write the cvec v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const std::string &str)
	Write the string str to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const mat &m)
	Write the mat m to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const imat &m)
	Write the imat m to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const bmat &m)
	Write the bmat m to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const cmat &m)
	Write the cmat m to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< float > &v)
	Write the float Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< double > &v)
	Write the double Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< int > &v)
	Write the int Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< bin > &v)
	Write the bin Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< std::complex< float > > &v)
	Write the float complex Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< std::complex< double > > &v)
	Write the double complex Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< vec > &v)
	Write the vec Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< ivec > &v)
	Write the ivec Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< bvec > &v)
	Write the bvec Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< cvec > &v)
	Write the cvec Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< std::string > &v)
	Write the string Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< mat > &v)
	Write the mat Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< imat > &v)
	Write the imat Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< bmat > &v)
	Write the bmat Array v to the it_file_old pointer.
it_file_old &	operator<< (it_file_old &f, const Array< cmat > &v)
	Write the cmat Array v to the it_file_old pointer.
it_file &	flush (it_file &f)
	Flush operatorFlushes the data. Usage:
it_ifile &	operator>> (it_ifile &f, const Name &s)
	Finds the variable Name in the it_ifile. Returns file pointer for reading.
it_file &	operator<< (it_file &f, const Name &s)
	Finds the variable Name in the it_file. Returns file pointer for writing.
template<class T >
void	it_save_var_as (const T &v, const std::string &name)
	Save the variable v in the file name.it as the name name.
template<class T >
void	it_load_var_as (T &v, const std::string &name)
	Load the variable v from the file name.it as the name name.
it_file_old &	flush (it_file_old &f)
	Flush operator.Flushes the data. Usage:
it_ifile_old &	operator>> (it_ifile_old &f, const Name &s)
	Finds the variable Name in the it_ifile_old. Returns file pointer for reading.
it_file_old &	operator<< (it_file_old &f, const Name &s)
	Finds the variable Name in the it_file_old. Returns file pointer for writing.
template<class Num_T >
Mat< Num_T >	concat_horizontal (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Horizontal concatenation of two matrices.
template<class Num_T >
Mat< Num_T >	concat_vertical (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Vertical concatenation of two matrices.
template<class Num_T >
Mat< Num_T >	operator+ (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Addition of two matrices.
template<class Num_T >
Mat< Num_T >	operator+ (const Mat< Num_T > &m, Num_T t)
	Addition of a matrix and a scalar.
template<class Num_T >
Mat< Num_T >	operator+ (Num_T t, const Mat< Num_T > &m)
	Addition of a scalar and a matrix.
template<class Num_T >
Mat< Num_T >	operator- (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Subtraction of two matrices.
template<class Num_T >
Mat< Num_T >	operator- (const Mat< Num_T > &m, Num_T t)
	Subtraction of matrix and scalar.
template<class Num_T >
Mat< Num_T >	operator- (Num_T t, const Mat< Num_T > &m)
	Subtraction of scalar and matrix.
template<class Num_T >
Mat< Num_T >	operator- (const Mat< Num_T > &m)
	Negation of matrix.
template<class Num_T >
Mat< Num_T >	operator* (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Multiplication of two matrices.
template<class Num_T >
Vec< Num_T >	operator* (const Mat< Num_T > &m, const Vec< Num_T > &v)
	Multiplication of matrix and vector.
template<class Num_T >
Mat< Num_T >	operator* (const Mat< Num_T > &m, Num_T t)
	Multiplication of matrix and scalar.
template<class Num_T >
Mat< Num_T >	operator* (Num_T t, const Mat< Num_T > &m)
	Multiplication of scalar and matrix.
template<class Num_T >
Mat< Num_T >	elem_mult (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Element wise multiplication of two matrices.
template<class Num_T >
void	elem_mult_out (const Mat< Num_T > &m1, const Mat< Num_T > &m2, Mat< Num_T > &out)
	Element wise multiplication of two matrices, storing the result in matrix out.
template<class Num_T >
void	elem_mult_out (const Mat< Num_T > &m1, const Mat< Num_T > &m2, const Mat< Num_T > &m3, Mat< Num_T > &out)
	Element wise multiplication of three matrices, storing the result in matrix out.
template<class Num_T >
void	elem_mult_out (const Mat< Num_T > &m1, const Mat< Num_T > &m2, const Mat< Num_T > &m3, const Mat< Num_T > &m4, Mat< Num_T > &out)
	Element wise multiplication of four matrices, storing the result in matrix out.
template<class Num_T >
void	elem_mult_inplace (const Mat< Num_T > &m1, Mat< Num_T > &m2)
	In-place element wise multiplication of two matrices. Fast version of B = elem_mult(A, B).
template<class Num_T >
Num_T	elem_mult_sum (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Element wise multiplication of two matrices, followed by summation of the resultant elements. Fast version of sumsum(elem_mult(A, B)).
template<class Num_T >
Mat< Num_T >	operator/ (const Mat< Num_T > &m, Num_T t)
	Element-wise division by a scalar.
template<class Num_T >
Mat< Num_T >	operator/ (Num_T t, const Mat< Num_T > &m)
	Element-wise division (t is the dividend, elements of m are divisors)
template<class Num_T >
Mat< Num_T >	elem_div (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Element wise division of two matrices.
template<class Num_T >
void	elem_div_out (const Mat< Num_T > &m1, const Mat< Num_T > &m2, Mat< Num_T > &out)
	Element wise division of two matrices, storing the result in matrix out.
template<class Num_T >
Num_T	elem_div_sum (const Mat< Num_T > &m1, const Mat< Num_T > &m2)
	Element wise division of two matrices, followed by summation of the resultant elements. Fast version of sumsum(elem_div(A, B)).
template<class Num_T >
std::ostream &	operator<< (std::ostream &os, const Mat< Num_T > &m)
	Output stream for matrices.
template<class Num_T >
std::istream &	operator>> (std::istream &is, Mat< Num_T > &m)
	Input stream for matrices.
template<class T >
int	length (const Vec< T > &v)
	Length of vector.
template<class T >
int	size (const Vec< T > &v)
	Length of vector.
template<class T >
T	sum (const Vec< T > &v)
	Sum of all elements in the vector.
template<class T >
Vec< T >	sum (const Mat< T > &m, int dim=1)
	Sum of elements in the matrix m, either along columns or rows.
template<class T >
T	sumsum (const Mat< T > &X)
	Sum of all elements in the given matrix. Fast version of sum(sum(X))
template<class T >
T	sum_sqr (const Vec< T > &v)
	Sum of square of the elements in a vector.
template<class T >
Vec< T >	sum_sqr (const Mat< T > &m, int dim=1)
	Sum of the square of elements in the matrix m.
template<class T >
Vec< T >	cumsum (const Vec< T > &v)
	Cumulative sum of all elements in the vector.
template<class T >
Mat< T >	cumsum (const Mat< T > &m, int dim=1)
	Cumulative sum of elements in the matrix m.
template<class T >
T	prod (const Vec< T > &v)
	The product of all elements in the vector.
template<class T >
Vec< T >	prod (const Mat< T > &m, int dim=1)
	Product of elements in the matrix m.
template<class T >
Vec< T >	cross (const Vec< T > &v1, const Vec< T > &v2)
	Vector cross product. Vectors need to be of size 3.
template<class T >
Vec< T >	zero_pad (const Vec< T > &v, int n)
	Zero-pad a vector to size n.
template<class T >
Vec< T >	zero_pad (const Vec< T > &v)
	Zero-pad a vector to the nearest greater power of two.
template<class T >
Mat< T >	zero_pad (const Mat< T > &m, int rows, int cols)
	Zero-pad a matrix to size rows x cols.
template<class T >
T	index_zero_pad (const Vec< T > &v, const int index)
template<class T >
void	transpose (const Mat< T > &m, Mat< T > &out)
	Transposition of the matrix m returning the transposed matrix in out.
template<class T >
Mat< T >	transpose (const Mat< T > &m)
	Transposition of the matrix m.
template<class T >
void	hermitian_transpose (const Mat< T > &m, Mat< T > &out)
template<class T >
Mat< T >	hermitian_transpose (const Mat< T > &m)
	Hermitian transpose (complex conjugate transpose) of the matrix m.
template<class Num_T >
bool	is_hermitian (const Mat< Num_T > &X)
	Returns true if matrix X is hermitian, false otherwise.
template<class Num_T >
bool	is_unitary (const Mat< Num_T > &X)
	Returns true if matrix X is unitary, false otherwise.
template<class Num_T >
Mat< Num_T >	kron (const Mat< Num_T > &X, const Mat< Num_T > &Y)
	Computes the Kronecker product of two matrices.
ITPP_EXPORT cmat	sqrtm (const cmat &A)
	Square root of the complex square matrix A.
ITPP_EXPORT cmat	sqrtm (const mat &A)
	Square root of the real square matrix A.
template<class T >
int	rank (const Mat< T > &m, double tol=-1.0)
	Calculate the rank of matrix m.
template<>
int	rank (const imat &m, double tol)
	Specialisation of rank() function.
template<>
int	rank (const smat &m, double tol)
	Specialisation of rank() function.
template<>
int	rank (const bmat &, double)
	Specialisation of rank() function.
template<class T >
Mat< T >	diag (const Vec< T > &v, const int K=0)
	Create a diagonal matrix using vector v as its diagonal.
template<class T >
void	diag (const Vec< T > &v, Mat< T > &m)
	Create a diagonal matrix using vector v as its diagonal.
template<class T >
Vec< T >	diag (const Mat< T > &m)
	Get the diagonal elements of the input matrix m.
template<class T >
Mat< T >	bidiag (const Vec< T > &main, const Vec< T > &sup)
	Returns a matrix with the elements of the input vector main on the diagonal and the elements of the input vector sup on the diagonal row above.
template<class T >
void	bidiag (const Vec< T > &main, const Vec< T > &sup, Mat< T > &m)
	Returns in the output variable m a matrix with the elements of the input vector main on the diagonal and the elements of the input vector sup on the diagonal row above.
template<class T >
void	bidiag (const Mat< T > &m, Vec< T > &main, Vec< T > &sup)
	Returns the main diagonal and the diagonal row above in the two output vectors main and sup.
template<class T >
Mat< T >	tridiag (const Vec< T > &main, const Vec< T > &sup, const Vec< T > &sub)
	Returns a matrix with the elements of main on the diagonal, the elements of sup on the diagonal row above, and the elements of sub on the diagonal row below.
template<class T >
void	tridiag (const Vec< T > &main, const Vec< T > &sup, const Vec< T > &sub, Mat< T > &m)
	Returns in the output matrix m a matrix with the elements of main on the diagonal, the elements of sup on the diagonal row above, and the elements of sub on the diagonal row below.
template<class T >
void	tridiag (const Mat< T > &m, Vec< T > &main, Vec< T > &sup, Vec< T > &sub)
	Returns the main diagonal, the diagonal row above, and the diagonal row below int the output vectors main, sup, and sub.
template<class T >
T	trace (const Mat< T > &m)
	The trace of the matrix m, i.e. the sum of the diagonal elements.
template<class T >
Vec< T >	reverse (const Vec< T > &in)
	Reverse the input vector.
template<class T >
Vec< T >	rvectorize (const Mat< T > &m)
	Row vectorize the matrix [(0,0) (0,1) ... (N-1,N-2) (N-1,N-1)].
template<class T >
Vec< T >	cvectorize (const Mat< T > &m)
	Column vectorize the matrix [(0,0) (1,0) ... (N-2,N-1) (N-1,N-1)].
template<class T >
Mat< T >	reshape (const Mat< T > &m, int rows, int cols)
	Reshape the matrix into an rows*cols matrix.
template<class T >
Mat< T >	reshape (const Vec< T > &v, int rows, int cols)
	Reshape the vector into an rows*cols matrix.
ITPP_EXPORT bool	all (const bvec &testvec)
	Returns true if all elements are ones and false otherwise.
ITPP_EXPORT bool	any (const bvec &testvec)
	Returns true if any element is one and false otherwise.
vec	operator+ (const double &s, const ivec &v)
	Addition operator for double and ivec.
vec	operator- (const double &s, const ivec &v)
	Subtraction operator for double and ivec.
vec	operator* (const double &s, const ivec &v)
	Multiplication operator for double and ivec.
vec	operator/ (const double &s, const ivec &v)
	Division operator for double and ivec.
vec	operator/ (const ivec &v, const double &s)
	Division operator for ivec and double.
cvec	operator+ (const std::complex< double > &s, const ivec &v)
	Addition operator for complex<double> and ivec.
cvec	operator- (const std::complex< double > &s, const ivec &v)
	Subtraction operator for complex<double> and ivec.
cvec	operator* (const std::complex< double > &s, const ivec &v)
	Multiplication operator for complex<double> and ivec.
cvec	operator/ (const std::complex< double > &s, const ivec &v)
	Division operator for complex<double> and ivec.
cvec	operator/ (const ivec &v, const std::complex< double > &s)
	Division operator for ivec and complex<double>
cvec	operator+ (const double &s, const cvec &v)
	Addition operator for double and cvec.
cvec	operator- (const double &s, const cvec &v)
	Subtraction operator for double and cvec.
cvec	operator* (const double &s, const cvec &v)
	Multiplication operator for double and cvec.
cvec	operator/ (const cvec &v, const double &s)
	Division operator for cvec and double.
cvec	operator/ (const double &s, const cvec &v)
	Division operator for double and cvec.
cmat	operator+ (const double &s, const cmat &m)
	Addition operator for double and cmat.
cmat	operator- (const double &s, const cmat &m)
	Subtraction operator for double and cmat.
cmat	operator* (const double &s, const cmat &m)
	Multiplication operator for double and cmat.
cmat	operator* (const std::complex< double > &s, const mat &m)
	Multiplication operator for complex<double> and mat.
cmat	operator/ (const cmat &m, const double &s)
	Division operator for cmat and double.
cvec	operator* (const std::complex< double > &s, const vec &v)
	Multiplication operator for complex<double> and vec.
cvec	operator* (const vec &v, const std::complex< double > &s)
	Multiplication operator for vec and complex<double>
vec	operator+ (const bvec &a, const vec &b)
	Addition operator for bvec and vec.
vec	operator+ (const svec &a, const vec &b)
	Addition operator for svec and vec.
vec	operator+ (const ivec &a, const vec &b)
	Addition operator for ivec and vec.
cvec	operator+ (const bvec &a, const cvec &b)
	Addition operator for bvec and cvec.
cvec	operator+ (const svec &a, const cvec &b)
	Addition operator for svec and cvec.
cvec	operator+ (const ivec &a, const cvec &b)
	Addition operator for ivec and cvec.
double	operator* (const bvec &a, const vec &b)
	Multiplication operator for bvec and vec.
double	operator* (const svec &a, const vec &b)
	Multiplication operator for svec and vec.
double	operator* (const ivec &a, const vec &b)
	Multiplication operator for ivec and vec.
std::complex< double >	operator* (const bvec &a, const cvec &b)
	Multiplication operator for bvec and cvec.
std::complex< double >	operator* (const svec &a, const cvec &b)
	Multiplication operator for svec and cvec.
std::complex< double >	operator* (const ivec &a, const cvec &b)
	Multiplication operator for ivec and cvec.
mat	operator+ (const bmat &a, const mat &b)
	Addition operator for bmat and mat.
mat	operator+ (const smat &a, const mat &b)
	Addition operator for smat and mat.
mat	operator+ (const imat &a, const mat &b)
	Addition operator for imat and mat.
cmat	operator+ (const bmat &a, const cmat &b)
	Addition operator for bmat and cmat.
cmat	operator+ (const smat &a, const cmat &b)
	Addition operator for smat and cmat.
cmat	operator+ (const imat &a, const cmat &b)
	Addition operator for imat and cmat.
cmat	operator+ (const mat &a, const cmat &b)
	Addition operator for mat and cmat.
std::complex< double >	operator+ (const int &x, const std::complex< double > &y)
	Addition operator for int and complex double.
std::complex< double >	operator+ (const float &x, const std::complex< double > &y)
	Addition operator for float and complex double.
std::complex< double >	operator+ (const std::complex< double > &x, const int &y)
	Addition operator for int and complex double.
std::complex< double >	operator+ (const std::complex< double > &x, const float &y)
	Addition operator for float and complex double.
std::complex< double >	operator- (const int &x, const std::complex< double > &y)
	Subtraction operator for int and complex double.
std::complex< double >	operator- (const float &x, const std::complex< double > &y)
	Subtraction operator for float and complex double.
std::complex< double >	operator- (const std::complex< double > &x, const int &y)
	Subtraction operator for int and complex double.
std::complex< double >	operator- (const std::complex< double > &x, const float &y)
	Subtraction operator for float and complex double.
std::complex< double >	operator* (const int &x, const std::complex< double > &y)
	Multiplication operator for int and complex double.
std::complex< double >	operator* (const float &x, const std::complex< double > &y)
	Multiplication operator for float and complex double.
std::complex< double >	operator* (const std::complex< double > &x, const int &y)
	Multiplication operator for int and complex double.
std::complex< double >	operator* (const std::complex< double > &x, const float &y)
	Multiplication operator for float and complex double.
std::complex< double >	operator/ (const std::complex< double > &x, const int &y)
	Division operator for complex double and int.
std::complex< double >	operator/ (const std::complex< double > &x, const float &y)
	Division operator for complex double and float.
vec	operator+ (const float &s, const vec &v)
	Addition operator for float and vec.
vec	operator+ (const short &s, const vec &v)
	Addition operator for short and vec.
vec	operator+ (const int &s, const vec &v)
	Addition operator for int and vec.
vec	operator+ (const vec &v, const float &s)
	Addition operator for vec and float.
vec	operator+ (const vec &v, const short &s)
	Addition operator for vec and short.
vec	operator+ (const vec &v, const int &s)
	Addition operator for vec and int.
vec	operator- (const float &s, const vec &v)
	Subtraction operator for float and vec.
vec	operator- (const short &s, const vec &v)
	Subtraction operator for short and vec.
vec	operator- (const int &s, const vec &v)
	Subtraction operator for int and vec.
vec	operator- (const vec &v, const float &s)
	Subtraction operator for vec and float.
vec	operator- (const vec &v, const short &s)
	Subtraction operator for vec and short.
vec	operator- (const vec &v, const int &s)
	Subtraction operator for vec and int.
vec	operator* (const float &s, const vec &v)
	Multiplication operator for float and vec.
vec	operator* (const short &s, const vec &v)
	Multiplication operator for short and vec.
vec	operator* (const int &s, const vec &v)
	Multiplication operator for int and vec.
vec	operator* (const vec &v, const float &s)
	Multiplication operator for vec and float.
vec	operator* (const vec &v, const short &s)
	Multiplication operator for vec and short.
vec	operator* (const vec &v, const int &s)
	Multiplication operator for vec and int.
vec	operator/ (const vec &v, const float &s)
	Division operator for vec and float.
vec	operator/ (const vec &v, const short &s)
	Division operator for vec and short.
vec	operator/ (const vec &v, const int &s)
	Division operator for vec and int.
vec	operator+ (const ivec &v, const double &s)
	Addition operator for ivec and double.
vec	operator- (const ivec &v, const double &s)
	Subtraction operator for ivec and double.
vec	operator* (const ivec &v, const double &s)
	Multiplication operator for ivec and double.
cvec	operator+ (const ivec &v, const std::complex< double > &s)
	Addition operator for ivec and complex<double>
cvec	operator- (const ivec &v, const std::complex< double > &s)
	Subtraction operator for ivec and complex<double>
cvec	operator* (const ivec &v, const std::complex< double > &s)
	Multiplication operator for ivec and complex<double>
cvec	operator+ (const float &s, const cvec &v)
	Addition operator for float and cvec.
cvec	operator+ (const short &s, const cvec &v)
	Addition operator for short and cvec.
cvec	operator+ (const int &s, const cvec &v)
	Addition operator for int and cvec.
cvec	operator+ (const cvec &v, const float &s)
	Addition operator for cvec and float.
cvec	operator+ (const cvec &v, const double &s)
	Addition operator for cvec and double.
cvec	operator+ (const cvec &v, const short &s)
	Addition operator for cvec and short.
cvec	operator+ (const cvec &v, const int &s)
	Addition operator for cvec and int.
cvec	operator- (const float &s, const cvec &v)
	Subtraction operator for float and cvec.
cvec	operator- (const short &s, const cvec &v)
	Subtraction operator for short and cvec.
cvec	operator- (const int &s, const cvec &v)
	Subtraction operator for int and cvec.
cvec	operator- (const cvec &v, const float &s)
	Subtraction operator for cvec and float.
cvec	operator- (const cvec &v, const double &s)
	Subtraction operator for cvec and double.
cvec	operator- (const cvec &v, const short &s)
	Subtraction operator for cvec and short.
cvec	operator- (const cvec &v, const int &s)
	Subtraction operator for cvec and int.
cvec	operator* (const float &s, const cvec &v)
	Multiplication operator for float and cvec.
cvec	operator* (const short &s, const cvec &v)
	Multiplication operator for short and cvec.
cvec	operator* (const int &s, const cvec &v)
	Multiplication operator for int and cvec.
cvec	operator* (const cvec &v, const float &s)
	Multiplication operator for cvec and float.
cvec	operator* (const cvec &v, const double &s)
	Multiplication operator for cvec and double.
cvec	operator* (const cvec &v, const short &s)
	Multiplication operator for cvec and short.
cvec	operator* (const cvec &v, const int &s)
	Multiplication operator for cvec and int.
cvec	operator/ (const cvec &v, const float &s)
	Division operator for cvec and float.
cvec	operator/ (const cvec &v, const short &s)
	Division operator for cvec and short.
cvec	operator/ (const cvec &v, const int &s)
	Division operator for cvec and int.
mat	operator+ (const float &s, const mat &m)
	Addition operator for float and mat.
mat	operator+ (const short &s, const mat &m)
	Addition operator for short and mat.
