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# pack

Compress a list of block-diagonal symmetric matrices.

### Syntax

CA = pack(A,blocksizes) [CA,sel] = pack(A,blocksizes)

### Arguments

- A
m-by-n real matrix of doubles, the entries of a list of block-diagonal symmetric matrices. n is the number of matrices stored into

`A`

.- blocksizes
b-by-1 real matrix of doubles, the sizes of the blocks.

- CA
p-by-n real matrix of doubles, a compressed representation of

`A`

.- sel
1-by-s real matrix of doubles, the indices of the rows of

`A`

which have been selected in`CA`

.

### Description

This function takes as input argument a list of
block-diagonal matrices stored in the m-by-n matrix `A`

.
Only the non-zero entries of the block-diagonal matrices are stored.
The integer `n`

is the number of block-diagonal matrices,
while the integer `m`

is the number of nonzero entries of
one single block-diagonal matrix.
The function removes the symmetric entries, and returns in `CA`

the compressed representation of `A`

.

In the `CA`

matrix, the symmetric entries stored in `A`

have been removed.
The rows which have been selected in `CA`

are stored in the vector
`sel`

, so that, on output, we have
`CA == A(sel,:)`

.

For example, the matrix

is stored as

[1; 2; 3; 4; 5; 6; 7; 8; 9; 10]

with `blocksizes=[2,3,1]`

.

This function is designed to be used when preparing the input arguments of the
`semidef`

function.

### Examples

In the following example, we compress a single block-diagonal symmetric matrix `Z`

.
This is the example presented in "SP: Software for Semidefinite Programming, User's Guide, Beta Version",
November 1994, L. Vandenberghe and S. Boyd, 1994, on page 5.

Z = [ 1 2 0 0 0 0 2 3 0 0 0 0 0 0 4 5 6 0 0 0 5 7 8 0 0 0 6 8 9 0 0 0 0 0 0 10 ]; blocksizes=[2,3,1]; Z1 = Z(1:2,1:2); Z2 = Z(3:5,3:5); Z3 = Z(6,6); A = list2vec(list(Z1,Z2,Z3)); [CA,sel] = pack(A,blocksizes)

In the following example, we compress three block-diagonal symmetric matrices `F0`

,
`F1`

and `F2`

.

// Define 3 symmetric block-diagonal matrices: F0, F1, F2 F0=[2,1,0,0; 1,2,0,0; 0,0,3,1; 0,0,1,3] F1=[1,2,0,0; 2,1,0,0; 0,0,1,3; 0,0,3,1] F2=[2,2,0,0; 2,2,0,0; 0,0,3,4; 0,0,4,4] // Define the size of the two blocks: // the first block has size 2, // the second block has size 2. blocksizes=[2,2]; // Extract the two blocks of the matrices. F01=F0(1:2,1:2); F02=F0(3:4,3:4); F11=F1(1:2,1:2); F12=F1(3:4,3:4); F21=F2(1:2,1:2); F22=F2(3:4,3:4); // Create 3 column vectors, containing nonzero entries // in F0, F1, F2. F0nnz = [F01(:);F02(:)]; F1nnz = [F11(:);F12(:)]; F2nnz = [F21(:);F22(:)]; // Create a 16-by-3 matrix, representing the // nonzero entries of the 3 matrices F0, F1, F2. A=[F0nnz,F1nnz,F2nnz] // Pack the list of matrices A into CA. [CA,sel] = pack(A,blocksizes) // Check that CA == A(sel,:) A(sel,:)

### References

L. Vandenberghe and S. Boyd, " Semidefinite Programming," Informations Systems Laboratory, Stanford University, 1994.

Ju. E. Nesterov and M. J. Todd, "Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming," Working Paper, CORE, Catholic University of Louvain, Louvain-la-Neuve, Belgium, April 1994.

SP: Software for Semidefinite Programming, User's Guide, Beta Version, November 1994, L. Vandenberghe and S. Boyd, 1994 http://www.ee.ucla.edu/~vandenbe/sp.html

### See also

- unpack — Uncompress a list of block-diagonal symmetric matrices.

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