Mercurial > octave
annotate libinterp/corefcn/pow2.cc @ 31234:a1318deb4584
sparse-xpow.cc: Improve consistency between sparse and full matrices (bug #63080)
sparse-xpow.cc: Return 0x0 matrix for empty inputs of all sizes.
Return early for all-zeros matrix with positive power.
Add FIXME for all-zeros matrix with negative power.
Add BISTs.
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Tue, 20 Sep 2022 09:00:02 -0400 |
parents | a885bdb22374 |
children | e88a07dec498 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
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28 #endif |
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29 |
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30 #include <cmath> |
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31 |
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32 #include "lo-array-errwarn.h" |
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33 |
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34 #include "defun.h" |
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35 #include "error.h" |
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36 #include "errwarn.h" |
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37 |
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38 // FIXME: According to cppreference.com the implementation of `ldexp (f, e)` |
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39 // might be less efficient that the corresponding `f * exp2 (e)`. Consider |
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40 // replacing our implementation with the latter. |
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41 |
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42 template <typename T> |
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43 void |
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44 map_2_xldexp (Array<T>& y, const Array<T>& f, const Array<T>& e) |
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45 { |
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46 if (f.numel () == e.numel () || e.numel () == 1) |
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47 y = Array<T> (f.dims ()); |
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48 else if (f.numel () == 1) |
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49 y = Array<T> (e.dims ()); |
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50 else |
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51 octave::err_nonconformant ("pow2", f.dims (), e.dims ()); |
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52 |
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53 octave_idx_type f_inc = (f.numel () == 1) ? 0 : 1; |
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54 octave_idx_type e_inc = (e.numel () == 1) ? 0 : 1; |
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55 |
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56 for (octave_idx_type i = 0; i < y.numel (); i++) |
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57 y.xelem (i) = std::ldexp (f.xelem (i * f_inc), |
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58 static_cast<int> (e.xelem (i * e_inc))); |
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59 } |
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60 |
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61 void |
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62 map_2_xldexp_sparse (SparseMatrix& y, const SparseMatrix& f, |
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63 const SparseMatrix& e) |
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64 { |
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65 if (e.numel () == 1) |
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66 { |
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67 int ee = static_cast<int> (e.data (0)); |
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68 for (octave_idx_type i = 0; i < y.nnz (); i++) |
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69 y.data (i) = std::ldexp (f.data (i), ee); |
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70 } |
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71 else if (f.numel () == e.numel ()) |
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72 { |
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73 octave_idx_type col = 1; |
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74 for (octave_idx_type i = 0; i < y.nnz (); i++) |
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75 { |
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76 // Determine current column. |
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77 while (i >= f.cidx (col)) |
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78 col++; |
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79 int ee = static_cast<int> (e.xelem (f.ridx (i), col - 1)); |
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80 y.data (i) = std::ldexp (f.data (i), ee); |
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81 } |
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82 } |
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83 else |
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84 octave::err_nonconformant ("pow2", f.dims (), e.dims ()); |
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85 } |
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86 |
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87 OCTAVE_NAMESPACE_BEGIN |
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88 |
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89 DEFUN (pow2, args, , |
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90 doc: /* -*- texinfo -*- |
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91 @deftypefn {} {@var{y} =} pow2 (@var{x}) |
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92 @deftypefnx {} {@var{y} =} pow2 (@var{f}, @var{e}) |
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93 With one input argument, compute |
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94 @tex |
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95 $y = 2^x$ |
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96 @end tex |
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97 @ifnottex |
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98 y = 2 .^ x |
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99 @end ifnottex |
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100 for each element of @var{x}. |
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101 |
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102 With two input arguments, return |
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103 @tex |
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104 $y = f \cdot 2^e$, |
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105 @end tex |
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106 @ifnottex |
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107 y = f .* (2 .^ e). |
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108 @end ifnottex |
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109 where for complex inputs only the real part of both inputs is regarded |
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110 and from @var{e} only the real integer part. This calling form corresponds |
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111 to C/C++ standard function @code{ldexp()}. |
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112 @seealso{log2, nextpow2, power} |
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113 @end deftypefn */) |
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114 { |
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115 if (args.length () < 1 || args.length () > 2) |
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116 print_usage (); |
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117 |
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118 if (! args(0).isfloat ()) |
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119 err_wrong_type_arg ("pow2", args(0)); |
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120 |
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121 // Call exp2(f) where possible for numerical more accurate results. |
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122 if (args.length () == 1) |
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123 { |
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124 if (args(0).iscomplex ()) |
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125 { |
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126 // The C++ standard does not define exp2 for complex arguments. |
