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Re: check if a square matrix is diagonal
*To*: mathgroup at smc.vnet.net
*Subject*: [mg115366] Re: check if a square matrix is diagonal
*From*: Bill Rowe <readnews at sbcglobal.net>
*Date*: Sun, 9 Jan 2011 02:17:54 -0500 (EST)
On 1/8/11 at 3:39 AM, akoz at mimuw.edu.pl (Andrzej Kozlowski) wrote:
>An simpler approach is:
>diagonalQ[m_] := UpperTriangularize[m] = LowerTriangularize[m]
>This is slower for diagonal matrices but very much faster for
>non-diagonal ones.
Even simpler is the suggestion Dr Bob made:
m==DiagonalMatrix[Diagonal@m]
And after I had made my post I thought of something else that
seems fast which is
Total[Unitize@m,2]==Total[Unitize@Diagonal[m]]
It terms of speed for non-diagonal matrices, the simple method
suggested by Dr Bob is the fastest
In[1]:= m = RandomReal[1, {10000, 10000}];
In[2]:= Timing[UpperTriangularize[m] == LowerTriangularize[m]]
Out[2]= {2.51418,False}
In[3]:= Timing[Total[Unitize@m, 2] == Total[Unitize@Diagonal[m]]]
Out[3]= {1.09644,False}
In[4]:= Timing[m == DiagonalMatrix[Diagonal@m]]
Out[4]= {0.770909,False}
But for a diagonal matrix
In[5]:= m = SparseArray[Band[{1, 1}] -> RandomReal[1, {10000}]];
In[6]:= Timing[UpperTriangularize[m] == LowerTriangularize[m]]
Out[6]= {0.099239,True}
In[7]:= Timing[Total[Unitize@m, 2] == Total[Unitize@Diagonal[m]]]
Out[7]= {0.049362,True}
In[9]:= Timing[m == DiagonalMatrix[Diagonal@m]]
Out[9]= {0.067637,True}
It appears using Total and Unitize to count the non-zero entries
of m is faster.
it would seem
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