1 | """Proof of concept sparse matrix code |
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2 | """ |
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3 | |
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4 | |
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5 | class Sparse: |
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6 | |
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7 | def __init__(self, *args): |
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8 | """Create sparse matrix. |
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9 | There are two construction forms |
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10 | Usage: |
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11 | |
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12 | Sparse(A) #Creates sparse matrix from dense matrix A |
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13 | Sparse(M, N) #Creates empty MxN sparse matrix |
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14 | |
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15 | |
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16 | |
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17 | """ |
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18 | |
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19 | self.Data = {} |
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20 | |
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21 | if len(args) == 1: |
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22 | from Numeric import array |
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23 | try: |
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24 | A = array(args[0]) |
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25 | except: |
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26 | raise 'Input must be convertable to a Numeric array' |
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27 | |
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28 | assert len(A.shape) == 2, 'Input must be a 2d matrix' |
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29 | |
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30 | self.M, self.N = A.shape |
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31 | for i in range(self.M): |
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32 | for j in range(self.N): |
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33 | if A[i, j] != 0.0: |
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34 | self.Data[i, j] = A[i, j] |
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35 | |
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36 | |
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37 | elif len(args) == 2: |
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38 | self.M = args[0] |
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39 | self.N = args[1] |
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40 | else: |
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41 | raise 'Invalid construction' |
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42 | |
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43 | self.shape = (self.M, self.N) |
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44 | |
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45 | |
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46 | def __repr__(self): |
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47 | return '%d X %d sparse matrix:\n' %(self.M, self.N) + `self.Data` |
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48 | |
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49 | def __len__(self): |
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50 | """Return number of nonzeros of A |
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51 | """ |
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52 | return len(self.Data) |
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53 | |
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54 | def nonzeros(self): |
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55 | """Return number of nonzeros of A |
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56 | """ |
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57 | return len(self) |
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58 | |
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59 | def __setitem__(self, key, x): |
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60 | |
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61 | i,j = key |
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62 | assert 0 <= i < self.M |
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63 | assert 0 <= j < self.N |
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64 | |
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65 | if x != 0: |
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66 | self.Data[key] = float(x) |
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67 | else: |
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68 | if self.Data.has_key( key ): |
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69 | del self.Data[key] |
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70 | |
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71 | def __getitem__(self, key): |
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72 | |
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73 | i,j = key |
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74 | assert 0 <= i < self.M |
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75 | assert 0 <= j < self.N |
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76 | |
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77 | if self.Data.has_key( key ): |
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78 | return self.Data[ key ] |
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79 | else: |
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80 | return 0.0 |
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81 | |
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82 | def copy(self): |
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83 | #FIXME: Use the copy module instead |
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84 | new = Sparse(self.M,self.N) |
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85 | |
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86 | for key in self.Data.keys(): |
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87 | i, j = key |
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88 | |
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89 | new[i,j] = self.Data[i,j] |
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90 | |
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91 | return new |
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92 | |
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93 | |
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94 | def todense(self): |
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95 | from Numeric import zeros, Float |
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96 | |
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97 | D = zeros( (self.M, self.N), Float) |
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98 | |
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99 | for i in range(self.M): |
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100 | for j in range(self.N): |
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101 | if self.Data.has_key( (i,j) ): |
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102 | D[i, j] = self.Data[ (i,j) ] |
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103 | return D |
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104 | |
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105 | |
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106 | |
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107 | def __mul__(self, other): |
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108 | """Multiply this matrix onto 'other' which can either be |
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109 | a Numeric vector, a Numeric matrix or another sparse matrix. |
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110 | """ |
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111 | |
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112 | from Numeric import array, zeros, Float |
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113 | |
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114 | try: |
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115 | B = array(other) |
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116 | except: |
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117 | msg = 'FIXME: Only Numeric types implemented so far' |
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118 | raise msg |
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119 | |
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120 | |
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121 | #Assume numeric types from now on |
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122 | |
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123 | if len(B.shape) == 0: |
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124 | #Scalar - use __rmul__ method |
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125 | R = B*self |
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126 | |
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127 | elif len(B.shape) == 1: |
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128 | #Vector |
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129 | assert B.shape[0] == self.N, 'Mismatching dimensions' |
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130 | |
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131 | R = zeros(self.M, Float) #Result |
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132 | |
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133 | #Multiply nonzero elements |
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134 | for key in self.Data.keys(): |
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135 | i, j = key |
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136 | |
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137 | R[i] += self.Data[key]*B[j] |
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138 | elif len(B.shape) == 2: |
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139 | |
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140 | |
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141 | R = zeros((self.M, B.shape[1]), Float) #Result matrix |
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142 | |
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143 | #Multiply nonzero elements |
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144 | for col in range(R.shape[1]): |
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145 | #For each column |
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146 | |
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147 | for key in self.Data.keys(): |
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148 | i, j = key |
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149 | |
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150 | R[i, col] += self.Data[key]*B[j, col] |
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151 | |
