1 | /*************************************************************************
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2 | Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).
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3 |
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4 | >>> SOURCE LICENSE >>>
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5 | This program is free software; you can redistribute it and/or modify
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6 | it under the terms of the GNU General Public License as published by
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7 | the Free Software Foundation (www.fsf.org); either version 2 of the
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8 | License, or (at your option) any later version.
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9 |
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10 | This program is distributed in the hope that it will be useful,
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11 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 | GNU General Public License for more details.
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14 |
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15 | A copy of the GNU General Public License is available at
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16 | http://www.fsf.org/licensing/licenses
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17 |
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18 | >>> END OF LICENSE >>>
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19 | *************************************************************************/
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20 |
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21 | using System;
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22 |
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23 | namespace alglib
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24 | {
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25 | public class blas
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26 | {
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27 | public static double vectornorm2(ref double[] x,
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28 | int i1,
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29 | int i2)
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30 | {
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31 | double result = 0;
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32 | int n = 0;
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33 | int ix = 0;
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34 | double absxi = 0;
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35 | double scl = 0;
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36 | double ssq = 0;
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37 |
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38 | n = i2-i1+1;
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39 | if( n<1 )
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40 | {
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41 | result = 0;
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42 | return result;
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43 | }
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44 | if( n==1 )
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45 | {
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46 | result = Math.Abs(x[i1]);
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47 | return result;
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48 | }
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49 | scl = 0;
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50 | ssq = 1;
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51 | for(ix=i1; ix<=i2; ix++)
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52 | {
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53 | if( (double)(x[ix])!=(double)(0) )
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54 | {
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55 | absxi = Math.Abs(x[ix]);
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56 | if( (double)(scl)<(double)(absxi) )
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57 | {
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58 | ssq = 1+ssq*AP.Math.Sqr(scl/absxi);
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59 | scl = absxi;
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60 | }
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61 | else
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62 | {
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63 | ssq = ssq+AP.Math.Sqr(absxi/scl);
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64 | }
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65 | }
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66 | }
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67 | result = scl*Math.Sqrt(ssq);
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68 | return result;
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69 | }
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70 |
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71 |
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72 | public static int vectoridxabsmax(ref double[] x,
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73 | int i1,
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74 | int i2)
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75 | {
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76 | int result = 0;
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77 | int i = 0;
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78 | double a = 0;
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79 |
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80 | result = i1;
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81 | a = Math.Abs(x[result]);
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82 | for(i=i1+1; i<=i2; i++)
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83 | {
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84 | if( (double)(Math.Abs(x[i]))>(double)(Math.Abs(x[result])) )
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85 | {
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86 | result = i;
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87 | }
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88 | }
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89 | return result;
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90 | }
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91 |
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92 |
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93 | public static int columnidxabsmax(ref double[,] x,
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94 | int i1,
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95 | int i2,
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96 | int j)
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97 | {
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98 | int result = 0;
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99 | int i = 0;
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100 | double a = 0;
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101 |
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102 | result = i1;
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103 | a = Math.Abs(x[result,j]);
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104 | for(i=i1+1; i<=i2; i++)
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105 | {
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106 | if( (double)(Math.Abs(x[i,j]))>(double)(Math.Abs(x[result,j])) )
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107 | {
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108 | result = i;
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109 | }
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110 | }
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111 | return result;
