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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

MORE INFORMATION

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.

EXAMPLES

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Basic Examples (1)

Create a band diagonal matrix:

Convert to normal lists:

Create a band diagonal matrix:

In[1]:=

Out[1]//MatrixForm=

Convert to normal lists:

In[2]:=

Out[2]=

Scope (11)

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:

Generalizations & Extensions (2)

Band works in sparse arrays of any rank:

Fill in a plane of values into a 3D sparse array:

Applications (2)

Make a tridiagonal matrix:

Build a tridiagonal linear system:

Properties & Relations (2)

Band works in SparseArray; use Normal to convert to normal lists:

The simplest case of Band is equivalent to DiagonalMatrix: