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1 ------------------------------------------------------------------------------
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2 -- --
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3 -- GNAT RUN-TIME COMPONENTS --
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4 -- --
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5 -- S Y S T E M . G E N E R I C _ A R R A Y _ O P E R A T I O N S --
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6 -- --
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7 -- S p e c --
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8 -- --
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131
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9 -- Copyright (C) 2006-2018, Free Software Foundation, Inc. --
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111
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10 -- --
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11 -- GNAT is free software; you can redistribute it and/or modify it under --
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12 -- terms of the GNU General Public License as published by the Free Soft- --
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13 -- ware Foundation; either version 3, or (at your option) any later ver- --
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14 -- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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15 -- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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16 -- or FITNESS FOR A PARTICULAR PURPOSE. --
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17 -- --
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18 -- As a special exception under Section 7 of GPL version 3, you are granted --
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19 -- additional permissions described in the GCC Runtime Library Exception, --
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20 -- version 3.1, as published by the Free Software Foundation. --
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21 -- --
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22 -- You should have received a copy of the GNU General Public License and --
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23 -- a copy of the GCC Runtime Library Exception along with this program; --
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24 -- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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25 -- <http://www.gnu.org/licenses/>. --
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26 -- --
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27 -- GNAT was originally developed by the GNAT team at New York University. --
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28 -- Extensive contributions were provided by Ada Core Technologies Inc. --
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29 -- --
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30 ------------------------------------------------------------------------------
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31
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32 package System.Generic_Array_Operations is
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33 pragma Pure (Generic_Array_Operations);
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34
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35 ---------------------
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36 -- Back_Substitute --
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37 ---------------------
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38
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39 generic
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40 type Scalar is private;
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41 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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42 with function "-" (Left, Right : Scalar) return Scalar is <>;
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43 with function "*" (Left, Right : Scalar) return Scalar is <>;
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44 with function "/" (Left, Right : Scalar) return Scalar is <>;
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45 with function Is_Non_Zero (X : Scalar) return Boolean is <>;
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46 procedure Back_Substitute (M, N : in out Matrix);
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47
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48 --------------
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49 -- Diagonal --
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50 --------------
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51
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52 generic
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53 type Scalar is private;
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54 type Vector is array (Integer range <>) of Scalar;
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55 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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56 function Diagonal (A : Matrix) return Vector;
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57
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58 -----------------------
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59 -- Forward_Eliminate --
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60 -----------------------
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61
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62 -- Use elementary row operations to put square matrix M in row echolon
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63 -- form. Identical row operations are performed on matrix N, must have the
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64 -- same number of rows as M.
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65
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66 generic
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67 type Scalar is private;
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68 type Real is digits <>;
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69 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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70 with function "abs" (Right : Scalar) return Real'Base is <>;
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71 with function "-" (Left, Right : Scalar) return Scalar is <>;
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72 with function "*" (Left, Right : Scalar) return Scalar is <>;
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73 with function "/" (Left, Right : Scalar) return Scalar is <>;
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74 Zero : Scalar;
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75 One : Scalar;
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76 procedure Forward_Eliminate
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77 (M : in out Matrix;
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78 N : in out Matrix;
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79 Det : out Scalar);
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80
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81 --------------------------
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82 -- Square_Matrix_Length --
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83 --------------------------
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84
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85 generic
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86 type Scalar is private;
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87 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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88 function Square_Matrix_Length (A : Matrix) return Natural;
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89 -- If A is non-square, raise Constraint_Error, else return its dimension
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90
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91 ----------------------------------
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92 -- Vector_Elementwise_Operation --
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93 ----------------------------------
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94
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95 generic
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96 type X_Scalar is private;
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97 type Result_Scalar is private;
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98 type X_Vector is array (Integer range <>) of X_Scalar;
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99 type Result_Vector is array (Integer range <>) of Result_Scalar;
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100 with function Operation (X : X_Scalar) return Result_Scalar;
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101 function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector;
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102
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103 ----------------------------------
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104 -- Matrix_Elementwise_Operation --
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105 ----------------------------------
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106
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107 generic
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108 type X_Scalar is private;
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109 type Result_Scalar is private;
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110 type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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111 type Result_Matrix is array (Integer range <>, Integer range <>)
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112 of Result_Scalar;
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113 with function Operation (X : X_Scalar) return Result_Scalar;
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114 function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix;
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115
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116 -----------------------------------------
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117 -- Vector_Vector_Elementwise_Operation --
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118 -----------------------------------------
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119