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152 | |
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153 | else: |
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154 | raise ValueError, 'Dimension too high: d=%d' %len(B.shape) |
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155 | |
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156 | return R |
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157 | |
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158 | |
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159 | def __add__(self, other): |
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160 | """Add this matrix onto 'other' |
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161 | """ |
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162 | |
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163 | from Numeric import array, zeros, Float |
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164 | |
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165 | new = other.copy() |
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166 | for key in self.Data.keys(): |
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167 | i, j = key |
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168 | |
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169 | new[i,j] += self.Data[key] |
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170 | |
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171 | return new |
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172 | |
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173 | |
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174 | def __rmul__(self, other): |
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175 | """Right multiply this matrix with scalar |
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176 | """ |
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177 | |
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178 | from Numeric import array, zeros, Float |
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179 | |
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180 | try: |
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181 | other = float(other) |
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182 | except: |
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183 | msg = 'Sparse matrix can only "right-multiply" onto a scalar' |
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184 | raise TypeError, msg |
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185 | else: |
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186 | new = self.copy() |
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187 | #Multiply nonzero elements |
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188 | for key in new.Data.keys(): |
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189 | i, j = key |
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190 | |
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191 | new.Data[key] = other*new.Data[key] |
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192 | |
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193 | return new |
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194 | |
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195 | |
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196 | def trans_mult(self, other): |
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197 | """Multiply the transpose of matrix with 'other' which can be |
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198 | a Numeric vector. |
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199 | """ |
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200 | |
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201 | from Numeric import array, zeros, Float |
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202 | |
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203 | try: |
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204 | B = array(other) |
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205 | except: |
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206 | print 'FIXME: Only Numeric types implemented so far' |
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207 | |
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208 | |
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209 | #Assume numeric types from now on |
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210 | if len(B.shape) == 1: |
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211 | #Vector |
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212 | |
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213 | assert B.shape[0] == self.M, 'Mismatching dimensions' |
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214 | |
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215 | R = zeros((self.N,), Float) #Result |
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216 | |
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217 | #Multiply nonzero elements |
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218 | for key in self.Data.keys(): |
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219 | i, j = key |
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220 | |
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221 | R[j] += self.Data[key]*B[i] |
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222 | |
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223 | else: |
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224 | raise 'Can only multiply with 1d array' |
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225 | |
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226 | return R |
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227 | |
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228 | class Sparse_CSR: |
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229 | |
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230 | def __init__(self, A): |
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231 | """Create sparse matrix in csr format. |
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232 | |
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233 | Sparse_CSR(A) #creates csr sparse matrix from sparse matrix |
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234 | Matrices are not built using this format, since it's painful to |
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235 | add values to an existing sparse_CSR instance (hence there are no |
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236 | objects to do this.) |
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237 | |
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238 | Rather, build a matrix, and convert it to this format for a speed |
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239 | increase. |
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240 | |
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241 | data - a 1D array of the data |
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242 | Colind - The ith item in this 1D array is the column index of the |
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243 | ith data in the data array |
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244 | rowptr - 1D array, with the index representing the row of the matrix. |
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245 | The item in the row represents the index into colind of the |
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246 | first data value of this row. |
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247 | Regard it as a pointer into the colind array, for the ith row. |
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248 | |
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249 | |
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250 | """ |
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251 | |
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252 | from Numeric import array, Float, Int |
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253 | |
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254 | if isinstance(A,Sparse): |
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255 | |
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256 | from Numeric import zeros |
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257 | keys = A.Data.keys() |
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258 | keys.sort() |
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259 | nnz = len(keys) |
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260 | data = zeros ( (nnz,), Float) |
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261 | colind = zeros ( (nnz,), Int) |
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262 | row_ptr = zeros ( (A.M+1,), Int) |
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263 | current_row = -1 |
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264 | k = 0 |
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265 | for key in keys: |
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266 | ikey0 = int(key[0]) |
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267 | ikey1 = int(key[1]) |
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268 | if ikey0 != current_row: |
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269 | current_row = ikey0 |
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270 | row_ptr[ikey0] = k |
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271 | data[k] = A.Data[key] |
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272 | colind[k] = ikey1 |
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273 | k += 1 |
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274 | for row in range(current_row+1, A.M+1): |
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275 | row_ptr[row] = nnz |
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276 | #row_ptr[-1] = nnz |
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277 | |
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278 | self.data = data |
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279 | self.colind = colind |
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280 | self.row_ptr = row_ptr |
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281 | self.M = A.M |
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282 | self.N = A.N |
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283 | else: |
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284 | raise ValueError, "Sparse_CSR(A) expects A == Sparse Matrix" |
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285 | |
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286 | def __repr__(self): |
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287 | return '%d X %d sparse matrix:\n' %(self.M, self.N) + `self.data` |
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288 | |
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289 | def __len__(self): |
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290 | """Return number of nonzeros of A |
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291 | """ |
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292 | return self.row_ptr[-1] |
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293 | |
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294 | def nonzeros(self): |