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112 | }
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113 |
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114 |
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115 | public static int rowidxabsmax(ref double[,] x,
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116 | int j1,
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117 | int j2,
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118 | int i)
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119 | {
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120 | int result = 0;
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121 | int j = 0;
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122 | double a = 0;
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123 |
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124 | result = j1;
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125 | a = Math.Abs(x[i,result]);
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126 | for(j=j1+1; j<=j2; j++)
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127 | {
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128 | if( (double)(Math.Abs(x[i,j]))>(double)(Math.Abs(x[i,result])) )
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129 | {
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130 | result = j;
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131 | }
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132 | }
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133 | return result;
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134 | }
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135 |
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136 |
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137 | public static double upperhessenberg1norm(ref double[,] a,
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138 | int i1,
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139 | int i2,
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140 | int j1,
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141 | int j2,
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142 | ref double[] work)
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143 | {
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144 | double result = 0;
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145 | int i = 0;
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146 | int j = 0;
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147 |
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148 | System.Diagnostics.Debug.Assert(i2-i1==j2-j1, "UpperHessenberg1Norm: I2-I1<>J2-J1!");
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149 | for(j=j1; j<=j2; j++)
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150 | {
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151 | work[j] = 0;
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152 | }
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153 | for(i=i1; i<=i2; i++)
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154 | {
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155 | for(j=Math.Max(j1, j1+i-i1-1); j<=j2; j++)
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156 | {
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157 | work[j] = work[j]+Math.Abs(a[i,j]);
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158 | }
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159 | }
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160 | result = 0;
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161 | for(j=j1; j<=j2; j++)
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162 | {
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163 | result = Math.Max(result, work[j]);
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164 | }
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165 | return result;
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166 | }
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167 |
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168 |
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169 | public static void copymatrix(ref double[,] a,
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170 | int is1,
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171 | int is2,
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172 | int js1,
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173 | int js2,
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174 | ref double[,] b,
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175 | int id1,
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176 | int id2,
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177 | int jd1,
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178 | int jd2)
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179 | {
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180 | int isrc = 0;
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181 | int idst = 0;
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182 | int i_ = 0;
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183 | int i1_ = 0;
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184 |
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185 | if( is1>is2 | js1>js2 )
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186 | {
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187 | return;
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188 | }
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189 | System.Diagnostics.Debug.Assert(is2-is1==id2-id1, "CopyMatrix: different sizes!");
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190 | System.Diagnostics.Debug.Assert(js2-js1==jd2-jd1, "CopyMatrix: different sizes!");
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191 | for(isrc=is1; isrc<=is2; isrc++)
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192 | {
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193 | idst = isrc-is1+id1;
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194 | i1_ = (js1) - (jd1);
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195 | for(i_=jd1; i_<=jd2;i_++)
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196 | {
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197 | b[idst,i_] = a[isrc,i_+i1_];
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198 | }
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199 | }
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200 | }
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201 |
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202 |
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203 | public static void inplacetranspose(ref double[,] a,
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204 | int i1,
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205 | int i2,
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206 | int j1,
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207 | int j2,
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208 | ref double[] work)
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209 | {
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210 | int i = 0;
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211 | int j = 0;
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212 | int ips = 0;
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213 | int jps = 0;
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214 | int l = 0;
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215 | int i_ = 0;
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216 | int i1_ = 0;
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217 |
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218 | if( i1>i2 | j1>j2 )
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219 | {
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220 | return;
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221 | }
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222 | System.Diagnostics.Debug.Assert(i1-i2==j1-j2, "InplaceTranspose error: incorrect array size!");
