/usr/include/itpp/base/specmat.h is in libitpp-dev 4.3.1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 | /*!
* \file
* \brief Definitions of special vectors and matrices
* \author Tony Ottosson, Tobias Ringstrom, Pal Frenger, Adam Piatyszek
* and Erik G. Larsson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* IT++ is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along
* with IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#ifndef SPECMAT_H
#define SPECMAT_H
#include <itpp/base/vec.h>
#include <itpp/base/mat.h>
#include <itpp/base/converters.h>
#include <itpp/itexports.h>
namespace itpp
{
/*!
\brief Return a integer vector with indicies where bvec == 1
\ingroup miscfunc
*/
ITPP_EXPORT ivec find(const bvec &invector);
/*!
\addtogroup specmat
*/
//!\addtogroup specmat
//!@{
//! A float vector of ones
ITPP_EXPORT vec ones(int size);
//! A Binary vector of ones
ITPP_EXPORT bvec ones_b(int size);
//! A Int vector of ones
ITPP_EXPORT ivec ones_i(int size);
//! A float Complex vector of ones
ITPP_EXPORT cvec ones_c(int size);
//! A float (rows,cols)-matrix of ones
ITPP_EXPORT mat ones(int rows, int cols);
//! A Binary (rows,cols)-matrix of ones
ITPP_EXPORT bmat ones_b(int rows, int cols);
//! A Int (rows,cols)-matrix of ones
ITPP_EXPORT imat ones_i(int rows, int cols);
//! A Double Complex (rows,cols)-matrix of ones
ITPP_EXPORT cmat ones_c(int rows, int cols);
//! A Double vector of zeros
ITPP_EXPORT vec zeros(int size);
//! A Binary vector of zeros
ITPP_EXPORT bvec zeros_b(int size);
//! A Int vector of zeros
ITPP_EXPORT ivec zeros_i(int size);
//! A Double Complex vector of zeros
ITPP_EXPORT cvec zeros_c(int size);
//! A Double (rows,cols)-matrix of zeros
ITPP_EXPORT mat zeros(int rows, int cols);
//! A Binary (rows,cols)-matrix of zeros
ITPP_EXPORT bmat zeros_b(int rows, int cols);
//! A Int (rows,cols)-matrix of zeros
ITPP_EXPORT imat zeros_i(int rows, int cols);
//! A Double Complex (rows,cols)-matrix of zeros
ITPP_EXPORT cmat zeros_c(int rows, int cols);
//! A Double (size,size) unit matrix
ITPP_EXPORT mat eye(int size);
//! A Binary (size,size) unit matrix
ITPP_EXPORT bmat eye_b(int size);
//! A Int (size,size) unit matrix
ITPP_EXPORT imat eye_i(int size);
//! A Double Complex (size,size) unit matrix
ITPP_EXPORT cmat eye_c(int size);
//! A non-copying version of the eye function.
template <class T>
void eye(int size, Mat<T> &m)
{
m.set_size(size, size, false);
m = T(0);
for (int i = size - 1; i >= 0; i--)
m(i, i) = T(1);
}
//! Impulse vector
ITPP_EXPORT vec impulse(int size);
//! linspace (works in the same way as the MATLAB version)
ITPP_EXPORT vec linspace(double from, double to, int length = 100);
//! linspace_fixed_step (works in the same way as "from:step:to" in MATLAB)
template<class T>
Vec<T> linspace_fixed_step(T from, T to, T step = 1)
{
int points = 0;
if (0 != step) {
points = itpp::floor_i(double(to-from)/step)+1;
}
if (0 >= points) {
return Vec<T>(0);
}
Vec<T> output(points);
output(0) = from;
for (int n = 1; n < points; ++n) {
output(n) = output(n-1)+step;
}
return output;
}
/*! \brief Zig-zag space function (variation on linspace)
This function is a variation on linspace(). It traverses the points
in different order. For example
\code
zigzag_space(-5,5,3)
\endcode
gives the vector
\code
[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75]
\endcode
and
\code
zigzag_space(-5,5,4)
\endcode
gives
the vector
\code
[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75 -4.375 -3.125 -1.875 -0.625 0.625 1.875 3.125 4.375]
\endcode
and so on.
I.e. the function samples the interval [t0,t1] with finer and finer
density and with points uniformly distributed over the interval,
rather than from left to right (as does linspace).
The result is a vector of length 1+2^K.
*/
ITPP_EXPORT vec zigzag_space(double t0, double t1, int K = 5);
/*!
* \brief Hadamard matrix
*
* This function constructs a \a size by \a size Hadammard matrix, where
* \a size is a power of 2.
*/
ITPP_EXPORT imat hadamard(int size);
/*!
\brief Jacobsthal matrix.
Constructs an p by p matrix Q where p is a prime (not checked).
The elements in Q {qij} is given by qij=X(j-i), where X(x) is the
Legendre symbol given as:
<ul>
<li> X(x)=0 if x is a multiple of p, </li>
<li> X(x)=1 if x is a quadratic residue modulo p, </li>
<li> X(x)=-1 if x is a quadratic nonresidue modulo p. </li>
</ul>
See Wicker "Error Control Systems for digital communication and storage", p. 134
for more information on these topics. Do not check that p is a prime.
*/
ITPP_EXPORT imat jacobsthal(int p);
/*!
\brief Conference matrix.
Constructs an n by n matrix C, where n=p^m+1=2 (mod 4) and p is a odd prime (not checked).
This code only work with m=1, that is n=p+1 and p odd prime. The valid sizes
of n is then n=6, 14, 18, 30, 38, ... (and not 10, 26, ...).
C has the property that C*C'=(n-1)I, that is it has orthogonal rows and columns
in the same way as Hadamard matricies. However, one element in each row (on the
diagonal) is zeros. The others are {-1,+1}.
For more details see pp. 55-58 in MacWilliams & Sloane "The theory of error correcting codes",
North-Holland, 1977.
*/
ITPP_EXPORT imat conference(int n);
/*!
* \brief Generate Toeplitz matrix from two vectors \c c and \c r.
*
* Returns the Toeplitz matrix constructed given the first column C, and
* (optionally) the first row R. If the first element of C is not the same
* as the first element of R, the first element of C is used. If the second
* argument is omitted, the first row is taken to be the same as the first
* column and a symmetric (Hermitian) Toeplitz matrix is created.
*
* An example square Toeplitz matrix has the form:
* \verbatim
* c(0) r(1) r(2) ... r(n)
* c(1) c(0) r(1) r(n-1)
* c(2) c(1) c(0) r(n-2)
* . .
* . .
* . .
*
* c(n) c(n-1) c(n-2) ... c(0)
* \endverbatim
*
* \author Adam Piatyszek
*/
template <typename Num_T>
const Mat<Num_T> toeplitz(const Vec<Num_T> &c, const Vec<Num_T> &r)
{
int n_rows = c.size();
int n_cols = r.size();
Mat<Num_T> output(n_rows, n_cols);
for (int i = 0; i < n_rows; ++i) {
int j_limit = std::min(n_cols, n_rows - i);
for (int j = 0; j < j_limit; ++j) {
output(i + j, j) = c(i);
}
}
for (int j = 1; j < n_cols; ++j) {
int i_limit = std::min(n_rows, n_cols - j);
for (int i = 0; i < i_limit; ++i) {
output(i, i + j) = r(j);
}
}
return output;
}
//! Generate symmetric Toeplitz matrix from vector \c c.
template <typename Num_T>
const Mat<Num_T> toeplitz(const Vec<Num_T> &c)
{
int s = c.size();
Mat<Num_T> output(s, s);
for (int i = 0; i < s; ++i) {
for (int j = 0; j < s - i; ++j) {
output(i + j, j) = c(i);
}
}
for (int j = 1; j < s; ++j) {
for (int i = 0; i < s - j; ++i) {
output(i, i + j) = c(j);
}
}
return output;
}
//! Generate symmetric Toeplitz matrix from vector \c c (complex valued)
ITPP_EXPORT const cmat toeplitz(const cvec &c);
//!@}
/*!
\brief Create a rotation matrix that rotates the given plane \c angle radians. Note that the order of the planes are important!
\ingroup miscfunc
*/
ITPP_EXPORT mat rotation_matrix(int dim, int plane1, int plane2, double angle);
/*!
\brief Calcualte the Householder vector
\ingroup miscfunc
*/
ITPP_EXPORT void house(const vec &x, vec &v, double &beta);
/*!
\brief Calculate the Givens rotation values
\ingroup miscfunc
*/
ITPP_EXPORT void givens(double a, double b, double &c, double &s);
/*!
