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50  <h1>Source code for GSASIIpy3</h1><div class="highlight"><pre>
51<span class="sd">&#39;&#39;&#39;</span>
52<span class="sd">*GSASIIpy3: Python 3.x Routines*</span>
53<span class="sd">================================</span>
54
55<span class="sd">Module to hold python 3-compatible code, to keep it separate from</span>
56<span class="sd">code that will break with __future__ options.</span>
57
58<span class="sd">&#39;&#39;&#39;</span>
59<span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
60<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
61<span class="kn">import</span> <span class="nn">GSASIIpath</span>
62<span class="n">GSASIIpath</span><span class="o">.</span><span class="n">SetVersionNumber</span><span class="p">(</span><span class="s">&quot;$Revision: 1658 $&quot;</span><span class="p">)</span>
63<span class="c"># declare symbol (pi) and functions allowed in expressions</span>
64<span class="n">sind</span> <span class="o">=</span> <span class="n">sin</span> <span class="o">=</span> <span class="n">s</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mf">180.</span><span class="p">)</span>
65<span class="n">cosd</span> <span class="o">=</span> <span class="n">cos</span> <span class="o">=</span> <span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mf">180.</span><span class="p">)</span>
66<span class="n">tand</span> <span class="o">=</span> <span class="n">tan</span> <span class="o">=</span> <span class="n">t</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">x</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">/</span><span class="mf">180.</span><span class="p">)</span>
67<span class="n">sqrt</span> <span class="o">=</span> <span class="n">sq</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
68<span class="n">pi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
69
70<div class="viewcode-block" id="FormulaEval"><a class="viewcode-back" href="../GSASIIGUIr.html#GSASIIpy3.FormulaEval">[docs]</a><span class="k">def</span> <span class="nf">FormulaEval</span><span class="p">(</span><span class="n">string</span><span class="p">):</span>
71    <span class="sd">&#39;&#39;&#39;Evaluates a algebraic formula into a float, if possible. Works</span>
72<span class="sd">    properly on fractions e.g. 2/3 only with python 3.0+ division.</span>
73
74<span class="sd">    Expressions such as 2/3, 3*pi, sin(45)/2, 2*sqrt(2), 2**10 can all</span>
75<span class="sd">    be evaluated.</span>
76
77<span class="sd">    :param str string: Character string containing a Python expression</span>
78<span class="sd">      to be evaluated.</span>
79
80<span class="sd">    :returns: the value for the expression as a float or None if the expression does not</span>
81<span class="sd">      evaluate to a valid number. </span>
82<span class="sd">    </span>
83<span class="sd">    &#39;&#39;&#39;</span>
84    <span class="k">try</span><span class="p">:</span>
85        <span class="n">val</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="nb">eval</span><span class="p">(</span><span class="n">string</span><span class="p">))</span>
86        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="ow">or</span> <span class="n">np</span><span class="o">.</span><span class="n">isinf</span><span class="p">(</span><span class="n">val</span><span class="p">):</span> <span class="k">return</span> <span class="bp">None</span>
87    <span class="k">except</span><span class="p">:</span>
88        <span class="k">return</span> <span class="bp">None</span>
89    <span class="k">return</span> <span class="n">val</span>
90</div>
91<div class="viewcode-block" id="FormatPadValue"><a class="viewcode-back" href="../GSASIIGUIr.html#GSASIIpy3.FormatPadValue">[docs]</a><span class="k">def</span> <span class="nf">FormatPadValue</span><span class="p">(</span><span class="n">val</span><span class="p">,</span><span class="n">maxdigits</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
92    <span class="sd">&#39;&#39;&#39;Format a float to fit in ``maxdigits[0]`` spaces with maxdigits[1] after decimal.</span>
93
94<span class="sd">    :param float val: number to be formatted.</span>
95
96<span class="sd">    :param list maxdigits: the number of digits &amp; places after decimal to be used for display of the</span>
97<span class="sd">      number (defaults to [10,2]).</span>
98
99<span class="sd">    :returns: a string with exactly maxdigits[0] characters (except under error conditions),</span>
100<span class="sd">      but last character will always be a space</span>
101<span class="sd">    &#39;&#39;&#39;</span>
102    <span class="k">if</span> <span class="n">maxdigits</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
103        <span class="n">digits</span> <span class="o">=</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
104    <span class="k">else</span><span class="p">:</span>
105        <span class="n">digits</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">)</span>
106    <span class="n">fmt</span> <span class="o">=</span> <span class="s">&#39;{:&#39;</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">+</span><span class="s">&#39;}&#39;</span>
107    <span class="n">s</span> <span class="o">=</span> <span class="n">fmt</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">FormatValue</span><span class="p">(</span><span class="n">val</span><span class="p">,</span><span class="n">digits</span><span class="p">))</span>
108    <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="s">&#39; &#39;</span><span class="p">:</span>
109        <span class="k">return</span> <span class="n">s</span>
110    <span class="k">else</span><span class="p">:</span>
111        <span class="k">return</span> <span class="n">s</span><span class="o">+</span><span class="s">&#39; &#39;</span>
112   
113</div>
114<div class="viewcode-block" id="FormatValue"><a class="viewcode-back" href="../GSASIIGUIr.html#GSASIIpy3.FormatValue">[docs]</a><span class="k">def</span> <span class="nf">FormatValue</span><span class="p">(</span><span class="n">val</span><span class="p">,</span><span class="n">maxdigits</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
115    <span class="sd">&#39;&#39;&#39;Format a float to fit in at most ``maxdigits[0]`` spaces with maxdigits[1] after decimal.</span>
116<span class="sd">    Note that this code has been hacked from FormatSigFigs and may have unused sections. </span>
117
118<span class="sd">    :param float val: number to be formatted.</span>
119
120<span class="sd">    :param list maxdigits: the number of digits &amp; places after decimal to be used for display of the</span>
121<span class="sd">      number (defaults to [10,2]).</span>
122
123<span class="sd">    :returns: a string with &lt;= maxdigits characters (usually).  </span>
124<span class="sd">    &#39;&#39;&#39;</span>
125    <span class="k">if</span> <span class="s">&#39;str&#39;</span> <span class="ow">in</span> <span class="nb">str</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">val</span><span class="p">))</span> <span class="ow">and</span> <span class="p">(</span><span class="n">val</span> <span class="o">==</span> <span class="s">&#39;?&#39;</span> <span class="ow">or</span> <span class="n">val</span> <span class="o">==</span> <span class="s">&#39;.&#39;</span><span class="p">):</span>
126        <span class="k">return</span> <span class="n">val</span>       
127    <span class="k">if</span> <span class="n">maxdigits</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span>
128        <span class="n">digits</span> <span class="o">=</span> <span class="p">[</span><span class="mi">10</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
129    <span class="k">else</span><span class="p">:</span>
130        <span class="n">digits</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">)</span>
131    <span class="n">fmt</span><span class="o">=</span><span class="s">&quot;{:.&quot;</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">+</span><span class="s">&quot;f}&quot;</span>
132    <span class="n">string</span> <span class="o">=</span> <span class="n">fmt</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">val</span><span class="p">))</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="c"># will standard .f formatting work?</span>
133    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">string</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
134        <span class="k">if</span> <span class="s">&#39;:&#39;</span> <span class="ow">in</span> <span class="n">string</span><span class="p">:</span> <span class="c"># deal with weird bug where a colon pops up in a number when formatting (EPD 7.3.2!)</span>
135            <span class="n">string</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
136        <span class="k">if</span> <span class="n">digits</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span> <span class="c"># strip off extra zeros on right side</span>
137            <span class="n">string</span> <span class="o">=</span> <span class="n">string</span><span class="o">.</span><span class="n">rstrip</span><span class="p">(</span><span class="s">&#39;0&#39;</span><span class="p">)</span>
138            <span class="k">if</span> <span class="n">string</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="s">&#39;.&#39;</span><span class="p">:</span> <span class="n">string</span> <span class="o">+=</span> <span class="s">&quot;0&quot;</span>
139        <span class="k">return</span> <span class="n">string</span>
140    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span> <span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span> <span class="c"># negative numbers, reserve space for the sign</span>
141    <span class="n">decimals</span> <span class="o">=</span> <span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">digits</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
142    <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">1e99</span><span class="p">:</span> <span class="c"># for very large numbers, use scientific notation and use all digits</span>
143        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">6</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
144    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">1e9</span><span class="p">:</span>
145        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">5</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
146    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="mi">4</span><span class="o">-</span><span class="n">decimals</span><span class="p">):</span> <span class="c"># make sure at least 4 decimals show</span>
147        <span class="c"># this clause is probably no longer needed since the number probably shows as 0.0</span>
148        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="n">digits</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
149        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
150    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">decimals</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span> <span class="c"># deal with large numbers in smaller spaces</span>
