Functions
int	SDPConeAddADotX (SDPCone sdpcone, int blockj, double alpha, double x[], int nn, double adotx[], int m)
	Compute the inner products of a dense matrix X with the data matrices. More...

int	SDPConeAddXVAV (SDPCone sdpcone, int blockj, double vin[], int n, double sum[], int mm)
	Compute $v^T A_{i,j} v$ for i = 0 through m. More...

int	SDPConeComputeS (SDPCone sdpcone, int blockj, double cc, double y[], int nvars, double r, int n, double s[], int nn)
	Compute the dual matrix S. More...

int	SDPConeComputeX (SDPCone sdpcone, int blockj, int n, double x[], int nn)
	Compute the matrix X. More...

int	SDPConeComputeXV (SDPCone sdpcone, int blockj, int *derror)
	Compute a factor V such that . More...

int	SDPConeGetBlockSize (SDPCone sdpcone, int blockj, int *n)
	Get the dimension of one block in the semidefinite cone. More...

int	SDPConeGetNumberOfBlocks (SDPCone sdpcone, int *nblocks)
	Get the number of blocks in the semidefinite cone. More...

int	SDPConeMatrixView (SDPCone sdpcone, int blockj)
	Print the dense array to the screen. More...

int	SDPConeRestoreXArray (SDPCone sdpcone, int blockj, double xx[], int nn)
	Restore the dense array and set these pointers to null. More...

int	SDPConeSetBlockSize (SDPCone sdpcone, int blockj, int n)
	Set the dimension of one block in the semidefinite cone. More...

int	SDPConeSetSparsity (SDPCone sdpcone, int blockj, int nnz)
	Set the number of nonzero matrices in a block of the semidefinite cone. More...

int	SDPConeSetXArray (SDPCone sdpcone, int blockj, int n, double xx[], int nn)
	Provide an array for the SDPCone object can use to store dense matrices. More...

int	SDPConeXVMultiply (SDPCone sdpcone, int blockj, double vin[], double vout[], int n)
	Multiply an array by a factor V such that . More...

Detailed Description

Additional routines that operate on the data.

#include dsdp5.h

In DSDP Standard Form a semidefinite program is given by the pair of problems

$\begin{array}{llllllllll} (P) \ \ \ & \mbox{minimize} & {\displaystyle \sum_{j=0}^{n_b-1} C_j \bullet X_j } &\mbox{subject to}& {\displaystyle \sum_{j=0}^{n_b-1} A_{i,j} \bullet X_{j} = b_i } ,& i=1,\ldots, m, & & X_j \succeq 0, \\ \end{array}$

$\begin{array}{lllllllll} (D) \ \ \ & \mbox{maximize} & {\displaystyle \sum_{i=1}^m b_i \ y_i } &\mbox{subject to}&{\displaystyle \sum_{i=1}^m A_{i,j}y_i + S_{j} } = C_{j}, & j=0, \ldots, n_b-1, & S_j \succeq 0 \\ \end{array}$

where the data $A_{i,j}$ and are symmetric matrices of the same dimension and the inner product of two $n \times n$ matrices $C=(c_{k,l})$ and $X=(x_{k,l})$ is defined by $C \bullet X := trace (C^T X) = \sum_{k,l}c_{k,l} x_{k,l}$ .

Blocks are labelled from 0 to nblocks, where nblocks is the total number of blocks in the SDPCone object.

Variables y are numbered 1 through m. Variable 0 designates the C matrices, which are also denoted $A_{0,j}$ .

Return values

0	if successful

Function Documentation

◆ SDPConeAddADotX()

int SDPConeAddADotX	(	SDPCone	sdpcone,
		int	blockj,
		double	alpha,
		double	x[],
		int	nn,
		double	adotx[],
		int	m
	)

Compute the inner products of a dense matrix X with the data matrices.

Parameters

sdpcone	semidefinite cone
blockj	block number
alpha	multiply inner product be this multiple
x	the dense array representing a matrix X.
nn	length of the array
adotx	array.
m	the length of the array and the number of variables y, plus two.

Definition at line 75 of file sdpcone.c.

◆ SDPConeAddXVAV()

int SDPConeAddXVAV	(	SDPCone	sdpcone,
		int	blockj,
		double	vin[],
		int	n,
		double	sum[],
		int	mm
	)

Compute $v^T A_{i,j} v$ for i = 0 through m.

Parameters

sdpcone	the SDP cone
blockj	block number
vin	array
n	dimension of the block and the length of the two arrays.
sum	input array
mm	the number of variables plus 2

See also: SDPConeAddADotX()

Definition at line 292 of file sdpcone.c.

Referenced by MaxCutRandomized(), and StableRandomized().

◆ SDPConeComputeS()

int SDPConeComputeS	(	SDPCone	sdpcone,
		int	blockj,
		double	cc,
		double	y[],
		int	nvars,
		double	r,
		int	n,
		double	s[],
		int	nn
	)

Compute the dual matrix S.

Parameters

sdpcone	semidefinite cone object
blockj	block number
cc	the multiple of the matrix C (or A_0)
y	an array of containing the variables y
nvars	the length of the array and the number of variables y
r	the multiple of the identity matrix to add
n	the dimension of the block
s	array to where the matrix S will be copied.
nn	length of the array s

Definition at line 42 of file sdpcone.c.

Referenced by DSDPPrintData(), and DSDPPrintSolution().