mat	operator+ (const int &s, const mat &m)
	Addition operator for int and mat.
mat	operator+ (const mat &m, const float &s)
	Addition operator for mat and float.
mat	operator+ (const mat &m, const short &s)
	Addition operator for mat and short.
mat	operator+ (const mat &m, const int &s)
	Addition operator for mat and int.
mat	operator- (const float &s, const mat &m)
	Subtraction operator for float and mat.
mat	operator- (const short &s, const mat &m)
	Subtraction operator for short and mat.
mat	operator- (const int &s, const mat &m)
	Subtraction operator for int and mat.
mat	operator- (const mat &m, const float &s)
	Subtraction operator for mat and float.
mat	operator- (const mat &m, const short &s)
	Subtraction operator for mat and short.
mat	operator- (const mat &m, const int &s)
	Subtraction operator for mat and int.
mat	operator* (const float &s, const mat &m)
	Multiplication operator for float and mat.
mat	operator* (const short &s, const mat &m)
	Multiplication operator for short and mat.
mat	operator* (const int &s, const mat &m)
	Multiplication operator for int and mat.
mat	operator* (const mat &m, const float &s)
	Multiplication operator for mat and float.
mat	operator* (const mat &m, const short &s)
	Multiplication operator for mat and short.
mat	operator* (const mat &m, const int &s)
	Multiplication operator for mat and int.
mat	operator/ (const mat &m, const float &s)
	Division operator for mat and float.
mat	operator/ (const mat &m, const short &s)
	Division operator for mat and short.
mat	operator/ (const mat &m, const int &s)
	Division operator for mat and int.
cmat	operator* (const mat &m, const std::complex< double > &s)
	Multiplication operator for mat and complex<double>
vec	operator+ (const vec &a, const bvec &b)
	Addition operator for vec and bvec.
vec	operator+ (const vec &a, const svec &b)
	Addition operator for vec and svec.
vec	operator+ (const vec &a, const ivec &b)
	Addition operator for vec and ivec.
vec	operator- (const bvec &a, const vec &b)
	Subtraction operator for bvec and vec.
vec	operator- (const svec &a, const vec &b)
	Subtraction operator for svec and vec.
vec	operator- (const ivec &a, const vec &b)
	Subtraction operator for ivec and vec.
vec	operator- (const vec &a, const bvec &b)
	Subtraction operator for vec and bvec.
vec	operator- (const vec &a, const svec &b)
	Subtraction operator for vec and svec.
vec	operator- (const vec &a, const ivec &b)
	Subtraction operator for vec and ivec.
double	operator* (const vec &a, const bvec &b)
	Multiplication operator for vec and bvec.
double	operator* (const vec &a, const svec &b)
	Multiplication operator for vec and svec.
double	operator* (const vec &a, const ivec &b)
	Multiplication operator for vec and ivec.
cvec	operator+ (const cvec &a, const bvec &b)
	Addition operator for cvec and bvec.
cvec	operator+ (const cvec &a, const svec &b)
	Addition operator for cvec and svec.
cvec	operator+ (const cvec &a, const ivec &b)
	Addition operator for cvec and ivec.
cvec	operator- (const bvec &a, const cvec &b)
	Subtraction operator for bvec and cvec.
cvec	operator- (const svec &a, const cvec &b)
	Subtraction operator for svec and cvec.
cvec	operator- (const ivec &a, const cvec &b)
	Subtraction operator for ivec and cvec.
cvec	operator- (const cvec &a, const bvec &b)
	Subtraction operator for cvec and bvec.
cvec	operator- (const cvec &a, const svec &b)
	Subtraction operator for cvec and svec.
cvec	operator- (const cvec &a, const ivec &b)
	Subtraction operator for cvec and ivec.
std::complex< double >	operator* (const cvec &a, const bvec &b)
	Multiplication operator for cvec and bvec.
std::complex< double >	operator* (const cvec &a, const svec &b)
	Multiplication operator for cvec and svec.
std::complex< double >	operator* (const cvec &a, const ivec &b)
	Multiplication operator for cvec and ivec.
mat	operator+ (const mat &a, const bmat &b)
	Addition operator for mat and bmat.
mat	operator+ (const mat &a, const smat &b)
	Addition operator for mat and smat.
mat	operator+ (const mat &a, const imat &b)
	Addition operator for mat and imat.
mat	operator- (const bmat &a, const mat &b)
	Subtraction operator for bmat and mat.
mat	operator- (const smat &a, const mat &b)
	Subtraction operator for smat and mat.
mat	operator- (const imat &a, const mat &b)
	Subtraction operator for imat and mat.
mat	operator- (const mat &a, const bmat &b)
	Subtraction operator for mat and bmat.
mat	operator- (const mat &a, const smat &b)
	Subtraction operator for mat and smat.
mat	operator- (const mat &a, const imat &b)
	Subtraction operator for mat and imat.
cmat	operator+ (const cmat &a, const bmat &b)
	Addition operator for cmat and bmat.
cmat	operator+ (const cmat &a, const smat &b)
	Addition operator for cmat and smat.
cmat	operator+ (const cmat &a, const imat &b)
	Addition operator for cmat and imat.
cmat	operator+ (const cmat &a, const mat &b)
	Addition operator for cmat and mat.
cmat	operator- (const bmat &a, const cmat &b)
	Subtraction operator for bmat and cmat.
cmat	operator- (const smat &a, const cmat &b)
	Subtraction operator for smat and cmat.
cmat	operator- (const imat &a, const cmat &b)
	Subtraction operator for imat and cmat.
cmat	operator- (const mat &a, const cmat &b)
	Subtraction operator for mat and cmat.
cmat	operator- (const cmat &a, const bmat &b)
	Subtraction operator for cmat and bmat.
cmat	operator- (const cmat &a, const smat &b)
	Subtraction operator for cmat and smat.
cmat	operator- (const cmat &a, const imat &b)
	Subtraction operator for cmat and imat.
cmat	operator- (const cmat &a, const mat &b)
	Subtraction operator for cmat and mat.
cmat	operator* (const mat &a, const cmat &b)
	Multiplication operator for mat and cmat.
cmat	operator* (const bmat &a, const cmat &b)
	Multiplication operator for bmat and cmat.
cmat	operator* (const smat &a, const cmat &b)
	Multiplication operator for smat and cmat.
cmat	operator* (const imat &a, const cmat &b)
	Multiplication operator for imat and cmat.
cmat	operator* (const cmat &a, const mat &b)
	Multiplication operator for cmat and mat.
cmat	operator* (const cmat &a, const bmat &b)
	Multiplication operator for cmat and bmat.
cmat	operator* (const cmat &a, const smat &b)
	Multiplication operator for cmat and smat.
cmat	operator* (const cmat &a, const imat &b)
	Multiplication operator for cmat and imat.
GlobalSeedProvider &	global_seed_provider ()
void	GlobalRNG_reset (unsigned int seed)
	Set the internal seed of the Global Seed Provider.
void	GlobalRNG_reset ()
	Reset the internal seed of the Global Seed Provider to the previously set value.
unsigned int	GlobalRNG_get_local_seed ()
	Get new seed to initialize thread-local generators.
void	GlobalRNG_randomize ()
	Set a random seed for the Global Seed Provider seed.
void	GlobalRNG_get_state (ivec &state)
	Save current full state of global seed provider in memory.
void	GlobalRNG_set_state (const ivec &state)
	Resume the global seed provider state saved in memory.
void	RNG_reset (unsigned int seed)
	Set the seed for all Random Number Generators in the current thread.
void	RNG_reset ()
	Reset the seed to the previously set value for all Random Number Generators in the current thread.
void	RNG_randomize ()
	Set a random seed for all Random Number Generators in the current thread.
void	RNG_get_state (ivec &state)
	Save Random Number generation context used in the current thread.
void	RNG_set_state (const ivec &state)
	Resume Random Number generation in the current thread with previously stored context.
bin	randb (void)
	Generates a random bit (equally likely 0s and 1s)
void	randb (int size, bvec &out)
	Generates a random bit vector (equally likely 0s and 1s)
bvec	randb (int size)
	Generates a random bit vector (equally likely 0s and 1s)
void	randb (int rows, int cols, bmat &out)
	Generates a random bit matrix (equally likely 0s and 1s)
bmat	randb (int rows, int cols)
	Generates a random bit matrix (equally likely 0s and 1s)
double	randu (void)
	Generates a random uniform (0,1) number.
void	randu (int size, vec &out)
	Generates a random uniform (0,1) vector.
vec	randu (int size)
	Generates a random uniform (0,1) vector.
void	randu (int rows, int cols, mat &out)
	Generates a random uniform (0,1) matrix.
mat	randu (int rows, int cols)
	Generates a random uniform (0,1) matrix.
int	randi (int low, int high)
	Generates a random integer in the interval [low,high].
ivec	randi (int size, int low, int high)
	Generates a random ivec with elements in the interval [low,high].
imat	randi (int rows, int cols, int low, int high)
	Generates a random imat with elements in the interval [low,high].
vec	randray (int size, double sigma=1.0)
	Generates a random Rayleigh vector.
vec	randrice (int size, double sigma=1.0, double s=1.0)
	Generates a random Rice vector (See J.G. Poakis, "Digital Communications, 3rd ed." p.47)
vec	randexp (int size, double lambda=1.0)
	Generates a random complex Gaussian vector.
double	randn (void)
	Generates a random Gaussian (0,1) variable.
void	randn (int size, vec &out)
	Generates a random Gaussian (0,1) vector.
vec	randn (int size)
	Generates a random Gaussian (0,1) vector.
void	randn (int rows, int cols, mat &out)
	Generates a random Gaussian (0,1) matrix.
mat	randn (int rows, int cols)
	Generates a random Gaussian (0,1) matrix.
std::complex< double >	randn_c (void)
	Generates a random complex Gaussian (0,1) variable.
void	randn_c (int size, cvec &out)
	Generates a random complex Gaussian (0,1) vector.
cvec	randn_c (int size)
	Generates a random complex Gaussian (0,1) vector.
void	randn_c (int rows, int cols, cmat &out)
	Generates a random complex Gaussian (0,1) matrix.
cmat	randn_c (int rows, int cols)
	Generates a random complex Gaussian (0,1) matrix.
template<class T >
Sparse_Mat< T >	operator+ (const Sparse_Mat< T > &m1, const Sparse_Mat< T > &m2)
	m1+m2 where m1 and m2 are sparse matrices
template<class T >
Sparse_Mat< T >	operator* (const T &c, const Sparse_Mat< T > &m)
	c*m where c is a scalar and m is a sparse matrix
template<class T >
Sparse_Mat< T >	operator* (const Sparse_Mat< T > &m1, const Sparse_Mat< T > &m2)
	m1*m2 where m1 and m2 are sparse matrices
template<class T >
Sparse_Vec< T >	operator* (const Sparse_Mat< T > &m, const Sparse_Vec< T > &v)
	m*v where m is a sparse matrix and v is a sparse vector
template<class T >
Vec< T >	operator* (const Sparse_Mat< T > &m, const Vec< T > &v)
	m*v where m is a sparse matrix and v is a full column vector
template<class T >
Vec< T >	operator* (const Vec< T > &v, const Sparse_Mat< T > &m)
	v'*m where m is a sparse matrix and v is a full column vector
template<class T >
Mat< T >	trans_mult (const Sparse_Mat< T > &m)
	m'*m where m is a sparse matrix
template<class T >
Sparse_Mat< T >	trans_mult_s (const Sparse_Mat< T > &m)
	m'*m where m is a sparse matrix
template<class T >
Sparse_Mat< T >	trans_mult (const Sparse_Mat< T > &m1, const Sparse_Mat< T > &m2)
	m1'*m2 where m1 and m2 are sparse matrices
template<class T >
Vec< T >	trans_mult (const Sparse_Mat< T > &m, const Vec< T > &v)
	m'*v where m is a sparse matrix and v is a full column vector
template<class T >
Sparse_Mat< T >	mult_trans (const Sparse_Mat< T > &m1, const Sparse_Mat< T > &m2)
	m1*m2' where m1 and m2 are sparse matrices
template<class T >
Sparse_Mat< T >	sparse (const Mat< T > &m, T epsilon)
	Convert a dense matrix m into its sparse representation.
template<class T >
Mat< T >	full (const Sparse_Mat< T > &s)
	Convert a sparse matrix s into its dense representation.
template<class T >
Sparse_Mat< T >	transpose (const Sparse_Mat< T > &s)
	Transpose a sparse matrix s.
ivec	find (const bvec &invector)
	Return a integer vector with indicies where bvec == 1.
vec	impulse (int size)
	Impulse vector.
vec	linspace (double from, double to, int length=100)
	linspace (works in the same way as the MATLAB version)
vec	zigzag_space (double t0, double t1, int K=5)
	Zig-zag space function (variation on linspace)
imat	hadamard (int size)
	Hadamard matrix.
imat	jacobsthal (int p)
	Jacobsthal matrix.
imat	conference (int n)
	Conference matrix.
const cmat	toeplitz (const cvec &c)
	Generate symmetric Toeplitz matrix from vector c (complex valued)
mat	rotation_matrix (int dim, int plane1, int plane2, double angle)
	Create a rotation matrix that rotates the given plane angle radians. Note that the order of the planes are important!
void	house (const vec &x, vec &v, double &beta)
	Calcualte the Householder vector.
void	givens (double a, double b, double &c, double &s)
	Calculate the Givens rotation values.
void	givens (double a, double b, mat &m)
	Calculate the Givens rotation matrix.
mat	givens (double a, double b)
	Calculate the Givens rotation matrix.
void	givens_t (double a, double b, mat &m)
	Calculate the transposed Givens rotation matrix.
mat	givens_t (double a, double b)
	Calculate the transposed Givens rotation matrix.
template void	eye (int, mat &)
	Template instantiation of eye.
template void	eye (int, bmat &)
	Template instantiation of eye.
template void	eye (int, imat &)
	Template instantiation of eye.
template void	eye (int, cmat &)
	Template instantiation of eye.
template vec	linspace_fixed_step (double, double, double)
	Template instantiation of linspace_fixed_step.
template ivec	linspace_fixed_step (int, int, int)
	Template instantiation of linspace_fixed_step.
template svec	linspace_fixed_step (short int, short int, short int)
	Template instantiation of linspace_fixed_step.
ITPP_EXPORT vec	ones (int size)
	A float vector of ones.
ITPP_EXPORT bvec	ones_b (int size)
	A Binary vector of ones.
ITPP_EXPORT ivec	ones_i (int size)
	A Int vector of ones.
ITPP_EXPORT cvec	ones_c (int size)
	A float Complex vector of ones.
ITPP_EXPORT mat	ones (int rows, int cols)
	A float (rows,cols)-matrix of ones.
ITPP_EXPORT bmat	ones_b (int rows, int cols)
	A Binary (rows,cols)-matrix of ones.
ITPP_EXPORT imat	ones_i (int rows, int cols)
	A Int (rows,cols)-matrix of ones.
ITPP_EXPORT cmat	ones_c (int rows, int cols)
	A Double Complex (rows,cols)-matrix of ones.
ITPP_EXPORT vec	zeros (int size)
	A Double vector of zeros.
ITPP_EXPORT bvec	zeros_b (int size)
	A Binary vector of zeros.
ITPP_EXPORT ivec	zeros_i (int size)
	A Int vector of zeros.
ITPP_EXPORT cvec	zeros_c (int size)
	A Double Complex vector of zeros.
ITPP_EXPORT mat	zeros (int rows, int cols)
	A Double (rows,cols)-matrix of zeros.
ITPP_EXPORT bmat	zeros_b (int rows, int cols)
	A Binary (rows,cols)-matrix of zeros.
ITPP_EXPORT imat	zeros_i (int rows, int cols)
	A Int (rows,cols)-matrix of zeros.
ITPP_EXPORT cmat	zeros_c (int rows, int cols)
	A Double Complex (rows,cols)-matrix of zeros.
ITPP_EXPORT mat	eye (int size)
	A Double (size,size) unit matrix.
ITPP_EXPORT bmat	eye_b (int size)
	A Binary (size,size) unit matrix.
ITPP_EXPORT imat	eye_i (int size)
	A Int (size,size) unit matrix.
ITPP_EXPORT cmat	eye_c (int size)
	A Double Complex (size,size) unit matrix.
template<class T >
void	eye (int size, Mat< T > &m)
	A non-copying version of the eye function.
template<class T >
Vec< T >	linspace_fixed_step (T from, T to, T step=1)
	linspace_fixed_step (works in the same way as "from:step:to" in MATLAB)
template<typename Num_T >
const Mat< Num_T >	toeplitz (const Vec< Num_T > &c, const Vec< Num_T > &r)
	Generate Toeplitz matrix from two vectors c and r.
template<typename Num_T >
const Mat< Num_T >	toeplitz (const Vec< Num_T > &c)
	Generate symmetric Toeplitz matrix from vector c.
template<class T >
Sparse_Vec< T >	operator+ (const Sparse_Vec< T > &v1, const Sparse_Vec< T > &v2)
	v1+v2 where v1 and v2 are sparse vector
template<class T >
T	operator* (const Sparse_Vec< T > &v1, const Sparse_Vec< T > &v2)
	v1*v2 where v1 and v2 are sparse vectors
template<class T >
T	operator* (const Sparse_Vec< T > &v1, const Vec< T > &v2)
	v1*v2 where v1 is a sparse vector and v2 is a dense vector
template<class T >
T	operator* (const Vec< T > &v1, const Sparse_Vec< T > &v2)
	v1*v2 where v1 is a dense vector and v2 is a sparse vector
template<class T >
Sparse_Vec< T >	elem_mult (const Sparse_Vec< T > &v1, const Sparse_Vec< T > &v2)
	Elementwise multiplication of two sparse vectors returning a sparse vector.
template<class T >
Vec< T >	elem_mult (const Sparse_Vec< T > &v1, const Vec< T > &v2)
	Elementwise multiplication of a sparse vector and a dense vector returning a dense vector.
template<class T >
Sparse_Vec< T >	elem_mult_s (const Sparse_Vec< T > &v1, const Vec< T > &v2)
	Elementwise multiplication of a sparse vector and a dense vector returning a sparse vector.
template<class T >
Vec< T >	elem_mult (const Vec< T > &v1, const Sparse_Vec< T > &v2)
	Elementwise multiplication of a dense vector and a sparse vector returning a dense vector.
template<class T >
Sparse_Vec< T >	elem_mult_s (const Vec< T > &v1, const Sparse_Vec< T > &v2)
	Elementwise multiplication of a dense vector and a sparse vector returning a sparse vector.
template<class T >
Sparse_Vec< T >	sparse (const Vec< T > &v)
	Convert a dense vector v into its sparse representation.
template<class T >
Sparse_Vec< T >	sparse (const Vec< T > &v, T epsilon)
	Convert a dense vector v into its sparse representation.
template<class T >
Vec< T >	full (const Sparse_Vec< T > &s)
	Convert a sparse vector s into its dense representation.
void	tic ()
	Reset and start timer.
double	toc ()
	Returns the elapsed time since last tic()
void	toc_print ()
	Prints the elapsed time since last tic()
void	pause (double t=-1)
	pause
template<class Num_T >
Vec< Num_T >	operator+ (const Vec< Num_T > &v1, const Vec< Num_T > &v2)
	Addition of two vectors.
template<class Num_T >
Vec< Num_T >	operator+ (const Vec< Num_T > &v, Num_T t)
	Addition of a vector and a scalar.
template<class Num_T >
Vec< Num_T >	operator+ (Num_T t, const Vec< Num_T > &v)
	Addition of a scalar and a vector.
template<class Num_T >
Vec< Num_T >	operator- (const Vec< Num_T > &v1, const Vec< Num_T > &v2)
	Subtraction of a vector from a vector.
template<class Num_T >
Vec< Num_T >	operator- (const Vec< Num_T > &v, Num_T t)
	Subtraction of a scalar from a vector.
template<class Num_T >
Vec< Num_T >	operator- (Num_T t, const Vec< Num_T > &v)
	Subtraction of vector from scalar. Results in a vector.
template<class Num_T >
Vec< Num_T >	operator- (const Vec< Num_T > &v)
	Negation of vector.
template<class Num_T >
Num_T	dot (const Vec< Num_T > &v1, const Vec< Num_T > &v2)
	Inner (dot) product of two vectors v1 and v2.
template<class Num_T >
Num_T	operator* (const Vec< Num_T > &v1, const Vec< Num_T > &v2)
	Inner (dot) product of two vectors v1 and v2.
template<class Num_T >
Mat< Num_T >	outer_product (const Vec< Num_T > &v1, const Vec< Num_T > &v2, bool hermitian=false)
	Outer product of two vectors v1 and v2.
template<class Num_T >
Vec< Num_T >	operator* (const Vec< Num_T > &v, Num_T t)
	Multiplication of a vector and a scalar.
template<class Num_T >
Vec< Num_T >	operator* (Num_T t, const Vec< Num_T > &v)
	Multiplication of a scalar and a vector. Results in a vector.
template<class Num_T >
Vec< Num_T >	elem_mult (const Vec< Num_T > &a, const Vec< Num_T > &b)
	Element-wise multiplication of two vectors.
template<class Num_T >
Vec< Num_T >	elem_mult (const Vec< Num_T > &a, const Vec< Num_T > &b, const Vec< Num_T > &c)
	Element-wise multiplication of three vectors.
template<class Num_T >
Vec< Num_T >	elem_mult (const Vec< Num_T > &a, const Vec< Num_T > &b, const Vec< Num_T > &c, const Vec< Num_T > &d)
	Element-wise multiplication of four vectors.
template<class Num_T >
void	elem_mult_out (const Vec< Num_T > &a, const Vec< Num_T > &b, Vec< Num_T > &out)
	Element-wise multiplication of two vectors, storing the result in vector out.
template<class Num_T >
void	elem_mult_out (const Vec< Num_T > &a, const Vec< Num_T > &b, const Vec< Num_T > &c, Vec< Num_T > &out)
	Element-wise multiplication of three vectors, storing the result in vector out.
template<class Num_T >
void	elem_mult_out (const Vec< Num_T > &a, const Vec< Num_T > &b, const Vec< Num_T > &c, const Vec< Num_T > &d, Vec< Num_T > &out)
	Element-wise multiplication of four vectors, storing the result in vector out.
template<class Num_T >
void	elem_mult_inplace (const Vec< Num_T > &a, Vec< Num_T > &b)
	In-place element-wise multiplication of two vectors. Faster version of b = elem_mult(a,b).
template<class Num_T >
Num_T	elem_mult_sum (const Vec< Num_T > &a, const Vec< Num_T > &b)
	Element-wise multiplication of two vectors, followed by summation of the resultant elements. Fast version of sum(elem_mult(a,b)).
template<class Num_T >
Vec< Num_T >	operator/ (const Vec< Num_T > &v, Num_T t)
	Division of all elements in v with t.
template<class Num_T >
Vec< Num_T >	operator/ (Num_T t, const Vec< Num_T > &v)
	Division of t with all elements in v.
template<class Num_T >
Vec< Num_T >	elem_div (const Vec< Num_T > &a, const Vec< Num_T > &b)
	Elementwise division of two vectors.
template<class Num_T >
Vec< Num_T >	elem_div (Num_T t, const Vec< Num_T > &v)
	This function is deprecated. Please use operator/(Num_T, const Vec<Num_T &) instead.
template<class Num_T >
void	elem_div_out (const Vec< Num_T > &a, const Vec< Num_T > &b, Vec< Num_T > &out)
	Elementwise division of two vectors, storing the result in vector out.
template<class Num_T >
Num_T	elem_div_sum (const Vec< Num_T > &a, const Vec< Num_T > &b)
	Elementwise division of two vectors, followed by summation of the resultant elements. Fast version of sum(elem_div(a,b))
template<class Num_T >
Vec< Num_T >	concat (const Vec< Num_T > &v, Num_T a)
	Append element a to the end of the vector v.
template<class Num_T >
Vec< Num_T >	concat (Num_T a, const Vec< Num_T > &v)
	Concat element a to the beginning of the vector v.
template<class Num_T >
Vec< Num_T >	concat (const Vec< Num_T > &v1, const Vec< Num_T > &v2)
	Concat vectors v1 and v2.
template<class Num_T >
Vec< Num_T >	concat (const Vec< Num_T > &v1, const Vec< Num_T > &v2, const Vec< Num_T > &v3)
	Concat vectors v1, v2 and v3.
template<class Num_T >
Vec< Num_T >	concat (const Vec< Num_T > &v1, const Vec< Num_T > &v2, const Vec< Num_T > &v3, const Vec< Num_T > &v4)
	Concat vectors v1, v2, v3 and v4.
template<class Num_T >
Vec< Num_T >	concat (const Vec< Num_T > &v1, const Vec< Num_T > &v2, const Vec< Num_T > &v3, const Vec< Num_T > &v4, const Vec< Num_T > &v5)
	Concat vectors v1, v2 v3, v4 and v5.
template<class Num_T >
std::ostream &	operator<< (std::ostream &os, const Vec< Num_T > &v)
	Output stream operator of a vector v.
template<class Num_T >
std::istream &	operator>> (std::istream &is, Vec< Num_T > &v)
	Input stream operator to read a vector.
bool	chol (const mat &X, mat &F)
	Cholesky factorisation of real symmetric and positive definite matrix.