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223 | for(i=i1; i<=i2-1; i++)
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224 | {
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225 | j = j1+i-i1;
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226 | ips = i+1;
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227 | jps = j1+ips-i1;
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228 | l = i2-i;
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229 | i1_ = (ips) - (1);
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230 | for(i_=1; i_<=l;i_++)
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231 | {
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232 | work[i_] = a[i_+i1_,j];
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233 | }
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234 | i1_ = (jps) - (ips);
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235 | for(i_=ips; i_<=i2;i_++)
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236 | {
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237 | a[i_,j] = a[i,i_+i1_];
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238 | }
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239 | i1_ = (1) - (jps);
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240 | for(i_=jps; i_<=j2;i_++)
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241 | {
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242 | a[i,i_] = work[i_+i1_];
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243 | }
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244 | }
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245 | }
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246 |
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247 |
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248 | public static void copyandtranspose(ref double[,] a,
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249 | int is1,
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250 | int is2,
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251 | int js1,
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252 | int js2,
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253 | ref double[,] b,
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254 | int id1,
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255 | int id2,
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256 | int jd1,
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257 | int jd2)
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258 | {
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259 | int isrc = 0;
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260 | int jdst = 0;
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261 | int i_ = 0;
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262 | int i1_ = 0;
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263 |
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264 | if( is1>is2 | js1>js2 )
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265 | {
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266 | return;
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267 | }
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268 | System.Diagnostics.Debug.Assert(is2-is1==jd2-jd1, "CopyAndTranspose: different sizes!");
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269 | System.Diagnostics.Debug.Assert(js2-js1==id2-id1, "CopyAndTranspose: different sizes!");
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270 | for(isrc=is1; isrc<=is2; isrc++)
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271 | {
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272 | jdst = isrc-is1+jd1;
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273 | i1_ = (js1) - (id1);
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274 | for(i_=id1; i_<=id2;i_++)
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275 | {
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276 | b[i_,jdst] = a[isrc,i_+i1_];
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277 | }
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278 | }
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279 | }
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280 |
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281 |
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282 | public static void matrixvectormultiply(ref double[,] a,
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283 | int i1,
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284 | int i2,
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285 | int j1,
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286 | int j2,
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287 | bool trans,
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288 | ref double[] x,
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289 | int ix1,
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290 | int ix2,
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291 | double alpha,
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292 | ref double[] y,
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293 | int iy1,
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294 | int iy2,
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295 | double beta)
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296 | {
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297 | int i = 0;
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298 | double v = 0;
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299 | int i_ = 0;
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300 | int i1_ = 0;
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301 |
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302 | if( !trans )
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303 | {
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304 |
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305 | //
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306 | // y := alpha*A*x + beta*y;
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307 | //
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308 | if( i1>i2 | j1>j2 )
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309 | {
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310 | return;
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311 | }
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312 | System.Diagnostics.Debug.Assert(j2-j1==ix2-ix1, "MatrixVectorMultiply: A and X dont match!");
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313 | System.Diagnostics.Debug.Assert(i2-i1==iy2-iy1, "MatrixVectorMultiply: A and Y dont match!");
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314 |
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315 | //
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316 | // beta*y
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317 | //
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318 | if( (double)(beta)==(double)(0) )
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319 | {
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320 | for(i=iy1; i<=iy2; i++)
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321 | {
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322 | y[i] = 0;
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323 | }
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324 | }
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325 | else
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326 | {
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327 | for(i_=iy1; i_<=iy2;i_++)
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328 | {
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329 | y[i_] = beta*y[i_];
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330 | }
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331 | }
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332 |
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333 | //
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334 | // alpha*A*x
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335 | //
