Detailed Description

Interface and wrapper to matrix/factorization (ladel) functions.

Author: Ben Hermans

This file includes all calls to ladel functions apart from scaling in scaling.c and memory allocation/deallocation in the main functions in qpalm.c. It includes all matrix operations, such as matrix vector products, row- and columnwise norms, cholesky factorizations, factorization updates and solving the linear system.

Definition in file solver_interface.c.

#include <qpalm/lin_alg.h>
#include <qpalm/solver_interface.h>
#include <stdio.h>
#include <ladel.h>

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Functions
void	qpalm_set_factorization_method (QPALMWorkspace work, solver_common c)
	Choose the linear systems solver method based on the problem data sizes.

void	mat_vec (solver_sparse A, solver_dense x, solver_dense y, solver_common c)
	Matrix-vector multiplication.

void	mat_tpose_vec (solver_sparse A, solver_dense x, solver_dense y, solver_common c)
	Matrix-transpose-vector multiplication.

void	qpalm_form_kkt (QPALMWorkspace *work)
	Form the KKT system \(\begin{bmatrix} Q & A^T \\ A & -\Sigma^{-1} \end{bmatrix} \).

void	qpalm_reform_kkt (QPALMWorkspace *work)
	Reform the KKT system (i.e.

void	kkt_update_entering_constraints (QPALMWorkspace work, solver_common c)
	Perform a factorization update for the entering constraints.

void	kkt_update_leaving_constraints (QPALMWorkspace work, solver_common c)
	Perform a factorization update for the leaving constraints.

void	kkt_solve (QPALMWorkspace work, solver_common c)
	Solve the KKT system \(\begin{bmatrix} Q + \frac{1}{\gamma}I & A^T \\ A & -\Sigma^{-1} \end{bmatrix} \begin{bmatrix} d \\ -\lambda \end{bmatrix} = \begin{bmatrix} -\nabla \varphi \\ 0 \end{bmatrix} \).

void	ldlchol (solver_sparse M, QPALMWorkspace work, solver_common *c)
	Calculate \(LDL^T\) factorization of a matrix \(M\).

void	ldlcholQAtsigmaA (QPALMWorkspace work, solver_common c)
	Calculate \(LDL^T\) factorization of \(Q+A{(a,:)}^T\Sigma{(a,a)}A{(a,:)}\), with \(\Sigma=diag(\sigma)\) and \(a\) the set of active constraints.

void	ldlupdate_entering_constraints (QPALMWorkspace work, solver_common c)
	Update the \(LDL^T\) factorization given a set of entering constraints.

void	ldldowndate_leaving_constraints (QPALMWorkspace work, solver_common c)
	Downdate the \(LDL^T\) factorization given a set of leaving constraints.

void	ldlupdate_sigma_changed (QPALMWorkspace work, solver_common c)
	Update the \(LDL^T\) factorization given a set of indexes where \(sigma\) has been updated.

void	ldlsolveLD_neg_dphi (QPALMWorkspace work, solver_common c)
	Solve the linear system \(LDL^T*d = -\nabla \varphi\).

Function Documentation

◆ qpalm_set_factorization_method()

void qpalm_set_factorization_method	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Choose the linear systems solver method based on the problem data sizes.

This chooses between forming and solving the KKT system or the SCHUR complement. The resulting method is in work->solver->factorization_method.

Parameters

work	Workspace
c	Linear systems solver environment

Definition at line 18 of file solver_interface.c.

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◆ mat_vec()

void mat_vec	(	solver_sparse *	A,
		solver_dense *	x,
		solver_dense *	y,
		solver_common *	c
	)

Matrix-vector multiplication.

\(y = A*x\)

Parameters

A	Sparse matrix
x	Dense input vector
y	Dense output vector
c	Solver environment

Definition at line 73 of file solver_interface.c.

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◆ mat_tpose_vec()

void mat_tpose_vec	(	solver_sparse *	A,
		solver_dense *	x,
		solver_dense *	y,
		solver_common *	c
	)

Matrix-transpose-vector multiplication.

\(y = A^T*x\)

Parameters

A	Sparse matrix
x	Dense input vector
y	Dense output vector
c	Solver environment

Definition at line 93 of file solver_interface.c.

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◆ qpalm_form_kkt()

void qpalm_form_kkt ( QPALMWorkspace * work )

Form the KKT system \(\begin{bmatrix} Q & A^T \\ A & -\Sigma^{-1} \end{bmatrix} \).

