Wolfram Language & System 11.0 (2016)|Legacy Documentation

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represents the sequence of positions on the diagonal band that starts with {i,j} in a sparse array.

represents the positions between {imin,jmin,} and {imax,jmax,}.

represents positions starting with {imin,jmin,} and then moving with step {di,dj,}.


  • Band[pos]->v represents values v that repeat along the diagonal band starting at pos.
  • Band[pos]->{v1,v2,} represents a sequence of values vn 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 an 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[start,{-1,-1,}].
  • For scalar values, Band[start,end] is equivalent to Band[start,end,{1,1,}].
  • Band[start,end,step] stops when any coordinate first exceeds its value in end.
  • Band[start,end]->{v1,v2,} takes the values vn 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 vi are exhausted.
Introduced in 2007