Built-in Mathematica Symbol

Band

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

Band[{i_min, j_min, ...}, {i_max, j_max, ...}]
represents the positions between {i_min, j_min, ...} and {i_max, j_max, ...}.

Band[{i_min, j_min, ...}, {i_max, j_max, ...}, {di, dj, ...}]
represents positions starting with {i_min, j_min, ...} and then moving with step {di, dj, ...}.

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 v_n 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 a_n 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 v_n 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 v_i are exhausted.

EXAMPLES

CLOSE ALL

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: