[35] | 1 | /*! |
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| 2 | * \file |
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| 3 | * \brief Definitions of special vectors and matrices |
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| 4 | * \author Tony Ottosson, Tobias Ringstrom, Pal Frenger, Adam Piatyszek and Erik G. Larsson |
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| 5 | * |
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| 6 | * ------------------------------------------------------------------------- |
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| 7 | * |
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| 8 | * IT++ - C++ library of mathematical, signal processing, speech processing, |
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| 9 | * and communications classes and functions |
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| 10 | * |
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| 11 | * Copyright (C) 1995-2007 (see AUTHORS file for a list of contributors) |
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| 12 | * |
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| 13 | * This program is free software; you can redistribute it and/or modify |
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| 14 | * it under the terms of the GNU General Public License as published by |
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| 15 | * the Free Software Foundation; either version 2 of the License, or |
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| 16 | * (at your option) any later version. |
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| 17 | * |
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| 18 | * This program is distributed in the hope that it will be useful, |
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| 19 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 20 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 21 | * GNU General Public License for more details. |
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| 22 | * |
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| 23 | * You should have received a copy of the GNU General Public License |
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| 24 | * along with this program; if not, write to the Free Software |
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| 25 | * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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| 26 | * |
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| 27 | * ------------------------------------------------------------------------- |
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| 28 | */ |
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| 29 | |
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| 30 | #ifndef SPECMAT_H |
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| 31 | #define SPECMAT_H |
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| 32 | |
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| 33 | #include <itpp/base/vec.h> |
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| 34 | #include <itpp/base/mat.h> |
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| 35 | |
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| 36 | |
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| 37 | namespace itpp { |
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| 38 | |
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| 39 | /*! |
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| 40 | \brief Return a integer vector with indicies where bvec == 1 |
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| 41 | \ingroup miscfunc |
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| 42 | */ |
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| 43 | ivec find(const bvec &invector); |
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| 44 | |
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| 45 | /*! |
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| 46 | \addtogroup specmat |
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| 47 | */ |
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| 48 | |
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| 49 | //!\addtogroup specmat |
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| 50 | //!@{ |
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| 51 | |
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| 52 | //! A float vector of ones |
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| 53 | vec ones(int size); |
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| 54 | //! A Binary vector of ones |
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| 55 | bvec ones_b(int size); |
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| 56 | //! A Int vector of ones |
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| 57 | ivec ones_i(int size); |
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| 58 | //! A float Complex vector of ones |
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| 59 | cvec ones_c(int size); |
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| 60 | |
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| 61 | //! A float (rows,cols)-matrix of ones |
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| 62 | mat ones(int rows, int cols); |
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| 63 | //! A Binary (rows,cols)-matrix of ones |
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| 64 | bmat ones_b(int rows, int cols); |
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| 65 | //! A Int (rows,cols)-matrix of ones |
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| 66 | imat ones_i(int rows, int cols); |
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| 67 | //! A Double Complex (rows,cols)-matrix of ones |
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| 68 | cmat ones_c(int rows, int cols); |
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| 69 | |
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| 70 | //! A Double vector of zeros |
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| 71 | vec zeros(int size); |
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| 72 | //! A Binary vector of zeros |
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| 73 | bvec zeros_b(int size); |
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| 74 | //! A Int vector of zeros |
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| 75 | ivec zeros_i(int size); |
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| 76 | //! A Double Complex vector of zeros |
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| 77 | cvec zeros_c(int size); |
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| 78 | |
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| 79 | //! A Double (rows,cols)-matrix of zeros |
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| 80 | mat zeros(int rows, int cols); |
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| 81 | //! A Binary (rows,cols)-matrix of zeros |
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| 82 | bmat zeros_b(int rows, int cols); |
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| 83 | //! A Int (rows,cols)-matrix of zeros |
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| 84 | imat zeros_i(int rows, int cols); |
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| 85 | //! A Double Complex (rows,cols)-matrix of zeros |
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| 86 | cmat zeros_c(int rows, int cols); |
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| 87 | |
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| 88 | //! A Double (size,size) unit matrix |
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| 89 | mat eye(int size); |
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| 90 | //! A Binary (size,size) unit matrix |
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| 91 | bmat eye_b(int size); |
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| 92 | //! A Int (size,size) unit matrix |
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| 93 | imat eye_i(int size); |
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| 94 | //! A Double Complex (size,size) unit matrix |
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| 95 | cmat eye_c(int size); |
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| 96 | //! A non-copying version of the eye function. |
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| 97 | template <class T> |
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| 98 | void eye(int size, Mat<T> &m); |
