This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Band

Band
represents the sequence of positions on the diagonal band that starts with in a sparse array.
Band
represents the positions between and .
Band
represents positions starting with and then moving with step .
  • Band[pos]->v represents values v that repeat along the diagonal band starting at pos.
  • Band[pos]->{v1, v2, ...} represents a sequence of values along the diagonal band starting at pos.
  • With an array a of the same rank as the whole sparse array, Band[start]->a by default inserts a at the position specified by start.
  • With arrays of the same rank as the whole sparse array, Band[pos]->{a1, a2, ...} represents a sequence of non-overlapping subarrays.
  • Band[start] is effectively equivalent to Band.
  • For scalar values, Band is equivalent to Band.
  • Band stops when any coordinate first exceeds its value in end.
  • Band[start, end]->{v1, v2, ...} takes the values to repeat cyclically until end is reached.
  • Band[start, Automatic, step]->a continues until the edge of the array is reached.
  • Band[start, Automatic, step]->{v1, v2, ...} continues until the are exhausted.
Create a band diagonal matrix:
Convert to normal lists:
Create a band diagonal matrix:
In[1]:=
Click for copyable input
Out[1]//MatrixForm=
Convert to normal lists:
In[2]:=
Click for copyable input
Out[2]=
Mix Band with other SparseArray element specifications:
Give explicit values to fill in on the band:
Repeat the values cyclically:
Start the band at any position in the matrix:
Specify any start and end locations:
Step by 2 between elements on the band:
Any step can be used:
Automatically continue the band to the edge of the array:
Specify a band that is part of a row:
Specify an anti-diagonal matrix:
Insert a submatrix beginning at position 3, 3:
Cyclically repeat the submatrix:
Alternate the submatrix with a single element:
Band works in sparse arrays of any rank:
Fill in a plane of values into a 3D sparse array:
Make a tridiagonal matrix:
Build a tridiagonal linear system:
Band works in SparseArray; use Normal to convert to normal lists:
The simplest case of Band is equivalent to DiagonalMatrix:
New in 6