annotate liboctave/Range.cc @ 11450:5eb10763069f

substitute and use LAPACK_LIBS in mkoctfile script
author John W. Eaton <jwe@octave.org>
date Thu, 06 Jan 2011 03:10:24 -0500
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1 /*
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2
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3 Copyright (C) 1993, 1994, 1995, 1996, 1997, 2000, 2001, 2002, 2004,
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4 2005, 2007, 2008, 2009 John W. Eaton
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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22 */
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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28 #include <cfloat>
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30 #include <iostream>
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31 #include <limits>
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33 #include "Range.h"
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34 #include "lo-error.h"
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35 #include "lo-mappers.h"
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36 #include "lo-math.h"
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37 #include "lo-utils.h"
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38 #include "Array-util.h"
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39
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40 Range::Range (double b, double i, octave_idx_type n)
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41 : rng_base (b), rng_limit (b + n * i), rng_inc (i),
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42 rng_nelem (n), cache ()
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43 {
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44 if (! xfinite (b) || ! xfinite (i))
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45 rng_nelem = -2;
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46 }
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47
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48 bool
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49 Range::all_elements_are_ints (void) const
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50 {
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51 // If the base and increment are ints, the final value in the range
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52 // will also be an integer, even if the limit is not. If there is one
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53 // or fewer elements only the base needs to be an integer
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54
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55 return (! (xisnan (rng_base) || xisnan (rng_inc))
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56 && (NINTbig (rng_base) == rng_base || rng_nelem < 1)
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57 && (NINTbig (rng_inc) == rng_inc || rng_nelem <= 1));
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58 }
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60 Matrix
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61 Range::matrix_value (void) const
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62 {
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63 if (rng_nelem > 0 && cache.nelem () == 0)
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64 {
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65 cache.resize (1, rng_nelem);
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66 double b = rng_base;
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67 double increment = rng_inc;
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68 for (octave_idx_type i = 0; i < rng_nelem; i++)
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69 cache(i) = b + i * increment;
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70
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71 // On some machines (x86 with extended precision floating point
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72 // arithmetic, for example) it is possible that we can overshoot
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73 // the limit by approximately the machine precision even though
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74 // we were very careful in our calculation of the number of
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75 // elements.
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76
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77 if ((rng_inc > 0 && cache(rng_nelem-1) > rng_limit)
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78 || (rng_inc < 0 && cache(rng_nelem-1) < rng_limit))
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79 cache(rng_nelem-1) = rng_limit;
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80 }
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81
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82 return cache;
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83 }
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85 double
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86 Range::checkelem (octave_idx_type i) const
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87 {
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88 if (i < 0 || i >= rng_nelem)
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89 gripe_index_out_of_range (1, 1, i+1, rng_nelem);
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90
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91 return rng_base + rng_inc * i;
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92 }
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93
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94 struct _rangeidx_helper
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95 {
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96 double *array, base, inc;
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97 _rangeidx_helper (double *a, double b, double i)
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98 : array (a), base (b), inc (i) { }
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99 void operator () (octave_idx_type i)
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100 { *array++ = base + i * inc; }
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101 };
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102
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103 Array<double>
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104 Range::index (const idx_vector& i) const
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105 {
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106 Array<double> retval;
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107
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108 octave_idx_type n = rng_nelem;
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109
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110 if (i.is_colon ())
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111 {
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112 retval = matrix_value ().reshape (dim_vector (rng_nelem, 1));
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113 }
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114 else
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115 {
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116 if (i.extent (n) != n)
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117 gripe_index_out_of_range (1, 1, i.extent (n), n); // throws
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118
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119 dim_vector rd = i.orig_dimensions ();
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120 octave_idx_type il = i.length (n);
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121
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122 // taken from Array.cc.
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123
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124 if (n != 1 && rd.is_vector ())
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125 rd = dim_vector (1, il);
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126
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127 retval.clear (rd);
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128
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129 i.loop (n, _rangeidx_helper (retval.fortran_vec (), rng_base, rng_inc));
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130 }
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131
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132 return retval;
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133 }
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134
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135 // NOTE: max and min only return useful values if nelem > 0.
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136
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137 double
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138 Range::min (void) const
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139 {
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140 double retval = 0.0;
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141 if (rng_nelem > 0)
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142 {
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143 if (rng_inc > 0)
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144 retval = rng_base;
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145 else
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146 {
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147 retval = rng_base + (rng_nelem - 1) * rng_inc;
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148
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149 // See the note in the matrix_value method above.
