# spDiagRvMat¶

## Purpose¶

Inserts submatrices along the diagonal of a sparse matrix.

## Format¶

y = spDiagRvMat(x, inds, size, a)
Parameters: x (MxN sparse matrix) – data inds (Kx2 vector or scalar 0) – row and column indices into x at which to place the corresponding submatrices in a. size (Kx2 vector or scalar 0) – sizes of the corresponding submatrices in a. a (KxLxP array) – containing the submatrices to insert into x. y (MxN sparse matrix) – a copy of x containing the specified insertions.

## Examples¶

declare sparse matrix x,y;

// Create a 10x10 sparse identity matrix
x = spEye(10);

sx1 = { 2 3, 5 8 };
sx2 = { 8 2 3 4, 7 9 5 6, 3 2 8 4 };
sx3 = { 4 7 2, 6 5 3 };
sx4 = { 9, 3 };

// Create a 4x3x4 dimensional array with every element set
// to 0
a = arrayinit(4|3|4, 0);

// Set some of the array values
a[1, 1:2, 1:2] = sx1;
a[2, ., .] = sx2;
a[3, 1:2, 1:3] = sx3;
a[4, 1:2, 1] = sx4;

The value of a is now:

Plane [1,.,.]

2.00000000    3.00000000    0.00000000    0.00000000
5.00000000    8.00000000    0.00000000    0.00000000
0.00000000    0.00000000    0.00000000    0.00000000

Plane [2,.,.]

8.00000000    2.00000000    3.00000000    4.00000000
7.00000000    9.00000000    5.00000000    6.00000000
3.00000000    2.00000000    8.00000000    4.00000000

Plane [3,.,.]

4.00000000    7.00000000    2.00000000    0.00000000
6.00000000    5.00000000    3.00000000    0.00000000
0.00000000    0.00000000    0.00000000    0.00000000

Plane [4,.,.]

9.00000000    0.00000000    0.00000000    0.00000000
3.00000000    0.00000000    0.00000000    0.00000000
0.00000000    0.00000000    0.00000000    0.00000000
inds = 0;
siz = { 2 2, 3 4, 2 3, 2 1 };

y = spDiagRvMat(x, inds, siz, a);

The output, in variable y, is:

2  3  0  0  0  0  0  0  0  0
5  8  0  0  0  0  0  0  0  0
0  0  8  2  3  4  0  0  0  0
0  0  7  9  5  6  0  0  0  0
0  0  3  2  8  4  0  0  0  0
0  0  0  0  0  1  4  7  2  0
0  0  0  0  0  0  6  5  3  0
0  0  0  0  0  0  0  1  0  9
0  0  0  0  0  0  0  0  1  3
0  0  0  0  0  0  0  0  0  1

## Remarks¶

Each row of inds must contain the row and column indices, respectively, that form the starting point for the insertion of the corresponding submatrix in a. If inds is a scalar 0, the starting point for the insertion of each submatrix will be one row and one column past the ending point of the previous insertion. The first insertion will begin at the $$[1, 1]$$ element.

Each row of size must contain the number of rows and columns in the corresponding submatrix in a. This allows you to insert submatrices of different sizes $$L_i \times P_i$$ by inserting them into the planes of an array that is $$K \times MAX(L) \times MAX(P)$$ and padding the submatrices with zeros to $$MAX(L) \times MAX(P)$$. For each plane in a, spDiagRvMat() extracts the submatrix a[i, 1:size[i, 1], 1:size[i, 2]] and inserts that into x at the location indicated by the corresponding row of inds. If size is a scalar 0, then each LxP plane of a is inserted into x as is.