bool	chol (const cmat &X, cmat &F)
	Cholesky factorisation of complex hermitian and positive-definite matrix.
cmat	chol (const cmat &X)
	Cholesky factorisation of complex hermitian and positive-definite matrix.
mat	chol (const mat &X)
	Cholesky factorisation of real symmetric and positive definite matrix.
double	det (const mat &X)
	Determinant of real square matrix.Calculate determinant of the real matrix .
std::complex< double >	det (const cmat &X)
	Determinant of complex square matrix.Calculate determinant of the complex matrix .
bool	eig_sym (const mat &A, vec &d, mat &V)
	Calculates the eigenvalues and eigenvectors of a symmetric real matrix.
bool	eig_sym (const mat &A, vec &d)
	Calculates the eigenvalues of a symmetric real matrix.
bool	eig_sym (const cmat &A, vec &d, cmat &V)
	Calculates the eigenvalues and eigenvectors of a hermitian complex matrix.
bool	eig_sym (const cmat &A, vec &d)
	Calculates the eigenvalues of a hermitian complex matrix.
bool	eig (const mat &A, cvec &d, cmat &V)
	Calculates the eigenvalues and eigenvectors of a real non-symmetric matrix.
bool	eig (const mat &A, cvec &d)
	Calculates the eigenvalues of a real non-symmetric matrix.
bool	eig (const cmat &A, cvec &d, cmat &V)
	Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix.
bool	eig (const cmat &A, cvec &d)
	Calculates the eigenvalues of a complex non-hermitian matrix.
vec	eig_sym (const mat &A)
	Calculates the eigenvalues of a symmetric real matrix.
vec	eig_sym (const cmat &A)
	Calculates the eigenvalues of a hermitian complex matrix.
cvec	eig (const mat &A)
	Calculates the eigenvalues of a real non-symmetric matrix.
cvec	eig (const cmat &A)
	Calculates the eigenvalues of a complex non-hermitian matrix.
bool	inv (const mat &X, mat &Y)
	Inverse of real square matrix.Calculate the inverse of the real matrix .
bool	inv (const cmat &X, cmat &Y)
	Inverse of complex square matrix.Calculate the inverse of the complex matrix .
cmat	inv (const cmat &X)
	Inverse of real square matrix.Calculate the inverse of the complex matrix .
mat	inv (const mat &X)
	Inverse of real square matrix.Calculate the inverse of the real matrix .
bool	ls_solve_chol (const mat &A, const vec &b, vec &x)
	Solve linear equation system by Cholesky factorisation.
bool	ls_solve_chol (const mat &A, const mat &B, mat &X)
	Solve linear equation system by Cholesky factorisation.
bool	ls_solve_chol (const cmat &A, const cvec &b, cvec &x)
	Solve linear equation system by Cholesky factorisation.
bool	ls_solve_chol (const cmat &A, const cmat &B, cmat &X)
	Solve linear equation system by Cholesky factorisation.
vec	ls_solve_chol (const mat &A, const vec &b)
	Solve linear equation system by Cholesky factorisation.
mat	ls_solve_chol (const mat &A, const mat &B)
	Solve linear equation system by Cholesky factorisation.
cvec	ls_solve_chol (const cmat &A, const cvec &b)
	Solve linear equation system by Cholesky factorisation.
cmat	ls_solve_chol (const cmat &A, const cmat &B)
	Solve linear equation system by Cholesky factorisation.
bool	ls_solve (const mat &A, const vec &b, vec &x)
	Solve linear equation system by LU factorisation.
bool	ls_solve (const mat &A, const mat &B, mat &X)
	Solve multiple linear equations by LU factorisation.
bool	ls_solve (const cmat &A, const cvec &b, cvec &x)
	Solve linear equation system by LU factorisation.
bool	ls_solve (const cmat &A, const cmat &B, cmat &X)
	Solve multiple linear equations by LU factorisation.
vec	ls_solve (const mat &A, const vec &b)
	Solve linear equation system by LU factorisation.
mat	ls_solve (const mat &A, const mat &B)
	Solve multiple linear equations by LU factorisation.
cvec	ls_solve (const cmat &A, const cvec &b)
	Solve linear equation system by LU factorisation.
cmat	ls_solve (const cmat &A, const cmat &B)
	Solve multiple linear equations by LU factorisation.
bool	ls_solve_od (const mat &A, const vec &b, vec &x)
	Solves overdetermined linear equation systems.
bool	ls_solve_od (const mat &A, const mat &B, mat &X)
	Solves overdetermined linear equation systems.
bool	ls_solve_od (const cmat &A, const cvec &b, cvec &x)
	Solves overdetermined linear equation systems.
bool	ls_solve_od (const cmat &A, const cmat &B, cmat &X)
	Solves overdetermined linear equation systems.
vec	ls_solve_od (const mat &A, const vec &b)
	Solves overdetermined linear equation systems.
mat	ls_solve_od (const mat &A, const mat &B)
	Solves overdetermined linear equation systems.
cvec	ls_solve_od (const cmat &A, const cvec &b)
	Solves overdetermined linear equation systems.
cmat	ls_solve_od (const cmat &A, const cmat &B)
	Solves overdetermined linear equation systems.
bool	ls_solve_ud (const mat &A, const vec &b, vec &x)
	Solves underdetermined linear equation systems.
bool	ls_solve_ud (const mat &A, const mat &B, mat &X)
	Solves underdetermined linear equation systems.
bool	ls_solve_ud (const cmat &A, const cvec &b, cvec &x)
	Solves underdetermined linear equation systems.
bool	ls_solve_ud (const cmat &A, const cmat &B, cmat &X)
	Solves underdetermined linear equation systems.
vec	ls_solve_ud (const mat &A, const vec &b)
	Solves overdetermined linear equation systems.
mat	ls_solve_ud (const mat &A, const mat &B)
	Solves underdetermined linear equation systems.
cvec	ls_solve_ud (const cmat &A, const cvec &b)
	Solves overdetermined linear equation systems.
cmat	ls_solve_ud (const cmat &A, const cmat &B)
	Solves underdetermined linear equation systems.
bool	backslash (const mat &A, const vec &b, vec &x)
	A general linear equation system solver.
vec	backslash (const mat &A, const vec &b)
	A general linear equation system solver.
bool	backslash (const mat &A, const mat &B, mat &X)
	A general linear equation system solver.
mat	backslash (const mat &A, const mat &B)
	A general linear equation system solver.
bool	backslash (const cmat &A, const cvec &b, cvec &x)
	A general linear equation system solver.
cvec	backslash (const cmat &A, const cvec &b)
	A general linear equation system solver.
bool	backslash (const cmat &A, const cmat &B, cmat &X)
	A general linear equation system solver.
cmat	backslash (const cmat &A, const cmat &B)
	A general linear equation system solver.
vec	forward_substitution (const mat &L, const vec &b)
	Forward substitution of square matrix.
void	forward_substitution (const mat &L, const vec &b, vec &x)
	Forward substitution of square matrix.
vec	forward_substitution (const mat &L, int p, const vec &b)
	Forward substitution of band matrices.
void	forward_substitution (const mat &L, int p, const vec &b, vec &x)
	Forward substitution of band matrices.
vec	backward_substitution (const mat &U, const vec &b)
	Backward substitution of square matrix.
void	backward_substitution (const mat &U, const vec &b, vec &x)
	Backward substitution of square matrix.
vec	backward_substitution (const mat &U, int q, const vec &b)
	Backward substitution of band matrix.
void	backward_substitution (const mat &U, int q, const vec &b, vec &x)
	Backward substitution of band matrix.
bool	lu (const mat &X, mat &L, mat &U, ivec &p)
	LU factorisation of real matrix.
bool	lu (const cmat &X, cmat &L, cmat &U, ivec &p)
	LU factorisation of real matrix.
void	interchange_permutations (vec &b, const ivec &p)
	Makes swapping of vector b according to the interchange permutation vector p.
bmat	permutation_matrix (const ivec &p)
	Make permutation matrix P from the interchange permutation vector p.
bool	qr (const mat &A, mat &Q, mat &R)
	QR factorisation of real matrix.
bool	qr (const mat &A, mat &R)
	QR factorisation of real matrix with suppressed evaluation of Q.
bool	qr (const mat &A, mat &Q, mat &R, bmat &P)
	QR factorisation of real matrix with pivoting.
bool	qr (const cmat &A, cmat &Q, cmat &R)
	QR factorisation of a complex matrix.
bool	qr (const cmat &A, cmat &R)
	QR factorisation of complex matrix with suppressed evaluation of Q.
bool	qr (const cmat &A, cmat &Q, cmat &R, bmat &P)
	QR factorisation of a complex matrix with pivoting.
bool	schur (const mat &A, mat &U, mat &T)
	Schur decomposition of a real matrix.
bool	schur (const cmat &A, cmat &U, cmat &T)
	Schur decomposition of a complex matrix.
mat	schur (const mat &A)
	Schur decomposition of a real matrix.
cmat	schur (const cmat &A)
	Schur decomposition of a complex matrix.
bool	svd (const mat &A, vec &s)
	Get singular values s of a real matrix A using SVD.
bool	svd (const cmat &A, vec &s)
	Get singular values s of a complex matrix A using SVD.
bool	svd (const mat &A, mat &U, vec &s, mat &V)
	Perform Singular Value Decomposition (SVD) of a real matrix A.
bool	svd (const cmat &A, cmat &U, vec &s, cmat &V)
	Perform Singular Value Decomposition (SVD) of a complex matrix A.
vec	svd (const mat &A)
	Return singular values of a real matrix A using SVD.
vec	svd (const cmat &A)
	Return singular values of a complex matrix A using SVD.
vec	sqr (const cvec &x)
	Absolute square of elements.
mat	sqr (const cmat &x)
	Absolute square of elements.
vec	abs (const cvec &x)
	Absolute value.
mat	abs (const cmat &x)
	Absolute value.
double	gamma (double x)
	Deprecated gamma function - please use tgamma() instead.
vec	gamma (const vec &x)
	Deprecated gamma function for vectors. Will be changed to tgamma().
mat	gamma (const mat &x)
	Deprecated gamma function for matrices. Will be changed to tgamma().
double	fact (int index)
	Calculates factorial coefficient for index <= 170.
double	binom (int n, int k)
	Compute the binomial coefficient "n over k".
int	binom_i (int n, int k)
	Compute the binomial coefficient "n over k".
double	log_binom (int n, int k)
	Compute the base 10 logarithm of the binomial coefficient "n over k".
int	gcd (int a, int b)
	Compute the greatest common divisor (GCD) g of the elements a and b.
vec	real (const cvec &x)
	Real part of complex values.
mat	real (const cmat &x)
	Real part of complex values.
vec	imag (const cvec &x)
	Imaginary part of complex values.
mat	imag (const cmat &x)
	Imaginary part of complex values.
vec	arg (const cvec &x)
	Argument (angle)
mat	arg (const cmat &x)
	Argument (angle)
double	sqr (double x)
	Square of x.
double	sqr (const std::complex< double > &x)
	Absolute square of complex-valued x, ||x||^2.
vec	sqr (const vec &x)
	Square of elements.
mat	sqr (const mat &x)
	Square of elements.
vec	abs (const vec &x)
	Absolute value.
mat	abs (const mat &x)
	Absolute value.
ivec	abs (const ivec &x)
	Absolute value.
imat	abs (const imat &x)
	Absolute value.
double	sign (double x)
	Signum function.
vec	sign (const vec &x)
	Signum function.
mat	sign (const mat &x)
	Signum function.
double	sgn (double x)
	Signum function.
vec	sgn (const vec &x)
	Signum function.
mat	sgn (const mat &x)
	Signum function.
int	sign_i (int x)
	Signum function.
ivec	sign_i (const ivec &x)
	Signum function.
imat	sign_i (const imat &x)
	Signum function.
int	sgn_i (int x)
	Signum function.
ivec	sgn_i (const ivec &x)
	Signum function.
imat	sgn_i (const imat &x)
	Signum function.
int	sign_i (double x)
	Signum function.
vec	sqrt (const vec &x)
	Square root of the elements.
mat	sqrt (const mat &x)
	Square root of the elements.
double	rem (double x, double y)
	The reminder of the division x/y.
vec	rem (const vec &x, double y)
	Elementwise reminder of the division x/y for vec and double.
vec	rem (double x, const vec &y)
	Elementwise reminder of the division x/y for double and vec.
mat	rem (const mat &x, double y)
	Elementwise reminder of the division x/y for mat and double.
mat	rem (double x, const mat &y)
	Elementwise reminder of the division x/y for double and mat.
int	mod (int k, int n)
	Calculates the modulus, i.e. the signed reminder after division.
vec	angle (const cvec &x)
	Angle.
mat	angle (const cmat &x)
	Angle.
cvec	conj (const cvec &x)
	Conjugate of complex value.
cmat	conj (const cmat &x)
	Conjugate of complex value.
std::complex< double >	cerfc_continued_fraction (const std::complex< double > &z)
std::complex< double >	cerf_continued_fraction (const std::complex< double > &z)
	Complementary function to cerfc_continued_fraction.
std::complex< double >	cerf_series (const std::complex< double > &z)
std::complex< double >	cerf_rybicki (const std::complex< double > &z)
std::complex< double >	erf (const std::complex< double > &z)
	Error function for complex argument.
double	erfinv (double x)
	Inverse of error function.
double	Qfunc (double x)
	Q-function.
vec	erf (const vec &x)
	Error function.
mat	erf (const mat &x)
	Error function.
cvec	erf (const cvec &x)
	Error function.
cmat	erf (const cmat &x)
	Error function.
vec	erfinv (const vec &x)
	Inverse of error function.
mat	erfinv (const mat &x)
	Inverse of error function.
vec	erfc (const vec &x)
	Complementary error function.
mat	erfc (const mat &x)
	Complementary error function.
vec	Qfunc (const vec &x)
	Q-function.
mat	Qfunc (const mat &x)
	Q-function.
template<typename Ftn >
double	quad (Ftn f, double a, double b, double tol=std::numeric_limits< double >::epsilon())
ITPP_EXPORT double	quad (double(*f)(double), double a, double b, double tol=std::numeric_limits< double >::epsilon())
template<typename Ftn >
double	quadl (Ftn f, double a, double b, double tol=std::numeric_limits< double >::epsilon())
ITPP_EXPORT double	quadl (double(*f)(double), double a, double b, double tol=std::numeric_limits< double >::epsilon())
vec	log2 (const vec &x)
	log-2 of the elements
mat	log2 (const mat &x)
	log-2 of the elements
double	log_add (double log_a, double log_b)
	Safe substitute for log(exp(log_a) + exp(log_b))
double	logb (double b, double x)
	Base-b logarithm.
int	pow2i (int x)
	Calculate two to the power of x (2^x); x is integer.
double	pow2 (double x)
	Calculate two to the power of x (2^x)
double	pow2 (int x)
	Calculate two to the power of x (2^x) for large integer x.
double	pow10 (double x)
	Calculate ten to the power of x (10^x)
double	dB (double x)
	Decibel of x (10*log10(x))
double	inv_dB (double x)
	Inverse of decibel of x.
int	int2bits (int n)
	Calculate the number of bits needed to represent an integer n.
int	levels2bits (int n)
	Calculate the number of bits needed to represent n different values (levels).
double	trunc_log (double x)
	Truncated natural logarithm function.
double	trunc_exp (double x)
	Truncated exponential function.
vec	exp (const vec &x)
	Exp of the elements of a vector x.
cvec	exp (const cvec &x)
	Exp of the elements of a complex vector x.
mat	exp (const mat &m)
	Exp of the elements of a matrix m.
cmat	exp (const cmat &m)
	Exp of the elements of a complex matrix m.
vec	pow (const double x, const vec &y)
	Calculates x to the power of y (x^y)
mat	pow (const double x, const mat &y)
	Calculates x to the power of y (x^y)
vec	pow (const vec &x, const double y)
	Calculates x to the power of y (x^y)
mat	pow (const mat &x, const double y)
	Calculates x to the power of y (x^y)
vec	pow2 (const vec &x)
	Calculates two to the power of x (2^x)
vec	pow2 (const ivec &x)
	Calculates two to the power of x (2^x) for integer x.
mat	pow2 (const mat &x)
	Calculates two to the power of x (2^x)
mat	pow2 (const imat &x)
	Calculates two to the power of x (2^x) for integer x.
vec	pow10 (const vec &x)
	Calculates ten to the power of x (10^x)
mat	pow10 (const mat &x)
	Calculates ten to the power of x (10^x)
vec	log (const vec &x)
	The natural logarithm of the elements.
mat	log (const mat &x)
	The natural logarithm of the elements.
cvec	log (const cvec &x)
	The natural logarithm of the elements.
cmat	log (const cmat &x)
	The natural logarithm of the elements.
vec	log10 (const vec &x)
	log-10 of the elements
mat	log10 (const mat &x)
	log-10 of the elements
vec	logb (double b, const vec &x)
	log-b of x
mat	logb (double b, const mat &x)
	log-b of x
vec	dB (const vec &x)
	Calculates 10*log10(x)
mat	dB (const mat &x)
	Calculates 10*log10(x)
vec	inv_dB (const vec &x)
	Calulates the inverse of dB, 10^(x/10)
mat	inv_dB (const mat &x)
	Calculates the inverse of dB, 10^(x/10)
ivec	int2bits (const ivec &v)
	Calculate the number of bits needed to represent each integer in a vector.
ivec	levels2bits (const ivec &v)
	Calculate the number of bits needed to represent a numer of levels saved in a vector.
template<class T >
T	max (const Vec< T > &v)
	Maximum value of vector.
template<class T >
T	max (const Vec< T > &v, int &index)
	Maximum value of vector, also returns the index position of max value.
template<class T >
Vec< T >	max (const Mat< T > &m, int dim=1)
template<class T >
Vec< T >	max (const Mat< T > &m, ivec &index, int dim=1)
template<class T >
T	min (const Vec< T > &in)
	Minimum value of vector.
template<class T >
T	min (const Vec< T > &in, int &index)
	Minimum value of vector, also returns the index position of min value.
template<class T >
Vec< T >	min (const Mat< T > &m, int dim=1)
template<class T >
Vec< T >	min (const Mat< T > &m, ivec &index, int dim=1)
template<class T >
int	max_index (const Vec< T > &in)
	Return the postion of the maximum element in the vector.
template<class T >
void	max_index (const Mat< T > &m, int &row, int &col)
	Return the postion of the maximum element in the matrix.
template<class T >
int	min_index (const Vec< T > &in)
	Return the postion of the minimum element in the vector.
template<class T >
void	min_index (const Mat< T > &m, int &row, int &col)
	Return the postion of the minimum element in the matrix.
std::string	itpp_version ()
	Returns IT++ library version number, e.g. "3.7.1".
bool	is_bigendian ()
	Returns true if machine endianness is BIG_ENDIAN.
bool	is_int (double x)
	Return true if x is an integer.
bool	is_even (int x)
	Return true if x is an even integer.
bool	check_big_endianness ()
	This function is deprecated. Please use is_bigendian() instead.
vec	asinh (const vec &x)
	Inverse sine hyperbolic function.
mat	asinh (const mat &x)
	Inverse sine hyperbolic function.
vec	acosh (const vec &x)
	Inverse cosine hyperbolic function.
mat	acosh (const mat &x)
	Inverse cosine hyperbolic function.
vec	atanh (const vec &x)
	Inverse tan hyperbolic function.
mat	atanh (const mat &x)
	Inverse tan hyperbolic function.
double	sinc (double x)
	Sinc function: sinc(x) = sin(pi*x)/pi*x.
vec	sin (const vec &x)
	Sine function.
mat	sin (const mat &x)
	Sine function.
vec	cos (const vec &x)
	Cosine function.
mat	cos (const mat &x)
	Cosine function.
vec	tan (const vec &x)
	Tan function.
mat	tan (const mat &x)
	Tan function.
vec	asin (const vec &x)
	Inverse sine function.
mat	asin (const mat &x)
	Inverse sine function.
vec	acos (const vec &x)
	Inverse cosine function.
mat	acos (const mat &x)
	Inverse cosine function.
vec	atan (const vec &x)
	Inverse tan function.
mat	atan (const mat &x)
	Inverse tan function.
vec	sinc (const vec &x)
	Sinc function, sin(pi*x)/(pi*x)
mat	sinc (const mat &x)
	Sinc function, sin(pi*x)/(pi*x)
vec	sinh (const vec &x)
	Sine hyperbolic function.
mat	sinh (const mat &x)
	Sine hyperbolic function.
vec	cosh (const vec &x)
	Cosine hyperbolic function.
mat	cosh (const mat &x)
	Cosine hyperbolic function.
vec	tanh (const vec &x)
	Tan hyperbolic function.
mat	tanh (const mat &x)
	Tan hyperbolic function.
bmat	graycode (int m)
	Generate Gray code of blocklength m.The codes are contained as binary codewords {0,1} in the rows of the returned matrix. See also the gray() function in math/scalfunc.h.
int	hamming_distance (const bvec &a, const bvec &b)
	Calculate the Hamming distance between a and b.
int	weight (const bvec &a)
	Calculate the Hamming weight of a.
vec	waterfilling (const vec &alpha, double P)
	Compute the water-filling solutionThis function computes the solution of the water-filling problem subject to .
int	reverse_int (int length, int in)
int	weight_int (int length, int in)
int	compare_spectra (ivec v1, ivec v2)
int	compare_spectra (ivec v1, ivec v2, vec weight_profile)
std::istream &	operator>> (std::istream &is, GF &ingf)
	Input stream operator for GF.
std::ostream &	operator<< (std::ostream &os, const GF &ingf)
	Output stream operator for GF.
std::ostream &	operator<< (std::ostream &os, const GFX &ingfx)
	Output stream operator for GFX.
GFX	divgfx (const GFX &c, const GFX &g)
	Division of two GFX (local help function)
GFX	modgfx (const GFX &a, const GFX &b)
	Modulo function of two GFX (local help function)
ITPP_EXPORT GFX	operator* (const GF &ingf, const GFX &ingfx)
	Multiplication of GF and GFX.
ITPP_EXPORT GFX	operator* (const GFX &ingfx, const GF &ingf)
	Multiplication of GFX and GF.
ITPP_EXPORT GFX	operator/ (const GFX &ingfx, const GF &ingf)
	Division of GFX by GF.
std::ostream &	operator<< (std::ostream &os, const LDPC_Code &C)
	Print some properties of the LDPC codec in plain text.
std::ostream &	operator<< (std::ostream &os, const LLR_calc_unit &lcu)
	Print some properties of the LLR calculation unit in plain text.
std::ostream &	operator<< (std::ostream &os, const Modulator_NRD &m)
	Print some properties of the MIMO modulator (mainly to aid debugging)
std::ostream &	operator<< (std::ostream &os, const Modulator_NCD &m)
	Print some properties of the MIMO modulator (mainly to aid debugging)
GFX	formal_derivate (const GFX &f)
	Local help function.
smat	wcdma_spreading_codes (int SF)
	Generates the OVSF (orthogonal variable spreading factor) spreading codes used in WCDMA.The codes are written row-wise in the return matrix.
int	calculate_uncoded_size (Punctured_Turbo_Codec &tc, int punctured_size, int &fill_bits)
ivec	wcdma_turbo_interleaver_sequence (int interleaver_size)
	Generates the interleaver sequence for the internal turbo encoder interleaver used in WCDMA.
ivec	lte_turbo_interleaver_sequence (int interleaver_size)
	Generates the interleaver sequence for the internal turbo encoder interleaver used in LTE.
int	assert_shifts (const CFix &x, const CFix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	assert_shifts (const CFix &x, const Fix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	assert_shifts (const CFix &x, int y)
	Check that x.shift==0 OR x==0 OR y==0 and return x.shift.
std::istream &	operator>> (std::istream &is, CFix &x)
	Input bit representation and, optionally, the shift.
std::ostream &	operator<< (std::ostream &os, const CFix &x)
	Output bit representation and, optionally, the shift.
int	assert_shifts (const Fix &x, const Fix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	assert_shifts (const Fix &x, int y)
	Check that x.shift==0 OR x==0 OR y==0 and return x.shift.
std::istream &	operator>> (std::istream &is, Fix &x)
	Input bit representation and, optionally, the shift.
std::ostream &	operator<< (std::ostream &os, const Fix &x)
	Output bit representation and, optionally, the shift.
std::ostream &	operator<< (std::ostream &os, const output_mode &o)
	Set output mode.
template<>
void	create_elements< Fix > (Fix *&ptr, const int n, const Factory &f)