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120 generic
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121 type Left_Scalar is private;
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122 type Right_Scalar is private;
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123 type Result_Scalar is private;
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124 type Left_Vector is array (Integer range <>) of Left_Scalar;
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125 type Right_Vector is array (Integer range <>) of Right_Scalar;
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126 type Result_Vector is array (Integer range <>) of Result_Scalar;
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127 with function Operation
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128 (Left : Left_Scalar;
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129 Right : Right_Scalar) return Result_Scalar;
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130 function Vector_Vector_Elementwise_Operation
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131 (Left : Left_Vector;
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132 Right : Right_Vector) return Result_Vector;
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133
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134 ------------------------------------------------
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135 -- Vector_Vector_Scalar_Elementwise_Operation --
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136 ------------------------------------------------
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137
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138 generic
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139 type X_Scalar is private;
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140 type Y_Scalar is private;
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141 type Z_Scalar is private;
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142 type Result_Scalar is private;
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143 type X_Vector is array (Integer range <>) of X_Scalar;
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144 type Y_Vector is array (Integer range <>) of Y_Scalar;
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145 type Result_Vector is array (Integer range <>) of Result_Scalar;
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146 with function Operation
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147 (X : X_Scalar;
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148 Y : Y_Scalar;
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149 Z : Z_Scalar) return Result_Scalar;
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150 function Vector_Vector_Scalar_Elementwise_Operation
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151 (X : X_Vector;
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152 Y : Y_Vector;
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153 Z : Z_Scalar) return Result_Vector;
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154
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155 -----------------------------------------
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156 -- Matrix_Matrix_Elementwise_Operation --
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157 -----------------------------------------
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158
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159 generic
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160 type Left_Scalar is private;
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161 type Right_Scalar is private;
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162 type Result_Scalar is private;
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163 type Left_Matrix is array (Integer range <>, Integer range <>)
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164 of Left_Scalar;
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165 type Right_Matrix is array (Integer range <>, Integer range <>)
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166 of Right_Scalar;
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167 type Result_Matrix is array (Integer range <>, Integer range <>)
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168 of Result_Scalar;
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169 with function Operation
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170 (Left : Left_Scalar;
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171 Right : Right_Scalar) return Result_Scalar;
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172 function Matrix_Matrix_Elementwise_Operation
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173 (Left : Left_Matrix;
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174 Right : Right_Matrix) return Result_Matrix;
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175
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176 ------------------------------------------------
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177 -- Matrix_Matrix_Scalar_Elementwise_Operation --
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178 ------------------------------------------------
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179
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180 generic
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181 type X_Scalar is private;
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182 type Y_Scalar is private;
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183 type Z_Scalar is private;
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184 type Result_Scalar is private;
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185 type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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186 type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
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187 type Result_Matrix is array (Integer range <>, Integer range <>)
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188 of Result_Scalar;
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189 with function Operation
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190 (X : X_Scalar;
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191 Y : Y_Scalar;
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192 Z : Z_Scalar) return Result_Scalar;
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193 function Matrix_Matrix_Scalar_Elementwise_Operation
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194 (X : X_Matrix;
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195 Y : Y_Matrix;
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196 Z : Z_Scalar) return Result_Matrix;
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197
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198 -----------------------------------------
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199 -- Vector_Scalar_Elementwise_Operation --
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200 -----------------------------------------
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201
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202 generic
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203 type Left_Scalar is private;
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204 type Right_Scalar is private;
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205 type Result_Scalar is private;
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206 type Left_Vector is array (Integer range <>) of Left_Scalar;
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207 type Result_Vector is array (Integer range <>) of Result_Scalar;
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208 with function Operation
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209 (Left : Left_Scalar;
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210 Right : Right_Scalar) return Result_Scalar;
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211 function Vector_Scalar_Elementwise_Operation
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212 (Left : Left_Vector;
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213 Right : Right_Scalar) return Result_Vector;
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214
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215 -----------------------------------------
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216 -- Matrix_Scalar_Elementwise_Operation --
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217 -----------------------------------------
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218
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219 generic
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220 type Left_Scalar is private;
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221 type Right_Scalar is private;
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222 type Result_Scalar is private;
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223 type Left_Matrix is array (Integer range <>, Integer range <>)
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224 of Left_Scalar;
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225 type Result_Matrix is array (Integer range <>, Integer range <>)
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226 of Result_Scalar;
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227 with function Operation
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228 (Left : Left_Scalar;
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229 Right : Right_Scalar) return Result_Scalar;
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230 function Matrix_Scalar_Elementwise_Operation
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231 (Left : Left_Matrix;
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232 Right : Right_Scalar) return Result_Matrix;
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233
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234 -----------------------------------------
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235 -- Scalar_Vector_Elementwise_Operation --
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236 -----------------------------------------
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237
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238 generic
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239 type Left_Scalar is private;
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240 type Right_Scalar is private;
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241 type Result_Scalar is private;
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242 type Right_Vector is array (Integer range <>) of Right_Scalar;
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243 type Result_Vector is array (Integer range <>) of Result_Scalar;
