Bout = spdiags(A)
extracts the nonzero diagonals from m-by-n matrix
A and returns them as the columns in
min(m,n)-by-p matrix Bout,
where p is the number of nonzero diagonals.

The columns of the first output Bout contain the nonzero diagonals of A. The second output d lists the indices of the nonzero diagonals of A. The longest nonzero diagonal in A is in column 3 of Bout. To give all columns of Bout the same length, the other nonzero diagonals of A have extra zeros added to their corresponding columns in Bout. For m-by-n matrices with m < n, the rules are:

For nonzero diagonals below the main diagonal of A, extra zeros are added at the tops of columns (as in the first two columns of Bout).

For nonzero diagonals above the main diagonal of A, extra zeros are added at the bottoms of columns (as in the last column of Bout).

spdiags pads Bout with zeros in this manner even if the longest diagonal is not returned in Bout.

Extract the main diagonal, and the first diagonals above and below it.

d = [-1 0 1];
Bout = spdiags(A,d)

Bout = 5×3
10 9 0
6 3 1
5 10 10
10 8 10
0 7 10

Try to extract the fifth super-diagonal (d = 5). Because A has only four super-diagonals, spdiags returns the diagonal as all zeros of the same length as the main (d = 0) diagonal.

Use spdiags to create a square 6-by-6 matrix with several of the columns of Bin as diagonals. Because some of the diagonals only have one or two elements, there is a mismatch in sizes between the columns in Bin and diagonals in A.

d = [-4 -2 -1 0 3 4 5];
A = spdiags(Bin,d,6,6);
full(A)

Each of the columns in Bin has six elements, but only the main diagonal in A has six elements. Therefore, all the other diagonals in A truncate the elements in the columns of Bin so that they fit on the selected diagonals:

The way spdiags truncates the diagonals depends on the size of m-by-n matrix A. When $\mathit{m}\ge \mathit{n}$, the behavior is as pictured above:

Diagonals below the main diagonal take elements from the tops of the columns first.

Diagonals above the main diagonal take elements from the bottoms of columns first.

This behavior reverses when $\mathit{m}<\mathit{n}$:

Input matrix. This matrix is typically (but not necessarily) sparse.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical Complex Number Support: Yes

d — Diagonal numbers scalar | vector

Diagonal numbers, specified as a scalar or vector of positive integers. The diagonal
numbers follow the same conventions as diag:

d < 0 is below the main diagonal, and satisfies d
>= -(m-1).

d = 0 is the main diagonal.

d > 0 is above the main diagonal, and satisfies d
<= (n-1).

An m-by-n matrix A has
(m + n - 1) diagonals. These diagonals are specified in the vector
d using indices from -(m-1) to
(n-1). For example, if A is 5-by-6, it has 10
diagonals, which are specified in the vector d using the indices -4,
-3 , ... 4, 5. The following diagram illustrates this diagonal numbering.

If you specify a diagonal that lies outside of A (such as
d = 7 in the example above), then spdiags
returns that diagonal as all zeros.

Example: spdiags(A,[3 5]) extracts the third and fifth diagonals
from A.

Bin — Diagonal elements matrix

Diagonal elements, specified as a matrix. This matrix is typically (but not
necessarily) full. spdiags uses the columns of
Bin to replace specified diagonals in A. If the
requested size of the output is m-by-n, then
Bin must have min(m,n) columns.

With the syntax S = spdiags(Bin,d,m,n), if a column of
Bin has more elements than the diagonal it is replacing, and
m >= n, then spdiags takes elements of
super-diagonals from the lower part of the column of
Bin, and elements of sub-diagonals from the
upper part of the column of Bin. However, if
m < n , then super-diagonals are from the
upper part of the column of Bin, and
sub-diagonals from the lower part. For an example of this behavior,
see Columns and Diagonals of Different Sizes.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical Complex Number Support: Yes

m, n — Dimension sizes nonnegative scalar integers

Dimension sizes, specified as nonnegative scalar integers.
spdiags uses these inputs to determine how large a matrix to
create.

Example: spdiags(Bin,d,300,400) creates a 300-by-400 matrix with
the columns of B placed along the specified diagonals
d.

Diagonal elements, returned as a full matrix. The columns of Bout
contain diagonals extracted from A. Any elements of
Bout corresponding to positions outside of A are
set to zero.

id — Diagonal numbers column vector

Diagonal numbers, returned as a column vector. See d for a
description of the diagonal numbering.

S — Output matrix matrix

Output matrix. S takes one of two forms:

With S = spdiags(Bin,d,A), the specified diagonals in
A are replaced with the columns in Bin to
create S.

With S = spdiags(Bin,d,m,n), the
m-by-n sparse matrix S
is formed by taking the columns of Bin and placing them along
the diagonals specified by d.

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

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