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Task/Conjugate-transpose/Phix/conjugate-transpose.phix
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Task/Conjugate-transpose/Phix/conjugate-transpose.phix
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">include</span> <span style="color: #004080;">complex</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">m_print</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_sprint</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"["</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #008000;">","</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"]"</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">conjugate_transpose</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_conjugate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">m_unitary</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">act</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- note: a was normal and act = a*ct already</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">act</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">re</span><span style="color: #0000FF;">,</span><span style="color: #000000;">im</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">act</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
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<span style="color: #000080;font-style:italic;">-- round to nearest billionth
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-- (powers of 2 help the FPU out)</span>
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<span style="color: #000000;">re</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">re</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">im</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">im</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">*</span><span style="color: #000000;">1024</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">im</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span>
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<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">j</span> <span style="color: #008080;">and</span> <span style="color: #000000;">re</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">j</span> <span style="color: #008080;">and</span> <span style="color: #000000;">re</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">m_mul</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">complex_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">complex_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">ct</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">conjugate_transpose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Original matrix:\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">m_print</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Conjugate transpose:\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">m_print</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ct</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">-- note: rounding similar to that in m_unitary may be rqd (in a similar
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-- loop in a new m_equal function) on these two equality tests,
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-- but as it is, all tests pass with the builtin = operator.</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Hermitian?: %t\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">ct</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (this one)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">act</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ct</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">cta</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">m_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ct</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">bool</span> <span style="color: #000000;">normal</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">act</span><span style="color: #0000FF;">=</span><span style="color: #000000;">cta</span> <span style="color: #000080;font-style:italic;">-- (&this one)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Normal?: %t\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">normal</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Unitary?: %t\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">normal</span> <span style="color: #008080;">and</span> <span style="color: #000000;">m_unitary</span><span style="color: #0000FF;">(</span><span style="color: #000000;">act</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}}},</span>
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<span style="color: #0000FF;">{{{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}}},</span>
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<span style="color: #0000FF;">{{{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">}}},</span>
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<span style="color: #0000FF;">{{{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
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<span style="color: #0000FF;">{{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}}},</span>
|
||||
|
||||
<span style="color: #0000FF;">{{{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
|
||||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">x</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}},</span>
|
||||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}}},</span>
|
||||
|
||||
<span style="color: #0000FF;">{{{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">5</span><span style="color: #0000FF;">}},</span>
|
||||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}}}</span>
|
||||
|
||||
<span style="color: #7060A8;">papply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">,</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
Loading…
Add table
Add a link
Reference in a new issue