Conjugate transpose: Difference between revisions
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m (→{{header|Phix}}: use complex.e, added syntax colouring, marked p2js compatible) |
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=={{header|Phix}}== |
=={{header|Phix}}== |
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Note this code has no testing for non-square matrices. |
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<lang Phix> |
<!--<lang Phix>(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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type complex(sequence s) |
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return length(s)=2 and atom(s[REAL]) and atom(s[IMAG]) |
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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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end type |
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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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function c_add(complex a, complex b) |
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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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return sq_add(a,b) |
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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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end function |
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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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function c_mul(complex a, complex b) |
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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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return {a[REAL] * b[REAL] - a[IMAG] * b[IMAG], |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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a[REAL] * b[IMAG] + a[IMAG] * b[REAL]} |
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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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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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function c_conj(complex a) |
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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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return {a[REAL],-a[IMAG]} |
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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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end function |
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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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function c_print(complex a) |
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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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if a[IMAG]=0 then return sprintf("%g",a[REAL]) end if |
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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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return sprintf("%g%+gi",a) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end function |
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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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procedure m_print(sequence a) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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integer l = length(a) |
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for i=1 to l do |
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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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for j=1 to l do |
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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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a[i][j] = c_print(a[i][j]) |
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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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end for |
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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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a[i] = "["&join(a[i],",")&"]" |
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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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end for |
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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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puts(1,join(a,"\n")&"\n") |
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<span style="color: #000080;font-style:italic;">-- round to nearest billionth |
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end procedure |
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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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function conjugate_transpose(sequence a) |
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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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sequence res = a |
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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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integer l = length(a) |
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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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for i=1 to l do |
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<span style="color: #008080;">return</span> <span style="color: #000000;">0</span> |
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for j=1 to l do |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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res[i][j] = c_conj(a[j][i]) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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end for |
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<span style="color: #008080;">return</span> <span style="color: #000000;">1</span> |
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return res |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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end function |
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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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function m_unitary(sequence act) |
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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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-- note: a was normal and act = a*ct already |
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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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integer l = length(act) |
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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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for i=1 to l do |
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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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for j=1 to l do |
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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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atom {re,im} = act[i,j] |
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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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-- round to nearest billionth |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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-- (powers of 2 help the FPU out) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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re = round(re,1024*1024*1024) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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im = round(im,1024*1024*1024) |
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span> |
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if im!=0 |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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or (i=j and re!=1) |
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or (i!=j and re!=0) then |
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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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return 0 |
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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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end if |
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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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end for |