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336 | for(i=i1; i<=i2; i++)
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337 | {
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338 | i1_ = (ix1)-(j1);
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339 | v = 0.0;
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340 | for(i_=j1; i_<=j2;i_++)
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341 | {
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342 | v += a[i,i_]*x[i_+i1_];
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343 | }
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344 | y[iy1+i-i1] = y[iy1+i-i1]+alpha*v;
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345 | }
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346 | }
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347 | else
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348 | {
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349 |
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350 | //
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351 | // y := alpha*A'*x + beta*y;
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352 | //
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353 | if( i1>i2 | j1>j2 )
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354 | {
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355 | return;
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356 | }
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357 | System.Diagnostics.Debug.Assert(i2-i1==ix2-ix1, "MatrixVectorMultiply: A and X dont match!");
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358 | System.Diagnostics.Debug.Assert(j2-j1==iy2-iy1, "MatrixVectorMultiply: A and Y dont match!");
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359 |
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360 | //
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361 | // beta*y
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362 | //
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363 | if( (double)(beta)==(double)(0) )
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364 | {
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365 | for(i=iy1; i<=iy2; i++)
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366 | {
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367 | y[i] = 0;
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368 | }
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369 | }
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370 | else
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371 | {
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372 | for(i_=iy1; i_<=iy2;i_++)
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373 | {
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374 | y[i_] = beta*y[i_];
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375 | }
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376 | }
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377 |
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378 | //
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379 | // alpha*A'*x
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380 | //
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381 | for(i=i1; i<=i2; i++)
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382 | {
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383 | v = alpha*x[ix1+i-i1];
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384 | i1_ = (j1) - (iy1);
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385 | for(i_=iy1; i_<=iy2;i_++)
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386 | {
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387 | y[i_] = y[i_] + v*a[i,i_+i1_];
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388 | }
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389 | }
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390 | }
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391 | }
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392 |
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393 |
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394 | public static double pythag2(double x,
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395 | double y)
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396 | {
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397 | double result = 0;
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398 | double w = 0;
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399 | double xabs = 0;
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400 | double yabs = 0;
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401 | double z = 0;
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402 |
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403 | xabs = Math.Abs(x);
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404 | yabs = Math.Abs(y);
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405 | w = Math.Max(xabs, yabs);
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406 | z = Math.Min(xabs, yabs);
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407 | if( (double)(z)==(double)(0) )
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408 | {
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409 | result = w;
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410 | }
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411 | else
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412 | {
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413 | result = w*Math.Sqrt(1+AP.Math.Sqr(z/w));
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414 | }
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415 | return result;
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416 | }
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417 |
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418 |
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419 | public static void matrixmatrixmultiply(ref double[,] a,
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420 | int ai1,
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421 | int ai2,
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422 | int aj1,
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423 | int aj2,
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424 | bool transa,
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425 | ref double[,] b,
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426 | int bi1,
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427 | int bi2,
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428 | int bj1,
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429 | int bj2,
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430 | bool transb,
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431 | double alpha,
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432 | ref double[,] c,
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433 | int ci1,
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434 | int ci2,
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435 | int cj1,
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436 | int cj2,
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437 | double beta,
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438 | ref double[] work)
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439 | {
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440 | int arows = 0;
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441 | int acols = 0;
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442 | int brows = 0;
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443 | int bcols = 0;
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444 | int crows = 0;
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445 | int ccols = 0;
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446 | int i = 0;
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447 | int j = 0;
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448 | int k = 0;
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449 | int l = 0;
