[35] | 1 | /*! |
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| 2 | * \file |
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| 3 | * \brief Logarithmic and exponenential functions - header file |
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| 4 | * \author Tony Ottosson, Adam Piatyszek and Conrad Sanderson |
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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 LOG_EXP_H |
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| 31 | #define LOG_EXP_H |
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| 32 | |
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| 33 | #ifndef _MSC_VER |
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| 34 | # include <itpp/config.h> |
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| 35 | #else |
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| 36 | # include <itpp/config_msvc.h> |
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| 37 | #endif |
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| 38 | |
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| 39 | #include <itpp/base/help_functions.h> |
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| 40 | #include <limits> |
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| 41 | |
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| 42 | |
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| 43 | /*! |
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| 44 | * \addtogroup logexpfunc |
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| 45 | * @{ |
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| 46 | */ |
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| 47 | |
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| 48 | #ifndef HAVE_LOG1P |
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| 49 | //! Lograrithm of an argument \c x plus one |
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| 50 | inline double log1p(double x) { return std::log(1.0 + x); } |
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| 51 | #endif |
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| 52 | |
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| 53 | #ifndef HAVE_LOG2 |
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| 54 | #undef log2 // This is required at least for Cygwin |
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| 55 | //! Base-2 logarithm |
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| 56 | inline double log2(double x) |
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| 57 | { |
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| 58 | return (std::log(x) * 1.442695040888963387004650940070860087871551513671875); |
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| 59 | } |
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| 60 | #endif |
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| 61 | |
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| 62 | /*! |
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| 63 | * @} |
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| 64 | */ |
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| 65 | |
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| 66 | |
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| 67 | namespace itpp { |
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| 68 | |
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| 69 | //!\addtogroup logexpfunc |
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| 70 | //!@{ |
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| 71 | |
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| 72 | // ---------------------------------------------------------------------- |
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| 73 | // scalar functions |
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| 74 | // ---------------------------------------------------------------------- |
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| 75 | |
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| 76 | //! Base-b logarithm |
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| 77 | inline double logb(double b, double x) |
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| 78 | { |
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| 79 | return (std::log(x) / std::log(b)); |
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| 80 | } |
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| 81 | |
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| 82 | //! Calculate two to the power of x (2^x); x is integer |
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| 83 | inline int pow2i(int x) { return ((x < 0) ? 0 : (1 << x)); } |
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| 84 | //! Calculate two to the power of x (2^x) |
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| 85 | inline double pow2(double x) { return pow(2.0, x); } |
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| 86 | |
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| 87 | //! Calculate ten to the power of x (10^x) |
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| 88 | inline double pow10(double x) { return pow(10.0, x); } |
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| 89 | |
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| 90 | //! Decibel of x (10*log10(x)) |
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| 91 | inline double dB(double x) { return 10.0 * log10(x); } |
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| 92 | //! Inverse of decibel of x |
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| 93 | inline double inv_dB(double x) { return pow(10.0, 0.1 * x); } |
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| 94 | |
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| 95 | //! Calculate the number of bits needed to represent an inteager \c n |
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| 96 | inline int int2bits(int n) |
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| 97 | { |
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| 98 | it_assert(n >= 0, "int2bits(): Improper argument value"); |
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| 99 | |
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| 100 | if (n == 0) |
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| 101 | return 1; |
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| 102 | |
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| 103 | int b = 0; |
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| 104 | while (n) { |
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| 105 | n >>= 1; |
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| 106 | ++b; |
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| 107 | } |
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| 108 | return b; |
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| 109 | } |
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| 110 | |
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| 111 | //! Calculate the number of bits needed to represent \c n different values (levels). |
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| 112 | inline int levels2bits(int n) |
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| 113 | { |
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| 114 | it_assert(n > 0,"levels2bits(): Improper argument value"); |
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| 115 | return int2bits(--n); |
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| 116 | } |
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| 117 | |
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| 118 | //! Deprecated function. Please use int2bits() or levels2bits() instead. |
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| 119 | inline int needed_bits(int n) |
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| 120 | { |
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| 121 | it_warning("needed_bits(): This function is depreceted. Depending on your needs, please use int2bits() or levels2bits() instead."); |
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| 122 | return int2bits(n); |
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| 123 | } |
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| 124 | |
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| 125 | //! Constant definition to speed up trunc_log() and trunc_exp() |
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| 126 | const double log_double_max = std::log(std::numeric_limits<double>::max()); |
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| 127 | //! Constant definition to speed up trunc_log(), trunc_exp() and log_add() |
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| 128 | const double log_double_min = std::log(std::numeric_limits<double>::min()); |
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| 129 | |
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| 130 | /*! |
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| 131 | \brief Truncated natural logarithm function |
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| 132 | |
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| 133 | This truncated function provides a solution in the cases when the |
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| 134 | logarithm argument is less or equal to zero or infinity. The function |
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| 135 | checks for such extreme values and use some kind of truncation |
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| 136 | (saturation) before calculating the logarithm. |