	Create an n-length array of Fix using Fix_Factory f.
template<>
void	create_elements< CFix > (CFix *&ptr, const int n, const Factory &f)
	Create an n-length array of CFix using Fix_Factory f.
const Fix_Factory	FIX1 (1, TC, WRAP)
	Fix_Factories for signed Fix/CFix with wrap-around (FIX1, FIX2, ..., FIX64)
const Fix_Factory	UFIX1 (1, US, WRAP)
	Fix_Factories for unsigned Fix/CFix with wrap-around (UFIX1, UFIX2, ..., UFIX64)
const Fix_Factory	SFIX1 (1, TC, SAT)
	Fix_Factories for unsigned Fix/CFix with wrap-around (SFIX1, SFIX2, ..., SFIX64)
const Fix_Factory	SUFIX1 (1, US, SAT)
	Fix_Factories for unsigned Fix/CFix with saturation (SUFIX1, SUFIX2, ..., SUFIX64)
vec	to_vec (const fixvec &v)
	Converts a fixvec to vec.
cvec	to_cvec (const cfixvec &v)
	Converts a cfixvec to cvec.
mat	to_mat (const fixmat &m)
	Converts a fixmat to mat.
cmat	to_cmat (const cfixmat &m)
	Converts a cfixmat to cmat.
Fix	abs (const Fix &x)
	Absolute value.
Fix	real (const CFix &x)
	Real part of complex value.
Fix	imag (const CFix &x)
	Imaginary part of complex value.
CFix	conj (const CFix &x)
	Conjugate of complex value.
template<class T >
bool	is_fix (const T &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	is_fix (const Fix &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	is_fix (const fixvec &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	is_fix (const fixmat &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	is_fix (const CFix &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<class T >
bool	is_fix (const Array< T > &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
void	set_fix (Fix &y, double x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (Fix &y, double x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (fixvec &y, const vec &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (fixvec &y, const vec &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (fixmat &y, const mat &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (fixmat &y, const mat &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (double &y, double x, int)
	Set y = x. Useful in templated code.
void	set_fix (double &y, double x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (vec &y, const vec &x, int)
	Set y = x. Useful in templated code.
void	set_fix (vec &y, const vec &x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (mat &y, const mat &x, int)
	Set y = x. Useful in templated code.
void	set_fix (mat &y, const mat &x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (CFix &y, std::complex< double > x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (CFix &y, double real, double imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	set_fix (CFix &y, std::complex< double > x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (CFix &y, double real, double imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	set_fix (cfixvec &y, const cvec &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (cfixvec &y, const vec &real, const vec &imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	set_fix (cfixvec &y, const cvec &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (cfixvec &y, const vec &real, const vec &imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	set_fix (cfixmat &y, const cmat &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	set_fix (cfixmat &y, const mat &real, const mat &imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	set_fix (cfixmat &y, const cmat &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	set_fix (cfixmat &y, const mat &real, const mat &imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	set_fix (std::complex< double > &y, const std::complex< double > &x, int)
	Set y = x. Useful in templated code.
void	set_fix (std::complex< double > &y, double real, double imag, int)
	Set y = real + i*imag. Useful in templated code.
void	set_fix (std::complex< double > &y, const std::complex< double > &x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (std::complex< double > &y, double real, double imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
void	set_fix (cvec &y, const cvec &x, int)
	Set y = x. Useful in templated code.
void	set_fix (cvec &y, const vec &real, const vec &imag, int)
	Set y = real + i*imag. Useful in templated code.
void	set_fix (cvec &y, const cvec &x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (cvec &y, const vec &real, const vec &imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
void	set_fix (cmat &y, const cmat &x, int)
	Set y = x. Useful in templated code.
void	set_fix (cmat &y, const mat &real, const mat &imag, int)
	Set y = real + i*imag. Useful in templated code.
void	set_fix (cmat &y, const cmat &x, int, q_mode)
	Set y = x. Useful in templated code.
void	set_fix (cmat &y, const mat &real, const mat &imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
template<class T1 , class T2 >
void	set_fix (Array< T1 > &y, const Array< T2 > &x, int n)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	set_fix (Array< T1 > &y, const Array< T2 > &real, const Array< T2 > &imag, int n)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	set_fix (Array< T1 > &y, const Array< T2 > &x, int n, q_mode q)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	set_fix (Array< T1 > &y, const Array< T2 > &real, const Array< T2 > &imag, int n, q_mode q)
	Call set_fix for each Array element.
void	lshift_fix (Fix &y, int n)
	Left shift n bits.
void	rshift_fix (Fix &y, int n)
	Right shift n bits using the quantization mode of y.
void	rshift_fix (Fix &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	lshift_fix (fixvec &y, int n)
	Left shift n bits.
void	rshift_fix (fixvec &y, int n)
	Right shift n bits using the quantization mode of y.
void	rshift_fix (fixvec &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	lshift_fix (fixmat &y, int n)
	Left shift n bits.
void	rshift_fix (fixmat &y, int n)
	Right shift n bits using the quantization mode of y.
void	rshift_fix (fixmat &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	lshift_fix (double &, int)
	Dummy function useful in templated code.
void	rshift_fix (double &, int)
	Dummy function useful in templated code.
void	rshift_fix (double &, int, q_mode)
	Dummy function useful in templated code.
void	lshift_fix (vec &, int)
	Dummy function useful in templated code.
void	rshift_fix (vec &, int)
	Dummy function useful in templated code.
void	rshift_fix (vec &, int, q_mode)
	Dummy function useful in templated code.
void	lshift_fix (mat &, int)
	Dummy function useful in templated code.
void	rshift_fix (mat &, int)
	Dummy function useful in templated code.
void	rshift_fix (mat &, int, q_mode)
	Dummy function useful in templated code.
void	lshift_fix (CFix &y, int n)
	Left shift n bits.
void	rshift_fix (CFix &y, int n)
	Right shift n bits using the quantization mode of y.
void	rshift_fix (CFix &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	lshift_fix (std::complex< double > &, int)
	Dummy function useful in templated code.
void	rshift_fix (std::complex< double > &, int)
	Dummy function useful in templated code.
void	rshift_fix (std::complex< double > &, int, q_mode)
	Dummy function useful in templated code.
void	lshift_fix (cvec &, int)
	Dummy function useful in templated code.
void	rshift_fix (cvec &, int)
	Dummy function useful in templated code.
void	rshift_fix (cvec &, int, q_mode)
	Dummy function useful in templated code.
void	lshift_fix (cmat &, int)
	Dummy function useful in templated code.
void	rshift_fix (cmat &, int)
	Dummy function useful in templated code.
void	rshift_fix (cmat &, int, q_mode)
	Dummy function useful in templated code.
template<class T >
void	lshift_fix (Array< T > &y, int n)
	Call lshift_fix for each Array element.
template<class T >
void	rshift_fix (Array< T > &y, int n)
	Call rshift_fix for each Array element.
template<class T >
void	rshift_fix (Array< T > &y, int n, q_mode q)
	Call rshift_fix for each Array element.
void	assert_fixshift (double, int)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	assert_fixshift (const std::complex< double > &, int)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	assert_fixshift (const Fix &x, int shift)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	assert_fixshift (const CFix &x, int shift)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
template<class T >
T	to (double x)
	Convert double to T.
template<class T >
T	to (const Fix &x)
	Convert Fix to T.
template<class T >
T	to (const std::complex< double > &x)
	Convert std::complex<double> to T.
template<class T >
T	to (const CFix &x)
	Convert CFix to T.
template<class T >
T	to (double real, double imag)
	Convert double (real and imaginary parts) to T.
template<class T >
T	to (const Fix &real, const Fix &imag)
	Convert Fix (real and imaginary parts) to T.
template<class T , class U >
Vec< T >	to (const Vec< U > &x)
	Convert Vec<U> to Vec<T>
template<>
vec	to< double > (const vec &x)
	Convert vec to vec.
template<>
cvec	to< std::complex< double > > (const cvec &x)
	Convert cvec to cvec.
template<>
fixvec	to< Fix > (const fixvec &x)
	Convert fixvec to fixvec.
template<>
cfixvec	to< CFix > (const cfixvec &x)
	Convert cfixvec to cfixvec.
template<class T , class U >
Vec< T >	to (const Vec< U > &real, const Vec< U > &imag)
	Convert Vec<U> (real and imaginary parts) to Vec<T>
template<class T , class U >
Mat< T >	to (const Mat< U > &x)
	Convert Mat<U> to Mat<T>
template<>
mat	to< double > (const mat &x)
	Convert mat to mat.
template<>
cmat	to< std::complex< double > > (const cmat &x)
	Convert cmat to cmat.
template<>
fixmat	to< Fix > (const fixmat &x)
	Convert fixmat to fixmat.
template<>
cfixmat	to< CFix > (const cfixmat &x)
	Convert cfixmat to cfixmat.
template<class T , class U >
Mat< T >	to (const Mat< U > &real, const Mat< U > &imag)
	Convert Mat<U> (real and imaginary parts) to Mat<T>
template<class T , class U >
Array< typename ConvertU2T< T, U >::result >	to (const Array< U > &x)
	Convert Array<U>, where U can be an Array/Vec/Mat, to a corresponding Array with T elements.
template<class T , class U >
Array< typename ConvertU2T< T, U >::result >	to (const Array< U > &real, const Array< U > &imag)
	Convert Array<U> (real and imaginary parts), where U can be an Array/Vec/Mat, to a corresponding Array with T elements.
double	unfix (const Fix &x)
	Convert Fix to double by multiplying the bit representation with pow2(-shift)
std::complex< double >	unfix (const CFix &x)
	Convert CFix to std::complex<double> by multiplying the bit representation with pow2(-shift)
vec	unfix (const fixvec &x)
	Convert fixvec to vec by multiplying the bit representations with pow2(-shift)
mat	unfix (const fixmat &x)
	Convert fixmat to mat by multiplying the bit representations with pow2(-shift)
double	unfix (double x)
	Convert double to double i.e. do nothing.
std::complex< double >	unfix (const std::complex< double > &x)
	Convert std::complex<double> to std::complex<double> i.e. do nothing.
vec	unfix (const vec &x)
	Convert vec to vec i.e. do nothing.
cvec	unfix (const cvec &x)
	Convert cvec to cvec i.e. do nothing.
mat	unfix (const mat &x)
	Convert mat to mat i.e. do nothing.
cmat	unfix (const cmat &x)
	Convert cmat to cmat i.e. do nothing.
template<class T >
Array< typename Convert< T > ::to_double >	unfix (const Array< T > &x)
	Convert floating- or fixed-point Array to floating-point Array.
Fix	operator+ (const Fix &x, const Fix &y)
	Fix + Fix.
Fix	operator- (const Fix &x, const Fix &y)
	Fix - Fix.
Fix	operator* (const Fix &x, const Fix &y)
	Fix * Fix.
Fix	operator/ (const Fix &x, const Fix &y)
	Fix / Fix using quantization mode TRN.
Fix	operator+ (const Fix &x, const int y)
	Fix + int.
Fix	operator- (const Fix &x, const int y)
	Fix - int.
Fix	operator* (const Fix &x, const int y)
	Fix * int.
Fix	operator/ (const Fix &x, const int y)
	Fix / int using quantization mode TRN.
Fix	operator+ (const int x, const Fix &y)
	int + Fix
Fix	operator- (const int x, const Fix &y)
	int - Fix
Fix	operator* (const int x, const Fix &y)
	int * Fix
Fix	operator/ (const int x, const Fix &y)
	int / Fix using quantization mode TRN
fixvec	operator+ (const fixvec &a, const ivec &b)
	fixvec + ivec
Fix	operator* (const fixvec &a, const ivec &b)
	fixvec * ivec
fixmat	operator+ (const fixmat &a, const imat &b)
	fixmat + imat
fixmat	operator* (const fixmat &a, const imat &b)
	fixmat * imat
CFix	operator+ (const CFix &x, const CFix &y)
	CFix + CFix.
CFix	operator- (const CFix &x, const CFix &y)
	CFix - CFix.
CFix	operator* (const CFix &x, const CFix &y)
	CFix * CFix.
CFix	operator/ (const CFix &x, const CFix &y)
	CFix / CFix using quantization mode TRN.
CFix	operator+ (const CFix &x, const Fix &y)
	CFix + Fix.
CFix	operator- (const CFix &x, const Fix &y)
	CFix - Fix.
CFix	operator* (const CFix &x, const Fix &y)
	CFix * Fix.
CFix	operator/ (const CFix &x, const Fix &y)
	CFix / Fix using quantization mode TRN.
CFix	operator+ (const Fix &x, const CFix &y)
	Fix + CFix.
CFix	operator- (const Fix &x, const CFix &y)
	Fix - CFix.
CFix	operator* (const Fix &x, const CFix &y)
	Fix * CFix.
CFix	operator/ (const Fix &x, const CFix &y)
	Fix / CFix using quantization mode TRN.
CFix	operator+ (const CFix &x, const int y)
	CFix + int.
CFix	operator- (const CFix &x, const int y)
	CFix - int.
CFix	operator* (const CFix &x, const int y)
	CFix * int.
CFix	operator/ (const CFix &x, const int y)
	CFix / int using quantization mode TRN.
CFix	operator+ (const int x, const CFix &y)
	int + CFix
CFix	operator- (const int x, const CFix &y)
	int - CFix
CFix	operator* (const int x, const CFix &y)
	int * CFix
CFix	operator/ (const int x, const CFix &y)
	int / CFix using quantization mode TRN
cfixvec	operator+ (const cfixvec &a, const fixvec &b)
	cfixvec + fixvec
CFix	operator* (const cfixvec &a, const fixvec &b)
	cfixvec * fixvec
cfixmat	operator+ (const cfixmat &a, const fixmat &b)
	cfixmat + fixmat
cfixmat	operator* (const cfixmat &a, const fixmat &b)
	cfixmat * fixmat
fixvec	operator+ (const fixvec &v, const int s)
	fixvec + int
fixvec	operator+ (const int s, const fixvec &v)
	int + fixvec
fixvec	operator- (const fixvec &v, const int s)
	fixvec - int
fixvec	operator- (const int s, const fixvec &v)
	int - fixvec
fixvec	operator* (const fixvec &v, const int s)
	fixvec * int
fixvec	operator* (const int s, const fixvec &v)
	int * fixvec
fixvec	operator/ (const fixvec &v, const int s)
	fixvec / int using quantization mode TRN
fixmat	operator+ (const fixmat &v, const int s)
	fixmat + int
fixmat	operator+ (const int s, const fixmat &v)
	int + fixmat
fixmat	operator- (const fixmat &v, const int s)
	fixmat - int
fixmat	operator- (const int s, const fixmat &v)
	int - fixmat
fixmat	operator* (const fixmat &v, const int s)
	fixmat * int
fixmat	operator* (const int s, const fixmat &v)
	int * fixmat
fixmat	operator/ (const fixmat &v, const int s)
	fixmat / int using quantization mode TRN
fixvec	operator+ (const ivec &a, const fixvec &b)
	ivec + fixvec
fixvec	operator- (const fixvec &a, const ivec &b)
	fixvec - ivec
fixvec	operator- (const ivec &a, const fixvec &b)
	ivec - fixvec
Fix	operator* (const ivec &a, const fixvec &b)
	ivec * fixvec
fixmat	operator+ (const imat &a, const fixmat &b)
	imat + fixmat
fixmat	operator- (const fixmat &a, const imat &b)
	fixmat - imat
fixmat	operator- (const imat &a, const fixmat &b)
	imat - fixmat
fixmat	operator* (const imat &a, const fixmat &b)
	imat * fixmat
cfixvec	operator+ (const fixvec &v, const CFix &s)
	fixvec + CFix
cfixvec	operator+ (const CFix &s, const fixvec &v)
	CFix + fixvec.
cfixvec	operator- (const fixvec &v, const CFix &s)
	fixvec - CFix
cfixvec	operator- (const CFix &s, const fixvec &v)
	CFix - fixvec.
cfixvec	operator* (const fixvec &v, const CFix &s)
	fixvec * CFix
cfixvec	operator* (const CFix &s, const fixvec &v)
	CFix * fixvec.
cfixvec	operator/ (const fixvec &v, const CFix &s)
	fixvec / CFix using quantization mode TRN
cfixmat	operator+ (const fixmat &m, const CFix &s)
	fixmat + CFix
cfixmat	operator+ (const CFix &s, const fixmat &m)
	CFix + fixmat.
cfixmat	operator- (const fixmat &m, const CFix &s)
	fixmat - CFix
cfixmat	operator- (const CFix &s, const fixmat &m)
	CFix - fixmat.
cfixmat	operator* (const fixmat &m, const CFix &s)
	fixmat * CFix
cfixmat	operator* (const CFix &s, const fixmat &m)
	CFix * fixmat.
cfixmat	operator/ (const fixmat &m, const CFix &s)
	fixmat / CFix using quantization mode TRN
cfixvec	operator+ (const ivec &v, const CFix &s)
	ivec + CFix
cfixvec	operator+ (const CFix &s, const ivec &v)
	CFix + ivec.
cfixvec	operator- (const ivec &v, const CFix &s)
	ivec - CFix
cfixvec	operator- (const CFix &s, const ivec &v)
	CFix - ivec.
cfixvec	operator* (const ivec &v, const CFix &s)
	ivec * CFix
cfixvec	operator* (const CFix &s, const ivec &v)
	CFix * ivec.
cfixvec	operator/ (const ivec &v, const CFix &s)
	ivec / CFix using quantization mode TRN
cfixmat	operator+ (const imat &m, const CFix &s)
	imat + CFix
cfixmat	operator+ (const CFix &s, const imat &m)
	CFix + imat.
cfixmat	operator- (const imat &m, const CFix &s)
	imat - CFix
cfixmat	operator- (const CFix &s, const imat &m)
	CFix - imat.
cfixmat	operator* (const imat &m, const CFix &s)
	imat * CFix
cfixmat	operator* (const CFix &s, const imat &m)
	CFix * imat.
cfixmat	operator/ (const imat &m, const CFix &s)
	imat / CFix using quantization mode TRN
cfixvec	operator+ (const cfixvec &v, const Fix &s)
	cfixvec + Fix
cfixvec	operator+ (const Fix &s, const cfixvec &v)
	Fix + cfixvec.
cfixvec	operator- (const cfixvec &v, const Fix &s)
	cfixvec - Fix
cfixvec	operator- (const Fix &s, const cfixvec &v)
	Fix - cfixvec.
cfixvec	operator* (const cfixvec &v, const Fix &s)
	cfixvec * Fix
cfixvec	operator* (const Fix &s, const cfixvec &v)
	Fix * cfixvec.
cfixvec	operator/ (const cfixvec &v, const Fix &s)
	cfixvec / Fix using quantization mode TRN
cfixmat	operator+ (const cfixmat &m, const Fix &s)
	cfixmat + Fix
cfixmat	operator+ (const Fix &s, const cfixmat &m)
	Fix + cfixmat.
cfixmat	operator- (const cfixmat &m, const Fix &s)
	cfixmat - Fix
cfixmat	operator- (const Fix &s, const cfixmat &m)
	Fix - cfixmat.
cfixmat	operator* (const cfixmat &m, const Fix &s)
	cfixmat * Fix
cfixmat	operator* (const Fix &s, const cfixmat &m)
	Fix * cfixmat.
cfixmat	operator/ (const cfixmat &m, const Fix &s)
	cfixmat / Fix using quantization mode TRN
cfixvec	operator- (const cfixvec &a, const fixvec &b)
	cfixvec - fixvec
cfixmat	operator- (const cfixmat &a, const fixmat &b)
	cfixmat - fixmat
vec	fminunc (double(*function)(const vec &), vec(*gradient)(const vec &), const vec &x0)
	Unconstrained minimization.
const Sequence_Number &	min (const Sequence_Number &n1, const Sequence_Number &n2)
	ADD DOCUMENTATION HERE.
const Sequence_Number &	max (const Sequence_Number &n1, const Sequence_Number &n2)
	ADD DOCUMENTATION HERE.
vec	fir1 (int N, double cutoff)
	Design a Nth order FIR filter with cut-off frequency cutoff using the window method.
void	filter_design_autocorrelation (const int N, const vec &f, const vec &m, vec &R)
	Calculate autocorrelation from the specified frequency-response (suitable for filter design)
void	modified_yule_walker (const int m, const int n, const int N, const vec &R, vec &a)
	Estimation of AR-part in an ARMA model given the autocorrelation.
void	arma_estimator (const int m, const int n, const vec &R, vec &b, vec &a)
	Estimation of ARMA model given the autocorrelation.
void	yulewalk (const int N, const vec &f, const vec &m, vec &b, vec &a)
	ARMA filter design using a least-squares fit to the specified frequency-response.
double	cheb (int n, double x)
	Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows: .
vec	cheb (int n, const vec &x)
	Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows: .
mat	cheb (int n, const mat &x)
	Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows: .
template ITPP_EXPORT vec	repeat (const vec &v, int norepeats)
template ITPP_EXPORT cvec	repeat (const cvec &v, int norepeats)
template ITPP_EXPORT svec	repeat (const svec &v, int norepeats)
template ITPP_EXPORT ivec	repeat (const ivec &v, int norepeats)
template ITPP_EXPORT bvec	repeat (const bvec &v, int norepeats)
template ITPP_EXPORT mat	repeat (const mat &m, int norepeats)
template ITPP_EXPORT cmat	repeat (const cmat &m, int norepeats)
template ITPP_EXPORT smat	repeat (const smat &m, int norepeats)
template ITPP_EXPORT imat	repeat (const imat &m, int norepeats)
template ITPP_EXPORT bmat	repeat (const bmat &m, int norepeats)
template ITPP_EXPORT vec	upsample (const vec &v, int usf)
template ITPP_EXPORT cvec	upsample (const cvec &v, int usf)
template ITPP_EXPORT svec	upsample (const svec &v, int usf)
template ITPP_EXPORT ivec	upsample (const ivec &v, int usf)
template ITPP_EXPORT bvec	upsample (const bvec &v, int usf)
template ITPP_EXPORT mat	upsample (const mat &v, int usf)
template ITPP_EXPORT cmat	upsample (const cmat &v, int usf)
template ITPP_EXPORT smat	upsample (const smat &v, int usf)
template ITPP_EXPORT imat	upsample (const imat &v, int usf)
template ITPP_EXPORT bmat	upsample (const bmat &v, int usf)
template ITPP_EXPORT void	upsample (const vec &v, int usf, vec &u)
template ITPP_EXPORT void	upsample (const cvec &v, int usf, cvec &u)
template ITPP_EXPORT void	upsample (const svec &v, int usf, svec &u)
template ITPP_EXPORT void	upsample (const ivec &v, int usf, ivec &u)
template ITPP_EXPORT void	upsample (const bvec &v, int usf, bvec &u)
template ITPP_EXPORT void	upsample (const mat &v, int usf, mat &u)
template ITPP_EXPORT void	upsample (const cmat &v, int usf, cmat &u)
template ITPP_EXPORT void	upsample (const smat &v, int usf, smat &u)
template ITPP_EXPORT void	upsample (const imat &v, int usf, imat &u)
template ITPP_EXPORT void	upsample (const bmat &v, int usf, bmat &u)
template ITPP_EXPORT vec	lininterp (const vec &v, int usf)
template ITPP_EXPORT cvec	lininterp (const cvec &v, int usf)
template ITPP_EXPORT mat	lininterp (const mat &v, int usf)
template ITPP_EXPORT cmat	lininterp (const cmat &v, int usf)
template ITPP_EXPORT void	lininterp (const vec &v, int usf, vec &u)
template ITPP_EXPORT void	lininterp (const cvec &v, int usf, cvec &u)
template ITPP_EXPORT void	lininterp (const mat &v, int usf, mat &u)
template ITPP_EXPORT void	lininterp (const cmat &v, int usf, cmat &u)
template ITPP_EXPORT mat	lininterp (const mat &m, double f_base, double f_ups, int nrof_samples, double t_start)
template ITPP_EXPORT cmat	lininterp (const cmat &m, double f_base, double f_ups, int nrof_samples, double t_start)
template ITPP_EXPORT vec	lininterp (const vec &v, double f_base, double f_ups, int nrof_samples, double t_start)