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127 // Therefore call `2.^x`. |
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128 octave_value retval = octave::binary_op (octave_value::op_el_pow, |
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129 2, args(0)); |
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130 |
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131 // Preserve sparse datatype, but even for sparse input fill-up |
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132 // is unavoidable `2^0 == 1` thus cast only. |
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133 if (args(0).issparse ()) |
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134 retval = octave_value (retval.sparse_complex_matrix_value ()); |
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135 |
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136 return ovl (retval); |
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137 } |
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138 else if (args(0).is_single_type ()) |
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139 { |
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140 FloatNDArray x = args(0).float_array_value (); |
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141 FloatNDArray y (x.dims ()); |
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142 for (octave_idx_type i = 0; i < y.numel (); i++) |
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143 y.xelem (i) = std::exp2 (x.xelem (i)); |
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144 return ovl (y); |
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145 } |
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146 else |
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147 { |
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148 NDArray x = args(0).array_value (); |
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149 NDArray y (x.dims ()); |
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150 for (octave_idx_type i = 0; i < y.numel (); i++) |
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151 y.xelem (i) = std::exp2 (x.xelem (i)); |
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152 |
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153 // Preserve sparse datatype, but even for sparse input fill-up |
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154 // is unavoidable `2^0 == 1` thus cast only. |
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155 if (args(0).issparse ()) |
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156 return ovl (SparseMatrix (y)); |
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157 else |
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158 return ovl (y); |
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159 } |
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160 } |
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161 |
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162 // For Matlab compatibility, the two argument call `y = pow2 (f, e)` |
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163 // corresponds to std::ldexp() (see bug #61968). The resulting y is |
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164 // computed quickly by adding the integer part of e to the floating-point |
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165 // exponent of f. |
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166 |
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167 if (! args(1).isfloat ()) |
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168 err_wrong_type_arg ("pow2", args(1)); |
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169 |
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170 if (args(0).iscomplex () || args(1).iscomplex ()) |
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171 warning_with_id ("Octave:pow2:imaginary-ignored", |
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172 "pow2: imaginary part is ignored"); |
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173 |
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174 // Note: Matlab R2021a errors on `pow2 (sparse (f), single (e))`, |
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175 // but sparsity in f determines output and can significantly |
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176 // reduce computation, e.g. `N=1e5; pow2(speye(N),sparse(N,N))`. |
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177 if (args(0).issparse ()) |
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178 { |
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179 SparseMatrix f = args(0).sparse_matrix_value (); |
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180 |
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181 // Special case: return a sparse zero matrix in size of e. |
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182 if ((f.numel () == 1) && (f.nnz () == 0)) |
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183 return ovl (SparseMatrix (args(1).rows (), args(1).columns ())); |
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184 |
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185 // Only do sparse computation, if it pays off. For scalar f fill-up |
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186 // is unavoidable even for sparse e because `f * 2^0 == f`. Use dense |
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187 // code below in this case. |
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188 if (f.numel () > 1) |
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189 { |
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190 SparseMatrix e = args(1).sparse_matrix_value (); |
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191 SparseMatrix y = SparseMatrix (f); |
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192 map_2_xldexp_sparse (y, f, e); |
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193 return ovl (y); |
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194 } |
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195 } |
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196 |
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197 if (args(0).is_single_type () || args(1).is_single_type ()) |
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198 { |
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199 FloatNDArray f = args(0).float_array_value (); |
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200 FloatNDArray e = args(1).float_array_value (); |
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201 FloatNDArray y; |
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202 map_2_xldexp (y, f, e); |
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203 return ovl (y); |
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204 } |
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205 else |
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206 { |
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207 NDArray f = args(0).array_value (); |
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208 NDArray e = args(1).array_value (); |
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209 NDArray y; |
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210 map_2_xldexp (y, f, e); |
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211 |
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212 // Preserve sparse datatype. |
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213 // Cases for efficient use of sparsity were treated above already. |
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214 if (args(0).issparse ()) |
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215 return ovl (SparseMatrix (y)); |
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216 else |
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217 return ovl (y); |
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218 } |
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219 } |
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220 |
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221 /* |
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222 ## Call `y = pow2 (x)` |
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223 |
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224 %!test |
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225 %! fcns = {@double, @single, @complex}; |
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226 %! x = [3, 0, -3]; |