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150
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151 if (retval < rng_limit)
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152 retval = rng_limit;
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153 }
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154
208
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155 }
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156 return retval;
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157 }
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158
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159 double
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160 Range::max (void) const
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161 {
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162 double retval = 0.0;
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163 if (rng_nelem > 0)
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164 {
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165 if (rng_inc > 0)
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166 {
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167 retval = rng_base + (rng_nelem - 1) * rng_inc;
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168
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169 // See the note in the matrix_value method above.
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170
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171 if (retval > rng_limit)
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172 retval = rng_limit;
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173 }
208
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174 else
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175 retval = rng_base;
208
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176 }
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177 return retval;
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178 }
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179
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180 void
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181 Range::sort_internal (bool ascending)
208
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182 {
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183 if (ascending && rng_base > rng_limit && rng_inc < 0.0)
208
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184 {
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185 double tmp = rng_base;
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186 rng_base = min ();
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187 rng_limit = tmp;
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188 rng_inc = -rng_inc;
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189 clear_cache ();
208
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190 }
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191 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0)
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192 {
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193 double tmp = rng_limit;
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194 rng_limit = min ();
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195 rng_base = tmp;
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196 rng_inc = -rng_inc;
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197 clear_cache ();
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198 }
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199 }
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200
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201 void
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202 Range::sort_internal (Array<octave_idx_type>& sidx, bool ascending)
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203 {
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204 octave_idx_type nel = nelem ();
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205
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206 sidx.resize (dim_vector (1, nel));
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207
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208 octave_idx_type *psidx = sidx.fortran_vec ();
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209
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210 bool reverse = false;
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211
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212 if (ascending && rng_base > rng_limit && rng_inc < 0.0)
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213 {
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214 double tmp = rng_base;
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215 rng_base = min ();
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216 rng_limit = tmp;
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217 rng_inc = -rng_inc;
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218 clear_cache ();
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219 reverse = true;
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220 }
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221 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0)
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222 {
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223 double tmp = rng_limit;
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224 rng_limit = min ();
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225 rng_base = tmp;
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226 rng_inc = -rng_inc;
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227 clear_cache ();
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228 reverse = true;
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229 }
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230
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231 octave_idx_type tmp = reverse ? nel - 1 : 0;
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232 octave_idx_type stp = reverse ? -1 : 1;
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233
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234 for (octave_idx_type i = 0; i < nel; i++, tmp += stp)
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235 psidx[i] = tmp;
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236
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237 }
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238
7620
36594d5bbe13 Move diag function into the octave_value class
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diff changeset
239 Matrix
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diff changeset
240 Range::diag (octave_idx_type k) const
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diff changeset
241 {
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967a692ddfe2 fix range arithmetics
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242 return matrix_value ().diag (k);
7620
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diff changeset
243 }
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244
7458
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245 Range
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246 Range::sort (octave_idx_type dim, sortmode mode) const
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247 {
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248 Range retval = *this;
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249
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250 if (dim == 1)
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251 {
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252 if (mode == ASCENDING)
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253 retval.sort_internal (true);
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diff changeset
254 else if (mode == DESCENDING)
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diff changeset
255 retval.sort_internal (false);
7458
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diff changeset
256 }
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diff changeset
257 else if (dim != 0)
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diff changeset
258 (*current_liboctave_error_handler) ("Range::sort: invalid dimension");
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diff changeset
259
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260 return retval;
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diff changeset
261 }
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262
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diff changeset
263 Range
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diff changeset
264 Range::sort (Array<octave_idx_type>& sidx, octave_idx_type dim,
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diff changeset
265 sortmode mode) const
7458
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diff changeset
266 {
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diff changeset
267 Range retval = *this;
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diff changeset
268
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diff changeset
269 if (dim == 1)
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diff changeset
270 {
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diff changeset
271 if (mode == ASCENDING)
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diff changeset
272 retval.sort_internal (sidx, true);
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diff changeset
273 else if (mode == DESCENDING)
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diff changeset
274 retval.sort_internal (sidx, false);
7458
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diff changeset
275 }
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diff changeset
276 else if (dim != 0)
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diff changeset
277 (*current_liboctave_error_handler) ("Range::sort: invalid dimension");
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diff changeset
278
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diff changeset