template ITPP_EXPORT cvec	lininterp (const cvec &v, double f_base, double f_ups, int nrof_samples, double t_start)
template<class T >
Vec< T >	repeat (const Vec< T > &v, int norepeats)
	Repeat each element in the vector norepeats times in sequence.
template<class T >
Mat< T >	repeat (const Mat< T > &m, int norepeats)
	Repeats each column norepeats times in sequence.
template<class T >
void	upsample (const Vec< T > &v, int usf, Vec< T > &u)
	Upsample a vector by inserting (usf-1) zeros after each sample.
template<class T >
Vec< T >	upsample (const Vec< T > &v, int usf)
	Upsample a vector by inserting (usf-1) zeros after each sample.
template<class T >
void	upsample (const Mat< T > &v, int usf, Mat< T > &u)
	Upsample each column by inserting (usf-1) zeros after each column.
template<class T >
Mat< T >	upsample (const Mat< T > &v, int usf)
	Upsample each column by inserting (usf-1) zeros after each column.
template<class T >
void	lininterp (const Mat< T > &m, int usf, Mat< T > &u)
	Upsample each column by a factor of (usf-1) by linear interpolation.
template<class T >
Mat< T >	lininterp (const Mat< T > &m, double f_base, double f_ups, int nrof_samples, double t_start=0)
	Upsample each column of matrix m to achieve f_ups frequency using linear interpolation.
template<class T >
Mat< T >	lininterp (const Mat< T > &m, int usf)
	Upsample each column by a factor of (usf-1) by linear interpolation.
template<class T >
void	lininterp (const Vec< T > &v, int usf, Vec< T > &u)
	Upsample by a factor of (usf-1) by linear interpolation.
template<class T >
Vec< T >	lininterp (const Vec< T > &v, int usf)
	Upsample by a factor of (usf-1) by linear interpolation.
template<class T >
Vec< T >	lininterp (const Vec< T > &v, double f_base, double f_ups, int nrof_samples, double t_start=0)
	Upsample vector v to achieve f_ups frequency using linear interpolation.
cvec	xcorr (const cvec &x, const int max_lag=-1, const std::string scaleopt="none")
	Cross Correlation.
cvec	xcorr (const cvec &x, const cvec &y, const int max_lag=-1, const std::string scaleopt="none")
	Cross Correlation.
void	xcorr (const cvec &x, const cvec &y, cvec &out, const int max_lag=-1, const std::string scaleopt="none", bool autoflag=true)
	Cross Correlation.
mat	cov (const mat &X, bool is_zero_mean=false)
	Covariance matrix calculation.
vec	spectrum (const vec &v, int nfft=256, int noverlap=0)
	Power spectrum calculation.
vec	spectrum (const vec &v, const vec &w, int noverlap=0)
	Power spectrum calculation.
vec	filter_spectrum (const vec &a, int nfft=256)
	Power spectrum calculation of a filter.
vec	filter_spectrum (const vec &a, const vec &b, int nfft=256)
	Power spectrum calculation of a filter.
ITPP_EXPORT bool	have_fourier_transforms ()
	Run-time test if library is built with Fast Fourier Transforms enabled.
ITPP_EXPORT void	fft (const cvec &in, cvec &out)
	Fast Fourier Transform.
ITPP_EXPORT cvec	fft (const cvec &in)
	Fast Fourier Transform.
ITPP_EXPORT cvec	fft (const cvec &in, const int N)
	Fast Fourier Transform with zero-padding up to size N.
ITPP_EXPORT void	ifft (const cvec &in, cvec &out)
	Inverse Fast Fourier Transform.
ITPP_EXPORT cvec	ifft (const cvec &in)
	Inverse Fast Fourier Transform.
ITPP_EXPORT cvec	ifft (const cvec &in, const int N)
	Inverse Fast Fourier Transform with zero-padding up to size N.
ITPP_EXPORT void	fft_real (const vec &in, cvec &out)
	Real Fast Fourier Transform.
ITPP_EXPORT cvec	fft_real (const vec &in)
	Real Fast Fourier Transform.
ITPP_EXPORT cvec	fft_real (const vec &in, const int N)
	Real Fast Fourier Transform with zero-padding up to size N.
ITPP_EXPORT void	ifft_real (const cvec &in, vec &out)
	Inverse Real Fast Fourier Transform.
ITPP_EXPORT vec	ifft_real (const cvec &in)
	Inverse Real Fast Fourier Transform.
ITPP_EXPORT vec	ifft_real (const cvec &in, const int N)
	Inverse Real Fast Fourier Transformon with zero-padding up to size N.
ITPP_EXPORT bool	have_cosine_transforms ()
	Run-time test if library is built with cosine transforms enabled.
ITPP_EXPORT void	dct (const vec &in, vec &out)
	Discrete Cosine Transform (DCT)
ITPP_EXPORT vec	dct (const vec &in)
	Discrete Cosine Transform (DCT)
ITPP_EXPORT vec	dct (const vec &in, const int N)
	Discrete Cosine Transform (DCT) with zero-padding up to size N.
ITPP_EXPORT void	idct (const vec &in, vec &out)
	Inverse Discrete Cosine Transform (IDCT)
ITPP_EXPORT vec	idct (const vec &in)
	Inverse Discrete Cosine Transform (IDCT)
ITPP_EXPORT vec	idct (const vec &in, const int N)
	Inverse Discrete Cosine Transform (IDCT) with zero-padding up to size N.
template<class T >
Vec< T >	dht (const Vec< T > &v)
	Fast Hadamard Transform.
template<class T >
void	dht (const Vec< T > &vin, Vec< T > &vout)
	Fast Hadamard Transform.
template<class T >
void	self_dht (Vec< T > &v)
	Fast Hadamard Transform - memory efficient. Stores the result in v.
template<class T >
Vec< T >	dwht (const Vec< T > &v)
	Fast Walsh Hadamard Transform.
template<class T >
void	dwht (const Vec< T > &vin, Vec< T > &vout)
	Fast Walsh Hadamard Transform.
template<class T >
void	self_dwht (Vec< T > &v)
	Fast Walsh Hadamard Transform - memory efficient (result in v)
template<class T >
Mat< T >	dht2 (const Mat< T > &m)
	Fast 2D Hadamard Transform.
template<class T >
Mat< T >	dwht2 (const Mat< T > &m)
	Fast 2D Walsh Hadamard Transform.
template<class T >
void	bitrv (Vec< T > &out)
	Bit reverse.
vec	hamming (int size)
	Hamming window.
vec	hanning (int n)
	Hanning window.
vec	hann (int n)
	Hanning window compatible with matlab.
vec	blackman (int n)
	Blackman window.
vec	triang (int n)
	Triangular window.
vec	sqrt_win (int n)
	Square root window.
vec	chebwin (int n, double at)
	Dolph-Chebyshev window.
bool	is_valid (const Audio_Stream_Description &d)
	validity check for stream description d
vec	snd_read_channel (const char *fname, int ch=0)
	Read audio channel.
vec	snd_read_channel (const char *fname, int ch, int len, std::streamoff beg=0)
	Read len audio channel samples starting at position beg.
mat	snd_read (const char *fname)
	Read audio data.
mat	snd_read (const char *fname, int len, std::streamoff beg=0)
	Read len audio samples starting at position beg.
bool	snd_write_channel (const char *fname, const Audio_Stream_Description &descr, const vec &s, int ch=0)
	Write audio channel from vector s using stream description descr.
bool	snd_write (const char *fname, const Audio_Stream_Description &descr, const mat &s)
	Write audio data.
template<typename T , T max_abs>
T	limit_audio_sample (double s)
	Helper function for scaling and limiting of audio samples.
template<typename T , T down_scaling>
double	audio_sample_to_double (T s)
	Helper function for scaling and limiting of audio samples.
template<typename Binary_Out_Stream >
Binary_Out_Stream &	operator<< (Binary_Out_Stream &s, Sample_24 v)
	insertion operator for 24-bit PCM sample
template<typename Binary_In_Stream >
Binary_In_Stream &	operator>> (Binary_In_Stream &s, Sample_24 &v)
	extraction operator for 24-bit PCM sample
std::size_t	encoded_sample_size (Audio_Encoding e)
	Size of encoded sample based on the encoding type e.
std::pair< int16_t, int16_t >	ulaw_range ()
	G.711 u-Law compressor input range. Returns (min,max) input values in std::pair.
uint8_t	ulaw_compress (int16_t s)
	G.711 u-Law compression function. Returns encoded value for sample s.
int16_t	ulaw_expand (uint8_t s)
	G.711 u-Law expansion function. Returns decoded value for previously compressed sample s.Expansion is performed by the table look up.
std::pair< int16_t, int16_t >	alaw_range ()
	G.711 a-Law compressor input range. Returns (min,max) input values in std::pair.
uint8_t	alaw_compress (int16_t s)
	G.711 a-Law compression function. Returns encoded value for sample s.
int16_t	alaw_expand (uint8_t s)
	G.711 u-Law expansion function. Returns decoded value for previously compressed sample s.Expansion is performed by the table look up.
ITPP_EXPORT GMM	gmmtrain (Array< vec > &TrainingData, int M, int NOITER=30, bool VERBOSE=true)
ITPP_EXPORT vec	chirp (const vec &a, double factor)
	Returns a chirped version of the input vector.
ITPP_EXPORT double	sd (const vec &In1, const vec &In2)
	Spectral distortion between two vectors, in dB.
ITPP_EXPORT double	sd (const vec &In1, const vec &In2, double highestfreq)
	Spectral distortion between two vectors, in dB, up to highest frequency highestfreq.
ITPP_EXPORT vec	lerouxguegenrc (const vec &R, int order)
	Computes reflection coefficients from autocorrelation, using the Le-Roux-Guegen algorithm.
ITPP_EXPORT vec	levinson (const vec &R2, int order)
	Levinson - Levinson-Durbin recursion.
ITPP_EXPORT vec	autocorr (const vec &x, int order)
	Computes the autocorrelation function.
ITPP_EXPORT vec	lpc (const vec &x, int order)
	lpc - Linear Predictive Coefficients using autocorrelation method.
ITPP_EXPORT vec	schurrc (const vec &R, int order)
	schurrc - Schur algorithm.
ITPP_EXPORT vec	ac2rc (const vec &ac)
	ac2rc - Autocorrelation sequence to reflection coefficients conversion.
ITPP_EXPORT vec	ac2poly (const vec &ac)
	ac2poly - Autocorrelation sequence to prediction polynomial conversion.
ITPP_EXPORT vec	is2rc (const vec &is)
	is2rc - Inverse sine parameters to reflection coefficients conversion.
ITPP_EXPORT vec	lar2rc (const vec &lar)
	lar2rc - Log area ratios to reflection coefficients conversion.
ITPP_EXPORT vec	lsf2poly (const vec &lsf)
	lsf2poly - Line spectral frequencies to prediction polynomial conversion.
ITPP_EXPORT vec	poly2ac (const vec &poly)
	poly2ac - Prediction polynomial to autocorrelation sequence conversion.
ITPP_EXPORT vec	poly2lsf (const vec &poly)
	poly2lsf - Prediction polynomial to line spectral frequencies conversion.
ITPP_EXPORT vec	poly2rc (const vec &poly)
	poly2rc - Prediction polynomial to reflection coefficients conversion.
ITPP_EXPORT vec	poly2cepstrum (const vec &a)
	poly2cepstrum - Prediction polynomial to cepstrum conversion.
ITPP_EXPORT vec	poly2cepstrum (const vec &a, int num)
	poly2cepstrum - Prediction polynomial to cepstrum conversion, to the specified order.
ITPP_EXPORT vec	cepstrum2poly (const vec &c)
	cepstrum2poly - Cepstrum to prediction polynomial conversion.
ITPP_EXPORT vec	rc2ac (const vec &rc)
	rc2ac - Reflection coefficients to autocorrelation sequence conversion.
ITPP_EXPORT vec	rc2is (const vec &rc)
	rc2is - Reflection coefficients to inverse sine parameters conversion.
ITPP_EXPORT vec	rc2lar (const vec &rc)
	rc2lar - Reflection coefficients to log area ratios conversion.
ITPP_EXPORT vec	rc2poly (const vec &rc)
	rc2poly - Reflection coefficients to prediction polynomial conversion.
ITPP_EXPORT char	pnm_type (const std::string &filename)
	Determines the type of a PNM file, based on magic numbers. The returned value is a character between '1' and '6'. If an error occured, the returned value is the character '0'.
ITPP_EXPORT bool	pnm_info (const std::string &filename, char &pnm_type, int &width, int &height, int &max_val, std::string &comments)
	Retrieve some information about an pnm file.
ITPP_EXPORT bool	pgm_read (const std::string &filename, imat &m, std::string &comments)
	Read the entire graymap into the matrix m or return false if the function failed.
ITPP_EXPORT bool	pgm_read (const std::string &filename, imat &m, int r1, int r2, int c1, int c2)
	Read a part of the graymap into the matrix m.
ITPP_EXPORT imat	pgm_read (const std::string &filename)
	Read a pgm file of name filename and return the corresponding matrix of integers. Return a void matrix if an error ocurred.
ITPP_EXPORT bool	pgm_write (const std::string &filename, const imat &m, const std::string &comments="Generated by IT++ (http://itpp.sourceforge.net)")
	Create an image file from the matrix of integer.
ITPP_EXPORT bool	ppm_read (const std::string &filename, imat &r, imat &g, imat &b, std::string &comments)
	Read the color image file in the format ppm. The image is retrieved as a set of three matrices, each of whom is a plan of RGB component.
ITPP_EXPORT bool	ppm_read (const std::string &filename, imat &r, imat &g, imat &b)
	Read the color image file in the PPM format.
ITPP_EXPORT bool	ppm_read (const std::string &filename, imat &r, imat &g, imat &b, int r1, int r2, int c1, int c2)
	Read a part of the pixmap into the matrix m. The parameters r1, r2, c1 and c2 are the rows and columns (inclusive) of the subimage.
ITPP_EXPORT bool	ppm_write (const std::string &filename, const imat &r, const imat &g, const imat &b, const std::string &comments="Generated by IT++ (http://itpp.sourceforge.net)", int max_val=255)
	Write the matrix m as a pixmap.
ITPP_EXPORT imat	img_double2int (const mat &m, int max_val=255, double double_min=0, double double_max=1)
	Prepare a matrix of double to be writted as an image.
ITPP_EXPORT mat	img_int2double (const imat &m, int max_val=255, double double_min=0, double double_max=1)
	Return a matrix of double which is a scaled version of the input matrix m of integers.
ITPP_EXPORT int	scalar_encode (double x, vec &Levels)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT ivec	scalar_encode (vec &x, vec &Levels)
	ADD DOCUMENTATION HERE.
double	scalar_quantize (double x, vec &Levels)
	ADD DOCUMENTATION HERE.
vec	scalar_quantize (vec &x, vec &Levels)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT double	kmeansiter (Array< vec > &DB, mat &codebook)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT mat	kmeans (Array< vec > &DB, int SIZE, int NOITER=9999, bool VERBOSE=true)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT mat	lbg (Array< vec > &DB, int SIZE, int NOITER=9999, bool VERBOSE=true)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT mat	vqtrain (Array< vec > &DB, int SIZE, int NOITER, double STARTSTEP=0.2, bool VERBOSE=true)
	Function for vector quantization training.
ITPP_EXPORT vec	sqtrain (const vec &inDB, int SIZE)
	ADD DOCUMENTATION HERE.
ITPP_EXPORT ivec	bitalloc (const vec &variances, int nobits)
	ADD DOCUMENTATION HERE.
double	mean (const vec &v)
	The mean value.
std::complex< double >	mean (const cvec &v)
	The mean value.
double	mean (const svec &v)
	The mean value.
double	mean (const ivec &v)
	The mean value.
double	mean (const mat &m)
	The mean value.
std::complex< double >	mean (const cmat &m)
	The mean value.
double	mean (const smat &m)
	The mean value.
double	mean (const imat &m)
	The mean value.
double	norm (const cvec &v)
	Calculate the 2-norm: norm(v)=sqrt(sum(abs(v).^2))
double	norm (const cvec &v, int p)
	Calculate the p-norm: norm(v,p)=sum(abs(v).^2)^(1/p)
double	norm (const cvec &v, const std::string &s)
	Calculate the Frobenius norm for s = "fro" (equal to 2-norm)
double	norm (const mat &m, int p)
double	norm (const cmat &m, int p)
double	norm (const mat &m, const std::string &s)
	Calculate the Frobenius norm of a matrix for s = "fro".
double	norm (const cmat &m, const std::string &s)
	Calculate the Frobenius norm of a matrix for s = "fro".
double	variance (const cvec &v)
	The variance of the elements in the vector. Normalized with N-1 to be unbiased.
double	moment (const vec &x, const int r)
	Calculate the central moment of vector x.
double	skewness (const vec &x)
	Calculate the skewness excess of the input vector x.
double	kurtosisexcess (const vec &x)
	Calculate the kurtosis excess of the input vector x.
template<class T >
double	geometric_mean (const Vec< T > &v)
	The geometric mean of a vector.
template<class T >
double	geometric_mean (const Mat< T > &m)
	The geometric mean of a matrix.
template<class T >
double	median (const Vec< T > &v)
	The median.
template<class T >
double	norm (const Vec< T > &v)
	Calculate the 2-norm: norm(v)=sqrt(sum(abs(v).^2))
template<class T >
double	norm (const Vec< T > &v, int p)
	Calculate the p-norm: norm(v,p)=sum(abs(v).^2)^(1/p)
template<class T >
double	norm (const Vec< T > &v, const std::string &s)
	Calculate the Frobenius norm for s = "fro" (equal to 2-norm)
template<class T >
double	variance (const Vec< T > &v)
	The variance of the elements in the vector. Normalized with N-1 to be unbiased.
template<class T >
double	energy (const Vec< T > &v)
	Calculate the energy: squared 2-norm. energy(v)=sum(abs(v).^2)
bool	within_tolerance (double x, double xref, double tol=1e-14)
	Return true if the input value x is within the tolerance tol of the reference value xref.
bool	within_tolerance (std::complex< double > x, std::complex< double > xref, double tol=1e-14)
	Return true if the input value x is within the tolerance tol of the reference value xref.
bool	within_tolerance (const vec &x, const vec &xref, double tol=1e-14)
	Return true if the input vector x is elementwise within the tolerance tol of the reference vector xref.
bool	within_tolerance (const cvec &x, const cvec &xref, double tol=1e-14)
	Return true if the input vector x is elementwise within the tolerance tol of the reference vector xref.
bool	within_tolerance (const mat &X, const mat &Xref, double tol=1e-14)
	Return true if the input matrix X is elementwise within the tolerance tol of the reference matrix Xref.
bool	within_tolerance (const cmat &X, const cmat &Xref, double tol=1e-14)
	Return true if the input matrix X is elementwise within the tolerance tol of the reference matrix Xref.
double	kurtosis (const vec &x)
	Calculate the kurtosis of the input vector x.
void	MOG_diag_ML (MOG_diag &model_in, Array< vec > &X_in, int max_iter_in, double var_floor_in, double weight_floor_in, bool verbose_in)
void	MOG_diag_MAP (MOG_diag &, MOG_diag &, Array< vec > &, int, double, double, double, bool)
void	MOG_diag_kmeans (MOG_diag &model_in, Array< vec > &X_in, int max_iter_in, double trust_in, bool normalise_in, bool verbose_in)
vec	filter (const vec &b, const vec &a, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const vec &b, const vec &a, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const cvec &a, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const cvec &a, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
vec	filter (const vec &b, const int one, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const vec &b, const int one, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const int one, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const int one, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
vec	filter (const int one, const vec &a, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const vec &a, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const cvec &a, const cvec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const cvec &a, const vec &input)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
vec	filter (const vec &b, const vec &a, const vec &input, const vec &state_in, vec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const vec &b, const vec &a, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const cvec &a, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const cvec &a, const vec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
vec	filter (const vec &b, const int one, const vec &input, const vec &state_in, vec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const vec &b, const int one, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const int one, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const cvec &b, const int one, const vec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
vec	filter (const int one, const vec &a, const vec &input, const vec &state_in, vec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const vec &a, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const cvec &a, const cvec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
cvec	filter (const int one, const cvec &a, const vec &input, const cvec &state_in, cvec &state_out)
	ARMA filter functionThese functions implements a autoregressive moving average (ARMA) filter according to .
void	polystab (const vec &a, vec &out)
	Polynomial Stabilization.
void	polystab (const cvec &a, cvec &out)
	Polynomial Stabilization.
vec	polystab (const vec &a)
	Polynomial Stabilization.
cvec	polystab (const cvec &a)
	Polynomial Stabilization.
void	freqz (const cvec &b, const cvec &a, const int N, cvec &h, vec &w)
	Frequency response of filter.
cvec	freqz (const cvec &b, const cvec &a, const int N)
	Frequency response of filter.
cvec	freqz (const cvec &b, const cvec &a, const vec &w)
	Frequency response of filter.
void	freqz (const vec &b, const vec &a, const int N, cvec &h, vec &w)
	Frequency response of filter.
cvec	freqz (const vec &b, const vec &a, const int N)
	Frequency response of filter.
cvec	freqz (const vec &b, const vec &a, const vec &w)
	Frequency response of filter.
void	poly (const vec &r, vec &p)
	Create a polynomial of the given rootsCreate a polynomial p with roots r.
void	poly (const cvec &r, cvec &p)
	Create a polynomial of the given rootsCreate a polynomial p with roots r.
vec	poly (const vec &r)
	Create a polynomial of the given rootsCreate a polynomial p with roots r.
cvec	poly (const cvec &r)
	Create a polynomial of the given rootsCreate a polynomial p with roots r.
void	roots (const vec &p, cvec &r)
	Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
void	roots (const cvec &p, cvec &r)
	Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
cvec	roots (const vec &p)
	Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
cvec	roots (const cvec &p)
	Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
vec	polyval (const vec &p, const vec &x)
	Evaluate polynomialEvaluate the polynomial p (of length at the points x The output is given by .
cvec	polyval (const vec &p, const cvec &x)
	Evaluate polynomialEvaluate the polynomial p (of length at the points x The output is given by .
cvec	polyval (const cvec &p, const vec &x)
	Evaluate polynomialEvaluate the polynomial p (of length at the points x The output is given by .
cvec	polyval (const cvec &p, const cvec &x)
	Evaluate polynomialEvaluate the polynomial p (of length at the points x The output is given by .
vec	xcorr_old (const vec &x, const int max_lag=-1, const std::string scaleopt="none")
	Auto-correlation calculation.
vec	xcorr (const vec &x, const int max_lag, const std::string scaleopt)
	Auto-correlation calculation.
vec	xcorr (const vec &x, const vec &y, const int max_lag, const std::string scaleopt)
	Cross-correlation calculation.
vec	xcorr_old (const vec &x, const vec &y, const int max_lag=-1, const std::string scaleopt="none")
	Cross-correlation calculation.
void	xcorr (const vec &x, const vec &y, vec &out, const int max_lag, const std::string scaleopt)
	Cross-correlation calculation.
void	xcorr_old (const vec &x, const vec &y, vec &out, const int max_lag=-1, const std::string scaleopt="none")
	Cross-correlation calculation.

