How to | Update Parts of a Matrix
Mathematica has many matrix operations that support operations such as building, computing, and visualizing matrices. It also has a rich language for picking out parts of matrices and assigning new values to them.
Define the following matrix:
Out[2]//MatrixForm= |
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Use 
(the short form of Part) on the left-hand side of an assignment to set an element:
| Out[3]= |  |
This shows that the element at position (1, 2) has been updated:
Out[4]//MatrixForm= |
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To set an entire row, use one index to specify the row and assign it to the new row:
Out[6]//MatrixForm= |
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To set an entire column, select all rows with All and specify the column:
Out[8]//MatrixForm= |
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To set a submatrix you can use the short form of Span (
).
First set up a 5×5 matrix of random integers between 0 and 10:
Out[25]//MatrixForm= |
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The top-left 3×4 matrix highlighted here corresponds to rows 1 through 3 and columns 1 through 4:
| Out[49]= |  |
Update the highlighted submatrix by using the short form of Span (
) to specify the relevant span of rows and columns:
Out[27]//MatrixForm= |
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Update all elements except the outermost rows and columns (negative indices count from the end):
Out[29]//MatrixForm= |
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When you update a large matrix you should try to avoid doing this in a loop. If you can use one of the updating techniques to update all elements in one command, this will typically be much faster:
This is a slow way to update every element in a row:
| Out[37]= |  |
This is much faster:
| Out[38]= |  |
If you cannot avoid updating a matrix in a loop, you need to take care to avoid extra references to the matrix. Otherwise the matrix will be copied and the loop will not run very fast:
This takes care to avoid extra references. The loop runs quite fast:
| Out[40]= |  |
This makes a copy of the matrix at every step, and the loop does not run very fast:
| Out[41]= |  |