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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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end for |
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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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return 1 |
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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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end function |
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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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function m_mul(sequence a, sequence b) |
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-- but as it is, all tests pass with the builtin = operator.</span> |
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sequence res = sq_mul(a,0) |
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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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integer l = length(a) |
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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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for i=1 to l do |
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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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for j=1 to l do |
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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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for k=1 to l do |
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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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res[i][j] = c_add(res[i][j],c_mul(a[i][k],b[k][j])) |
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span> |
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end for |
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end for |
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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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end for |
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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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return res |
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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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end function |
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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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procedure test(sequence a) |
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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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sequence ct = conjugate_transpose(a) |
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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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printf(1,"Original matrix:\n") |
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m_print(a) |
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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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printf(1,"Conjugate transpose:\n") |
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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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m_print(ct) |
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-- note: rounding similar to that in m_unitary may be rqd (in a similar |
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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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-- loop in a new m_equal function) on these two equality tests, |
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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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-- but as it is, all tests pass with the builtin = operator. |
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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> |
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printf(1,"Hermitian?: %s\n",{iff(a=ct?"TRUE":"FALSE")}) -- (this one) |
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sequence act = m_mul(a,ct), cta = m_mul(ct,a) |
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<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> |
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bool normal = act=cta -- (&this one) |
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<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> |
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printf(1,"Normal?: %s\n",{iff(normal?"TRUE":"FALSE")}) |
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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;">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> |
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printf(1,"Unitary?: %s\n\n",{iff(normal and m_unitary(act)?"TRUE":"FALSE")}) |
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end procedure |
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<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> |
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<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> |
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constant x = sqrt(2)/2 |
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<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> |
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constant tests = {{{{3, 0},{2,1}}, |
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<!--</lang>--> |
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{{2,-1},{1,0}}}, |
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{{{ 1, 0},{ 1, 1},{ 0, 2}}, |
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{{ 1,-1},{ 5, 0},{-3, 0}}, |
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{{ 0,-2},{-3, 0},{ 0, 0}}}, |
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{{{0.5,+0.5},{0.5,-0.5}}, |
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{{0.5,-0.5},{0.5,+0.5}}}, |
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{{{ 1, 0},{ 1, 0},{ 0, 0}}, |
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{{ 0, 0},{ 1, 0},{ 1, 0}}, |
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{{ 1, 0},{ 0, 0},{ 1, 0}}}, |
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{{{x, 0},{x, 0},{0, 0}}, |
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{{0,-x},{0, x},{0, 0}}, |
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{{0, 0},{0, 0},{0, 1}}}, |
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{{{2,7},{9,-5}}, |
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{{3,4},{8,-6}}}} |
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for i=1 to length(tests) do test(tests[i]) end for</lang> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Original matrix: |
Original matrix: |
||
[3,2+ |
[3,2+i] |
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[2- |
[2-i,1] |
||
Conjugate transpose: |
Conjugate transpose: |
||
[3,2+ |
[3,2+i] |
||
[2- |
[2-i,1] |
||
Hermitian?: |
Hermitian?: true |
||
Normal?: |
Normal?: true |
||
Unitary?: |
Unitary?: false |
||
Original matrix: |
Original matrix: |
||
[1,1+ |
[1,1+i,2i] |
||
[1- |
[1-i,5,-3] |
||
[ |
[-2i,-3,0] |
||
Conjugate transpose: |
Conjugate transpose: |
||
[1,1+ |
[1,1+i,2i] |
||
[1- |
[1-i,5,-3] |
||
[ |
[-2i,-3,0] |
||
Hermitian?: |
Hermitian?: true |
||
Normal?: |
Normal?: true |
||
Unitary?: |
Unitary?: false |
||
Original matrix: |
Original matrix: |
||
Line 2,594: | Line 2,574: | ||
[0.5-0.5i,0.5+0.5i] |
[0.5-0.5i,0.5+0.5i] |
||
[0.5+0.5i,0.5-0.5i] |
[0.5+0.5i,0.5-0.5i] |
||
Hermitian?: |
Hermitian?: false |
||
Normal?: |
Normal?: true |
||
Unitary?: |
Unitary?: true |
||
Original matrix: |
Original matrix: |
||
Line 2,606: | Line 2,586: | ||
[1,1,0] |
[1,1,0] |
||
[0,1,1] |
[0,1,1] |
||
Hermitian?: |
Hermitian?: false |
||
Normal?: |
Normal?: true |
||
Unitary?: |
Unitary?: false |
||
Original matrix: |
Original matrix: |
||
[0.707107,0.707107,0] |
[0.707107,0.707107,0] |
||
[ |
[-0.707107i,0.707107i,0] |
||
[0,0, |
[0,0,i] |
||
Conjugate transpose: |
Conjugate transpose: |
||
[0.707107, |
[0.707107,0.707107i,0] |
||
[0.707107, |
[0.707107,-0.707107i,0] |
||
[0,0, |
[0,0,-i] |
||
Hermitian?: |
Hermitian?: false |
||
Normal?: |
Normal?: true |
||
Unitary?: |
Unitary?: true |
||
Original matrix: |
Original matrix: |
||
Line 2,628: | Line 2,608: | ||
[2-7i,3-4i] |
[2-7i,3-4i] |
||
[9+5i,8+6i] |
[9+5i,8+6i] |
||
Hermitian?: |
Hermitian?: false |
||
Normal?: |
Normal?: false |
||
Unitary?: |
Unitary?: false |
||
</pre> |
</pre> |
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