Variables
const Factory	DEFAULT_FACTORY
	Default (dummy) factory.
Real_Timer	__tic_toc_timer
	Global object for tic and toc functions.
const double	log_double_max = std::log(std::numeric_limits<double>::max())
	Constant definition to speed up trunc_log() and trunc_exp()
const double	log_double_min = std::log(std::numeric_limits<double>::min())
	Constant definition to speed up trunc_log(), trunc_exp() and log_add()
const double	pi = 3.14159265358979323846
	Constant Pi.
const double	m_2pi = 2 * pi
	Constant 2*Pi.
const double	eps = std::numeric_limits<double>::epsilon()
	Constant eps.
template class ITPP_EXPORT	Block_Interleaver< double >
template class ITPP_EXPORT	Block_Interleaver< short >
template class ITPP_EXPORT	Block_Interleaver< int >
template class ITPP_EXPORT	Block_Interleaver< bin >
template class ITPP_EXPORT	Cross_Interleaver< double >
template class ITPP_EXPORT	Cross_Interleaver< short >
template class ITPP_EXPORT	Cross_Interleaver< int >
template class ITPP_EXPORT	Cross_Interleaver< bin >
template class ITPP_EXPORT	Sequence_Interleaver< double >
template class ITPP_EXPORT	Sequence_Interleaver< short >
template class ITPP_EXPORT	Sequence_Interleaver< int >
template class ITPP_EXPORT	Sequence_Interleaver< bin >
static const int	LDPC_binary_file_version = 2
	Version of the binary file with generator and decoder data.
template class ITPP_EXPORT	Pulse_Shape< double, double, double >
template class ITPP_EXPORT	Root_Raised_Cosine< double >
template class ITPP_EXPORT	Raised_Cosine< double >
double(*	com_log )(double, double) = NULL
	Pointer to logarithmic branch metric function.
template class ITPP_EXPORT	CFixed< 64, TC, WRAP >
const int	MAX_WORDLEN = 64
	Max word length.
const uint64_t	UINT64_POW2 [64]
	Table for fast multiplication or division by 2^n.
const double	DOUBLE_POW2 [128]
	Table for fast multiplication by 2^(n-64)
template class ITPP_EXPORT	Fixed< 64, TC, WRAP >
template class ITPP_EXPORT	MA_Filter< double, double, double >
template class ITPP_EXPORT	AR_Filter< double, double, double >
template class ITPP_EXPORT	ARMA_Filter< double, double, double >