151        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">5</span><span class="p">)</span>
152        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
153    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span> <span class="c"># use f format for small numbers</span>
154        <span class="c"># this clause is probably no longer needed since the number probably shows as 0.0</span>
155        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span><span class="n">digits</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
156        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}f&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
157    <span class="k">else</span><span class="p">:</span> <span class="c"># in range where g formatting should do what I want</span>
158        <span class="c"># used? </span>
159        <span class="n">decimals</span> <span class="o">=</span> <span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>
160        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">digits</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
161    <span class="k">try</span><span class="p">:</span>
162        <span class="k">return</span> <span class="n">fmt</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">val</span><span class="p">))</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span>
163    <span class="k">except</span> <span class="ne">ValueError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
164        <span class="k">print</span> <span class="s">&#39;FormatValue Error with val,maxdigits,fmt=&#39;</span><span class="p">,</span><span class="n">val</span><span class="p">,</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">fmt</span>
165        <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
166</div>
167<div class="viewcode-block" id="FormatSigFigs"><a class="viewcode-back" href="../GSASIIGUIr.html#GSASIIpy3.FormatSigFigs">[docs]</a><span class="k">def</span> <span class="nf">FormatSigFigs</span><span class="p">(</span><span class="n">val</span><span class="p">,</span> <span class="n">maxdigits</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">sigfigs</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">treatAsZero</span><span class="o">=</span><span class="mf">1e-20</span><span class="p">):</span>
168    <span class="sd">&#39;&#39;&#39;Format a float to use ``maxdigits`` or fewer digits with ``sigfigs``</span>
169<span class="sd">    significant digits showing (if room allows).</span>
170
171<span class="sd">    :param float val: number to be formatted.</span>
172
173<span class="sd">    :param int maxdigits: the number of digits to be used for display of the</span>
174<span class="sd">       number (defaults to 10).</span>
175
176<span class="sd">    :param int sigfigs: the number of significant figures to use, if room allows</span>
177
178<span class="sd">    :param float treatAsZero: numbers that are less than this in magnitude</span>
179<span class="sd">      are treated as zero. Defaults to 1.0e-20, but this can be disabled</span>
180<span class="sd">      if set to None. </span>
181
182<span class="sd">    :returns: a string with &lt;= maxdigits characters (I hope).  </span>
183<span class="sd">    &#39;&#39;&#39;</span>
184    <span class="k">if</span> <span class="s">&#39;str&#39;</span> <span class="ow">in</span> <span class="nb">str</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">val</span><span class="p">))</span> <span class="ow">and</span> <span class="p">(</span><span class="n">val</span> <span class="o">==</span> <span class="s">&#39;?&#39;</span> <span class="ow">or</span> <span class="n">val</span> <span class="o">==</span> <span class="s">&#39;.&#39;</span><span class="p">):</span>
185        <span class="k">return</span> <span class="n">val</span>       
186    <span class="k">if</span> <span class="n">treatAsZero</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
187        <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">treatAsZero</span><span class="p">:</span>
188            <span class="k">return</span> <span class="s">&#39;0.0&#39;</span>
189    <span class="c"># negative numbers, leave room for a sign</span>
190    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span> <span class="n">maxdigits</span> <span class="o">-=</span> <span class="mi">1</span>
191    <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-99</span> <span class="ow">or</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">9.999e99</span><span class="p">:</span>
192        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">maxdigits</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span><span class="n">sigfigs</span><span class="p">)</span>
193        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span> <span class="c"># create format string</span>
194    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">1e-9</span> <span class="ow">or</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">9.999e9</span><span class="p">:</span>
195        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">maxdigits</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="n">sigfigs</span><span class="p">)</span>
196        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
197    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">9.9999999</span><span class="o">*</span><span class="mi">10</span><span class="o">**</span><span class="p">(</span><span class="n">sigfigs</span><span class="o">-</span><span class="n">maxdigits</span><span class="p">):</span>