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| 99 | |
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| 100 | //! Impulse vector |
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| 101 | vec impulse(int size); |
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| 102 | //! Linspace (works in the same way as the matlab version) |
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| 103 | vec linspace(double from, double to, int length = 100); |
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| 104 | /*! \brief Zig-zag space function (variation on linspace) |
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| 105 | |
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| 106 | This function is a variation on linspace(). It traverses the points |
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| 107 | in different order. For example |
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| 108 | \code |
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| 109 | zigzag_space(-5,5,3) |
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| 110 | \endcode |
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| 111 | gives the vector |
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| 112 | \code |
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| 113 | [-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75] |
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| 114 | \endcode |
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| 115 | and |
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| 116 | \code |
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| 117 | zigzag_space(-5,5,4) |
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| 118 | \endcode |
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| 119 | gives |
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| 120 | the vector |
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| 121 | \code |
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| 122 | [-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] |
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| 123 | \endcode |
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| 124 | and so on. |
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| 125 | |
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| 126 | I.e. the function samples the interval [t0,t1] with finer and finer |
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| 127 | density and with points uniformly distributed over the interval, |
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| 128 | rather than from left to right (as does linspace). |
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| 129 | |
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| 130 | The result is a vector of length 1+2^K. |
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| 131 | */ |
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| 132 | vec zigzag_space(double t0, double t1, int K=5); |
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| 133 | |
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| 134 | /*! |
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| 135 | * \brief Hadamard matrix |
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| 136 | * |
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| 137 | * This function constructs a \a size by \a size Hadammard matrix, where |
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| 138 | * \a size is a power of 2. |
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| 139 | */ |
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| 140 | imat hadamard(int size); |
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| 141 | |
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| 142 | /*! |
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| 143 | \brief Jacobsthal matrix. |
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| 144 | |
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| 145 | Constructs an p by p matrix Q where p is a prime (not checked). |
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| 146 | The elements in Q {qij} is given by qij=X(j-i), where X(x) is the |
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| 147 | Legendre symbol given as: |
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| 148 | |
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| 149 | <ul> |
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| 150 | <li> X(x)=0 if x is a multiple of p, </li> |
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| 151 | <li> X(x)=1 if x is a quadratic residue modulo p, </li> |
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| 152 | <li> X(x)=-1 if x is a quadratic nonresidue modulo p. </li> |
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| 153 | </ul> |
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| 154 | |
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| 155 | See Wicker "Error Control Systems for digital communication and storage", p. 134 |
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| 156 | for more information on these topics. Do not check that p is a prime. |
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| 157 | */ |
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| 158 | imat jacobsthal(int p); |
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| 159 | |
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| 160 | /*! |
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| 161 | \brief Conference matrix. |
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| 162 | |
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| 163 | Constructs an n by n matrix C, where n=p^m+1=2 (mod 4) and p is a odd prime (not checked). |
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| 164 | This code only work with m=1, that is n=p+1 and p odd prime. The valid sizes |
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| 165 | of n is then n=6, 14, 18, 30, 38, ... (and not 10, 26, ...). |
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| 166 | C has the property that C*C'=(n-1)I, that is it has orthogonal rows and columns |
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| 167 | in the same way as Hadamard matricies. However, one element in each row (on the |
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| 168 | diagonal) is zeros. The others are {-1,+1}. |
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| 169 | |
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| 170 | For more details see pp. 55-58 in MacWilliams & Sloane "The theory of error correcting codes", |
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| 171 | North-Holland, 1977. |
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| 172 | */ |
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| 173 | imat conference(int n); |
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| 174 | |
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| 175 | /*! |
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| 176 | \brief Computes the Hermitian Toeplitz matrix. |
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| 177 | |
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| 178 | Return the Toeplitz matrix constructed given the first column C, |
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| 179 | and (optionally) the first row R. If the first element of C is not |
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| 180 | the same as the first element of R, the first element of C is |
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| 181 | used. If the second argument is omitted, the first row is taken |
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| 182 | to be the same as the first column. |
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| 183 | |
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| 184 | A square Toeplitz matrix has the form: |
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| 185 | \verbatim |
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| 186 | c(0) r(1) r(2) ... r(n) |
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| 187 | c(1)* c(0) r(1) r(n-1) |
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| 188 | c(2)* c(1)* c(0) r(n-2) |
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| 189 | . . |
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| 190 | . . |
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| 191 | . . |
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| 192 | |
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| 193 | c(n)* c(n-1)* c(n-2)* ... c(0) |
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| 194 | \endverbatim |
