Band

Band[{i,j}]

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

Band[{imin,jmin,},{imax,jmax,}]

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

Band[{imin,jmin,},{imax,jmax,},{di,dj,}]

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

Details

  • 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.

Examples

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Basic Examples  (1)

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]=

Scope  (11)

Generalizations & Extensions  (2)

Applications  (2)

Properties & Relations  (2)

See Also

ArrayFlatten  ArrayPad  SparseArray  Minors  DiagonalMatrix  Take  Span  Diagonal  LowerTriangularize  UpperTriangularize  Extract

Tutorials

Introduced in 2007
(6.0)