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244 with function Operation
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245 (Left : Left_Scalar;
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246 Right : Right_Scalar) return Result_Scalar;
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247 function Scalar_Vector_Elementwise_Operation
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248 (Left : Left_Scalar;
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249 Right : Right_Vector) return Result_Vector;
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250
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251 -----------------------------------------
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252 -- Scalar_Matrix_Elementwise_Operation --
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253 -----------------------------------------
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254
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255 generic
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256 type Left_Scalar is private;
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257 type Right_Scalar is private;
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258 type Result_Scalar is private;
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259 type Right_Matrix is array (Integer range <>, Integer range <>)
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260 of Right_Scalar;
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261 type Result_Matrix is array (Integer range <>, Integer range <>)
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262 of Result_Scalar;
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263 with function Operation
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264 (Left : Left_Scalar;
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265 Right : Right_Scalar) return Result_Scalar;
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266 function Scalar_Matrix_Elementwise_Operation
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267 (Left : Left_Scalar;
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268 Right : Right_Matrix) return Result_Matrix;
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269
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270 -------------------
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271 -- Inner_Product --
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272 -------------------
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273
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274 generic
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275 type Left_Scalar is private;
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276 type Right_Scalar is private;
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277 type Result_Scalar is private;
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278 type Left_Vector is array (Integer range <>) of Left_Scalar;
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279 type Right_Vector is array (Integer range <>) of Right_Scalar;
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280 Zero : Result_Scalar;
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281 with function "*"
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282 (Left : Left_Scalar;
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283 Right : Right_Scalar) return Result_Scalar is <>;
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284 with function "+"
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285 (Left : Result_Scalar;
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286 Right : Result_Scalar) return Result_Scalar is <>;
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287 function Inner_Product
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288 (Left : Left_Vector;
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289 Right : Right_Vector) return Result_Scalar;
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290
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291 -------------
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292 -- L2_Norm --
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293 -------------
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294
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295 generic
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296 type X_Scalar is private;
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297 type Result_Real is digits <>;
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298 type X_Vector is array (Integer range <>) of X_Scalar;
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299 with function "abs" (Right : X_Scalar) return Result_Real is <>;
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300 with function Sqrt (X : Result_Real'Base) return Result_Real'Base is <>;
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301 function L2_Norm (X : X_Vector) return Result_Real'Base;
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302
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303 -------------------
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304 -- Outer_Product --
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305 -------------------
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306
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307 generic
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308 type Left_Scalar is private;
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309 type Right_Scalar is private;
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310 type Result_Scalar is private;
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311 type Left_Vector is array (Integer range <>) of Left_Scalar;
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312 type Right_Vector is array (Integer range <>) of Right_Scalar;
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313 type Matrix is array (Integer range <>, Integer range <>)
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314 of Result_Scalar;
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315 with function "*"
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316 (Left : Left_Scalar;
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317 Right : Right_Scalar) return Result_Scalar is <>;
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318 function Outer_Product
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319 (Left : Left_Vector;
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320 Right : Right_Vector) return Matrix;
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321
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322 ---------------------------
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323 -- Matrix_Vector_Product --
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324 ---------------------------
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325
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326 generic
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327 type Left_Scalar is private;
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328 type Right_Scalar is private;
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329 type Result_Scalar is private;
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330 type Matrix is array (Integer range <>, Integer range <>)
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331 of Left_Scalar;
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332 type Right_Vector is array (Integer range <>) of Right_Scalar;
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333 type Result_Vector is array (Integer range <>) of Result_Scalar;
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334 Zero : Result_Scalar;
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335 with function "*"
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336 (Left : Left_Scalar;
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337 Right : Right_Scalar) return Result_Scalar is <>;
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338 with function "+"
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339 (Left : Result_Scalar;
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340 Right : Result_Scalar) return Result_Scalar is <>;
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341 function Matrix_Vector_Product
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342 (Left : Matrix;
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343 Right : Right_Vector) return Result_Vector;
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344
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345 ---------------------------
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346 -- Vector_Matrix_Product --
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347 ---------------------------
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348
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349 generic
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350 type Left_Scalar is private;
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351 type Right_Scalar is private;
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352 type Result_Scalar is private;
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353 type Left_Vector is array (Integer range <>) of Left_Scalar;
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354 type Matrix is array (Integer range <>, Integer range <>)
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355 of Right_Scalar;
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356 type Result_Vector is array (Integer range <>) of Result_Scalar;
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357 Zero : Result_Scalar;
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358 with function "*"
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359 (Left : Left_Scalar;
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360 Right : Right_Scalar) return Result_Scalar is <>;
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361 with function "+"
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362 (Left : Result_Scalar;
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363 Right : Result_Scalar) return Result_Scalar is <>;
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364 function Vector_Matrix_Product
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365 (Left : Left_Vector;
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366 Right : Matrix) return Result_Vector;
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367
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368 ---------------------------
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369 -- Matrix_Matrix_Product --
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370 ---------------------------