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295 | """Return number of nonzeros of A |
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296 | """ |
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297 | return len(self) |
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298 | |
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299 | def todense(self): |
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300 | from Numeric import zeros, Float |
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301 | |
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302 | D = zeros( (self.M, self.N), Float) |
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303 | |
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304 | for i in range(self.M): |
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305 | for ckey in range(self.row_ptr[i],self.row_ptr[i+1]): |
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306 | j = self.colind[ckey] |
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307 | D[i, j] = self.data[ckey] |
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308 | return D |
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309 | |
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310 | def __mul__(self, other): |
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311 | """Multiply this matrix onto 'other' which can either be |
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312 | a Numeric vector, a Numeric matrix or another sparse matrix. |
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313 | """ |
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314 | |
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315 | from Numeric import array, zeros, Float |
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316 | |
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317 | try: |
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318 | B = array(other) |
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319 | except: |
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320 | print 'FIXME: Only Numeric types implemented so far' |
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321 | |
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322 | return csr_mv(self,B) |
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323 | |
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324 | |
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325 | |
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326 | def csr_mv(self, B): |
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327 | """Python version of sparse (CSR) matrix multiplication |
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328 | """ |
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329 | |
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330 | from Numeric import zeros, Float |
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331 | |
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332 | |
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333 | #Assume numeric types from now on |
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334 | |
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335 | if len(B.shape) == 0: |
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336 | #Scalar - use __rmul__ method |
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337 | R = B*self |
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338 | |
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339 | elif len(B.shape) == 1: |
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340 | #Vector |
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341 | assert B.shape[0] == self.N, 'Mismatching dimensions' |
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342 | |
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343 | R = zeros(self.M, Float) #Result |
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344 | |
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345 | #Multiply nonzero elements |
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346 | for i in range(self.M): |
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347 | for ckey in range(self.row_ptr[i],self.row_ptr[i+1]): |
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348 | j = self.colind[ckey] |
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349 | R[i] += self.data[ckey]*B[j] |
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350 | |
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351 | elif len(B.shape) == 2: |
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352 | |
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353 | R = zeros((self.M, B.shape[1]), Float) #Result matrix |
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354 | |
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355 | #Multiply nonzero elements |
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356 | |
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357 | for col in range(R.shape[1]): |
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358 | #For each column |
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359 | for i in range(self.M): |
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360 | for ckey in range(self.row_ptr[i],self.row_ptr[i+1]): |
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361 | j = self.colind[ckey] |
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362 | R[i, col] += self.data[ckey]*B[j,col] |
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363 | |
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364 | else: |
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365 | raise ValueError, 'Dimension too high: d=%d' %len(B.shape) |
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366 | |
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367 | return R |
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368 | |
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369 | |
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370 | |
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371 | #Setup for C extensions |
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372 | import compile |
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373 | if compile.can_use_C_extension('sparse_ext.c'): |
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374 | #Replace python version with c implementation |
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375 | from sparse_ext import csr_mv |
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376 | |
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377 | if __name__ == '__main__': |
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378 | |
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379 | from Numeric import allclose, array, Float |
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380 | |
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381 | A = Sparse(3,3) |
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382 | |
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383 | A[1,1] = 4 |
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384 | |
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385 | |
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386 | print A |
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387 | print A.todense() |
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388 | |
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389 | A[1,1] = 0 |
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390 | |
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391 | print A |
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392 | print A.todense() |
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393 | |
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394 | A[1,2] = 0 |
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395 | |
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396 | |
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397 | A[0,0] = 3 |
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398 | A[1,1] = 2 |
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399 | A[1,2] = 2 |
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400 | A[2,2] = 1 |
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401 | |
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402 | print A |
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403 | print A.todense() |
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404 | |
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405 | |
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406 | #Right hand side vector |
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407 | v = [2,3,4] |
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408 | |
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409 | u = A*v |
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410 | print u |
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411 | assert allclose(u, [6,14,4]) |
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412 | |
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413 | u = A.trans_mult(v) |
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414 | print u |
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415 | assert allclose(u, [6,6,10]) |
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416 | |
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417 | #Right hand side column |
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418 | v = array([[2,4],[3,4],[4,4]]) |
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419 | |
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420 | u = A*v[:,0] |
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421 | assert allclose(u, [6,14,4]) |
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422 | |
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423 | #u = A*v[:,1] |
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424 | #print u |
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425 | print A.shape |
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426 | |
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427 | B = 3*A |
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428 | print B.todense() |
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429 | |
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430 | B[1,0] = 2 |
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431 | |
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432 | C = A+B |
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433 | |
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434 | print C.todense() |
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435 | |
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436 | C = Sparse_CSR(C) |
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437 | |
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438 | y = C*[6,14,4] |
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439 | |
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440 | print y |
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441 | |
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442 | y2 = C*[[6,4],[4,28],[4,8]] |
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443 | |
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444 | print y2 |
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