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| 137 | |
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| 138 | The truncated logarithm function can be used for calculation of |
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| 139 | log-likelihood in soft demodulators, when numerical instability problem |
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| 140 | might occur. |
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| 141 | */ |
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| 142 | inline double trunc_log(double x) |
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| 143 | { |
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| 144 | if (std::numeric_limits<double>::is_iec559) { |
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| 145 | if (x == std::numeric_limits<double>::infinity()) |
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| 146 | return log_double_max; |
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| 147 | if (x <= 0) |
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| 148 | return log_double_min; |
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| 149 | } |
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| 150 | return std::log(x); |
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| 151 | } |
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| 152 | |
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| 153 | /*! |
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| 154 | \brief Truncated exponential function |
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| 155 | |
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| 156 | This truncated function provides a solution in the case when the |
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| 157 | exponent function results in infinity. The function checks for an |
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| 158 | extreme value and use truncation (saturation) before calculating |
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| 159 | the result. |
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| 160 | |
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| 161 | The truncated exponential function can be used when numerical |
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| 162 | instability problem occurs for a standard exp function. |
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| 163 | */ |
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| 164 | inline double trunc_exp(double x) |
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| 165 | { |
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| 166 | if (std::numeric_limits<double>::is_iec559 |
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| 167 | && (x >= log_double_max)) |
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| 168 | return std::numeric_limits<double>::max(); |
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| 169 | return std::exp(x); |
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| 170 | } |
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| 171 | |
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| 172 | |
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| 173 | //! Safe substitute for <tt>log(exp(log_a) + exp(log_b))</tt> |
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| 174 | inline double log_add(double log_a, double log_b) |
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| 175 | { |
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| 176 | if (log_a < log_b) { |
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| 177 | double tmp = log_a; |
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| 178 | log_a = log_b; |
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| 179 | log_b = tmp; |
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| 180 | } |
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| 181 | double negdelta = log_b - log_a; |
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| 182 | if (negdelta < log_double_min) |
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| 183 | return log_a; |
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| 184 | else |
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| 185 | return (log_a + log1p(std::exp(negdelta))); |
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| 186 | } |
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| 187 | |
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| 188 | |
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| 189 | // ---------------------------------------------------------------------- |
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| 190 | // functions on vectors and matrices |
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| 191 | // ---------------------------------------------------------------------- |
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| 192 | |
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| 193 | //! Exp of the elements of a vector \c x |
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| 194 | inline vec exp(const vec &x) |
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| 195 | { |
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| 196 | return apply_function<double>(std::exp, x); |
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| 197 | } |
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| 198 | //! Exp of the elements of a complex vector \c x |
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| 199 | inline cvec exp(const cvec &x) |
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| 200 | { |
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| 201 | return apply_function<std::complex<double> >(std::exp, x); |
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| 202 | } |
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| 203 | //! Exp of the elements of a matrix \c m |
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| 204 | inline mat exp(const mat &m) |
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| 205 | { |
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| 206 | return apply_function<double>(std::exp, m); |
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| 207 | } |
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| 208 | //! Exp of the elements of a complex matrix \c m |
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| 209 | inline cmat exp(const cmat &m) |
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| 210 | { |
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| 211 | return apply_function<std::complex<double> >(std::exp, m); |
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| 212 | } |
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| 213 | |
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| 214 | //! Calculates x to the power of y (x^y) |
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| 215 | inline vec pow(const double x, const vec &y) |
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| 216 | { |
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| 217 | return apply_function<double>(std::pow, x, y); |
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| 218 | } |
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| 219 | //! Calculates x to the power of y (x^y) |
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| 220 | inline mat pow(const double x, const mat &y) |
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| 221 | { |
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| 222 | return apply_function<double>(std::pow, x, y); |
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| 223 | } |
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| 224 | //! Calculates x to the power of y (x^y) |
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| 225 | inline vec pow(const vec &x, const double y) |
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| 226 | { |
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| 227 | return apply_function<double>(std::pow, x, y); |
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| 228 | } |
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| 229 | //! Calculates x to the power of y (x^y) |
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| 230 | inline mat pow(const mat &x, const double y) |
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| 231 | { |
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| 232 | return apply_function<double>(std::pow, x, y); |
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| 233 | } |
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| 234 | |
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| 235 | //! Calculates two to the power of x (2^x) |
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| 236 | inline vec pow2(const vec &x) |
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| 237 | { |
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| 238 | return apply_function<double>(pow2, x); |
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| 239 | } |
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| 240 | //! Calculates two to the power of x (2^x) |
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| 241 | inline mat pow2(const mat &x) |
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| 242 | { |
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| 243 | return apply_function<double>(pow2, x); |
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| 244 | } |
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| 245 | |
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| 246 | //! Calculates ten to the power of x (10^x) |