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371
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372 generic
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373 type Left_Scalar is private;
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374 type Right_Scalar is private;
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375 type Result_Scalar is private;
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376 type Left_Matrix is array (Integer range <>, Integer range <>)
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377 of Left_Scalar;
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378 type Right_Matrix is array (Integer range <>, Integer range <>)
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379 of Right_Scalar;
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380 type Result_Matrix is array (Integer range <>, Integer range <>)
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381 of Result_Scalar;
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382 Zero : Result_Scalar;
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383 with function "*"
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384 (Left : Left_Scalar;
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385 Right : Right_Scalar) return Result_Scalar is <>;
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386 with function "+"
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387 (Left : Result_Scalar;
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388 Right : Result_Scalar) return Result_Scalar is <>;
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389 function Matrix_Matrix_Product
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390 (Left : Left_Matrix;
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391 Right : Right_Matrix) return Result_Matrix;
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392
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393 ----------------------------
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394 -- Matrix_Vector_Solution --
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395 ----------------------------
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396
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397 generic
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398 type Scalar is private;
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399 Zero : Scalar;
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400 type Vector is array (Integer range <>) of Scalar;
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401 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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402 with procedure Back_Substitute (M, N : in out Matrix) is <>;
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403 with procedure Forward_Eliminate
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404 (M : in out Matrix;
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405 N : in out Matrix;
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406 Det : out Scalar) is <>;
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407 function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector;
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408
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409 ----------------------------
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410 -- Matrix_Matrix_Solution --
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411 ----------------------------
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412
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413 generic
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414 type Scalar is private;
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415 Zero : Scalar;
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416 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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417 with procedure Back_Substitute (M, N : in out Matrix) is <>;
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418 with procedure Forward_Eliminate
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419 (M : in out Matrix;
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420 N : in out Matrix;
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421 Det : out Scalar) is <>;
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422 function Matrix_Matrix_Solution (A : Matrix; X : Matrix) return Matrix;
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423
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424 ----------
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425 -- Sqrt --
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426 ----------
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427
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428 generic
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429 type Real is digits <>;
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430 function Sqrt (X : Real'Base) return Real'Base;
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431
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432 -----------------
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433 -- Swap_Column --
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434 -----------------
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435
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436 generic
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437 type Scalar is private;
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438 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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439 procedure Swap_Column (A : in out Matrix; Left, Right : Integer);
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440
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441 ---------------
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442 -- Transpose --
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443 ---------------
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444
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445 generic
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446 type Scalar is private;
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447 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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448 procedure Transpose (A : Matrix; R : out Matrix);
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449
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450 -------------------------------
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451 -- Update_Vector_With_Vector --
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452 -------------------------------
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453
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454 generic
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455 type X_Scalar is private;
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456 type Y_Scalar is private;
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457 type X_Vector is array (Integer range <>) of X_Scalar;
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458 type Y_Vector is array (Integer range <>) of Y_Scalar;
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459 with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
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460 procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector);
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461
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462 -------------------------------
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463 -- Update_Matrix_With_Matrix --
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464 -------------------------------
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465
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466 generic
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467 type X_Scalar is private;
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468 type Y_Scalar is private;
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469 type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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470 type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
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471 with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
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472 procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix);
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473
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474 -----------------
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475 -- Unit_Matrix --
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476 -----------------
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477
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478 generic
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479 type Scalar is private;
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480 type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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481 Zero : Scalar;
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482 One : Scalar;
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483 function Unit_Matrix
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484 (Order : Positive;
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485 First_1 : Integer := 1;
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486 First_2 : Integer := 1) return Matrix;
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487
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488 -----------------
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489 -- Unit_Vector --
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490 -----------------
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491
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492 generic
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493 type Scalar is private;
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494 type Vector is array (Integer range <>) of Scalar;
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495 Zero : Scalar;
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496 One : Scalar;
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497 function Unit_Vector
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498 (Index : Integer;
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499 Order : Positive;
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500 First : Integer := 1) return Vector;
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501
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502 end System.Generic_Array_Operations;
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