Detailed Description

itpp namespace

Typedef Documentation

typedef CFixed< 1, TC, WRAP > itpp::cfixed1

Typedefs for CFixed (cfixed1, cfixed2, ..., cfixed64)

Typedefs for saturated CFixed (scfixed1, scfixed2, ..., scfixed64)

Definition at line 105 of file cfixed.h.

Enumeration Type Documentation

enum itpp::SORTING_METHOD

Sorting algorithms that can be used in a Sort class.

• Introsort (the default and the fastest method in most cases)
• Quicksort
• Heapsort
• Insertion Sort (suitable for very short vectors)

Definition at line 48 of file sort.h.

Function Documentation

template<class T >

const Array< T > itpp::concat	(	const T &	e,
		const Array< T > &	a
	)

Append element e to the beginning of the Array a.

Concat element e to the beginning of the Array a.

Definition at line 498 of file array.h.

References itpp::Array< T >::size().

ITPP_EXPORT GF2mat operator*	(	const GF2mat &	X,
		const GF2mat &	Y
	)

GF(2) matrix multiplication.

Multiplication operator.

Definition at line 847 of file gf2mat.cpp.

References it_assert, mult_trans(), and itpp::GF2mat::transpose().

Referenced by operator*().

ITPP_EXPORT bvec operator*	(	const GF2mat &	X,
		const bvec &	y
	)

GF(2) matrix multiplication with "regular" binary vector.

Multiplication operator with binary vector.

Definition at line 873 of file gf2mat.cpp.

References it_assert, length(), and mult_trans().

ITPP_EXPORT GF2mat operator+	(	const GF2mat &	X,
		const GF2mat &	Y
	)

GF(2) matrix addition.

Addition operator.

Subtraction is not implemented because it is equivalent to addition.

Definition at line 948 of file gf2mat.cpp.

References it_assert.

ITPP_EXPORT std::ostream & operator<<	(	std::ostream &	os,
		const GF2mat &	X
	)

Output stream (plain text) operator for dense GF(2) matrices.

Output stream operator (plain text)

Definition at line 1001 of file gf2mat.cpp.

References itpp::GF2mat::density(), and itpp::GF2mat::get().

ITPP_EXPORT it_file & itpp::operator<<	(	it_file &	f,
		const GF2mat &	X
	)

/relatesalso GF2mat /brief Write GF(2) matrix to file.

Definition at line 1032 of file gf2mat.cpp.

References itpp::it_file::low_level_write(), and itpp::it_file::write_data_header().

ITPP_EXPORT it_ifile & itpp::operator>>	(	it_ifile &	f,
		GF2mat &	X
	)

/relatesalso GF2mat /brief Read GF(2) matrix from file.

Definition at line 1050 of file gf2mat.cpp.

References it_error, itpp::it_ifile::low_level_read(), itpp::it_ifile::read_data_header(), itpp::Mat< Num_T >::set_size(), and itpp::it_file_base::data_header::type.

template<class Num_T >

Mat< Num_T > itpp::concat_horizontal	(	const Mat< Num_T > &	m1,
		const Mat< Num_T > &	m2
	)

Horizontal concatenation of two matrices.

Concatenate the matrices m1 and m2 horizontally.

Definition at line 1194 of file mat.h.

References itpp::Mat< Num_T >::data, it_assert_debug, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

Referenced by itpp::Extended_Golay::Extended_Golay(), and fpica().

template<class Num_T >

Mat< Num_T > itpp::concat_vertical	(	const Mat< Num_T > &	m1,
		const Mat< Num_T > &	m2
	)

Vertical concatenation of two matrices.

Concatenate the matrices m1 and m2 vertically.

Definition at line 1216 of file mat.h.

References itpp::Mat< Num_T >::data, it_assert_debug, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator+	(	const Mat< Num_T > &	m,
		Num_T	t
	)

Addition of a matrix and a scalar.

Addition of matrix and scalar.

Definition at line 1331 of file mat.h.

References itpp::Mat< Num_T >::data, itpp::Mat< Num_T >::datasize, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator+	(	Num_T	t,
		const Mat< Num_T > &	m
	)

Addition of a scalar and a matrix.

Addition of scalar and matrix.

Definition at line 1342 of file mat.h.

References itpp::Mat< Num_T >::data, itpp::Mat< Num_T >::datasize, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator-	(	const Mat< Num_T > &	m1,
		const Mat< Num_T > &	m2
	)

Subtraction of two matrices.

Subtraction of m2 from m1.

Definition at line 1382 of file mat.h.

References itpp::Mat< Num_T >::data, it_assert_debug, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator-	(	const Mat< Num_T > &	m,
		Num_T	t
	)

Subtraction of matrix and scalar.

Subtraction of scalar from matrix.

Definition at line 1410 of file mat.h.

References itpp::Mat< Num_T >::data, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator-	(	Num_T	t,
		const Mat< Num_T > &	m
	)

Subtraction of scalar and matrix.

Subtract matrix from scalar.

Definition at line 1427 of file mat.h.

References itpp::Mat< Num_T >::data, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Mat< Num_T > itpp::operator-

(

const Mat< Num_T > &

m

)

Negation of matrix.

Subtraction of matrix.

Definition at line 1444 of file mat.h.

References itpp::Mat< Num_T >::data, itpp::Mat< Num_T >::no_cols, and itpp::Mat< Num_T >::no_rows.

template<class Num_T >

Vec< Num_T > itpp::operator*	(	const Mat< Num_T > &	m,
		const Vec< Num_T > &	v
	)

Multiplication of matrix and vector.

Multiplication of matrix m and vector v (column vector)

Definition at line 1536 of file mat.h.

References itpp::Mat< Num_T >::_data(), itpp::Mat< Num_T >::cols(), it_assert_debug, itpp::Mat< Num_T >::rows(), and itpp::Vec< Num_T >::size().

template<class Num_T >

std::istream & itpp::operator>>	(	std::istream &	is,
		Mat< Num_T > &	m
	)

Input stream for matrices.

The input can be on the form "1 2 3; 4 5 6" or "[[1 2 3][4 5 6]]", i.e. with brackets or semicolons as row delimiters. The first form is compatible with the set method, while the second form is compatible with the ostream operator. The elements on a row can be separated by blank space or commas. Rows that are shorter than the longest row are padded with zero elements. "[]" means an empty matrix.

Definition at line 1765 of file mat.h.

References itpp::Mat< Num_T >::set(), and itpp::Mat< Num_T >::set_size().

template<class T >

Sparse_Mat< T > itpp::operator+	(	const Sparse_Mat< T > &	m1,
		const Sparse_Mat< T > &	m2
	)

m1+m2 where m1 and m2 are sparse matrices

Addition m1+m2 where m1 and m2 are sparse matrices.

Definition at line 760 of file smat.h.

References it_assert_debug.

template<class T >

Sparse_Mat< T > itpp::operator*	(	const T &	c,
		const Sparse_Mat< T > &	m
	)

c*m where c is a scalar and m is a sparse matrix

Multiplication c*m where c is a scalar and m is a sparse matrix.

Definition at line 774 of file smat.h.

References itpp::Sparse_Mat< T >::set_new().

template<class T >

Sparse_Mat< T > itpp::operator*	(	const Sparse_Mat< T > &	m1,
		const Sparse_Mat< T > &	m2
	)

m1*m2 where m1 and m2 are sparse matrices

Multiplication m1*m2 where m1 and m2 are sparse matrices.

Definition at line 789 of file smat.h.

References itpp::Sparse_Mat< T >::compact(), itpp::Sparse_Vec< T >::get_nz_data(), itpp::Sparse_Vec< T >::get_nz_index(), it_assert_debug, and itpp::Sparse_Vec< T >::nnz().

template<class T >

Sparse_Vec< T > itpp::operator*	(	const Sparse_Mat< T > &	m,
		const Sparse_Vec< T > &	v
	)

m*v where m is a sparse matrix and v is a sparse vector

Multiplication m*v where m is a sparse matrix and v is a sparse vector.

Definition at line 860 of file smat.h.

References itpp::Sparse_Vec< T >::get_nz_data(), itpp::Sparse_Vec< T >::get_nz_index(), it_assert_debug, itpp::Sparse_Vec< T >::nnz(), and itpp::Sparse_Vec< T >::size().

template<class T >

Vec< T > itpp::operator*	(	const Sparse_Mat< T > &	m,
		const Vec< T > &	v
	)

m*v where m is a sparse matrix and v is a full column vector

Multiplication m*v where m is a sparse matrix and v is a full column vector.

Definition at line 886 of file smat.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class T >

Vec< T > itpp::operator*	(	const Vec< T > &	v,
		const Sparse_Mat< T > &	m
	)

v'*m where m is a sparse matrix and v is a full column vector

Multiplication v'*m where m is a sparse matrix and v is a full column vector.

Definition at line 902 of file smat.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class T >

Mat< T > itpp::trans_mult

(

const Sparse_Mat< T > &

m

)

m'*m where m is a sparse matrix

Multiplication m'*m where m is a sparse matrix. Returns a full, dense matrix.

Definition at line 916 of file smat.h.

References itpp::Mat< Num_T >::cols().

Referenced by mult_trans().

template<class T >

Sparse_Mat< T > itpp::trans_mult_s

(

const Sparse_Mat< T > &

m

)

m'*m where m is a sparse matrix

Multiplication m'*m where m is a sparse matrix, Returns a sparse matrix.

Definition at line 934 of file smat.h.

template<class T >

Sparse_Mat< T > itpp::trans_mult	(	const Sparse_Mat< T > &	m1,
		const Sparse_Mat< T > &	m2
	)

m1'*m2 where m1 and m2 are sparse matrices

Multiplication m1'*m2 where m1 and m2 are sparse matrices.

Definition at line 957 of file smat.h.

References it_assert_debug.

template<class T >

Vec< T > itpp::trans_mult	(	const Sparse_Mat< T > &	m,
		const Vec< T > &	v
	)

m'*v where m is a sparse matrix and v is a full column vector

Multiplication m'*v where m is a sparse matrix and v is a full column vector.

Definition at line 973 of file smat.h.

template<class T >

Sparse_Mat< T > itpp::mult_trans	(	const Sparse_Mat< T > &	m1,
		const Sparse_Mat< T > &	m2
	)

m1*m2' where m1 and m2 are sparse matrices

Multiplication m1*m2' where m1 and m2 are sparse matrices.

Definition at line 983 of file smat.h.

References trans_mult(), and itpp::Sparse_Mat< T >::transpose().

template<class T >

Sparse_Vec< T > itpp::operator+	(	const Sparse_Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

v1+v2 where v1 and v2 are sparse vector

Addition v1+v2 where v1 and v2 are sparse vector.