279 return retval;
208
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diff changeset
280 }
380cb9ccc889 [project @ 1993-11-12 10:35:05 by jwe]
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diff changeset
281
8721
e9cb742df9eb imported patch sort3.diff
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diff changeset
282 sortmode
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diff changeset
283 Range::is_sorted (sortmode mode) const
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diff changeset
284 {
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diff changeset
285 if (rng_nelem > 1 && rng_inc < 0)
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diff changeset
286 mode = (mode == ASCENDING) ? UNSORTED : DESCENDING;
e9cb742df9eb imported patch sort3.diff
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diff changeset
287 else if (rng_nelem > 1 && rng_inc > 0)
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diff changeset
288 mode = (mode == DESCENDING) ? UNSORTED : ASCENDING;
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diff changeset
289 else
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diff changeset
290 mode = mode ? mode : ASCENDING;
8742
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diff changeset
291
d2b06871afac add missing return statement
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parents: 8721
diff changeset
292 return mode;
8721
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diff changeset
293 }
e9cb742df9eb imported patch sort3.diff
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diff changeset
294
3504
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe]
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parents: 3503
diff changeset
295 std::ostream&
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe]
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parents: 3503
diff changeset
296 operator << (std::ostream& os, const Range& a)
3
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe]
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parents:
diff changeset
297 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe]
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parents:
diff changeset
298 double b = a.base ();
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe]
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parents:
diff changeset
299 double increment = a.inc ();
5275
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parents: 5105
diff changeset
300 octave_idx_type num_elem = a.nelem ();
3
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parents:
diff changeset
301
5275
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parents: 5105
diff changeset
302 for (octave_idx_type i = 0; i < num_elem-1; i++)
3
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe]
jwe
parents:
diff changeset
303 os << b + i * increment << " ";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe]
jwe
parents:
diff changeset
304
4791
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parents: 4192
diff changeset
305 // Prevent overshoot. See comment in the matrix_value method
62f2fb593455 [project @ 2004-02-20 18:02:59 by jwe]
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parents: 4192
diff changeset
306 // above.
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307
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308 os << (increment > 0 ? a.max () : a.min ()) << "\n";
3
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309
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310 return os;
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311 }
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312
3504
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313 std::istream&
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314 operator >> (std::istream& is, Range& a)
3
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315 {
208
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316 is >> a.rng_base;
3
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317 if (is)
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318 {
208
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319 is >> a.rng_limit;
3
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320 if (is)
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321 {
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322 is >> a.rng_inc;
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323 a.rng_nelem = a.nelem_internal ();
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324 }
3
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325 }
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326
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327 return is;
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328 }
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329
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330 Range
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331 operator - (const Range& r)
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332 {
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333 return Range (-r.base (), -r.inc (), r.nelem ());
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334 }
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335
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336 Range operator + (double x, const Range& r)
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337 {
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338 Range result (x + r.base (), r.inc (), r.nelem ());
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339 if (result.rng_nelem < 0)
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340 result.cache = x + r.matrix_value ();
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341
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342 return result;
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343 }
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344
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345 Range operator + (const Range& r, double x)
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346 {
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347 Range result (r.base () + x, r.inc (), r.nelem ());
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348 if (result.rng_nelem < 0)
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349 result.cache = r.matrix_value () + x;
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350
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351 return result;
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352 }
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353
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354 Range operator - (double x, const Range& r)
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355 {
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356 Range result (x - r.base (), -r.inc (), r.nelem ());
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357 if (result.rng_nelem < 0)
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358 result.cache = x - r.matrix_value ();
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359
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360 return result;
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361 }
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362
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363 Range operator - (const Range& r, double x)
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364 {
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365 Range result (r.base () - x, r.inc (), r.nelem ());
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366 if (result.rng_nelem < 0)
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367 result.cache = r.matrix_value () - x;
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368
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369 return result;
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370 }
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371
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372 Range operator * (double x, const Range& r)
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373 {
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374 Range result (x * r.base (), x * r.inc (), r.nelem ());
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375 if (result.rng_nelem < 0)
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376 result.cache = x * r.matrix_value ();
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377
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378 return result;
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379 }
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380
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381 Range operator * (const Range& r, double x)
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382 {
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383 Range result (r.base () * x, r.inc () * x, r.nelem ());
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384 if (result.rng_nelem < 0)
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385 result.cache = r.matrix_value () * x;
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386
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387 return result;
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388 }
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389
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390
1546
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391 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5.
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392 // C
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393 // C===Tolerant FLOOR function.
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diff changeset
394 // C
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diff changeset
395 // C X - is given as a Double Precision argument to be operated on.
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396 // C It is assumed that X is represented with M mantissa bits.
