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| 50 | <h1>Source code for sas.data_util.err1d</h1><div class="highlight"><pre> |
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| 51 | <span class="c"># This program is public domain</span> |
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| 52 | <span class="sd">"""</span> |
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| 53 | <span class="sd">Error propogation algorithms for simple arithmetic</span> |
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| 54 | |
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| 55 | <span class="sd">Warning: like the underlying numpy library, the inplace operations</span> |
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| 56 | <span class="sd">may return values of the wrong type if some of the arguments are</span> |
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| 57 | <span class="sd">integers, so be sure to create them with floating point inputs.</span> |
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| 58 | <span class="sd">"""</span> |
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| 59 | <span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span> <span class="c"># Get true division</span> |
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| 60 | <span class="kn">import</span> <span class="nn">numpy</span> |
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| 61 | |
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| 62 | |
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| 63 | <div class="viewcode-block" id="div"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.div">[docs]</a><span class="k">def</span> <span class="nf">div</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 64 | <span class="sd">"""Division with error propagation"""</span> |
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| 65 | <span class="c"># Direct algorithm:</span> |
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| 66 | <span class="c"># Z = X/Y</span> |
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| 67 | <span class="c"># varZ = (varX/X**2 + varY/Y**2) * Z**2</span> |
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| 68 | <span class="c"># = (varX + varY * Z**2) / Y**2</span> |
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| 69 | <span class="c"># Indirect algorithm to minimize intermediates</span> |
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| 70 | <span class="n">Z</span> <span class="o">=</span> <span class="n">X</span><span class="o">/</span><span class="n">Y</span> <span class="c"># truediv => Z is a float</span> |
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| 71 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">Z</span><span class="o">**</span><span class="mi">2</span> <span class="c"># Z is a float => varZ is a float</span> |
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| 72 | <span class="n">varZ</span> <span class="o">*=</span> <span class="n">varY</span> |
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| 73 | <span class="n">varZ</span> <span class="o">+=</span> <span class="n">varX</span> |
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| 74 | <span class="n">T</span> <span class="o">=</span> <span class="n">Y</span><span class="o">**</span><span class="mi">2</span> <span class="c"># Doesn't matter if T is float or int</span> |
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| 75 | <span class="n">varZ</span> <span class="o">/=</span> <span class="n">T</span> |
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| 76 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 77 | |
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| 78 | </div> |
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| 79 | <div class="viewcode-block" id="mul"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.mul">[docs]</a><span class="k">def</span> <span class="nf">mul</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 80 | <span class="sd">"""Multiplication with error propagation"""</span> |
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| 81 | <span class="c"># Direct algorithm:</span> |
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| 82 | <span class="n">Z</span> <span class="o">=</span> <span class="n">X</span> <span class="o">*</span> <span class="n">Y</span> |
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| 83 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">Y</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">varX</span> <span class="o">+</span> <span class="n">X</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">varY</span> |
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| 84 | <span class="c"># Indirect algorithm won't ensure floating point results</span> |
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| 85 | <span class="c"># varZ = Y**2</span> |
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| 86 | <span class="c"># varZ *= varX</span> |
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| 87 | <span class="c"># Z = X**2 # Using Z to hold the temporary</span> |
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| 88 | <span class="c"># Z *= varY</span> |
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| 89 | <span class="c"># varZ += Z</span> |
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| 90 | <span class="c"># Z[:] = X</span> |
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| 91 | <span class="c"># Z *= Y</span> |
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| 92 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 93 | |
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| 94 | </div> |
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| 95 | <div class="viewcode-block" id="sub"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.sub">[docs]</a><span class="k">def</span> <span class="nf">sub</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 96 | <span class="sd">"""Subtraction with error propagation"""</span> |
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| 97 | <span class="n">Z</span> <span class="o">=</span> <span class="n">X</span> <span class="o">-</span> <span class="n">Y</span> |
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| 98 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">varX</span> <span class="o">+</span> <span class="n">varY</span> |
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| 99 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 100 | |
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| 101 | </div> |
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| 102 | <div class="viewcode-block" id="add"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.add">[docs]</a><span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 103 | <span class="sd">"""Addition with error propagation"""</span> |
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| 104 | <span class="n">Z</span> <span class="o">=</span> <span class="n">X</span> <span class="o">+</span> <span class="n">Y</span> |
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| 105 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">varX</span> <span class="o">+</span> <span class="n">varY</span> |