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450 | int r = 0;
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451 | double v = 0;
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452 | int i_ = 0;
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453 | int i1_ = 0;
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454 |
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455 |
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456 | //
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457 | // Setup
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458 | //
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459 | if( !transa )
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460 | {
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461 | arows = ai2-ai1+1;
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462 | acols = aj2-aj1+1;
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463 | }
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464 | else
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465 | {
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466 | arows = aj2-aj1+1;
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467 | acols = ai2-ai1+1;
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468 | }
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469 | if( !transb )
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470 | {
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471 | brows = bi2-bi1+1;
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472 | bcols = bj2-bj1+1;
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473 | }
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474 | else
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475 | {
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476 | brows = bj2-bj1+1;
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477 | bcols = bi2-bi1+1;
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478 | }
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479 | System.Diagnostics.Debug.Assert(acols==brows, "MatrixMatrixMultiply: incorrect matrix sizes!");
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480 | if( arows<=0 | acols<=0 | brows<=0 | bcols<=0 )
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481 | {
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482 | return;
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483 | }
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484 | crows = arows;
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485 | ccols = bcols;
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486 |
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487 | //
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488 | // Test WORK
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489 | //
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490 | i = Math.Max(arows, acols);
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491 | i = Math.Max(brows, i);
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492 | i = Math.Max(i, bcols);
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493 | work[1] = 0;
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494 | work[i] = 0;
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495 |
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496 | //
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497 | // Prepare C
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498 | //
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499 | if( (double)(beta)==(double)(0) )
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500 | {
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501 | for(i=ci1; i<=ci2; i++)
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502 | {
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503 | for(j=cj1; j<=cj2; j++)
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504 | {
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505 | c[i,j] = 0;
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506 | }
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507 | }
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508 | }
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509 | else
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510 | {
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511 | for(i=ci1; i<=ci2; i++)
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512 | {
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513 | for(i_=cj1; i_<=cj2;i_++)
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514 | {
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515 | c[i,i_] = beta*c[i,i_];
|
---|
516 | }
|
---|
517 | }
|
---|
518 | }
|
---|
519 |
|
---|
520 | //
|
---|
521 | // A*B
|
---|
522 | //
|
---|
523 | if( !transa & !transb )
|
---|
524 | {
|
---|
525 | for(l=ai1; l<=ai2; l++)
|
---|
526 | {
|
---|
527 | for(r=bi1; r<=bi2; r++)
|
---|
528 | {
|
---|
529 | v = alpha*a[l,aj1+r-bi1];
|
---|
530 | k = ci1+l-ai1;
|
---|
531 | i1_ = (bj1) - (cj1);
|
---|
532 | for(i_=cj1; i_<=cj2;i_++)
|
---|
533 | {
|
---|
534 | c[k,i_] = c[k,i_] + v*b[r,i_+i1_];
|
---|
535 | }
|
---|
536 | }
|
---|
537 | }
|
---|
538 | return;
|
---|
539 | }
|
---|
540 |
|
---|
541 | //
|
---|
542 | // A*B'
|
---|
543 | //
|
---|
544 | if( !transa & transb )
|
---|
545 | {
|
---|
546 | if( arows*acols<brows*bcols )
|
---|
547 | {
|
---|
548 | for(r=bi1; r<=bi2; r++)
|
---|
549 | {
|
---|
550 | for(l=ai1; l<=ai2; l++)
|
---|
551 | {
|
---|
552 | i1_ = (bj1)-(aj1);
|
---|
553 | v = 0.0;
|
---|
554 | for(i_=aj1; i_<=aj2;i_++)
|
---|
555 | {
|
---|
556 | v += a[l,i_]*b[r,i_+i1_];
|
---|
557 | }
|
---|
558 | c[ci1+l-ai1,cj1+r-bi1] = c[ci1+l-ai1,cj1+r-bi1]+alpha*v;
|
---|
559 | }
|
---|
560 | }
|
---|
561 | return;
|
---|
562 | }
|
---|
563 | else
|
---|
564 | {
|
---|
565 | for(l=ai1; l<=ai2; l++)
|
---|
566 | {
|
---|
567 | for(r=bi1; r<=bi2; r++)
|
---|
568 | {
|
---|
569 | i1_ = (bj1)-(aj1);
|
---|
570 | v = 0.0;
|
---|
571 | for(i_=aj1; i_<=aj2;i_++)
|
---|
572 | {
|
---|
573 | v += a[l,i_]*b[r,i_+i1_];
|
---|
574 | }
|
---|
575 | c[ci1+l-ai1,cj1+r-bi1] = c[ci1+l-ai1,cj1+r-bi1]+alpha*v;
|
---|
576 | }
|
---|
577 | }
|
---|
578 | return;
|
---|
579 | }
|
---|
580 | }
|
---|
581 |
|
---|
582 | //
|
---|
583 | // A'*B
|
---|
584 | //
|
---|
585 | if( transa & !transb )
|
---|
586 | {
|
---|
587 | for(l=aj1; l<=aj2; l++)
|
---|
588 | {
|
---|
589 | for(r=bi1; r<=bi2; r++)
|
---|
590 | {
|
---|
591 | v = alpha*a[ai1+r-bi1,l];
|
---|
592 | k = ci1+l-aj1;
|
---|
593 | i1_ = (bj1) - (cj1);
|
---|
594 | for(i_=cj1; i_<=cj2;i_++)
|
---|
595 | {
|
---|
596 | c[k,i_] = c[k,i_] + v*b[r,i_+i1_];
|
---|
597 | }
|
---|
598 | }
|
---|
599 | }
|
---|
600 | return;
|
---|
601 | }
|
---|
602 |
|
---|
603 | //
|
---|
604 | // A'*B'
|
---|
605 | //
|
---|
606 | if( transa & transb )
|
---|
607 | {
|
---|
608 | if( arows*acols<brows*bcols )
|
---|
609 | {
|
---|
610 | for(r=bi1; r<=bi2; r++)
|
---|
611 | {
|
---|
612 | for(i=1; i<=crows; i++)
|
---|
613 | {
|
---|
614 | work[i] = 0.0;
|
---|
615 | }
|
---|
616 | for(l=ai1; l<=ai2; l++)
|
---|
617 | {
|
---|
618 | v = alpha*b[r,bj1+l-ai1];
|
---|
619 | k = cj1+r-bi1;
|
---|
620 | i1_ = (aj1) - (1);
|
---|
621 | for(i_=1; i_<=crows;i_++)
|
---|
622 | {
|
---|
623 | work[i_] = work[i_] + v*a[l,i_+i1_];
|
---|
624 | }
|
---|
625 | }
|
---|
626 | i1_ = (1) - (ci1);
|
---|
627 | for(i_=ci1; i_<=ci2;i_++)
|
---|
628 | {
|
---|
629 | c[i_,k] = c[i_,k] + work[i_+i1_];
|
---|
630 | }
|
---|
631 | }
|
---|
632 | return;
|
---|
633 | }
|
---|
634 | else
|
---|
635 | {
|
---|
636 | for(l=aj1; l<=aj2; l++)
|
---|
637 | {
|
---|
638 | k = ai2-ai1+1;
|
---|
639 | i1_ = (ai1) - (1);
|
---|
640 | for(i_=1; i_<=k;i_++)
|
---|
641 | {
|
---|
642 | work[i_] = a[i_+i1_,l];
|
---|
643 | }
|
---|
644 | for(r=bi1; r<=bi2; r++)
|
---|
645 | {
|
---|
646 | i1_ = (bj1)-(1);
|
---|
647 | v = 0.0;
|
---|
648 | for(i_=1; i_<=k;i_++)
|
---|
649 | {
|
---|
650 | v += work[i_]*b[r,i_+i1_];
|
---|
651 | }
|
---|
652 | c[ci1+l-aj1,cj1+r-bi1] = c[ci1+l-aj1,cj1+r-bi1]+alpha*v;
|
---|
653 | }
|
---|
654 | }
|
---|
655 | return;
|
---|
656 | }
|
---|
657 | }
|
---|
658 | }
|
---|
659 | }
|
---|
660 | }
|
---|