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397 // C CT - is given as a Comparison Tolerance such that
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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398 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between
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399 // C X and A whole number is less than CT, then TFLOOR is
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diff changeset
400 // C returned as this whole number. By treating the
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
401 // C floating-point numbers as a finite ordered set note that
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diff changeset
402 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
403 // C arguments of TFLOOR/TCEIL to be treated as whole numbers
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diff changeset
404 // C if they are exactly whole numbers or are immediately
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
405 // C adjacent to whole number representations. Since EPS, the
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
406 // C "distance" between floating-point numbers on the unit
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
407 // C interval, and M, the number of bits in X'S mantissa, exist
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diff changeset
408 // C on every floating-point computer, TFLOOR/TCEIL are
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diff changeset
409 // C consistently definable on every floating-point computer.
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diff changeset
410 // C
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diff changeset
411 // C For more information see the following references:
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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412 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
413 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5.
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
414 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
415 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
416 // C FL5, the history of five years of evolutionary development of
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
417 // C FL5 - the seven lines of code below - by open collaboration
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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418 // C and corroboration of the mathematical-computing community.
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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419 // C
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420 // C Penn State University Center for Academic Computing
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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421 // C H. D. Knoble - August, 1978.
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422
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423 static inline double
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diff changeset
424 tfloor (double x, double ct)
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diff changeset
425 {
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426 // C---------FLOOR(X) is the largest integer algebraically less than
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diff changeset
427 // C or equal to X; that is, the unfuzzy FLOOR function.
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diff changeset
428
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429 // DINT (X) = X - DMOD (X, 1.0);
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430 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0);
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431
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432 // C---------Hagerty's FL5 function follows...
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diff changeset
433
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
434 double q = 1.0;
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diff changeset
435
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
436 if (x < 0.0)
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diff changeset
437 q = 1.0 - ct;
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diff changeset
438
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
439 double rmax = q / (2.0 - ct);
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diff changeset
440
11450
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diff changeset
441 double t1 = 1.0 + gnulib::floor (x);
1546
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442 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1);
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443 t1 = rmax < t1 ? rmax : t1;
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diff changeset
444 t1 = ct > t1 ? ct : t1;
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parents: 10366
diff changeset
445 t1 = gnulib::floor (x + t1);
1546
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diff changeset
446
1555
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diff changeset
447 if (x <= 0.0 || (t1 - x) < rmax)
1546
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diff changeset
448 return t1;
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diff changeset
449 else
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450 return t1 - 1.0;
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diff changeset
451 }
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diff changeset
452
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diff changeset
453 static inline double
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diff changeset
454 tceil (double x, double ct)
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diff changeset
455 {
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
456 return -tfloor (-x, ct);
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diff changeset
457 }
a272c4056bab [project @ 1995-10-07 03:38:40 by jwe]
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diff changeset
458
3753
f751e43de300 [project @ 2000-12-14 03:01:23 by jwe]
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diff changeset
459 static inline bool
f751e43de300 [project @ 2000-12-14 03:01:23 by jwe]
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460 teq (double u, double v, double ct = 3.0 * DBL_EPSILON)
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461 {
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462 double tu = fabs (u);
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463 double tv = fabs (v);
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464
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465 return fabs (u - v) < ((tu > tv ? tu : tv) * ct);
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466 }
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467
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468 octave_idx_type
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469 Range::nelem_internal (void) const
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470 {
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471 octave_idx_type retval = -1;
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472
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473 if (rng_inc == 0
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474 || (rng_limit > rng_base && rng_inc < 0)
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475 || (rng_limit < rng_base && rng_inc > 0))
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476 {
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477 retval = 0;
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478 }
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479 else
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480 {
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481 double ct = 3.0 * DBL_EPSILON;
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482
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483 double tmp = tfloor ((rng_limit - rng_base + rng_inc) / rng_inc, ct);
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484
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485 octave_idx_type n_elt = (tmp > 0.0 ? static_cast<octave_idx_type> (tmp) : 0);
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486
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487 // If the final element that we would compute for the range is
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488 // equal to the limit of the range, or is an adjacent floating
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489 // point number, accept it. Otherwise, try a range with one
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490 // fewer element. If that fails, try again with one more
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491 // element.
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492 //
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493 // I'm not sure this is very good, but it seems to work better than
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494 // just using tfloor as above. For example, without it, the
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495 // expression 1.8:0.05:1.9 fails to produce the expected result of
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496 // [1.8, 1.85, 1.9].
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497
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498 if (! teq (rng_base + (n_elt - 1) * rng_inc, rng_limit))
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499 {
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500 if (teq (rng_base + (n_elt - 2) * rng_inc, rng_limit))
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501 n_elt--;
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502 else if (teq (rng_base + n_elt * rng_inc, rng_limit))
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503 n_elt++;
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504 }
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505
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506 retval = (n_elt >= std::numeric_limits<octave_idx_type>::max () - 1) ? -1 : n_elt;
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507 }
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508
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509 return retval;
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510 }