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| 106 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 107 | |
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| 108 | </div> |
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| 109 | <div class="viewcode-block" id="exp"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.exp">[docs]</a><span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">):</span> |
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| 110 | <span class="sd">"""Exponentiation with error propagation"""</span> |
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| 111 | <span class="n">Z</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> |
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| 112 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">varX</span> <span class="o">*</span> <span class="n">Z</span><span class="o">**</span><span class="mi">2</span> |
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| 113 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 114 | |
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| 115 | </div> |
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| 116 | <div class="viewcode-block" id="log"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.log">[docs]</a><span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">):</span> |
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| 117 | <span class="sd">"""Logarithm with error propagation"""</span> |
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| 118 | <span class="n">Z</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> |
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| 119 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">varX</span> <span class="o">/</span> <span class="n">X</span><span class="o">**</span><span class="mi">2</span> |
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| 120 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 121 | |
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| 122 | <span class="c"># Confirm this formula before using it</span> |
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| 123 | <span class="c"># def pow(X,varX, Y,varY):</span> |
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| 124 | <span class="c"># Z = X**Y</span> |
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| 125 | <span class="c"># varZ = (Y**2 * varX/X**2 + varY * numpy.log(X)**2) * Z**2</span> |
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| 126 | <span class="c"># return Z,varZ</span> |
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| 127 | <span class="c">#</span> |
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| 128 | |
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| 129 | </div> |
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| 130 | <div class="viewcode-block" id="pow"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.pow">[docs]</a><span class="k">def</span> <span class="nf">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span> |
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| 131 | <span class="sd">"""X**n with error propagation"""</span> |
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| 132 | <span class="c"># Direct algorithm</span> |
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| 133 | <span class="c"># Z = X**n</span> |
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| 134 | <span class="c"># varZ = n*n * varX/X**2 * Z**2</span> |
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| 135 | <span class="c"># Indirect algorithm to minimize intermediates</span> |
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| 136 | <span class="n">Z</span> <span class="o">=</span> <span class="n">X</span><span class="o">**</span><span class="n">n</span> |
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| 137 | <span class="n">varZ</span> <span class="o">=</span> <span class="n">varX</span> <span class="o">/</span> <span class="n">X</span> |
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| 138 | <span class="n">varZ</span> <span class="o">/=</span> <span class="n">X</span> |
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| 139 | <span class="n">varZ</span> <span class="o">*=</span> <span class="n">Z</span> |
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| 140 | <span class="n">varZ</span> <span class="o">*=</span> <span class="n">Z</span> |
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| 141 | <span class="n">varZ</span> <span class="o">*=</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span> |
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| 142 | <span class="k">return</span> <span class="n">Z</span><span class="p">,</span> <span class="n">varZ</span> |
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| 143 | |
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| 144 | </div> |
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| 145 | <div class="viewcode-block" id="div_inplace"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.div_inplace">[docs]</a><span class="k">def</span> <span class="nf">div_inplace</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 146 | <span class="sd">"""In-place division with error propagation"""</span> |
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| 147 | <span class="c"># Z = X/Y</span> |
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| 148 | <span class="c"># varZ = (varX + varY * (X/Y)**2) / Y**2 = (varX + varY * Z**2) / Y**2</span> |
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| 149 | <span class="n">X</span> <span class="o">/=</span> <span class="n">Y</span> <span class="c"># X now has Z = X/Y</span> |
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| 150 | <span class="n">T</span> <span class="o">=</span> <span class="n">X</span><span class="o">**</span><span class="mi">2</span> <span class="c"># create T with Z**2</span> |
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| 151 | <span class="n">T</span> <span class="o">*=</span> <span class="n">varY</span> <span class="c"># T now has varY * Z**2</span> |
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| 152 | <span class="n">varX</span> <span class="o">+=</span> <span class="n">T</span> <span class="c"># varX now has varX + varY*Z**2</span> |
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| 153 | <span class="k">del</span> <span class="n">T</span> <span class="c"># may want to use T[:] = Y for vectors</span> |
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| 154 | <span class="n">T</span> <span class="o">=</span> <span class="n">Y</span> <span class="c"># reuse T for Y</span> |
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| 155 | <span class="n">T</span> <span class="o">**=</span> <span class="mi">2</span> <span class="c"># T now has Y**2</span> |
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| 156 | <span class="n">varX</span> <span class="o">/=</span> <span class="n">T</span> <span class="c"># varX now has varZ</span> |
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| 157 | <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">varX</span> |