The result is in work->solver->kkt.

Note: Only the rows of A corresponding to active constraints are included in the system above. This routine also saves some structures that are useful in updating the kkt system later.

Parameters

work Workspace

Definition at line 114 of file solver_interface.c.

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◆ qpalm_reform_kkt()

void qpalm_reform_kkt ( QPALMWorkspace * work )

Reform the KKT system (i.e.

delete constraints which are no longer active and add those that are now active).

Parameters

work Workspace

Definition at line 172 of file solver_interface.c.

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◆ kkt_update_entering_constraints()

void kkt_update_entering_constraints	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Perform a factorization update for the entering constraints.

Parameters

work	Workspace
c	Linear systems solver environment

Definition at line 197 of file solver_interface.c.

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◆ kkt_update_leaving_constraints()

void kkt_update_leaving_constraints	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Perform a factorization update for the leaving constraints.

Parameters

work	Workspace
c	Linear systems solver environment

Definition at line 215 of file solver_interface.c.

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◆ kkt_solve()

void kkt_solve	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Solve the KKT system \(\begin{bmatrix} Q + \frac{1}{\gamma}I & A^T \\ A & -\Sigma^{-1} \end{bmatrix} \begin{bmatrix} d \\ -\lambda \end{bmatrix} = \begin{bmatrix} -\nabla \varphi \\ 0 \end{bmatrix} \).

Parameters

work	Workspace
c	Linear systems solver environment

Definition at line 233 of file solver_interface.c.

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◆ ldlchol()

void ldlchol	(	solver_sparse *	M,
		QPALMWorkspace *	work,
		solver_common *	c
	)

Calculate \(LDL^T\) factorization of a matrix \(M\).

If work->settings->proximal = true, use \(M+\frac{1}{\gamma}*I\) instead.

Parameters

M	Matrix to be factorized
work	Workspace
c	Solver environment

Definition at line 246 of file solver_interface.c.

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◆ ldlcholQAtsigmaA()

void ldlcholQAtsigmaA	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Calculate \(LDL^T\) factorization of \(Q+A{(a,:)}^T*\Sigma{(a,a)}*A{(a,:)}\), with \(\Sigma=diag(\sigma)\) and \(a\) the set of active constraints.

If work->settings->proximal = true, use \(Q+\frac{1}{\gamma}*I+A{(a,:)}^T*\Sigma{(a,a)}*A{(a,:)}\) instead.

Parameters

work	Workspace
c	Solver environment

Definition at line 274 of file solver_interface.c.

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◆ ldlupdate_entering_constraints()

void ldlupdate_entering_constraints	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Update the \(LDL^T\) factorization given a set of entering constraints.

The index set of entering constraints is assumed to be set in work->solver->enter.

Parameters

work	Workspace
c	Solver environment

Definition at line 297 of file solver_interface.c.

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◆ ldldowndate_leaving_constraints()

void ldldowndate_leaving_constraints	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Downdate the \(LDL^T\) factorization given a set of leaving constraints.

The index set of leaving constraints is assumed to be set in work->solver->leave.

Parameters

work	Workspace
c	Solver environment

Definition at line 306 of file solver_interface.c.

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◆ ldlupdate_sigma_changed()

void ldlupdate_sigma_changed	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Update the \(LDL^T\) factorization given a set of indexes where \(sigma\) has been updated.

The index set of changed \(sigma\) is assumed to be set in work->solver->enter.

Parameters

work	Workspace
c	Solver environment

Definition at line 315 of file solver_interface.c.

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◆ ldlsolveLD_neg_dphi()

void ldlsolveLD_neg_dphi	(	QPALMWorkspace *	work,
		solver_common *	c
	)

Solve the linear system \(LDL^T*d = -\nabla \varphi\).

Parameters

work	Workspace
c	Solver environment

Definition at line 359 of file solver_interface.c.

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Detailed Description

Functions

Function Documentation

◆ qpalm_set_factorization_method()

◆ mat_vec()

◆ mat_tpose_vec()

◆ qpalm_form_kkt()

◆ qpalm_reform_kkt()

◆ kkt_update_entering_constraints()

◆ kkt_update_leaving_constraints()

◆ kkt_solve()

◆ ldlchol()

◆ ldlcholQAtsigmaA()

◆ ldlupdate_entering_constraints()

◆ ldldowndate_leaving_constraints()

◆ ldlupdate_sigma_changed()

◆ ldlsolveLD_neg_dphi()