198        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">maxdigits</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="n">sigfigs</span><span class="p">)</span>
199        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
200    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">10</span><span class="o">**</span><span class="n">sigfigs</span><span class="p">:</span> <span class="c"># deal with large numbers in smaller spaces</span>
201        <span class="n">decimals</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">maxdigits</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="n">sigfigs</span><span class="p">)</span>
202        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}g&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
203    <span class="k">elif</span> <span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span> <span class="c"># small numbers, add to decimal places</span>
204        <span class="n">decimals</span> <span class="o">=</span> <span class="n">sigfigs</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)))</span>
205        <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}f&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
206    <span class="k">else</span><span class="p">:</span> <span class="c"># larger numbers, remove decimal places</span>
207        <span class="n">decimals</span> <span class="o">=</span> <span class="n">sigfigs</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">-</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">val</span><span class="p">)))</span>
208        <span class="k">if</span> <span class="n">decimals</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span> 
209            <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.0f&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}.&quot;</span>
210        <span class="k">else</span><span class="p">:</span>
211            <span class="n">fmt</span> <span class="o">=</span> <span class="s">&quot;{&quot;</span> <span class="o">+</span> <span class="p">(</span><span class="s">&quot;:{:d}.{:d}f&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">maxdigits</span><span class="p">,</span><span class="n">decimals</span><span class="p">))</span><span class="o">+</span><span class="s">&quot;}&quot;</span>
212    <span class="k">try</span><span class="p">:</span>
213        <span class="k">return</span> <span class="n">fmt</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">val</span><span class="p">))</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span>
214    <span class="k">except</span> <span class="ne">ValueError</span> <span class="k">as</span> <span class="n">err</span><span class="p">:</span>
215        <span class="k">print</span> <span class="s">&#39;FormatValue Error with val,maxdigits, sigfigs, fmt=&#39;</span><span class="p">,</span><span class="n">val</span><span class="p">,</span> <span class="n">maxdigits</span><span class="p">,</span><span class="n">sigfigs</span><span class="p">,</span> <span class="n">fmt</span>
216        <span class="k">return</span> <span class="nb">str</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
217</div>
218<span class="k">if</span> <span class="n">__name__</span> <span class="o">==</span> <span class="s">&#39;__main__&#39;</span><span class="p">:</span>
219    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="p">(</span><span class="mf">1.23456789e-129</span><span class="p">,</span><span class="mf">1.23456789e129</span><span class="p">,</span><span class="mf">1.23456789e-99</span><span class="p">,</span><span class="mf">1.23456789e99</span><span class="p">,</span><span class="o">-</span><span class="mf">1.23456789e-99</span><span class="p">,</span><span class="o">-</span><span class="mf">1.23456789e99</span><span class="p">):</span>
220        <span class="k">print</span> <span class="n">FormatSigFigs</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="n">i</span>
221    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">100</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">100000</span><span class="p">,</span><span class="mi">1000000</span><span class="p">,</span><span class="mi">10000000</span><span class="p">,</span><span class="mi">100000000</span><span class="p">,</span><span class="mi">1000000000</span><span class="p">):</span>
222        <span class="k">print</span> <span class="n">FormatSigFigs</span><span class="p">(</span><span class="mf">1.23456789e-9</span><span class="o">*</span><span class="n">i</span><span class="p">),</span><span class="mf">1.23456789e-9</span><span class="o">*</span><span class="n">i</span>
223    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">100</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">100000</span><span class="p">,</span><span class="mi">1000000</span><span class="p">,</span><span class="mi">10000000</span><span class="p">,</span><span class="mi">100000000</span><span class="p">):</span>
224        <span class="k">print</span> <span class="n">FormatSigFigs</span><span class="p">(</span><span class="mf">1.23456789e9</span><span class="o">/</span><span class="n">i</span><span class="p">),</span><span class="mf">1.23456789e9</span><span class="o">/</span><span class="n">i</span>
225
226    <span class="k">print</span> <span class="n">FormatSigFigs</span><span class="p">(</span><span class="mi">200</span><span class="p">,</span><span class="mi">10</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
227</pre></div>
228
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