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| 158 | |
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| 159 | </div> |
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| 160 | <div class="viewcode-block" id="mul_inplace"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.mul_inplace">[docs]</a><span class="k">def</span> <span class="nf">mul_inplace</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 161 | <span class="sd">"""In-place multiplication with error propagation"""</span> |
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| 162 | <span class="c"># Z = X * Y</span> |
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| 163 | <span class="c"># varZ = Y**2 * varX + X**2 * varY</span> |
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| 164 | <span class="n">T</span> <span class="o">=</span> <span class="n">Y</span><span class="o">**</span><span class="mi">2</span> <span class="c"># create T with Y**2</span> |
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| 165 | <span class="n">varX</span> <span class="o">*=</span> <span class="n">T</span> <span class="c"># varX now has Y**2 * varX</span> |
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| 166 | <span class="k">del</span> <span class="n">T</span> <span class="c"># may want to use T[:] = X for vectors</span> |
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| 167 | <span class="n">T</span> <span class="o">=</span> <span class="n">X</span> <span class="c"># reuse T for X**2 * varY</span> |
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| 168 | <span class="n">T</span> <span class="o">**=</span><span class="mi">2</span> <span class="c"># T now has X**2</span> |
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| 169 | <span class="n">T</span> <span class="o">*=</span> <span class="n">varY</span> <span class="c"># T now has X**2 * varY</span> |
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| 170 | <span class="n">varX</span> <span class="o">+=</span> <span class="n">T</span> <span class="c"># varX now has varZ</span> |
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| 171 | <span class="n">X</span> <span class="o">*=</span> <span class="n">Y</span> <span class="c"># X now has Z</span> |
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| 172 | <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">varX</span> |
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| 173 | |
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| 174 | </div> |
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| 175 | <div class="viewcode-block" id="sub_inplace"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.sub_inplace">[docs]</a><span class="k">def</span> <span class="nf">sub_inplace</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 176 | <span class="sd">"""In-place subtraction with error propagation"""</span> |
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| 177 | <span class="c"># Z = X - Y</span> |
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| 178 | <span class="c"># varZ = varX + varY</span> |
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| 179 | <span class="n">X</span> <span class="o">-=</span> <span class="n">Y</span> |
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| 180 | <span class="n">varX</span> <span class="o">+=</span> <span class="n">varY</span> |
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| 181 | <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">varX</span> |
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| 182 | |
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| 183 | </div> |
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| 184 | <div class="viewcode-block" id="add_inplace"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.add_inplace">[docs]</a><span class="k">def</span> <span class="nf">add_inplace</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">varY</span><span class="p">):</span> |
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| 185 | <span class="sd">"""In-place addition with error propagation"""</span> |
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| 186 | <span class="c"># Z = X + Y</span> |
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| 187 | <span class="c"># varZ = varX + varY</span> |
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| 188 | <span class="n">X</span> <span class="o">+=</span> <span class="n">Y</span> |
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| 189 | <span class="n">varX</span> <span class="o">+=</span> <span class="n">varY</span> |
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| 190 | <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">varX</span> |
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| 191 | |
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| 192 | </div> |
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| 193 | <div class="viewcode-block" id="pow_inplace"><a class="viewcode-back" href="../../../dev/api/sas.data_util.html#sas.data_util.err1d.pow_inplace">[docs]</a><span class="k">def</span> <span class="nf">pow_inplace</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">varX</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span> |
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| 194 | <span class="sd">"""In-place X**n with error propagation"""</span> |
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| 195 | <span class="c"># Direct algorithm</span> |
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| 196 | <span class="c"># Z = X**n</span> |
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| 197 | <span class="c"># varZ = abs(n) * varX/X**2 * Z**2</span> |
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| 198 | <span class="c"># Indirect algorithm to minimize intermediates</span> |
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| 199 | <span class="n">varX</span> <span class="o">/=</span> <span class="n">X</span> |
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| 200 | <span class="n">varX</span> <span class="o">/=</span> <span class="n">X</span> <span class="c"># varX now has varX/X**2</span> |
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| 201 | <span class="n">X</span> <span class="o">**=</span> <span class="n">n</span> <span class="c"># X now has Z = X**n</span> |
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| 202 | <span class="n">varX</span> <span class="o">*=</span> <span class="n">X</span> |
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| 203 | <span class="n">varX</span> <span class="o">*=</span> <span class="n">X</span> <span class="c"># varX now has varX/X**2 * Z**2</span> |
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| 204 | <span class="n">varX</span> <span class="o">*=</span> <span class="n">n</span><span class="o">**</span><span class="mi">2</span> <span class="c"># varX now has varZ</span> |
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| 205 | <span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">varX</span></div> |
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| 206 | </pre></div> |
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