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| 195 | */ |
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| 196 | cmat toeplitz(const cvec &c, const cvec &r); |
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| 197 | //! Computes the Hermitian Toeplitz matrix. |
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| 198 | cmat toeplitz(const cvec &c); |
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| 199 | //! Computes the Hermitian Toeplitz matrix. |
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| 200 | mat toeplitz(const vec &c, const vec &r); |
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| 201 | //! Computes the Hermitian Toeplitz matrix. |
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| 202 | mat toeplitz(const vec &c); |
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| 203 | |
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| 204 | //!@} |
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| 205 | |
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| 206 | |
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| 207 | /*! |
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| 208 | \brief Create a rotation matrix that rotates the given plane \c angle radians. Note that the order of the planes are important! |
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| 209 | \ingroup miscfunc |
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| 210 | */ |
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| 211 | mat rotation_matrix(int dim, int plane1, int plane2, double angle); |
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| 212 | |
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| 213 | /*! |
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| 214 | \brief Calcualte the Householder vector |
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| 215 | \ingroup miscfunc |
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| 216 | */ |
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| 217 | void house(const vec &x, vec &v, double &beta); |
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| 218 | |
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| 219 | /*! |
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| 220 | \brief Calculate the Givens rotation values |
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| 221 | \ingroup miscfunc |
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| 222 | */ |
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| 223 | void givens(double a, double b, double &c, double &s); |
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| 224 | |
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| 225 | /*! |
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| 226 | \brief Calculate the Givens rotation matrix |
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| 227 | \ingroup miscfunc |
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| 228 | */ |
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| 229 | void givens(double a, double b, mat &m); |
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| 230 | |
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| 231 | /*! |
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| 232 | \brief Calculate the Givens rotation matrix |
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| 233 | \ingroup miscfunc |
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| 234 | */ |
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| 235 | mat givens(double a, double b); |
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| 236 | |
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| 237 | /*! |
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| 238 | \brief Calculate the transposed Givens rotation matrix |
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| 239 | \ingroup miscfunc |
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| 240 | */ |
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| 241 | void givens_t(double a, double b, mat &m); |
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| 242 | |
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| 243 | /*! |
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| 244 | \brief Calculate the transposed Givens rotation matrix |
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| 245 | \ingroup miscfunc |
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| 246 | */ |
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| 247 | mat givens_t(double a, double b); |
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| 248 | |
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| 249 | /*! |
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| 250 | \relates Vec |
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| 251 | \brief Vector of length 1 |
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| 252 | */ |
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| 253 | template <class T> |
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| 254 | Vec<T> vec_1(T v0) |
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| 255 | { |
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| 256 | Vec<T> v(1); |
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| 257 | v(0) = v0; |
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| 258 | return v; |
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| 259 | } |
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| 260 | |
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| 261 | /*! |
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| 262 | \relates Vec |
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| 263 | \brief Vector of length 2 |
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| 264 | */ |
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| 265 | template <class T> |
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| 266 | Vec<T> vec_2(T v0, T v1) |
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| 267 | { |
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| 268 | Vec<T> v(2); |
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| 269 | v(0) = v0; |
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| 270 | v(1) = v1; |
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| 271 | return v; |
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| 272 | } |
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| 273 | |
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| 274 | /*! |
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| 275 | \relates Vec |
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| 276 | \brief Vector of length 3 |
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| 277 | */ |
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| 278 | template <class T> |
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| 279 | Vec<T> vec_3(T v0, T v1, T v2) |
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| 280 | { |
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| 281 | Vec<T> v(3); |
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| 282 | v(0) = v0; |
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| 283 | v(1) = v1; |
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| 284 | v(2) = v2; |
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| 285 | return v; |
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| 286 | } |
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| 287 | |
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| 288 | /*! |
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| 289 | \relates Mat |
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| 290 | \brief Matrix of size 1 by 1 |
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| 291 | */ |
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| 292 | template <class T> |
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| 293 | Mat<T> mat_1x1(T m00) |
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| 294 | { |
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| 295 | Mat<T> m(1,1); |
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| 296 | m(0,0) = m00; |
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| 297 | return m; |
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| 298 | } |
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| 299 | |
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| 300 | /*! |
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| 301 | \relates Mat |
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| 302 | \brief Matrix of size 1 by 2 |
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| 303 | */ |
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| 304 | template <class T> |