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| 247 | inline vec pow10(const vec &x) |
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| 248 | { |
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| 249 | return apply_function<double>(pow10, x); |
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| 250 | } |
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| 251 | //! Calculates ten to the power of x (10^x) |
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| 252 | inline mat pow10(const mat &x) |
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| 253 | { |
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| 254 | return apply_function<double>(pow10, x); |
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| 255 | } |
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| 256 | |
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| 257 | //! The natural logarithm of the elements |
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| 258 | inline vec log(const vec &x) |
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| 259 | { |
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| 260 | return apply_function<double>(std::log, x); |
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| 261 | } |
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| 262 | //! The natural logarithm of the elements |
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| 263 | inline mat log(const mat &x) |
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| 264 | { |
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| 265 | return apply_function<double>(std::log, x); |
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| 266 | } |
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| 267 | //! The natural logarithm of the elements |
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| 268 | inline cvec log(const cvec &x) |
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| 269 | { |
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| 270 | return apply_function<std::complex<double> >(std::log, x); |
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| 271 | } |
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| 272 | //! The natural logarithm of the elements |
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| 273 | inline cmat log(const cmat &x) |
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| 274 | { |
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| 275 | return apply_function<std::complex<double> >(std::log, x); |
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| 276 | } |
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| 277 | |
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| 278 | //! log-2 of the elements |
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| 279 | inline vec log2(const vec &x) |
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| 280 | { |
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| 281 | return apply_function<double>(::log2, x); |
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| 282 | } |
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| 283 | //! log-2 of the elements |
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| 284 | inline mat log2(const mat &x) |
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| 285 | { |
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| 286 | return apply_function<double>(::log2, x); |
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| 287 | } |
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| 288 | |
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| 289 | //! log-10 of the elements |
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| 290 | inline vec log10(const vec &x) |
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| 291 | { |
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| 292 | return apply_function<double>(std::log10, x); |
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| 293 | } |
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| 294 | //! log-10 of the elements |
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| 295 | inline mat log10(const mat &x) |
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| 296 | { |
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| 297 | return apply_function<double>(std::log10, x); |
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| 298 | } |
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| 299 | |
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| 300 | //! log-b of \c x |
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| 301 | inline vec logb(double b, const vec &x) |
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| 302 | { |
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| 303 | return apply_function<double>(itpp::logb, b, x); |
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| 304 | } |
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| 305 | //! log-b of \c x |
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| 306 | inline mat logb(double b, const mat &x) |
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| 307 | { |
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| 308 | return apply_function<double>(itpp::logb, b, x); |
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| 309 | } |
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| 310 | |
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| 311 | //! Calculates 10*log10(x) |
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| 312 | inline vec dB(const vec &x) |
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| 313 | { |
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| 314 | return apply_function<double>(dB, x); |
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| 315 | } |
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| 316 | //! Calculates 10*log10(x) |
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| 317 | inline mat dB(const mat &x) |
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| 318 | { |
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| 319 | return apply_function<double>(dB, x); |
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| 320 | } |
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| 321 | |
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| 322 | //! Calulates the inverse of dB, 10^(x/10) |
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| 323 | inline vec inv_dB(const vec &x) |
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| 324 | { |
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| 325 | return apply_function<double>(inv_dB, x); |
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| 326 | } |
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| 327 | //! Calculates the inverse of dB, 10^(x/10) |
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| 328 | inline mat inv_dB(const mat &x) |
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| 329 | { |
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| 330 | return apply_function<double>(inv_dB, x); |
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| 331 | } |
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| 332 | |
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| 333 | //! Deprecated function. Please use int2bits() or levels2bits() instead. |
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| 334 | inline ivec needed_bits(const ivec& v) |
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| 335 | { |
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| 336 | it_warning("needed_bits(): This function is depreceted. Depending on your needs, please use int2bits() or levels2bits() instead."); |
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| 337 | return apply_function<int>(int2bits, v); |
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| 338 | } |
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| 339 | |
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| 340 | //! Calculate the number of bits needed to represent each inteager in a vector |
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| 341 | inline ivec int2bits(const ivec& v) |
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| 342 | { |
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| 343 | return apply_function<int>(int2bits, v); |
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| 344 | } |
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| 345 | |
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| 346 | //! Calculate the number of bits needed to represent a numer of levels saved in a vector |
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| 347 | inline ivec levels2bits(const ivec& v) |
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| 348 | { |
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| 349 | return apply_function<int>(levels2bits, v); |
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| 350 | } |
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| 351 | |
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| 352 | //!@} |
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| 353 | |
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| 354 | } // namespace itpp |
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| 355 | |
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| 356 | #endif // #ifndef LOG_EXP_H |
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| 357 | |
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| 358 | |
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| 359 | |
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