Definition at line 1171 of file svec.h.

References itpp::Sparse_Vec< T >::compact(), it_assert_debug, and itpp::Sparse_Vec< T >::resize_data().

template<class T >

T itpp::operator*	(	const Sparse_Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

v1*v2 where v1 and v2 are sparse vectors

Scalar product v1*v2 where v1 and v2 are sparse vectors.

Definition at line 1041 of file svec.h.

References itpp::Sparse_Vec< T >::full(), it_assert_debug, and sum().

template<class T >

T itpp::operator*	(	const Sparse_Vec< T > &	v1,
		const Vec< T > &	v2
	)

v1*v2 where v1 is a sparse vector and v2 is a dense vector

Scalar product v1*v2 where v1 is a sparse vector and v2 is a dense vector.

Definition at line 1057 of file svec.h.

References it_assert_debug, itpp::Sparse_Vec< T >::size(), itpp::Vec< Num_T >::size(), and sum().

template<class T >

T itpp::operator*	(	const Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

v1*v2 where v1 is a dense vector and v2 is a sparse vector

Scalar product v1*v2 where v1 is a dense vector and v2 is a sparse vector.

Definition at line 1069 of file svec.h.

References it_assert_debug, itpp::Sparse_Vec< T >::size(), itpp::Vec< Num_T >::size(), and sum().

template<class T >

Sparse_Vec< T > itpp::elem_mult	(	const Sparse_Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

Elementwise multiplication of two sparse vectors returning a sparse vector.

Element wise multiplication of two sparse vectors.

Definition at line 1081 of file svec.h.

References itpp::Sparse_Vec< T >::compact(), it_assert_debug, and itpp::Sparse_Vec< T >::resize_data().

template<class T >

Vec< T > itpp::elem_mult	(	const Sparse_Vec< T > &	v1,
		const Vec< T > &	v2
	)

Elementwise multiplication of a sparse vector and a dense vector returning a dense vector.

Element wise multiplication of a sparse vector and a dense vector.

Definition at line 1105 of file svec.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class T >

Sparse_Vec< T > itpp::elem_mult_s	(	const Sparse_Vec< T > &	v1,
		const Vec< T > &	v2
	)

Elementwise multiplication of a sparse vector and a dense vector returning a sparse vector.

Element wise multiplication of a sparse vector and a dense vector returning a sparse vector.

Definition at line 1118 of file svec.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class T >

Vec< T > itpp::elem_mult	(	const Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

Elementwise multiplication of a dense vector and a sparse vector returning a dense vector.

Element wise multiplication of a a dense vector and a sparse vector.

Definition at line 1138 of file svec.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class T >

Sparse_Vec< T > itpp::elem_mult_s	(	const Vec< T > &	v1,
		const Sparse_Vec< T > &	v2
	)

Elementwise multiplication of a dense vector and a sparse vector returning a sparse vector.

Element wise multiplication of a a dense vector and a sparse vector returning a sparse vector.

Definition at line 1151 of file svec.h.

References it_assert_debug, and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::operator-	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2
	)

Subtraction of a vector from a vector.

Subtraction of v2 from v1.

Definition at line 943 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, and it_assert_debug.

template<class Num_T >

Vec< Num_T > itpp::operator-	(	const Vec< Num_T > &	v,
		Num_T	t
	)

Subtraction of a scalar from a vector.

Subtraction of scalar from vector.

Definition at line 956 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::datasize.

template<class Num_T >

Vec< Num_T > itpp::operator-	(	Num_T	t,
		const Vec< Num_T > &	v
	)

Subtraction of vector from scalar. Results in a vector.

Subtraction of vector from scalar.

Definition at line 968 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::datasize.

template<class Num_T >

Mat< Num_T > itpp::outer_product	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2,
		bool	hermitian = false
	)

Outer product of two vectors v1 and v2.

When v1 and v2 are complex vectors (cvec), the third boolean argument hermitian can be set to true to conjugate v2 (Matlab's v1 * v2' operation). This parameter is ignored for types other then cvec.

Definition at line 1021 of file vec.h.

References itpp::Vec< Num_T >::_data(), it_assert_debug, and itpp::Vec< Num_T >::length().

Referenced by itpp::Newton_Search::search().

template<class Num_T >

Vec< Num_T > itpp::operator*	(	const Vec< Num_T > &	v,
		Num_T	t
	)

Multiplication of a vector and a scalar.

Elementwise multiplication of vector and scalar.

Definition at line 1044 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::datasize.

template<class Num_T >

Vec< Num_T > itpp::operator* ( Num_T  t, const Vec< Num_T > &  v  )

inline

Multiplication of a scalar and a vector. Results in a vector.

Elementwise multiplication of vector and scalar.

Definition at line 1055 of file vec.h.

References operator*().

template<class Num_T >

Vec< Num_T > itpp::elem_mult ( const Vec< Num_T > &  a, const Vec< Num_T > &  b  )

inline

Element-wise multiplication of two vectors.

Elementwise multiplication.

Definition at line 1061 of file vec.h.

References elem_mult_out().

template<class Num_T >

Vec< Num_T > itpp::elem_mult ( const Vec< Num_T > &  a, const Vec< Num_T > &  b, const Vec< Num_T > &  c  )

inline

Element-wise multiplication of three vectors.

Elementwise multiplication of three vectors.

Definition at line 1069 of file vec.h.

References elem_mult_out().

template<class Num_T >

Vec< Num_T > itpp::elem_mult ( const Vec< Num_T > &  a, const Vec< Num_T > &  b, const Vec< Num_T > &  c, const Vec< Num_T > &  d  )

inline

Element-wise multiplication of four vectors.

Elementwise multiplication of four vectors.

Definition at line 1078 of file vec.h.

References elem_mult_out().

template<class Num_T >

void itpp::elem_mult_out	(	const Vec< Num_T > &	a,
		const Vec< Num_T > &	b,
		Vec< Num_T > &	out
	)

Element-wise multiplication of two vectors, storing the result in vector out.

Elementwise multiplication, storing the result in vector out.

Definition at line 1087 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, it_assert_debug, and itpp::Vec< Num_T >::set_size().

template<class Num_T >

void itpp::elem_mult_out	(	const Vec< Num_T > &	a,
		const Vec< Num_T > &	b,
		const Vec< Num_T > &	c,
		Vec< Num_T > &	out
	)

Element-wise multiplication of three vectors, storing the result in vector out.

Elementwise multiplication of three vectors, storing the result in vector out.

Definition at line 1097 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, it_assert_debug, and itpp::Vec< Num_T >::set_size().

template<class Num_T >

void itpp::elem_mult_out	(	const Vec< Num_T > &	a,
		const Vec< Num_T > &	b,
		const Vec< Num_T > &	c,
		const Vec< Num_T > &	d,
		Vec< Num_T > &	out
	)

Element-wise multiplication of four vectors, storing the result in vector out.

Elementwise multiplication of four vectors, storing the result in vector out.

Definition at line 1108 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, it_assert_debug, and itpp::Vec< Num_T >::set_size().

template<class Num_T >

void itpp::elem_mult_inplace ( const Vec< Num_T > &  a, Vec< Num_T > &  b  )

inline

In-place element-wise multiplication of two vectors. Faster version of b = elem_mult(a,b).

In-place element-wise multiplication of two vectors. Fast version of b = elem_mult(a,b).

Definition at line 1123 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, and it_assert_debug.

template<class Num_T >

Num_T itpp::elem_mult_sum ( const Vec< Num_T > &  a, const Vec< Num_T > &  b  )

inline

Element-wise multiplication of two vectors, followed by summation of the resultant elements. Fast version of sum(elem_mult(a,b)).

Element-wise multiplication of two vectors, followed by summation of the resultant elements. Fast version of sum(elem_mult(a,b))

Definition at line 1132 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, and it_assert_debug.

template<class Num_T >

Vec< Num_T > itpp::operator/	(	const Vec< Num_T > &	v,
		Num_T	t
	)

Division of all elements in v with t.

Elementwise division.

Definition at line 1143 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::datasize.

template<class Num_T >

Vec< Num_T > itpp::operator/	(	Num_T	t,
		const Vec< Num_T > &	v
	)

Division of t with all elements in v.

Elementwise division.

Definition at line 1155 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::datasize.

template<class Num_T >

Vec< Num_T > itpp::elem_div ( const Vec< Num_T > &  a, const Vec< Num_T > &  b  )

inline

Elementwise division of two vectors.

Elementwise division.

Definition at line 1196 of file vec.h.

References elem_div_out().

template<class Num_T >

Vec< Num_T > itpp::elem_div	(	Num_T	t,
		const Vec< Num_T > &	v
	)

This function is deprecated. Please use operator/(Num_T, const Vec<Num_T &) instead.

This function is deprecated. Please use operator/(Num_T, const Vec<Num_T> &) instead.

Definition at line 1167 of file vec.h.

References it_warning, and operator/().

template<class Num_T >

void itpp::elem_div_out	(	const Vec< Num_T > &	a,
		const Vec< Num_T > &	b,
		Vec< Num_T > &	out
	)

Elementwise division of two vectors, storing the result in vector out.

Elementwise division.

Definition at line 1204 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, it_assert_debug, itpp::Vec< Num_T >::set_size(), and itpp::Vec< Num_T >::size().

template<class Num_T >

Num_T itpp::elem_div_sum ( const Vec< Num_T > &  a, const Vec< Num_T > &  b  )

inline

Elementwise division of two vectors, followed by summation of the resultant elements. Fast version of sum(elem_div(a,b))

Elementwise division, followed by summation of the resultant elements. Fast version of sum(elem_mult(a,b))

Definition at line 1215 of file vec.h.

References itpp::Vec< Num_T >::data, itpp::Vec< Num_T >::datasize, and it_assert_debug.

template<class Num_T >

Vec< Num_T > itpp::concat	(	const Vec< Num_T > &	v,
		Num_T	a
	)

Append element a to the end of the vector v.

Append element t to the end of the vector v.

Definition at line 1324 of file vec.h.

References itpp::Vec< Num_T >::data, size(), and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::concat	(	Num_T	a,
		const Vec< Num_T > &	v
	)

Concat element a to the beginning of the vector v.

Insert element t at the beginning of the vector v.

Definition at line 1334 of file vec.h.

References itpp::Vec< Num_T >::data, size(), and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::concat	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2
	)

Concat vectors v1 and v2.

Concatenate vectors v1 and v2.

Definition at line 1344 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::concat	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2,
		const Vec< Num_T > &	v3
	)

Concat vectors v1, v2 and v3.

Concatenate vectors v1, v2 and v3.

Definition at line 1355 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::concat	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2,
		const Vec< Num_T > &	v3,
		const Vec< Num_T > &	v4
	)

Concat vectors v1, v2, v3 and v4.

Concatenate vectors v1, v2, v3 and v4.

Definition at line 1369 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::size().

template<class Num_T >

Vec< Num_T > itpp::concat	(	const Vec< Num_T > &	v1,
		const Vec< Num_T > &	v2,
		const Vec< Num_T > &	v3,
		const Vec< Num_T > &	v4,
		const Vec< Num_T > &	v5
	)

Concat vectors v1, v2 v3, v4 and v5.

Concatenate vectors v1, v2, v3, v4 and v5.

Definition at line 1385 of file vec.h.

References itpp::Vec< Num_T >::data, and itpp::Vec< Num_T >::size().

std::complex<double> itpp::cerfc_continued_fraction

(

const std::complex< double > &

z

)

Abramowitz and Stegun: Eq. (7.1.14) gives this continued fraction for erfc(z)

erfc(z) = sqrt(pi).exp(-z^2). 1 1/2 1 3/2 2 5/2 — — — — — — ... z + z + z + z + z + z +

This is evaluated using Lentz's method, as described in the narative of Numerical Recipes in C.

The continued fraction is true providing real(z) > 0. In practice we like real(z) to be significantly greater than 0, say greater than 0.5.

Definition at line 52 of file error.cpp.

References abs(), eps, exp(), min(), pi, and sqrt().

Referenced by cerf_continued_fraction().

std::complex<double> itpp::cerf_series

(

const std::complex< double > &

z

)

Abramawitz and Stegun: Eq. (7.1.5) gives a series for erf(z) good for all z, but converges faster for smallish abs(z), say abs(z) < 2.

Definition at line 100 of file error.cpp.

References abs(), min(), pi, sqrt(), and sum().

Referenced by erf().

std::complex<double> itpp::cerf_rybicki

(

const std::complex< double > &

z

)

Numerical Recipes quotes a formula due to Rybicki for evaluating Dawson's Integral:

exp(-x^2) integral exp(t^2).dt = 1/sqrt(pi) lim sum exp(-(z-n.h)^2) / n 0 to x h->0 n odd

This can be adapted to erf(z).

Definition at line 124 of file error.cpp.

References exp(), pi, and sum().

Referenced by erf().

int itpp::reverse_int ( int  length, int  in  )

related

Reverses the bitrepresentation of in (of size length) and converts to an integer

Definition at line 1442 of file convcode.cpp.

Referenced by itpp::Rec_Syst_Conv_Code::set_generator_polynomials().

int itpp::weight_int ( int  length, int  in  )

related

Calculate the Hamming weight of the binary representation of in of size length

Definition at line 1460 of file convcode.cpp.

References length().

int itpp::compare_spectra ( ivec  v1, ivec  v2  )

related

Compare two distance spectra. Return 1 if v1 is less, 0 if v2 less, and -1 if equal.

Definition at line 1472 of file convcode.cpp.

References it_assert_debug.

int itpp::compare_spectra ( ivec  v1, ivec  v2, vec  weight_profile  )

related

Compare two distance spectra using a weight profile.

Return 1 if v1 is less, 0 if v2 less, and -1 if equal.

Definition at line 1492 of file convcode.cpp.

std::istream& itpp::operator>>	(	std::istream &	is,
		GF &	ingf
	)

Input stream operator for GF.

Input stream for GF(q)

Definition at line 93 of file galois.cpp.

References itpp::GF::get_size(), and itpp::GF::set().

std::ostream& itpp::operator<<	(	std::ostream &	os,
		const GF &	ingf
	)

Output stream operator for GF.

Output stream for GF(q)

Definition at line 125 of file galois.cpp.

ITPP_EXPORT std::ostream & itpp::operator<<	(	std::ostream &	os,
		const GFX &	ingfx
	)

Output stream operator for GFX.

Output stream.

Definition at line 135 of file galois.cpp.

GFX itpp::operator* ( const GF &  ingf, const GFX &  ingfx  )

inline

Multiplication of GF and GFX.

Multiply a GF element with a GF(q)[x].

Definition at line 543 of file galois.h.

References itpp::GF::get_size(), and it_assert_debug.

GFX itpp::operator* ( const GFX &  ingfx, const GF &  ingf  )

inline

Multiplication of GFX and GF.

Multiply a GF(q)[x] with a GF element.

Definition at line 552 of file galois.h.

GFX itpp::operator/ ( const GFX &  ingfx, const GF &  ingf  )

inline

Division of GFX by GF.

Divide a GF(q)[x] with a GF element.

Definition at line 557 of file galois.h.

References itpp::GF::get_size(), and it_assert_debug.

ITPP_EXPORT std::ostream & operator<<	(	std::ostream &	os,
		const LDPC_Code &	C
	)

Print some properties of the LDPC codec in plain text.

Print some properties of the codec in plain text.

Definition at line 1791 of file ldpc.cpp.

References itpp::LDPC_Code::get_decoding_method(), itpp::LDPC_Code::get_ncheck(), itpp::LDPC_Code::get_nvar(), itpp::LDPC_Code::get_rate(), max(), and zeros_i().

ITPP_EXPORT std::ostream & operator<<	(	std::ostream &	os,
		const Modulator_NRD &	mod
	)

Print some properties of the MIMO modulator (mainly to aid debugging)

Output some properties of the MIMO modulator (mainly to aid debugging)

Definition at line 679 of file modulator_nd.cpp.

References itpp::Modulator_ND::bitmap, itpp::Modulator_ND::get_llrcalc(), itpp::Modulator_ND::k, itpp::Array< T >::left(), itpp::Modulator_ND::M, itpp::Modulator_ND::nt, and itpp::Modulator_NRD::symbols.

int itpp::calculate_uncoded_size	(	Punctured_Turbo_Codec &	tc,
		int	punctured_size,
		int &	fill_bits
	)

Calculates length of the turbo code input block required to produce output block of length punctured_size. Some puncturing patterns might not allow to create block with such a length and then fill_bits of dummy bits must be used.

Parameters

tc	Instance of Punctured_Turbo_Codec
punctured_size	Required size of punctured encoded block
fill_bits	Number of dummy bits that must be attached to the encoded block (parameter calculated within the function)

Definition at line 874 of file turbo.cpp.

References ceil(), and itpp::Punctured_Turbo_Codec::Period.

ITPP_EXPORT ivec lte_turbo_interleaver_sequence

(

int

interleaver_size

)

Generates the interleaver sequence for the internal turbo encoder interleaver used in LTE.

Author

qdelfin and Stephan Ludwig

Definition at line 1135 of file turbo.cpp.

References it_assert.

void itpp::MOG_diag_MAP	(	MOG_diag &	model_in,
		MOG_diag &	prior_model_in,
		Array< vec > &	X_in,
		int	max_iter_in = 10,
		double	alpha_in = 0.5,
		double	var_floor_in = 0.0,
		double	weight_floor_in = 0.0,
		bool	verbose_in = false
	)

NOT YET IMPLEMENTED. Maximum a Posteriori (MAP) Expectation Maximisation optimiser for Mixtures of Gaussians.

Parameters

model_in	The model to optimise (MOG_diag)
prior_model_in	The model representing the prior
X_in	The training data (array of vectors)
max_iter_in	Maximum number of iterations
alpha_in	Coefficient for combining the parameters with the prior. 0 <= _alpha <= 1.
var_floor_in	Variance floor (lowest allowable variance). Set to 0.0 to use the default.
weight_floor_in	Weight floor (lowest allowable weight). Set to 0.0 to use the default.
verbose_in	ADD DOCUMENTATION HERE

Note

NOT YET IMPLEMENTED.

The variance and weight floors are set to std::numeric_limits<double>::min() if they are below that value. The largest allowable weight floor is 1/K, where K is the number of Gaussians.

Definition at line 322 of file mog_diag_em.cpp.

References it_error.

Variable Documentation

const int itpp::LDPC_binary_file_version = 2

static

Version of the binary file with generator and decoder data.

This has to be global since it is used in LDPC_Generator and LDPC_Code classes

Definition at line 42 of file ldpc.cpp.

Referenced by itpp::LDPC_Generator_Systematic::load(), itpp::BLDPC_Generator::load(), itpp::LDPC_Code::load_code(), itpp::LDPC_Generator_Systematic::save(), itpp::BLDPC_Generator::save(), and itpp::LDPC_Code::save_code().