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| 305 | Mat<T> mat_1x2(T m00, T m01) |
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| 306 | { |
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| 307 | Mat<T> m(1,2); |
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| 308 | m(0,0) = m00; m(0,1) = m01; |
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| 309 | return m; |
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| 310 | } |
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| 311 | |
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| 312 | /*! |
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| 313 | \relates Mat |
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| 314 | \brief Matrix of size 2 by 1 |
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| 315 | */ |
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| 316 | template <class T> |
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| 317 | Mat<T> mat_2x1(T m00, |
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| 318 | T m10) |
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| 319 | { |
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| 320 | Mat<T> m(2,1); |
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| 321 | m(0,0) = m00; |
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| 322 | m(1,0) = m10; |
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| 323 | return m; |
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| 324 | } |
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| 325 | |
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| 326 | /*! |
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| 327 | \relates Mat |
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| 328 | \brief Matrix of size 2 by 2 |
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| 329 | */ |
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| 330 | template <class T> |
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| 331 | Mat<T> mat_2x2(T m00, T m01, |
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| 332 | T m10, T m11) |
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| 333 | { |
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| 334 | Mat<T> m(2,2); |
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| 335 | m(0,0) = m00; m(0,1) = m01; |
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| 336 | m(1,0) = m10; m(1,1) = m11; |
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| 337 | return m; |
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| 338 | } |
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| 339 | |
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| 340 | /*! |
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| 341 | \relates Mat |
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| 342 | \brief Matrix of size 1 by 3 |
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| 343 | */ |
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| 344 | template <class T> |
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| 345 | Mat<T> mat_1x3(T m00, T m01, T m02) |
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| 346 | { |
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| 347 | Mat<T> m(1,3); |
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| 348 | m(0,0) = m00; m(0,1) = m01; m(0,2) = m02; |
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| 349 | return m; |
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| 350 | } |
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| 351 | |
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| 352 | /*! |
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| 353 | \relates Mat |
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| 354 | \brief Matrix of size 3 by 1 |
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| 355 | */ |
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| 356 | template <class T> |
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| 357 | Mat<T> mat_3x1(T m00, |
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| 358 | T m10, |
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| 359 | T m20) |
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| 360 | { |
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| 361 | Mat<T> m(3,1); |
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| 362 | m(0,0) = m00; |
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| 363 | m(1,0) = m10; |
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| 364 | m(2,0) = m20; |
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| 365 | return m; |
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| 366 | } |
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| 367 | |
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| 368 | /*! |
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| 369 | \relates Mat |
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| 370 | \brief Matrix of size 2 by 3 |
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| 371 | */ |
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| 372 | template <class T> |
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| 373 | Mat<T> mat_2x3(T m00, T m01, T m02, |
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| 374 | T m10, T m11, T m12) |
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| 375 | { |
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| 376 | Mat<T> m(2,3); |
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| 377 | m(0,0) = m00; m(0,1) = m01; m(0,2) = m02; |
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| 378 | m(1,0) = m10; m(1,1) = m11; m(1,2) = m12; |
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| 379 | return m; |
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| 380 | } |
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| 381 | |
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| 382 | /*! |
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| 383 | \relates Mat |
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| 384 | \brief Matrix of size 3 by 2 |
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| 385 | */ |
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| 386 | template <class T> |
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| 387 | Mat<T> mat_3x2(T m00, T m01, |
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| 388 | T m10, T m11, |
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| 389 | T m20, T m21) |
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| 390 | { |
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| 391 | Mat<T> m(3,2); |
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| 392 | m(0,0) = m00; m(0,1) = m01; |
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| 393 | m(1,0) = m10; m(1,1) = m11; |
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| 394 | m(2,0) = m20; m(2,1) = m21; |
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| 395 | return m; |
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| 396 | } |
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| 397 | |
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| 398 | /*! |
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| 399 | \relates Mat |
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| 400 | \brief Matrix of size 3 by 3 |
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| 401 | */ |
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| 402 | template <class T> |
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| 403 | Mat<T> mat_3x3(T m00, T m01, T m02, |
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| 404 | T m10, T m11, T m12, |
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| 405 | T m20, T m21, T m22) |
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| 406 | { |
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| 407 | Mat<T> m(3,3); |
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| 408 | m(0,0) = m00; m(0,1) = m01; m(0,2) = m02; |
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| 409 | m(1,0) = m10; m(1,1) = m11; m(1,2) = m12; |
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| 410 | m(2,0) = m20; m(2,1) = m21; m(2,2) = m22; |
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| 411 | return m; |
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| 412 | } |
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| 413 | |
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| 414 | } //namespace itpp |
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| 415 | |
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| 416 | #endif // #ifndef SPECMAT_H |
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