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227 %! v = [8, 1, .125]; |
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228 %! for i = 1:numel (fcns) |
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229 %! fcn = fcns{i}; |
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230 %! assert (pow2 (fcn (x)), fcn (v), sqrt (eps)); |
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231 %! endfor |
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232 |
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233 %!test |
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234 %! fcns = {@double, @single, @complex, @sparse}; |
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235 %! x = [3, 1, -3]; |
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236 %! v = [8, 2, .125]; |
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237 %! for i = 1:numel (fcns) |
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238 %! fcn = fcns{i}; |
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239 %! assert (pow2 (fcn (x)), fcn (v), sqrt (eps)); |
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240 %! endfor |
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241 |
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242 %!test |
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243 %! fcns = {@double, @single, @complex, @sparse}; |
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244 %! x = [1, 1+1i, 1i]; |
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245 %! for i = 1:numel (fcns) |
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246 %! fcn = fcns{i}; |
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247 %! assert (pow2 (fcn (x)), fcn (2) .^ fcn (x), sqrt (eps)); |
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248 %! endfor |
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249 |
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250 ## Call `y = pow2 (f, e)` |
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251 |
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252 %!test |
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253 %! fcns = {@double, @single, @complex, @sparse}; |
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254 %! f = [2 2]; |
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255 %! e = [2 2]; |
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256 %! z = [8 8]; |
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257 %! warning ("off", "Octave:pow2:imaginary-ignored", "local"); |
30716
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258 %! for i = 1:numel (fcns) |
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259 %! fcn = fcns{i}; |
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260 %! assert (pow2 (fcn (f), fcn (e)), real (fcn (z))); |
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261 %! endfor |
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262 |
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263 ## Only integer part is taken into account. |
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264 %!test |
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265 %! f = 2; |
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266 %! e = [2, 2.1, 2.2, 2.4, 2.5, 2.8]; |
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267 %! z = 8 .* ones (1, length (e)); |
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268 %! assert (pow2 (f, e), z); |
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269 |
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270 ## Only real part is taken into account. |
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271 %!test |
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272 %! f = [1+1i, 1]; |
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273 %! e = 2; |
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274 %! z = [4, 4]; |
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275 %! warning ("off", "Octave:pow2:imaginary-ignored", "local"); |
30716
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276 %! assert (pow2 (f, e), z); |
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277 |
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278 %!test |
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279 %! f = 1; |
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280 %! e = [1+1i, 1]; |
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281 %! z = [2, 2]; |
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282 %! warning ("off", "Octave:pow2:imaginary-ignored", "local"); |
30716
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283 %! assert (pow2 (f, e), z); |
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284 |
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285 %!test |
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pow2: Minor changes (bug #61968).
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286 %! f = [1/2, pi/4, -3/4, 1/2, 1-eps()/2, 1/2]; |
30716
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287 %! e = [1, 2, 2, -51, 1024, -1021]; |
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288 %! z = [1, pi, -3, eps(), realmax(), realmin()]; |
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289 %! assert (pow2 (f, e), z); |
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290 |
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291 ## Tests for sparsity. |
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292 %!assert (pow2 (sparse (0), ones (3)), sparse (3, 3)); |
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293 %!assert (pow2 (sparse (1), ones (3)), 2 .* sparse (ones (3))); |
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294 %!assert (pow2 (sparse (1), speye (3)), sparse (ones (3) + eye (3))); |
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295 %!assert (pow2 (sparse (3, 3), ones (3)), sparse (3, 3)); |
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296 %!assert (pow2 (speye (3), ones (3)), 2 .* speye (3)); |
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297 %!assert (pow2 (speye (3), 1), 2 .* speye (3)); |
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298 |
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299 %!test |
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300 %! f = speye (3); |
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301 %! e = sparse (3, 3); |
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302 %! e(1,1) = 1; |
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303 %! e(1,3) = 1; |
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304 %! z = f; |
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305 %! z(1,1) = 2; |
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306 %! assert (pow2 (f, e), z); |
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307 |
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308 ## Large sparse matrix (only few real elements). |
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309 %!test |
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310 %! ## FIXME: `N = 1e5` would be a better test, but `assert` fills-up somehow. |
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311 %! N = 1e3; |
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312 %! assert (pow2 (speye (N), sparse (N,N)), speye (N)); |
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parents:
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313 %! assert (pow2 (sparse (0), speye (N)), sparse(N,N)); |
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314 |
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315 %!error <Invalid call> pow2 () |
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316 %!error <Invalid call> pow2 (1,2,3) |
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317 %!error <wrong type argument> pow2 (int8 (1)) |
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318 %!error <wrong type argument> pow2 (2, int8 (1)) |
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319 %!warning <imaginary part is ignored> pow2 (i, 2); |
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320 %!warning <imaginary part is ignored> pow2 (2, i); |
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321 %!error <pow2: nonconformant arguments> pow2 ([1,2], [3,4,5]) |
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322 %!error <pow2: nonconformant arguments> pow2 (sparse ([1,2]), sparse ([3,4,5])) |
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323 */ |
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324 |
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325 OCTAVE_NAMESPACE_END |