\brief Calculate the Givens rotation matrix
\ingroup miscfunc
*/
ITPP_EXPORT void givens(double a, double b, mat &m);
/*!
\brief Calculate the Givens rotation matrix
\ingroup miscfunc
*/
ITPP_EXPORT mat givens(double a, double b);
/*!
\brief Calculate the transposed Givens rotation matrix
\ingroup miscfunc
*/
ITPP_EXPORT void givens_t(double a, double b, mat &m);
/*!
\brief Calculate the transposed Givens rotation matrix
\ingroup miscfunc
*/
ITPP_EXPORT mat givens_t(double a, double b);
/*!
\relates Vec
\brief Vector of length 1
*/
template <class T>
Vec<T> vec_1(T v0)
{
Vec<T> v(1);
v(0) = v0;
return v;
}
/*!
\relates Vec
\brief Vector of length 2
*/
template <class T>
Vec<T> vec_2(T v0, T v1)
{
Vec<T> v(2);
v(0) = v0;
v(1) = v1;
return v;
}
/*!
\relates Vec
\brief Vector of length 3
*/
template <class T>
Vec<T> vec_3(T v0, T v1, T v2)
{
Vec<T> v(3);
v(0) = v0;
v(1) = v1;
v(2) = v2;
return v;
}
/*!
\relates Mat
\brief Matrix of size 1 by 1
*/
template <class T>
Mat<T> mat_1x1(T m00)
{
Mat<T> m(1, 1);
m(0, 0) = m00;
return m;
}
/*!
\relates Mat
\brief Matrix of size 1 by 2
*/
template <class T>
Mat<T> mat_1x2(T m00, T m01)
{
Mat<T> m(1, 2);
m(0, 0) = m00;
m(0, 1) = m01;
return m;
}
/*!
\relates Mat
\brief Matrix of size 2 by 1
*/
template <class T>
Mat<T> mat_2x1(T m00,
T m10)
{
Mat<T> m(2, 1);
m(0, 0) = m00;
m(1, 0) = m10;
return m;
}
/*!
\relates Mat
\brief Matrix of size 2 by 2
*/
template <class T>
Mat<T> mat_2x2(T m00, T m01,
T m10, T m11)
{
Mat<T> m(2, 2);
m(0, 0) = m00;
m(0, 1) = m01;
m(1, 0) = m10;
m(1, 1) = m11;
return m;
}
/*!
\relates Mat
\brief Matrix of size 1 by 3
*/
template <class T>
Mat<T> mat_1x3(T m00, T m01, T m02)
{
Mat<T> m(1, 3);
m(0, 0) = m00;
m(0, 1) = m01;
m(0, 2) = m02;
return m;
}
/*!
\relates Mat
\brief Matrix of size 3 by 1
*/
template <class T>
Mat<T> mat_3x1(T m00,
T m10,
T m20)
{
Mat<T> m(3, 1);
m(0, 0) = m00;
m(1, 0) = m10;
m(2, 0) = m20;
return m;
}
/*!
\relates Mat
\brief Matrix of size 2 by 3
*/
template <class T>
Mat<T> mat_2x3(T m00, T m01, T m02,
T m10, T m11, T m12)
{
Mat<T> m(2, 3);
m(0, 0) = m00;
m(0, 1) = m01;
m(0, 2) = m02;
m(1, 0) = m10;
m(1, 1) = m11;
m(1, 2) = m12;
return m;
}
/*!
\relates Mat
\brief Matrix of size 3 by 2
*/
template <class T>
Mat<T> mat_3x2(T m00, T m01,
T m10, T m11,
T m20, T m21)
{
Mat<T> m(3, 2);
m(0, 0) = m00;
m(0, 1) = m01;
m(1, 0) = m10;
m(1, 1) = m11;
m(2, 0) = m20;
m(2, 1) = m21;
return m;
}
/*!
\relates Mat
\brief Matrix of size 3 by 3
*/
template <class T>
Mat<T> mat_3x3(T m00, T m01, T m02,
T m10, T m11, T m12,
T m20, T m21, T m22)
{
Mat<T> m(3, 3);
m(0, 0) = m00;
m(0, 1) = m01;
m(0, 2) = m02;
m(1, 0) = m10;
m(1, 1) = m11;
m(1, 2) = m12;
m(2, 0) = m20;
m(2, 1) = m21;
m(2, 2) = m22;
return m;
}
} //namespace itpp
#endif // #ifndef SPECMAT_H
|