◆ SDPConeComputeX()

int SDPConeComputeX	(	SDPCone	sdpcone,
		int	blockj,
		int	n,
		double	x[],
		int	nn
	)

Compute the matrix X.

Parameters

sdpcone	semidefinite cone
n	di
blockj	block number
n	the dimension of the block
x	array to where the matrix X will be copied.
nn	length of the array x

See also: DSDPComputeX()

Definition at line 191 of file sdpcone.c.

◆ SDPConeComputeXV()

int SDPConeComputeXV	(	SDPCone	sdpcone,
		int	blockj,
		int *	derror
	)

Compute a factor V such that .

Parameters

sdpcone	the SDP cone
blockj	block number
derror	nonzero if no such factor could be computed.

See also: SDPConeXVMultiply()

This routine is helpful in semidefinite relaxations of combinatorial problems.

Definition at line 325 of file sdpcone.c.

Referenced by MaxCutRandomized(), and StableRandomized().

◆ SDPConeGetBlockSize()

int SDPConeGetBlockSize	(	SDPCone	sdpcone,
		int	blockj,
		int *	n
	)

Get the dimension of one block in the semidefinite cone.

Parameters

sdpcone	semidefinite cone object
blockj	block number
*n	set to the dimension of the block

See also: SDPConeSetBlockSize()

Definition at line 560 of file dsdpadddata.c.

Referenced by DSDPPrintData(), DSDPPrintSolution(), and SDPConeAddADotX().

◆ SDPConeGetNumberOfBlocks()

int SDPConeGetNumberOfBlocks	(	SDPCone	sdpcone,
		int *	nblocks
	)

Get the number of blocks in the semidefinite cone.

Parameters

sdpcone	semidefinite cone object
*nblocks	set to the dimension of the block

See also: DSDPCreateSDPCone()

Definition at line 578 of file dsdpadddata.c.

Referenced by DSDPPrintData(), and DSDPPrintSolution().

◆ SDPConeMatrixView()

int SDPConeMatrixView	(	SDPCone	sdpcone,
		int	blockj
	)

Print the dense array to the screen.

Parameters

sdpcone	semidefinite cone object
blockj	block number

See also: SDPConeGetXArray()

Definition at line 372 of file dsdpadddata.c.

◆ SDPConeRestoreXArray()

int SDPConeRestoreXArray	(	SDPCone	sdpcone,
		int	blockj,
		double *	xx[],
		int *	nn
	)

Restore the dense array and set these pointers to null.

Parameters

sdpcone	semidefinite cone object
blockj	block number
xx	address of an array for dense matrices
*nn	the length of the array

See also: SDPConeGetXArray()

Definition at line 351 of file dsdpadddata.c.

Referenced by DSDPPrintSolution().

◆ SDPConeSetBlockSize()

int SDPConeSetBlockSize	(	SDPCone	sdpcone,
		int	blockj,
		int	n
	)

Set the dimension of one block in the semidefinite cone.

Parameters

sdpcone	semidefinite cone object
blockj	block number
n	dimension of the block

Note: This routine is optional, but its use can help the object detect input errors.

Definition at line 535 of file dsdpadddata.c.

Referenced by LovaszTheta(), MaxCut(), mexFunction(), MinColoring(), ReadSDPAFile(), SDPConeCheckN(), and StableSet().

◆ SDPConeSetSparsity()

int SDPConeSetSparsity	(	SDPCone	sdpcone,
		int	blockj,
		int	nnz
	)

Set the number of nonzero matrices in a block of the semidefinite cone.

Parameters

sdpcone	semidefinite cone object
blockj	block number
nnz	number of nonzero matrices in the block

Note: This routine is optional, but its use can improve the memory allocation within the SDPCone object.

Definition at line 596 of file dsdpadddata.c.

Referenced by LovaszTheta(), mexFunction(), MinColoring(), ReadSDPAFile(), and StableSet().

◆ SDPConeSetXArray()

int SDPConeSetXArray	(	SDPCone	sdpcone,
		int	blockj,
		int	n,
		double	xx[],
		int	nn
	)

Provide an array for the SDPCone object can use to store dense matrices.

Parameters

sdpcone	semidefinite cone object
blockj	block number
n	dimension of the block
xx	array for dense matrices
nn	length of array

This routine elimates the need to copy the solution X into a separate array.

See also: SDPConeGetXArray()

Definition at line 278 of file dsdpadddata.c.

Referenced by mexFunction(), and ReadSDPAFile().

◆ SDPConeXVMultiply()

int SDPConeXVMultiply	(	SDPCone	sdpcone,
		int	blockj,
		double	vin[],
		double	vout[],
		int	n
	)

Multiply an array by a factor V such that .

Parameters

sdpcone	the SDP cone
blockj	block number
vin	input array
vout	the product V vin
n	dimension of the block and the length of the two arrays.

See also: SDPConeComputeXV(); SDPConeAddXVAV()

Definition at line 251 of file sdpcone.c.

Referenced by MaxCutRandomized(), and StableRandomized().

Functions

Detailed Description

Function Documentation

◆ SDPConeAddADotX()

◆ SDPConeAddXVAV()

◆ SDPConeComputeS()

◆ SDPConeComputeX()

◆ SDPConeComputeXV()

◆ SDPConeGetBlockSize()

◆ SDPConeGetNumberOfBlocks()

◆ SDPConeMatrixView()

◆ SDPConeRestoreXArray()

◆ SDPConeSetBlockSize()

◆ SDPConeSetSparsity()

◆ SDPConeSetXArray()

◆ SDPConeXVMultiply()