Getting Pieces of MatricesExtracting elements, rows, and columns of a sparse matrix is quite straightforward with the Mathematica function Part. Typically Part is entered with [[ ]] notation. Ways to get pieces of matrices. Here is a sample sparse matrix. In[1]:=  |
Out[2]//MatrixForm=
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This gets the third element in the first row. In[3]:=  |
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This gets the third row; the row is returned as a sparse vector. In[4]:=  |
Out[4]=
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It can also obtain a column by using All to specify all rows; the column is returned as a sparse vector. In[5]:=  |
Out[5]=
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Negative indices are used to refer to the end of the matrix. The following gets the last element of the last row. In[6]:=  |
Out[6]=
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The function Tr works on the diagonal elements of a matrix. The one argument form adds them up. In[7]:=  |
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Tr can also take a function as its second argument, which will apply to the diagonal elements. If List is used, this returns the diagonal elements. In[8]:=  |
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Getting Multiple PiecesIt is possible to extract multiple elements by using indices in lists. This will be demonstrated with the following sample matrix. In[1]:=  |
Out[2]//MatrixForm=
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The following gets the first and third elements of the third row. In[3]:=  |
Out[3]=
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The following gets the first and third rows. In[4]:=  |
Out[4]=
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The following gets the first and third elements of the first and second rows. In[5]:=  |
Out[5]=
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